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+{"text": "This paper investigates the problem of synchronization of fractional-order complex-variable chaotic systems (FOCCS) with unknown complex parameters. Based on the complex-variable inequality and stability theory for fractional-order complex-valued system, a new scheme is presented for adaptive synchronization of FOCCS with unknown complex parameters. The proposed scheme not only provides a new method to analyze fractional-order complex-valued system but also significantly reduces the complexity of computation and analysis. Theoretical proof and simulation results substantiate the effectiveness of the presented synchronization scheme. In the past 20 years, fractional-order chaotic systems have been extensively studied due to their wide applications in the fields of secure communication, control engineering, finance, physical and mathematical science, entropy, encryption and signal processing ,2,3,4. MThe aforementioned works mainly investigated the fractional-order systems with real variables, not involving complex variables. Because complex variables that double the number of variables can generate complicated dynamical behaviors, enhance anti-attack ability and achieve higher transmission efficiency ,19,20, mInspired by the above discussions, the synchronization problem of FOCCS with unknown complex parameters was investigated in this paper. Using the inequality of the fractional derivative containing complex variable and the stability theory for fractional-order complex-valued system, we realized synchronization of such systems by constructing a suitable response system. It should be noted that we deal with the synchronization problem of fractional-order uncertain complex-variable system in complex-valued domain. That is to say, it is not necessary to separate the complex-variable system into its real and imaginary parts. This greatly reduces the complexity of computation and the difficulty of theoretical analysis.n-dimensional space. For l2-norm of Notation: Definition 1\u00a0.The fractional integral of order \u03b1 for a function f is defined as:0 and \u03b1 > 0.where t \u2265 t.The fraDefinition 2\u00a0.Caputo\u2019s fractional derivative of orderfor a functionis defined by:0 and n is a positive integer such that n \u2212 < \u03b1 < 1where t \u2265 t..Caputo\u2019Lemma 1\u00a0.Let0 andbe a continuous and derivable vector function. Then, for any time instant t \u2265 t.Letx and letandare continuously differentiable functions. If:and:whereis a positive constant. Then z(t) = 0 is asymptotically stable.Proof.\u00a0See the Remark\u00a01.Using Lemmas 2.2\u20132.3, one can directly analyze fractional order complex-variable system in the complex space.We considered a kind of FOCCS described by:Proposition\u00a01.1 such that the following inequality holds:There exists a positive constant lProof.\u00a0Given that ectively ,37.Let Proposition 2\u00a0. For the Lipschitz continuous function l2 such that the following inequality holds:\u00a0. For thProof.\u00a0For Remark\u00a02.It is easy to check that many typical FOCCSs, such as the fractional-order complex-variable Chen system , T systeChoose system (11) as the master system, then the controlled response system is given by:Theorem\u00a01.Asymptotically synchronization and parameter identification of systems (13) and (11) can be achieved under adaptive controller:and the complex update laws:whereis the error vector,is the parameter error, \u03c3, \u03b7 are two arbitrary positive constants.Proof.\u00a0From the error vector and systems (11) and (13), it yields:Using Lemma 2.1, Corollary 2.1 and Lemma 2.2, we have:Substitute Equations (15) and (16) into the inequality above, we further have:According to Lemma 2.3, one has rem 1 in , parametRemark\u00a03.In previous work ,27,28,29Remark\u00a04.If the system parameters are known, the update law will be reduced to (15) only.In this section, in order to show the effectiveness of the proposed scheme in preceding section, numerical example on fractional-order complex chaotic system will be provided. When numerically solving such systems, we first adopt the predictor\u2013corrector method  by MATLAa, b, c are system parameters; let Consider the Lorenz-like fractional-order complex chaotic system with commensurate order:Recently, ref.  describeia (the imaginary of a) is depicted in Field-programmable gate array (FPGA)-based implementation of chaotic oscillators has demonstrated its usefulness in the development of engineering applications in a wide variety of fields, such as: random number generators, robotics and chaotic secure communication systems, signal processing. Very recently, Pano-Azucena et al.  implemena, b and c are unknown, the response system is given as follows:Taking the system (19) as master system, and assuming the parameters According to Theorem 1, the controllers and the update rules are selected as:a, b, c) = , the initial conditions In the simulation, let We studied the adaptive synchronization of FOCCS with unknown complex parameters, and proposed a method for analyzing FOCCS without separating system into real and imaginary parts. By this method, the constructed response system can be asymptotically synchronized to an uncertain drive system with a desired complex scaling diagonal matrix. The proposed synchronization scheme retains the complex nature of fractional-order complex chaotic system. It not only provides a new method of analyzing FOCCS, but also significantly decreases the complexity of computation and analysis. We hope that the work performed will be helpful to further research of nonlinear fractional order complex-variable systems."}
+{"text": "For any k-CNF to d-regular -CNF is given. Here regular -CNF is a subclass of CNF, where each clause of the formula has exactly k distinct variables, and each variable occurs in exactly s clauses. A d-regular -CNF formula is a regular -CNF formula, in which the absolute value of the difference between positive and negative occurrences of every variable is at most a nonnegative integer d. We prove that for all s, such that every d-regular -CNF formula is satisfiable. In this study, s such that there exists a uniquely satisfiable d-regular -CNF formula. We further show that for d-regular Unique  The r k\u22653 in . That isr k\u22653 in , Glucoser k\u22653 in . The conk-SAT denotes the promise search problem of k-SAT where the number of solutions is either 0 or 1. The harder instances should have fewer solutions. But Calabro and Paturi in [k-CNF formula has a solution is the same as that of deciding whether it has exactly one solution, both when it is promised and when it is not promised that the input formula has a solution. Thus, the research of uniquely satisfiable SAT instances is a very significant work.A natural measure of the solution space is the number of solutions. Unique aturi in  proved tk distinct variables per clause and at most s occurrences of each variable. Regular -SAT problem in [k-SAT problem showed that the constrained density k-SAT problem such that(i)k-CNF instances with all random (ii)k-CNF instances with all random The  of each variable have its own characteristics.In ,14, M. Wuses. In , Johannsd-regular , if F is unsatisfiable and F, a minimal unsatisfiable formula can be obtained by removing some clauses from F.If the formulas Definition\u00a01.For each Definition\u00a02.A k-CNF formula F is called a k-forced-once d-regular ((i)\u00a0there exist k variables (ii)\u00a0except for the k variables, every variable occurs in exactly s clauses, and the absolute value of the difference between positive and negative occurrences of every variable is no more than the nonnegative integer d.(iii)\u00a0F is satisfiable and for any truth assignment \u03c4 satisfying F, it holds thatWe can represent a CNF formula as a matrix. Each variable F is a CNF formula with 15 variables F isLet F is a 3-forced 0-regular -CNF formula. Each of the three variables F and is forced to be Clearly, Definition\u00a03.In the context of SAT, a reduction M is identified to be parsimonious if x and Lemma\u00a01.Let , and each new variable occurs F and the absolute value of the difference between positive and negative occurrences of each variable is no more than d. Therefor, F is turned into an unsatisfiable d-regular Z occurs positively in Every variable of (ii)All literals of (iii)Z.Every clause of Introduce a new boolean variable set Define Z does not occur in Z be x and all literals of x, every variable of s clause, and meet the d-regularity  and (ii) of Definition 2 hold in d-regular . Therefore, Next, we will assess the feasibility of the construction of Lemma\u00a04.For Proof.\u00a0k-forced-once d-regular X and Y occurs in exactly every variable of (ii)Every clause of We construct a Define s clauses, and the absolute value of the difference between positive and negative occurrences of every variable is at most d. The number of unforced variables in n. So d-regular Let (ii)LetFor simplicity, let Define Step 3 We will make up the gap of the number of occurrences of every variable. Using the variables in sets X and (i)For (ii)For (iii)x in Each variable (iv)x in Each variable (v)Every clause of Step 4 Let d-regular -CNF formula is unsatisfiable, then d-regular -CNF formula is unsatisfiable, then d-regular (By 7)\u226417 in , if a -CNF formula is unsatisfiable, then d-regular (By 8)\u226429 in , all +2 in , we obtaCorollary\u00a01.For  \u03a8 that has exactly one satisfying assignment.Proof.\u00a0The statement follows directly from Lemmas 5 and 6.\u2003\u25a1k-CNF formula into a d-regular . The variables in Z are sorted by their subscripts.Step 4 We construct a k-CNF formula X and Z, satisfying the following conditions.(i)Z occurs in exactly Every variable Otherwise(ii)X occurs in exactly For (iii)X occurs in exactly For (iv)X.Every clause of Step 5 We construct the formula s clauses, and the absolute value of the difference between positive and negative occurrences of every variable of d. Therefore, d-regular (Obviously, every variable of X in First, we focus on the feasibility of X and Z. The variable set X generates Z generates The variables of For X in For For X is more than the number of clauses in Obviously, the number of positive literals of Second, we will prove that the formula It is assumed that X. As a result, Obvious, the truth assignment It is assumed that We substitute Equation  into \u03a83,Obviously, the truth assignment Therefore, X are forced to be Z that replaced the same variable of Z. Due to only one solution of Finally, we will explain why the polynomial-time reduction is parsimonious. If k-SAT problem is a NP-complete problem. From Theorem 5, it demonstrates that there exists a polynomial time reduction from k-SAT to d-regular (d-regular (For d-regular (F in which the positive and negative occurrences number of every variable do not exceed F is a (F must be satisfiable for k, can be satisfiable for From Lemma 6, this suggests that for d-regular (d-regular (We present the construction method of a uniquely satisfiable"}
+{"text": "Correction to: Trialshttps://doi.org/10.1186/s13063-019-3351-2After publication of our article  we have n\u00a0=\u20091013 per group), instead of 6000. Moreover, degrees of freedom should equal to 1, since there are two study groups.According to the calculation described in the article, sample size should be 2026 in total  would be required for our study. If the attrition rate was set at 10%, a total of 2026 patients (1013 in each group) would be required.Figure"}
+{"text": "A symmetric block cipher employing a substitution\u2013permutation duo is an effective technique for the provision of information security. For substitution, modern block ciphers use one or more substitution boxes (S-Boxes). Certain criteria and design principles are fulfilled and followed for the construction of a good S-Box. In this paper, an innovative technique to construct substitution-boxes using our cubic fractional transformation (CFT) is presented. The cryptographic strength of the proposed S-box is critically evaluated against the state of the art performance criteria of strong S-boxes, including bijection, nonlinearity, bit independence criterion, strict avalanche effect, and linear and differential approximation probabilities. The performance results of the proposed S-Box are compared with recently investigated S-Boxes to prove its cryptographic strength. The simulation and comparison analyses validate that the proposed S-Box construction method has adequate efficacy to generate efficient candidate S-Boxes for usage in block ciphers. Cryptography helps individuals and organizations to protect their data. For this purpose, different symmetric and asymmetric ciphers have been designed. Symmetric ciphers possess simplicity and efficiency, and consume fewer computational resources as compared to asymmetric ciphers. Symmetric ciphers have two major categories as stream and block ciphers . A streaA block cipher is particularly useful to achieve data confidentiality, which is one of the cryptography goals. It is considered as one of the most widely used tools for the provision of data security . The mosAn S-Box is a crucial part of modern-day block ciphers and is used to create a muddled ciphertext from the given plaintext. An S-Box is one of the fundamental techniques used to provide candid confusion. Confusion is the complex relationship that must be established between the plaintext and the ciphertext . The strIn , the autGenerally, a block cipher consists of many parts. An S-Box, being the lone non-linear part of a block cipher, is very useful for enhancing the security of the plaintext by creating confusion in the ciphertext. The non-linearity provided by an S-Box offers defense against linear cryptanalysis . Block cAES is one of the popular block ciphers which use S-Boxes in the encryption and decryption processes. Sahmoud et al.  proposedThe Feistel structure has been used as the main construct in many of the symmetric ciphers, like DES, GOST, RC5, etc. DES and GOST each uses eight S-Boxes with sizes 6 \u00d7 4 and 4 \u00d7 4, respectively. The authors in  used theOne of the desirable properties of modern block ciphers is the avalanche effect . This prChaotic cryptography is among the most interesting areas in the field of information security in the recent era as the chaotic systems possess the property of randomness . Many reAnother popular area in cryptography is DNA computing, which is being considered as a possible solution to the design of resilient ciphers. Kadhim et al.  and Al-WCiphers using S-Boxes highly depend on the security of the S-Boxes. Thus, the identification of a tool to evaluate and find an S-Box with high security that can also assist in the design of efficient S-Boxes is considered critical. Wang et al.  developeLinear fractional transformation (LFT) is another area which helps in the generation of better S-Boxes. Farwa et al.  proposedThe techniques and methods for the generation of S-Boxes presented in the literature are either suitable for the creation of static S-boxes or are very complicated and time-consuming. Static S-Boxes have their own limitations and weaknesses. These S-Boxes may help attackers in the cryptanalysis of the captured ciphertext and hence they may reach the original plaintext. On the other hand, the methods presented in the literature that generate dynamic and key-dependent S-boxes are very complex and less efficient. Thus, the need for a simple and efficient method to generate dynamic S-Boxes exists.An S-box that helps in the security enhancement of the block cipher and resists cryptanalysis;An S-Box that is simple to construct;An S-Box that is generated dynamically using sub-keys;An S-Box that fulfills the most needed S-Box criteria, like NL, SAC, BIC, LP, DP, etc.In this paper, a novel design method for the construction of efficient S-Boxes for block ciphers is proposed. The following considerations were kept in mind while designing the proposed S-Box:The method proposed in this paper for the construction of an S-Box is an innovative one and is quite different from the approaches presented in the literature. A cubic fractional transformation is proposed for the construction of strong S-Boxes. After the S-Box was designed, a performance analysis was performed to show its strength. The proposed S-Box demonstrated a very good cryptographic strength when compared with other recently designed S-Boxes. The results indicated that the proposed S-Box is a good choice for block ciphers.The structure of the rest of the paper is as follows. Modern block ciphers employ byte substitution to replace a complete byte (one element) of a matrix with another complete byte using the substitution box (S-Box). Generally, the design of an S-Box involves nonlinear mapping, which results in bijection. Many researchers have designed S-Boxes that are cryptographically strong using such mappings. One such mapping is linear fractional transformation (LFT), which was exhaustively explored for the construction of the S-boxes ,50,51,52Z = {0, 1, \u2026\u2026, 2n \u2212 1}, both \u03b1 and \u03b2 are not 0 at the same time, and \u03b1(z)3 + \u03b2 \u2260 0 is used to construct the n \u00d7 n S-box. The nonlinear nature of CFT stimulates its usage in byte substitution. The procedure to generate the proposed S-Box for n = 8 is illustrated in In this paper, we extend the idea of LFT and construct our new transformation to generate an S-Box using another nonlinear mapping method in a simple and efficient way. We call this extended transformation cubic fractional transformation (CFT). A cubic fractional transformation is a function of the form:Z = {0, 1, \u2026, 2n \u2212 1} = {0, 1, \u2026, 28 \u2212 1} = {0, 1, 2, \u2026, 254, 255} for n = 8. Any values can be chosen for \u03b1 and \u03b2  that gratify the condition of \u03b1(z)3 + \u03b2 \u2260 0. For the sake of the calculations here, we have chosen \u03b1 = 95 and \u03b2 = 15. The CFT function, C(z), given in Equation (2) generates values of Z \u2013 {0, 106} when z \u2208 Z \u2013 {176, 184}. When z = 176, C(z) evaluates to 256 \u2209 Z. When z = 184, the denominator of Equation (2) evaluates to 0. To keep the function, C(z), bijective, we explicitly define C(z) for z \u2208 {176, 184} as conditioned in Equation (2). An example S-Box of a size of 8 \u00d7 8 is generated using a CFT function, c: To elaborate the construction of the proposed S-Box using Equation (1), let us have a specific type of cubic fractional transformation as given in Equation (2). Let This particular cubic fractional transformation of Equation (2) generates the elements of our proposed S-Box, which are organized in a 16 \u00d7 16 matrix as shown in \u03b1 and \u03b2  can be used in Equation (1) to generate an S-Box. One can choose sub-keys as the values for \u03b1 and \u03b2 to generate dynamic and key-dependent S-boxes.As mentioned above, any values for In this section, we analyze our method and S-Box given in f: yY\u2208, \u2203 a unique x \u2208 X, such that f(x) = y. For n-bit inputs, this property maps all possible 2n input values to distinct output values. In other words, when x1 \u2260 x2, then f(x1) \u2260 f(x2). All component Boolean functions (f1 to f8) of the proposed S-box are balanced (number of 1\u2019s = number of 0\u2019s). Further, all 28 output values of the S-box are distinctive where each output value \u2208 Z = {0, 1, \u2026., 255}.A function, n-bit Boolean function, f, is calculated as [fW(z) = Walsh spectrum of the coordinate Boolean function, f, which is measured as:t.z is the dot product of t and z in bit-by-bit fashion and z \u2208 {0, 1}n. The nonlinearity values, NL(f), of the Boolean functions of our S-Box are given in An S-Box operation should not be a linear mapping of an input to an output as it weakens the strength of any cipher. A high value of non-linearity provides resistance against linear cryptanalysis. The nonlinearity of an lated as ,56:(3)NLWebster et al.  introducx, is inverted; this changes the output bits, y and z, independently. For greater security, efforts are made to decrease the dependence between output bits. If a given S-Box satisfies the BIC, all the component Boolean functions possess high nonlinearity and meet the SAC [The authors in  introduc the SAC . Table 5Considering the nonlinearities and SAC, the average BIC values are 103.5 and 0.5, respectively. If a given S-Box is non-linear and demonstrates the SAC, it fulfills BIC . These vModern block ciphers are designed to create as much diffusion and confusion of the bits as possible for the security of data and provide a shield against different approaches that cryptanalysts adopt to obtain the plaintext. Mostly, this is achieved by S-Boxes, which provide nonlinear transformations. If an S-Box is designed with a low linear probability (LP), it is a very good cryptographic tool against linear cryptanalysis.xA and xB represent the input and output masks, respectively and Z = {0, 1, \u2026., 255}. The linear probability of an S-Box is calculated using the following equation :(4)LP=maThe maximum value of LP of our S-box is only 0.156, and thus our S-Box provides good resistance against linear cryptanalysis.x and \u0394y are the input and output differentials, respectively. An S-box with smaller differentials is better at repelling differential cryptanalysis. Differential cryptanalysis is one of the most commonly used methods to reach the plaintext. Here, the differences in the original message (plaintext) and the differences in the ciphertext are obtained. The pairing of these differences may help reach some of the key values. To defy differential cryptanalysis, a small value of differential uniformity (DU) for a given S-Box is required. Differential uniformity is calculated as :(5)DU=maA high value of non-linearity provides resistance against linear cryptanalysis . The aveAn SAC value near 0.5  is the ultimate goal of every S-Box designer. Similarly, the BIC value of our S-box is better than the BIC values of more than half of the other S-boxes. Any S-Box with a lesser value of differential probability is more resilient against differential cryptanalysis. The DP value of our S-Box is 0.039, which is better than the DP values of nine other S-Boxes and equal to the DP values of two other S-Boxes as shown in To defy linear cryptanalysis, a smaller value of LP for a given S-Box is desired by S-Box designers. The LP value of our S-Box is 0.156. Due to this small value, we can say that our S-box is resistant to linear cryptanalysis.From the above comparison it is evident that our S-Box fulfills the most needed S-Box criteria and benchmarks, like SAC, BIC, NL, LP, DP, etc., and hence possesses better cryptographic strength.In this paper, we proposed a new transformation and suggested a novel method to construct efficient S-Boxes using cubic fractional transformation. The security strength of the proposed S-Box was studied using different standard criteria. The simulation results were in accordance with other relevant S-Boxes, rationalizing the performance of our S-Box method. The performance of our S-Box was good in most of the cases when compared with other recent S-Boxes. In particular, the scores of the SAC, BIC, nonlinearity, LP, and DP of the proposed S-Box provide evidence for it as a new alternative in the S-Box design domain. The promising results of the proposed S-Box analysis make it a potential candidate for usage in modern-day block ciphers. It is worth mentioning that our method is the first to explore the cubic fractional transformation for S-Box construction. Stronger S-boxes using cubic fractional transformation, like the proposed S-Box, are expected to emerge for usage in practical systems for secure communication."}
+{"text": "Since reachability is already known to be undecidable in the fragment of PS 2.0 with only release-acquire accesses (PS 2.0-ra), we consider the fragment with only relaxed accesses and promises (PS 2.0-rlx). We show that reachability under PS 2.0-rlx is undecidable in general and that it becomes decidable, albeit non-primitive recursive, if we bound the number of promises.We consider the reachability problem for finite-state multi-threaded programs under the view-switches\u201d, i.e., the number of times the processes may switch their local views of the global memory. We provide a code-to-code translation from an input program under PS 2.0  to a program under SC, thereby reducing the bounded reachability problem under PS 2.0 to the bounded context-switching problem under SC. We have implemented a tool and tested it on a set of benchmarks, demonstrating that typical bugs in programs can be found with a small bound.Given these results, we consider a bounded version of the reachability problem. To this end, we bound both the number of promises and of \u201c"}
+{"text": "This paper investigates the problem of complex modified projective synchronization (CMPS) of fractional-order complex-variable chaotic systems (FOCCS) with unknown complex parameters. By a complex-variable inequality and a stability theory for fractional-order nonlinear systems, a new scheme is presented for constructing CMPS of FOCCS with unknown complex parameters. The proposed scheme not only provides a new method to analyze fractional-order complex-valued systems but also significantly reduces the complexity of computation and analysis. Theoretical proof and simulation results substantiate the effectiveness of the presented synchronization scheme. In the past twenty years, the application of fractional calculus has become a focus of attention, since fractional derivatives can more accurately describe the actual physical model. So, it has become an efficient and an excellent tool in physics, mathematical science, chemistry, control engineering, finance, signal processing and other fields ,3,4,5,6.The above-mentioned works mainly investigated the fractional-order systems with real variables, not involving complex variables. It is well known that complex variables, which double the number of variables, can generate complicated dynamical behaviors, enhance anti-attack ability and achieve higher transmission efficiency ,24,25. TInspired by the above discussions, the CMPS problem of FOCCS with unknown complex parameters is investigated in this paper. First, we present a stability theory for fractional-order uncertain nonlinear systems. Then, using this theory, the inequality proposed by Xu et al.  and compn-dimensional space. l2-norm of Notation: Definition\u00a01The fractional integral of order \u03b1 for a function f is defined as0 and where t . The fraDefinition\u00a02Caputo\u2019s fractional derivative of order 0 and n is a positive integer such that where t . Caputo\u2019Lemma\u00a01.0 and Let  Let x(t)Corollary\u00a01.For a scalar derivable function Lemma\u00a02.Let where  Let z\u2009\u2208\u2102Lemma\u00a03. Let andwhere Proof.\u00a0By Next, we adopt contradiction to prove rem 1 in .k = 1, 2, 3, \u2026, from (7), we have:d is bounded). Obviously, Suppose that Remark\u00a01.1(t) and V2(t).Lemma 3 provides a stability criterion for the fractional-order nonlinear uncertain system by choosing a Lyapunov function that includes two parts VRemark\u00a02.Lemma 3 provides a Lyapunov-based adaptive control method for stability analysis and synchronization of fractional-order systems (FOS).Remark\u00a03.Lemma 3 is suitable for verifying the stability and stabilization controller design of FOS with unknown parameters and external disturbances.Remark\u00a04.If the FOS has no uncertainties, then Lemma 3 is still valid.Lemma\u00a04.For the fractional-order complex-variable systemswhere andwhere  For the Lemma\u00a05.1 such that the following inequality holds:For all where ,46 For aLemma\u00a06.2 such that the following inequality holds:For the Lipschitz continuous function ,46 For tWe consider a kind of fractional-order complex-variable chaotic drive and response systemsDefinition\u00a03.For given drive system (8) and response system (9), it is said to achieve CMPS ifwhere  For giveRemark\u00a05.Obviously, some known synchronization ways are the special cases of CMPS, such as CS, AS, PS and MPS.We consider a kind of FOCCS with unknown complex parameters asSystem (13) was chosen as the master system. In this case, we constructed the slave system as follows:Remark 2. From (13), it follows that Theorem\u00a01.Asymptotically CMPS of systems (13) and (14) can be achieved under adaptive controllerand the complex update laws:where Proof.\u00a0From the error vector and systems (13) and (14), it follows:Using Lemma 1, Corollary 1 and Lemma 2, we have:L1, l2 and L2 are three positive constants. Then, one has:Substituting Equations (16) and(17) into the inequality above, we further have:By en, from , V1(t)=eTherefore, the systems (13) and (14) can reach asymptotically CMPS under the adaptive control strategy (15\u201317). \u2610Remark\u00a06.Unlike previous works, in our proposed method, the entire analysis process is performed in the complex-valued domain, and the complex function theory is used to derive synchronization conditions without separating the original complex-valued chaotic system into two real-valued systems, which reduces the complexity of analysis and computation.Remark\u00a07.If the system parameters are known, the update law will be reduced to (16) only.In this section, in order to show the effectiveness of the proposed scheme in preceding section, numerical example on fractional-order complex chaotic system will be provided. When numerically solving such systems, we adopted the Gr\u00fcnwald\u2013Letnikov (G-L) method  using MAa, b, c are system parameters, let ia (the imaginary of a) is depicted in Consider the fractional-order Chen complex chaotic system with commensurate order:Assuming the parameters The error vector a, b, c) = , the initial conditions In the simulation, let We study the CMPS of FOCCS with unknown complex parameters, and propose a method for analyzing FOCCS without separating systems into real and imaginary parts. By this method, the constructed response system can be asymptotically synchronized to an uncertain drive system with a desired complex scaling diagonal matrix. The proposed synchronization scheme retains the complex nature of fractional-order complex chaotic systems. It not only provides a new method of analyzing FOCCS but also significantly decreases the complexity of computation and analysis. In future works, we will further investigate the synchronization of FOCCS, and generalize the obtained results to more general cases, i.e., FOCCS with time delay and external disturbances."}
+{"text": "They form complex communities and collectively affect host health. Recently, the advances in next-generation sequencing technology enable the high-throughput profiling of the human microbiome. This calls for a statistical model to construct microbial networks from the microbiome sequencing count data. As microbiome count data are high-dimensional and suffer from uneven sampling depth, over-dispersion, and zero-inflation, these characteristics can bias the network estimation and require specialized analytical tools. Here we propose a general framework, HARMONIES, Hybrid Approach foR MicrobiOme Network Inferences via Exploiting Sparsity, to infer a sparse microbiome network. HARMONIES first utilizes a zero-inflated negative binomial (ZINB) distribution to model the skewness and excess zeros in the microbiome data, as well as incorporates a stochastic process prior for sample-wise normalization. This approach infers a sparse and stable network by imposing non-trivial regularizations based on the Gaussian graphical model. In comprehensive simulation studies, HARMONIES outperformed four other commonly used methods. When using published microbiome data from a colorectal cancer study, it discovered a novel community with disease-enriched bacteria. In summary, HARMONIES is a novel and useful statistical framework for microbiome network inference, and it is available at  Microbiota form complex community structures and collectively affect human health. Studying their relationship as a network can provide key insights into their biological mechanisms. The exponentially growing large datasets made available by next-generation sequencing (NGS) technology Metzker, , such asIn sequencing-based microbial association studies, the enormous amount of NGS data can be summarized in a sample-by-taxon count table where each entry is a proxy to the underlying true abundance. However, there is no simple relationship between the true abundances and the observed counts. Additionally, microbiome sequencing data usually have an inflated amount of zeros, uneven sequencing depths across samples, and over-dispersion. Initial attempts at constructing microbial association networks with this type of data , to infer the microbiome networks. It consists of two major steps: (1) normalization of the microbiome count data by fitting a zero-inflated negative binomial (ZINB) model with the Dirichlet process prior (DPP), (2) application of Glasso to ensure sparsity and using a stability-based approach to select the tuning parameter in Glasso. The estimated network contains the information of both the degree and the direction of associations between taxa, which facilitates the biological interpretation. We demonstrated that HARMONIES could outperform other state-of-the-art tools on extensive simulated and synthetic data. Further, we used HARMONIES to uncover unique associations between disease-specific genera from microbiome profiling data generated from a colorectal cancer study. Based on these results, HARMONIES will be a valuable statistical model to understand the complex microbial associations in microbiome studies. The Y denote the n-by-p taxonomic count matrix obtained from either the 16S rRNA or the metagenomic shotgun sequencing (MSS) technology. Each entry yij, i = 1, \u2026, n, j = 1, \u2026, p is a non-negative integer, indicating the total reads related to taxon j observed in sample i. It is recommended that all chosen taxa should be at the same taxonomic level  since that mixing different taxonomic levels in the proposed model could lead to improper biological interpretation. As the real microbiome data are characterized by zero-inflation and over-dispersion, we model yij through a zero-inflated negative binomial (ZINB) model asLet i representing the proportion of \u201cextra\u201d zeros in sample i. The second component, NB, models the \u201ctrue\u201d zeros and all the nonzero observed counts. i.e., counts generated from a negative binomial (NB) distribution with the expectation of \u03bbij and dispersion 1/\u03d5j. Here, \u201ctrue\u201d zero refers to a taxon that is truly absent in the corresponding sample. The variance of the random variable from NB distribution, under the current parameterization, equals to j can lead to over-dispersion.The first component in the Equation (1) models whether zeros come from a degenerate distribution with a point mass at zero. It can be interpreted as the \u201cextra\u201d zeros due to insufficient sequencing effort. We can assume there exists a true underlying abundance for the taxon in its sample, but we fail to observe it with the mixture probability \u03c0i's and \u03d5j's, we use a Bayesian hierarchical model for parameter inference. First, we rewrite the model (1) by introducing a binary indicator variable \u03b7ij ~ Bernoulli(\u03c0i), such that yij = 0 if \u03b7ij = 1, and yij ~ NB if \u03b7ij = 0. Then, we formulate a beta-Bernoulli prior of \u03b7ij by assuming \u03c0i ~ Beta, and we let a\u03c0 = b\u03c0 = 1 to obtain a non-informative prior on \u03b7ij. We specify independent Gamma prior Ga for each dispersion parameter \u03d5j. Letting a\u03d5 = b\u03d5 = 0.001 results in a weakly informative gamma prior.To avoid explicitly fixing the value of \u03c0ij, contains the key information of the true underlying abundance of the corresponding count. As \u03bbij is affected by the varying sequencing effort across samples, we use a multiplicative characterization of the NB mean to justify the latent heterogeneity in microbiome sequencing data. Specifically, we assume \u03bbij = si\u03b1ij. Here, si is the sample-specific size factor that captures the variation in sequencing depth across samples, and \u03b1ij is the normalized abundance of taxon j in sample i.The mean parameter of the NB distribution, \u03bbsi and \u03b1ij. For example, si can be the reciprocal of the total number of reads in sample i. The resulted \u03b1ij is often called relative abundance, which represents the proportion of taxon j in sample i. In this setting, the relative abundances of all the taxa in one sample always sum up to 1. Similarly, other methods have been proposed with different constraints for normalizing the sequencing data  = 0. For the outer mixtures, M is an arbitrarily large positive integer. Letting M \u2192 \u221e and defining the weight \u03c8m by the stick-breaking procedure  such that \u03bdm ~ N, tm ~ Beta, and Vm ~ Beta. We further set where \u03c8A = {\u03b1ij} represents the true underlying abundance of the original count matrix. We further assume ij not only reduces the skewness of the normalized abundance, but converts the non-negative \u03b1ij to a real number. We apply the following conjugate setting to specify the priors for \u03bcj and j and j follows a non-standardized Student's t-distribution, i.e.,In our model, the normalized abundance matrix a0, b0, h0, and a0 = 2, b0 = 1 to obtain a weakly informative prior for h0 = 10 such that the normal prior on \u03bcj is fairly flat. We adopt the following prior specification for the rest model parameters. First, we assume an noninformative prior for each \u03c0i by letting a\u03c0 = b\u03c0 = 1. Next, we specify a\u03d5 = b\u03d5 = 0.001 in the Gamma prior distribution for all \u03d5j's. Then, we apply the following prior setting for the DPP: M = n/2, \u03c3s = 1, \u03c4\u03bd = 1, at = bt = 1, and am = bm = 1.As for the fixed parameters i et al.  and set A, denoted as Z = log A, represents the normalized microbiome abundances on the log scale. We use Markov chain Monte Carlo (MCMC) algorithm for model parameter estimation  based on the estimated \u03b7ij for each observed yij = 0 in the data. In particular, suppose that we observe L zeros in total. We calculate the marginal posterior probability of being 1 for each \u03b7l, l = 1, \u2026, L as B is the number of MCMC iteration after burn-in. This marginal posterior probability pl represents the proportion of MCMC iterations in which the lth 0 is essentially a missing value rather than the lowest count in the corresponding sample. Then, the observed zeros can be dichotomized by thresholding the L probabilities. The zeros with pl greater than the threshold are considered as \u201ctrue\" zeros in the data, whereas the rest are imputed by the corresponding posterior mean of log\u03b1j\u00b7. We used the method proposed by Newton et al. , which guarantees the imputed zeros have a Bayesian FDR to be smaller than c\u03b7,The logarithmic scale of n et al.  to deterc\u03b7 = 0.01 guarantees that the Bayesian FDR to be at most 0.01. We set c\u03b7 = 0.05 for the simulation study and c\u03b7 = 0.01 for the real data analysis.In practice, a choice of G =  is used to illustrate the associations among vertices V = {1, \u2026, p}, representing the p microbial taxa. E = {emk} is the collection of (undirected) edges, which is equivalently represented via a p-by-p adjacency matrix with emk = 1 or 0 according to whether vertices m and k are directly connected in G or not. GGM assumes that the joint distribution of p vertices is multivariate Gaussian N, yielding the following relationship between the dependency structure and the network: a zero entry in the precision matrix \u03a9 = \u03a3\u22121 indicates the corresponding vertices are conditional independent, and there is no edge between them in the graph G. Hence, a GGM can be defined in terms of the pairwise conditional independence. If X ~ N, thenBased on the normalized microbial abundances, we estimate their partial correlation matrix in order to construct the microbiome network under the Gaussian graphical model (GGM) framework. An undirected graph m and k, representing the degree and direction of association between two vertices, conditional on the rest variables. Consequently, learning the network is equivalent to estimating the precision matrix \u03a9. For real microbiome data, we set the taxa (on the same taxonomic level) as vertices. Hence, a zero partial correlation in the precision matrix can be interpreted as no association between the corresponding pair of taxa, while a nonzero partial correlation can be interpreted as cooperative or competing associations between that taxa pair.where \u03a9. The sparsity can be achieved by imposing l1-penalized log-likelihood,In biological applications, we often require a sparse and stable estimation of the precision matrix S is the sample covariance matrix. The coordinate descent algorithm can iteratively solve p. The estimated precision matrix is sparsistent   to simulate the count table Yn \u00d7 p from a DM model, with its parameters being exp(D); (5) to mimic the zero-inflation in real microbiome data by randomly setting part of entries in the count table to zeros. Note that the data generative scheme is different from the model assumption, which is given in Equation (1). The detailed generative models are described below.We generated the simulated datasets from a Dirichlet-multinomial (DM) model using the following steps: (1) to generate the binary adjacency matrix; (2) to simulate the precision matrix and the corresponding covariance matrix; (3) to generate p-by-p adjacency matrix for the p taxa in the network. Here, the adjacency matrix was generated according to an Erd\u0151s\u2013R\u00e9nyi (ER) model. An ER model ER generates each edge in a graph G with probability \u03c1 independently from every other edge. Therefore, all graphs with p nodes and M edges have an equal probability of G correspond to the 1's in the resulted binary adjacency matrix. Next, we simulated the precision matrix \u03a9 following Peng et al. . To ensure positive definiteness of the precision matrix, we followed Peng et al.  to represent the true underlying abundances D. To obtain a count matrix that fully mimics the microbiome sequencing data, we generated counts from a DM model with parameter exp(D). Specifically, we first sampled the underlying fractional abundances for the ith sample from a Dirichlet distribution. The ith underlying fractional abundance was then denoted as \u03c8i ~ Dirichlet(exp(Di\u00b7)). Next, the counts in the ith sample were generated from Multinomial. Finally, we randomly selected \u03c00% out of n \u00d7 p counts and set them to zeros to mimic the zero-inflation observed in the real microbiome data. In general, the generative process had different assumptions from the proposed method. Under the appropriate choice of parameters, the simulated count data was zero-inflated, overdispersed, and the total reads varied largely between samples. In practice, we let \u03c1 = 0.1 in the ER model. The mean parameter \u03bc of the underlying multivariate Gaussian variable was randomly sampled from a uniform distribution Unif. The number of total counts across samples Ni, i = 1, \u2026, n was sampled from a discrete uniform distribution with range . Under each combination of n, p, and \u03c00, we generated 50 replicated datasets by repeating the process above.Next, we simulated p taxa from a real microbiome dataset, the NorTA generates the synthetic data with n samples as follows: (1) to calculate the p-by-p covariance matrix \u03a30 from the input real dataset; (2) to generate an n-by-p matrix, denoted by Z0, from a multivariate Gaussian distribution with a mean of 0p1 \u00d7  and the covariance matrix of \u03a30; (3) to use standard normal cumulative distribution function to scale values in each column of Z0 within ; (4) to apply the quantile function of a ZINB distribution to generate count data from those scaled values in each column of Z0. In practice, we used R package SPIEC-EASI to implement the above data generative scheme, where the real data were from those healthy control subjects in our case study presented in section 3.2. Under each combination of n and p, we generated 50 replicated datasets.We generated synthetic data following the Normal-to-Anything (NorTA) approach proposed in Kurtz et al. . NorTA wl1 regularization. However, as discussed in section 1, representing the dependency structure by the correlation matrix may lead to the detection of spurious associations.We considered the four commonly used network learning methods. The first two methods, SPIEC-EASI-Glasso and SPIEC-EASI-mb, use the transformed microbiome abundances which are different from the normalized abundances estimated by HARMONIES. Both infer the microbial network by estimating a sparse precision matrix. The former method (SPIEC-EASI-Glasso) measures the dependency among microbiota by their partial correlation coefficients, and the latter method (SPIEC-EASI-mb) uses the \u201cneighborhood selection\u201d introduced by Meinshausen and B\u00fchlmann  to constm and taxon k to be true positive if \u03c9mk \u2260 0, mk. We calculated the number of true negative (TN), false positive (FP), and false negative (FN) in a similar manner. Therefore, each tuning parameter defined a point on a ROC curve. As for the correlation-based methods, we started with ranking the absolute values in the estimated correlation matrices, denoted as We quantified the model performances on the simulated data by computing their receiver operating characteristic (ROC) curves and area under the ROC curve (AUC). For the HARMONIES or SPIEC-EASI, the network inference was based on the precision matrix. Hence, under each tuning parameter of Glasso, we calculated the number of edges being true positive (TP) by directly comparing the estimated precision matrix against the true one. More specifically, we considered an edge between taxon We further used the Matthew's correlation coefficient (MCC) to evaluate results from the simulated data. The MCC is defined asHere, the MCC was particularly suitable for evaluating network models. As the number of conditionally independent taxa pairs was assumed to be much greater than the number of dependent pairs in a sparse network, MCC was preferable to quantify the performances under such an imbalanced situation. Note that MCC ranges from , with a value close to 1 suggesting a better performance. Since each value of MCC was calculated using a given set of TP, TN, FP, and FN, we adopted the optimal choice of tuning parameter for the HARMONIES or SPIEC-EASI (with either Glasso or MB for network inference), given by StARS. As for the correlation-based methods, CClasso outputted a sparse correlation matrix. We used the result to calculate TP, TN, FP, and FN directly. For Pearson-corr, we set the threshold such that the resulted number of nonzero entries in the sparse correlation matrix was the same as the number of non-zero entries in the true sparse partial correlation matrix. In fact, this choice could favor the performance of Pearson-corr for larger sample size, as shown in section 3.1.p-values were used.To assess model performances on the synthetic datasets, we followed Kurtz et al.  to use an = 60, 100, 200, or 500), total numbers of taxa (p = 40 or 60), extra percentages of zeros added . In each subfigure, the HARMONIES outperformed the alternative methods in terms of both AUC and MCC, and it maintained this advantage even with the number of sample size greatly increases. Further, a smaller sample size, a larger proportion of extra zeros added (\u03c00 = 20%), as well as a larger number of taxa in the network (p = 60), would hamper the performance of all the methods, as we expected. Two modes of SPIEC-EASI, SPIEC-EASI-Glasso, and SPIEC-EASI-mb, showed very similar performances under all the scenarios, with SPIEC-EASI-Glasso having only a marginal advantage over the other. Further, we observed that the Pearson-corr method yielded higher AUCs even than the precision matrix based methods, especially when there was a lager proportion of extra zeros or larger number of taxa in the network. This result suggested that the Pearson-corr could capture the overall rank of the signal strength in the actual network. However, under a fixed cut-off value that gave a sparse correlation network, the MCCs from the Pearson-corr were always smaller than the precision matrix based methods. Note that the cut-off value we specified for Pearson's correlation method indeed favored its performance. In general, the alternative methods considered here were able to reflect the overall rank of the signal strength by showing reasonable AUCs. However, they failed to give an accurate estimation of the network under a fixed cut-off value.n or decreasing the number of features p would improve the performance of all methods and lead to greater disparity between partial and pairwise correlation-based methods. In general, our HARMONIES maintained the best in all simulation and evaluation settings except for one case, where the SPIEC-EASI-mb only showed a marginal advantage  is the third most common cancer diagnosed in both men and women in the United States .The datasets generated for the simulation study can be found in the author's Github page\u2014SJ performed the experiments. GX and AK provided resources and helpful discussions. SJ, QL, and XZ designed the experiment, performed data analysis, wrote the software, and the manuscript. SJ, YC, BY, and XZ developed the website for online implementation of HARMONIES.AK is a consultant for Merck and the principal investigator on a Norvatis sponsored study. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Scientific Reports 10.1038/s41598-019-41394-9, published online 22 March 2019Correction to: The original version of this Article contained errors.The title included the \u201c\u2264\u201d symbol at the beginning as a result of typesetting error.In addition, as a result of figure assembly errors, panels B and F of Figure\u00a02 were duplicated from author\u2019s previous research. This figure is now correct, and the raw data underlying it is now also included in the Supplementary Information file.These have now been corrected in the HTML and PDF versions of this Article, and in the accompanying Supplemental Material."}
+{"text": "Scientific Reports 10.1038/s41598-020-65076-z, published online 25 May 2020Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201ccooperation\u201d was incorrectly given as \u201ccooperaion\u201d. This has now been corrected in the PDF and HTML versions of the Article and in the accompanying Supplementary Information file."}
+{"text": "While equilibrium phase transitions are easily described by order parameters and free-energy landscapes, for their non-stationary counterparts these quantities are usually ill-defined. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity. We quench the system to a far-from-equilibrium state and find delayed condensation close to a critical excitation energy, a transient equivalent of critical slowing down. Besides number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit timing jitter in the condensate formation. This jitter is a manifestation of the randomness associated with spontaneous emission, showing that condensation is a stochastic, rather than deterministic process. Despite the non-equilibrium character of this phase transition, we construct an effective free-energy landscape that describes the formation jitter and allows, in principle, its generalization to a wider class of processes. Description of non-equilibrium phase transitions is problematic, due to the absence of suitable free energy landscapes. Here, the authors experimentally show delayed photon condensation and timing jitter in a dye-filled microcavity, modelled by a non-equilibrium extension of the free-energy landscape. This relation is particularly relevant near a second-order phase transition, where all the relevant macroscopic details are described by an emergent order parameter. This is, on average, located at the minimum of the free-energy landscape3, with its neighbourhood being locally probed as the system is driven through configuration space by fluctuations . While we still lack a universal generalization of these ideas to non-equilibrium systems, Jaynes has suggested its possibility4. Some well-established, near-equilibrium stochastic descriptions of relaxation involving free-energy surfaces are known5, but are not necessarily valid far from equilibrium. A particular example in this direction has been constructed for the laser6, a fundamentally non-equilibrium system whose steady state can be described as the minimum of a properly defined effective free energy, corresponding to a detailed balance between driving and dissipation.The connection between the properties of a system at thermal equilibrium and the geometry of its free-energy landscape is a powerful concept that dates back to original ideas developed by Gibbs8 or the build-up of anti-ferromagnetic correlations in Ising models9. Non-Hamiltonian quenches contain a more general class of processes. In cold atoms, for instance, the Kibble\u2013Zurek mechanism11 is observed by evaporatively cooling the system at a finite rate, quenching the system through a BEC phase transition. We shall refer to a quench as a sudden change in one of the system parameters that brings it to a far-from-equilibrium state, without affecting its Hamiltonian.While the previous arguments are relevant for systems close to a steady state, a sudden parameter change, often called a quench, necessarily brings the system sufficiently far from equilibrium to question the validity of such approaches. The meaning of a quench depends on context and, in particular, one can distinguish between Hamiltonian and non-Hamiltonian cases. The former consist of time-dependent variations in some sort of interaction term, involved, for instance, in the Mott insulator-superfluid transition15. Following the initial observation of Bose\u2013Einstein condensation of photons16, a number of experiments on grand-canonical fluctuations17, spontaneous symmetry breaking18, emergence of long-range order19, among other aspects of equilibrium physics21 have been described. Their non-equilibrium counterparts, however, remain greatly unexplored.Photon condensates are ideal platforms to explore both equilibrium and non-equilibrium physics. A thermalizing medium, typically a dye solution, is placed inside an incoherently pumped optical microcavity. The combined rates of thermalization, pumping and cavity loss enable such a driven-dissipative system to be tuned between in- and out-of-equilibrium regimesg(2). It provides access to the statistical properties of the photon condensation transition, and is particularly relevant in non-stationary systems, when the full knowledge of individual realizations is inaccessible. While the usual stationary correlation function, g(2)(\u03c4), accurately accounts for fluctuations in steady state, g(2) is the appropriate quantity to describe the evolution of transient, non-equilibrium systems. The averaged condensate intensity as a function of time shows width broadening, a manifestation of diverging jitter in the condensate formation time upon approaching the critical excitation energy. This effect is directly witnessed by distinctive off-diagonal anti-correlations in g(2) and originates from quantum fluctuations associated with spontaneous emission. By properly defining an effective (non-equilibrium) free energy, we suggest that jitter may be a universal feature of transient phase transitions in systems obeying relatively general conditions on the convexity of their free-energy landscape.Here, we study the transient dynamics of photon condensation that follows a quench in a dye-filled optical microcavity. Besides measuring the ensemble-averaged photon number dynamics, we introduce the non-stationary, two-time, second-order correlation function \u03ba and \u0393\u2193, respectively. The essentials of the cavity dynamics are described by the density operator \u03c1, for both photons and molecules, which obeys the master equation23E and A the dye emission and absorption rates, respectively, \u0393\u2191 the incoherent  pumping rate and Nmol the total number of molecules inside the cavity. In general, \u0393\u2191 is a time-dependent quantity, such as in the case of pulsed pumping. Due to the high collision rate between dye and solvent molecules, all the relevant cavity processes, including light\u2013matter interactions, are incoherent.Despite the fundamentally multi-mode character of our optical cavity, the phenomenology described here is essentially that of a single-mode system. Cavity excitations (photons and excited molecules) can be lost by two processes: mirror transmission and molecular spontaneous emission into free space, at rates f\u2009=\u2009fc, and in the absence of pumping and losses (\u03ba\u2009=\u2009\u0393\u2193\u2009=\u2009\u0393\u2191\u2009=\u20090), an equilibrium (steady state) between molecular excitations and photons is established by a principle of detailed balance13. The photon number in this equilibrium state would show a phase transition as the total number of cavity excitations, Nex\u2009=\u2009n\u2009+\u2009f\u2009Nmol, which is the control parameter, is increased. The photon number, or order parameter, ranges from a disordered phase (n\u2009\u2272\u20091) dominated by spontaneous emission to an ordered phase (n\u2009\u226b\u20091) dominated by stimulated emission. While there is, in principle, a U(1) symmetry breaking upon crossing the condensation phase transition, the full dynamics can be described simply through photon number n12. By exciting a large number of dye molecules over a short period of time, the cavity can be quenched through this phase transition to a far-from-equilibrium state. The subsequent relaxation dynamics correspond to a non-stationary, transient counterpart of the equilibrium phase transition described above. In this way, we define a transient phase transition as the evolution in configuration space after a jump across a phase transition in parameter space (a quench), where \u201cphase transition\u201d has its usual time-independent, thermodynamic meaning. This is distinct from the recently introduced concept of dynamical phase transitions25. The non-linear coupling between photons and molecular excitations occurring during this transient relaxation process gives rise to non-trivial fluctuation and correlation properties. Finally, given its lossy character, the light will transition back to the phase dominated by spontaneous emission before all excitations are lost.Mean-field rate equations are obtained by taking expectation values and neglecting correlation terms in Eq.\u00a0. The num\u2193 accounts for emission both into free space and cavity modes that do not reach the regime of stimulated emission (do not condense), which will be discussed in more detail later. Also, and despite not being relevant for the results discussed here, effects associated with the multi-mode character as well as spatially resolved molecular reservoirs have been appreciated in the context of gain clamping26 and decondensation mechanisms14.A few notes are in order regarding the multi-mode nature of our cavity. Within the single-mode approximation, the rate term \u0393\u03bcm. A 40\u2009ps laser pulse at 532\u2009nm, typically ranging from 0.5 to 2\u2009nJ in energy, is used to rapidly excite the molecules, quenching the cavity to a far-from-equilibrium state. In response, a much longer pulse (\u22731\u2009ns) of light leaks from the cavity mirrors, the exact temporal shape of which depends both on the cavity parameters  as well as the number of molecular excitations that follow the pump pulse, which is the control parameter used to select the different dynamical phases. A portion of pump light is directed onto two saturated avalanche single-photon detectors (APDs), O1 and O2, where a coincident detection is used as a time stamp for the beginning of the experiment, with a measured uncertainty of about 10\u2009ps. The cavity output light is directed onto two unsaturated APDs, B1 and B2, with an average of 0.1 detections per pulse, on each detector. The experiment is conducted at a repetition rate of 11\u2009kHz. Such a low repetition rate ensures a complete decay of all excitations and statistical independence between different realizations. We describe the experimental results in the form of following three sets:zero-time statistics: full time-averaged cavity output;one-time statistics: time-resolved, but averaged over all forms of fluctuations and correlations in the cavity output;two-time statistics: unequal time, cross-correlated signal from detectors B1 and B2, providing access to fluctuations in the cavity output.The experimental configuration is sketched in Fig.\u00a0P is increased beyond a critical value Pth, as shown in Fig.\u00a014. Consequently, and despite the absence of a full thermal distribution, parallels may be drawn with Bose\u2013Einstein condensation of photons28. While BEC is only strictly defined in thermal equilibrium as the macroscopic occupation of the ground state, we are assuming here a broader concept of condensation, as discussed in such diverse fields as physics, ecology, network theory or social sciences31. This can be thought of as the process where a particular, or small set of modes, in a multi-mode system becomes macroscopically occupied while the remaining ones saturate or become depleted.We begin by demonstrating the existence of a (condensation) phase transition in the total amount of light emitted by the cavity as the excitation energy, or pump energy, \u03b1 is an empirical parameter set by fitting the light-yield curve to the mean-field rate equations. Loosely speaking, \u03b1 determines the fraction of spontaneous emission into non-modelled cavity modes and is expected to be a small contribution, which will be verified in \u201cOne-time statistics\u201d section.By counting the rate of detection events in B1 and B2, we measure the total cavity output as a function of input pulse energy , as shown in the inset of Fig.\u00a0P\u2009<\u2009Pth) display a simple exponential decay on a time scale of about \u03c40\u2009~\u20094\u2009ns, the molecular excited-state lifetime. Above threshold, stimulated emission becomes important, leading to a large increase in photon number, followed by rapid depopulation of the condensate before a final decay at the slower time scale of the molecular excited-state decay.Here, we expand the time-averaged results of the previous section to the time-dependent cavity output pulse shape, as shown in Fig.\u00a0f, and the number of cavity photons, n. In equilibrium, the molecular excitation fraction, f, cannot exceed its critical value, fc. Under non-equilibrium conditions, however, if at any instant f\u2009>\u2009fc (e.g. after a quench), the photon population will grow exponentially until f drops below fc. This exponential increase in the number of photons, resulting from the onset of stimulated emission, is accompanied by rapid de-excitation of molecules, as shown in Fig.\u00a0f\u2009Nmol, and the photon number n. We choose experimental parameters that make the number of photons comparable with f\u2009Nmol, such that the effects of this two-way coupling become more prominent. On the opposite limit of f\u2009Nmol\u2009\u226b\u2009n, which is approached for lower values of \u03bb0 (the cavity cutoff wavelength), the larger molecular reservoir becomes insensitive to photon number fluctuations, approaching the limit of a Markovian bath. This limit is at the origin of the observation of grand-canonical number statistics in photon BECs17.It is instructive at this point to reflect upon the interplay and coupled dynamics of the molecular excitation fraction, \u2193 and \u03ba to the results in Fig.\u00a0\u03ba\u2009=\u20091010\u2009s\u22121, corresponding to a cavity lifetime of 100\u2009ps, and \u0393\u2193\u2009=\u20090.998\u03930, with \u03930\u2009=\u20091\u2215\u03c40 the molecular fluorescence decay rate. Within the single-mode approximation, this means that only 0.2% of the total molecular emission goes into the condensing mode while 99.8% goes both into free space and excited modes that do not reach the regime of stimulated emission. Together with the light-yield curves in Fig.\u00a0\u03b1\u2009=\u20090.13; small as expected. The emission and absorption rates are not taken as fitting parameters but rather calculated from experimental absorption and emission data for rhodamine-6G32. The total number of molecules is calculated from the dye concentration and cavity volume to be Nmol\u2009=\u20091.9\u2009\u00d7\u2009108.We fit \u0393f approaches fc from above, the cavity dynamics become slow, as dictated by Eq. . Second-order correlations are typically described by the single-time g(2)(\u03c4) function, with \u03c4\u2009=\u2009t1\u2009\u2212\u2009t2, due to time-translation symmetry in steady-state conditions. In transient systems, however, the absence of this symmetry means that the full two-time, t1 and t2, dependence must be retained. We can then defineP is the joint probability of photon detection at times t1 and t2 in detectors B1 and B2, respectively. By marginalizing over the second detector, P(t1) and P(t2) are obtained as the single-detector probabilities. The approximation in Eq. (a\u2020(t1),\u00a0a(t2)]\u2009\u2248\u20090 or \u2329a\u2020(t)a(t)\u232a\u2009\u226b\u20091. The former is satisfied when \u2223t1\u2009\u2212\u2009t2\u2223 is larger than the coherence time , and the latter is true for large photon numbers, as verified in Fig.\u00a0Correlations and fluctuations of the cavity output can now be investigated by retaining the labelling of detection timestamps in B1 and B2. We then construct the two-time, non-stationary, second-order correlation function g(2)\u2009>\u20091) and the off-diagonal anti-correlation (g(2)\u2009<\u20091) lobes. These features are mainly a manifestation of the same kind of fluctuations\u2014jitter, or shot-to-shot timing fluctuations, in the condensate formation\u2014which become amplified near the critical excitation energy. In the remainder of this section, we discuss this effect associated with transient phase transitions.The second-order correlation function is shown in Fig.\u00a0g(2) provides immediate information on number, or intensity, fluctuations, namely g(2)\u2009\u2243\u20091\u2009+\u2009\u2329\u0394n(t)2\u232a\u2215\u2329n(t)\u232a2. As such, periods of larger fluctuations coincide with the inflection point of the average pulse shape, consistent with a condensate forming at slightly different instants in each realization of the experiment. In a microscopic picture of the cavity dynamics, spontaneously emitted photons are required to seed the condensate growth. The randomness associated with the quantum nature of spontaneous emission then leads to such shot-to-shot time fluctuations, or jitter in the condensate formation. As we shall demonstrate in the next section, these periods of larger fluctuations correspond to a passage through the convex part of an effective free-energy landscape.Let us proceed by separately analysing diagonal and anti-diagonal correlations, as shown in Fig.\u00a0g(2)\u2009<\u20091 are then an immediate witness of fluctuations in formation time. Also, it is further evidence of the two-way coupling between photons and molecules, as discussed previously.The above interpretation is further supported by the off-diagonal anti-correlation lobes, as seen in Figs.\u00a037, the two-time correlation function can be obtained via the quantum regression theorem38, as shown in Fig.\u00a042. Different classes of events  are defined and drawn at random given their respective rates. These are dynamically calculated as the number of photons and molecular excitations are updated at each step. Full details of this model can be found in \u201cMethods\u201d section. In the limit of a large number of realizations, this approach is equivalent to evolving the density matrix according to Eq.\u00a0(By retaining correlations up to second-order in Eq.\u00a0 using a g to Eq.\u00a0. By retag(2). However, the quantum trajectories method allows us to easily appreciate the effect of formation jitter, depicted in Fig.\u00a0g(2) depends on both the individual pulse shapes and their uncertainty in formation time. As it turns out, the earlier forming pulses (relatively far above threshold) are of shorter duration than later forming pulses . This effect competes with the larger fluctuations in formation time closer to threshold, such that a diverging behaviour may not be extractable from the g(2) maps alone.The experiment does not allow direct access to individual trajectories, only the effect of their relative fluctuations on 17, which predicts g(2)(0)\u2009=\u20092. In the latter, a steady state is achieved by a detailed balance between cavity loss and continuous pumping, with the fluctuations being related to the coupling between the photons and the molecular grand-canonical reservoir in conditions of thermal equilibrium. There is time-translation symmetry and number fluctuations are damped within a 2\u2009ns time scale17. In contrast, the g(2) structure we identify here reflects the propagation of the initial fluctuations associated with the spontaneous emission events that trigger the growth of the condensate pulse. The system never reaches a steady state and all the dynamics are fundamentally transient. In principle, g(2), which depends on both the individual pulse shapes and their formation jitter, can even be larger than 2.Note that the fluctuations described here are of a different origin than those arising from the grand-canonical nature of a photon BEC\u03c8(t) towards its equilibrium value \u03c80 can be generically modelled by the time-dependent Landau equation45F\u2009=\u2009F(\u03c8) the near-equilibrium free energy and \u03b7 a generic Langevin stochastic force. This defines a universal class of dissipative relaxation processes5, typically valid near thermal equilibrium, where F\u2009=\u2009F(\u03c8) can be expanded in Taylor serious around \u03c80. We shall undertake here a different approach that will extend the validity of the model above into far-from-equilibrium conditions.We now develop a general treatment of the relaxation process described in \u201cResults\u201d section, thus highlighting its universal features and applicability outside the particular case of photon condensates. Relaxation of an order parameter \u03ba\u2009=\u2009\u0393\u2193\u2009=\u2009\u0393\u2191\u2009\u2261\u20090), the full non-equilibrium dynamics described by Eqs. (47\u03c8\u2009\u2192\u2009n) and total number of excitations, Nex\u2009=\u2009n\u2009+\u2009f\u2009Nmol, the control parameter, as defined earlier. By retaining the full dynamical information contained in the mean-field rate Eqs.   \u03ba\u2009=\u2009\u0393\u2193\u2009= by Eqs. , which dentclass1pt{minima\u03b7 accounts for spontaneous emission, such that \u2329\u03b7(t)\u03b7(0)\u232a\u2009=\u2009f\u20092E\u20092\u03b4(t)50. This allows us to include fluctuations and beyond-mean field effects in an universal model of relaxation. An alternative, and formally equivalent, approach would be the construction of a Fokker\u2013Planck equation5 for the probability density function (PDF) Pn(t), with a drift term given by the derivative of the effective free energy, as in Eq. , and shown in Fig.\u00a0F. While the free-energy landscape is more convex for larger values of the control parameter, which increases number fluctuations, these are longer-lived close to threshold (larger jitter). This effect witnesses the complex interplay between number and time fluctuations associated with the stochastic transient relaxation process determined by Eq.  curvature in the free energy tends to localise it. At a second-order phase transition, the curvature at the minimum of the free energy (defining an equilibrium order parameter) vanishes and the PDF shows diverging fluctuations that persist for long times, giving rise to critical slowing down. In transient, non-equilibrium systems dramatic features also occur, with regions of negative (convex) curvature acting to amplify fluctuations. A PDF evolving through these regions while relaxing towards the free-energy minimum experiences a short-lived but large increase of fluctuations, as shown in Fig.\u00a0d by Eq. . Even in\u03ba, as in the case of the experiment described in \u201cResults\u201d section, the rate of change of the free-energy landscape depends on the photon number n, which is itself described by a given PDF. The landscape is now neither constant, nor a simple function of time, but rather coupled to the photon number history, such that for trajectories where the condensate forms early, it also decays early, leading to the anti-correlation lobes seen in g(2). This is essentially the same result as depicted by the quantum trajectories simulation in Fig.\u00a0In the presence of loss by cavity transmission, the free energy and photon number PDF are coupled in a non-trivial way. For sufficiently large Nex, the control parameter, to be fixed, such that all molecular excitations are converted into cavity photons, corresponding to the limit of negligible losses. As a final remark, Eq. (F(\u03c8), from the observed average dynamics of the order parameter, \u03c8(t), although in practice the results are not very informative.The free-energy description assumes the total number of cavity excitations ark, Eq.  allows fIn this work, we have described the transient non-equilibrium dynamics of light in a dye-filled optical cavity quenched through a condensation phase transition. By rapidly exciting a large number of dye molecules, the system is brought to a far-from-equilibrium state. By averaging over all forms of fluctuations, we observed a delayed formation of the condensed phase, interpreted as a transient equivalent of critical slowing down. When quenched above the condensation threshold excitation energy, the quantum fluctuations associated with spontaneous emission seed the growth of the order parameter as the system relaxes into equilibrium. The relaxation dynamics is slower close to the critical point, a feature easily interpreted under the geometrical properties of the effective free-energy landscape, which becomes flat. The same mechanism is responsible for the usual critical slowing down in the relaxation rate of the ordered phase that follows a second-order phase transition. Also, despite the absence of latent heat and the fact that we are dealing with second-order and not first-order phase transitions, analogies can be drawn with the precipitation in supercooled, or supersaturated, liquids. Even quenched above the critical point, a seed of spontaneously emitted photons is needed to nucleate condensation, playing the role of the seeding crystals in supercooled, or supersaturated, liquids. Also, once seeded, crystallization across the entire liquid is faster for liquids quenched further across their critical parameters, with temperature playing the same role as the excitation fraction that follows the quench, in the optical cavity context.g(2). More precisely, we demonstrated that while the diagonal of g(2) is a powerful probe of the geometrical properties of the free-energy landscape, its off-diagonal elements reflect the relevant dissipation processes, with the anti-correlation lobes a joint effect of jitter and cavity loss. Fluctuations, arising from spontaneous emission, are highly amplified as the order parameter goes through the convex part of the free-energy landscape towards its equilibrium point.By measuring the statistical properties of this transient condensation, we describe a novel form of diverging fluctuations around the critical point, jitter in the formation of the ordered phase. These are witnessed by strong diagonal correlations and off-diagonal anti-correlations in the non-stationary, second-order correlation function, 54 may now benefit from being re-examined. Despite some recent efforts in describing time fluctuations and other non-equilibrium features of micro- and nano-lasers57, and to the best of our knowledge, we present here for the first time a generic and comprehensive description of the relation between temporal and number fluctuations in the non-stationary dynamics of systems undergoing second-order phase transitions. Finally, the system studied in this work, as well as the related examples stated above can be described by single-value order parameters. One may wonder on the generalization of these effects in spatially extended systems, where the order parameter is a function of both space and time. In the context of the Kibble\u2013Zurek mechanism11, for instance, most studies are simply concerned with the defect number scaling after the system relaxes to some steady state, with the intrinsic relaxation dynamics often ignored. As such, although we cannot anticipate specific effects, one wonders about the correspondence between transient fluctuation dynamics of the zero-dimensional system described in our paper and that of spatially extended systems.The description in terms of the geometric properties of the effective free-energy landscape, being independent of the microscopical details of our particular system, allows us to generalize our observations. In particular, both the transient critical slowing down and the jitter in the formation of the order parameter are expected to be universal features of the dynamics that follows a quench through a second-order phase transition. In micro- and nano-lasers, in particular, the full two-time, non-stationary analysis of the relaxation process has been greatly overlooked and previous resultsFrom the non-equilibrium model introduced in Eq.\u00a0, one cannm\u232a depends on the estimation of \u2329n2m\u232a, \u2329nm2\u232a, \u2329n3\u232a,\u00a0\u2026\u00a0, which requires solving a large number of ordinary differential equations. These can be reduced with an hierarchical set of approximations. For instance, in the semi-classical limit, the expectation values for n and m are factorized, \u2329mn\u232a\u2009\u2248\u2009\u2329m\u232a\u2329n\u232a, reducing Eq.\u00a0..3). Here37 given byIn order to account for correlations and fluctuations, one needs to go beyond the semi-classical approximation. In particular, the expectation values can be expanded in a hierarchical mannerx2\u232a\u2009\u2212\u2009\u2329x\u232a2, with x\u2009=\u2009{n,\u00a0m}, we explicitly writeThese represent the second, third, and fourth order cumulants, with the summation referring to all possible combination of variables. A minimal description of correlations is constructed by truncating the hierarchy at second order. In this way, and by defining g(2)(t), follow immediately asThe second-order photon correlation function at zero-time delay, 38, which allows us to calculate any quantity of the form \u2329X(t\u2009+\u2009\u03c4)Y(t)\u232a using two single-time evolutions. Let the initial state of the system be \u03c7(0), and the evolution be given by the map, \u03c7(t)\u2009=\u2009The two-time second-order correlation function can be obtained by invoking the quantum regression theorem\u03c7(0) from 0 to t, followed by the conditional state Y\u03c7(t) from t to t\u2009+\u2009\u03c4. For our cavity model, we begin by first evolving the density operator, \u03c1, from t\u2009=\u20090 to t\u2009=\u2009t1, using the second-order rate Eqs. (g(2)(t1). Second, the first-order rate Eqs. \u03c7(0) frome Eqs. (g(t1). Secate Eqs.  are usedwing Eq.\u00a0, one the42. Here, the Lindblad dynamics of the density operator \u03c1 is replaced by a wavefunction whose evolution is given by a non-Hermitian effective Hamiltonian, interspersed with stochastic quantum jumps. Subsequently, evolution of \u03c1 is approximated by an ensemble average of wavefunctions, or trajectories, say z, the average of any observable is then given byThe second-order approach described above corresponds to a first-level approximation to the description of correlations and fluctuations in the cavity dynamics. Moving to higher-order expansions increases the number of ordinary differential equations needed to resolve the dynamics, which soon becomes cumbersome and impractical. An alternative approach to solve the master Eq.\u00a0 is to usJk are the jump operators defining the stochastic dynamics. In the non-equilibrium cavity model, coherences cannot be created by Jk, occuring at rates Rk:The effective non-Hermitian Hamiltonian for the non-equilibrium cavity model in Eq.\u00a0 is givenRk. The time between consecutive events is drawn from an exponential distribution, whose mean is the inverse of total rate of events. From a large ensemble of trajectories, we can calculate the non-stationary second-order correlation function, g(2), asA particular quantum trajectory is constructed by drawing a series of stochastic events, with their individual probabilities proportional to the rates Peer Review File"}
+{"text": "The support of a patch is the union of the supports of the tiles that are in it. The translate of a patch P by translationally equivalent if tiling of patch. Recall that a tiling repetitive if every finite local complexity (FLC) if, for every R > 0, there are finitely many equivalence classes of R.We let 2.2.set in Delone \u03ba-set in A \u03ba-Meyer set in F  of points for Delone \u03ba-sets have a meaning analogous to the colours of tiles for tilings. We define repetitivity and FLC for a Delone \u03ba-set in the same way as for tilings. A Delone set \u039b is called a 2.3.expansive if there is a constant c > 1 with d on We say that a linear map prototiles. Denote by tile-substitution (or simply substitution) with an expansive map \u03d5 if there exist finite sets digit set  (b)  consists of a collection of spaces and mappings as follows: H is a locally compact Abelian group, i.e. a discrete subgroup for which the quotient group H. For a subset model set in regular if the boundary of Wmodel \u03ba-set  if each H is a Euclidean space, we call the model set \u039b a Euclidean model set rigid if A tiling 3.1.J, and et al. For any Note that \u25a1<!?tpb=-12pt>4. here.et al., 2007(Schlottmann, 2000From the assumption of pure discrete spectrum and Remark 5.5Let Under the assumption of pure discrete spectrum, we know that myak 2019 and \u03d5 fumyak 2019. From Th\u25a1Let It is known that any regular model sets have pure discrete spectrum in quite a general setting (Schlottmann, 2000\u25a1The next example shows that the unimodularity of \u03d5 is necessary.et al. (1998et al. (1998Let us consider an example of non-unimodular substitution tiling which is studied by Baake  al. 1998. This ex al. 1998 with thea to the right-hand side by the substitution and the letter b to the left-hand side. So we can get a bi-infinite sequence fixed under the substitution. A geometric substitution tiling arising from this substitution can be obtained by replacing symbols a and b in this sequence by the intervals of length a, and b, we can check The substitution matrix of the primitive two-letter substitution 6.et al. (1998et al. (1998We have mainly considered unimodular substitution tilings in this paper. Example 5.11 al. 1998. It cann al. 1998, which s"}
+{"text": "The standard tool to classify ceers is provided by the computable reducibility  Computable reducibility is a longstanding notion that allows classifying equivalence relations on natural numbers according to their complexity.R,\u00a0S be equivalence relations with domain R is computably reducible to S, denoted f such that, for all Let f is a computable function that reduces R to S; c-degrees are introduced in the standard way.We write universal ceers, i.e., ceers to which all other ceers are computably reducible. The degree of universal ceers is by now significantly explored: for instance, in , where s. Except for R[0], which is the empty set, for every R[s] is an equivalence relation in which almost all equivalence classes are singletons. Notice that we do not define here R with an accompanying R so that f must start with x.Let us define the Strategies for the requirements and their interactions The strategy for Q-requirement i. The reason we choose P-requirements. The requirement u,\u00a0v, both even, or both odd, which avoid the finitely many classes restrained by higher priority requirements. When found, it simply R-collapses u,\u00a0v : this ensures that R. Notice that if R-collapsing two even numbers or two odd numbers, since the construction will ensure that a necessary condition, at any stage s, for which we may have x,\u00a0y have different parity.For the R, i.e., R being in When at a stage The construction The construction is in stages: at stage s we define the approximation R[s] to R, and the approximations to the various parameters initialize a Q-requirement at stage s means to set as undefined at that stage the current value of its witness. A pair active witness for s if the pair has been appointed as a witness for inactive at the end of stage s if there are already distinct numbers s; it is active otherwise.Trequires attention at stageT is initialized; ore: s, and at the current stage there is a pair of distinct numbers u,\u00a0v bigger than all numbers in the union of all current equivalence classes of numbers u,\u00a0v are respectful of the restraint imposed by higher priority requirements);T at the end of stage s.one of the following holds, for some Stage 0 Initialize all Q-requirements. Define x; consequently A requirement Stage 1 Define x, leaving f and StageT that requires attention.  Action: T is initialized, then e: choose a fresh witness T, i.e. i is bigger than all numbers so far used in the construction ; in turn, R is not re-initialized: this string automatically becomes R in the priority ordering. The strings s.The strategy for U-equivalence classes of i and The strategy for P-requirement U,\u00a0V so that there are distinct u,\u00a0v can be V-collapsed without injuring higher priority restraints. It sets up a restraint asking that the initial segment U, sufficient to keep Let us now consider a P- and Q-requirements may have to be (re-)initialized as in the proof of Theorem\u00a0V-collapses a pair of distinct numbers, then this collapse is forever, reflected in the fact that we define U and V are interchanged.Due to the action of higher priority requirements, Rrequires attention at stageR is initialized and R is a Q-requirement; orU and V): R is active at the end of s  of distinct numbers of the same parity such that: (i)U[s]), and (ii)V[s] give the same equivalence classes relatively to the V-equivalence classes restrained by higher priority V-collapse of the equivalence classes of u,\u00a0v does not alter R at the end of stage s.one of the following holds, with A requirement The construction At stage s we define approximations to U[s] and V[s] will be the equivalence relations having U[s] and V[s] are equivalence relations with only finite equivalence classes and such that almost all equivalence classes are singletons; on the other hand we define Stage 0 Initialize all P- and Q-requirements; for x; consequently Stage 1 For x, keeping the values already defined at 0 for the other values of both StageR that requires attention.  Action: R is initialized, then e and U and V. As in the proof of Theorem\u00a0R, i.e. i is bigger than all numbers so far used in the construction, bigger than the length of s; consequently If e and U and V. Then pick the least (by code) triple V-collapsed following the V-collapse of u and v performed by s. Consequently U and V. Define U against s. Consequently U[s] on all other pairs.  and thuc-incomparable dark equivalence relations R and S have an infimum.There are E and F have an infimum.For every m-degrees. We choose c.e. sets Q.(1) Let X and T is a lower bound for R and S, and R and S are Q ensures that R and S are dark.We will show that the equivalence relations E is a lower bound of R and S. Consider a reduction E to Q, and we have E to There is only one class g(x) must be an odd number.There are two different classes S contains only one non-computable co-c.e. class, namely, the S-class X and Y implies that the set m-reducible to both X and Y, and thus would be computable), which gives a contradiction.We distinguish two cases. If the class In each of the cases above, we showed that T is the greatest lower bound of R and S.Assume that X and Y such that m-degrees a), there are T-degrees that form a minimal pair and do not contain any set of a lower (2) The proof of the second part is similar to the first one, modulo the following key modification: One needs to choose X,\u00a0Y such that For every notation This theorem is a combination of the two following results. The first one is Selivanov\u2019s result  about prN-requirement, see . Moreover, R-part and the S-part of R-part of B is guaranteed by the fact that each equivalence class of the R-part of U with an equivalence class of the S-part of T to U that hits only the S-part of U,Assume that there is P-requirements are satisfied. The last lemma guarantees that, given T to U or by providing two equivalence classes that can be collapsed in U to diagonalize against Q-requirements are also satisfied because we carefully avoid, within the construction, to collapse classes of the same parity. We are in the position now to show that all By modifying the last proof, we can obtain something stronger.R is S-dark or S is R-dark, then R,\u00a0S have no If S is R-dark. Then the proof of Proposition\u00a0Suppose that T is a U by employing precisely the same construction as in Theorem\u00a0Assume that the function R-part or the S-part of the relation Thus, one of the following two cases holds.Suppose that for some Case 1. The function R-part and infinitely many classes in the S-part. Then the same argument as in the proof of Lemma\u00a0R-darkness of S.Case 2. Assume that R-part and only finitely many classes in the S-part. Then choose a computable function S to U, the c.e. set R-classes. Therefore, one can choose an infinite R-c.e. set A with the following properties: A is an R-c.e. transversal of S, which contradicts the R-darkness of S.Therefore, one can re-prove Lemma\u00a0R,\u00a0S are mutually dark equivalence relations of any complexity, then they have no sup.The above result contrasts with the fact that R is essentiallyn-dimensional if R has exactly n noncomputable equivalence classesWe finally turn to the problem of whether there are equivalence relations now from  that thiR and S such that both R and S properly belong to R,\u00a0S have no Suppose that A properly belonging to the class U and V such that U and V are Q, R, and S as follows:Q,\u00a0R,\u00a0S is light and properly belongs to Fix a set T is the supremum of R and S, we have T must be essentially 1-dimensional. Let T-class. The conditions T should be reducible to F, we have either U and V. Thus, R and S have no supremum. Assume that mentclass2pt{minimWe conclude the paper with the following open question.For which"}
+{"text": "Nature Communications 10.1038/s41467-020-18005-7, published online 24 August 2020.Correction to: The original version of this Article contained an error in Fig. 1c. The length of the silicon core at the center of the panel was incorrectly labelled as \u20184\u2009mm\u2019, rather than the correct \u20184\u2009\u00b5m\u2019. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Nature Communications 10.1038/s41467-020-20265-2, published online 4 January 2021.Correction to: The original version of this Article contained an error in the title, which was previously incorrectly given as \u2018Three-phase electric power driven electoluminescent devices\u2019. The correct version states \u2018electroluminescent\u2019 in place of \u2018electoluminescent\u2019.This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "We established a universality of logarithmic loss over a finite alphabet as a distortion criterion in fixed-length lossy compression. For any fixed-length lossy-compression problem under an arbitrary distortion criterion, we show that there is an equivalent lossy-compression problem under logarithmic loss. The equivalence is in the strong sense that we show that finding good schemes in corresponding lossy compression under logarithmic loss is essentially equivalent to finding good schemes in the original problem. This equivalence relation also provides an algebraic structure in the reconstruction alphabet, which allows us to use known techniques in the clustering literature. Furthermore, our result naturally suggests a new clustering algorithm in the categorical data-clustering problem. Logarithmic loss is a unique distortion measure in the sense that it allows a \u201csoft\u201d estimation (or reconstruction) of the source. Although logarithmic loss plays a crucial role in learning theory, not much work has been published regarding lossy compression until recently. A few exceptions are a line of work on multiterminal source coding ,2,3, theoptimal schemes for the two problems are the same; anda good scheme for one problem is also a good scheme for the other.In this paper, we present a new universal property of logarithmic loss in fixed-length lossy-compression problems. Consider an arbitrary fixed-length lossy-compression problem, where source and reconstruction alphabets \ud835\udcb3 and We are more precise about the \u201coptimal\u201d and \u201cgoodness\u201d of the scheme in later sections. This finding essentially implies that it is enough to consider the lossy-compression problem under logarithmic loss.The above correspondence provides new insights into the fixed-length lossy-compression problem. In general, the reconstruction alphabet in the lossy-compression problem does not have any well-defined operations. However, in the corresponding lossy compression under logarithmic loss, reconstruction symbols are probability distributions that have their own algebraic structure. Thus, under the corresponding setting, we can apply various techniques, such as the information geometric approach, clustering with Bregman divergence, and relaxation of the optimization problem. Furthermore, the equivalence relation suggests a new algorithm in the categorical data-clustering problem, where data are not in the continuous space.The remainder of the paper is organized as follows. In Notation: Uppercase X denotes a random variable, where \ud835\udcb3 denotes a set of alphabet. On the other hand, lowercase x denotes a specific possible realization of random variable X, i.e., n-dimensional random vector Suppose \ud835\udcb3 is a finite set of discrete symbols, and X with finite alphabet M messages. On the other side, a decoder In this section, we briefly introduce the basic settings of the fixed-length lossy-compression problem . In a fiFirst, we can define the code that the expected distortion is lower than a given distortion level.Definition\u00a01.An (Average distortion criterion)The minimum number of codewords required to achieve average distortion not exceeding D is defined bySimilarly, we can define the minimum achievable average distortion given number of codewords M.One may consider a stronger criterion that restricts the probability of exceeding a given distortion level.Definition\u00a02.An (Excess distortion criterion)The minimum number of codewords required to achieve excess distortion probability \u03f5, and distortion D is defined bySimilarly, we can define the minimum achievable excess distortion probability given target distortion D and number of codewords M.D and Given target distortion There exists a unique rate-distortion function achieving conditional distribution We assume that x, then, there is no difference between If We make the following benign assumptions:Define the information density of joint distribution D-tilted information that plays a key role in fixed-length lossy compression.Then, we are ready to define Definition\u00a03.The D-tilted information in where the expectation is with respect to the marginal distribution of ]\u2265H(X|X^\u22c6)X and In the above theorem, distortion Equation  is the \u201cX and reconstruction M, the minimal achievable distortion is given by X and X and On the other hand, we viewed the \u201cinformation\u201d rate-distortion function differently. We considered the one-shot setting where source Remark\u00a01.In the corresponding fixed-length lossy-compression problem under logarithmic loss, the minimal achievable average distortion given number of codewords M iswhere the conditional entropy is with respect to distribution Remark\u00a02.From now on, we denote the original lossy-compression problem under given distortion measure n-dimensional binary vector where n is fixed, so the problem is in the one-shot setting. Distortion measure d is separable Hamming distortion, i.e.,M be the number of messages. Then, we are interested in optimal encoding and decoding schemes that achieve distortion In this section, we consider the memoryless Bernoulli source under Hamming distortion measure as an example of the above equivalence. Let In this scenario, the information rate-distortion function is not hard to compute :7)R(D)=R(D)=(7)RThen, the corresponding problem is the rate-distortion problem under logarithmic loss where the set of reconstruction symbols isRemark\u00a03.We can rewrite Equation  in this The above equation explicitly shows the correspondence between logarithmic loss and the original distortion measure.Theorem 2 implies that, for any fixed-length lossy-compression problem, we can find an equivalent problem under logarithmic loss where optimal encoding schemes are the same. Thus, without loss of generality, we can restrict our attention to the problem under logarithmic loss with reconstruction alphabet f and g are a suboptimal encoder and decoder for the original fixed-length lossy-compression problem. Then, the theorem impliesSuppose The left-hand side of Equation (9) is the cost of suboptimality for the corresponding lossy-compression problem. On the other hand, the right-hand side is proportional to the cost of suboptimality for the original problem. In In general, reconstruction alphabet M. Note that this is a single-letter version of  We alssion of  coincides with Equation (10), we haveRemark\u00a04.In extend the reconstruction set from \ud835\udcb4 to find the measure The above result (13) implies that In the previous section, we obtained the optimal reconstruction symbol from the extended reconstruction alphabet, and projected it to the feasible set. In this section, instead of direct projection to \ud835\udcb4, we propose another slight extension of \ud835\udcb4, namely, log-convex hull. As we show in the following sections, the log-convex hull has interesting properties.p and q be probability distributions in p and q is given byBefore defining the log-convex hull, we need to define the log-convex combination of probability distributions. Let r is a weight vector (i.e., It is clear to see that Instead of having projection of convex, (, [TheorerI-projection of Projection rI-projection satisfies the following inequality for all Csisz\u00e1r and Mat\u00fa\u0161 (, [TheoreOn the other hand, the log-convex combination of probability measures measures . The autThe above result holds for any Remark\u00a05.The above result is similar to the projection to polytope in Euclidean space. Suppose vectors where As we saw in the previous section, we want to find Since the first term is not a function of Thus, minimizing Since the objective function is a convex function of In the corresponding lossy-compression problem under logarithmic loss, reconstruction symbols are probability measures that have a natural algebraic structure, as we discussed in k-means clustering to a lossy-compression problem [k-means clustering is only available when there exists a well-defined operation in k-means clustering requires computing the mean of data points, which is the center of each cluster. In general lossy-compression problems, reconstruction alphabet k-medoidlike clustering [k-medoidlike algorithm in the context of lossy compression is shown in Algorithm 1.Lossy compression is closely related to the clustering problem ,20,21. M problem ,23,24, w problem ,26. Howeustering , where tAlgorithm 1k-medoidlike clustering in lossy compression.\u2003repeat\u2003\u2003Set \u2003\u2003fordo\u2003\u2003\u2003\u2003\u2003end for\u2003\u2003forMdo\u2003\u2003\u2003\u2003\u2003end for\u2003until converge\u2003Randomly initialize k-meanslike clustering algorithm, as shown in Algorithm 2.On the other hand, in the corresponding problem, the reconstruction alphabet is the set of probability distributions where operations such as log-convex combinations are well-defined. This allows us to propose a Algorithm 2k-meanslike clustering in lossy compression.\u2003repeat\u2003\u2003Set \u2003\u2003fordo\u2003\u2003\u2003\u2003\u2003\u2003Set \u2003\u2003end for\u2003\u2003forMdo\u2003\u2003\u2003\u2003\u2003end for\u2003until converge\u2003Randomly initialize k-means clustering [The main idea of the above algorithm is that log-convex combination ustering ,29. The mean are not well-defined in this case, it is hard to apply known data-clustering algorithms in continuous space. The key idea is that the equivalence relation with logarithmic loss allows the algebraic structure on any set. More precisely, we can transform any clustering problem to the clustering problem in continuous space and apply known techniques such as variations of k-means.The idea of the previous section can be applied to an actual clustering problem. We mainly focus on clustering categorical data where data points are not in continuous space ,32,33,34M clusters.A more rigorous definition of the problem is given below. Assume that we have a finite set of data points \ud835\udcb3, and each data point has its weight M. Let k-means to the corresponding problem. For example, Algorithm 2 can be applied to the corresponding problem.If we let Equation . Then, wRemark\u00a06.Note that it is hard to have an exact analytic formula for k-meanslike clustering algorithm in categorical data-clustering problems.To conclude our discussion, we summarize our main contributions. We showed that for any fixed-length lossy-compression problem under an arbitrary distortion measure, there exists a corresponding lossy-compression problem under logarithmic loss where optimal schemes coincide. We also proved that a good scheme for one lossy-compression problem is also good for another problem. This equivalence provides an algebraic structure on any reconstruction alphabet that allows using various optimization techniques in lossy-compression problems, such as log-convex relaxation. Furthermore, our results naturally suggest a"}
+{"text": "With the great significance of biomolecular flexibility in biomolecular dynamics and functional analysis, various experimental and theoretical models are developed. Experimentally, Debye-Waller factor, also known as B-factor, measures atomic mean-square displacement and is usually considered as an important measurement for flexibility. Theoretically, elastic network models, Gaussian network model, flexibility-rigidity model, and other computational models have been proposed for flexibility analysis by shedding light on the biomolecular inner topological structures. Recently, a topology-based machine learning model has been proposed. By using the features from persistent homology, this model achieves a remarkable high Pearson correlation coefficient (PCC) in protein B-factor prediction. Motivated by its success, we propose weighted-persistent-homology (WPH)-based machine learning (WPHML) models for RNA flexibility analysis. Our WPH is a newly-proposed model, which incorporate physical, chemical and biological information into topological measurements using a weight function. In particular, we use local persistent homology (LPH) to focus on the topological information of local regions. Our WPHML model is validated on a well-established RNA dataset, and numerical experiments show that our model can achieve a PCC of up to 0.5822. The comparison with the previous sequence-information-based learning models shows that a consistent improvement in performance by at least 10% is achieved in our current model. Biomolecular functions usually can be analyzed by their structural properties through quantitative structure-property relationship (QSPR) models (or quantitative structure-activity relationship (QSAR) models). Among all the structural properties, biomolecular flexibility is of unique importance, as it can be directly or indirectly measured by experimental tools. Debye-Waller factor or B-factor, which is the atomic mean-square displacement, provides a quantitative characterization of the flexibility and rigidity of biomolecular structures. With the strong relationship between structure flexibility and functions, various theoretical and computational methods have been proposed to model the flexibility of a biomolecular. Such methods include molecular dynamics (MD) , normal Other than the above deterministic models, data-driven machine learning models are also considered in flexibility analysis \u201329, thanMore recently, a persistent-homology (PH)-based machine learning model is proposed . In thisk-simplexes with k starting from 0. In particular, by assigning a weight value of 0 or 1 to each point, we can naturally arrive at a local PH model and element-specific PH model  is divided into N bins of equal size f. The number of barcodes which are located on each bin are then counted and used as feature vector [i is defined as:bj and dj are referring to birth and death of bar j. B is referring to the collections of barcodes with \u03b1 referring to the selection of atoms and D referring to the dimension of the Betti numbers. Essentially, for each C1 atom, we have a N * 1 topological vector for each element and dimension of the Betti numbers.In this paper, we only consider topological features constructed using a binning approach . More spe vector , 55. MorAfter the topological features are represented as a feature vector, it can serve as input to predict B-factor values with ML algorithms. We consider four main ML models, namely regularized linear regression, tree-based methods (including random forest and extreme gradient boosting), support vector regression, and artificial neural networks. All our ML algorithms are implemented in Python (packages mentioned below refer to the packages in Python).n data ith sample , ith sample, and p is the number of structured features. Conventionally, we denote by \u0177 the predicted normalized B-factor value of a sample.In the following descriptions of the ML models, we assume that we train our models with x by \u0177 [Linear regression is a straightforward yet efficient approach to model the relationship between a quantitative response and features. The incorporation of regularization can effectively address the high dimensionality setting where the number of features is larger than the sample size. The variable selection feature of the regularized linear regression makes it particularly suitable for our task as our feature vector is usually lengthy. The general formulation of regularized linear regression can be read as the following regularized minimization problem:acy of \u0177 \u201360.\u03b1\u2016\u03b2\u20161), where \u03b1 is the tuning parameter that strikes the balance between efficiency and regularization. The regression problem with these two types of regularization are also known as Ridge regression [least absolute shrinkage and selection operator (LASSO) [scikit-learn\u201d [In our study, we consider the two typical choices of gression  and leas (LASSO) , respectt-learn\u201d .Random Forest (RF) [Extreme Gradient Boosting (XGBoost) [Classification And Regression Tree (CART)  or decisest (RF) , 64 and XGBoost) .RH. RH is an ensemble learning method that creates a variety of decision (regression) trees independently during training, where each decision tree is constructed using a random subset of the features as split candidates. During the training of each tree, the split at each node is determined by the least-square method. In other words, for each region of each tree, we predict the B-factor value with the average of the B-factor values of the samples fallen in the region. In a regression RF, the final prediction is the average of the predicted values of all individual trees. In the implementation of ensemble trees, the number of trees, minimum number of samples at each leaf node, and the number of split candidates in each splitting, i.e., parameter mtry, are all tuning parameters. In our application of RF, we choose scikit-learn\u201d [ Breiman  and tunet-learn\u201d .XGBoost. Has been one of the popular ML tools used by the winning teams of many ML challenges and competitions, such as the Netflix prize [xgboost\u201d [ix prize  and varixgboost\u201d .\u03b20 + x\u22a4\u03b2 that has at most \u03f5 deviation from the actual target values yi for all the training data while trying to be as flat as possible [\u03b20, \u03b2) is determined by the following minimization problem:\u03be and C determines the trade-off between the efficiency and the amount up to which deviation larger than \u03f5 is tolerable. Typically, we adopt kernel methods to transform the input features from a lower to a higher dimensional space, where a linear fit is feasible. Common choices of kernel include polynomial kernel, Gaussian kernel, and radial basis function (RBF) kernel. In our study, we have opted to use RBF kernel, i.e., scikit-learn\u201d [SVR , as a vepossible . Sometimpossible . The SVRt-learn\u201d .ANN has been proved to be capable of learning to recognize patterns or categorize input data after training on a set of sample data from the domain . The abikeras\u201d [In our study, the number of hidden layers, number of nodes in each hidden layer, and the number of epochs are treated as hyperparameters. The hidden and output activation functions are set as sigmoid and leaky ReLU functions respectively. The dropout rate is set to 20% and the remaining hyperparameters are set to default values as defined by the package. ANN is implemented with the package \u201ckeras\u201d .We consider the same RNA dataset and data preprocessing by Guruge et al. . The chaThe values of B-factors may differ significantly from chain to chain due to reasons such as a relatively small number of residues in a protein chain or differences in refinement methods used . Thus, tE, F/E ratio, and bin size f are the hyperparameters to be optimized. We chose the value of E to be in the range from 10 \u00c5 to 45 \u00c5 with a stepsize of 5 \u00c5, i.e., E = {10 \u00c5, 15 \u00c5, 20 \u00c5, 25 \u00c5, 30 \u00c5, 35 \u00c5, 40 \u00c5, 45 \u00c5}. The filtration interval F is defined such that the ratio of F/E is between 0.5 to 1.0 with a stepsize of 0.1, i.e., F/E = {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}. Bin size f is chosen to be in the range from 0.15 \u00c5 to 1.50 \u00c5, i.e., f = {0.15 \u00c5, 0.50 \u00c5, 1.00 \u00c5, 1.50 \u00c5}. A total of 32,823 PBs are generated based on the Vietoris-Rips complex for each combination of element type, E and F/E ratio. Both \u201cGUDHI\u201d [Dionysus\u201d [In our dataset, cut-off distance  \u201cGUDHI\u201d  and \u201cDioionysus\u201d  packagesTo determine the optimal hyperparameter values for each ML model, we conduct a five-fold cross validation (CV) using the training set. Specifically, the training set is randomly divided into five folds with a similar number of chains. In each fold, for each combination of the hyperparameters, we find the predicted B-factor values for the left-out training set with the ML model trained by the remaining training set. The optimal hyperparameter set maximizes the out-of-sample PCC between the predicted and actual values across all folds. The optimal hyperparameter values for each ML model can be found in i-th B-factor value, Once the hyperparameter values of the dataset and models have been optimized, the trained models are evaluated using a test set that was non-overlapping with the training set. The PCC between the predicted and actual normalized B-factor values in the test set is calculated for each modelIn this section, we demonstrate the performance of our WPHML model. For both single-element and four-element-combined models, it can be seen that WPHML models are able to consistently outperform the evolution-based method (PSSM) by at least approximately 10% with only the exception of linear regression models (Ridge and LASSO). Among all the models, RF achieves the best result with PCC = 0.5788 (15.1% improvement). Moreover, the performance of the RF model further improves to 0.5822 when the topological features for all four elements were used, which is about 15.8% improvement.The comparison between the results from single-element and four-element-combined models shows that generally there is no significant improvement. In fact, SVM improves only slightly (approximately 0.8%), while XGBoost and ANN models even show some small reduction of accuracy (1.8% and 2.4% respectively). The results seem to be different from previous studies that concluded that element-specific models always deliver better results , 36\u201338. Comparably speaking, RNA structures are more regular and relatively simple. Similar topological features may be embedded in different types of element models. In this way, the additional features do not incorporate new information, instead they will contribute more noises, which causes the drop in performances. Noted that the best test performance of all the models except linear regression using a single element are all based on element P.One of the reasons that larger cut-off distance delivers good results is that our predicted PCC values are predominantly determined by the several larger-sized RNAs. From In this paper, we propose the weighted-persistent-homology-based machine learning (WPHML) models and use them in the RNA B-factor prediction. We found that our WPHML models can consistently deliver a better performance than the evolution-based learning models. In particular, local persistent homology and element-specific persistent homology are considered for topological feature generation. These topological-feature-based random forest models can deliver a PCC up to 0.5822, which is 15.8% increase as compared to the performance of the previous model. Our WPHML models are suitable for any biomolecular-structure-based data analysis. Note that more sophisticated feature engineering of sequence-based information can further improve the accuracy to 0.61 . This agS1 Table(PDF)Click here for additional data file.S2 Table(PDF)Click here for additional data file."}
+{"text": "In the original article, there was an error in the title. Instead of \u201cHypernetwork Construction and Feature Fusion Analysis Based on Sparse Group Lasso Method on Functional fMRI Dataset\u201d it should be \u201cHypernetwork Construction and Feature Fusion Analysis Based on Sparse Group Lasso Method on fMRI Dataset\u201d.Additionally, in Equations (4) and (7) the parameters mentioned and its explanations were wrong. \u201cn\u201d should be superscript and not subscript. Also in Equation (4), \u201cx\u201d should not be in italics and \u201c\u03b1\u201d should be in italics. A correction has been made to the following sections:The Materials and Methods section, subsection Construction of Hypernetwork, sub-subsection Sparse Linear Regression Model, paragraph 2:m-th ROI for n-th subject, m-th ROI for n-th subjects, with T being the number of time points in the time series; m-th ROI ; m-th ROI; and m-th ROI.\u201d\u201cThe average time series of The Materials and Methods section, subsection Construction of Hypernetwork, Construction of Hypernetworks Based on the Sparse Group Lasso Method, paragraph 3:\u201cSimilar to the gLasso method, clustering was adopted before creating the hyperedge, and then the sgLasso method was used to construct the hyperedge by solving the sparse linear regression model. The method is represented by the optimization objective function:Gi is a node with tree structure. \u03bb1 and \u03bb2 are regression parameters, with \u03bb1 being used to adjust the sparsity of intra-groups to control the number of non-zero coefficients in non-zero groups, and \u03bb2 being used to adjust group-level sparsity  of all three models, when \u03bb2was equal to 0.4. .\u201dThe authors apologize for these errors and state that this does not change the scientific conclusions of the article in any way. The original article has been updated."}
+{"text": "As of April 16, 2020, the novel coronavirus disease  spread to more than 185 countries/regions with more than 142,000 deaths and more than 2,000,000 confirmed cases. In the bioinformatics area, one of the crucial points is the analysis of the virus nucleotide sequences using approaches such as data stream, digital signal processing, and machine learning techniques and algorithms. However, to make feasible this approach, it is necessary to transform the nucleotide sequences string to numerical values representation. Thus, the dataset provides a chaos game representation (CGR) of SARS-CoV-2 virus nucleotide sequences. The dataset provides the CGR of 100 instances of SARS-CoV-2 virus, 11540 instances of other viruses from the Virus-Host DB dataset, and three instances of Riboviria viruses from NCBI . With this form of the data, it is possible to use data stream, digital signal processing, and machine learning algorithms.\u2022All researchers in bioinformatics, computing science, and computing engineering field can benefit from these data because by using this numeric representation they can apply several techniques such as machine learning and digital signal processing in genomic information.\u2022Data experiments that use clustering and classification techniques in SARS-CoV-2 virus genomic information can be used with this dataset.\u2022These data represent an easy way to evaluate the SARS-CoV-2 virus genome.1This work presents a new dataset of a chaos game representation (CGR) of SARS-CoV-2 virus nucleotide sequences. The dataset contains two kinds of data, the raw data, and the processing data. The raw data is composed of the 100 instances of the SARS-CoV-2 virus genome collected from the National Center for Biotechnology Information (NCBI) The dataset provides two groups of formats files for all data. In the first group, all data are stored in Matlab file format (.mat), and in the second group, part of the data is stored in Microsoft Excel (.xlsx) and another part in the text file (.txt). The two groups have the same information. The data is organized into three main directories: \u201cSARS-CoV-2 data\u201d, \u201cVirus-Host DB data\u201d and \u201cOther viruses data.\u201d Each main directory is formed by two sub-directories: \u201cMatlab\u201d and \u201cExcel and txt.\u201dk-th file is called \u201cRawData_k.mat.\u201dEach sub-directory \u201cMatlab\u201d contains three files called \u201cRawDataTable.mat\u201d, \u201cRawData.mat\u201d and \u201cCGRData.mat\u201d. \u201cRawDataTable.mat\u201d and \u201cRawData.mat\u201d files store the raw data information from the viruses database; they have the same information, however in the \u201cRawDataTable.mat\u201d the attributes are stored in Matlab table format (after 2013b version) and in \u201cRawData.mat\u201d the attributes are stored in Matlab cell arrays format. Each \u201cCGRData.mat\u201d file stores the CGR values of all viruses presented in each \u201cRawDataTable.mat\u201d and \u201cRawData.mat\u201d file. For the main directory \u201cVirus-Host DB data\u201d, the CGR values are stored in 10 files where each COD.txt\u201d where COD is the code (locus name) associated with the virus in Genbank Each sub-directory \u201cExcel and txt\u201d is composed of a file and another sub-directory called \u201cRawData.xlsx\u201d and \u201cCGRData\u201d, respectively. Each \u201cRawData.xlsx\u201d file has the raw data information from the viruses database, and each \u201cCGRData\u201d has the CGR of viruses presented in each \u201cRawData.xlsx\u201d file. The points of the CGR associated with each virus are stored in a text file called \u201cLocusName_2The Chaos Game Representation (CGR), proposed by H. Joel Jeffrey in s, expressed asN is the length of sequence and ns is the n-th nucleotide of the sequence. Each n-th nucleotide, ns, is mapped to bi-dimensional symbol (xs(n), ys(n)) and it can be expressed asn-th symbol (xs(n), ys(n)) is transformed in CGR values by equations expressed asxp(n), yp(n)) from dataset presented in this work.The CGR has with input the nucleotide sequence, ressed ass=[s1,\u22ef,s"}
+{"text": "Recently X. Fang et al. using a method given in previous research, where several classes of new MDS self-dual codes were constructed through (extended) generalized Reed-Solomon codes, in this paper, based on the method given in we achieve several classes of MDS self-dual codes.Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes are completely determined by the length  A q-ary k-dimensional subspace of Let The study of MDS self-dual codes has attracted a great deal of attention in recent years due to its theoretical and practical importance. The center of the study of MDS codes includes the existence of MDS codes , classifn, the main interest here is to determine the existence and give the construction of q-ary MDS self-dual codes for various lengths. The problem is completely solved for the case where q is even [As the parameters of an MDS self-dual code are completely determined by the code\u2019s length  is even . Many MD is even ,12,13,14In , Jin andIn this section we introduce some basic notations of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes. For more details, the reader is referred to .q is a prime power, q elements and let n be a positive integer with Throughout this paper, n distinct elements of n nonzero elements k-dimensional generalized Reed-Solomon code (GRS for short) of length n associated with Let q-ary It is well known that the code .g., see ).q-ary Furthermore, the extended generalized Reed-Solomon code .g., see ).Put Lemma\u00a01.The solution space of the equation system .The soWe defineThe conclusion of the following lemma is straightforward. For completeness, we provide its proof.Lemma\u00a02.Let n be an even number, if there exists .Let n Proof.\u00a0Let This implies that H. Yan  observedLemma\u00a03.Let n be an even integer and .Let n Lemma\u00a04.Let .Let m\u2223r is odd prime power, q elements. Suppose m-th root of unity and Let Theorem\u00a01.Let Proof.\u00a0m-th root of unity and Let t distinct elements, such that Let Then the entries of It is known that Let So g be a generator of Let q-ary This implies there exists a Example\u00a01.Let  13,932.Theorem\u00a02.Let Proof.\u00a0t distinct even number Let v is a square element of q-ary Let Example\u00a02.Let Theorem\u00a03.Let Proof.\u00a0t distinct even number Let For any t is odd, so q-ary Since Example\u00a03.Let Theorem\u00a04.Let Proof.\u00a0Let For any Case 1: If m is even, t is odd.Case 2: If m and t are even, A is an even integer. It follows that Case 3: If m is odd, t is even.(1)If (2)If (1)If (2)If \u2003\u25a1We can extend the Theorem 1 to a more general case.Theorem\u00a05.Let Proof.\u00a0m-th root of unity and Let t distinct elements, such that Let Similar with Theorem 1, we gets-th primitive root of unity. So Since So g be a generator of Let Case 1: If m odd and t even, we can take Case 2: If m even and q-ary MDS self-dual code with length So there exists a In this paper, based on the method from , we cons"}
+{"text": "R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size s-divergence, the Bhattacharyya Upper Bound (BUB) -based binary classification problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank- N-dimensional measurement vector N) relied on the exponential rate of s-divergence over parameter s. To circumvent this difficulty, a simplified case of s is often called s-divergence is the so-called Chernoff Evaluating the performance limit for the \u201cGaussian information plus noise\u201d binary classification problem is a challenging research topic, see for instance ,4,5,6,7.ds ratio  since anractable ,8. To cin theory ,11,12,13n theory ,15 is asetection , sparse etection , energy etection , multi-ietection ,20, netwetection , angularetection , detectietection , just to problem  and oftevergence .P-order tensor is equal to the minimal positive integer, say R, of unit rank tensors that must be summed up for perfect recovery. A unit rank tensor is the outer product of P vectors. In addition, the CPD has remarkable uniqueness properties [R. Unfortunately, unlike the matrix case, the set of tensors with fixed  rank is not close [p-th mode. Following the Eckart-Young theorem at each mode level [The tensor decomposition theory is a timely and prominent research topic ,26. Confot close ,30. Thisot close . Note thot close . The TKDot close  and the ot close  are two de level , this code level  or adaptde level , it is sde level . More prThe classification performance of a multilinear tensor following the CPD and TKD can be derived and studied. It is interesting to note that the classification theory for tensors is very under studied. Based on our knowledge on the topic, only the publication  tackles R tensor admitting a Q-order CPD with large factors of size More precisely, we consider two cases where the observations are either (1) a noisy rank-s-divergence, the Bhattacharyya Upper Bound (BUB)\u2014Chernoff Information calculated at Under the null hypothesis ibutions ,38,39 foWe note that Random Matrix Theory (RMT) has attracted both mathematicians and physicists since they were first introduced in mathematical statistics by Wishart in 1928 . When Wis-divergence, Chernoff Upper Bound, Fisher Information, etc.), but completes [Finally, let us underline that many arguments of this paper differ from the works presented in ,48. In , we tackThe organization of the paper is as follows: In the second section, we introduce some definitions, tensor models, and the Marchenko-Pastur distribution from random matrix theory. The third section is devoted to present Chernoff Information for binary hypothesis test. The fourth section gives the main results on Fisher Information and the Chernoff bound. The numerical simulation results are given in the fifth section. We conclude our work by giving some perspectives in the In this section, we introduce some useful definitions from tensor algebra and from the spectral theory of large random matrices.Definition\u00a01.The Kronecker product of matrices We have Definition\u00a02.The vectorization where Definition\u00a03.The q-mode product denoted by where Definition\u00a04.The q-mode unfolding matrix of size where R CPD of order Q is defined according toThe rank- product , \u03d5r(q)\u2208Rq-mode product defined in Definition 3 isq-th factor matrix of size An equivalent formulation using the q-mode unfolding matrix for tensor The  product .Q is defined according toThe Tucker tensor model of order q-mode product of q-mode unfolding matrix for tensor q-mode unfolding matrix of tensor The Following the definitions, we note that the CPD and TKD scenarios imply that vector M-dimensional vectors for which M remains fixed, matrix The Marchenko-Pastur distribution was introduced half a century ago  in 1967,Theorem\u00a01\u00a0The empirical eigenvalue value distribution . The emN large enough, all the eigenvalues are located in a neighbourhood of interval We also observe that Theorem 1 remains valid if ee e.g., ). TheoreWe denote by We note that the estimated hypothesis ce (KLD) . The expce (KLD) . Howeversed-form ,8.The minimal Bayes\u2019 error probability conditionally to vector s-divergence for X. The error exponent, denoted by According to , the relrding to \u2212limN\u2192\u221elAs parameter Finally, using Equations (5) and (7), the Chernoff Upper Bound (CUB) is obtained. Instead of solving Equation (7), the Bhattacharyya Upper Bound (BUB) is calculated by Equation (5) and by fixing Lemma\u00a01.The log-moment generating function given by Equation (6) for test of Equation (4) is given byProof.\u00a0See From now on, to simplify the presentation and the numerical results later on, we denote byRemark\u00a01.The functions s-divergence in the small In the small deviation regime, we assume that Lemma\u00a02.The s-divergence in the small deviation regime can be approximated according towhere the Fisher information  is givenProof.\u00a0See s-value at low s-value for larger According to Lemma 2, the optimal Lemma\u00a03.In case of large where Proof.\u00a0See Q-order tensor of size Q-order CPD with a canonical rank of M, we haveWhen tensor Q-order TKD of multilinear rank of When tensor The measurement tensor follows a noisy We recall that in the CPD case, matrix Result\u00a01.In the asymptotic regime where with with Proof.\u00a0See Remark\u00a02.In , the CenIn this section, we assume that Result\u00a02.In the small Proof.\u00a0Using Lemma 2, we can notice thatinstance ).\u2003\u25fbNote that Result\u00a03.In case of large Proof.\u00a0It is straightforward to notice thatThe last equality can be obtained as in . Using LRemark\u00a03.It is interesting to note that for as long as Proof.\u00a0It is straightforward to note thatUsing Equation (14) and condition R is supposed to be small compared to N, it is realistic to assume In the case of low rank CPD where its rank Result\u00a04.Under this regime, the error exponent can be approximated as follows:Proof.\u00a0See It is easy to notice that the second-order derivative of At low Equation s\u22c6\u224821+1SResult 1 and the above approximation allow us to get the best error exponent at low Contrarily, when The two following scenarios can be considered:In the TKD case, we recall that matrix Result\u00a05.In the asymptotic regime where where Proof.\u00a0See Remark\u00a04.We can notice that for where ee e.g., ). As a cResult\u00a06.In case of large Proof.\u00a0We have thatUsing Lemma 3, we get immediately Equation (17).\u2003\u25fbUnder this regime, we have the following resultsResult\u00a07.For small Proof.\u00a0Using Lemma 2, we can notice thatEach term in the product converges a.s towards the second moment of Marchenko-Pastur distributions Remark\u00a05.Contrary to the Remark 3, it is interesting to note that for which does not depend on Q, andwhich depends on Q.In practice, when c is close to 1, we have to carefully check if Q is in the neighbourhood of In this section, we consider cubic tensors of order s-value, L = 10,000 the number of samples for Monte\u2013Carlo process and where Firstly, for the CPD model, in s-divergences: s-divergence obtained by fixing In c goes to zero as predicted by our theoretical analysis.In For the TKD scenario, we follow the same methodology as above for CPD, s-value.For TKD scenario, the mean square relative error is in mean of order We can also notice that the convergence of In this work, we derived and studied the limit performance in terms of minimal Bayes\u2019 error probability for the binary classification of high-dimensional random tensors using both the tools of Information Geometry (IG) and of Random Matrix Theory (RMT). The main results on Chernoff Bounds and Fisher Information are illustrated by Monte\u2013Carlo simulations that corroborated our theoretical analysis.For future work, we would like to study the rate of convergence and the fluctuation of the statistics"}
+{"text": "Many-valued -algebras are algebraic systems that generalize Boolean algebras. The MV-algebraic probability theory involves the notions of the state and observable, which abstract the probability measure and the random variable, both considered in the Kolmogorov probability theory. Within the MV-algebraic probability theory, many important theorems  have been recently studied and proven. In particular, the counterpart of the Kolmogorov strong law of large numbers (SLLN) for sequences of independent observables has been considered. In this paper, we prove generalized MV-algebraic versions of the SLLN, i.e., counterparts of the Marcinkiewicz\u2013Zygmund and Brunk\u2013Prokhorov SLLN for independent observables, as well as the Korchevsky SLLN, where the independence of observables is not assumed. To this end, we apply the classical probability theory and some measure-theoretic methods. We also analyze examples of applications of the proven theorems. Our results open new directions of development of the MV-algebraic probability theory. They can also be applied to the problem of entropy estimation. MV-algebras, being generalizations of Boolean algebras, were introduced by Chang  and usedM is a normalized Carath\u00e9odory defined the basic notions of point-free probability, replacing Kolmogorovian probability measures on e, e.g., ). The MV Mundici  as a nor Mundici ) and RieM is weakly Main theorems of the MV-algebraic probability theory, including the basic version of the central limit theorem (CLT), laws of large numbers, and the individual ergodic theorem, can be found in ,8,9. In yniewicz . It is iThe MV-algebraic probability theory was also applied in the Atanassov intuitionistic fuzzy sets and interval-valued fuzzy sets settings , are deWe present three examples of the applications of the Marcinkiewicz\u2013Zygmund, Brunk\u2013Prokhorov, and Korchevsky SLLN for sequences of observables with convergent scaled sums. In particular, independent identically continuously distributed, as well as both independent and dependent discretely-distributed observables are considered.The problem of entropy estimation is important from both theoretical and practical points of view. Classical versions of the law of large numbers are used in this field. In particular, the authors of ,26,27 apThe paper is organized as follows. We present some notations that are used in the paper.We denote by Let X on a probability space X and by X with respect to P (if they exist).For each real-valued random variable The foundations of the theory of MV-algebras can be found in . In thisDefinition\u00a01.An MV-algebra\u2295 is associative and commutative with zero as the neutral element,is an algebra, where M is a non-empty set, the operation and for each:In an MV-algebra, a partial order is defined by the relation:The underlying lattice of M is the distributive latticewith the least element zero and the greatest element one, where the join and the meet are defined as follows:for each.Definition\u00a02.An MV-algebra M is called \u03c3-complete (complete) if every sequence  of elements of M has the supremum in M.X and an MV-algebra M, we introduce the notations:for for for For a non-empty set Definition\u00a03.Given a \u03c3-complete MV-algebra M, a functionis called a state on M if it satisfies the following conditions for eachand:(i)\u00a0(ii)\u00a0if, then(iii)\u00a0if, thenA state m on M is called faithful iffor each non-zero element x of M.Definition\u00a04.A probability MV-algebra is a pairconsisting of a \u03c3-complete MV-algebra M and a faithful state m on M.M is complete (see Theorem 13.8 in [If  13.8 in ).Definition\u00a05.Given a \u03c3-complete MV-algebra M, a functionis called an n-dimensional observable in M if it satisfies the following conditions:(i)\u00a0(ii)\u00a0andfor eachsuch that(iii)\u00a0for eachTheorem\u00a01.Given M a \u03c3-complete MV-algebra, an n-dimensional observable, and a state m on M, the functiondescribed by:is a probability measure on.The proof of the above theorem can be found in .Definition\u00a06.Letbe a probability MV-algebra. We call an observableintegrable inif the expectationexists. Moreover, we writeforifwhereis the absolutemoment of x. If, then the variance of x is given by the formula.Definition\u00a07.Observablesin a probability MV-algebraare said to be independent (with respect to m) if there exists an n-dimensional observable such that for arbitrary:Remark\u00a01.Letbe independent observables in a probability MV-algebraandbe their joint observable. Then, for arbitrary Borel measurable function, the mapping given by:is an observable.Convergence almost everywhere of observables in a probability MV-algebra was defined by Rie\u010dan and Mundici .Definition\u00a08.A sequenceof observables in a probability MV-algebrais said to converge to zero m-almost everywhere (m-a.e.), if:In the further part of this section, we will use the Kolmogorov probability space of observables considered by Rie\u010dan and Mundici .Let Kolmogorov probability space of the observablesWe call the triplet For each Proposition\u00a01.Letbe a probability MV-algebra andbe a sequence of independent observables in, withbeing the joint observable of. Letbe the Kolmogorov probability space of the observablesin. For eachletbe an arbitrary Borel function. Let further the observablebe defined byand the random variablebe described by. Then:and the convergence ofto zero P-a.s.implies the convergence ofto zero m-a.e.In this section, we formulate and prove MV-algebraic counterparts of the Marcinkiewicz\u2013Zygmund and Brunk\u2013Prokhorov SLLN see .In the following part of the paper, in formulas containing integrals, we will assume that image measureLet 3.2 from ), which Lemma\u00a01.Letbe a probability MV-algebra and. Then, for any-valued Borel functionand observablesin, the expected valueexists if and only if:Furthermore, if the above condition is satisfied, then:Proof.\u00a0Let 16.12 in ):(5)\u222bXTn as follows.The MV-algebraic version of the Marcinkiewicz\u2013Zygmund SLLN concerns the case of independent observables belonging to Theorem\u00a02.Given a probability MV-algebra, letbe an independent sequence of observables inhaving the same distribution. Let,,forandfor. Then:converges to zero m-a.e.Proof.\u00a0m-a.e.\u2003\u25a1Let The following MV-algebraic version of the Brunk\u2013Prokhorov SLLN concerns sequences of observables that are not necessarily identically distributed.Theorem\u00a03.Let. Given a probability MV-algebra, letbe an independent sequence of observables insuch that,for each. Let:Then:Proof.\u00a0We denote by fore, by  and TheoIn this subsection, we consider the convergence of observables in a probability MV-algebra with product Remark\u00a02.Letbe observables in a probability MV-algebra with product. By Proposition 2.4 from [such that for arbitrary:called the joint observable of. Moreover, for arbitrary Borel measurable function, the formula:defines a one-dimensional observable.Kolmogorov probability space of the observablesLet given by . We callThe following proposition is a consequence of Theorem 3.17 and Proposition 3.16 from .Proposition\u00a02.Letbe a probability MV-algebra with product andbe a sequence of observables in, withbeing the joint observable of. Letbe the Kolmogorov probability space of the observablesin. For eachletbe an arbitrary Borel function. Let further the observablebe defined byand the random variablebe described by. Then, the convergence ofto zero P-a.s. implies the convergence ofto zero m-a.e.We formulate and prove the main theorem of this subsection. For its classical counterpart and some notations, we refer the reader to Theorem\u00a04.Let observablesin a probability MV-algebra with productbe non-negative, i.e.,and their absolute moments of some orderbe finite. Letbe a non-decreasing unbounded sequence of positive numbers. If, where:and:where \u03c8 is a function belonging to, then:Proof.\u00a0Let We also present two special cases of the above theorem, corresponding to Theorem 2 and 3, formulated by Korchevsky  within tTheorem\u00a05.Let observablesin a probability MV-algebra with productbe non-negative and have finite variances. Letbe a non-decreasing unbounded sequence of positive numbers. Ifand:for some function, then:Theorem\u00a06.Let observablesin a probability MV-algebra with productbe non-negative and have finite absolute moments of some order. Letbe a sequence of positive numbers,,and:for some function. Then:Theorem 5 follows from Theorem 4 applied for We analyze the asymptotic behavior of scaled sums of three sequences of observables. They are independent identically continuously distributed in the first sequence and independent identically discretely distributed in the second one, whereas the third example concerns non-negative dependent observables. The MV-algebraic version of the Kolmogorov SLLN, presented in , cannot m of the form We consider observables taking values in the probability MV-algebra Let Let for each ented in , does noLet n, the joint observable We fix S-measurable functions full tribe, equipped with the operations c on We consider a probability MV-algebra with the product, presented in . Let \u03a9,Suct (see ).Let This paper is devoted to the development of MV-algebraic probability theory. We formulate and prove three generalized versions of the strong law of large numbers. The first two versions of the strong law, i.e., the MV-algebraic Marcinkiewicz\u2013Zygmund SLLN and Brunk\u2013Prokhorov SLLN, describe the asymptotic behavior of the sums of independent observables, whereas the third one, i.e., the Korchevsky SLLN, concerns the case of dependent observables. Their proofs require an application of the Kolmogorov theory of probability and some measure-theoretic techniques. To illustrate our theoretical results, we also present and analyze some examples of sequences of observables in a probability MV-algebra. We believe that our results open new possibilities for further development of the MV-algebraic probability theory in the non-Kolmogorovian setting. In particular, they can be used for the future development of the theory of fuzzy, intuitionistic fuzzy, and interval-valued fuzzy random events in complex spaces. We would like to apply the proven theorems to the estimation of logical entropy, as well as other types of entropy in the case of intuitionistic fuzzy random events. This requires, among other things, the definition of entropy for observables in MV-algebras."}
+{"text": "Scientific Reports 10.1038/s41598-020-57777-2, published online 22 January 2020Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cspectrophotometry\u201d was incorrectly given as \u201c|spectrophotometry\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Nature Communications 10.1038/s41467-020-16154-3, published online 8 May 2020.Correction to: Nucleic Acids Res.44, 6994\u20137005 (2016), when describing construction of the blue-light activation tool (BLAT). The sentence \u201cThe construction of BLAT and BLRT follows a previously reported strategy38\u201d has been added to the beginning of the second paragraph of the \u201cResults\u201d subsection \u201cConstructing the basic tools for powering cell division\u201d. Reference 38 has also been added to the sentence following: \u201cTo construct a BLAT, two units were designed and assembled : a blue optogenetics unit (BOU) to express light-sensitive protein EL222, and an activation reporter unit to replace the LuxR-binding region with an EL222-binding region by overlapping the -35 region (E. coli consensus -35 and -10 regions) of the LuxI promoter38.\u201dThe original version of this Article omitted a reference to previous work in reference 38, Jayaraman et al. Blue light-mediated transcriptional activation and repression of gene expression in bacteria. 38\u201d has been added to the legend of Fig. 4 to clarify this.Furthermore, Fig. 4, panels a and b, are adapted from reference 38 Figure 1, panels a and c, and this was not clear in the figure legend. The sentence \u201cPanels a and b are adapted from Jayaraman et al.These have been corrected in both the PDF and HTML versions of the Article."}
+{"text": "This approach increases exponentially, in the number of variables, the search space of the state-of-the-art tDBN algorithm. Concerning worst-case time complexity, given a Markov lag m, a set of n random variables ranging over r values, and a set of observations of N individuals over T time steps, the bcDBN algorithm is linear in N, T and m; polynomial in n and r; and exponential in p and k. We assess the bcDBN algorithm on simulated data against tDBN, revealing that it performs well throughout different experiments.Dynamic Bayesian networks (DBN) are powerful probabilistic representations that model stochastic processes. They consist of a prior network, representing the distribution over the initial variables, and a set of transition networks, representing the transition distribution between variables over time. It was shown that learning complex transition networks, considering both intra- and inter-slice connections, is NP-hard. Therefore, the community has searched for the largest subclass of DBNs for which there is an efficient learning algorithm. We introduce a new polynomial-time algorithm for learning optimal DBNs consistent with a breadth-first search (BFS) order, named bcDBN. The proposed algorithm considers the set of networks such that each transition network has a bounded in-degree, allowing for  Bayesian networks (BN) represent, in an efficient and accurate way, the joint probability of a set of random variables . Dynamicmth-order Markov DBNs such that each transition network has inter- and intra-slice connections. More recently, a polynomial-time algorithm was proposed that learns both the inter- and intra-slice connections in a transition network [The problem of learning a BN given data consists in finding the network that best fits the data. In\u00a0a score-based approach, a scoring criterion is considered, which measured how well the network fits the data ,7,8,9,10 network . The seaBy looking into lower-bound complexity results for learning BNs, it is known that learning tree-like structures is polynomial . HoweverIn this paper, we propose a generalization of the tDBN algorithm, considering DBNs such that each transition network is consistent with the order induced by the BFS order of the optimal branching of the tDBN network, that we call bcDBN. Furthermore, we prove that the search space increases exponentially, in the number of attributes, comparing with the tDBN algorithm, while running in polynomial time.We start by reviewing the basic concepts of Bayesian networks, dynamic Bayesian networks and their learning algorithms. Then, we present the proposed algorithm and the experimental results. The\u00a0paper concludes with a brief discussion and directions for future work.X denote a discrete random variable that takes values over a finite set n-dimensional random vector, where each n random variables Let , let X=X,\u2026,Xn repDefinition\u00a01 (Bayesian Network).A n-dimensional Bayesian Network (BN) is a triple where B induces a unique joint probability distribution over A BN D of size N, where variable D where the set of parents Let Observe that,Intuitively, the graph of a BN can be viewed as a network structure that provides the skeleton for representing the joint probability compactly in a factorized way, and making inferences in the probabilistic graphical model provides the mechanism for gluing all these components back together in a probabilistic coherent manner .M\u2014Maintenance problems; S\u2014Severe weather; F\u2014Flight delay; O\u2014Overnight accommodation; and C\u2014Cash compensation. In this simple example, all variables are Bernoulli (ranging over T and F). Inside the callouts only the CPTs for variables taking the value T are given.An example of a BN is depicted in G is given, and our goal is to estimate the set of parameters of the network G, given\u00a0only the training data. We assume data is complete, i.e., each instance is fully observed, there are no missing values nor hidden variables, and the training set N i.i.d. instances. Using general results of the maximum likelihood estimate in a multinomial distribution we get the following estimate for the parameters of a BN B:Learning a Bayesian network is two-fold: parameter learning and structure learning. When learning the parameters, we assume the underlying graph B fits the data D  and Minimum Description Length (MDL) . InformaThe LL is given by:This criterion favours complete network structures, and does not generalize well, leading to the overfitting of the model to the training data. The MDL criterion, proposed by Rissanen , imposesThe penalty introduced by MDL creates a trade off between fitness and model complexity, providing a model selection criterion robust to overfitting.n random variables by The structure learning reduces to an optimization problem: given a scoring function, a data set, a\u00a0search space and a search procedure, find the network that maximizes this score. Denote the set of BNs with Definition\u00a02 (Learning a Bayesian Network).Given a data n nodes has a superexponential number of structures, k-graphs (CkG) [k-graphs (BCkG) [kG and BCkG graphs are exponentially larger, in the number of variables, when compared with branchings [The space of all Bayesian networks with  problem ,21,22. Hructures ,23 or toructures , it is phs (CkG)  and breas (BCkG)  network anchings ,17.Definition\u00a03 (k-graph).A k-graph is a graph where each node has in-degree at most k.Definition\u00a04 (Consistent k-graph).Given a branching R over a set of nodes V, a graph Definition\u00a05 (BFS-consistent k-graph).Given a branching R over a set of nodes V, a graph k-graph, there can only exist an edge from R. We assume that if R reaches Observe that the order induced by the optimal branching might be partial, while its BFS order is always total (and refines it). Given a BFS-consistent t. Furthermore, let T sequential instants of time. The set of observations is represented as n attributes, measured at time t and referring to individual h.Dynamic Bayesian networks (DBN) model the stochastic evolution of a set of random variables over time . Considet, In the setting of DBNs the goal is to define a probability joint distribution over all possible trajectories, i.e., possible values for each attribute t, the probability distribution is considered constant, i.e., Observations are viewed as i.i.d. samples of a sequence of probability distributions Definition\u00a06 (mth-Order Markov assumption).A stochastic process over In this case m is called the Markov lag of the process.mth-order Markov process.If all conditional probabilities in Equation\u00a0 are invaDefinition\u00a07 (First-order Markov DBN).A non-stationary first-order Markov DBN consists of:A prior network A set of transition networks We denote by p parents from the previous time slices.Learning DBNs, considering no hidden variables or missing values, i.e., considering a fully observable process, reduces simply to applying the methods described for BNs for each transition of time . SeveralDefinition\u00a08 (Tree-augmented DBN).A dynamic Bayesian network is called tree-augmented (tDBN) if for each transition network k and is consistent with the BFS order of the tDBN; the inter-slice network has in-degree of at most p. The main idea of this approach is to add dependencies that were lost due to the tree-augmented restriction of the tDBN and, furthermore, remove irrelevant ones that might be present because a connected graph was imposed. Moreover, we also consider the BFS order of the intra-slice network as an heuristic for a causality order between variables. We make this concept rigorous with the following definition.We introduce a polynomial-time algorithm for learning DBNs such that: the intra-slice network has in-degree at most Definition\u00a09 (BFS-consistent k-graph DBN).A dynamic Bayesian network is called BFS-consistent k-graph (bcDBN) if for each intra-slice network Given an optimal branching Moreover, each node Before we present the learning algorithm, we need to introduce some notation, namely, the\u00a0concept of ancestors of a node.Definition\u00a010 (Ancestors of a node).The ancestors of a node mth-order bcDBN. Let p. For each node We will now describe briefly the proposed algorithm for learning a transition network of a p parents from past time slices, and the one in Equation (p parents from the past time slices when We note that the set quations  and 9)  Xps[t\u2212m+quations  refers tk. Note that, if\u00a0A complete directed graph is built such that each edge  network . In ordeD, a Markov lag m, a decomposable scoring function p and a maximum number of intra-slice parents k.The pseudo-code of the proposed algorithm is given in Algorithm 1. As parameters, the algorithm needs: a dataset Algorithm 1 Learning optimal mth-order Markov bcDBN1:for each transition do2:\u2003Build a complete directed graph in 3:\u2003Weight all edges Equation   in the intra-slice network the graph is consistent with a total order (so no cycle can occur); and (ii) in the inter-slice network there are only dependencies from previous time slices to the present one (and not on the other way).\u2003\u2610Let Algorithm 2 Compute all the weights 1:for all nodes do2:\u2003Let 3:fordo\u20034:ifthen\u2003\u20035:\u2003\u2003\u2003Let 6:end if\u2003\u20037:end for\u20038:for all nodes do\u20039:\u2003\u2003Let 10:fordo\u2003\u200311:ifthen\u2003\u2003\u200312:\u2003\u2003\u2003\u2003Let 13:end if\u2003\u2003\u200314:end for\u2003\u200315:end for\u200316:\u2003Let 17:end forAlgorithm 3 Compute the set of parents of 1:Let 2:fordo3:fordo\u20034:ifthen\u2003\u20035:\u2003\u2003\u2003Let max = 6:\u2003\u2003\u2003Let the parents of 7:end if\u2003\u20038:end for\u20039:end forTheorem\u00a02.Algorithm 1 takes timegiven a decomposable scoring function \u03d5, a Markov lag m, a set of n random variables, a bounded in-degree of each intra-slice transition network of k, a bounded in-degree of each inter-slice transition network of p and a set of observations of N individuals over T time steps.Proof.\u00a0p elements is given by:For each time transition r, and that each variable has at most p from the past and 1 in p elements from the past and k elements from the present is upper bounded by Calculating the score of each parent set (Step 11 of Algorithm 2), considering that the maximum number of states a variable may take is Theorem\u00a03.There are at least Proof.\u00a0i-th node of V with at most k lower nodes. When V with at most k lower nodes exist. Therefore, there are at leastk-graphs.Consider without loss of generality the time transition k-graphs.Let There are https://margaridanarsousa.github.io/learn_cDBN/). The experiments were run on an Intel\u00ae Core\u2122 i5-3320M CPU @ 2.60GHz\u00d74 machine.We assess the merits of the proposed algorithm comparing it with one state-of-the-art DBN learning algorithm, tDBN . Our algN. The parameters p and k were taken to be the maximum in-degree of the inter and intra-slice network, respectively, of the transition network considered.We analyze the performance of the proposed algorithm for synthetic data generated from stationary first-order Markov bcDBNs. Five bcDBN structures were determined, parameters were generated arbitrarily, and observations were sampled from the networks, for a given number of observations one intra-slice complete bcDBN network with me slice a;one incomplete bcDBN network, such that each node in nd p+k\u22644 b;two incomplete intra-slice bcDBN network , with higher precision scores and similar recall, comparing with tDBN+MDL.For both algorithms, in general, the LL gives raise to better results, when considering a complete network structure and a lower number of instances, whereas taking an incomplete network structure and a higher number of instances, the MDL outperforms LL. The complexity penalization term of MDL prevents the algorithms of choosing false positive edges and gives raise to higher precision scores. The LL selects more complex structures, such that each node has exactly N. In order to understand the number of instances N needed to fully recover the initial transition network, we designed two new experiments where five samples where generated from the first-order Markov transition networks depicted in We stress that in all settings considered both algorithms improve their performance when increasing the number of observations k, the number of necessary observations to totally recover the initial structure increases significantly.The number of observations needed for the bcDBN+MDL to recover the aforementioned networks are 0\u00b1478.18 a and 290\u00b11134.77 b, with ak-structures, the bcDBN algorithm achieved consistently significantly higher When considering more complex BFS-consistent The bcDBN learning algorithm has polynomial-time complexity with respect to the number of attributes and can be applied to stationary and non-stationary Markov processes. The proposed algorithm increases the search space exponentially, in the number of attributes, comparing with the state-of-the-art tDBN algorithm. When considering more complex structures, the bcDBN is a good alternative to the tDBN. Although a higher number of observations are necessary to fully recover the transition network structure, bcDBN is able to recover a significantly larger number of dependencies and surpasses, in all experiments, the tDBN algorithm in terms of A possible line of future research is to consider hidden variables and incorporate a structural Expectation-Maximization procedure in order to generalize hidden Markov models. Another possible path to follow is to consider mixtures of bcDBNs, both for classification and clustering."}
+{"text": "The frequency distribution of the h-index rank follows an exponential decay curve with the following formula y\u2009=\u2009152.94e\u22120.0312x, where x is the rank of the entry and y is the h-index, and R2\u00a0=\u00a00.9812 . The remaining 141 countries have an h-index\u2009>\u20092, 78 of those have an h-index\u2009>\u200911, just 53 of them have an h-index\u2009>\u200922 and 36 have an h-index\u2009>\u200944 , with the exception of Iran . We have also included three other entries in this list, namely Argentina , Estonia  and Hungary  on the basis of their h-index performance (h-index ranks of those can be examined in comparison to a group of 30 countries that produce >98% of the world\u2019s highly cited (top 1%) papers  (h-index per million inhabitants) , climbing to 0.964 if Greece, Iran, Italy and Russia are excluded  is missing , raising questions about barriers to entry, and despite a wealth of opportunities for international collaboration, that will need to be addressed in the future.To examine whether the use of the formance . Interesformance . The h-ied here)  and two bitants) . These 4milarity . The ran missing . Dispari missing . It is wAs the field of bioinformatics has expanded across all of the life sciences , the prebtaa132_Supplementary_DataClick here for additional data file."}
+{"text": "Moreover, we provide a polynomial-time algorithm to identify all u-fp orthology assignments in a BMG. Simulations show that at least not on any a priori knowledge about underlying gene or species trees.Genome-scale orthology assignments are usually based on reciprocal best matches. In the absence of horizontal gene transfer (HGT), every pair of orthologs forms a reciprocal best match. Incorrect orthology assignments therefore are always false positives in the reciprocal best match graph. We consider duplication/loss scenarios and characterize unambiguous false-positive ( Orthology is one of the key concepts in evolutionary biology: Two genes are orthologs if their last common ancestor was a speciation event Fitch . Distingevolutionary scenario comprising a gene tree T and a species tree S together with a reconciliation mapT to S. The map In this contribution, we consider exclusively duplication/loss scenarios, i.e., we explicitly exclude horizontal gene transfer. Characterizations of reconciliation maps are given e.g. in G\u00f3recki and Tiuryn inaccuracies in the assignment of best matches from sequence similarity data Stadler et\u00a0al. , and(ii)limits in the reconstruction of the \u201ctrue\u201d orthology relation from best match graphs Gei\u00df et\u00a0al. .We consider best matches as an evolutionary concept: A gene y in species s is a best match of a gene x from species s contains no gene x. That is, best matches capture the idea of phylogenetically most closely related genes. Maybe surprisingly, the combinatorial structure of best matches has become a focus only very recently Gei\u00df et\u00a0al.  and  in the BMG. Here, we aim to identify false-positive edges from the structure of the BMG itself.Of course, the \u00df et\u00a0al.  showed t\u00df et\u00a0al.  below. Oxy is a reciprocal best match. If there are no other descendants that harbor genes witnessing the duplication event, then the framework of best matches provides no information to recognize xy as a false-positive assignment.We first note that false positives cannot be avoided altogether, i.e., not all false positives can be identified from a BMG alone. The simplest example, Fig.\u00a0On the other hand, RBMGs and thus BMGs contain at least some information on false positives. Since the orthology relation forms a cograph but RBMGs are not cographs in general Gei\u00df et\u00a0al. , incorrez et\u00a0al.  noted thz et\u00a0al. . The remz et\u00a0al. . Here, wz et\u00a0al.  to a comGood quartets cannot be defined on RBMGs because information on non-reciprocal best matches is also needed explicitly. This suggests to consider BMGs rather than RBMGs as the first step in graph-based orthology detection methods. In practice, best matches are approximated by sequence similarity and thus are subject to noise and biases Stadler et\u00a0al. . The empunambiguous false-positive (u-fp) edges, i.e., reciprocal best matches that cannot be orthologs w.r.t. to any gene tree explaining the BMG. Sec.\u00a0We provide a full characterization of unambiguous false-positive orthology assignments in BMGs.We provide a polynomial-time algorithm to determine all unambiguous false-positive orthology assignments in BMGs.In Sec.\u00a0Sec.\u00a0Since the material is extensive and very technical, we subdivide our presentation into a main narrative part Secs.\u00a0\u20136 and a xy is an edge in undirected. A graph subgraph of symmetric part of a directed graph induced, denoted by vertex-colored graphs M of colors. A vertex-coloring is called proper if x,\u00a0y) in We consider finite, directed graphs path (of length) in a directed graph G is a subgraph induced by a nonempty sequence of pairwise distinct vertices A treesundirected, planted and phylogenetic, that is, they satisfy (i) the root L(T) for the leaves  the subtree of T rooted in v. The set of clusters of a tree T is TSemple and Steel  best matches of the same color clusters of orthologous groups (COGs) concept  if there exists a leaf-colored tree explainsreciprocal best match graph (RBMG) if it is the symmetric part of a BMG An arbitrary vertex-colored graph x and y are reciprocal best matches in For the symmetric part of the BMG \u00df et\u00a0al. .evolutionary scenario extends the map L(T) only contains extant genes. Inner vertices in the gene tree T that designate speciations have their correspondence in inner vertices of the species tree. In contrast, gene duplications occur independently of speciations and thus belong to edges of the species tree. The embedding of T into S is formalized byAn (Reconciliation Map) Let S is a map (R0)Root Constraint.(R1)Leaf Constraint. If (R2)Ancestor Preservation. If (R3)Speciation Constraints. Suppose (i)x in T.(ii)S for any two distinct children x in T.Several alternative definitions of reconciliation maps for duplication/loss scenarios have been proposed in the literature, many of which have been shown to be equivalent. This type of reconciliation map has been established in Gei\u00df et\u00a0al. . MoreoveS with leaf set  is the map Given a reconciliation map The following result is a simple but useful consequence of combining the axioms of the reconciliation map with the event labeling of Def.\u00a0S and suppose that  endowed with a map Lemma\u00a0\u00df et\u00a0al. ,\u00a0Lemma\u00a02extremal event labeling of T is the map Let T and a reconciliation of T with a species tree S, a duplication vertex of T is an AD vertex if its two subtrees have at least one color in common. In contrast, it is a non-apparent duplication (NAD) vertex if the color sets of its subtrees are disjoint. This notion is useful for a variety of parsimony problems that usually aim to avoid or minimize the number of NAD vertices Swenson et\u00a0al.  has vertex set L(T) and edges The The orthology graph is often referred to as the orthology relation. Orthology graphs coincide with a well-known graph class:G is an orthology graph for some event-labeled tree , i.e. G is a cograph. for any given reconciliation map connecting a gene with a species tree.S. Then  Let xy in false-positive, or fp for short, if for every reconciliation map S we have xy is called fp whenever x and y cannot be orthologous w.r.t. any possible reconciliation fp s can be identified without considering reconciliation maps explicitly.In other words, xy be an edge in xy is fp.The edge There are two children For the extremal labeling Let fp can be verified in polynomial time for any given gene tree fp edges coincide with the edges xy in Lemma\u00a0entclass1pt{minimaxz, yz are fp but not fp. Since we assume that no information on a priori, it is natural to consider the set of edges that are false positives for all trees explaining a given BMG.As shown in Fig.\u00a0 Let xy in unambiguous false-positive (u-fp) if for all trees xy is fp.xy in u-fp, then it is in particular fp in the true history that explains u-fp edges are always correctly identified as false positives. Not all \u201ccorrect\u201d false-positive edges are u-fp, however. It is possible that, for an edge xy in xy is not fp for some gene tree xy is not fp and therefore not u-fp.Hence, if an edge entclass1pt{minimaentclass1pt{minimax and y for which T rooted in the children of u-fp edges in a BMG.In order to adapt the concept of AD vertices for our purposes, we introduce the color-intersection mentclass2pt{minimxy in a BMG fp for every tree u-fp.Every edge As we shall see below, the converse of Prop.\u00a0xy in xy is fp.The edge xy is u-fp.The edge Let Prop.\u00a0ab, bc, and cd.Since every orthology graph is a cograph Thm.\u00a0 and thus Let L, and let Q, resp., the induced subgraph good quartet if (i) a bad quartet if (i) a ugly quartet if an The edge xy in a good quartet middle edge. The edge zx of an ugly quartet first edge. First edges in ugly quartets are uniquely determined due to the colors. In bad quartets, this is not the case and therefore, the edge r, s, and t must be pairwise distinct. Note that (R)BMGs may also contain induced The three different types of quartets are shown in Fig.\u00a0mentclasspt{minimaz and u-fp edges. We collect here the main results of Sec.\u00a0Good quartets are characteristic of a complementary gene loss yz is u-fp.If (ii)xy and its middle edge yz are u-fp.If (iii)xy and zw are u-fp.If Let Not surprisingly, quartets are intimately linked to color-intersections:xy. Then, xy is either the middle edge of some good quartet or the first edge of some ugly quartet, which in turn implies that xy is u-fp.Let u-fp edges xy with xy must be u-fp since u-fp. Moreover, xy, on the other hand, is the first edge of the ugly quartet All mentclass2pt{minimxy is the middle edge of a good quartet, then u-fp edges that are not identified with the help of the color-intersection u-fp edges. The edge xy in the BMG shown in Fig.\u00a0u-fp, but it is not contained in a good, bad, or ugly quartet.Furthermore, if an edge u-fp edges that are not identified by quartets, we first introduce an additional motif that may occur in vertex-colored graphs.In order to characterize the (Hourglass) An hourglass in a proper vertex-colored graph xy and Note that Condition (i) rules out arcs between Every hourglass is a BMG since it can be explained by a tree as shown in Fig.\u00a0Hourglasses are not necessarily part of an induced xy with Hourglasses xy is u-fp.If a BMG u-fp edges that are not contained in a quartet, see Fig.\u00a0Prop.\u00a0(Hourglass chain) An hourglass chainA vertex z is called a left  tail of the hourglass chain tailed if it has a left or right tail.u which is common to all hourglasses in the chain  Let augmented tree ofIn particular, the augmented tree preserves the best match relation:For every leaf-colored tree We now have everything in place to present the main results of this section.Let u-fp edges \u00a0On\u00a0S, we use a variant of the well-known constant-rate birth-death process with a given age \u00a0A planted species tree nd Klemm , which mbona fide multifurcations of species Kliman et\u00a0al. . Multifurcating gene trees were produced for p and T, the true BMG G are known, we can also determine the setu-fp edges as well as the subsets u-fp edges that are middle edges of a good or first edges of an ugly quartet, respectively. Note that in general we have u-fp edges in good and ugly quartets increases moderately for larger p.The simulated data set of evolutionary scenarios comprises species trees with 10 to 30 species (drawn uniformly). The time difference between the planted root and the leaves of u-fp edges in Fig.\u00a0u-fp edges that appear only as first edges of bad quartets is even smaller; only 2-3% of the u-fp edges associated with hourglass chains, i.e., less than 0.15% of all u-fp edges are of this type. The overwhelming majority of u-fp edges associated with quartets thus appear  as middle edges of good quartets. This observation provides an explanation for the excellent performance of removing the u-fp edges, which are completely covered by First, we note that, consistent with Gei\u00df et\u00a0al. , Stadler\u00df et\u00a0al. . In part\u00df et\u00a0al. , there iu-fp edges in terms of underlying subgraphs and refinements of trees. Since the best match graph contains only false positives, we have obtained a characterization of all unambiguously incorrect orthology assignments. Simulations showed that the majority of false positives comprises middle edges of good quartets, while u-fp edges that appear only as first edges of an ugly quartet are rare. Not surprisingly, the hourglass-related u-fp edges become important in gene trees with many multifurcations. They do not appear in scenarios derived from binary gene trees. For the theory developed here, it makes no difference whether polytomies in the gene tree appear as genuine features, or whether limited accuracy of the approximation from underlying sequence data produced the equivalent of a soft polytomy in the BMG.We have shown here how all unambiguously false-positive orthology assignments can be identified in polynomial time provided that all best matches are known. In particular, we have provided several characterizations for The augmented tree d et\u00a0al. , i.e., dd et\u00a0al. , Lafond d et\u00a0al.  with besT and species tree S, we ask here about the information contained in the BMG implies a set S Hernandez-Rosales et\u00a0al.  hits into evolutionary best matches in a systematic manner Stadler et\u00a0al. , estimatclusters of orthologous groups (COGs) in an empirically estimated RBMG Tatusov et\u00a0al. (u-fp edges and thus, it is the closest orthology graph. However, Orthology prediction tools intended for large data sets often do not attempt to infer the orthology graph, but instead are content with summarizing the information as v et\u00a0al. , Roth etv et\u00a0al. . Formall"}
+{"text": "Simultaneous search for one of two targets is slower and less accurate than search for a single target. Within the Signal Detection Theoretic (SDT) framework, this can be attributed to the division of resources during the comparison of visual input against independently cued targets. The current study used one or two cues to elicit single- and dual-target searches for orientation targets among similar and dissimilar distractors. In Experiment The online version of this article (10.3758/s13414-019-01854-w) contains supplementary material, which is available to authorized users. Finding a target-object in the scene requires observers to compare visual input at different locations with an internal representation of the target\u2019s features. This ability is thought to rely on components of selective attention that integrate information across frontal, parietal and visual cortical regions Ptak, . Prior tMost studies of search have focussed on the accuracy and speed of detection for a single target. In this situation, selection elicits a topographic map that represents objects in terms of their similarity to the target\u2019s features . Evidence to suggest independently cued features can also mediate perceptual categorisation was reported by Roper and Vecera . They usThe results above suggest the selection of visual input for independently cued targets generalises from electrophysiological to behavioural responses during search. Evidence that MITs can also guide oculomotor behaviour has been reported by Beck and colleagues . All reported normal or corrected-to-normal visual acuity. Recruitment, consent and all experimental procedures conformed to American Psychological Association (APA) ethics standards.We used a small-The experiment was run on an IBM PC with a 19-in. CRT View Sonic G90fB monitor . The display resolution was 1,240 \u00d7 768 pixels and the frame rate was 85 Hz. Stimulus presentation and data collection were controlled using custom-built software in MATLAB  with Psychophysics toolbox extensions  Landholt\u2019s C-shapes and grey  annuli that subtended 3.0\u00b0 \u00d7 3.0\u00b0. Stimuli were presented at 12 equally spaced locations on the circumference of a virtual circle with a radius of 7.0\u00b0. C-shapes and annuli were presented on a uniform black  background.Displays contained red (C-shapes). Experimental blocks contained four repetitions of this structure . On each block of trials, two target and four distractor orientation values were assigned. Target orientations were sampled from 90\u00b0 and 270\u00b0 \u00b1 15\u00b0 to 30\u00b0. Distractor orientations for each observer differed from Target-Left or Target-Right by an angle of rotation that produced 80% accuracy on a pre-test (see below). Target and distractor values were fixed within experimental blocks to produce symmetric target-distractor similarity distributions for two targets among numerically equivalent subsets of leftward and rightward Cs. ; trial type (target-present or -absent); target identity (Target-Left or -Right), and set size . At set size two, one leftward and one rightward distractor were randomly sampled from the four alternatives. At set size one, a single leftward or rightward distractor was sampled with equal probability. On target-present trials, displays contained one C-shape at the orientation assigned to Target-Left or Target-Right. Targets always replaced a similar distractor from the same (leftward or rightward) group and displays always contained one C-shape from a group that was cued. Search displays were presented for 94 ms and followed by blank screen, which remained visible until a response was recorded. Short-duration displays were used to equate processing time and prevent eye movements on single- and dual-target searches.Figure C-shape in the same displays as the experimental session but varied the orientations of the target and distractor across the range \u00b1 5\u00b0 to 30\u00b0 using a method of constant stimulus. Individual responses were fitted with a cumulative Gaussian function to estimate the angle of rotation required by each observer to distinguish targets from distractors on 80% of trials.Observers completed ten blocks of trials in a single experimental session. In each block, single- and dual-target cues were equally likely for leftward and rightward targets. A cued target appeared in the search display on 50% of trials, and the order of presentation for each target, search type and trial was randomly assigned for each block. Prior to experimental sessions, observers completed two pre-test blocks of 80 trials. These presented a single i to the visual response to each object in the display j. The result of each comparison describes the perceived similarity between the cue and the object, which is represented by a real number sij. To classify the display, observers evaluate whether the maximum similarity value is less than or equal to a response criterion. The cumulative probability distribution function P(sij \u2264R) ;of sij depends on three factors: (1) The type of comparison C, which can be a target(t) similar distractor(s) or dissimilar distractor(d), depending on the relationship between the cue and the object in the display. (2) The set size D, which can equal 1, 2 or 4. (3) The number T of templates used to guide search, which is determined by the number of cues. These dependencies are indicated by the notation P. As a simplifying assumption, all comparisons between cues and objects with opposite orientations are modelled by the same probability distribution. In particular, the target is considered a dissimilar distractor for the second cue on dual-target searches. In agreement with standard SDT  and variance 1, i.e., P = \u03a6 ), where \u03a6 denotes the standard normal cumulative probability distribution . The statistical modelling of this process is based on signal detection theory (SDT) and the assumption of independent comparisons . Because of independence, the probability that none of the comparisons exceed the response criterion equals the product of the probabilities for each individual comparison being less than \u03bb:To distinguish between theoretical accounts of attentional control during search, we introduce additional assumptions to derive two types of SDT model. Multiple-item template (MIT) models simulate display classification based on the evaluation of similarity values for independently cued feature values during dual-target search. We assume that the observer reports target-absent if none of the comparisons exceed a response criterion D,T). Conditional probabilities for hits and false alarms are obtained as 1-P(target-absent), depending on whether the target is present or absent in the display.In Eq. \u03bb and 18 \u03bc parameters . However, the experimental design yields only 12 observations for each subject . To derive useful and testable models, we therefore impose restrictions on the model parameters: First, we note that model predictions do not change if the same constant value is added to all parameters appearing together in a product term  = 0 . Target discriminability is modelled as the difference between the means of the distributions for the target and those for similar and dissimilar distractors. For similar distractors, d'S = \u03bc-\u03bc. For dissimilar distractors, d'D = \u03bc-\u03bc. We then distinguish between noise- and capacity-limited search. In the former, we assume that d\u2019 is independent of set size and search type, i.e., d\u2019 = d\u2019(C). As a shorthand, we set d\u2019(C=s) = d\u2019S and d\u2019(C=d) = d\u2019D. For capacity-limited models, we assume that d\u2019 scales with the inverse root of the total number of comparisons in each search: with d\u2019(C=t)=0, this can be written as d\u2019 = d\u2019S/\u221a(D*T) with d\u2019S =d\u2019. This parameterisation produces negative d\u2019 values for distractors that are differentiated from the target distribution on the basis of their dissimilarity from the cue, while scaling d\u2019 by 1/\u221a(D*T) conforms to the decline in discriminability predicted by the SDT sample-size model of search  = \u03bb(D*T), as the number of comparisons is the product of set size and cued orientations. The various \u03bb values are denoted \u03bb1, \u03bb2, \u03bb4, \u03bb8. Equation Applying Eq. as there is one cue-target comparison (CL-TL), three comparisons with similar distractors (CL-DL & CR-DR * 2) and four comparisons with dissimilar distractors .\u03bb. To represent the qualitative distinction between cues during the comparison process, SIT derivations contain separate terms to compute similarity values for objects depending on which template is active during search. For example, the estimated hit rate for the noise-limited SIT model on a dual-target search with a set size of 4 is given byIn contrast to MIT models, single-item template (SIT) models simulate search guided by a single attentional template. On a dual-target search, target detection is based on pairwise comparisons between the active attentional template and the objects in the display. We assume that the observer reports target absent if these comparisons fall below a response criterion d\u2019 is independent of set size, i.e., d\u2019 = d\u2019(C). For the capacity-limited model, d\u2019 scales with the inverse root of the number of objects in the display, because the number of active attentional templates is fixed at 1. With d\u2019(C=t)=0, this can be written as d\u2019 = d\u2019S/\u221aD with d\u2019S =d\u2019. Similarly, we set \u03bb = \u03bb(D) to model decision-noise and changes in threshold as a function of the number of comparisons between one attentional template and objects in the display. The various \u03bb values are denoted \u03bb1, \u03bb2, \u03bb4.In this equation, the observer randomly selects one of the cues and performs a single-target search based on the selected (active) attentional template. If the selected template matches the target in the display, performance will be equivalent to a single-target search. If the selected template matches the target that does not appear, hits are highly unlikely, because the cue-target comparison will yield a low similarity value. Accuracy across dual-target searches is predicted to be the average of the two terms. As for MIT models, we also distinguish noise- and capacity-limited derivations of SIT search. For the former, we assume d\u2019 and three or four \u03bb values) producing 5 or 6 error degrees of freedom. Fitting was carried out using maximum likelihood estimation and goodness of fit was assessed using a parametric bootstrap technique for Pearson\u2019s \u03c72 statistic. To do this, SDT models were fitted to each observer\u2019s data to compute the observed \u03c72 statistic. Parameter estimates for the fitted model were then used to simulate observations over K repetitions of the experiment (we used K = 500). By re-fitting and computing the \u03c72 statistic for each repetition, the \u03c72 distribution that would derive under the fitted model was estimated. Comparing the observed \u03c72 statistic against this \u03c72 distribution yielded the probability  that the fitted model generates data that are at least as extreme as those observed. The larger this probability, the \u2018more typical\u2019 the observed data are under the fitted model, and the stronger the evidence for its plausibility. As an additional, more intuitive measure of fit, we also calculated the mean absolute difference between corresponding observed and estimated probabilities. For brevity, we report mean group estimates in the text. Model estimates for individuals are reported in the Electronic Supplementary Material  at a set size of one.t(10) = 1.31, p > 0.20, Cohen\u2019s d = 0.34), and the remaining analyses collapse responses across both targets during search. Table F = 144.80, p < 0.001 , \u03b7p2 = .94, set size, F = 138.80, p < 0.001, \u03b7p2 = .93, and a significant Search Type by Set Size interaction, F = 4.97, p = 0.018, \u03b7p2 = 0.32. Two-template SDT models predict a reciprocal relationship between search accuracy and the number of comparisons required to classify the display. Planned contrasts to compare single- and dual-target searches across equivalent set sizes revealed non-significant differences at two, t(10) = .14, p = 0.89, d = 0.04, and four comparisons, t(10) = .67, p = 0.52, Cohen\u2019s d = 0.21, respectively. These data provide initial evidence that accuracy is related to the number of comparisons required to classify the display rather than qualitatively different strategies of attentional control on single- and dual-target searches.Accuracy for leftward and rightward leaning targets did not differ significantly  and response bias (\u03bb) across equivalent set sizes, as well as statistical comparisons for the four models. All reveal a monotonic increase in \u03bb as a function of set size. Estimates of d\u2019D were smaller than those for d\u2019S for the both SIT models and the MIT, noise-limited model, reversing the expected pattern of discriminability for targets among similar and dissimilar distractors. Allowing d\u2019s to scale with set size produced less variable \u03bb estimates, and the expected relationship between d\u2019S, and d\u2019 D for the MIT model only. AIC values were also smaller for the MIT than SIT models, with the smallest value obtained under the MIT, capacity-limited model \u2013 indicating a better fit between the observed and predicted hits and false alarms when accuracy was inversely scaled by the product of set size and the number of cued orientations. This group-level advantage was replicated at the individual level, where AIC values were smallest and goodness-of-fit indices largest for the MIT, capacity-limited model for 10/11 observers. The mean absolute difference between observed and estimated data was also smaller for the MIT, capacity- (0.03) than the MIT, noise-limited (0.05), and SIT, capacity- (0.07) and noise-limited (0.06) models ). This interpretation is consistent with capacity-limited decision processes based on the concurrent evaluation of similarity distributions for independently cued targets.SDT models of single-target search have been successfully used to characterise the relationships between decision-noise, discriminability and set size for different stimuli . All reported normal or normal-to-corrected visual acuity.Twelve observers were recruited to the study: Two were male and age ranged from 18 to 52 years . The display resolution was 1,280 \u00d7 1,024 pixels and the frame rate 100 Hz. Stimulus presentation and data collection were controlled using custom-built software in MATLAB  with Psychophysics toolbox extensions  Landholt\u2019s Cs presented on a black background . Cs subtended 5.0\u00b0 \u00d7 5.0\u00b0 at equally spaced locations on the circumference of a virtual circle with a radius of 7.0\u00b0. In contrast to Experiment Displays contained four red  and stimulus type . On each block, Target-Left and Target-Right orientations were sampled from 90\u00b0 and 270\u00b0 \u00b1 15\u00b0 to 30\u00b0, respectively. Distractor orientations were assigned as Target-Left and -Right \u00b1 25\u00b0. Target and distractor orientations were fixed and the order of presentation for each target and search type were randomly assigned within each block.C-shape at the orientation assigned to Target-Left or Target-Right and one annulus. On dual-target searches the cue contained two C-shapes at the orientations assigned to Target-Left and Target-Right. Single- and dual-target cues were presented for 500 ms and 1,000 ms, respectively, before being replaced by a fixation cross for 1,000 ms. Search displays followed and always contained four objects \u2013 a cued target and one similar and two dissimilar distractors \u2013 which were randomly assigned to the four possible locations. Observers were instructed to fixate the object that matched a cue, and responses were measured using a box criterion to record the first fixation falling within the 5.0\u00b0 \u00d7 5.0\u00b0 area surrounding each C-shape in the display. This method excludes saccades falling outside stimulus locations but produces results similar to the nearest endpoint criteria , observers were prompted to press a key to begin each block of trials.Observers completed a short practice  followed by four blocks of 60 trials in a single experimental session. Before each block, a 5-point calibration sequence was performed to ensure fixations to each i = 1 to 2) with those in the display (j = 1 to 4) and fixates the comparison that produces the maximum similarity sij to select the most likely target. The probability of the cue-object comparison  to yield maximum similarity is given byThe observer\u2019s task on each trial is to indicate which of four stimuli match the cue by fixating the target. Our statistical description of this task uses the SDT framework derived for Experiment p,D,T) denotes the probability density associated with P,D,T). The equation can be interpreted as follows: The product term in the integrand describes the probability that all comparisons different from  have results less than y. Weighing this value with the probability density for obtaining response y in the  comparison and integrating over all possible values of y yields the total probability for selecting comparison .In Eq. D fixed to 4 and setting \u03bc = 0 as in Experiment s) and dissimilar (d) distractors on single- (ST) and dual-target (DT) searches; d\u2019(sST), d\u2019(dST), d\u2019(sDT) and d\u2019(dDT). For each observer, there are four observed quantities, i.e., the probabilities for selecting the target and similar distractor on single- and dual-target searches, respectively (the probability for choosing the dissimilar distractor is fixed because of P(t)+P(s)+2P(d) = 1). Without any further restrictions on the d\u2019 parameters, the model is fully identified and would reproduce the observations perfectly. However, in analogy to Experiment d\u2019(sST) = d\u2019(sDT) = d\u2019S and d\u2019(dST) = d\u2019(dDT) = d\u2019D. We also compute estimates for a capacity-limited MIT model in which d\u2019 scales with the number of comparisons required to search for one or two cued-targets  = d\u2019S, d\u2019(sDT) = d\u2019S/\u221a2 and d\u2019(dST) = d\u2019(dDT) = d\u2019D). As set size is fixed across search types in this experiment, scaling d\u2019s by \u221a2 models a capacity limit that is specific to the MIT model when VSTM resources are distributed across independent attentional templates during search. All three models have two free parameters and 2 error degrees of freedom at the subject level.With i,j) but only the corresponding display object j. Therefore, the statistical model has to provide expressions for P(j) rather than P. This does not cause any complications for single-target searches, as there is only one cue i=1 and P(j) = P. For dual-target searches in the MIT model, saccades to object j could be based on the comparison for either cue, i.e.,  or  so that the corresponding probabilities have to be added: P(j) = P+P. For the SIT model, the overall probability of fixating the target in a DT search is given byThe subject does not directly report the chosen comparison . For MIT models, the overall probability of selecting the target object in the noise-limited model is given byThis equation is interpreted as follows. On a dual-target search, the participant performs one target comparison, three similar-distractor comparisons and four dissimilar-distractor comparisons. The first integral describes the probability that the subject selects the comparison between the target cue and target object. The second pertains to choosing the comparison between the cued target that is not present and the target object, which is considered a dissimilar-distractor comparison . Models are again fitted using maximum-likelihood estimation. For the computation of integrals, we make use of the fact that \u03c6 is a normal distribution and apply Gauss-Hermite quadrature . Accuracy for Target-Left and Target-Right were not significantly different, t(11) = 0.07, p > 0.95, Cohen\u2019s d = 0.019, and the following analyses collapse responses across both targets. Table t(11) = 16.61, p < 0.001, Cohen\u2019s d = 4.80, and increase in fixations to dissimilar distractors, t(11) = 12.32, p < 0.001, Cohen\u2019s d = 3.56, on dual- compared to single-target searches. The proportion of fixations to similar distractors for each type of search was not significantly different, t(11) = 0.52, p > 0.05, Cohen\u2019s d = 0.15.Trials in which fixations to a display object were recorded in less than 100 ms or longer than 3 standard deviations from the mean of single- and dual-target searches, respectively, were excluded from further analyses  = 3.79, p = 0.038, \u03b7p2 = .26, and a significant Search by Object type interaction, F = 8.44, p = 0.002, \u03b7p2 = .43. The main effect of search did not reach statistical significance, F = 4.57, p > 0.05, \u03b7p2 = .29, Post hoc tests revealed median saccadic latencies to dissimilar distractors were significantly faster on single- than dual-target searches , while differences to targets  and similar distractors  were not statistically significant.Our focus in this study was to investigate changes in the accuracy of saccadic targeting during single- and dual-target searches. In Experiment Figure The results of Experiment d\u2019 is independent of the number of comparisons required to localise the target. Group and individual comparisons also reveal better fit indices for the MIT, capacity-limited than the SIT, noise-limited model, supporting saccadic targeting based on separate similarity distributions for each cue. As with Experiment Figure The current study was designed to investigate the nature of the dual-target cost on perceptual decisions and saccadic targeting during covert and overt search. To do this, we applied SIT and MIT SDT models to predict observers\u2019 accuracy when comparisons between visual input and VSTM are limited to (1) a single-item attentional template or (2) multiple-item templates for independently cued targets during dual-target search. In addition, we compared observers\u2019 accuracy to noise- and capacity-limited derivations for both models of attentional control. Each assumes search entails the comparison of noisy internal representations of visual input with one or two cued-orientations. Noise-limited derivations model the dual-target cost as an increase in stochastic noise when the number of comparisons doubles on dual- compared to single-target searches. Capacity-limited derivations apply an inverse square-root relationship to model an additional dependency between discriminability and the number of comparisons during search"}
+{"text": "Namely, every clause must contain at least two satisfied literals. Because of its robustness, super solutions are concerned in combinatorial optimization problems and decision problems. In this paper, we investigate the existence conditions of the -super solution of  Then the solution is an -super solution. For example, the solution In combinatorial optimization problems and decision problems, the robustness of solutions is a valuable property. A robust solution is not sensitive to small changes in dynamic and uncertain environments, and guarantees the existence of a small set of repairs when the future changes in a small way. R. Weigel and C. Bliek in  introduca,b)-super solution of a CNF formula with special structure is undoubtedly of realistic significance. Therefore, we focus on some special k,s)-SAT has a SAT-UNSAT transition phenomenon and investigate the characteristics of the transition phenomenon.Encoding into a CNF formula is a common way to solve a practical problem. These CNF formulas often have some regular structures. A -super solution is a generalization of Supermodels in SAT problems. Some algorithms of finding super solutions were presented in [An -SAT where each clause has exactly k distinct literals. Zhang P in [k-SAT is in P for Specially, a -super solution is a satisfying assignment such that if any one variable is flipped to the opposite value, the new assignment is still a satisfying assignment. In other words, a -super solution of a CNF formula must satisfy at least two liters of every clause. The decision problem whether a CNF formulas has a -super solution is denoted as -SAT. -ang P in  proved thou G in  obtainedk-SAT is NP-complete. It implies that for k-SAT can not be solved in polynomial time. What happens if the number of occurrences of each variable is limited? So we expand -k-SAT to -d-regular d-regular k distinct literals per clause and at most s occurrences of each variable. A regular -CNF formula is a k-CNF formula, in which each variable occurs exactly in s clauses. A d-regular d. The NP-completeness of the special SAT problems worth further study.-3-SAT problem is in P. This shows that there is a polynomial time algorithm to decide whether a 3-CNF formula has a -super solution. For Kratochv\u00edl in  pointed (i) for (ii) for s such that all shown in . In [12,shown in ,14,15, ik-SAT to -In this study, we give a polynomial time reduction that transforms (i) every (ii) -That is to say, for x or a negated propositional variable x is called a positive literal, and C is a disjunction of literals, F is a conjunction of clauses, F, and F. x in F.A literal is a propositional variable F, if F but their variable sets are disjoint. We divide variables into forced variables or unforced variables. A forced variable is a variable forced a same value by all satisfying assignments of a formula.If the formulas F is denoted by d-Hamming neighbourhood F is a satisfying assignment such that for any A satisfying assignment is also called a solution. The set of solutions of a CNF formula Definition\u00a01.A CNF formula is called a regular Definition\u00a02.For each Definition\u00a03.\u03a8 is a forced-A -CNF formula (i) there exist two variables \u03a8 has a -super solution and for any -super solution \u03c4 of \u03a8, it holds that (ii) Definition\u00a04.The projection Lemma\u00a01.An assignment is a -super solution of F if and only if it satisfies .An assLemma\u00a02.If .If k\u22653Lemma\u00a03.The critical function .The crLemma\u00a04.An instance of SAT is satisfiable if:.An ins(i) all of its clauses contain more than one variable, and(ii) each variable appears exactly once complemented and once uncomplemented.Lemma\u00a05.If the representation matrix of a formula F isthen the formula is satisfiable and every satisfying assignment forces all variables to a same value.ith variable occurs positively in the jth clause; if ith variable occurs negatively in the jth clause; if F expresses a cyclic of implicationHere, if an element A -super solution has certain robustness, but some CNF formula with special structures may not have a -super solution.Theorem\u00a01.Every regular -CNF Formula without pure literals does not have a -super solution.Proof.\u00a0F is a regular -CNF without pure literals, then each clause has exactly 3 distinct literals and each variable occurs exactly 2 times (one negative occurrence and another positive occurrence). Suppose, F has F. However, a -super solution must satisfy at least two literals of every clause. That is to say, a -super solution must satisfy at least F. Clearly, there is not a -super solution. Therefore, no regular -CNF Formula without pure literals has a -super solution.\u2003\u25a1If a CNF formula By bounding the difference between positive and negative occurrences of every variable, we find other CNF formulas without a -super solution.Corollary\u00a01.For Proof.\u00a0F is a 1-regular s times, and the absolute value of the difference between positive and negative occurrences of each variable is at most 1. Suppose F has F, but every -super solution must satisfy at least F. For Let F. Suppose F has F . Because every -super solution must satisfy at least F, only an assignment F. In other words, if F does not have a -super solution. That is, if the formula has a -super solution, the -super solution must be Now we consider an arbitrary 1-regular -CNF formula Moreover, we also find some Theorem\u00a02.Every regular Proof.\u00a0m clauses. By definition, each clause has exactly 4 distinct literals, and each variable occurs exactly in 2 clauses (one negative occurrence and another positive occurrence). We divide each clauses Suppose iable in . SupposeTheorem 2 can be considered as an extension of Hall\u2019s Marriage Theorem. Suppose we have a finite set of single men and women. If each man is attracted by two women and each woman is attracted by four man, then there must be a way that each woman could be married with two men at the same time.Using Lemma 4, it is easy to obtain the following corollaries by using the proof method of Theorem 2.Corollary\u00a02.For Corollary\u00a03.A CNF formula must have a -super solution if:(i) each clause has at least 4 distinct variables and(ii) each variable occurs exactly in two clauses(one negative occurrence and another positive occurrence).For the formula in Corollary 3, all clauses may not have the same number of variables.Theorem\u00a03.All -CNF formulas and -CNF formulas must have a -super solution.Proof.\u00a0Suppose 8)\u226429 in , all -CNF formulas must have a -super solution by 9)\u226451 in .\u2003\u25a1In , it has In this section we study in what conditions -Theorem\u00a04.For Proof.\u00a0We will present a polynomial time reduction method from -super solution of the formula f.Step 2 Let f with the variables f being renamed as Step 3 We construct the formula s clauses. So Obviously, every clause of It is supposed that It is supposed that For The critical function Corollary\u00a04.If Proof.\u00a0The statement follows directly from Lemma 2 and Theorem 4.\u2003\u25a1By Hall\u2019s Marriage Theorem, -CNF and -CNF are satisfiable. But --SAT and --SAT are NP-complete because -SAT and -SAT are NP-complete.Next, we make some modifications of the reduction method in the proof of Theorem 4. We introduce a sufficient number of new variables, add some new clauses to make up the gap of the occurrence number of every variable, and guarantee that every new clause have at least a positive occurrence of two new variables -super solution). Because Corollary\u00a05.If Here, -regular -super solution have a -super solution. First we flip a unsatisfied literal of any one clause with only one satisfied literal. If the formula still does not have a -super solution, then we flip a unsatisfied literal of other clause with only one satisfied literal, until the formula has a -super solution. When the formula has a -super solution, the flipped literal is a key-literal.It is supposed that a  can make c and only two literals of the flipped clause. This also indicates that all -super solutions satisfy the literal y -super solution. There are two cases to consider.It is supposed that a -super solution. Lemma 6 entails that we can construct a forced-k-SAT to an instance of --(s)-SAT exists, then Z occurs in three clauses and every variable of X occurs in two clauses. Obviously, the formula Using Corollary 2, if n cyclic of implication. That is, if It is assumed that an assignment It is assumed that k-SAT is NP-complete, - every ((ii) --super satisfiability of (k. Besides, for larger values of k, the upper and lower bounds of Although we obtain some results about"}
+{"text": "This is a comment on \u201cManifestations of Sasang Typology according to Common Chronic Diseases in Koreans\u201d recently published by Hong et al.  that exaAs for the SPQ measuring biopsychological characteristics of Yin-Yang personality traits, the SPQ and its subscale scores of DM, hypertension, FD, and MDD were correctly illustrated, but their implications were not discussed in the context of recently published reports , 5. The The SPQ-E score of the FD group was significantly higher than that of the hypertension and adenomyosis groups, and the MDD group was similar to the FD group . A persoAs for the SDFI measuring good digestive function and appetite, the article of Hong et al.  made crir\u2009=\u2009\u22120.585) and Functional Dyspepsia-Related Quality of Life (r\u2009=\u2009\u22120.433), while the SDFI-E  has a positive correlation with Dutch Eating Behavior Questionnaire (r\u2009=\u20090.481) [r\u2009=\u20090.299) and SDFI-D (r\u2009=\u20090.310) scores [The operational definition of SDFI-D is a measure of good and hyperactivated digestive function, and a person with high SDFI-D should have a high BMI , 6\u20138. A  r\u2009=\u2009\u22120.43, while In the article by Hong et al. , the BMIFrom this perspective, the high score of SDFI-D would be a typical clinical feature of metabolic disease showing DM, hypertension, and obesity (high BMI) distinguished from other chronic diseases. The FD patients with low SDFI-D and high SPQ-E scores might be recognized as bad or hypoactive digestive function along with psychopathological vulnerability in traditional Korean medicine.The SDFI-A score of MDD group was significantly lower than that of DM, hypertension, FD, and adenomyosis groups in Hong's study . ConsideAs a conclusion, with consideration of the latest clinical studies \u20137, the c"}
+{"text": "The generator matrices of polar codes and Reed\u2013Muller codes are submatrices of the Kronecker product of a lower-triangular binary square matrix. For polar codes, the submatrix is generated by selecting rows according to their Bhattacharyya parameter, which is related to the error probability of sequential decoding. For Reed\u2013Muller codes, the submatrix is generated by selecting rows according to their Hamming weight. In this work, we investigate the properties of the index sets selecting those rows, in the limit as the blocklength tends to infinity. We compute the Lebesgue measure and the Hausdorff dimension of these sets. We furthermore show that these sets are finely structured and self-similar in a well-defined sense, i.e., they have properties that are common to fractals. The fractal dimension of In his book on fractal geometry, Falconer characterizes a set operties   still eludes us. Nevertheless, our results may apply in areas beyond channel coding: Ar\u0131kan\u2019s polarization technique was used to polarize R\u00e9nyi information dimension  and to cSince we consider the case Lemma\u00a01Let  W20y2|u1:=12\u2211W20y2|u1: channelW21=2I(W)  (ProposiLemma\u00a02 (Bounds on the Bhattacharyya Parameter).with equality in Proof.\u00a0W is a BEC [The equality and inequality in  follow f\u22641, from   the cardinality of the output alphabet increases exponentially in If we stop the polarization procedure at a finite blocklength ly in 2n  (Chapterly in 2n  (p. 36).ly in 2n  .A channel  degraded w.r.t. the channel W  channels remains upgraded (degraded) during polarization:Lemma\u00a03Suppose that ( (Lemma 4Lemma\u00a04( (p. 9) &Proof.\u00a0By choosingls, take  .Let Let W is nontrivial, i.e., that If Proposition\u00a02 (Denseness).Proof.\u00a0See f is not injective. It is not obvious, however, that the intersection exhausts the set on which f is non-injective. A consequence of this proposition is that there is no interval that contains only good channels. This has implications for code construction techniques. Indeed, the authors of [It is not really surprising that thors of ,19 suggeProposition\u00a03 (Symmetry).There exists a function \u03d1, defined for almost all values in Proof.\u00a0See alignment of the sets W and Proposition 3 has two implications. The first implication concerns the negative . Indeed,arameter .The second implication is that, at least for BECs, the sets recurring, i.e., there is a length-k sequence z close to zero and z close to one, the operation x, It is possible to define Example\u00a02.Let Now suppose that W is a BEC with Bhattacharyya parameter Proposition 4 (Lebesgue Measure & Hausdorff Dimension).Proof.\u00a0See W. The fact that W. A positive Lebesgue measure and a Hausdorff dimension equal to one are not indicators of fractality.Loosely speaking, the Lebesgue measure of quasi self-similar. Along the same lines, the quasi self-similarity of The last fractal property we consider is self-similarity. As Falconer notes  (p. xxviProposition\u00a05 (Self-Similarity).Let  quasi self-similar in the sense that, for all n and all k, If W is symmetric, Proof.\u00a0See In other words, at least for a symmetric channel, self see . The selExample\u00a03.We want to determine whether r, length-Hamming weight of i-th row of r, length-An order-dexed by (20)F={iTo analyze the effect of doubling the block length, note thati-th row be indexed by Assume that we indicate the rows of his with  yieldswDefining n tends to infinity. An important ingredient in our proofs is the concept of normal numbers.In Definition\u00a03 .A number  simply normal to base 2.Let fractional Hamming weight larger than a given threshold.Loosely speaking, the set of heavy codewords corresponds to those rows of Example\u00a05.Proposition\u00a06 (Denseness).For all n to be even and set n, and one needs to depart from intuition based on these finite-blocklength considerations.Similarly as for polar codes, also Reed\u2013Muller codes are such that no interval is contained in either Proof.\u00a0See Proposition 7 (Lebesgue Measure & Hausdorff Dimension).The Hausdorff dimension satisfieswhere Proof.\u00a0See W. In contrast, the set W. Rather, Proposition 7 suggests that the order parameter phase transition for the rate of Reed\u2013Muller codes: If Loosely speaking, the Lebesgue measure of Let us briefly consider the case The sets cale cf. . We nextal codes  (ProposiProposition\u00a08 (Self-Similarity).Let  quasi self-similar in the sense that, for all n and all k, Proof.\u00a0See The set has a fine structure, i.e., there is detail on arbitrarily small scales;It does not admit a description in traditional geometrical language, neither locally nor globally; it is irregular in some sense;It has some form of self-similarity, at least approximate or statistical;The fractal dimension of the set exceeds its topological dimension.That Kronecker product-based codes possess fractal properties has long been suspected. The present manuscript contains several results that back this suspicion with solid mathematical analyses. Specifically, we assumed that the blocklength tends to infinity and investigated the properties of the set operties  (p. xxviIndeed, the sets R. In other words, while fractional order of the code, R and that, thus, its Hausdorff dimension equals one. An appropriate definition of R, length-One reviewer pointed out that our definition of q is prime. One can show that this matrix is polarizing as long as it is not upper-triangular [\u2113-ary expansion of real numbers in q-ary Reed\u2013Muller codes, e.g., [Another obvious extension of our work are non-binary polar and Reed\u2013Muller codes. For example, consider an iangular  (Theorems, e.g., ,24."}
+{"text": "Scientific Reports 10.1038/s41598-019-41202-4, published online 20 March 2019Correction to: The original PDF version of this Article contained a typographical error in the publication date \u201820th March 2019\u2019 which was incorrectly given as \u201818th March 2019\u2019. This has now been corrected in the PDF version of the Article. The HTML version was correct at the time of publication."}
+{"text": "Nature Communications 10.1038/s41467-020-17611-9, published online 30 July 2020.Correction to: The original version of this Article contained an error in the Abstract, in which the word \u2018erosive\u2019 was misspelled \u2018eros0ive\u2019. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "R \u22481.In a comment on our recent paper , the comR \u2248 1. We do not do that. Throughout the paper and its extensive supporting information, we emphasize that the derivation of the estimates for the critical connectivity R \u2248 1, or, equivalently, D \u2248 Dc.We are surprised to see that the commentators in ref. R \u2248 1 or D \u2248 Dc are not sharp, and, as we state explicitly in ref. R \u2248 1. Within the context of the entire paper (1) and its supporting information, this is completely clear. It seems that the commentators in ref. The critical values A in ref. A in ref. In addition, the analysis of close-to-critical spreading on Erd\u0151s-R\u00e9nyi (ER) networks in ref. It is fortunate, however, that this comment gives us the opportunity to cite a work that noted the possibility of linear spreading of diseases on SW networks before (figure 5 in ref."}
+{"text": "Here, the zero-temperature phase behavior of bosonic particles living on the nodes of a regular spherical mesh (\u201cPlatonic mesh\u201d) and interacting through an extended Bose-Hubbard Hamiltonian has been studied. Only the hard-core version of the model for two instances of Platonic mesh is considered here. Using the mean-field decoupling approximation, it is shown that the system may exist in various ground states, which can be regarded as analogs of gas, solid, supersolid, and superfluid. For one mesh, by comparing the theoretical results with the outcome of numerical diagonalization, I manage to uncover the signatures of diagonal and off-diagonal spatial orders in a finite quantum system. Gases of ultracold bosonic atoms loaded in an optical lattice provide the unique opportunity to study quantum many-body effects under controlled conditions ,2. To a In a system at zero temperature . Experig., Ref.  or dysprg., Ref. ) and molt, in absolute terms) to the on-site interaction (U) is reduced. The overall number density of particles is controlled via a chemical-potential parameter t and U, the lattice becomes increasingly filled with particles, but this can only occur outside the Mott regions since the insulator phase is incompressible [V is introduced between nearest-neighbor atoms (\u201cextended BH model\u201d), new phases may arise, in primis a supersolid phase [The usual BH model predicts a ressible . The BH ressible ,10,11, pressible ,14,15,16ressible ,18, to nid phase ,25,26,27\u2192\u221e limit ,30,31,32I hereafter present the results of yet another investigation of the extended BH model, now choosing a finite graph as hosting space for bosons. Even though clearcut phase transitions  cannot occur in a few-particle system, a convenient choice of boundary conditions may alleviate the difference with an infinite system, making the study of a finite quantum system valuable anyway. A practical solution is to use spherical boundary conditions (SBCs), which have often been exploited in the past to discourage long-range triangular ordering at high density ,36,37,38The plan of this paper is the following. After introducing the models in i can only be 0 or 1 . In theThe rationale behind the choice of a cubic mesh is now clear: by introducing a repulsion between occupied NN sites, we promote the occurrence of a Platonic \u201ccrystal\u201d, i.e., the regular tetrahedron , the total energy (E), and the order parameters for tetrahedral  are considered below.H describes a system of bosons on a spherical mesh of M sites, U term in  a density wave at low t, as well as a supersolid phase at the boundary between the insulator and superfluid phases. These features are also present in the hard-core limit, as reported, e.g., in Refs. [In the BH model on a standard lattice, at in Refs. ,32.MF theory is the method of choice when a new many-body problem is attacked; it has been frequently applied for continuous quantum systems as well, as an effective means to identify the ground states and quantum transitions between them . i, respectively. For hard-core bosons, we readily obtain i-th site. For a bipartite mesh, sites are either of type A or B, hence the unknown parameters are four, namely In the decoupling approximation, the two-site terms in the Hamiltonian  are lineHMF withHMF=\u2212t\u2211iFA has three neighbors, all belonging to grid B, and vice versa. Hence,A (B) for operators relative to a single A (B) site, the MF Hamiltonian reads:B \u201ccrystal\u201d), A \u201ccrystal\u201d), and For the QCT model, the mesh is bipartite and formed by two tetrahedral sub-meshes with four points each. A point of grid an reads:HMF=E0\u221212H for A and B; hence, our search can be restricted to homogeneous (superfluid) solutions: E isSuperfluid and supersolid \u201cphases\u201d have non-zero, possibly distinct, complex values of rrive at(\u03bb\u2212b)2(\u03bb\u2212root of (E=b\u2212(a\u2212b)oot of (1E=b\u2212(a\u2212b) to give\u03c1=\u03bc+3t3V+By comparing the grand potentials of all the \u201cphases\u201d, we arrive at the ground-state diagram in A, 8 sites) and a co-cube . We have:The decoupling approximation for the QDC model works similarly as for the QCT model. Again, the starting point is Equation  and the en reads:HMF=E0\u221224Moving to phases with o be see :(31)E=12Equation ).E satisfy the following linear system: Using he state  describia priori assuming them to be equal in pairs  and diagonalizing the ensuing matrix. An extensive mapping of a few quantum averages enables us to clarify the nature of the \u201cphases\u201d present.Let us again reconsider the QCT model at A or B, they belong to. Then, I compute the average occupancies of A and B sites . In A and a B site, with the only exception of A-B inversion are the same. I show in N operator, implying that the ground state (which is non-degenerate for N. Like in MF theory, the occupancy is zero below t, with no abrupt transition from \u201ccrystal\u201d to superfluid values.As far as the occupancies are concerned, exact diagonalization shows that they are always equal for an t and t lines; each jump discontinuity of Another difference with MF theory concerns the ground-state averages of Equation . In the t values in the range 0 to 0.5. In the MF curves, cusp singularities are associated with the crossing of first-order transition lines. We see that MF theory systematically overestimates exact values, the more so the larger t is.Finally, in I have worked out the zero-temperature phase diagram of two systems of hard-core bosons defined on the nodes of a regular spherical mesh. The interaction is of Bose\u2013Hubbard type, with a further repulsion between neighboring particles. Choosing a suitable mesh, bosons are pushed to form a Platonic \u201ccrystal\u201d in a range of chemical potentials. In the QCT model, the mesh is cubic and a tetrahedral \u201ccrystal\u201d is formed; in the QDC model, the mesh is dodecahedral and a cubic \u201ccrystal\u201d is formed instead.Using a mean-field approximation, I have obtained fully analytic results for the thermodynamic properties of the two models. In addition to a number of insulating phases, both systems also exhibit a superfluid ground state. In the QDC model, triple coexistence between two solids and the superfluid is superseded by the occurrence of a more stable supersolid phase. Clearly, while the predictions of mean-field theory are generally accurate for an infinite Bose\u2013Hubbard system, deviations will unavoidably be observed in a small system, where no true singularity can occur. However, discrepancies are probably less strong for bosons on a regular spherical mesh, which has equivalent sites and is devoid of natural boundaries.To check this expectation for the QCT model, I have diagonalized its Hamiltonian exactly, finding the ground state and a number of ground-state averages. Overall, the exact"}
+{"text": "Scientific Reports, 10.1038/s41598-020-71679-3, published online 09 September 2020Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cHumid\u201d was incorrectly given as \u201cHuman\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Information file."}
+{"text": "We read with interest the paper by Jun S.Y. et al.  dealing As survival rate is similarly low in patients with Crohn\u2019s disease-associated SBA and those with sporadic SBA ,5,6, it"}
+{"text": "This paper studies index coding with two senders. In this setup, source messages are distributed among the senders possibly with common messages. In addition, there are multiple receivers, with each receiver having some messages a priori, known as side-information, and requesting one unique message such that each message is requested by only one receiver. Index coding in this setup is called two-sender unicast index coding (TSUIC). The main goal is to find the shortest aggregate normalized codelength, which is expressed as the optimal broadcast rate. In this work, firstly, for a given TSUIC problem, we form three independent sub-problems each consisting of the only subset of the messages, based on whether the messages are available only in one of the senders or in both senders. Then, we express the optimal broadcast rate of the TSUIC problem as a function of the optimal broadcast rates of those independent sub-problems. In this way, we discover the structural characteristics of TSUIC. For the proofs of our results, we utilize confusion graphs and coding techniques used in single-sender index coding. To adapt the confusion graph technique in TSUIC, we introduce a new graph-coloring approach that is different from the normal graph coloring, which we call two-sender graph coloring, and propose a way of grouping the vertices to analyze the number of colors used. We further determine a class of TSUIC instances where a certain type of side-information can be removed without affecting their optimal broadcast rates. Finally, we generalize the results of a class of TSUIC problems to multiple senders. In this scenario, if the sender is informed about the side-information available at all receivers, then it can leverage that information whilst encoding to reduce the required number of broadcast transmissions, in comparison with a naive approach of transmitting all requested messages uncoded and separately. Such an encoding process is called index coding, and the resulting sequence of coded messages is known as an index code. Moreover, each receiver upon receiving the index code will be able to decode its required message by utilizing its side-information. The main aim of index coding is to find the optimal (shortest) codelength and the corresponding coding scheme. Index coding was introduced by Birk and Kol [Consider a communication scenario over a noiseless channel where a sender is required to broadcast messages to multiple receivers, each caching some messages requested by other receivers a priori. The messages cached at each receiver is known as its  and Kol ,2, and f and Kol ,11,12,13Macro-cell networks with caching helpers \u2014cellularcooperative data exchange \u2014peer-to-distributed storage\u2014storage networks where data are distributed over multiple storage devices/locations.Most existing works on index coding deal only with a single sender, capturing scenarios with centralized transmissions. However, many communication scenarios such as the following have messages distributed among multiple senders:In addition, each sender can be constrained to know only a subset of the total messages due to reasons such as limited storage, or error whilst receiving some messages over noisy channels, or server failure to deliver all messages. In this case, distributed transmissions are required, where multiple senders broadcast messages to the receivers. One metric to maximize the transmission efficiency in this scenario is to minimize the aggregate number of transmissions from all senders in such a way that all receivers\u2019 demands can be fulfilled. As this problem is more general than an index-coding problem with a single sender and is of practical interest , it is a useful research avenue to study index-coding problems with multiple senders, known as multi-sender index-coding problems.broadcast-rate formulation of the problems. In their work, they devised lower and upper bounds on the optimal broadcast rate by implementing a graph-theoretic approach. The results were established using information-flow graphs, which represent receivers\u2019 request, and message graphs, which represent senders\u2019 message setting. Furthermore, they showed problem instances for which the upper and lower bounds coincide. A class of such instances is where no two senders have messages in common.The multi-sender index-coding problem was first studied by Ong et al. . They counicast message setting, meaning each message is requested by only one receiver, each receiver requests only one message, and each receiver knows a subset of messages requested by other receivers a priori. Based on graph-theoretic approaches, they established upper bounds on the optimal broadcast rate. In particular, they focused on the two-sender case, called two-sender unicast index coding (TSUIC). They extended existing single-sender index-coding schemes, namely the cycle-cover scheme [In another work, Thapa et al.  considerr scheme ,19, the r scheme  and the r scheme  to the cSadeghi et al.  considerdecentralized data shuffling problems in which the receivers/workers can communicate with one another via a shared link. The decentralized data shuffling phase with uncoded storage (which stores a subset of bits of the data set) is equivalent to a multi-sender index coding problem. For this problem, they proposed converse and achievable bounds that are to within a factor of 3/2 of one another. Moreover, the proposed schemes were shown to be optimal for some classes of the problem. Recently, Porter et al. [embedded index coding (EIC), in which each node acts as both sender and receiver. With the help of several results, they showed the relationship between single-sender index coding and EICs. Furthermore, they developed heuristics to solve EIC problems efficiently.In a recent work by Li et al. , a new rr et al.  introducconfusion graphs in index coding [Different approaches have been attempted to solve the multi-sender index-coding problems. However, the problems are more difficult and computationally complex than their single-sender counterparts, and we know very little about the characteristics of the problems. This paper studies the broadcast-rate formulation of TSUIC problems by implementing a graph-theoretic approach. More precisely, in the same spirit of studying structural properties of index-coding capacity in the single-sender case by Arbabjolfaei et al. , we examx coding  along wiProposing a new coloring concept for confusion graphs in TSUIC, called two-sender graph coloring . However, for TSUIC, as the two senders (encoders) contain some messages in common, the standard method of graph coloring of the confusion graph may not lead us to an index code. In this regard, we need a different kind of coloring function in TSUIC, and thus, in this paper, we propose a novel coloring technique to color the confusion graphs in TSUIC, and its optimization gives the optimal broadcast rate and optimal index code.Presenting a way of grouping the vertices of confusion graphs in TSUIC : By exploiting the symmetry of the confusion graph, we propose a way of grouping its vertices for analysis purposes mainly in its two-sender graph coloring. In particular, this grouping helps us to analyze the number of colors used in two-sender graph coloring of a confusion graph.Deriving the optimal broadcast rates of TSUIC problems as a function of the optimal broadcast rates of its sub-problems (Theorems 4\u20138): We divide a TSUIC problem into three independent sub-problems based on the requested messages by receivers, specifically whether the messages are present in only one of the senders or in both senders. Now in TSUIC, considering the interactions (defined by side-information available at the receivers) between these three independent sub-problems, we derive the optimal broadcast rate (in both asymptotic and non-asymptotic regimes in the message size) of the problem as a function of the optimal broadcast rates of its sub-problems. Moreover, we bound the optimal broadcast rate, and show that the bounds are tight for several classes of TSUIC instances (sometimes with conditions). Furthermore, we find a class of TSUIC instances where a TSUIC scheme can achieve the same optimal broadcast rate as the same instances when the two senders form a single sender having all messages.Characterizing a class of TSUIC instances where a certain type of side-information is not critical (Corollary 1): For a class of TSUIC instances, we prove that certain interactions between the three independent sub-problems can be removed without affecting the optimal broadcast rate (in the asymptotic regime). This means that those interactions are not critical.Generalizing the results of some classes of TSUIC problems to multiple senders : For some classes of TSUIC problems, we generalize the two-sender graph coloring of confusion graphs and the proposed grouping of their vertices. Then, we compute the optimal broadcast rates of those problems as a function of the optimal broadcast rates of their sub-problems.The contributions of this paper are summarized as follows:After posting the first draft of this paper  on ArxivN independent messages t binary bits. There are N receivers S, having all N messages In this paper, we consider unicast index coding. There are Definition\u00a01\u00a0(Two-sender\u00a0index\u00a0code).A two-sender index code ((i)\u00a0an encoding function for each sender (ii)\u00a0a decoding function for every receiver r, r receives sub-codewords from both senders without any noise, and decodes This means that each sender Now, we define the aggregate normalized codelength, which measures the performance of a code Definition\u00a02\u00a0.The broadcast rate of an index code (with a single sender or two senders) is the total number of transmitted bits  per received message bit. In TSUIC, it is denoted by  achievable for a UIC problem if there exists an index code of normalized length \u2113.For the rest of the paper, we refer to normalized codelength simply as codelength.Definition\u00a03\u00a0.The optimal broadcast rate for a given index-coding problem with t-bit messages is  SSUIC and  TSUIC. The optimal broadcast rate over all t is defined as \u2019s lemma .Remark\u00a01.With the  broadcast rate as a performance metric, we can treat SSUIC as a special case of TSUIC when An index-coding problem can be modeled by graphs, which are defined as follows:Definition\u00a04\u00a0(Directed\u00a0graphs\u00a0and\u00a0undirected\u00a0graphs).A directed graph is an ordered pair From now on in this paper, we call directed graphs simply digraphs, and undirected graphs simply graphs.N receivers, and the arc set i to vertex j if and only if receiver i has message j) in its side-information. Thus, in a side-information digraph, i in D. In this paper, for convenience, a receiver i is also referred to as a vertex i, and vice versa. We also use the compact form of representation of an instance of UIC problems as used by Arbabjolfaei et al. [The receivers\u2019 message setting of a UIC problem is represented by a side-information digraph i et al. , where aprivate messages and common messages defined as follows: Let D, without loss of generality, we define the following sub-digraphs induced by the following vertex subsets that partition D induced by vertices D such that In TSUIC, Definition\u00a05\u00a0(Constraint\u00a0due\u00a0to\u00a0the\u00a0two\u00a0senders).The constraint due to the two senders is the following: whilst encoding, any two private messages sender-constraint graph.In TSUIC, to reflect the senders\u2019 message setting, we introduce an undirected graph, denoted by D and t, and over all t, respectively. As a TSUIC problem is described by D, three sub-problems based on the type of messages are In a TSUIC problem, if there is no common message, i.e., roblems .For simplicity, an interaction between the sub-digraphs H, we get a total of 64 possible cases of the orientation of arcs among its vertices. As the vertices 1 and 2 of H can be swapped because we can interchange H. Now, depending upon the type of orientation of arcs among the vertices of H, we classify all unique cases into two categories: (i) CASE I\u2014Acyclic orientation , and (ii) CASE II\u2014with some cyclic orientation (22 cases). CASE II is further classified into smaller sub-cases II-A, II-B, II-C, and II-D. Refer to H is labeled D defines arcs between them (not within the sub-digraph), and the cases of interactions (acyclic or cyclic) are defined with respect to the orientation of the arcs between the sub-digraphs. In this paper, a fully-participated interaction and a partially-participated interaction between D are called a cyclic-fully-participated interaction and a cyclic-partially-participated interaction between the sub-digraphs, respectively, if and only if Considering the digraph D. Moreover, structural properties can be used to determine the criticality/non-criticality of arcs in TSUIC as in its SSUIC counterpart [For SSUIC, Arbabjolfaei and Kim   for an index-coding problem is represented by a graph called a confusion graph, defined as follows:For an index-coding problem modeled by a side-information digraph Definition\u00a06\u00a0(Confusion\u00a0graph).The confusion graph, denoted (i)\u00a0(ii)\u00a0Before proposing a notion of coloring for TSUIC, we first recall the standard definition of the graph coloring in the following:Definition\u00a07\u00a0(Graph\u00a0coloring\u00a0and\u00a0Chromatic\u00a0number).A proper graph coloring of a graph G is an onto function sets of independent vertices where all vertices belonging to one set are assigned with the same color in the graph coloring. Here, a set of independent vertices refers to a vertex set where any pair of vertices are not connected by an edge in independent vertex set. The tuples representing vertices within an independent vertex set are not confusable, and hence they can be coded into the same codeword. Assigning each independent vertex set  a unique codeword provides us a valid index code having D with t-bit messages can be obtained by using confusion graphs. This is stated in the following theorem.Consider coloring a confusion graph Theorem\u00a01. is used for a general case, and the remaining two indices . In ourIn the form of lemmas, we discuss two-sender graph coloring of In TSUIC, the two senders encode separately, so, in the aforementioned definition, we need to assign an ordered pair of colors for each vertex, where the first color is associated with Lemma\u00a01.For any two distinct vertices Proof.\u00a0Since In a similar reasoning as in the above proof (of Lemma 1), one can prove the following lemma:Lemma\u00a02.For any two distinct vertices, If Lemma\u00a03.For any two distinct vertices, If Lemma\u00a04.For any two vertices, t-bit messages, we have the following theorem:For a TSUIC problem with Theorem\u00a02.The optimal broadcast rate for a TSUIC problem with t-bit messages isProof.\u00a0t), we getFor lting in\u03b2t=, we get\u03b2t\u2264 p2\u2032 in \u2265lity in <We illustrate two-sender graph coloring of a confusion graph in TSUIC, and a mapping function that maps colors to codewords at each sender from the following example.Example\u00a01.Consider a TSUIC problem  1. The confusion graph  1 . Since any index code for D, but the converse is not always true, so we have the following:For any Lemma\u00a05\u00a0(A\u00a0simple\u00a0lower\u00a0bound).For any D and t-bit messages in the following lemma.In TSUIC, each sender Lemma\u00a06\u00a0(A\u00a0lower\u00a0bound).For any two-sender index-coding problem Proof.\u00a0For any two-sender index-coding problem +\u03b2t(D2) .\u03b2t(D2) \u2265\u25a1To compute the simple lower bound to the optimal broadcast rate of a given problem in TSUIC, we utilize the following SSUIC results by Arbabjolfaei and Kim \u00a0(ii)\u00a0D whose For a digraph II-A see , we haveTheorem\u00a04\u00a0(CASE\u00a0I).For any D having any interaction  between its sub-digraphs Proof.\u00a0f =\u03b2\u2265\u03b2In TSUIC, if we consider the sub-digraphs 3). From , 12) an anD1, D2aphs, so\u03b2\u2264\u03b2Example\u00a02.Consider a TSUIC problem of the following: Proposition\u00a01.For any D having a fully-participated interaction between its sub-digraphs Proof.\u00a0Refer to Definition\u00a09\u00a0(Vertex-transitive\u00a0graphs).An undirected graph G is vertex-transitive if for every pair Remark\u00a03.The proof of the Proposition 1 is based on the analysis of the confusion graph  TSUIC problem whose sub-problems interact with each other in some way, we can reduce the complexity arising during its analysis .For any D having any interaction  between its sub-digraphs Proof.\u00a0For convenience, let ition 1:\u03b2tNow, taking a limit sides in , we getRemark\u00a04.For any D having non-empty  SSUIC, we have  TSUIC, Corollary\u00a01.For any D having any interaction  between its sub-digraphs  TSUIC in the asymptotic regime in message size (considering infinitely long messages).Proof.\u00a0The proof follows from Theorems 4 and 5.\u2003\u25a1Theorem\u00a06\u00a0(CASE\u00a0II-B).For any D having a fully participated interaction between its sub-digraphs Proof.\u00a0Refer to Corollary\u00a02.For any D having a fully participated interaction between its sub-digraphs Proof.\u00a0The result follows from Theorems 3 and 6.\u2003\u25a1Remark\u00a05.In TSUIC, for any D having a fully participated interaction between its non-empty sub-digraphs  TSUIC scheme achieves Example\u00a03.Consider a TSUIC problem of the following: Theorem\u00a07\u00a0(CASE\u00a0II-C).For any D having a fully participated interaction between its sub-digraphs (i)\u00a0(ii)\u00a0(iii)\u00a0(iv)\u00a0Proof.\u00a0Refer to Case Proposition\u00a02\u00a0(CASE\u00a0II-C).For any D having a fully participated interaction between its sub-digraphs Proof.\u00a0D whose D where D with It follows from Theorem 7 that a 5), so\u03b2\u2265\u03b2)\u2264\u03b2(D3),\u03b2\u2264\u03b2a 5), so\u03b2\u2265\u03b2, we get\u03b2Corollary\u00a03.For any D having a fully participated interaction between its sub-digraphs Proof.\u00a0D, by applying Theorem 3, one can get For the given digraph Corollary\u00a04.For any D such that (i)\u00a0if (ii)\u00a0if (a)\u00a0if (b)\u00a0if Proof.\u00a0If Remark\u00a06.Let (i)\u00a0(ii)\u00a0Example\u00a04.Consider a TSUIC problem D of the following: Theorem\u00a08\u00a0(CASE\u00a0II-D).For any D having a fully participated interaction between its sub-digraphs (i)\u00a0(ii)\u00a0(iii)\u00a0(iv)\u00a0Proof.\u00a0Refer to Proposition\u00a03.For any D having a fully participated interaction between its sub-digraphs Proof.\u00a0It follows from Theorem 8 that 2), then\u03b2\u2264\u03b21), then\u03b2\u2264\u03b2). From \u2264\u03b2, we get\u03b2\u2265\u03b2Now, for UIC problems with more than two senders, we study some classes of interactions between the sub-digraphs of a digraph (representing the UIC problem) in the following sub-section.In this section, we illustrate how the method proposed in this paper can be generalized to scenarios with more than two senders.D, we have D associated with vertices of those requesting the private messages, and Let Observe that the extensions of Definition 5  between its sub-digraphs Remark\u00a07.Extending the other cases of TSUIC to MSUIC is a laborious task as it involves a construction of multi-dimensional blocks and sub-blocks in a confusion graph.D and its sub-digraphs u of D. Now, we make the following two observations in TSUIC:The role of side-information of the vertices in  TSUIC: It is proved in SSUIC that, if the interaction between D can be removed without affecting the optimal broadcast rate of D; in other words, those are non-critical arcs. In this paper, we have proved that this result is also true in TSUIC (by Theorem 5). Moreover, in TSUIC, we have proved that, for D, if the vertices in Non-critical arcs in SSUIC are not necessarily non-critical in TSUIC: We illustrate this with an example. Consider the TSUIC problem stated in Example 1 , there have been many important contributions made in the literature. In this paper, we solved TSUIC instances by expressing the optimal broadcast rates in terms of that of SSUIC. To this end, we introduced a two-sender graph coloring of confusion graphs in TSUIC, and propose a way of grouping the vertices of a confusion graph for analysis. Using these techniques, we derived optimal broadcast rates of TSUIC problems, both in the asymptotic and non-asymptotic regime, as a function of the optimal broadcast rates of their sub-problems. We have also presented a class of TSUIC instances where the interactions between the sub-problems of the problem are not critical. We illustrated that our proposed approach to TSUIC can be extended to some cases with multiple senders.Study of the critical edges in the TSUIC problems: It is observed that the non-critical arcs in SSUIC can be critical arcs in TSUIC. This requires further study.Study of a general distributed index coding: As our study is a step towards understanding multi-sender index coding, it is left as a future work to extend the approaches implemented and the results obtained in this paper to more general setups.Finding the optimal broadcast rates of TSUIC problems with cyclic-partially-participated interactions: The analysis of D with partially-participated interactions between its sub-digraphs Some open problems for future works are the following:"}
+{"text": "The family of all \u03c9-open sets of X which is finer than \u03c4 and this topology is denoted by \u03c9-open sets played a vital role in general topology research see, A in \u03b8-closure and the A is \u03b8-closed A is \u03b8-open \u03b8-closed  Since by f is weakly continuous. Since (b) Suppose to the contrary that Theorem 2.39Every faintly-continuous function is faintly continuous.ProofThe implication in Example 2.40f is faintly continuous but not faintly Consider the identity function We can summarize the results and examples above by means of the following diagram:S. Al Ghour, B. Irshidat: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.The authors declare no conflict of interest.No additional information is available for this paper."}
+{"text": "This is a novel version of de Finetti\u2019s problem of coherence checking for probabilistic assessments. We show how to reduce the coherence checking problem in relational Bayesian networks to a validity problem in first-order logic augmented with a transitive closure operator and how to combine this logic-based approach with faster, but incomplete algorithms.There are several formalisms that enhance Bayesian networks by including relations amongst individuals as modeling primitives. For instance, Probabilistic Relational Models (PRMs) use diagrams and relational databases to represent repetitive Bayesian networks, while Relational Bayesian Networks (RBNs) employ first-order probability formulas with the same purpose. We examine the  N independent biased coins, so that p for each one of them.\u00a0Then, the probability of a particular configuration of all coins is exactly n is the number of coherent as they are satisfied by a probability distribution\u00a0[Most statistical models are couched so as to guarantee that they specify a single probability measure. For instance, suppose we have xactly pn\u2212pN\u2212n, whribution\u00a0,3, as a ribution\u00a0,5 and geribution\u00a0,7,8.In this paper, we examine the coherence checking problem for probabilistic models that enhance Bayesian networks with relations and first-order formulas: more precisely, we introduce techniques that allow one to check whether a given relational Bayesian network, or a given probabilistic relational model is guaranteed to specify a probability distribution. Note that \u201cstandard\u201d Bayesian networks are, given some intuitive assumptions, guaranteed to be coherent\u00a0,10,11.\u00a0TX is a parent of node Y if there is an edge from X to Y. The\u00a0set of parents of node X is denoted To recap, a Bayesian network consists of a directed acyclic graph, where each node is a random variable, and a joint probability distribution over those variables, such that the distribution and the graph satisfy a Markov condition: each random variable is independent of its non-descendants given its parents.  Consider that now we have three people, (Scenario 2) It is also straightforward to expand our Bayesian network to accommodate n individuals (Scenario 3) Consider a slightly different situation with three people, where: (Scenario 4) Suppose we want to extend Scenario 3 to a town with n people. Without knowing which pairs are neighbors, there is no way we can predict in advance the structure of the resulting Bayesian network. However, we can reason about the possible networks: for instance, we know that each set of n people produces a\u00a0valid Bayesian network, without any cycles amongst random variables.X at a time, we deal with parameterized random variables [x in a domain; if we consider individuals a and b in a domain, we obtain random variables There are many other scenarios where probabilistic modeling must handle repetitive patterns such as the ones described in the previous examples, for instance in social network analysis or in processing data in the semantic web ,13,14. Tariables . We writPlates offer a popular scheme to manipulate parameterized random variables [ariables . A platePlates appeared with the BUGS package, to facilitate the specification of hierarchical models, and have been successful in applications . One resSeveral other combinations of parameterized random variables and graph-theoretical representations have been proposed, often grouped under the loose term \u201cProbabilistic Relational Model (PRM)\u201d ,19,20.\u00a0USuppose that we want a PRM to represent Scenario 4 in Example 2. Now, the class xpressed .burglary(x)\u00a0=\u00a00.001;alarm(x)\u00a0=\u00a00.9\u00a0*\u00a0burglary(x)\u00a0+\u00a00.01\u00a0*\u00a0(1-burglary(x));calls(x)\u00a0=\u00a0NoisyOR\u00a0{\u00a0alarm(y)\u00a0|\u00a0y;\u00a0neighbor\u00a0};Instead of resorting to diagrams, one may instead focus just on textual languages to specify repetitive Bayesian networks. A very solid formalism that follows this strategy is Jaeger\u2019s Relational Bayesian Networks (RBNs) ,23. In ROne problem that surfaces when we want to use an expressive formalism, such as RBNs or PRMs, is whether a particular model is guaranteed to always produce consistent Bayesian networks. Consider a simple example .Example\u00a03.Suppose we are modeling genetic relationships using the parameterized random variable If y and z are such that It we try to specify a PRM for this setting, we face a difficulty in that some instances of r et al. . We woulThe possibility that RBNs and PRMs may lead to cyclic (thus inconsistent) Bayesian networks has been noticed before. Jaeger  suggestecoherent in the sense that it can be always satisfied by a probability distribution? Is it coherent in the sense that it always produces a unique probability distribution? Such are the questions we address, by exploring a cross-pollination of ideas described in the previous paragraph. In doing so, we bring logical rigor to the problem of coherence of PRMs and present a practical alternative to identifying coherent RBNs.Thus, we have arrived at the problems of interest in this paper: Suppose we have an RBN or a PRM. Is it After formally introducing relational Bayesian networks in In this section, we briefly introduce the formalism of Relational Bayesian Networks (RBNs). We use the version of RBNs presented in , as thatS and R be disjoint sets of relation symbols, called the predefined relations and probabilistic relations, respectively. We assume that S contains the equality symbol =, to be interpreted in the usual way. Each predicate symbol is associated with a positive integer k, which is its arity. Given a finite domain V is a set of relation symbols (as R or S), a V-structureV into sets of tuples in D. Formally, a V-structure k into a subset of V-structures over a given finite domain D. Given a domain D, a k and a tuple ground V-atom. A V-structure v is mapped to a relation containing t, we say that satisfied byLet V, together with variables, quantifiers and Boolean connectives. We call these V-formulas, and their meaning is given by the first-order logic semantics, as usual, through the V-structures. We denote by V-formula where V-formula and V-structure, Employing the syntax of function-free first-order logic, we can construct formulas using a vocabulary of relations random relational structure model for S and R is a partial function P that takes an S-structure D, and returns a probability distribution R-structures on the same domain. As an R-structure can be seen as total assignment over the ground R-atoms, S-structure of neighbors and returns a joint probability distribution over ground atoms for D, implies a specific Bayesian network whose variables are the ground atoms for A S-structure into a ground Bayesian network that encodes a probability distribution over R-structures. To begin, this ground Bayesian network has nodes representing k is the arity of r. Thus, given the domain D of the input S-structure, the nodes in the corresponding Bayesian network are already determined. To define the arcs and parameters of the Bayesian network associated with an arbitrary S-structure, relational Bayesian networks employ their central notion of probability formula.Relational Bayesian networks provide a way to compactly represent random relational structure models. This is achieved by mapping each S-structure. Once an R-structure and an S-structure are fixed, then for elements D, a probability formula Probability formulas are syntactical constructions intended to link the probability of a ground atom combination functions, which are functions from finite multi-sets over the interval oisyOR is a combination function such that, if oisyORThe definition of probability formulas makes use of Definition\u00a01.S and R of relation symbols and a tuple x of k variables, -probability formula if:(constants) k;(indicator functions) (convex combinations) y is a tuple of variables and S-formula.(combination functions) Given disjoint sets x is a tuple of k variables, with k the arity of Relational Bayesian networks associate a probability formula Definition\u00a02.S and R, the predefined and probabilistic relations, a relational Bayesian network is a set S,R)-probability formula.Given disjoint sets of relation symbols S-structure D. Then, an R-structure D entails a numeric value for each ground probability formulat is tuple of elements in D. This is done inductively, by initially defining t. The numeric value of c. As the set of ground atoms whose evaluation is needed to compute S-structure t and Here, To have an idea of how probability formulas work, consider a fixed S-structure For a given Definition\u00a03.Relation \u2aaf, over ground R-atoms, is defined as follows:S-structure D, a probability distribution over the R-structures D via:When this relation is acyclic, a relational Bayesian network Example\u00a04.Scenario 4 of Example 2: We can define a relational Bayesian network that returns the corresponding Bayesian network for each number and configuration of neighbors. Let  \u03a6:oisyOR; a combination function.Note that, if  NoisyOR above are in \u03a6 determines a joint probability distribution over the ground R-atoms, via a Bayesian network. If we take an S-structure Given an S-structure S-structures yield a cyclic dependency relation \u2aaf. When the relation \u2aaf is cyclic for an S-structure, no probability distribution is defined over the R-structures. In such a case, we say incoherent for that S-structure. This notion can be generalized to a class of S-structures coherent for S-structure in S-structures is precisely one of the problems we are interested in this work.It may happen for a relational Bayesian network S-structures and the coherence of a relational Bayesian network S-structures, note that they can be seen as first-order structures over which S-formulas are interpreted. That is, an S-formula defines the set of S-structures satisfying it. If S-formula (without free variables), we say that S-structures S-formula satisfied exactly by the S-structures in a given class In order to reason about the relation between a class of S-structure. Ideally, we would like to have a (first-order) S-formula, say S-structures yielding acyclic dependency relations \u2aaf. If that formula were available, a decision about the coherence of S-structure in the class S-structure in S-formulas, only S-structures matter, and we could ignore any relation not in S. To be precise, if a first-order structure S-structure To encode the coherence of Alas, to encode cycles in a graph, one needs to encode the notion of path, which is the transitive closure of a relation encoding arcs. It is a well-known fact that first-order logic cannot express transitivity. To circumvent that, we can add a (strict) transitive closure operator to the logic, arriving at the so-called transitive closure logics, as described for instance in .S-formula S and R, one could hope to obtain a formula S-structure n, with one node per ground atom, so a cycle can also contain more nodes than n. There seems to be no direct way of employing the transitive closure operator to devise a formula n nodes and that is to be satisfied by some structures n elements. In the next sections, we review a technique  to encoV-formula V containing S, that is satisfiable only by V-structures that encode both an S-structure V-structures should contain, besides an S-structure Our idea to construct a formula S and v. Consider a relational Bayesian network S,R)-probability formula. Let V-structure satisfying S-structure V a unary predicate S-structure V-structure Suppose we have two disjoint vocabularies V that includes the predefined relations in S and contains the unary predicate S). Furthermore, V must contain a binary relation r and to tuples S-structure V binary relations Firstly, we need to define a vocabulary x in the domain represents the ground atom To save notation, we use V-structure Now, we proceed to list, step-by-step, the set of conjuncts required in We have to ensure that the elements in Each element in No element may correspond to ground atoms for two different Each element corresponding to a ground atom should correspond to exactly one tuple. To achieve that, let Each element corresponding to a ground atom for a Only elements in Each ground atom must be represented by at least one element  is s is s8) iD representing ground atoms S-structure R, are determined by the size of S-formulas that hold for the S-structure S-structures to be specified by For all The binary relation The formula above forces that S-structure S-structure S-formula S-formula that is satisfied by For a known If If k is the arity of t. These base cases are in line with the recursive definition of If Above, In other words, the computation of S-formula involved. Recall that if S-formula that is satisfied by an S-structure The more elaborated case happens when If The inner union is analogous to the definition of Now, we can employ the formulas For each pair t and x and y. We point out that such construction depends only on probability formulas in the relational Bayesian network S-structure. To build each S-formulas In the formula above, The relation y and For each pair R, and let y and y denote the tuples Let Definition\u00a04.Given disjoint sets of relations S and R and a relational Bayesian network mulas in \u201312)..\u03a6={Fri\u2223rV-structures S are interpreted in S-structure the relations in b between the domain R-atoms formed by the tuples in there is a bijection each the relation For some fixed relational Bayesian networks V-structure satisfying V-structures S-structure V-structures satisfying it.The original formula V-structure D iff there exists a x to itself. Consequently, detecting y is x, in a V-structure k, we can define reachability through kk) is unbounded a priori, as the domain D can be arbitrarily large. Therefore, there is no means in the first-order logic language to encode reachability, via arbitrarily large paths, with a finite number of formulas. In order to circumvent this situation, we can resort to a transitive closure logic.There is a cycle with y is x, with a non-empty path. Accordingly, a V-structure D, satisfies Transitive closure logics enhance first-order logics with a transitive closure operator e strict . If \u03c6 is encoded directly by Employing the transitive closure operator, the existence of a V-structures D satisfying S-structure in acyclic ground Bayesian network either it encodes an S-structure in or it is not the case that At this point, the S-structures ensures the acyclicity of the resulting ground Bayesian network S-formula S-structures without cycles, for instance.Back to the coherence-checking problem, we need to decide, for a fixed relational Bayesian network S-structures over D, while S-structure is given only over S-structures S-structure D. The formula S-structures, like To check the coherence of mulas in , so no xmulas in , contradmulas in  that reqidity of:\u03b8S\u2192 S-structures Finally, we can define the formula that encodes the coherence of a relational Bayesian network Definition\u00a06.S and R, a given relational Bayesian network S-structures defined by For disjoint sets of relations Putting all those arguments together, we obtain the translation of the coherence-checking problem to the validity of a formula from the transitive closure logic:Theorem\u00a01.\u03a6 and a class of S-structures \u03a6 is coherent for For disjoint sets of relations S and R, a given relational Bayesian network (De Bona and Cozman ).For diR to be unary and assuming a decidable As first-order logic in general is already well-known to be undecidable, adding a transitive closure operator clearly does not make things easier. Nevertheless, decidability remains an open problem, even restricting the relations in perators ,26). SimJaeger introduced the coherence problem for RBNs as checking whether every input structure in a given class yields a probability distribution via an acyclic ground Bayesian network. Alternatively, we might define the coherence of an RBN as the existence of at least one input structure, out of a given class, resulting in an acyclic ground Bayesian network. This is closer to the satisfiability-like notion of coherence discussed by de Finetti and closer to work on probabilistic logic ,28.In this section, we show that, if one is interested in a logical encoding for this type of coherence for RBNs, the transitive closure operator can be dispensed with.S-structure in Suppose we have an RBN The idea to construct V is augmented with the binary relation In order to build By construction, one can verify the following result:Theorem\u00a02.\u03a6 and a class of S-structures \u03a6 is coherent for some structure in For disjoint sets of relations S and R, a given relational Bayesian network The fact that In this section, we introduce the machinery of PRMs by following the terminology by Getoor et al. , focusindescriptive attributesreference slotsX (denoted range type) specified in the schema. The domain type of X. We can view this reference slot To define a PRM, illustrated in Example 5, we need a relational model, with classes associated with descriptive attributes and reference slots that behave like foreign keys. Intuitively, each object in a class is described by the values of its descriptive attributes, and reference slots link different objects. Formally, a relational schema is described by a set of classes inverse slotx from the class slot chain if i. The function corresponding to a slot chain x from For any reference slot An instance relational skeletoncompletion of a relational skeleton Given a relational schema, a PRM defines a probability distribution over its instances. In the simplest form, on which we focus, objects and the relations between them are given as input, and there is uncertainty only over the descriptive attributes values. A dependency graph; and the set of parameters define the conditional probability tables. The attributes in formal parents, as they will be instantiated for each object x in X according to the relational skeleton. There two types of formal parents: K is a slot chain.The format of a PRM resembles that of a Bayesian network: for each attribute x, aggregation is used. The attribute In general, for an object Definition\u00a07.probabilistic Relational modelA ground Bayesian network induced by a relational skeleton, where the descriptive attributes of each object are the random variables.The semantics of a PRM is given by the Definition\u00a08.There is a node representing each attribute For each Each Each The CPD for The CPD for A PRM simplified ground Bayesian network. The latter can be employed to factor the joint probability distribution over the descriptive attributes:The joint probability distribution over the descriptive attributes can be factored as usual to compute the probability of a specific instance Viewing Example\u00a05.Recall again Scenario 4 in Example 2. We can define a PRM that returns the corresponding Bayesian network for each number and configuration of neighbors. In our relational schema, we have a class We assume that the relation For each descriptive attribute in our relational schema, we associate a set of formal parents and a conditional probability table, forming the following PRM \u03a0 to encode Scenario 4:Given a relational skeleton  \u03a0 determines a joint probability distribution over the the descriptive attributes, via a Bayesian network. Consider a skeleton all possible relational skeletons. To achieve that, possible cycles are detected in the class dependency graph.As with RBNs, for the model to be coherent, one needs to guarantee that the ground Bayesian network is acyclic. Getoor et al.  focused Definition\u00a09.class dependency graphType I arcs: Type II arcs: Given a PRM guaranteed acyclic if we are guaranteed that, for any possible relational skeleton x and When the class dependency graph is acyclic, so is the ground Bayesian network for any relational skeleton. Nevertheless, it may be the case that, even for cyclic class dependency graphs, any relational skeleton occurring in practice leads to a coherent model. In other words, there might be classes of skeletons for which the PRM is coherent. To easily recognize some of these classes, Getoor et al.  put forwDefinition\u00a010.colored class dependency graphYellow arcs: Green arcs: Red arcs: Given a PRM x is different from y, and there is no cycle. If there is a red arc in a cycle, however, one may have a skeleton that produces a cycle.Intuitively, yellow cycles in the colored class dependency graph correspond to attributes of the same object, yielding a cycle in the ground Bayesian network. If we add some green arcs to such a cycle, then it is guaranteed that, departing from a node stratified if every cycle contains at least one green arc and no red arc. Then:A colored class dependency graph is Theorem\u00a03.Given a PRM \u03a0 and a set of guaranteed acyclic slot chains .Given a priori knowledge on the possible skeletons in practice. For instance, consider a slot chain In the result above and in the definition of guaranteed acyclic slot chains, \u201cpossible relational skeleton\u201d refers to the class of skeletons that can occur in practice. The user must detect the guaranteed acyclic slot chains, taking advantage of his Identifying guaranteed acyclic slot chains is by no means trivial. In fact, Getoor et al.  also defThe simplest approach to the coherence of PRMs, via the non-colored class dependency graph, is intrinsically incomplete, in the sense that some skeletons might yield a coherent ground Bayesian network even for cyclic graphs. The approach via colored class dependency graph allows some cyclic graphs (the stratified ones) to guarantee consistency for the class of all possible skeletons. However, this method depends on a pre-specified set of guaranteed acyclic slot chains, and the colored class dependency graph being stratified for this set is only a sufficient, not a necessary condition for coherence. Therefore, the colored class dependency graph method is incomplete, as well. Even using different sets of g.a. slot chains (corresponding to shades of green) to eventually capture all of them, it is still possible that a cycle with red arcs cannot entail incoherence in practice. Besides being incomplete, the graph-based method is not easily applicable to an arbitrary class of skeletons. Given a class of skeletons as input, the user would have to detect somehow which slot chains are guaranteed acyclic for that specific class; this can be considerably more difficult than ensuring acyclicity in the general case.To address these issues, thus obtaining a general, complete method for checking the coherence of PRMs for a given class of skeletons, we can resort to the logic-based approach we introduced for the RBNs in previous sections. The goal of this section is to adapt the logic-basic techniques to PRMs.S-structures to probability distributions on R-structures. While the S-vocabulary is used to specify classes of objects and relations between them , the R-vocabulary expresses the descriptive attributes of the objects. Employing this logical encoding of PRMs, we can apply the approach from PRMs can be viewed as RBNs, as conditional probability tables of the former can be embedded into combination functions of the latter. This translation is out of our scope though, and it suffices for our purposes to represent PRMs as random relational structures, taking To follow this strategy, we first show how a PRM can be seen as a random relational structure described by a logical language.S-structure over a set of objects and a set of unary relations R denotes their attributes, the PRM becomes a random relational structure.Consider a PRM S-structure D of S to denote the class of each object. Accordingly, for each We need to represent a skeleton S-structure S, all objects of a given class, as well as the relations between them specified in the reference slots. In other words, there is a computable function S-structures The first-order R-atom R-structure R-structures R-structure The probabilistic vocabulary of the random relational structure corresponding to a PRM is formed by the descriptive attributes of every class in the relational schema. We assume that attributes in different classes have different names, as well, in order to define the vocabulary of unary relations D, let R-structures such that Now, we can define a random relational structure R-atoms. The structure of this network is isomorphic to the simplified ground Bayesian network yielded by The probability distribution S-structures We want to construct a formula that is satisfied only by those R-atoms K, then x via To encode the arcs, we employ once more a relation K. Thus, we define Note that it is possible that both S-structure Analogously to S-structures satisfying a first-order formula Consider now a class We have thus succeeded in turning coherence checking for PRMs into a logical inference, by adapting techniques we developed for RBNs. In the next section, we travel, in a sense, the reverse route: we show how to adapt the existing graph-based techniques for coherence checking of PRMs to coherence checking of RBNs.only if such a formula is valid. Nonetheless, completeness and flexibility regarding the input class come at a very high price, as deciding the validity of this first-order formula involving a transitive closure operator may be computationally hard, if at all decidable. Therefore, RBNs users can benefit from the ideas introduced by Getoor et al. [a priori knowledge, the RBN user perhaps can attest to the acyclicity of the resulting ground Bayesian network for all possible inputs.The logic-based approach to the coherence problem for RBNs can be applied to an arbitrary class of input structures, as long as the class can be described by a first-order formula, possibly with a transitive closure operator. Given any class of input structures r et al.  for the r et al.  proposesr et al.  are inteAny arc Definition\u00a011.R-dependency graphType I arcs: Type II arcs: Given an RBN R-dependency graph of an RBN D and any tuple S-structure, t. Type II arcs capture dependencies that are contingent on the S-relations holding in the input structure. In other words, a Type II arc S-formula D) in the output ground Bayesian network iff the input S-formula might be fairly complicated. Nevertheless, the point here is simply noting that, given a Type II arc S-formula parametrized by Intuitively, a Type I arc R-dependency graph, when the latter is acyclic, so will be the former, for any input structure. As it happens with class dependency graphs and PRMs, though, a cycle in the R-dependency graph does not entail a cycle in the ground Bayesian network if a Type II arc is involved. It might well be the case that the input structures R-dependency graph.As each arc in the ground Bayesian network corresponds to an arc on the R-dependency graph of an RBN, these arcs encode the dependency between relations R-dependency graph whose sequence will prevent cycles in the ground Bayesian network, via a partial ordering over the tuples.In the same way that Type I arcs in the class dependency graph of a PRM relate to attributes of different objects, in the S of predefined relations, let D. We say a set D, there is a partial ordering \u2aaf over For a vocabulary Definition\u00a012.R-dependency graph of an RBN colored R-dependency graphR-dependency graph;Yellow arcs: Type I arcs in the R-dependency graph such that Green arcs: Type II arcs R-dependency graph.Red arcs: The remaining (Type II) arcs in the Given the R-dependency graph correspond to relations t, yielding a cycle in the ground Bayesian network. If green arcs are added to a cycle, then it is guaranteed that, departing from a node stratified a R-dependency graph whose every cycle contains at least one green arc and no red arc, we have:Again, yellow cycles in the colored Theorem\u00a04.\u03a6 and a set Given the R-dependency graph of an RBN R-dependency graphs of RBNs is even harder than, as a generalization of, detecting guaranteed acyclic slot chains in PRMs. In any case, if the involved relations Of course, detecting guaranteed acyclic Type II arcs in coherence checking, a central problem in the foundations of probability as conceived by de Finetti. The simplest formulation of coherence checking takes a set of events and their probabilities and asks whether there can be a probability measure over an appropriate sample space [In this paper, we examined a new version of le space . This sole space . Unsurprle space . Our focle space .S cannot be followed as originally stated; as we have argued, the possible number of tuples built from a domain typically outnumbers its size, so that there is no straightforward way to encode the ground Bayesian network, whose nodes are ground atoms, into the input S-structure. Therefore, it is hard to think of a method that translates the acyclicity of the ground Bayesian network into a formula S (satisfying S-structure and the corresponding Bayesian network. We have also extended those results to PRMs, in fact mixing the existing graph-based techniques for coherence checking with our logic-based approach. Our results seem to be the most complete ones in the literature.We have first examined the problem of checking the coherence of relational Bayesian networks for a given class of input structures. We used first-order logic to encode the output ground Bayesian network into a first-order structure, and we employed a transitive closure operator to express the acyclicity demanded by coherence, finally reducing the coherence checking problem to that of deciding the validity of a logical formula. We conjecture that Jaeger\u2019s original proposal concerning the format of the formula encoding the consistency of a relational Bayesian network Future work includes searching for decidable instances of the formula encoding the consistency of a relational Bayesian network for a class of input structures and exploring new applications for the logic techniques herein developed."}
+{"text": "Nature Communications 10.1038/s41467-020-17945-4, published online 20 August 2020.Correction to: The original version of this Article contained an error in Fig. 4a, in which the value for the \u2018partition coefficient\u2019 for phenyltriethylammonium was incorrectly given as 0. The correct value for the \u2018partition coefficient\u2019 is 2.9.This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "The VIKOR model has been considered a viable tool for many decision-making applications in the past few years, given the advantages of considering the compromise between maximizing the utility of group and minimizing personal regrets. The q-rung interval-valued orthopair fuzzy set (q-RIVOFS) is a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and has emerged to solve more complex and uncertain decision making problems which IFS and PFS cannot handle. In this manuscript, the key innovation is to combine the traditional VIKOR model with q-RIVOFS to develop the q-rung interval-valued orthopair fuzzy VIKOR model. In the new developed model, to express more information, the attribute\u2019s values in MAGDM problems are depicted by q-RIVOFNs. First of all, some basic theories and aggregation operators of q-RIVOFNs are simply introduced. Then we develop the origin VIKOR model to q-RIVOFS environment and briefly express the computing steps of this new established model. Thereafter, the effectiveness of the model is verified by an example of supplier selection of medical consumer products and through comparative analysis, the superiority of the new method is further illustrated. In view of the merits of the VIKOR model in considering the compromise between group utility maximization and individual regret minimization, in recent years, it has been recognized as a meaningful tool that can be applied to many decision areas. In previous literature, some traditional decision models have been applied to MADM problems, such as the ELECTRE model ,2,3,4, tBecause of the uncertainty and decision problem of decision support system (DSS), in the practical DSS problem, we often cannot give the accurate evaluation value of the alternative to choose the best one. To overcome this problem, in 1965, the fuzzy set theory defined by Zadeh , initialNevertheless, to describe more decision information, Yager  later deand Wang  put forwand Wang  defined and Wang  gave somand Wang  providedand Wang  came up and Wang  offered and Wang  gave theHowever, to date, it is clear that the VIKOR model with q-RIVOFNs information has not been studied. Therefore, it\u2019s essential to take q-RIVOF-VIKOR model into consideration. The aim of our manuscript is to create an enlarged VIKOR model with the original VIKOR method and q-RIVOF information to settle MADM problems more effectively. Our manuscript is structured as: the definition, score function, accuracy function, operation rules, and some aggregation operators of q-RIVOFSs are briefly given in Based on the theorems of q-ROFSs and the interval values, the essential definition and theorems of q-RIVOFSs are retrospected in brief below.Definition\u00a01\u00a0 .Let:where the function\u00a0defines the membership degree and the function\u00a0defines the non-membership degree of the element\u00a0to\u00a0respectively, and, for every x \u2208 X, it meets that\u00a0\u00a0is the degree of indeterminacy membership. For convenience, we called\u00a0\u00a0a q-RIVOFN.Definition\u00a02\u00a0.Let\u00a0be a q-RIVOFN, a score function S can be written as follows:Definition\u00a03\u00a0.Let\u00a0be a q-RIVOFN, an accuracy functioncan be written as follows:S and H, the order relation between two q-RIVOFNs will be obtained as below:According to Definition\u00a04\u00a0.Let\u00a0\u00a0and\u00a0 be two q-RIVO FNs, assume that\u00a0and\u00a0\u00a0be the scores of\u00a0\u00a0and\u00a0and let\u00a0and\u00a0be the accuracy degrees of\u00a0and\u00a0respectively, then when\u00a0when\u00a0(1) if\u00a0then\u00a0(2) if\u00a0Definition\u00a05\u00a0.Let\u00a0and\u00a0be three q-RIVOFNs, and some basic rules about them are defined as follows:Definition\u00a06\u00a0.Let\u00a0be a list of q-RIVOFNs with weighting vector be\u00a0thereby satisfying\u00a0and\u00a0then the q-RIVOFWA operator can be written as:Definition\u00a07\u00a0 .Let\u00a0be a list of q-RIVOFNs with weighting vector be\u00a0thereby satisfying\u00a0and\u00a0then the q-RIVOFWG operator can be written as:The VIKOR model, which firstly define by Opricovic and Tzeng , is a meStep 1. Establish the decision matrixes Step 2. Calculate PIS Step 3. According to the Formula (7) and the attribute weighting vector Step 4. Calculate the results of Step 5. Then according to Assume that there are Step 1. Give the q-RIVOFNs decision making matrixes Step 2. Calculate PIS For benefit attribute:For cost attribute:Step 3. On the basis of the Equations (17) and (18) and Step 4. Calculate the results of Step 5. According to 1 is the environmental improvement quality; \u2461 G2 is the transportation convenience of suppliers; \u2462 G3 is the green image; \u2463 G4 is the environmental competencies. The five feasible medical consumption products suppliers The supplier terms of an enterprise is undoubtedly very important, and in the future will be an even more important influence on the quality of a vendor\u2019s business, as it will affect the business of purchasing, production, inventory and sales, and so on. The relationship between suppliers and future enterprise is not a simple relationship between management and managed, suppliers will become a strategic partner companies, it is a win-win relationship. So supplier preliminary evaluation and selection is quite important. Medical supplies products have their own characteristics to distinguish it from other types of products, which can be distinguished from their production, transportation, marketing, and other aspects. It can be seen that supplier selection of medical consumption products is the classical MADM or MAGDM issue ,70,71,72Next, we make use of the VIKOR technique with q-RIVOFNs developed for medical consumption products supplier selection.Step 1. Give the q-RIVOFNs decision making matrixes Then according to q-RIVOFWA operator and q-RIVOFNs given in Step 2. Calculate PIS Step 3. According to the Formulas (19) and (20) and Then the results of Step 4. On the basis of Step 5. According to In this subsection, we shall compare our presented VIKOR model for q-RIVOFNs with other existing q-RIVOF decision making tools including q-RIVOFWA operator and q-RIVOFWG operator proposed by Wang, Gao, Wei and Wei  to explaAccording to the score function of q-RIVOFNs, the score results For q-RIVOFWA operator:For q-RIVOFWG operator:Then the ordering of alternatives by q-RIVOFWA and q-RIVOFWG operators is listed in Compare the results of the q-RIVOF-VIKOR model with q-RIVOFWA and q-ROIVFWG operators, the aggregation results are a little bit different in ranking of alternatives but the optimal scheme is the same. However, q-RIVOF-VIKOR model has the remarkable characteristics of considering the compromise between group utility maximization and individual regret minimization and can be more accuracy and valid in MAGDM problems.In this manuscript, the q-RIVOF-VIKOR model based on the traditional VIKOR model is presented. Firstly, we started with a review of the concept of q-RIVOFSs and introduced the score function, accuracy function, operation rules, and some aggregation operators of q-RIVOFNs. Furthermore, we combined the traditional VIKOR technique with q-RIVOFNs information, the q-RIVOF-VIKOR model is built and the calculational steps are detailedly given. The proposed model considers the compromise between group utility maximization and individual regret minimization, which is proved to be more accurate and effective. Finally, the new model is illustrated by taking the supplier selection of medical consumer products as an example, and the advantages of the new method are further illustrated by comparing q-RIVOF-VIKOR model with two q-RIVOFNs aggregation operators. In the future, the q-RIVOF-VIKOR model can be used in many other uncertain and fuzzy environments, such as risk analysis ,82,83,84"}
+{"text": "Scientific reports, 10.1038/s41598-020-65364-8 published online 26 May 2020.Correction to: The original version of this Article contained an error in the title of the paper, where the space between words \u201cthe\u201d and \u201cAmalda\u201d was omitted. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Leishmania infantum, little is known about how co-infections with or co-seropositivities for other pathogens can influence aggravation of this disease. Therefore, the objectives of this study were to evaluate the frequency of co-infections with or co-seropositivities for certain pathogens in dogs seropositive for L. infantum and their relationship with clinical signs, histological changes and L. infantum load. Sixty-six L. infantum-seropositive dogs were submitted to clinical examination, collection of blood and bone marrow, culling, and necropsy. Antibodies against Anaplasma spp., Borrelia burgdorferi sensu lato, Ehrlichia spp. and Toxoplasma gondii and Dirofilaria immitis antigens were investigated in serum. Samples from different tissues were submitted to histopathology and immunohistochemistry for the detection of Leishmania spp. and T. gondii. Quantitative real-time PCR was used to assess the L. infantum load in spleen samples. For detection of Coxiella burnetii, conventional PCR and nested PCR were performed using bone marrow samples. All 66 dogs tested positive for L. infantum by qPCR and/or culture. Fifty dogs (76%) were co-seropositive for at least one pathogen: T. gondii (59%), Ehrlichia spp., (41%), and Anaplasma spp. (18%). Clinical signs were observed in 15 (94%) dogs monoinfected with L. infantum and in 45 (90%) dogs co-seropositive for certain pathogens. The L. infantum load in spleen and skin did not differ significantly between monoinfected and co-seropositive dogs. The number of inflammatory cells was higher in the spleen, lung and mammary gland of co-seropositive dogs and in the mitral valve of monoinfected dogs. These results suggest that dogs infected with L. infantum and co-seropositive for certain pathogens are common in the region studied. However, co-seropositivities for certain pathogens did not aggravate clinical signs or L. infantum load, although they were associated with a more intense inflammatory reaction in some organs.In canine leishmaniosis caused by the protozoan  Leishmania (Leishmania) infantum is a zoonosis of important public health concern. From 1990 to 2019, there were 93,614 confirmed human cases of VL in Brazil, with an average of 3,120 new cases per year Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes**********2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes**********3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data\u2014e.g. participant privacy or use of data from a third party\u2014those must be specified.The Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1:\u00a0Under my review criteria, this is a well-written manuscript, which deserves to be considered for publication after the necessary explanations and adaptations as described below. My main concern is whether the number of dogs may be considered as numerically sufficient, together with the hypothesis that these animals might not be representative of dogs from other breeds.Line 27 \u2013 delete \u201cvisceral\u201d, as canine leishmaniasis caused by L. infantum is a generalized disease \u2013 change accordingly throughout the manuscriptLine 32 \u2013 the word \u201ceuthanasia\u201d presupposes that the dogs were sick \u2013 if this was not the case, use \u201cculling\u201d insteadLine 39 \u2013 \u201cco-infected\u201d may not be the right word for all the pathogens; for example, regarding T. gondii, seropositivity may not mean infection \u2013 change accordingly  for this and other agentsLine 54 \u2013 delete \u201cbiological\u201d \u2013 including this word suggests that there are also mechanical vectors and this is not the caseLine 59 \u2013 whenever possible, display agents alphabetically \u2013 change accordingly throughout the manuscriptLine 60 \u2013 Isospora is now Cystoisospora; there is more than one species, so please write \u201cCystoisospora spp.\u201dLine 64 \u2013 replace VL with leishmaniasisMaterials and methods \u2013 which criteria have determined a sample size of 66 dogs? Furthermore, this sample composition may not allow extrapolation of results to other breeds.Line 92 \u2013 not clear whether the owners provided signed consent for euthanasia  or to sample collection \u2013 please make clearerLine 112 \u2013 abbreviate as T. gondiiLine 174 \u2013 Leishmania spp.Line 181 \u2013 L. infantumLine 234 \u2013 Serological detection of antibodies to Anaplasma spp., B. burgdorferi and Ehrlichia spp., and of D. immitis antigensLine 239 \u2013 inform on the per cent sensitivity and specificity for each agentLine 242 \u2013 replace Diagnosis with DetectionLine 247 \u2013 which values for this IFAT?Line 254 \u2013 median was calculated, but minimum and maximum were just copied Line 290 \u2013 these dogs may not be infected but only seropositive; please, take this into account in the textLine 415 \u2013 rates are different from percentages; and this is the case of percentagesDiscussion \u2013 comparison with results from other studies could have included a statistical assessment.Reviewer #2:\u00a0It is a very interesting research and very well presented. Please use the term leishmaniosis, instead of leishmaniasis .My main concern is that you have selected some common and important pathoges to test and if negative you present the dog as a single infection case. However, there are many other important pathogens to be present and contribute. For example sarcoptic mange or worms. I did not see other tests for them. I would suggest to revise the text and title using the phrase certain or common pathogens, which is closer to your work. Also please revise your conclusions accordingly.**********what does this mean?). If published, this will include your full peer review and any attached files.6. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool,\u00a0 28 Jan 2021Dear Dr. Caldas Menezes,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE\u2019s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.A well written manuscript, which deserves consideration. However, the authors should consider to not generalise their results. Also, seropositivity is not equivalent of infection.plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.Please submit your revised manuscript by 31.01.2021. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at Please include the following items when submitting your revised manuscript:\u2022 A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.\u2022 A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.\u2022 An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocolsIf applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: We look forward to receiving your revised manuscript.Kind regards,Angela Monica Ionica, Ph.D.Academic EditorPLOS ONEJournal Requirements:When submitting your revision, we need you to address these additional requirements.1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found athttps://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf andhttps://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdfRESPONSE TO REVIEWER #1Reviewers' comments:Reviewer's Responses to QuestionsComments to the AuthorReviewer #1: Under my review criteria, this is a well-written manuscript, which deserves to be considered for publication after the necessary explanations and adaptations as described below. My main concern is whether the number of dogs may be considered as numerically sufficient, together with the hypothesis that these animals might not be representative of dogs from other breeds.Line 27 \u2013 delete \u201cvisceral\u201d, as canine leishmaniasis caused by L. infantum is a generalized disease \u2013 change accordingly throughout the manuscriptResponse:Line 27. The word \u201cvisceral\u201d was deleted and the word \u201cleishmaniasis\u201d was replaced with \u201cleishmaniosis\u201d, as recommended by the reviewer#2. In addition, following the recommendations of both reviewers, the word \u201cvisceral\u201d was deleted, the word \u201cleishmaniasis\u201d was replaced with \u201cleishmaniosis\u201d and the abbreviation \u201cCVL\u201d was replaced with \u201cCanL\u201d along the text, as indicated below:Line 101. \u201ccanine visceral leishmaniasis (CVL)\u201d was replaced with \u201c canine leishmaniosis caused by L. infantum (CanL)\u201dLines 105, 292, 295, 446, 447, 453, 513, 530, 531 and 549. The abbreviation \u201cCVL\u201d was replaced with the abbreviation \u201cCanL\u201d.Lines 487 and 527. \u201cVL\u201d was replaced with \u201cCanL\u201d.Lines 27, 52, 64, 85 and 101. The word \u201cleishmaniasis\u201d was replaced with \u201cleishmaniosis\u201d.Line 472- \u201cclinical VL caused by caused by L. infantum\u201d was replaced by \u201cCanL\u201dLine 32 \u2013 the word \u201ceuthanasia\u201d presupposes that the dogs were sick \u2013 if this was not the case, use \u201cculling\u201d insteadResponse: Lines 33, 92 and 93. The word \u201ceuthanasia\u201d was replaced with \u201cculling\u201d.Lines 91, 117 and 274. The word \u201ceuthanized\u201d was replaced with \u201cculled\u201d.Line 39 \u2013 \u201cco-infected\u201d may not be the right word for all the pathogens; for example, regarding T. gondii, seropositivity may not mean infection \u2013 change accordingly  for this and other agentsIn fact, we can\u2019t prove the infection by the pathogens investigated in this study except for L. infantum. Therefore, the terms \u201cco-infected\u201d, \u201cco-infection\u201d and \u201cco-infections\u201d were replaced with \u201cco-seropositive\u201d, \u201cco-seropositivity\u201d and \u201cco-seropositivities\u201d along all the text, respectively, when refers to the results of this study or to the results of other authors when appropriate. We preferred these terms other than \u201cseropositive\u201dor \u201cseropositivity\u201d for the results of this manuscript, because all the dogs were seropositive for L. infantum. The term \u201cmonoinfected\u201d was maintained, because we confirmed the infection with L. infantum by qPCR and/or culture in all the 66 dogs investigated in this study. These modifications were done in the following parts of the text:The title of the manuscript was altered to: \u201cFrequency of co-seropositivities for certain pathogens and their relationship with clinical and histopathological changes and parasite load in dogs infected with Leishmania infantum\u201dThe short title \u201cCo-infections in dogs naturally infected with L. infantum\u201d was replaced with \u201cCo-seropositivities in dogs naturally infected with L. infantum\u201dThe keyword \u201cCo-infection\u201d was replaced with \u201cCo-seropositivity\u201dAbstractLines 28, 29-30. The text \u201cco-infection with other pathogens\u201d was replaced with \u201cco-infections with or co-seropositivities for\u201d.Line 30. The text \u201cinfected with\u201d was replaced with \u201cseropositive for\u201d.Line 39. The text \u201cco-infected with\u201d was replaced with \u201cco-seropositive for\u201d.Line 41. The text \u201cco-infected dogs\u201d was replaced with \u201cdogs co-seropositive for certain pathogens\u201d.Lines 42-43 and 44. The text \u201cco-infected dogs\u201d was replaced with \u201cco-seropositive dogs\u201d.Line 45. The text \u201cco-infections with L. infantum and other pathogens\u201d was replaced with \u201cinfected with L. infantum and co-seropositive for certain pathogens\u201d.Line 46. The text \u201c these co-infections\u201d was replaced with\u201d \u201cco-seropositivities for certain pathogens\u201d.IntroductionLine 58. The text \u201cCo-infections with\u201d was replaced with \u201cCo-infections with or co-seropositivities for\u201d.Line 67. The text \u201cco-infections with\u201d was replaced with \u201cco-infections with or co-seropositivities for\u201d.Lines 68-70. The text \u201cco-infected with other pathogens\u201d was replaced with \u201cco-infected with or co-seropositive for certain pathogens\u201d.Lines 71-72. The text \u201cof co-infections with pathogens\u201d was replaced with\u201d co-infections with or co-seropositivities for certain pathogens\u201d.MethodsLine 264. The word \u201cco-infected\u201d was replaced with \u201cco-seropositive\u201d.ResultsLines 283-284. The text \u201cThe following pathogens causing co-infections and their frequencies were detected in the 66 dogs investigated:\u201d was replaced with \u201cThe following frequencies of co-seropositivity for certain pathogens were observed in the 66 dogs investigated:\u201dLines 281, 286, 287, 294, 295, 297, Table 1, 309, 318, 321-326, 330-331, 336, 338, Table 2, 355, 361, 365-366, 370, Table 3, 372, 378, 385-386, Table 4, 392, 398, 401-402, 409, 411, 412, 414-415, 417, 421, 425 and 435. \u201cThe word \u201cco-infected\u201d was replaced with \u201cco-seropositive\u201d.Lines 321-326. The text \u201c for co-infection with\u201d was replaced with \u201cwhen co-seropositive for\u201d.Line 367. The text \u201ccoinfecting pathogen\u201d was replaced with \u201cthe co-seropositivity for certain pathogens\u201d.Figures 1 and 3. The word \u201cco-infected\u201d was replaced with \u201cco-seropositive\u201d in the legend. DiscussionLines 442-444. The phrase \u201cA high frequency of seropositivity for pathogens coinfecting dogs naturally infected with L. infantum was found, especially co-infection with T. gondii\u201d was replaced with the \u201cA high frequency of co-seropositivity for certain pathogens in L. infantum seropositive dogs with infection with this parasite confirmed by PCR and/or culture was found, especially co-seropositivity for T. gondii.Lines 442, 443, 462, 469 and 505. The word \u201cco-infection\u201d was replaced with \u201cco-seropositivity\u201d.Line 474 and 476. The text \u201cco-infection with\u201d was replaced with \u201cco-infection with or co-seropositivity for\u201d.Line 482. The text \u201cinfection of dogs with\u201d was replaced with \u201cseropositivity of dogs for\u201d.Lines 483. The text \u201cby serology\u201d was deleted.Line 487 and 501. The texts \u201cor co-seropositivities\u201d or \u201cor co-seropositivity\u201d were added.Line 507. The text \u201cthis co-infection\u201d was replaced with \u201cthis co-seropositivity or co-infection\u201d.Lines 523-524. The text \u201cfrequency of co-infections among dogs with VL found in this and other studies .\u201d was replaced with \u201cfrequency of co-seropositivities among dogs seropositive for and/or infected with L. infantum found in this study and in other studies .Lines 541, 548, 572, 577, 591 and 596. The word \u201cco-infected\u201d was replaced with \u201cco-seropositive\u201d.Lines 549-552. The text \u201cAnother hypothesis for the lack of aggravation of CVL due to co-infection with other pathogens in the present study was the use of serological techniques for the detection of most of the pathogens investigated. This methodology may have contributed to the classification of exposed animals, but without active infection, as co-infected when, in fact, serological tests may have detected memory antibodies.\u201d was replaced with the text below:\u201cAnother hypothesis for the lack of aggravation of CanL due to co-seropositivity for certain pathogens in the present study is that the seropositive dogs may not be co-infected or infection with these pathogens is not active, but they were previously exposed to the pathogens and exhibited detectable memory antibodies.\u201dLines 566 to 568. The phrase \u201cHowever, 12.5% of monoinfected dogs and 10% of co-infected dogs did not have a positive culture or IHC result, suggesting that infection with L. infantum was not active in these dogs\u201d was deleted.Line 602. The text \u201cwhy co-infections\u201d was replaced with \u201cwhy co-seropositivity for certain pathogens\u201d.ConclusionsLines 605 and 607. The word \u201cco-infections\u201d was replaced with \u201cco-seropositivities\u201d.Other alterationsIn addition, due to the alterations in the terms and to make clearer that all the dogs investigated were infected with L. infantum and not only seropositive for this parasite, we reviewed the definition of the groups of dogs of our study, as follows:Co-seropositive: L. infantum seropositive dogs with confirmed infection with this parasite by qPCR and/or culture and antibodies against at least one pathogen other than L. infantum.Monoinfected: L. infantum seropositive dogs with confirmed infection with this parasite by qPCR and/or culture and without antibodies against certain pathogens other than L. infantum.These new definitions of the groups were described in lines 309-312, 355-358, 372-375 and 392-395.The term \u201cmonoinfected\u201d was maintained, because we confirmed the infection with L. infantum by qPCR and/or culture in all the 66 dogs investigated in this study.The titles of Tables 1, 2, 4 and S1 were also modified as shown below:Tables 1, 2, 4 and S1. The text \u201cLeishmania infantum-seropositive dogs\u201d was replaced with \u201cdogs infected with Leishmania infantum\u201d.Table S1. The text \u201caccording to the co-infecting pathogen\u201d was replaced with \u201caccording to the co-seropositivity for certain pathogens\u201d.In addition, the following texts were included:AbstractLines 38 to 39. \u201cAll 66 dogs tested positive for L. infantum by qPCR and/or culture.\u201dResultsLines 279 and 280. \u201cAll 66 L. infantum-seropositive dogs investigated in this study had infection with L. infantum confirmed by qPCR and/or culture, as described below.\u201d DiscussionLines 442-443\u201c\u2026co-seropositivity for certain pathogens in L. infantum-seropositive dogs with infection with this parasite confirmed by PCR and/or culture\u2026\u201dLine 54 \u2013 delete \u201cbiological\u201d \u2013 including this word suggests that there are also mechanical vectors and this is not the caseResponse:Line 54. The word \u201cbiological\u201d was deleted, as recommended.Line 59 \u2013 whenever possible, display agents alphabetically \u2013 change accordingly throughout the manuscriptResponse:We desplayed agents alphabetically whenever possible in the following parts of the text:\u2022 AbstractLines 33 to 34.\u2022 IntroductionLines 59 to 64.\u2022 Materials and methodsLines 115 to 116, 236 to 237 and 239-240.\u2022 ResultsLine 286.\u2022 DiscussionLines 491-492 and 559-560.\u2022 ConclusionsLine 605.Line 60 \u2013 Isospora is now Cystoisospora; there is more than one species, so please write \u201cCystoisospora spp.\u201dLine 59. \u201c Isospora sp.\u201d was replaced with \u201c\u201cCystoisospora spp.\u201d, as recommended. Line 64 \u2013 replace VL with leishmaniasisResponse:VL was replaced with \u201cwith leishmaniosis caused by L. infantum\u201d. We replace \u201cleishmaniasis\u201d with \u201cleishmaniosis\u201d along the text, as recommended by the other reviewer (indicated above).Materials and methods \u2013 which criteria have determined a sample size of 66 dogs? The sample size included all dogs of the study population, i.e., all dogs that tested seropositive for L. infantum in the town of Barra Mansa and that were sent to INI-Fiocruz during the study period (n=66).In order to make clearer the criteria for sample size, the following text was included in the materials and methodsLines 94 to 96. \u201cThe sample size included all dogs of the study population, i.e., all dogs that tested seropositive for L. infantum in the town of Barra Mansa and that were sent to INI-Fiocruz during the study period.\u201d Furthermore, this sample composition may not allow extrapolation of results to other breeds.Response:This is a limitation of the study. Considering the breed, the results of this study can only be extrapolated to other similar populations, composed mainly by mongrel dogs (85%). In addition, statistical analysis of the association of breed with the monoinfected and co-seropositive groups was not possible because of the small number of breed dogs (n=10).In order to make these limitations clearer in the text, the following texts were included:ResultsLines 290-291. \u201cStatistical analysis of the association of breed with the monoinfected and co-seropositive groups was not possible because of the small number of breed dogs.\u201dDiscussionLines 444-445. Considering the breed, the results of this study can only be extrapolated to other similar populations composed mainly of mongrel dogs (85%).Line 92 \u2013 not clear whether the owners provided signed consent for euthanasia  or to sample collection \u2013 please make clearerResponse:The owners provided signed consent for culling. We clarify this in the line 93.Line 112 \u2013 abbreviate as T. gondiiResponse:Line 116. Toxoplasma gondii was abbreviated as T. gondii.Line 174 \u2013 Leishmania spp.Response:Line 177. \u201cLeishmania species\u201d was replaced with \u201cLeishmania spp.\u201dLine 181 \u2013 L. infantumResponse:Line 184. \u201cLeishmania infantum\u201d was replaced with \u201cL. infantum\u201d.Line 234 \u2013 Serological detection of antibodies to Anaplasma spp., B. burgdorferi and Ehrlichia spp., and of D. immitis antigensResponse:Lines 236 to 237. The text \u201cDetection of antibodies against Ehrlichia spp., Anaplasma spp. and B. burgdorferi and D. immitis antigens in serum\u201d was replaced with: \u201cSerological detection of antibodies to Anaplasma spp., B. burgdorferi and Ehrlichia spp., and of D. immitis antigens\u201dLines 238 to 240. The text \u201c...to detect antibodies against E. canis/E. ewingii, A. platys/A. phagocytophilum and Borrelia burgdorferi and antigens of D. immitis\u2026\u201d was replaced with:\u201c... for the serological detection of antibodies to A. platys/A. phagocytophilum, B. burgdorferi and E. canis/E. ewingii, and of D. immitis antigens...\u201dLine 239 \u2013 inform on the per cent sensitivity and specificity for each agenteResponse:Lines 241-243. The following text was included, as recommended:\u201c\u2026has the following sensitivities and specificities, respectively: 90.3% and 94.3% for Anaplasma spp., 94.1% and 96.2% for B. burgdorferi, 99.0% and 99.3% for D. immitis, and 97.1% and 95.3% for Ehrlichia spp. Line 242 \u2013 replace Diagnosis with DetectionResponse:Line 245. \u201cDiagnosis\u201d was replaced with \u201cDetection\u201d.Line 247 \u2013 which values for this IFAT?Response:There is no information in the literature about the values of specificity and sensibility of IFAT for the detecion of anti-T. gondii antibodies in the serum of dogs . However, IFAT is considered to have good specificity and sensitivity and is recommended for the immunodiagnosis of T. gondii infection in dogs, where it can be used as the only test .References:Dubey JP, Murata FHA, Cerqueira-C\u00e9zar CK, Kwok OCH, Yang Y, SU C. Toxoplasma gondii infections in dogs: 2009-2020. Vet Parasitol. 2020; 287:109223.Leal PDS, Coelho CD. Toxoplasmosis in dogs: a brief review. Coccidia. 2014; 2: 2-39.Line 254 \u2013 median was calculated, but minimum and maximum were just copied Response:Lines 256 to 258. The text \u201cFor the description of continuous variables (number of inflammatory cells and parasite load), the median (50th percentile) and the minimum and maximum values were calculated.\u201d was replaced with:\u201d\u201cFor the description of continuous variables (number of inflammatory cells and parasite load), the median (50th percentile) was calculated and the minimum and maximum values are reported.\u201dLine 290 \u2013 these dogs may not be infected but only seropositive; please, take this into account in the textResponse:The terms \u201cco-infected\u201d, \u201cco-infection\u201d and \u201ccoinfections\u201d were replaced with \u201cco-seropositive\u201d, co-seropositivity\u201d and \u201cco-seropositivities\u201d, respectively, along all the text, when refers to the results of this study or to the results of other authors, when appropriate. These alterations are explained in more details above.Line 415 \u2013 rates are different from percentages; and this is the case of percentagesResponse:Line 450. The word \u201crates\u201d was replaced with \u201cpercentages\u201d, as recommended.Discussion \u2013 comparison with results from other studies could have included a statistical assessment.Response:This study had a descriptive observational design. Therefore, we chose to compare the findings of our study with the others in the discussion, punctuating whenever possible, the differences in the characteristics of the compared population such as geographical location and study design. To compare specific measurements of our findings with those of other studies using statistical analysis, this study should be designed for systematic review and meta-analysis, with a review carried out with key terms in a systematic way. In addition, detailed results of specific measurements and variability described in the various studies will be necessary, which is outside the scope of this article.RESPONSE TO REVIEWER #2Reviewer #2: It is a very interesting research and very well presented. Please use the term leishmaniosis, instead of leishmaniasis .Response: Lines 27, 52, 64, 85, and 101. The term \u201cleishmaniasis\u201d was replaced with\u201dleishmaniosis\u201d.My main concern is that you have selected some common and important pathoges to test and if negative you present the dog as a single infection case. However, there are many other important pathogens to be present and contribute. For example sarcoptic mange or worms. I did not see other tests for them. I would suggest to revise the text and title using the phrase certain or common pathogens, which is closer to your work. Also please revise your conclusions accordingly.Response:The text was revised and the term \u201cpathogens\u201d was replaced with \u201ccertain pathogens\u201d, when reffered to the pathogens investigated in this study.Therefore, the following modifications were done:The title of the manuscript was altered to: \u201cFrequency of co-seropositivities for certain pathogens and their relationship with clinical and histopathological changes and parasite load in dogs infected with Leishmania infantum\u201dThe word \u201cpathogens\u201d was replaced with \u201ccertain pathogens\u201d in the following parts of the text:Abstract. Lines 30, 41, 45 and 46.Introduction. Lines 69 and 72.Results. Lines 282, 284, 312, 358, 363, 367, 375 and 395.Discussion. Lines 442, 549 and 602.Legend of S1 Table. Line 816.AttachmentResponse to reviewers_PONE-D-20-37262.docxSubmitted filename: Click here for additional data file. 10 Feb 2021Frequency of co-seropositivities for certain pathogens and their relationship with clinical and histopathological changes and parasite load in dogs infected with Leishmania infantumPONE-D-20-37262R1Dear Dr. Caldas Menezes,We\u2019re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you\u2019ll receive an e-mail detailing the required amendments. When these have been addressed, you\u2019ll receive a formal acceptance letter and your manuscript will be scheduled for publication.http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. 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Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1:\u00a0YesReviewer #3:\u00a0Yes**********6. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1:\u00a0I am very happy to see that the authors have addressed all my comments and made a substantial effort to accommodate my suggestions.Reviewer #3:\u00a0The manuscript PONE-D-20-37262R1 'Frequency of co-seropositivities for certain pathogens and their relationship with clinical and histopathological changes and parasite load in dogs infected with Leishmania infantum' is a well-written and concise manuscript well worth publishing in PLOS ONE. The article presents complex data involving co-infections associated with CanL. The article is very clear and objective and the authors have adequately addressed all comments raised in the previous round of review. This Reviewer has very little else to comment.**********what does this mean?). If published, this will include your full peer review and any attached files.7. PLOS authors have the option to publish the peer review history of their article (If you choose \u201cno\u201d, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #1:\u00a0NoReviewer #3:\u00a0No 22 Feb 2021PONE-D-20-37262R1 Leishmania infantumFrequency of co-seropositivities for certain pathogens and their relationship with clinical and histopathological changes and parasite load in dogs infected with Dear Dr. Menezes:I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. onepress@plos.org.If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. 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+{"text": "Scientific Reports 10.1038/s41598-020-67594-2, published online 07 July 2020Correction to: The original version of this Article contained an error in the title of the paper, where \u201cCRISPR\u201d was incorrectly given as \u201cCRISRP\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "To recognize abnormal electroencephalogram (EEG) signals for epileptics, in this study, we proposed an online selective transfer TSK fuzzy classifier underlying joint distribution adaption and manifold regularization. Compared with most of the existing transfer classifiers, our classifier has its own characteristics: (1) the labeled EEG epochs from the source domain cannot accurately represent the primary EEG epochs in the target domain. Our classifier can make use of very few calibration data in the target domain to induce the target predictive function. (2) A joint distribution adaption is used to minimize the marginal distribution distance and the conditional distribution distance between the source domain and the target domain. (3) Clustering techniques are used to select source domains so that the computational complexity of our classifier is reduced. We construct six transfer scenarios based on the original EEG signals provided by the Bonn University to verify the performance of our classifier and introduce four baselines and a transfer support vector machine (SVM) for benchmarking studies. Experimental results indicate that our classifier wins the best performance and is not very sensitive to its parameters. The maturity of the brain\u2013computer interface (BCI) technology has provided an important channel for the human to use artificial intelligence (AI) to explore the cognitive activities of the brain. For example, many AI methods have been proposed for an intelligent diagnosis of epilepsy instead of neurological physicians through electroencephalogram (EEG) signals  for epilepsy EEG signal recognition. First, it further explores the marginal probability distribution adaption between the source domain and the target domain from two aspects. One is that it additionally introduces conditional probability distribution adaption to further minimize the distribution difference. The second is that it preserves manifold consistency underlying the marginal probability distribution. Second, it can selectively leverage knowledge from multiple source domains.Data and Methods, we give the EEG data and our proposed method. In Results, we report the experimental results. Discussions about experimental results are presented in Discussions, and the whole conclusions are summarized in the last section.The following sections are organized as follows: in In this study, we download very commonly used epilepsy EEGThree feature extraction algorithms, that is, wavelet packet decomposition (WPD) Li, , short-tWavelet Packet DecompositionWavelet packet decomposition is used to extract time-frequency features from epilepsy EEG signals. More specifically, the epilepsy EEG signals are disassembled into six different frequency bands with the Daubechies 4 wavelet coefficients. Each band is considered as one feature. Short-Time Fourier TransformShort-time Fourier transform is used to extract frequency-domain features from epilepsy EEG signals. More specifically, the epilepsy EEG signals are disassembled into different local stationary signal segments, and then the Fourier transform is used to extract a group of spectra of the local segments, which are with evident time-varying characteristics at different times. Finally, six frequency bands are extracted from each group of spectra. Kernel Principal Component AnalysisKernel principal component analysis is used to extract time-domain features from epilepsy EEG signals. More specifically, the Gaussian function is chosen as the kernel to map the original features nonlinearly. Then six kinds of features are selected from the top six PC eigenvectors. We construct six online transfer scenarios from the EEG data after feature extraction . Each scM = 20 subject-specific objects from the target domain. The online calibration flowchart is shown in m0.In general, calibration in BCIs can be divided into two types, that is, offline calibration and online calibration . Lastly, we give the detailed algorithm steps of OS-JDA-MR-T-TSK-FC including how to select source domains.X, P(x)} in the transfer learning or domain adaption scenario consists of a d-dimensional feature space \u2208 Rd and a marginal distribution P(x), and a task \u0393 = {Y, P(y|x)} in the similar scenario consists of a one-dimensional label space Y and a conditional distribution P(y|x), where y \u2208 Y. Suppose that \u03a8s and \u03a8t are two domains derived from \u03a8, they are deemed to be different when Xs \u2260 Xt and/or Ps(x) \u2260 Pt(x). Homoplastically, two tasks \u0393s and \u0393t derived from \u0393 are different when Ys \u2260 Yt and/or Ps(y|x) \u2260 Pt(y|x).A domain \u03a8 = {s having N-labeled EEG epochs t having M-labeled EEG subject-specific epochs s = \u03a8t, Ys = Yt, Ps(x) \u2260 Pt(x), and Ps(y|x) \u2260 Pt(y|x).Based on the above definitions, the target of OS-JDA-MR-T-TSK-FC is to train a predictive function on a source domain \u03a8Online Transfer Learning FrameworkBecause the classic one-order TSK fuzzy classifier (1-TSK-FC)  for an unseen object x is formulated as the following form:k(x) is expressed asif parts, and then parts. Referring to the literature   in (2) as the following form:pg:pg to zero, that is, \u2202Jorder\u2212TSK\u2212FS1\u2212(pg)/\u2202pg = 0, we can compute pg analytically ast in the first term is the overall weights of the specific-subject objects. Generally, \u03c9t should be larger than 1 so that more emphasis is given to objects in \u03a8s than \u03a8t. Therefore, we set \u03c9t to \u03c9t = max. \u03bb1 and \u03bb2 are regularization parameters. The first term contains two parts: the first is to measure the loss on \u03a8s, and the second is to measure the loss in \u03a8t. The second one is the joint distribution adaption term, and the third one is the manifold regularization term. Below, we will explain how to embody them formally.The . et al. . When cju et al.  and Zhanu et al. , we formObjective function of OS-JDA-MR-T-TSK-FCUnder the framework shown in (11), we specify each term to get the objective function of our online transfer TSK fuzzy classifier OS-JDA-MR-T-TSK-FC.s and \u03a8t; hence, the first term in (11) can be formulated asThe squared loss is taken as the loss function to measure the sum of squared training errors on both \u03a8s and \u03a8t are extracted in the same way, the joint distributions  between \u03a8s and \u03a8t are generally different. In order to meet practical requirements, we assume that Ps(x) \u2260 Pt(x) and Ps(y|x) \u2260 Pt(y|x). Therefore, a joint distribution adaptation should be designed to minimize the distribution similarity (distance) D between \u03a8s and \u03a8t.As all we know that even EEG epoch features in \u03a8D between \u03a8s and \u03a8t. As a result, D can be expressed ass,c belongs to \u03a8s and its objects are selected by {xi|xi \u2208 \u03a8s \u2227 yi = c}, and \u03a8t,c belongs to \u03a8t and its objects are selected by {xi|xi \u2208 \u03a8t \u2227 yi = c}, where c means the cth class in one domain. Also, for the source domain, Nc is used to denote the number of objects in the cth class, and for the specific-subject objects in the target domain, Mc is used to denote the number of objects in the cth class. Hence, D can be expressed asc is an MMD matrix defined as follows:D = D+D so that the joint distribution adaptation can be formulated asFirst, the projected MMD  and P(xj), then the corresponding Q(yi|ix) and Q(yj|xj) are considered as being similar. That is to say, for the objects in \u03a8s and the calibration objects in \u03a8t, if they are in a manifold, it is expected that their output  differences should be as small as possible. Therefore, the manifold regularization can be formulated as follows under geodesic smoothness,W = [wij]N+M)\u00d7(N+M)( is the graph affinity matrix in which each element is defined as\u03bd(xi) represents a set of v-nearest neighbors of object xi. L = [lij]N+M)\u00d7(N+M) by setting its derivative w.r.t pg to zero asBy substituting (14), (19), and (20) into our transfer learning framework shown in (12), we can obtain a transfer learning model, that is, OS-JDA-MR-T-TSK-FC asDifferent from most of the existing transfer models, OS-JDA-MR-T-TSK-FC can leverage knowledge from multiple source domains. However, as we know, too many source domains will improve computational complexity. Additionally, some source domains having significant differences with the target domain may bring some negative transfer knowledge. Therefore, according to Wu et al. , we adopvz,c to denote the mean vector of each class in the zth source domain, where z = 1,2,\u2026, Z. Similarly, vt,c is used to denote the mean vector of each class in the target domain. The Euclidean distance between the zth source domain and the target domain can be computed asd, d, \u2026, d} that contains Z domain distances. The distance set then is partitioned by k-means to k groups , and the source domains are selected from the cluster who has the smallest center.We use As a whole, the training of OS-JDA-MR-T-TSK-FC contains three parts: the first one is source domain selection, the second one is model training on a source domain combining with the target domain, and the last is classifier combination. Algorithm 1 shows the detailed training steps of OS-JDA-MR-T-TSK-FC.y from the space R to the space RC by that yij = 1 if y(xi) = j, and yij = 0 otherwise, where i = 1, 2, \u2026, N + M, j = 1, 2, \u2026, C, and C represents the number of classes. Thus, the label space becomes Rd+1 to Rd+1)\u00d7C. Its training set consists of the five source domains directly connected, and its testing set is the target domain. Therefore, BL1 is considered as a calibration-independent classifier, which does not use the subject-specific data in the target domain for training.Baseline 2 (BL2). It uses only subject-specific calibration EEG data in the target domain for training. Its testing set is the unlabeled data in the target domain. Therefore, BL2 is considered as a source domain-independent classifier, which does not consider the EEG data in the source domains at all.Baseline 3 (BL3). BL3 is trained on five training sets, receptively. Each set consisted of a source domain and the subject-specific data in the target domain. The five trained models are finally combined by a weight schema that is also used in Algorithm 1. Its testing set is the unlabeled data in the target domainTransfer support vector machine (TSVM) , \u03bb1, and \u03bb2 that should be fixed before a classification task. So, we should consider the robustness OS-JDA-MR-T-TSK-FC to them. The sensitivity analysis results are shown in From the objective function of OS-JDA-MR-T-TSK-FC, we see that there are three parameters, that is, \u03c9We observe from Moreover, the classification results in M, whereas the other four classifiers depend on M, and it is intuitive that they gradually perform better than BL1 with the increasing of M.BL1 does not use the specific-subject objects, so its accuracy is independent on M is set to 0. But BL1, BL3, TSVM, and OS-JDA-MR-T-TSK-FC can work because, except subject-specific objects, they also leverage training objects from the source domains. Compared with other algorithms, when M is too small, BL2 performs so badly because it cannot get enough training patterns from subject-specific objects.BL2 is only trained by the subject-specific objects. Therefore, BL2 becomes unusable when M is set to 0, TSVM always achieves the best performance. With the subject-specific objects gradually added into the training set, OS-JDA-MR-T-TSK-FC soon performs better than TSVM, which indicates that significant differences exist among the domains. Hence, a domain-dependent classifier, for example, TSVM is not very expected in our online transfer scenarios.When When one batch (four subject-specific objects are taken as a batch in our experiments) or at most two batches of subject-specific objects are added into the training set, the classification performance of OS-JDA-MR-T-TSK-FC becomes stable. That is to say, the number of subject-specific objects OS-JDA-MR-T-TSK-FC needs is very small. So, OS-JDA-MR-T-TSK-FC meets the practical requirements because subject-specific objects are very few in real-world applications.x1 is In addition to classification performance, interpretability is also a main characteristic of the proposed OS-JDA-MR-T-TSK-FC. From If the energy of an EEG signal band (band 1) is \u201chigh,\u201d and the energy of an EEG signal band (band 2) is \u201ca little low,\u201d and the energy of an EEG signal band (band 3) is \u201clow,\u201d and the energy of an EEG signal band (band 4) is \u201clow,\u201d and the energy of an EEG signal band (band 5) is \u201clow,\u201d and the energy of an EEG signal band (band 6) is \u201clow,\u201dthenthe consequent of the first fuzzy rule can be expressed as:x1+0.4452x2\u22120.5342x3+0.2342x4\u22120.9734x5\u22120.3244x6.1 in the range of (Geng et al., 2 in the range of (Ghosh-Dastidar et al., From In this study, we propose a seizure classification model OS-JDA-MR-T-TSK-FC using an online selective transfer TSK fuzzy classifier with a joint distribution adaption and manifold regularization. We use epilepsy EEG signals provided by the University of Bonn as the original data and construct six transfer scenarios in three kinds of feature spaces to demonstrate the promising performance of OS-JDA-MR-T-TSK-FC. We also generate four baselines and introduce a transfer SVM model for fair comparison. The experimental results show that OS-JDA-MR-T-TSK-FC performs better than baselines and the introduced two transfer models. However, in this study, we only consider how to select the source domains. Recent studies show that dynamically selecting useful samples from the source domain can effectively induce the learning on the target domain. Therefore, in our future work, we will try to develop a mechanism, for example, classification error consensus to select most useful samples from the source domain.http://www.meb.unibonn.de/epileptologie/science/physik/eegdata.html.The original EEG data are available in YZ designed the whole algorithm and experiments. ZZ, HB, and WL contributed on code implementation, and LW gave some suggestions to the writing.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Correction to: Modern Pathology10.1038/s41379-019-0359-9This article was erroneously published with standard licence and copyright, but it is in fact published with open access, so has a CC BY licence and the copyright line is \u2018The Author(s)\u2019. This has been updated in the original article."}
+{"text": "Nature Communications 10.1038/s41467-019-13286-z, published online 12 December 2019.Correction to: The original version of this Article contained an error in Fig.\u00a04, in which samples marked with blue dots were labelled with the suffix \u2018WD\u2019 instead of \u2018DD\u2019. This has now been corrected in both the PDF and HTML versions of the Article."}
+{"text": "The  Contingency tables and their analysis are of special importance for various diverse fields, like\u00a0medical sciences, psychology, education, demography and social sciences. In these fields, categorical variables and their cross-classification play a predominant role, since characteristics of interest are often categorical, nominal or most frequently ordinal. For example, diagnostic ratings, strength of opinions or preferences, educational attainments and socioeconomic characteristics are expressed in ordinal scales. The origins of contingency table analysis (CTA) lie back in 1900 with the well-known contributions by Pearson and Yule, while, for the history of CTA before 1900, we refer to the interesting paper by Stigler [of Pardo . For\u00a0logof Pardo .Here, we aim at highlighting a different structural role of els see ,5) while while\u03d5-dThe organization of the paper is as follows. Preliminaries on log-linear models, divergence measures, association and correlation models for two-way tables are provided in X and Y, respectively, where Consider an X and Y /x (cf. ). Settingiven byI\u03d5C=given byI\u03d5C=For nd \u03bb\u2192\u22120,  convergeThe goodness of fit (GOF) of model  is usualsed (see ).In case of ordinal classification variables, the association models (AMs) impose a special structure on the underlying association and thus provide non-saturated models of dependence. AMs are based on scores Usually, the uniform (Linear-by-Linear (LL) AM. In case the vector Row effect (R) AM, while the Column effect (C) AM is defined analogously. Finally, when the row and the column scores are all unknown parameters to be estimated, (multiplicative Row-Column (RC)\u00a0AM. Scores that are unknown need not necessarily to be ordered. Note that models\u00a0LL, R and C are log-linear while the RC is not. The degrees of freedom (Uniform (U) AM.If ed, then  has justunknown, \u00a0is the Rtimated, \u00a0is the mM-th order is defined asM is the rank of In case the RC model is not of adequate fit, multiplicative row-column AMs of higher order can be considered. Such a model of ed model . The sumfined aslogmij=\u03bb+im\u03bdjm in , \u039b=\u03bbijXYman Recall that the e, model  is alterMM, while, for A popular, mainly descriptive method for exploring the pattern of association in contingency tables is correspondence analysis (CA). The detailed discussion of CA is beyond our scope. For this, we refer to the book of Greenacre . Correspstraints  subject  between , expressMpij=pi+p+Mpij=pi+p+M1pij=pi+p+ Goodman .AMs and correlation models were developed competitively and opposed to each other (cf. ), until Under the conditions of , namely aioannou  derived straints  with marthe form\u03c0ij=\u03c0i+\u03c0+ied that  with marstraints\u2211i\u03c0i+\u03b1i=\u2211the form\u03c0ij=\u03c0i+\u03c0+Model , with knegories,\u00a0 becomes fined by  for M=1, models,  simplifiFor the power divergence (for ), model  becomesd Sarkar . Express, model  model\u00a0(The RCrictions  with marM) model\u00a0 is derivgiven by\u03c0ij=\u03c0i+\u03c0+2, model  with \u03bcm=Models  and 21)21) can aFor )=xlogx,  becomes elled in  and fromRemark\u00a01.Kateri and Papaioannou  studied In order to understand the role and nature of the scaled measures of local association , one canis case,  becomes ization,  for I=J=d Kateri . For theratio CI . Here, tRemark\u00a02.The idea of viewing a model as a departure from a parsimonious reference model, with the property of being the closest to this reference model under certain conditions in terms of the KL divergence, can be adopted for other types of models as well, such as the quasi symmetry (QS) model and the logistic regression, lightening thus a different interpretational aspect of these models. Substitution of the KL divergence by the \u03d5-divergence, leads further, in an analogous manner to AMs, to the derivation of generalized \u03d5-divergence based classes of QS models , ordinalWe shall focus on the case of uniform local association and the corresponding fined by  or 22)  \u03d5 divergfined by . Model Umpare to  for the mphR-package. The standard U model, denoted in the sequel as UR for the example of R-function for constructing the design matrix The MLEs of the marginal probabilities are the corresponding marginal sample proportions ) models . It is s) models . In pracression2L(mv)=Cloression2L(mv)=ClopressionL(mv)=CloUnder Ursion of , is giver is the sample correlation between the row and column scores (compare to (Another option ismeasures . For thetimators  and 29)(29)\u03b8\u00af(\u03d5)stimator  takes thmpare to ).Under the Udel (see  and Sectdel (see ).Remark\u00a03.For model UTomizawa  proposed Salicr\u00fa  extendedTomizawa  as well Remark\u00a04.For square contingency tables with commensurable classification variables, analogous to the measure of departure from Ua et al.  introduca et al.  a measura et al.  extendeda et al. ,24 is alWe revisit a classical data set of Grizzle , providedel see ,19). Our. Our0 model (see  and prov [0 (see ). The maThe stimates  for TablWe observe that all considered U not see . The\u00a0maxObserve in  that theWe revealed the role of Crucial quantities are the  Agresti .It is important to realize that, due to the scale difference, The conditional test of independence  can be btel (see ). It con also of , is inteR-package mph.Throughout this paper, we assumed a multinomial sampling scheme. For the models considered here, the other two classical sampling schemes for contingency tables  are inferentially equivalent. Furthermore, for ease of presentation, we restricted here to two-way tables. The proposed models extend straightforwardly to multi-way tables. For\u00a0two- or higher-dimensional tables, the subset of models that are linear in their parameters  models  and can"}
+{"text": "Saccharomyces cerevisiae plays an important role in nutrient storage. Arginine, in particular, accumulates in the vacuole of nitrogen-replete cells and is mobilized to the cytosol under nitrogen starvation. The arginine import and export systems involved remain poorly characterized, however. Furthermore, how their activity is coordinated by nitrogen remains unknown. Here we characterize Vsb1 as a novel vacuolar membrane protein of the APC (amino acid-polyamine-organocation) transporter superfamily which, in nitrogen-replete cells, is essential to active uptake and storage of arginine into the vacuole. A shift to nitrogen starvation causes apparent inhibition of Vsb1-dependent activity and mobilization of stored vacuolar arginine to the cytosol. We further show that this arginine export involves Ypq2, a vacuolar protein homologous to the human lysosomal cationic amino acid exporter PQLC2 and whose activity is detected only in nitrogen-starved cells. Our study unravels the main arginine import and export systems of the yeast vacuole and suggests that they are inversely regulated by nitrogen.The vacuole of the yeast  Saccharomyces cerevisiae is an important storage compartment for diverse nutrients, including the cationic amino acid arginine, which accumulates at high concentrations in this organelle in nitrogen-replete cells. When these cells are transferred to a nitrogen-free medium, vacuolar arginine is mobilized to the cytosol, where it is used as an alternative nitrogen source to sustain growth. Although this phenomenon has been observed since the 1980s, the identity of the vacuolar transporters involved in the accumulation and the mobilization of arginine is not well established, and whether these processes are regulated according to nutritional cues remains unknown. In this study, we exploited in vitro and in vivo uptake assays in vacuoles to identify and characterize Vsb1 and Ypq2 as vacuolar membrane proteins mediating import and export of arginine, respectively. We further provide evidence that Vsb1 and Ypq2 are inversely regulated according to the nitrogen status of the cell. Our study sheds new light on the poorly studied topic of the diversity and metabolic control of vacuolar transporters. It also raises novel questions about the molecular mechanisms underlying their coordinated regulation and, by extension, the regulation of lysosomal transporters in human cells.The lysosome-like vacuole of the yeast  Saccharomyces cerevisiae is the counterpart of the lysosome and has proved to be a valuable model for studying this organelle Please let us know if you have any questions while making these revisions.Yours sincerely,Widmar TannerGuest EditorPLOS GeneticsGregory P. CopenhaverEditor-in-ChiefPLOS GeneticsConcerning the aspects reviewer 2 raised as major concerns, it would suffice if the authors state more clearly that they present no direct evidence for the genes under discussion representing transport proteins.Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: This is a description of a well carried out study of how vacuoles help cells store and mobilize organic nitrogen. Two important gene-function relationships are identified, and kinetics and/or other important characteristics of their encoded transporters are described. Furthermore, the authors show the nitrogen status to have strong regulatory effects on the two transporters in a way that makes biological sense, although the mechanisms are yet obscure.The manuscript is also well-written, creating a flow where generally the results from one experiment suggest questions that are addressed in the next one. This makes it easy and pleasant to read.I have one general comment. The exchange function of Ypq2 is pointed out in a slightly wrong way. At places, the reader will think that Ypq2 has two states, one in which it is a uniporter and another where it exchanges molecules; that is in my view unlikely and would be a complicated assumption. All observations agree with the highly efficient exchange reaction being a side reaction that will always take place when there is Arg on both sides. It requires no energy, and there is no reason to think that it has any important biological consequence. Such exchange is also named counterflow and is a priori expected to be very commonly occurring. Let us assume that the function important for fitness in nature is uniport (export in the case of Ypq2) function and not exchange. All you need to explain the occurrence of a much higher rate of exchange than rate of net transport is a kinetic bottleneck in the conformational shift of the transporter without ligand between the inward-open conformation and the outward-open conformation. Such bottlenecks should a priori be expected to commonly arise in evolution on a seemingly random basis in various steps of transport cycles including the conformational shift mentioned, and indeed counterflow is often found in transporters when it is looked for, also when it has no apparent biological significance. Not only uniporters exhibit counterflow; good old LacY also has it  Lessons from lactose permease. Annu Rev Biophys Biomol Struct 35:67\u201391). I encourage you to state this or parts of it, perhaps in the Discussion. I have below indicated a few places in the manuscript where changes should be made with this view; there may be others. Nevertheless, I fully agree that the exchange function is an important part of the story that contributes to the flow guiding the reader.I have many minor comments:P1 Italicize \u201cVSB1\u201d.Line 4 Consider changing \u201c, and\u201d into a semicolon.15 Insert a comma after \u201cnutrients\u201d and another one after \u201carginine\u201d, in both cases to indicate a non-defining relation.76 Change \u201cVTC\u201d into \u201cvacuolar transporter chaperone (VTC)\u201d.77 Change \u201cmM)\u201d into \u201cmM phosphate groups)\u201d.103 Consider changing \u201cseemed\u201d into \u201cappeared\u201d.125 I suggest changing \u201care\u201d into \u201cappear\u201d, since the experiments described immediately above concern a single amino acid only.136-140 First, you do not at this point of the story need to indicate one interpretation as being simpler than others. Second, if you wish to list possible explanations here, you need to mention a third, and in my mind even simpler, possible explanation, namely the one you reach later in the manuscript: [14C]Arg uptake can take place through Ypq2 by exchange with intravacuolar amino acid(s).149 Change \u201cw-t\u201d into \u201cw-t (23344c)\u201d here and perhaps other places.171 Change \u201cUnsurprisingly, cold\u201d into \u201cAs expected, non-radioactive\u201d in order to make text understandable to readers unfamiliar to the convention \u201chot\u201d-\u201ccold\u201d. Furthermore, change \u201cneutral amino acids such as\u201d into \u201cthe neutral amino acids\u201d. I agree that it is likely that other neutral amino acids behave the same, but you should not conclude it unless of course you tried them, in which case you should describe it.180 and 205 Insert \u201cprimarily\u201d or \u201cmainly\u201d after \u201cis\u201d.191 Change \u201cpreviously described,\u201d into \u201cdescribed for intact vacuoles,\u201d.199 Change \u201cnot.\u201d into \u201cnot, although ATP stimulated the uptake.\u201d.204 Insert \u201cinto vacuole-derived vesicles\u201d after \u201cuptake\u201d.210-212 This is an overstatement. Instead, it would be correct to say \u201cAppreciable Ypq2 activity does require, however, the presence of at least one of its substrates inside the vacuole, since little 14C-Arg was taken up by vacuolar vesicles devoid of Arg or His .\u201d, of course with \u201c14\u201d in superscript.213-215 This is also an overstatement; it gives a wrong impression of the content of the three references given. None of the two first references mention a switch. In each case, a mitochondrial carrier is described which has a high kcat for exchange and a much lower yet significant kcat for uniporter activity. It is expected, and not a consequence of a shift of mechanism, that the relative significance of the latter becomes larger when the concentration ratio across the membrane increases. The third reference, on GLUT1, does describe a switch, but also in this case is the statement misleading. The effect of lowering the external glucose concentration has a large delay and occurs indirectly via the ATP/AMP energy system, a fact that in my view makes this reference less relevant; there is nothing that points to a similar mechanism for Ypq2. Most unprepared readers who do not read the three cited papers will erroneously think that the papers show cases where a high concentration ratio of a ligand (transport substrate) directly causes a change of transporter mechanism. This is not so; in references 30 and 31 one just sees a consequence of different experiments emphasizing different capabilities of the protein in question. The wording must be corrected, see my general comment and e.g. my comment to line 977.223-225 Modify wording. I do not see that the hypothetical pH profile itself argues for the model, but it is indeed important to point out as an explanation for the effect of ATP, based on evolutionary considerations. I agree that, otherwise, readers might at this point think that the effect of ATP suggests that the pmf can drive transport through Ypq2, which I also agree appears unlikely.261 Insert \u201cthan\u201d after \u201cmore\u201d.297 I encourage you to reserve the name with SGD.457 Consider changing \u201cour observations show\u201d into \u201cwe find\u201d; the first could to some readers mean all observations described in the manuscript.461 Consider changing \u201cis\u201d into \u201cshows up as\u201d.533 Make \u201c4\u201d subscript.595 \u201cadopt\u201d is misleading, see my general comment, and reconsider reference 32, see my comment to lines 213-215.600 Also here, please rephrase slightly and avoid \u201cswitch\u201d.611 Insert \u201cthe\u201d before \u201cprotein\u201d.657-659 The nomenclature for PS buffer must be clarified. Strictly interpreted, the layer e.g. immediately over the lysate should contain 15+8 percent Ficoll, but I think it only contains 8.665 Change \u201cO\u201d to lower case, italic, since it means ortho; otherwise some readers will think it refers to binding to an oxygen atom. Another common name that you can choose is 1,10-phenanthroline. You can also add a vendor or producer and a catalog number.669 and 996 Insert comma before \u201cand\u201d, since a new independent sentence starts.691 Consider changing \u201cCorrected for\u201d into \u201cnormalized to\u201d.704-705 Specify the scintillation liquid. Counting efficiency depends on the identity of the scintillation liquid, the sample solvent, and the mixing ratio.736 Change \u201cm\u201d into \u201cnm\u201d.804 Delete \u201c (80-)\u201d.819 Change \u201cenzymology\u201d into \u201cEnzymology\u201d, and consider changing \u201c177-96 p\u201d into \u201cpp 177-96\u201d. Check full reference list for similar cases.821 Change \u201cVacuolar\u201d into \u201cvacuolar\u201d and \u201cCellular\u201d into \u201ccellular\u201d. Check full reference list for similar cases.831 Make the \u201c+\u201d superscript. Check full reference list for other cases of possible subscripts and superscripts.955 Change \u201cArg uptake into\u201d into \u201cArg uptake through Ypq2 into isolated\u201d.955-957 Specify in this experiment whether ATP was present or absent.956-957 and 959 Change \u201c (see text for the strains used)\u201d into \u201c. Values for the ypq1-2-3\u0394 strain were subtracted from those for the ypq1-3\u0394 strain\u201d, of course with the genotypes in italics.958 Insert \u201cof Ypq2\u201d after \u201cselectivity\u201d.963 Change \u201cVacuoles were\u201d into \u201cVesicles were\u201d.965, 1049, 1052 and 1069 and Table 1 header: Make \u201c14\u201d superscript.967, 971, 1007, 1010 and 1046 Change \u201cctrl\u201d into \u201cCtrl\u201d.967, 971, 1008 and 1011 Consider changing \u201ccold\u201d into \u201cnon-radioactive\u201d.977 Change \u201cYpq2 switches into an exchange mode of transport\u201d into \u201cexchange will dominate, and net transport will slowly cease\u201d.1025 Change \u201cw-t and vsb1\u0394\u201d into \u201cw-t (SL073) and vsb1\u0394 (SL074)\u201d.1032 Change \u201cctrl\u201d into \u201ccontrol (Ctrl)\u201d or \u201cuntreated (Ctrl)\u201d.1085 Insert space between number and unit. Check full manuscript for similar cases.Figures: In micrograph panels, either insert an indicated 10-micrometer bar (one per figure is sufficient) or indicate the length of sides of the panels.Fig. 1A: Explain in the legend the scissors depicted in right panel.Fig. 4A: Please delete this. The text is easy to understand by itself and can even be improved, and the two drawings make more confusion than explanation. There are at least two problems with them. First, the exchange reaction has no consequence on any concentrations; it is the uniporter function for both directions that assures that an equilibrium is approached. Second, the membrane potential and the negative charges of the polyphosphates make it unlikely that a cation like Arg will have the same concentration on both sides at equilibrium.Fig. 4C: The ordinate axis of the right panel needs some explanation for non-experts on survival curves to understand. Move, e.g., the explanation on s from Materials and methods to the figure legend.Fig.5A: Most genotype designations here end correctly with a delta, and that was intended also under the rightmost open bar. However, on my screen the character is erroneously a framed cross.Fig. 5D: This is the first time the authors present CMAC. A brief explanation, at least of the purpose and principle, is needed in the legend.Reviewer #2: The manuscript from Cools et al. focuses on the principal proteins that control arginine transport from and to the vacuoles in yeast, and provide evidence that this transport is regulated by nutrient requirements of the cell. The authors identify a novel vacuolar transmembrane protein, Vsb1, and provide compelling evidence that Vsb1 is as a major contributor to drive arginine transport into the vacuole. The authors also address the role of another transporter, Ypq2, a previously described exchanger of arginine  at the vacuole. The authors propose a model where Vsb1 imports arginine to the vacuole under nutrient rich conditions, and Ypq2 mediates the export to the cytosol during nitrogen starvation.The authors present an overall convincing and elaborate study. They show by an elegant assay the contribution of each transporter to arginine uptake into the vacuole in vivo. Their method is based on the selective permeabilization of the plasma membrane followed by the osmotic rupture of the vacuole, thus allowing the recovery of the cytoplasmic and vacuolar pools of arginine.Although the authors propose that Vsb1 is the main transporter of arginine import into the vacuole, they were not able to demonstrate Vsb1-dependent transport in vitro or its transport activity per se. Similarly, they propose that Ypq2 acts as an exporter  during starvation conditions, yet they only show impaired uptake if the protein is deleted. Direct transport activity of these proteins by reconstitution was not shown, though also admitted by the authors. It is important to note that measurements in the Wiemken and collaborators study, as also in this work includes the whole set of transporters at the vacuole, so it is difficult to assign the observed exchange rates to only one transporter My major concerns are listed below:1. The authors claim that Ypq2 is a transporter (Lines 177-179); however, neither they nor others have shown direct activity of this protein, they probe activity in system (intact vacuoles) containing all or most of vacuolar protein. It would be important to stress this in their manuscript.2. Along the same line, the authors show that Ypq2-dependent uptake is dependent on the intra-vacuolar concentration of arginine  and propose that transport is bidirectional, and only unidirectional during starvation, although this was not assessed. Interestingly, they are able to detect activity even in the control condition that, although it is low, it is still stimulated by ATP. Can the authors rule out that the proposed exchange reaction is carried out by more than one transporter and that Ypq2 is rather the importer?3. The authors propose that Ypq2 would mobilize Arg from the vacuole to the cytosol during nitrogen starvation . They convincingly show that Ypq2 is required for intracellular consumption of arginine during starvation; however, they do not show direct Ypq2-dependet export from the vacuole. To address this a bit more directly, the authors could measure the efflux of radioactive arginine that was previously incorporated into vacuoles before to demonstrate Ypq2-dependent export of this amino acid. Additionally, the export could be assessed under conditions of nutrient rich and starvation conditions.4. The assumption that Ypq proteins are arginine transporters seem to be supported by the fact they homologues to the PLQ2 mammalian transporter. For PLQ2 it has been shown that mutation in P55 abolished arginine uptake. To demonstrate homologous activity, the authors could mutate the equivalent position in Ypq2 to test if the mutant is able or not to rescue the uptake phenotype they observe.5. The authors claim that Vsb1 is a transporter, but do not show transporter activity. Although I do not expect them to demonstrate activity in vitro, I find it important that they remain cautious with their interpretation as also in their statements along the manuscript, as they refer to this protein as an essential transporter.6. Figure 7: The analysis using bafilomicin A was performed in wt cells, so it is difficult to claim that the block in V-ATPase function specifically affects the activity of Vsb1. Please rephrase.7. Along their entire manuscript the authors mix up a few things in my view. They observe under different conditions (N-depleted/repleted) different requirements of their transporters, and do so by comparing deletion mutants with wild-type. They then conclude that each of the transporters is regulated (in abstract and throughout the manuscript). However, they have no evidence at all that this is the case. Results from Figure 8 do not strictly show that these proteins are inactive in each condition, they are just not required. I agree that nitrogen regulation may be likely, but they do not show regulation of either transporter, and they should thus rephrase these passages accordingly.8. I found the entire discussion too long and too excessive. The repeat many aspects of their results section. I recommend to condense it strongly (by \u00bd) to make to more accessible.Minor issues:1. Line 124: \u201c\u2026the intact yeast vacuoles isolated via the above methods\u2026\u201d. The authors refer to the \u201cabove methods\u201d as if they would explain them, but they do not describe the isolation method itself, so it would be suitable to say \u201cour method\u201d or \u201cthe used method\u201d.2 .Paragraph between lines 112-115 can be interpreted as they could not establish the pH measurement when incubated with the inhibitor. \u201c the pH measured in isolated vacuoles became more acidic in the presence of ATP , this acidification was partially lost upon addition of the K+/H+ ionophore nigericin, and it could not be established if the vacuoles were pre-incubated with the V-ATPase inhibitor bafilomycin A \u201d3. Figure 7C: It would be helpful for readers if the authors name of the protein fused to GFP (Can1) also in the figure.4. Many experiments have been repeated only twice. Particularly, Figures 3B and 6D show the same control condition but the effect of ATP is only evidenced in Fig 3B. In this case as in other in which the n=2, at least 3 repeats should be included.**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: Yes**********what does this mean?). 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PLOS Genetics may also choose to issue a press release for your article. If there's anything the journal should know or you'd like more information, please get in touch via  4 Aug 2020PGENETICS-D-20-00303R1 Nitrogen coordinated import and export of arginine across the yeast vacuolar membrane Dear Dr Andr\u00e9, We are pleased to inform you that your manuscript entitled \"Nitrogen coordinated import and export of arginine across the yeast vacuolar membrane\" has been formally accepted for publication in PLOS Genetics! Your manuscript is now with our production department and you will be notified of the publication date in due course.The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. 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+{"text": "Critical Care [We have read with attention the commentary from von D\u00fcring et al. questioning our research letter on safe doubling of ventilator capacity recently published in cal Care . Our pubIn fact, we argue for the idea of ventilating two patients with a single ventilator, not against. This is a serious misunderstanding of our work proposing a safe way to ventilate two patients at once, so as von D\u00fcring et al. note, a second life can be saved.in-series (one-after-the-other) breathing circuit (Fig.\u00a0We proposed a safe, innovative method based on a simple uit Fig.\u00a0. It direWhile we agree with von D\u00fcring et al. when they say \u201cThe objective of ventilator sharing is to save a second life by buying time to find a second ventilator\u201d , but we safe last resort proposal for last resorts, rather than a desperate measure.So yes, we believe our in-series setup is a"}
+{"text": "The details of the folding mechanisms have not yet been fully understood for many proteins, and it is believed that the information on the folding mechanism of a protein is encoded in its amino acid sequence. \u03b2-trefoil proteins are known to have the same 3D scaffold, namely, a three-fold symmetric scaffold, despite the proteins\u2019 low sequence identity among superfamilies. In this study, we extract an initial folding unit from the amino acid sequences of irregular \u03b2-trefoil proteins by constructing an average distance map (ADM) and utilizing inter-residue average distance statistics to determine the relative contact frequencies for residue pairs in terms of F values. We compare our sequence-based prediction results with the packing between hydrophobic residues in native 3D structures and a G\u014d-model simulation.The ADM and F-value analyses predict that the N-terminal and C-terminal regions are compact and that the hydrophobic residues at the central region can be regarded as an interaction center with other residues. These results correspond well to those of the G\u014d-model simulations. Moreover, our results indicate that the irregular parts in the \u03b2-trefoil proteins do not hinder the protein formation. Conserved hydrophobic residues on the \u03b25 strand are always the interaction center of packing between the conserved hydrophobic residues in both regular and irregular \u03b2-trefoil proteins.We revealed that the \u03b25 strand plays an important role in \u03b2-trefoil protein structure construction. The sequence-based methods used in this study can extract the protein folding information from only amino acid sequence data, and well corresponded to 3D structure-based G\u014d-model simulation and available experimental results. A \u03b2-trefoil protein exhibits pseudo three-fold symmetry and is observed widely in the protein 3D structure space. We show the 3D structure and schematic drawings of the three symmetrical units of cytokine (2K8R) as a representative \u03b2-trefoil protein in Fig.\u00a0In the present study, we investigate the relationship between the folding mechanisms of \u03b2-trefoil proteins with irregular structures and their amino acid sequences. We utilize the same techniques as in our previous study,  in whichWe also focus on the hydrophobic packing formed by conserved hydrophobic residues in the native structures and compare the packing hydrophobic residues and the residues significant in folding. To confirm the results that we predict from the amino acid sequence information, we conduct G\u014d-model simulations. From the results obtained, we identify the residues significant for irregular \u03b2-trefoil proteins to fold into the 3D structures.In the present study, we apply the coarse-grained G\u014d model which we have developed \u201315. Thishttps://www.rcsb.org/) [Clostridium sp. While 1TTU was detected in transparent nematode, Caenorhabditis elegans, which classified as a part of CSL protein and associated with cell to cell communication. These four 3D structures are illustrated in Fig.\u00a0In our previous study, we examined regularly structured single-domain proteins of up to 180 residues. That is, we excluded proteins in the STI-like, DNA-binding protein LAG-1 (CSL), and Agglutinin superfamilies. In this study, we selected trefoil proteins containing approximately 180 residues with irregular structures (due to insertion or deletion) from either the STI-like superfamily and the DNA-binding protein LAG-1 (CSL) superfamily: Tetanus toxin (PDB ID (sb.org/) : 1A8D), sb.org/) \u201328. The An average distance map (ADM) is a kind of predicted contact map constructed from the inter-residue average distance statistics, which is created using only the amino acid sequence information of a protein. This method was originally developed to predict the location of structural domains in a protein . The metThe inter-residue average distance for a pair of residues refers to the inter-C\u03b1 atomic distance between these residues. Every pair of amino acid type were considered in the calculations of the inter-residue average distances. The separation of the two residues along the amino acid sequence of a protein was considered in calculating the average distance of a residue pair. This separation is called the \u201crange\u201d. The ranges are defined as follows: M\u2009=\u20091 when 1\u2009\u2264\u2009k\u2009\u2264\u20098, M\u2009=\u20092 when 9\u2009\u2264\u2009k\u2009\u2264\u200920, M\u2009=\u20093 when 21\u2009\u2264\u2009k\u2009\u2264\u200930, M\u2009=\u20094 when 31\u2009\u2264\u2009k\u2009\u2264\u200940, and so on, where k\u2009=\u2009|i - j| and M is a range. That is, in each range, the average distances for all pairs of all amino acid types were calculated. Let d be the average distance of amino acid types A and B in the range M.t, P(M)c, and D are the total number of residue pairs with statistically significant average distances, [c is the number of residue pairs with statistically significant average distances smaller than the cutoff distance for M, and D is an adjustable parameter that provides the average plot density of the corresponding ADM close to that of the contact map constructed based on the spatial distances calculated from the actual 3D structure of a protein , respectively. The average plot density is approximated by the following formula: [When d is less than the cutoff distance previously determined for the range M, a plot is made on the map. The set of cutoff distances for the ranges is defined by the following equation:stances,  P(M)c isformula: .2\\docum\u03c1av when we use C\u2009=\u200936.12 [c. Thus, a map is derived from only the amino acid sequence of a protein based on the inter-residue average distance statistics.Here, N is the total number of residues in a protein and C is the constant value derived from our previous study . The plo\u2009=\u200936.12 . To cons\u2206\u03c1i are estimated from residue 1 to the total number of residues in a given protein. The plots obtained by the line parallel to the x-axis are called vertical scanning, and those obtained by the line parallel to the y-axis is called horizontal scanning. The v of With the constructed ADM for a given protein, a compact region in the protein is predicted as follows. First, the plot density differences in the map are calculated. A density difference means the difference in plot density values between the triangular and trapezoidal parts of the ADM, The detection of a compact region\u2019s boundaries is made based on s of m-p .A region with a high density of plots, with a high \u019e value, is regarded as a predicted compact region in a 3D structure. We also regard the predicted region as compact in the early stage of folding.Multiple sequence alignment provides valuable information about many protein characteristics, including conserved regions which might be related to 3D structure or functional property.In general, the sequence identities of \u03b2-trefoil proteins from different superfamilies are relatively low, making accurate multiple alignments based on only sequences difficult. To detect the relationships among sequences with relatively low sequence identity, this study utilized a multiple sequence alignment technique using secondary structure information, the Combinatorial Extension  program Sequence conservation is provided by evolutionary pressure to maintain a given structure and/or structure functions , 33. In The similarity of the location of the predicted compact regions can be regarded as conservation of the predicted compact regions during molecular evolution. A multiple sequence alignment is used to define the conservation of the regions predicted by the ADMs. The procedure is as follows.The number of residues at a given site that are commonly included in the predicted compact regions is counted to calculate the conserved ratio . We then make a histogram of this ratio versus the site number. A region covering several residues with high ratios denotes a conserved predicted compact region during evolution. Currently, the predicted compact regions are regarded as being conserved when the conservation ratios exceed 70% in the same position of the aligned samples .i,j derived from average distance \u00afri,j and its standard deviation \u03c3i,j, was employed in a simulation of protein conformations. The bond and dihedral angles of the initial conformation were randomly selected. During a simulation, the bond and dihedral angles between the residue i and i\u2009+\u20091 are bent and rotated randomly. That is, a simulation is performed starting from a totally random distribution and the restrictions derived from the average distance statistics. The alteration of all the bond and dihedral angles is included in one MC step followed by the Metropolis judgment. We made an assumption that density of the potential between two residues, An effective inter-residue potential can be derived from the present inter-residue average distance statistics. In order to analyze the initial folding process of a protein, we performed conformational sampling of a protein in a random state, that is, no secondary or tertiary structure formed, with this potential to identify a residue where initial folding events, such as hydrophobic collapse, occurs . A modelwhere this equation is expressed by Eq. We obtain Eqs. where kT is set so that the MC acceptance ratio is 0.5. The obtained potential is a harmonic potential to reproduce average distances and standard deviations in the statistics. The significant value in a calculation is the difference between the energy values of conformations, and Z does not appear in the calculation explicitly. Thus, we ignored Z in the calculations.It is expected that ensembles with reproducible inter-residue average distance statistics using this potential can be obtained. The contact frequency, g, for each pair of residues is estimated with structures generated from a simulation using the potential energy function. Then the residue contact frequency, g, in the same range M is normalized, that is, the value corresponding to the z-value in statistical theory. We refer this value as Q. Here, D(M) is the standard deviation of the contact frequency g with two residues separated in range M. These are expressed by Eq. where i and j are the residue numbers.i, by summing the normalized contact frequencies, Q, from j\u2009=\u20091 to N for each residue i, where N is the total number of residues:Finally, we obtain the relative contact frequency, Fi the \u201cF value\u201d. Residues at the peaks in the plot of F values are expected to be located in the center of many inter-residue contacts, such as a hydrophobic cluster. A region near a peak (within \u00b1 5 residues) [Fcut) as presented in Eq. We call the value Fesidues)  of an F-i is the F value of residue i and N is the total residue number, this residue is defined as a peak.where FIt has been confirmed for several proteins \u20138, 12 thA G\u014d model technique has been applied widely to the folding simulation of a protein \u201315, 34. The potential energy of a structure \u0393 is defined by Eq. ij, NC, and NNC indicate the bond angle, dihedral angle, inter-residue distance, native contacts, and non-native contacts, respectively. The subscript 0 refers to the values related to the native structure. We use the parameters, K\u03b8\u2009=\u200920\u03b5, ij corresponds to the number of inter-heavy atom contacts divided by the average number of inter-heavy atom contacts per residue pair; it indicates the strength of the scaled inter-residue interactions. Bij (\u0398ij), which is defined by Eqs. The first, second, third, and fourth terms correspond to the energies of the bond angle, dihedral angle, native interactions, and non-native interactions, respectively. \u03b8, \u03d5, r\u2009+\u20091.4\u2009\u00c5 . The locmentclasspt{minimaij indicates the relative orientation of the side chains of the i-th and j-th residues implicitly, namely, the relative angle between hi and hj. hi is defined as ri, i\u2009\u2212\u20091\u2009+\u2009ri, i\u2009+\u20091, and ri, i\u2009\u2212\u20091 denotes a vector between the i-th and (i\u2009-\u20091) th residues. hi is used to define a bond vector mimicking the C\u03b2-C\u03b1 vector in the combination of ri, i\u2009\u2212\u20091\u2009\u00d7\u2009ri, i\u2009+\u20091 [ij is close to the native value, Bij\u2009~\u20091, the residues make a contact. When \u0398ij exceeds a cutoff value, Bij ~\u20090, the residues cannot make a contact. A cutoff value a\u0398\u2009=\u20090.6\u03c0 was used [Bij\u2009=\u20091 because we cannot define the vector hi. We keep \u03b8\u2009<\u2009\u03c0 to prevent hi\u2009=\u20090.\u0398i, i\u2009+\u20091 . When \u0398iwas used . For theA replica exchange MC simulation was used in the present study . M iteraIn this study, an order parameter indicating the closeness of a sampled structure to the native structure of a protein is defined by the following equation.The structural features of sampled structures with a specific Q are expressed using a contact frequency map. A contact frequency map is constructed by plotting the contact frequencies of various pairs of residues on a contact map. Thus, a contact frequency map shows the features of an intermediate state during folding.Figure\u00a0The result of the ADM analysis of 1A8D is shown in Fig.\u00a0The peaks of the F-value plot appear near \u03b25-\u03b26 and \u03b27 as shown in Fig.\u00a0Figure\u00a0Figure As is common with the proteins in the STI-like superfamily, the ADM predicted regions at N-terminus and C-terminus correspond well to the N-terminal and C-terminal trefoil units in each of the three proteins. The results of the present study show a remarkable correspondence of the ADM predicted regions at the N-terminus and C-terminus with those predicted in the previous study . As mentFigure Next, we analyze the hydrophobic packing among CHRs in a protein based on its 3D structure. In particular, we analyze how CHRs near the peaks of the F-value plot form hydrophobic packing in the native structure of a protein. First of all, three proteins in the STI-like superfamily are treated. Figure\u00a0The F-value plot for 1EPW shows the highest peak at a residue in \u03b25. Figure In the 3D structure of 3BTA, CHR-\u03b25C interacts with CHR-\u03b24N and CHR-\u03b24C in the predicted region-2, as shown in Fig.\u00a0There are 26 common contacts formed by CHRs in three proteins of the STI-like superfamily. Figure\u00a0In the case of 1TTU, as shown in Fig. Let us compare the hydrophobic packing in the symmetric \u03b2-trefoil proteins with that in the proteins with irregular structures Fig. b. The coIt is interesting to see the interaction between CHR-\u03b26 and CHR-\u03b27 conserved in 26 \u03b2-trefoil proteins with the high symmetry structures and three STI-like superfamily proteins. However, this packing disappears in 1TTU because \u03b27 is missing. Instead of this packing, a new interaction between CHR-\u03b26 and CHR-\u03b210 is observed. It is thought that this interaction between CHR-\u03b26 and CHR-\u03b210 in 1TTU compensates for the missing interaction between CHR-\u03b26 and CHR-\u03b28.In this section, we present the results of the G\u014d-model simulations. Figure\u00a0Next, we present the result of G\u014d-model simulation for 1A8D. In Fig. The second transition state presents at Q\u2009=\u20090.4. From the observation of the contacts at Q\u2009=\u20090.4, the CHRs in trefoil unit-2 tend to form contacts with the CHRs in trefoil unit-1 and unit-3 rather than within trefoil unit-2.In the present study, the folding initiation sites in the \u03b2-trefoil proteins with irregular structures were predicted from their amino acid sequences and further analyses were made regarding the packing formed by CHRs based on the 3D structures. These results were verified by G\u014d-model simulations. As a result, CHRs in the central trefoil unit with high F-value peaks interact with CHRs within the trefoil unit and with CHRs in other trefoil units, followed by the stabilization and structural formation of ADM-predicted regions corresponding to the N-terminal and C-terminal trefoil units. For example, in the folding of 1A8D, the hydrophobic packing formed by CHRs in the ADM-predicted region-1 (\u03b21-\u03b24) and region-3 (\u03b210-\u03b212) play significant roles in forming the N-terminal and C-terminal units, respectively, as indicated in Fig. These facts suggest that the information about the initial stage of folding of a protein can be extracted from its sequence by ADMs and F-value analyses. A G\u014d-model simulation in the present study demonstrates that CHRs that form contacts are mainly within an ADM-predicted region in the early stage of folding. These CHRs are located around F-value peaks. Contacts by CHRs between ADM-predicted regions start to form with increasing Q value, as is the case for 1A8D in Fig.\u00a0As an attempt, we perform the predictions of disordered regions based on our new technique . The resIn this study, the common 14 contacts formed by CHRs in the \u03b2-trefoil proteins with high symmetry could be defined. According to this result, 11 of the 14 common contacts are also observed in the \u03b2-trefoil proteins with irregular structures. Thus, these 11 contacts seem to be especially significant in the formation of the \u03b2-trefoil scaffold. Two of four deficient contacts, namely, the contacts between \u03b26 and \u03b27 and between \u03b27 and \u03b210, are caused by the deficiency of \u03b27 in 1TTU. The corresponding contacts are observed in the other three proteins, that is, 1A8D, 1EPW, and 3BTA. These corresponding contacts seem to be significant but not indispensable for \u03b2-trefoil structure formation. The other contact between \u03b26 and \u03b28 is not observed in 3BTA and 1TTU. It should be noted that the residues corresponding to this contact pair are close to each other in 3BTA. In 1TTU, these corresponding two residues are located within three residues along the sequence. Therefore, we do not take these two residues into account.In the three STI-like superfamily proteins, the ADM-predicted regions always contain the insertion parts, suggesting that this insertion does not disturb the N-terminal trefoil-unit formation. In the G\u014d-model simulations, some contacts formed by the residues in the insertion part are observed in the early stage of folding (Q\u2009=\u20090.2).The native contacts in 1TTU show that \u03b26 interacts with \u03b210 in the C-terminal side Fig. . This coIn the present study, the results from G\u014d-model simulations coincide well with the predictions made by the ADMs and F-value analyses based on the amino acid sequence information. ADMs and F-value analyses can decode the folding information from the amino acid sequences of not only the \u03b2-trefoil proteins with high symmetry but also of those with irregular structures.Finally, we mention that we are currently thinking to make a webserver to perform present analyses for various proteins in near future.The present study demonstrates that the ADM-predicted regions in the N-terminal and C-terminal parts correspond well to the N-terminal and C-terminal \u03b2-trefoil units of a \u03b2-trefoil protein with an irregular structure. The insertion part is always in the N-terminal ADM-predicted region for each of the three proteins in the STI-like superfamily. In contrast, a loop region tends to be excluded from an ADM-predicted region for a highly symmetrical \u03b2-trefoil protein . These fThe property of the peak(s) of the F-value plot for a highly symmetrical \u03b2-trefoil protein appearing in the central region is also observed for a \u03b2-trefoil protein with an irregular structure. Thus, this property is quite common in the space of \u03b2-trefoil protein 3D structures.The analyses of the packing formed by CHRs in the native structures reveal 11 common interactions, which are considered to be significant factors in constructing the \u03b2-trefoil scaffold. In particular, we revealed the central role of CHR-\u03b25N and CHR-\u03b25C in forming both symmetric and irregular \u03b2-trefoil scaffolds.Thus, our results suggest that the folding properties of highly symmetrical and irregular \u03b2-trefoil proteins are basically conserved, and our sequence-based techniques can decode these properties from their amino acid sequences.Additional file 1."}
+{"text": "Many previous clinical studies have found that accumulated sequential mutations are statistically related to tumorigenesis. However, they are limited in fully elucidating the significance of the ordered-mutation because they did not focus on the network dynamics. Therefore, there is a pressing need to investigate the dynamics characteristics induced by ordered-mutations.To quantify the ordered-mutation-inducing dynamics, we defined the mutation-sensitivity and the order-specificity that represent if the network is sensitive against a double knockout mutation and if mutation-sensitivity is specific to the mutation order, respectively, using a Boolean network model.Through intensive investigations, we found that a signaling network is more sensitive when a double-mutation occurs in the direction order inducing a longer path and a smaller number of paths than in the reverse order. In addition, feedback loops involving a gene pair decreased both the mutation-sensitivity and the order-specificity. Next, we investigated relationships of functionally important genes with ordered-mutation-inducing dynamics. The network is more sensitive to mutations subject to drug-targets, whereas it is less specific to the mutation order. Both the sensitivity and specificity are increased when different-drug-targeted genes are mutated. Further, we found that tumor suppressors can efficiently suppress the amplification of oncogenes when the former are mutated earlier than the latter.Taken together, our results help to understand the importance of the order of mutations with respect to the dynamical effects in complex biological systems. Myeloproliferative Neoplasms that JAK2 mutation followed by TET2 mutation influenced the clinical features \u2009\u2208\u2009{0,\u20091}N. Every network state transits to another network state determined by a set of Boolean update functions F\u2009=\u2009{f1,\u2009f2,\u2009\u2026,\u2009fN} which is synchronously updated f1, f2, \u2026fN, and f1, f2, \u2026fN eventually converges to either a fixed point or a limit-cycle attractor. The attractor is rigorously defined as follows.A Definition. Let v(0), v(1), \u22efv(t), \u22ef be a network state trajectory starting at v(0). Then, the attractor denoted by \u2329G,\u2009F,\u2009v(0)\u232a is represented by an ordered finite sub-list of the trajectory, , where \u03c4 is the smallest time-step such that v(t)\u2009=\u2009v(t\u2009+\u2009p) for \u2200t\u2009\u2265\u2009\u03c4 with v(i)\u2009\u2260\u2009v(j)\u00a0for \u2200\u2009i\u2009\u2260\u2009j\u2009\u2208\u2009{\u03c4,\u2009\u03c4\u2009+\u20091,\u2009\u2026,\u2009\u03c4\u2009+\u2009p\u2009\u2212\u20091}. Herein, p is called the attractor length.t is found such that v(t)\u2009=\u2009v(t\u2009+\u2009p).To identify an attractor, the network state trajectory is computed by synchronously updating the state values of all nodes until the time-step G with a set of nodes V\u2009=\u2009{v1,\u2009v2,\u2009\u2026,\u2009vN} specified by a set of corresponding update-rules F\u2009=\u2009{f1,\u2009f2,\u2009\u2026,\u2009fN}, consider a state trajectory starting from an arbitrary initial state. When a network is subject to a mutation, the trajectory may converge to a different attractor. Then, the network is regarded as sensitive to the mutation. Let W\u2009\u2286\u2009V be a set of genes subject to knockout mutations [FW as a set of update-rules where every gene in W\u2009\u2286\u2009V is frozen to 0 (off state) in F. In this work, we investigate the effect of the ordered double-mutations on the network dynamics. Let  be an ordered pair of nodes subject to a double-mutation with a time gap T, which means that vk is first mutated at time-step t\u2009=\u20090, and then vl is mutated at time-step t\u2009=\u2009T. In other words, the time gap represents the time-step lag between the occurrences of the first and the second mutation. We can implement it by assuming that t\u2009<\u2009T and t\u2009\u2265\u2009T, respectively. It has been known that the notion of the time gap is important since it can affect the mutation process [vk,\u2009vl)-ordered double-mutation, we can define the mutation-sensitivity as follows:S is a set of considered initial-states and I(condition) denotes an indicator function that returns 1 if the condition is true and 0, otherwise. In other words, \u03b4 represents the probability that a network converges to a different attractor by the double knockout mutation. To quantify the specificity of dynamics with respect to the mutation order, we define the order-specificity as follows:Given a Boolean network utations , 42, and process , 43, 44.v3,\u2009v4} be a pair of genes subject to mutations and 0100 be a given initial state. Then, a wild-type attractor denoted by Att1 is computed by applying F all the time. Next, we compute Att2 and Att3 to which the network converges against - and -ordered mutations, respectively. Note that t\u2009<\u2009T and t\u2009\u2265\u2009T, respectively, in computing Att2 (resp. Att3). When Att2 (or Att3) is not identical to Att1, the network is regarded as sensitive to the -ordered -ordered) mutation. In addition, the network dynamics are specific to the mutation order if Att2 and Att3 are not identical to each other. We note that a pair of genes  with a common child node in the network are excluded from analysis in this study. In case that there exists such a common child node vc, it is probable that the update of vc is differently affected by the -ordered and the -ordered mutations, because the occurrence order of vk and vl in the NCF to update vc represents the degree of influence on the update of vc. Finally, we note that the network dynamics can depend on the initial network states. Therefore, a total of 1000 initial-states  were randomly generated to compute the mutation-sensitivity and the order-specificity values in Eqs. (1) and (2) in all simulations of this study.In other words, \u0394 represents the probability of a network converging to different attractors by different mutation orders. Figure\u00a0vi,\u2009vj) denoted by l is defined by the number of links included in the shortest path from vi and vj.The path length of  denoted by n is defined by the number of non-identical paths from vi and vj.The number of paths of (A feedback loop (FBL) is a sequence of nodes where no node is repeated except the starting and the ending nodes. It has been known that FBLs play an important role in controlling dynamics behaviors of cellular signaling networks , 46, 47.Some structural characteristics of genes are related to network dynamic stability . In thisTo verify that the results of mutation-sensitivity and order-specificity in the real molecular interaction networks are consistent with randomly structured networks, we generated random networks using the Barab\u00e1si Albert (BA)  model whin-silico simulations, we basically implemented the program code using PANET [For efficient ng PANET  which isIn this paper, we conducted the Mann-Whitney U test to see if the mutation-sensitivity and the order-specificity are significantly different between any two groups, because they are not normally distributed. The Mann-Whitney U test combines two groups and ranks them. Then, it calculates a statistic of the difference of the rank sum between two resampled groups. We used MedCalc  Statisti\u03a9, for tractable simulation. It consists of all ordered pairs of genes in the case of TGL network with a small number of nodes (|N|\u2009=\u200961), whereas 30,000 randomly selected gene pairs in the case of large-scale networks of HCS (|N|\u2009=\u20091192) and KEGG (|N|\u2009=\u20091659). Considering the different network size, we also set the time gap (T) to 2\u201320 in HCS and KEGG, and 1\u201310 in TGL, respectively.In this study, we simulated the ordered-mutation-inducing dynamics of three real biological networks using the Boolean network model (see Methods for details). As explained in Methods section, we note that a total of 1000 initial-states were randomly generated to compute the mutation-sensitivity and the order-specificity values in Eqs. (1) and (2) in all simulations. In addition, we constructed a set of ordered gene pairs to be investigated, \u03b4) and order-specificity (\u0394) values of examined gene pairs (\u03a9) in three signaling networks . In the figure, the y-axis value means the cumulative probability of mutation-sensitivity or order-specificity larger or equal to the x-axis value. We observed that the cumulative probabilities of \u03b4\u2009\u2265\u20090.1 in HCS, KEGG, and TGL were 0.56, 0.62, and 0.39, respectively. This implies that it is not rare to observe that the network dynamics are sensitive against the double-mutations. It was also observed that the cumulative probabilities of \u0394\u2009\u2265\u20090.1 in HCS, KEGG, and TGL were 0.38, 0.54, and 0.32, respectively. We need to note that an order-specificity of zero can be observed even in the case of gene pairs with nonzero mutation-sensitive values according to the definitions. Therefore, the observed distribution of the order-specificity implies that the mutation order is considerably critical to the network dynamics.To see how frequently the network dynamics are affected by ordered mutations, we examined the accumulative distributions of the mutation-sensitivity  in \u03a9 into \u2018Shorter-path direction\u2019 and \u2018Longer-path direction\u2019 groups if l\u2009<\u2009l and l\u2009>\u2009l (see Methods for the definition), respectively, and forced knockout mutations in the order of vi and vj. We note that the gene pair  which is not bidirectionally connected was excluded from analysis to remove the effect of the connectedness factor on the dynamics. We compared the average mutation-sensitivity values between them . As shown in the figure, the mutation-sensitivity of the \u2018Longer-path direction\u2019 group is significantly higher than that of the \u2018Shorter-path direction\u2019 group in all signaling networks for most time gap parameter values. In other words, the network is more sensitive when the double knockout mutation occurs in the order inducing a longer path than in the reverse order. Next, we classified every ordered gene pair  into \u2018More-paths direction\u2019 and \u2018Fewer-paths direction\u2019 groups if n\u2009>\u2009n and n\u2009<\u2009n (see Methods for the definition), respectively, and forced knockout mutations in the order of vi and vj. We compared the average mutation-sensitivity values between them . As shown in the figure, the mutation-sensitivity of the former group is significantly smaller than that of the latter group in both signaling networks, almost irrespective of the time gap parameter. In other words, the network is more sensitive when the double knockout mutation occurs in the order involving fewer paths than in the reverse order. We note that our previous study showed that the dynamics influence from a gene on another gene is likely to be lessened as the path length increases and the number of paths decreases [P-values using the Mann-Whitney U test). As shown in the figure, the mutation-sensitivity of the former group is significantly smaller than that of the latter group in both signaling networks regardless of the time gap parameter. In addition, we further compared the order-specificity between the two groups . As shown in the figure, the values of \u2018Non-DT \u2192 Non-DT\u2019 and \u2018DT \u2192 DT\u2019 groups were highest and lowest, and they were the bounds for the values of other groups. Furthermore, the sensitivity of the \u2018Non-DT \u2192 DT\u2019 group was significantly higher than that of the \u2018DT \u2192 Non-DT\u2019 group, for most time gap values. Considering that these two groups are identical to each other except for the order in a gene pair, the result implies that the sensitivity difference was caused by only the mutation order. We further examined the order-specificity values of DT and Non-DT groups  and found that the former is larger than the latter. This finding is interesting considering that the mutation-sensitivity of \u2018DT \u2192 DT\u2019 was smaller than that of \u2018Non-DT \u2192 Non-DT\u2019 in Fig. roscovitine before doxorubicin is synthetically lethal in breast cancer cell [Some previous studies have investigated the characteristics of drug-target genes through network-based structural analysis , 55, andcer cell  and the cer cell . In addi\u03a9, \u2018TSG \u2192 OCG\u2019 and \u2018OCG \u2192 TSG\u2019. For every ordered pair of genes, we computed the mutation-sensitivity after forcing double knockout mutations according to the order of gene pair. Then, we compared the average mutation-sensitivity value between those two groups . As shown in the figure, the mutation-sensitivity value of the former group was significantly smaller than that of the latter group in all signaling networks, almost irrespective of the time gap. In other words, the network is more sensitive when oncogenes were mutated before tumor suppressors than the reverse order. In addition, we further compared the order-specificity between two groups, \u2018TSG\u2019 and \u2018OCG\u2019, and found that the order-specificity values of the former group were smaller than the latter group, almost irrespective of the time gap . This finding can be also related to some previous studies on the ordered mutations between oncogenes and tumor suppressor genes. For example, the double mutation in the order of TP53 and NOTCH, which are representative tumor-suppressor and oncogenes, respectively, was frequently observed in early stage of esophageal carcinoma patients [RAS, which is another oncogene, before loss of P53 formed a malignant tumor with metastatic behavior, but the reverse-ordered mutation resulted in benign tumors [It is known that tumor suppressors and oncogenes perform their cellular functions jointly in tumor progressions , 60, andpatients , 64. It n tumors , 65.FigIn this study, we defined the mutation-sensitivity and the order-specificity based on a Boolean network model to unravel the effects of ordered mutations on dynamics in signaling networks. It was interesting to observe that some structural properties of signaling networks can be a good indicator to explain the dynamical behavior with respect to ordered-mutation experiments. In addition, it was shown that various functionally important genes are related to the ordered-mutation-inducing dynamic. These results can enhance the understanding of the dynamic effects of ordered double-mutations on complex dynamics of large-scale biological systems, which supports the usefulness of our approach. Despite the usefulness of our approach, there are some limitations to be discussed. In this study, we employed the random nested canalyzing function to simulate the Boolean dynamics of the molecular signaling networks. This artificial specification can be a limitation of this study, although some previous studies have proven the usefulness of the model in fitting the update rules from the real biological data , 38. AnoMany previous studies investigated ordered mutations and found statistical relations with cancer development. Recently, these studies were extended to incorporate the analysis of biological networks. However, they are limited in identifying the significance of ordered mutations because they did not focus on analysis of the network dynamics. In this regard, we quantified the ordered-mutation-inducing dynamics by defining the mutation-sensitivity and the order-specificity measures using a Boolean network model. Specifically, they represent the probability that a network converges to a different attractor by a double knockout mutation, and the probability with which a network converges to different attractors by different mutation orders, respectively. It was not rare to observe both nonzero sensitivity and specificity values in large-scale signaling networks. In addition, we examined the relationship between the structural characteristics such as the path length, the number of paths, and the feedback loop with the ordered-mutation-inducing dynamics in the signaling networks. Interestingly, they showed significant relationships, which implies that such structural properties need to be considered in experimental studies with respect to ordered-mutation experiments. Next, we investigated the ordered-mutation-inducing dynamics of various functionally important genes. The numbers of drug-targets genes were negatively correlated to the mutation-sensitivity, whereas the network was more specific to the order of mutations subject to drug-targets genes than the rest genes. In addition, we found that tumor suppressors can efficiently suppress the amplification of oncogenes when the former genes are mutated earlier than the latter genes. Taken together, our results enhance the understanding of the dynamic effects of ordered double-mutations on complex dynamics of large-scale biological systems.Additional file 1 Figure S1. Relations of structural properties with ordered-mutation-inducing dynamics in BA network. A total of 250 BA random networks with |V|\u2009=\u200950 and |A|\u2009=\u2009100 were generated. The time gap (T) was set to 1\u201310. (a) Mutation-sensitivity result with respect to the shortest path length. All pairs of nodes involving an FBL were classified into \u2018Shorter-path direction\u2019 and \u2018Longer-path direction\u2019 groups according that l\u2009<\u2009l and l\u2009>\u2009l, respectively. (b) Mutation-sensitivity result with respect to the number of paths. All pairs of nodes were classified into \u2018More-paths direction\u2019 and \u2018Fewer-paths direction\u2019 groups according that n\u2009>\u2009n and n\u2009<\u2009n, respectively. (c) Mutation-sensitivity result with respect to the FBLs. All pairs of nodes were classified into \u2018FBL\u2019 and \u2018Non-FBL\u2019 groups, according that any gene of the pair is involved by an FBL or not. (d) Order-specificity result with respect to the FBLs. All P-values were computed using the Mann-Whitney U test. Table S1. Gene information of HCS consisting 1192 genes, including its association with drug-target, tumor suppressor, and oncogene. Table S2. Gene information of KEGG consisting 1659 genes, including its association with drug-target, tumor suppressor, and oncogene. Table S3. Gene information of TGL consisting 61 genes, including its association with drug-target, tumor suppressor, and oncogene."}
+{"text": "Correction to: Inj Epidemiol 7, 46 (2020)https://doi.org/10.1186/s40621-020-00272-zInserting the word \u2018insidious\u2019 in the first sentence to stet the author\u2019s original text.Adding a \u2018s\u2019 to \u2018invite\u2019 in the last sentence so that the verb will match the singular subject of the sentence.In the original publication of this article Swanson, , the autThe publisher apologizes to the readers and authors for the inconvenience.The original publication has been corrected."}
+{"text": "Glynne-Jones R, Sebag-Montefiore D, Meadows HM, et al. Best time to assess complete clinical response after chemoradiotherapy in squamous cell carcinoma of the anus (ACT II): a post-hoc analysis of randomised controlled phase 3 trial. Lancet Oncol 18: 347\u2013562017; \u2014This Article should have been published under the copyright \u201c\u00a9 The Authors. Published by Elsevier Ltd. This is an Open Access article under the CC BY license\u201d. This correction has been made to the online version as of March 2, 2017."}
+{"text": "In both, we suggest and solve various definitions of ge-synthesis, corresponding to different ways a designer may want to take hopefulness into account. We show that in all variants, ge-synthesis is not computationally harder than traditional synthesis, and can be implemented on top of existing tools. Our algorithms are based on careful combinations of nondeterministic and universal automata. We augment systems that ge-realize their specifications by monitors that provide satisfaction information. In the multi-valued setting, we provide both a worst-case analysis and an expectation-based one, the latter corresponding to an interaction with a stochastic environment.We study  Synthesis is the automated construction of a system from its specification: given a specification I and O of input and output signals, the goal is to construct a finite-state system that satisfies I, and responds with an assignment to the signals in O. Thus, with every input sequence, the system associates an output sequence. The system realizesocument}. At eachonments\u00a0.autonomous systems, which interact with unexpected environments and often replace human behavior, which is only expected to be good enough. Throughout the paper, we construct products of automata whose state space is O. Accordingly, the product can be minimized to include only consistent pairs. Also, since traditional-synthesis algorithms, in particular the Safraless algorithms we use, can handle automata with generalized B\u00fcchi and co-B\u00fcchi acceptance condition, we need only one copy of the product. \u00a0\u00a0\u00a0[Determinancy of thege-synthesis game]. Determinancy of games implies that in traditional synthesis, a specification I/O-realizable iff O/I-realizable This is useful, for example when we want to synthesize a transducer of a bounded size and proceed simultaneously, aiming to synthesize either a system transducer that realizes ge-synthesis, simple dualization does not hold, but we do have determinancy in the sense that I/O-realizable iff O/I-realizable. Accordingly, ge-realizable iff the environment has a strategy that generates, for each output sequence ocument}. For ge-ge-synthesis is that we do not actually know whether the specification is satisfied. In this section we describe two ways to address this drawback. The first way goes beyond providing satisfaction information and enables the designer to partition the specification into to a strong component, which should be satisfied in all environments, and a weak component, which should be satisfied only in hopeful ones. The second way augments ge-realizing transducers by flags, raised to indicate the status of the satisfaction.A drawback of ge-realizability is suitable especially in settings where we design a system that has to do its best in all environments. ge-synthesis with a guarantee is suitable in settings where we want to make sure that some components of the specification are satisfied in all environment. Accordingly, a specification is an LTL formula ge-synthesizewith guaranteege-realizes x is hopeful for Recall that ge-synthesis with guarantee problem is 2EXPTIME-complete.The LTL ge-realizes ge-synthesis. \u00a0\u00a0\u00a0Consider an LTL formula mentclass2pt{minimL that have w as a prefix. We say that a word green forL if green forL if there is L. When a system is lucky to interact with an environment that generates a green input sequence, we want the system to react in a way that generates a green prefix, and then realizes the specification. Formally, we say that a strategy green realizesL if for every x is green for L, then L.light green forL if light green forL if there is L. It is not hard to see that for ge-realizable languages, green and light green coincide. Indeed, if L is universally satisfiable and ge-realizable, then L is realizable.For a language mentclass2pt{minimge-realizability is strictly stronger than green realizability.ge-realizes a specification fge-realizes f green realizes We first prove that every strategy ge-realizable. Let q before a value for Xp is known. Likewise, no word ge-synthesis coincide for ge-realizable. \u00a0\u00a0\u00a0We continue and describe a specification that is green realizable and not ge-realizing transducer has the desired property of being also green realizing. The second has to do with our goal of providing the user with information about the satisfaction status, in particular raising a green flag whenever a green prefix is detected. By Theorem\u00a0ge-realizing transducer satisfies the specification. A naive way to detect green prefixes for a specification ge-realizing transducer, and raise the green flag whenever a green prefix is detected. This, however, requires a generation of ge-realizes the specification.Theorem\u00a0L is universally satisfiable and ge-realizable, then L is realizable. Accordingly, given a transducer ge-realizes Recall that if Given an LTL formula M follows the subset construction of x iff x is not light green, and accepts it otherwise. Note that the definition of F involves universality checking, possibly via complementation, yet no determinization is required, and the size of Let Note that once we reach an accepting state in red forL if red forL if for all L. Thus, when the environment generates x, then no matter how the system responds, L is not satisfied.A word blue forL when blue forL if there is L. Thus, when the environment generates x, the system can respond in a way that guarantees satisfaction no matter how the interaction continues.a word Green flags provide information about satisfaction. Two additional flags of interest are related to safety and co-safety properties:L can be added to a transducer that ge-realizes L. As has been the case with the monitor for green prefixes, its construction is based on applying the subset construction on an NBW for L. It is tempting to interpret an expression like y such that y, we have that x is v-hopeful forge-synthesis:ge-synthesis with a threshold, the input is an v-hopeful has satisfaction value at least v. Formally, a function ge-realizes v if for every x is v-hopeful, then In ge-synthesis, the input is an ge-realizes x is v-hopeful, then In For a value x is hopeful, then ge-realization with a threshold is not monotone, in the sense that decreasing the threshold need not lead to ge-realization. Indeed, the lower is the threshold v, the more input sequences are v-helpful  difference function: The ratio function, given by some normalization to  of the function There are different ways to analyze the relation between The choice of an appropriate mentclass2pt{minimn-floor building. The environment sends to the controller requests, by means of a truth assignment to n, and is 1 when the slowest request is granted immediately. Sure enough, there is no controller that attains satisfaction value 1 on all input sequences, and so ge-realizability, we can synthesize a controller that behaves in an optimal way. For example, using the difference function, we measure the performance of the controller on an input sequence x. Note that such a best performance needs a look-ahead on requests yet to come, which is indeed the satisfaction value of x. Thus, the assumption off-line controller. Accordingly, using the ratio function, we can synthesize a system with the best competitive ratio for an on-line interaction. The two approaches taken in Sect.\u00a0ge-synthesis with a threshold, we can use the function ge-synthesis (without a threshold), we can use the function ge-synthesis studied in Sects.\u00a0ge-realizable, or is not. In particular, in case the specification is not ge-realizable, synthesis algorithms only return \u201cno\u201d. In this section we add a quantitative measure also to the underlying realizability question. We do so by assuming a stochastic environment, with a known distribution on the inputs sequences, and analyzing the expected performance of the system.The setting of probability distribution over I always holds in probability random variable is then a function X has a finite image V, which is the case in our setting, its expected value is X attains. Next, consider an eventconditional expectation ofX with respect toE is X(w) to X attains when restricting to words in E, and normalizing according to the probability of E itself.For completeness, we remind the reader of some basics of probability theory. For a comprehensive reference see e.g.,\u00a0. Let \\doentclass1pt{minimahigh-quality synthesis problem Given an LTL formula a-la, indicating the announced satisfaction level. Thus, rather than talking about prefixes being green, red, or blue, we talk about them being v-green, v-red, and v-blue, for v is guarantees (in green and blue flags) or is impossible (in red ones). We can think of those as \u201cdegrees\u201d of green, red, and blue. Below, we formalize this intuition and argue that even an augmentation of a transducer that ge-realizes quantitative language over L and a word v-green forL if v-realizable. That is, there is a transducer v-green forL if there is v-green for L. Thus, when the environment generates x, the system can respond in a way that would guarantee v-realizability. Finally, we say that L is green realizable if there is a strategy v and for every input v-green for L, we have that v-green for L. It is not hard to see that Theorem\u00a0A ge-synthesis. Our complexity results are tight and show that ge-synthesis is not more complex than traditional synthesis. In practice, however, traditional synthesis algorithms do not scale well, and much research is devoted for the development of methods and heuristics for coping with the implementation challenges of synthesis. A natural future research direction is to extend these heuristics and methods for ge-synthesis. We mention here two specific examples.We introduced and solved several variants of GR(1) fragment\u00a0[ge-synthesis, is not handled by its known algorithms, and is an interesting challenge. The success of SAT-based model-checking have led to the development of SAT-based synthesis algorithms[ge-synthesis. A related effort is bounded synthesis algorithms[Efficient synthesis algorithms have been developed for fragments of LTL. Most noragment\u00a0, which sgorithms, where tgorithms, 24, whegorithms."}
+{"text": "The One-to-one Pickup and Delivery Problem with Shortest-path Transport along Real-life Paths (OPDPSTRP) is presented in this paper. It is a variation of the One-to-one Pickup and Delivery Problem (OPDP), which is common in daily life, such as the Passenger Train Operation Plans (PTOP) and partial Taxi-sharing Problem. Unlike the classical OPDP, in the OPDPSTRP, (1) each demand must be transported along the shortest path according to passengers/shippers requirements, and (2) each vehicle should travel along a real-life path. First, six route structure rules are proposed for the OPDPSTRP, and a kind of Mixed-Integer Programming (MIP) models is formulated for it. Second, A Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) with five neighborhood operators has been developed to solve the problem. Finally, The Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS have been compared with each other by 84 random instances partitioned in small size connected graphs, medium size connected graphs and large size connected graphs. From the test results we found that solutions generated by these approaches are often comparable with those found by the Gurobi solver, and the solutions found by these approaches are better than the solutions found by the Gurobi solver when solving instances with larger numbers of demands. In almost all instances, the MS_VND significantly outperforms the VND and the VNS in terms of solution quality, and outperforms the MS_VNS both in terms of solution quality and CPU time. In the instances with large numbers of demands, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances. Nowadays, a China high-speed rail network has been formed, it is an urgent problem to design the Passenger Train Operation Plans (PTOP) based on networks, which is different from the general PTOP based on lines. Generally, there are two features in the PTOP that (1) passengers should be transported through the shortest path and (2) trains cannot visit any station more than once. So the PTOP based on networks can be refined as: There are several pickup-delivery demands (pd-pairs) and vehicles in a real-life connected graph. Each pd-pair chosen must be transported through the shortest path from the pickup point to the delivery point according to passenger/shipper requirements. Each vehicle starts at a given location and ends at the final delivery point of the pd-pairs transported by the vehicle, and cannot visit (stop at or pass through) any point more than once, namely each vehicle should travel along a real-life path. Constraints, such as vehicle load capacities, vehicle travel distances, and vehicle stops, need to be considered. This problem can be addressed by introducing a set of maximum-income routes to be driven by a fleet of vehicles to serve a group of known pd-pairs. Referred to as One-to-one Pickup and Delivery Problems with Shortest-path Transport along Real-life Paths (OPDPSTRP), this can be classed under One-to-one Pickup and Delivery Problem (OPDP). Since each pd-pair must be transported along the shortest path and vehicle stops need to be considered, the OPDPSTRP will be studied based on connected graphs, which shouldn\u2019t be abstracted into complete graphs. The OPDPSTRP can also be applied in some transportation problems with these two features of the PTOP based on real-life connected graph, such as partial Taxi-sharing Problem. To the best of our knowledge, the OPDPSTRP has rarely been studied in the literature. So the model of the OPDPSTRP will be studied and efficient algorithms will be proposed for it in this paper.Section 2 presents related studies, while Section 3 studies the relationships between pd-pairs and presents the model for the OPDPSTRP. Section 4 presents a Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) based on 5 new neighborhoods for the OPDPSTRP. Section 5 proposes a set of random instances and analyses the efficiency of the Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS for the OPDPSTRP. Finally, conclusions and future work are presented in Section 6.The OPDPSTRP belongs to the General Pickup and Delivery Problem (GPDP), which is an NP-hard problem.Many scholars have carried out research on the GPDP over the past few years, in response to numerous kinds of GPDP being applied in real-life, such as GPDP with Time Windows, Dynamic, Stochastic, Unpaired/Paired, Single/Multi vehicle, Single/Multi depot and Single/Multi commodity.Parragh et al. , 2] rev rev2] reThe GVRPPD can be further divided into two sub-classes: unpaired and paired. The first sub-class refers to situations where pickup and delivery locations are unpaired and each unit picked up can be used to fulfill the demands of any delivery customer, such as Many-to-many PDP . The seBerbeglia et al. , 10] di di10] diMost classical OPDPs are studied in complete graphs, and pickup points must be visited prior to delivery points  and ends at the final delivery point of the contents transported by the vehicle, so it can be considered as a multi-depot (vehicles) problem. Most OPDP research is based on single depot, such as that reviewed by Psaraftis , 13] , in which N = {1,\u2026,n} for vertexes, E = {1,\u2026,e} for edges, P = {1,\u2026,p} for pd-pairs, and K = {1,\u2026,m} for vehicles. Each pd-pair i with demand qi yields revenue \u03c0i. Each vehicle k\u2208K has a maximum capacity Qk and a fixed cost vck. The transportation cost per unit length of vehicle k is tck. Each vehicle k has a stop cost n.In order to define the proposed the OPDPSTRP in mathematical terms, we specify an connected graph The system also obeys the following assumptions.Each pd-pair attribute is different  is The total cost of each vehicle consists of constant cost, travel cost, and stop cost. In order to maximize income, not all pd-pairs need to be transported.There is only one shortest path between any two nodes in the graph.By defining the afore-mentioned problem, we hope to identify a suitable scheme to help optimize the benefit.The constants and variables used in this paper are listed in The model of the OPDPSTRP is formulated in this section, and the route structure of the OPDPSTRP will be studied for it in Section 3.4.i and j. Constraints (7) ensure that each pd-pair i is transported no more than once. Constraint (8) ensures that each vehicle is not over-loading. Constraint (9) determines whether the vehicle stops at node n or not. Constraint (10) ensures that the number of stops for each route (not including the depot/vehicle) does not exceed M. Constraint (11) determines whether edge e is traveled along or not. Constraints (12) ensure that each route with pd-pairs is assigned to one vehicle. Constraint (13) ensures that the length of each route (not including the depot/vehicle) is not longer than D. Constraints (14), (15), (16) and (17) introduce the decision variables.The objective function (1) maximizes the total profit, in which The route structure of the OPDPSTRP will be studied for the model.Definition 1: In a real-life connected graph, if all pd-pairs are transported through the shortest path in a route i starting with the first pickup point, and the route is a path, then it is defined that route i is Route-Structure-Feasible (RSF for short).Definition 2: If a RSF route stems from inserting pd-pair i into route j, then it is defined that pd-pair i can be inserted into route j according route structure. pd_R_rs_judgei,j is defined as the route structure feasibility judgement parameter of inserting  pd-pair i into route j.  is defined as the route structure feasibility judgement matrix of inserting (RSFJMI for short).Definition 3: If a RSF route is a combination of pd-pair i and pd-pair j, then it is defined that pd-pair i can be combined with pd-pair j according route structure. pd_combine_rs_judgei,j is defined as route structure feasibility judgement parameter of combining  pd-pair i with j.  is defined as the route structure feasibility judgement matrix of combining (RSFJMC for short). It is assumed that each pd-pair can combine with any vehicle, that is pd_combine_rs_judgep+1,j = 1.Definition 4: In a RSF route, if pd-pair j can be picked up not prior to vehicle/pd-pair i, then it is defined that pd-pair j can connect to vehicle/pd-pair i. The parameter connect_to_judgei,j  is defined as the judgment parameter for pd-pair j connecting to vehicle/pd-pair i. It is assumed that each pd-pair can connect to any vehicle, that is connect_to_judgep+1,j = 1. One vehicle cannot connect to another vehicle.Definition 5: If pd-pair i can connect to vehicle/pd-pair i , and pd-pair j can be delivered not prior to vehicle/pd-pair i, then it is defined that pd-pair j can connect after vehicle/pd-pair i. The parameter connect_after_judgei,j is defined as the judgment parameter for pd-pair j connecting after vehicle/pd-pair i. It is assumed that each pd-pair can connect after any vehicle, that is, connect_after_judgep+1,j =1.Definition 6: The nodes traveled by vehicle k in the route combined by pd-pair i and pd-pair j can be classified into stop nodes (stopped at by vehicle k) and pass nodes (passed but not stopped at by vehicle k). pi and di are pickup point and delivery point of pd-pair i correspondingly. sn_odi,n is defined as the judgment parameter of whether pd-pair i picks-up/delivers at node n.Definition 7: The sections in the route combined with pd-pair i and pd-pair j include weighting sections (sections traveled by a vehicle with pd-pairs), and connecting sections (sections traveled by a vehicle without pd-pairs). The constants lee and lci,j are defined as their lengths.i and pd-pair j in j connects to pd-pair i or not, and connect_after_judgei,j = 1 means pd-pair j can connect after pd-pair i, so j connects after pd-pair i successfully (Definition 4 and Definition 5). According to the above research, in a route combined with more than two pd-pairs/vehicle traveled by vehicle k, the lengths of the weighting sections and connecting sections can be formulated as k stopping at node n or not can be determined by Since Rule 1: Pd-pair j can connect to vehicle/pd-pair i when connect_to_judgei,j = 1.Rule 2: Each pd-pair transported by a vehicle must connect to the vehicle, or another pd-pair that connects after the third pd-pair or vehicle only once.Rule 3: Each vehicle/pd-pair must not be connected after by more than one pd-pair.Rule 4: Each pd-pair must not connect to itself.Rule 5: There cannot be circles in any route.Rule 6: Each pd-pair not being transported should not connect to any pd-pair or vehicle.Rule 1, Rule 4, Rule 5 and Rule 6 are apparent.i1, i2 and i3 are transported by vehicle k. The vehicle route must be as follows: pd-pair i1 connects after vehicle k (namely i2 connects to pd-pair i1 (namely i3 connects after pd-pair i1 (namely Rule 2 and Rule 3. If e5+e6+e7) between points di2 and di1 may be double-counted, because pd-pair i2 does not connect after any pd-pair or vehicle. If e1+e2+e3+e4+e5+e6+e7) between point k and di1 may be double-counted, as vehicle k has been connected after by pd-pair i1 already.Take All the rules have been considered in Section 3.3 .i5 can be inserted into route 1 while pd-pair i4 cannot; Pd-pair i3 can be combined with i1 while pd-pair i4 cannot; Pd-pair i2 and i3 can connect to pd-pair ii, pd-pair i4 can connect to pd-pair i5, and pd-pair i5 can connect to pd-pair i4; pd-pair i3 can connect after pd-pair i1 and i2, pd-pair i4 can connect after pd-pair i5, each pd-pairs can connect after all vehicles; Points 1 and 6 are vehicles locations, points 2, 3, 4, 15, 14, 12, 6, 8 and 10 are stop nodes; lck1,i1 = lee1, lci1,i3 = lee22.\u03c0i = 15, vck = 1, tck = 1, and Let So Cordeau et al.  presenteDefinition 3 in Section 3.4) were applied in neighborhood transform methods  to ensure that each selected pd-pair can be inserted into the selected route. The evolution of RSFJPC will be studied in Section 4.3.Additionally, studies of Grimault et al.  and Ho eInsert, pd-pair i  is selected randomly and inserted into a new route j chosen according pd_R_rs_judgei,j = 1.In i is inserted into route j2 from route j1, the scheme showed in r3 is removed from route j1 because there is no pd-pair requiring transportation from/to r3, while structure of route j2 remains the same. By reducing the number of stops, the route has been improved.As in Spread, a pd-pair is selected and inserted into a new route as an Insert operation. Should the vehicle be overloaded, the success rate can be improved by choosing a new pd-pair i from route and transferring this into a new route j selected by pd_R_rs_judgei,j = 1, and this cycle will continue until the vehicle is no longer overloaded, or if the cyclic number k exceed the preset iterative numbers controlling value K. The task of preset value K is to control the computing time of this operation.In i1 transported through route j1 is inserted into route j2, and the new scheme is shown in r4 is deleted from route j1 because there is no pd-pair requiring transportation from/to r4, and the structure of route j2 remains the same. Since the vehicle is overloaded at section r3-r4 in route j2, pd-pair i2 is selected from route j2 and inserted into j3, and then the new scheme is obtained as r3-r4, while the structure of route j3 remains unchanged, and the scheme is finally improved.As illustrated in Point-delete starts by choosing a route at random, before isolating the point with the minimal number picking stops and delivery stops on the route, and these pd-pairs i\u2208P are subsequently inserted into different routes j selected by pd_R_rs_judgei,j = 1, thus making it possible to delete the point from the first route.Point-delete is operated on stop point r4 in route j1, pd-pair i1 and i2 are inserted into route j2 and j3 respectively, and then the new scheme is obtained as r4 is deleted from route j1 because there is no pd-pair requiring transportation from/to it, while the structure of routes j2 and route j3 remains the same. The scheme is improved due to the reduction of stop point r4.As in Route-delete, net incomes nei of each route i are computed; route k is selected according to the probability Pk = nek/\u2211nei before being deleted from the scheme. All pd-pairs transported by route k are transferred to the state of non-carried. If there is no route with non positive net incomes, then the Point-delete should be executed.In the Reassign-vehicle is an Assignment Problem (AP) in which: rvi,j = 1 means route i being transported by vehicle j, and rv_benefiti,j is defined as its income. In this strategy, vehicles are reassigned to routes to achieve the best scheme by the Gurobi solver in Matlab.Reassign-vehicle may delivers the most significant change to the solution but cannot always improve the solution and requires more computer memory and time, it\u2019s better to be chosen according to a low probability to perturb the local best solution, so a kind of Perturbation is proposed to shock the local best solution instead of Reassign-vehicle. In Perturbation, Insert, Spread, Point-delete, Rout-delete and Reassign-vehicle are chosen according to the operators choosing probabilitiesp1, p2, p3, p4 and p5 respectively.Since Insert, Spread, Point-delete, Rout-delete, and Perturbation are defined as operators opt(k) in this paper.Above all, Operators for routes construction and adjusting can be classed into three separate categories: pd-pair insertion, pd-pair deletion, and route deletion.Muelas et al.  arrayed ri and ri+1 in route R is the shortest path since all pd-pairs must be transported along the shortest path. Once pd-pair k needs to be inserted into route R(r1\u2212r2\u2212r3\u2026rn), we have to find the right inserting location of pickup point pk and delivery point dk in route R first. Let ri and rj and let ri\u2212rj\u2212rk in route R. A point ri meeting the condition rj meeting the condition R. Finally, pk and dk need to be inserted into the rear of the two points respectively, and we may get three types of results as follows: both ri and rj can be found, only one of ri and rj can be found, neither ri nor rj can be found.Firstly, it is evident that the section between any two neighbor stop points ri and rj can be found:Both r\u2212p\u2212r\u2212d\u2212r\u27a2ri and rj can be found, and i<j, the structure form of the new route R' must be r\u2212p\u2212r\u2212d\u2212r. In order to ensure feasibility of the route structure, pd-pair k should be transported along the shortest path in route R\u2019, that is, k cannot be inserted into R. As in If both r\u2212p\u2212d\u2212r\u27a2ri and rj can be found, and i = j, the route structure form of R' must be r\u2212p\u2212d\u2212r. In order to ensure feasibility of the route structure, ri\u2212pk\u2212dk must be the shortest path, that is, k cannot be inserted into route R. As in If both \u27a2 Other casesri and rj are found, and i>j, pd-pair k are opposite to route R and cannot be inserted into it, as in If both ri or rj satisfying the criteria, it must be sure that pk or dk is in route R already, then point pk or dk need not be inserted into it repeatedly. As in r2 is dk, so R(\u2026r1\u2212r2\u2212r3\u2026) remains the same after inserting dk into it.Because there is only one shortest path between any two nodes in this paper, if there is more than one ri and rj can be found:Only one of r\u2212p\u2212r\u2212d\u27a2ri can be found, the route structure form of R' must be r\u2212p\u2212r\u2212d. Pd-pair k must be transported along the shortest path in route R', that is, k cannot be inserted into R. As in If only p\u2212r\u2212d\u2212r\u27a2rj can be found, the route structure form of R' must be p\u2212r\u2212d\u2212r. Pd-pair k must be transported along the shortest path in route R', that is, k cannot be inserted into route R. As in If only ri nor rj can be found:Neither p\u2212r\u2212r\u2212d\u27a2ri and rj can be found, and R' must be p\u2212r\u2212r\u2212d, pd-pair k is transported along the shortest path in route R', and the route structure must be feasible, that is, pd-pair k can be inserted into route R. As in If none of p\u2212d\u2212r\u2212r\u27a2ri nor rj are found, and k must be connected to the front of route R, the route structure form of R' must be p\u2212d\u2212r\u2212r to minimize the length of R'. Set path(R) is the vehicle path which consists of all pass points in route R. Pd-pair k must be transported along the shortest path and each point must not be visited more than once in route R' to ensure feasibility of the route structure, that is, k cannot be inserted into route R. As in If neither r\u2212r\u2212p\u2212d\u27a2ri nor rj are found, and k must be connected to the back of route R, and the route structure form of route R' must be r\u2212r\u2212p\u2212d to minimize the length of route R\u2019. Pd-pair k must be transported along the shortest path and each point must not be visited more than once in route R' to ensure feasibility of the route structure, that is, If neither pk or dk needs to be deleted if there is no other pd-pair that needs picking up from it or delivering to it after deleting pd-pair k from route R. Otherwise, it should remain in route R.Point For Route-delete strategy, all pd-pairs are removed and route is deleted.pd_combine_rs_judgei,j] will remain the same, while RSFJMI  will change with the changes of route j. In order to update  quickly, some theories will be studied as follows.At each local search move step, RSFJMC ==0}, [pd_R_rs_judge] for route k\u2019 can be updated by formula ==0}, and let L2 = {pl\u2212dl}, a set of pd-pairs transported by route k'. [pd_R_rs_judge] for route k' can be updated by formula  is defined as the length between point k and point l.It is important to obtain a higher-level initial solution for such a large-scale and complex problem. In this paper, a generation method of initial solution is proposed, based on the idea of maximum saving. Algorithm 1 .Generation steps of initial solution are presented in Many Local Search (LS) meta-heuristics are studied for the VRP, such as the ALNS proposed by Ropke et al. , PisingeSince the major neighbourhood operator is pd-pair insertion and a choosing pd-pair need be inserted a fixed position in a route at each local search move step in the OPDPSTRP, solutions are not easy to be changed and always cannot be improved by only one operator obviously. That is to say that new methods which is different from traditional LS need be proposed for the OPDPSTRP. A basic VND and a basic VNS are proposed for the OPDPSTRP based on the above five neighborhoods. A new MS_VND and a new MS_VNS are developed to improve the efficiency of the proposing neighborhoods and algorithms in this paper.Algorithm 2  and Algorithm 3 .A VND and a VNS are processed to solve the OPDPSTRP, Pseudo-code of them are presented as in In order to achieve a near optimal solution of this problem, we propose a new MS_VND metaheuristic and a new Multi-Start Variable Neighborhood Search (MS_VNS) metaheuristic.Algorithm 4 .The steps of MS_VND in this paper are presented as in Algorithm 5 .The steps of MS_VNS in this paper are presented as in Algorithm 4 and Algorithm 5, the MS_VND and the MS_VNS have been improved in the following ways: (1) A Multi-start candidate solution set with size of n is acquired from the initial solution and updated to diversify the search, and parts of worse candidate solutions are replaced by the best solution according replacing proportion m if the solution is improving. (2) Five new operators  are utilized to improve the solution, which is different from traditional VNS. (3) In MS_VND, each candidate solution is transformed only once at a step (Multi-start-candidate-solution and One-operator), which is different from traditional LS . (4) A new local solution inferior to the primary one can also be accepted on the basis of two hypotheses: the iterations of that the solution keep the same are more than half of the presetting value, and the evaluation of the new solution is not drastically worse than the primary one.As in Insert<Spread<Point-delete<Route-delete<Perturbation according to the features of them. And this ranking will be tested further in Section 5.Changes and complexity ranking (from low to high) of operators can be primarily concluded as: To evaluate the performance of the VNS, the VND, the MS_VND and the MS_VNS, we designed 84 of the OPDPSTRP instances partitioned in small size connected graphs (3\u00d74), medium size connected graphs (6\u00d78) and large size connected graphs (10\u00d710) at random. The Gurobi MIP solver (version 7.5.2) was used to compare with these approaches proposed in this paper. The following sections will describe the generation of instances, list the parameter values used in these approaches, and provide test results and optimality gaps.m0\u00d7m1\u2212m2\u2212m3\u2212m4\u2212L/H, in which m0\u00d7m1 is the size of a connected graph, each edge in this graph is deleted according to 1/m2, 1/m3 is the pd-pairs generation probability between each two nodes, 1/m4 is the vehicle generation percentage for each node and L/H is low or high cost. Consider instance 3\u00d74-10-3-3-L as an example: the size of the incomplete digraph is 3\u00d74(12 nodes and 144 node-pairs), the deletion probability of each edge is 1/10, pd-pair generation probability between each two nodes is 1/3, the vehicle generation percentage for each node is 1/3 and L means low cost. It has been checked that there is only one shortest path between any two nodes in each graph. Data of these 84 instances can be found in Each instance name has a format All experiments were conducted on a desktop equipped with an Intel(R) Core(TM) i7-4510U 2.00 gigahertz processor and 8 Gigabyte RAM. The operating system of this PC is a 64-bit Window 8. The Gurobi solver 7.5.2 was used to solve the MIP model, and all algorithms in this paper was coded in Matlab R2015a.The MIP model is solved by the Gurobi solver with termination conditions wherein computing time is over 108000 seconds or the Gurobi_Gap  is less than 5%. The long preset time aims to ensure that the Gurobi solver can obtain at least one feasible solution served as a comparison indicator with the proposed approaches, although in some cases it failed to achieve this goal. We have provided the upper bounds found by Gurobi solver as well, for a more in depth reference to the performance of the proposed approaches.The parameter setting of the algorithms have been tested based on 9 instances mention in Insert, Spread, Point-delete, Rout-delete and Perturbation  in these approaches, and the values of the parameters are gathered in According to The abbreviations of the experimental indicators and corresponding definitions are listed in Results solved by the Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS are shown in Comparison of the average calculation efficiency of the VND, the VNS, the MS_VND and the MS_VNS are shown in Figs The above results shows that:CPU time of the Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS are independent of road network scale. Numbers of pd-pairs and vehicles are the major influential factors to the CPU time of the Gurobi solver, numbers of pd-pairs are the major influential factors to the CPU time of the VND, the VNS, the MS_VND and the MS_VNS.Gap_Gurobi within an acceptable CPU time (108000 seconds) by Gurobi solver. Large instances with over 40000 (pd-pairs\u00d7vehicles) always cannot get feasible solutions within 108,000 seconds by the Gurobi solver.In general, instances with no more than 100 pd-pairs can get an optimum solution by the Gurobi solver in preset termination CPU time (108000 seconds). Instances with more than 5000 (pd-pairs\u00d7vehicles) always cannot receive the optimal solution with no more than 20% Gap to the Gurobi solver within an acceptable CPU time. The MS_VND can acquire the optimal solution with no more than 5% Gap to the Gurobi solver within an acceptable CPU time. The MS_VNS always takes a little more CPU time than the MS_VND to solve the instances with more pd-pairs.In almost all instances, the VND, the VNS, the MS_VND and the MS_VNS with the operators proposed in this paper always can acquire the optimal solution with no more than 10% The VND, the VNS, the MS_VND and the MS_VNS can even get better solutions than the Gurobi solver for the instances with large numbers of pd-pairs and vehicles.In almost all instances, the MS_VND significantly outperforms the VND, the VNS and the MS_VNS in terms of average solution quality Figs \u201324. The Gap to the Gurobi solver within an acceptable CPU time. In almost all instances, the MS_VND significantly outperforms the VND the VNS and the MS_VNS in terms of solution quality. The MS_VNS always takes a little more CPU time than the MS_VND to solve the instances with more pd-pairs. In the large instances, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances.A new Pickup and Delivery Problem with new route structure, the OPDPSTRP, which is proposed in real-life connected graphs, is introduced and formulated in a new way. Five operators are proposed for the OPDPSTRP. A basic VND, a basic VND, a new MS_VND, and a new MS_VNS are developed for this problems and compared with the Gurobi solver. The test results show that the VND, the VNS, the MS_VND and the MS_VNS always can acquire the optimal solution with no more than 10% Our future work will concentrate on three aspects: (1) In order to improve the algorithm efficiency of the OPDPSTRP, path feasible strategy for neighborhoods will be studied. (2) There is only one shortest path between any two nodes in the connected graph in this paper, but there may be more than one shortest path between two nodes in some other real-life road networks, which we are going to study in the future. (3) The OPDPSTRP with time windows will be studied in the future.S1 Appendix(DOC)Click here for additional data file.S2 Appendix(DOC)Click here for additional data file.S3 Appendix(DOC)Click here for additional data file.S4 Appendix(DOC)Click here for additional data file."}
+{"text": "Thanks to this representation, existing non-linear code typechecks as it is, and newly written linear code can be used with existing non-linear code in many cases. However, little is known about the type inference of OutsideIn(X) , we propose an inference system for a rank 1 qualified-typed variant of Bernardy et al. [2018] proposed a linear type system"}
+{"text": "Scientific Reports 10.1038/s41598-019-48216-y, published online 12 August 2019Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cunderlying\u201d was incorrectly given as \u201cunderling\u201d. This has now been corrected in the PDF and HTML versions of the Article and in the accompanying Supplementary Information file."}
+{"text": "Action and vision are known to be tightly coupled with each other. In a previous study, we found that repeatedly grasping an object without any visual feedback might result in a perceptual aftereffect when the object was visually presented in the context of a perceptual judgement task. In this study, we explored whether and how such an effect could be modulated by presenting the object behind a transparent barrier. Our conjecture was that if perceptual judgment relies, in part at least, on the same processes and representations as those involved in action, then one should expect to find a slowdown in judgment performance when the target object looks to be out of reach. And this was what we actually found. This indicates that not only acting upon an object but also being prevented from acting upon it can affect how the object is perceptually judged. Action and vision are known to be tightly coupled with each other. Many studies show that visual perception might affect action. For instance, when visually presented with various objects, participants are faster in performing a compatible action, even when the action does not pertain to the viewed object , such as its shape (its being handled or not). We found that repeated grasping actions produced a perceptual after-effect, with participants being slower in detecting the visually presented handled mugs when their handles were oriented congruently with the grasping hand. Interestingly, the same effect did not occur when participants were asked to detect the visually presented mugs after repeatedly performing reach-to-touch actions  are processed motorically. In a behavioural study, we instructed participants to pantomime a reach-to-grasp action, with either the right or the left hand, on the presentation of a task-irrelevant go-signal. The go-signal was a 3D scene in which a mug, placed on a table, had the handle oriented toward the left or right, thus being congruent or incongruent with the pantomimed action. In half of the trials, the mug was located in front of a transparent plexiglas panel, whereas in the other half, it was located beyond the same panel, thus appearing to be out of reach. The results showed that participants were faster in responding with their reach-to-grasp pantomime when the handle of the mug was oriented congruently with the hand to be used, provided that the mug was presented in front of (but not behind) the plexiglas , respectively. Participants were all right-handed, with normal or corrected-to-normal vision, and with no history of either psychiatric or neurological disorders as self-reported. The study was approved by the local ethics committee and carried out in accordance with the principles of the revised Helsinki Declaration . Written informed consent was obtained from all the participants.Eighty participants were recruited and randomly assigned to each of four groups: Grasp-without-barrier (mean age\u2009\u00b1\u2009s.d.\u2009=\u200922.40\u2009\u00b1\u20092.32), Touch-without-barrier (mean age\u2009\u00b1\u2009s.d.\u2009=\u200922.35\u2009\u00b1\u20092.43), Grasp-with-barrier (mean age\u2009\u00b1\u2009s.d.\u2009=\u200922.60\u2009\u00b1\u20093.57), and Touch-with-barrier \u2009=\u20090.495, Experimental stimuli consisted of six pictures (1920\u2009\u00d7\u20091040) representing a 3D room with a table and a mug on it, similar to the stimuli used in our previous study , so that each movement lasted approximately 1500\u00a0ms. Each participant performed 120 movements. A black box was used to prevent participants from seeing their own movement or the mug, and back tissue covered participants\u2019 right hand throughout the motor training. Participants assigned to both the Touch-without-barrier and Touch-with-barrier groups were given different motor training: rather than reaching for and grasping the handle of the mug, participants assigned to these groups were asked to close their hands in a fist and repeatedly reach for and touch the mug with their knuckles.In the perceptual judgment task, participants sat in front of a 21-inch computer screen  at a viewing distance of 60\u00a0cm. They were asked to detect the presence or the absence of the handle by saying into a microphone \u201cs\u00ec\u201d (yes) when the handle was present and \u201cno\u201d otherwise. Each trial started with a fixation cross lasting 3000\u00a0ms, followed by one of the stimuli lasting 100\u00a0ms. After the stimulus, a response slide consisting of a black screen was displayed for 1900\u00a0ms  is different in terms of labial articulation and, consequently, in their acoustic wave forms. Since vocal reaction times are computed on the base of words\u2019 wave forms, the criteria  by which we select vocal initiation of \u2018yes\u2019 and \u2018no\u2019 words are very different and, therefore, not directly comparable. Furthermore, in visual search tasks, reaction time (RT) is a roughly linear function of set size. Note that RTs will increase at a rate of approximately 20\u201330\u00a0ms/item for target-present trials and 40\u201360\u00a0ms/item for target-absent trials Wolfe , 2020. RIn line with previous studies on perceptual adaptation  with handle orientation (left vs. right) as a within-subject factor and group (1 vs. 2 vs. 3 vs. 4) as a between-subject factor. For all the statistical tests, the alpha level was set to 0.05. All multiple comparisons were Bonferroni corrected.p\u2009=\u20090.031, \u03b7p2\u2009=\u20090.066): participants were slower at detecting right-handled stimuli (Log-RT: 6.34\u2009\u00b1\u20090.01) than left-handled stimuli (Log-RT: 6.32\u2009\u00b1\u20090.01). Furthermore, ANOVA results revealed a main effect of group \u2009=\u20093.384, p\u2009=\u20090.023, \u03b7p2\u2009=\u20090.13). Post hoc comparisons showed that RTs of participants assigned to the Grasp-with-barrier group (Log-RT: 6.4\u2009\u00b1\u20090.03) were slower than RTs of participants assigned to the Grasp-without-barrier group (Log-RT: 6.25\u2009\u00b1\u20090.01), no other comparisons were significant . Post hoc comparisons showed that RTs of participants assigned to the Grasp-without-barrier and Grasp-with-barrier groups were slower at detecting right-handled stimuli than left-handled stimuli . RTs of participants assigned to the Touch-without-barrier and Touch-with-barrier groups did not show any difference .Accuracy was equal or larger than 97% in all the groups and conditions, thus not further analyzed. ANOVA on RTs revealed a main effect of handle orientation \u2009=\u20094.826, The aim of the present study was to investigate action\u2013vision coupling by assessing whether and how making a visually presented object out of reach would impact on perceptual judgment. We, therefore, contrasted participants\u2019 performance in judging the shape of a mug , which was sometimes presented behind a transparent barrier, immediately after motor training consisting of repeatedly executing either a reach-to-grasp or a reach-to-touch action without any visual feedback. There were two main findings.The first finding was that participants were slower in judging the shape of the visually presented mug when it was right-handled compared to when it was left-handled, with this effect occurring immediately after the reach-to-grasp motor training only. This finding replicates a previous study from our group  can be processed by a specific class of visuomotor neurons, that is, canonical neurons, which are typically recruited both when executing object-related actions, such as grasping, and when merely viewing objects with different sizes and shapes, without any intention to act on them (Jeannerod Even more interestingly, a recent study on canonical neurons in monkeys demonstrated that their responses dramatically decrease when the target object looked like as something that could not be acted upon, being either too far from the viewer or behind a barrier (Bonini, Maranesi, Livi, Fogassi, and Rizzolatti, Although further research is needed, our findings seem to enrich the view that visual perception can be affected by processes and representation involved in action preparation. Not only may acting on an object impact the way in which the object is perceptually judged, but also being prevented from acting on an object may also impact visual perception as measured by readiness to make perceptual judgements."}
+{"text": "We develop an auto-reservoir computing framework, Auto-Reservoir Neural Network (ARNN), to efficiently and accurately make multi-step-ahead predictions based on a short-term high-dimensional time series. Different from traditional reservoir computing whose reservoir is an external dynamical system irrelevant to the target system, ARNN directly transforms the observed high-dimensional dynamics as its reservoir, which maps the high-dimensional/spatial data to the future temporal values of a target variable based on our spatiotemporal information (STI) transformation. Thus, the multi-step prediction of the target variable is achieved in an accurate and computationally efficient manner. ARNN is successfully applied to both representative models and real-world datasets, all of which show satisfactory performance in the multi-step-ahead prediction, even when the data are perturbed by noise and when the system is time-varying. Actually, such ARNN transformation equivalently expands the sample size and thus has great potential in practical applications in artificial intelligence and machine learning. Predicting future values of a short time series remains a challenge. Here, the authors propose an auto-reservoir computing framework, which achieved accurate and robust multistep ahead prediction by transforming high-dimensional data into temporal dynamics. On the other hand, neural networks including the RNN and LSTM can theoretically learn the nonlinear dynamics from the observed data18. However, these methods typically suffer from the overfitting problem due to the lack of sufficiently many samples when only a single short-term time series is available to train the networks. In addition, training a neural network sometimes costs considerable time and computing resources20, which also preclude the traditional neural networks from being applied to many real-world systems.It is a challenging task to make multistep-ahead predictions of a nonlinear dynamical system based only on a short-term time series due to its complicated nonlinearity and insufficient information. Although many methods including statistical regression , and an output or readout layer22. RC has drawn much attention because of its dynamical property and easy scalability since the recurrent connections in the network are  fixed in advance rather than trained. In other words, training is performed only at the readout stage due to the fixed/random reservoir, thus significantly reducing the training parameters and the computational cost. RC has been applied to a series of real-world studies, such as Great Lakes water level prediction23, handwritten digit image recognition24, NARMA time-series prediction25, limit cycle generation26, and temporal parity tasks27. However, the current RC framework requires knowledge of the external/additional dynamics that generates the reservoir, which is unrelated to the observed/target system.Reservoir computing (RC) is an extension of neural networks recently developed following RNN frameworks that is suitable for temporal/sequential information processing30. Nevertheless, the most recent short-term time series usually contains more information on its immediate future evolution than the remote-past time series owing to the time-varying non-stationary nature of many real-world dynamical systems34. Thus, even if long-term data are measured, prediction effectiveness depends mainly on recent short-term data. On the other hand, notably short-term but high-dimensional data possess rich information due to the high-dimensional variables, whose dynamics is intertwined and thus can be exploited for the prediction. Therefore, it is natural and important to predict future states on the basis of a short-term high-dimensional series, which is also widely available in real-world cases. Actually, by assuming that the steady state is contained in a low-dimensional manifold even for a high-dimensional system that is generally satisfied for dissipative real-world systems, the spatiotemporal information (STI) transformation has theoretically been derived from the delay-embedding theory37. This method can transform the spatial information of high-dimensional data to the temporal dynamics of any target variable. Based on the STI transformation, the randomly distributed embedding (RDE) framework has been developed for one-step-ahead prediction from the short-term time series by separately constructing multiple maps using the original primary STI equations or the linearized STI equations36. Furthermore, the multistep-ahead prediction was also performed by adopting a multilayer neural network as the STI transformation37. However, there are two issues that remain unsolved for the prediction: one is the computation cost, and the other is the robustness.Compared with many existing studies on predictions based on long-term time-series data, there have been only a few studies on predictions from short-term but high-dimensional dataF as a reservoir structure based on both the primary and conjugate forms of the STI equations, thus constructing the ARNN-based equations. Based on such equations, ARNN encodes F(X)t to Yt and decodes Yt to F(Xt), where Yt is the temporal  dynamics across multiple time points and Xt is the spatial  information at one time point. Hence, ARNN transforms the known spatial information of high-dimensional data to the unknown temporal/dynamical information or prediction of any target variable. On the other hand, the reservoir of ARNN is a multilayer neural network F in which the weights among neurons are randomly given and fixed in advance, while the weights of the output are determined directly from solving the ARNN-based STI equations with the dropout scheme38. In other words, there is no traditional training process for the neural network in the ARNN algorithm. Unlike traditional RC using external/additional dynamics (irrelevant to the target system), ARNN transforms the dynamics of the observed high-dimensional data as the reservoir, therefore exploiting the intrinsic dynamics of the observed/target system. ARNN actually has a similar form to the autoencoder , as illustrated in \u201cMethods\u201d. Such a transformation makes ARNN robust.In this study, by taking advantage of both the RC structure and STI transformation, we propose a novel auto-reservoir computing approach, namely, the Auto-Reservoir Neural Network (ARNN), to achieve an accurate, robust and computationally efficient multistep-ahead prediction with short-term high-dimensional data. In particular, we take a nonlinear function To validate ARNN, it is applied to a representative model, i.e., a 90-dimensional coupled Lorenz system under different noise and parametric conditions. Furthermore, ARNN is applied to predict many real-world systems. The results show that ARNN achieves multistep-ahead prediction with only a short-term series, which is better than other existing methods in terms of accuracy, efficiency and robustness.D variables and t\u2009=\u20091, 2, \u2026, m, we construct a corresponding delayed vector Yt\u2009=\u2009, there are actually L\u2009\u2212\u20091 unknown future values of the target variable y, i.e., {Yt . For each observed high-dimensional state ion Fig.\u00a0, where s, m Fig.\u00a0. Thus, tion Fig.\u00a0. In Eq. mentclass2pt{minim Yt Fig.\u00a0. However Yt Fig.\u00a0 at t\u2009=\u20091F as a reservoir structure based on both the primary and the conjugate forms of the STI equations , thus g(see Eq.  or 9) i iF as a . Note that we can also directly adopt (Yt\u22121) as the input of f instead of B.Note that n of Eq.  can be rn of Eq.  can be rA with F maps/encodes the spatial information to the temporal information in the primary STI equation, whereas the matrix B with F maps/decodes the encoded temporal information to the original spatial information in the conjugate STI equation . It shoion (Eq. . The det43G(\u00b7) is the nonlinear function set of the Lorenz system with P is a parameter vector. The exact Lorenz system and detailed description are provided in Supplementary Note\u00a0To illustrate the mechanism and the basic idea of the ARNN framework, a 90-dimensional coupled Lorenz modely1, y2, and y3, each of which is randomly selected from {x1, x2, \u2026, x90}. In one prediction, we use the 90-dimensional data from the initial 50 steps as known information/input, and ARNN outputs 18-step-ahead prediction for the target variables, i.e., D\u2009=\u200990, m\u2009=\u200950, and L\u2009\u2212\u20091\u2009=\u200918. For all the noise-free cases . The performance of ARNN and that of the traditional prediction methods were compared. Specifically, three cases are selected in Fig.\u00a0\u03c3\u2009=\u20091), ARNN remains robust and is capable of providing accurate prediction in both future states and dynamical tendency with RMSE\u2009=\u20090.333 in Fig.\u00a0Second, we discuss the situation when there is additive noise. ARNN (Eq. ) and eigm\u2009=\u200950 steps as the input and a prediction L\u2009\u2212\u20091\u2009=\u200918 steps ahead as the output), ARNN was applied to a 90D time-varying/time-switching Lorenz system,G(\u00b7) is the nonlinear function of the Lorenz system with P(t) is the time-varying/time-switching parameter vector. In other words, the parameters of the Lorenz system change as time evolves; that is, when the time variable t moves forward every 10 units, the parameters P(t) change once. The exact expression of the time-varying Lorenz system and other detailed information are provided in Supplementary Note\u00a0Third, with the same setting , its sh\u03c3\u2009=\u20091, and (iii) time varying and noise free. Under each condition, the performance of nine prediction methods is compared based on short-term series with parameter sets m\u2009=\u200950, L\u2009\u2212\u20091\u2009=\u200918 and m\u2009=\u200915, L\u2009\u2212\u20091\u2009=\u20096.In Supplementary Table\u00a0m\u2009=\u200950 and the prediction length is L\u2009\u2212\u20091\u2009=\u200918, the average normalized RMSE of ARNN is 0.397, which is better than those of the other prediction methods with RMSE\u2009\u2208\u2009. When the known length becomes even shorter (m\u2009=\u200915), the performance of ARNN (RMSE\u2009=\u20090.168) is still better than that of the other methods with RMSE\u2009\u2208\u2009; that is, ARNN achieves at least 42% more accuracy than the other methods and is at least 31% faster than the traditional neural network methods. In particular, when the known length is only 15, the LSTM shows a poorer result (RMSE\u2009=\u20090.538) but still incurs three times the running cost of ARNN  in Wakkanai, Japan, provided by the Japan Meteorological Agency44. The wind speed was recorded every 10\u2009min during the total period of 138,600\u2009min in 2011. We take the length of the known series as m\u2009=\u2009110. Based on ARNN, the wind speed of one randomly selected site  and that of the real data (in cyan) are all above 0.90  dataset of wind speed generated from 155 sampling sites  with different prediction steps Fig.\u00a0. When th\u200950 Fig.\u00a0, the ove\u200930 Fig.\u00a0 and 10 . The correlation that reflects the consistency between the real and predicted dynamical trends by ARNN reaches 0.961.The second real-world dataset contains solar irradiance data generated from min Fig.\u00a0. Each prD\u2009=\u200972) recorded every 1\u2009h, collected from 1998 to 2004 in the Houston, Galveston and Brazoria areas45. The sea-level pressure (SLP) and average temperature were predicted as shown in Fig.\u00a0m\u2009=\u200960 steps, and the outputs were the 25-step-ahead values of a target index (L\u2009\u2212\u20091\u2009=\u200925).Next, ARNN was applied to the third dataset, a 72-dimensional ground meteorological dataset . The dataset is composed of a series of 241 cloud images from 15 March 2018 to 24 March 2018 with one image taken per hour. There are D\u2009=\u20092402 variables in each image. Thus, the 241 images can be regarded as a time series within a period of 241\u2009h. For each prediction, the initial m\u2009=\u200950 images were regarded as known information, and ARNN was applied to forecast the central position of the tropical cyclone for the next L\u2009\u2212\u20091\u2009=\u200921 time points, i.e., 21-step-ahead prediction in one output. The predicted results are shown in Fig.\u00a0The fifth dataset, satellite cloud image records of typhoon Marcus, comes from the National Institute of Informatics  from 1 May 2018 to 22 November 2018. Due to the linkage effect in the stock market, different sectors of the stock market interact internally and form a complex system. By applying ARNN with m\u2009=\u200950 (days) and L\u2009\u2212\u20091\u2009=\u200920 (days), we predicted the B-Share index of the Shanghai Stock Exchange  values of nge Fig.\u00a0.47. According to the high correlation between the cardiovascular inpatients and air pollutants48, ARNN was applied to forecast the inpatient number based on a set of air pollutant indices. Considering the delay effect of every potential factor as well as a dummy vector of the weekday effect48, we obtained a 48-dimensional system (D\u2009=\u200948). Based on the daily concentrations of pollutants, ARNN predicted the short-term dynamical trend of the daily cardiovascular disease admissions  and L\u2009\u2212\u20091\u2009=\u200960 (days).The prediction accuracy of ARNN was also validated in a real-world dataset that contains several time series, including the index series of air pollutants and the number series of cardiovascular inpatients in major hospitals in Hong Kongons Fig.\u00a0, leadingons Fig.\u00a0, where mD\u2009=\u2009207 loop detectors in Highway 134 of Los Angeles County49. Each detector was regarded as a variable. By applying ARNN, a multistep prediction (L\u2009\u2212\u20091\u2009=\u200930 time points ahead), was obtained from the high-dimensional data with m\u2009=\u200980 time points at four adjacent locations  based on a dataset collected from ons Fig.\u00a0. SupplemClearly, these results show that ARNN accurately predicted the dynamical behaviors for non-periodic and highly-fluctuating cases based on only short-term data.Xt and temporal vector Yt) correspond to each other one-by-one via a smooth map36, and thus we obtain the primary and conjugate STI equations  to the temporal information of a target variable Yt, while the conjugate equation decodes/recovers the (encoded) temporal information Yt to the high-dimensional variables F(Xt), i.e.,  In this study, we propose the ARNN framework to make multistep-ahead predictions based on short-term high-dimensional data in an accurate, efficient, and robust manner. The delay-embedding theorem ensures that two vectors , i.e., ARNN is computationally efficient and accurate because it incorporates both the STI transformation and the RC structure. On the one hand, by the STI transformation, ARNN transforms the spatial information of high-dimensional data to the temporal information of any target variable, thus equivalently expanding the sample size and alleviating the small sample size problem. On the other hand, by the RC structure, ARNN requires fewer parameters to train, thereby avoiding the overfitting problem. Moreover, in contrast to the external dynamics used in traditional RC, ARNN takes the inherent dynamics of the high-dimensional data themselves as the reservoir.51 of all datasets used in this work in Supplementary Table\u00a0Notably, most long-term data, such as expression data from biological systems and interest-rate swaps data from financial systems, may also be regarded as short-term data because those systems are generally not stationary but highly time-varying with many hidden variables. Therefore, to characterize or forecast their future states, it is more reliable to employ recent short-term data, than a long-term series of past data. Therefore, ARNN is a general method suitable for many real-world complex systems even when only recent short-term data are available. To check the assumption of STI equations, i.e., the low dimensionality of the underlying attractors, we estimated the box-counting dimensions52. On the other hand, the critical transitions resulting from bifurcation can be detected by dynamical network marker methods55. In addition, ARNN cannot make accurate predictions for strongly noisy data because its theoretical framework is mainly based on deterministic dynamics. Besides, given a low-dimensional sequence, the prediction of ARNN may be similar to the traditional approaches in terms of accuracy due to insufficient spatial information to be transformed.One limitation of ARNN is that it is unable to accurately forecast sudden changes or critical transitions in real-world systems. The critical transitions in complex systems are often led by changes in external factors, whose information is generally not included in the measured dataIn summary, compared with traditional prediction methods, ARNN possesses the following advantages. First, ARNN achieves multistep-ahead prediction even with only short-term data due to the transformation from high-dimensional spatial information into temporal information. In contrast to many deep learning methods that suffer from overfitting problems when a large number of parameters are to be trained but with only a single short-time series, ARNN has much fewer parameters due to its reservoir structure where most of the parameters are randomly given. Thus, in practical applications, ARNN requires less computing resources. In particular, ARNN takes the observed high-dimensional variables as the reservoir which represents the inherent dynamics of the target variable, rather than the external dynamics. Third, by simultaneously solving a conjugated pair of STI equations (similar to an autoencoder with both encoding and decoding), ARNN is highly robust and performs well in both noise-perturbed and time-varying-parameter cases, which widely exist in real-world systems. In addition, ARNN has a solid theoretical background based on the delay-embedding theorem. The results for the applications to a variety of real-world problems demonstrate the effectiveness and efficiency of our method. Therefore, ARNN paves a new way for short-term prediction in terms of computationally efficiency, accuracy, and robustness, which is of high potential in real-world applications.The descriptions on the parameters and variables in ARNN framework are summarized in Supplementary Table\u00a057, derived from independently proposed RNN models, such as the echo state network (ESN)58 and the liquid state machine (LSM)59. Generally, ESN is the widely studied RC framework.Reservoir computing (RC) is a unified computational framework58. When feedback from the output to the reservoir is absent, the time evolution of the neuronal states in the reservoir is described as follows58:t denotes the discrete time, rt is the state vector of the reservoir units, Xt is the input vector, Win is the weight matrix for the input-reservoir connections, and W is the weight matrix for the recurrent connections in the reservoir. The function fk among f\u2009=\u2009 represents the kth elementwise activation function of the reservoir units, which is typically a sigmoid-type activation function. Equation .ESN uses an RNN-based reservoir consisting of discrete-time artificial neuronsn-dimensional state space t where symbol \u201c\u2032\u201d is the transpose of a vector, and any time interval between two consecutive time points is equal. After a sufficiently long time, all of states are converged into a compact manifold 40.For a general discrete-time dissipative system, the dynamics can be defined asd, for a smooth diffeomorphism L\u2009>\u20092d, that is,X\u2009=\u2009Xt and h(Xt)\u2009=\u2009yt where Xt is n-dimensional variables here, but sometimes it is used as D-dimensional variables (D\u2009\u2264\u2009n) in this work.If mentclass2pt{minimmentclass2pt{minim37 has theoretically been derived from the delay-embedding theory40, which can transform the spatial information of high-dimensional data to the temporal information of any target variable. The related description is given in Supplementary Note\u00a0L\u2009>\u20092d where d is the box-counting dimension of the attractor, the STI equations  or one-Actually, all of the above conditions are generally approximately satisfied for a real-world system. The conditions above are sufficient conditions to ensure a one-to-one mapping. In practice, even if the conditions are not fully satisfied, e.g., the system is not in a steady state but in a transient state, ARNN also gives an accurate prediction for many cases, since usually the transient dynamics of a dynamical system is also constrained to a lower dimensional space or manifold.AB\u2009=\u2009I, A and B are L\u2009\u00d7\u2009D and D\u2009\u00d7\u2009L matrices, respectively, and I represents an L\u2009\u00d7\u2009L identity matrix. Clearly, the first and second equations represent the linearized primary and conjugate forms, respectively. We can use the matrix form to represent these equations, i.e., AX\u2009=\u2009Y and X\u2009=\u2009BY where X and Y are defined asY\u00a0represents the unknown/future information y by estimating the maps \u03a6 and \u03a8 via A and B, respectively, but the accumulated error drastically increases with the prediction horizon. The prediction performance of the linear method based on the linearized STI equations was provided in Supplementary Figs.\u00a0Generally, \u03a6 and \u03a8 are nonlinear functions, which can be linearized as Eq.  Fig.\u00a01b1b at \\doXt as an input and Yt as an output, i.e.,AB\u2009=\u2009I, A is an B is a I represents an L\u2009\u00d7\u2009L identity matrix. Note that ARNN can be represented by the ARNN-based STI equations Eq.  Fig.\u00a01c1c at \\doentclass1pt{minimaAF(X)\u2009=\u2009Y and F(X)\u2009=\u2009BY where Xt or F(Xt) with t\u2009=\u20091, 2, \u2026, m, we can obtain the unknown future values A and B.Equations above or Eq.  can alsoons (Eq. ) for givXt or F(Xt), we solve the ARNN-based STI equations Eq. -step-ahead prediction, rather than the one-step-ahead prediction. It should be noted that when we solve the ARNN equations, {y1, \u2026, ym} are known but {ym+1, \u2026, ym+L\u22121} are unknown future values of the target variable because of the delay embedding. Therefore, it is similar to a semi-supervised learning process. The detailed algorithm of ARNN is given in Supplementary Note\u00a0It is clear that the future states including ARNN Eq.  with then-dimensional variables y1, y2, \u2026, ym}, we select the most correlated variables  with the target variable y, i.e., variables with the high mutual information with y, and obtain the following input vectors and matrixD is the number of the selected variables with n\u2009\u2265\u2009D, and m is the length of the known time series.Although high-dimensional data have rich information, they may also have a noisy effect on the prediction if some of the high-dimensional variables contain little information on the target variable. Thus, choosing relevant variables or eliminating irrelevant variables to the target variable from the high-dimensional data may significantly enhance the performance of ARNN in practical applications. Given a time series of Compared with traditional neural network method, ARNN takes much less time and computing resources in decoding the intertwined information among massive variables of a complex system, for the future value prediction of the target variable. A comparison between the ARNN and traditional neural network method on the computational complexity is demonstrated in Supplementary Note\u00a0Supplementary Information"}
+{"text": "More explicitly, we consider consequences of f being We are interested in how stronger convexity properties of of Sason , who demf-divergence inequality is Pinsker\u2019s inequality, which bounds the square of the total variation above by a constant multiple of the relative entropy. That is for probability measures P and Q, Perhaps the most well known example of an les, see ,10,11). les, see  and Topsf is restricted to a sub-interval of the real line. This observation is especially relevant to the situation in which one wishes to study f-divergences realized as linear combinations of skewed divergences.Aside from the total variation, most divergences of interest have stronger than affine convexity, at least when vergence  based onvergence ,14, callvergence  and its vergence  based onvergence  and its vergence  give exaf. As a consequence, we obtain bounds between the mean square total variation distance of a set of distributions from its barycenter, and the average f-divergence from the set to the barycenter.Let us outline the paper. In f-divergences. In particular, we introduce the skew-symmetrization of an f-divergence, which recovers the Jensen\u2013Shannon divergence and the Vincze\u2013Le Cam divergences as special cases. We also show that a scaling of the Vincze\u2013Le Cam divergence is minimal among skew-symmetrizations of In  Nielsen   We use this decomposition to sharpen, for f-divergences. We then demonstrate explicitly, using an argument of Tops\u00f8e, how our sharpening of Guntuboyina\u2019s inequality gives a new sharpening of Pinsker\u2019s inequality in terms of the convex decomposition induced by the Bayes estimator.In tuboyina  that genf denotes a convex function P and Q on a Polish space f-divergence from P to Q, via densities p for P and q for Q with respect to a common reference measure Throughout, We note that this representation is independent of f-divergenceX and a set A, we denote the probability that X takes a value in A by A, we write For Definition\u00a01.A f is twice differentiable,  (see ); in ourThe next lemma is a restatement of Jensen\u2019s inequality.Lemma\u00a01.If f is \u03ba-convex on the range of X,Proof.\u00a0Apply Jensen\u2019s inequality to f such that For a convex function Definition\u00a03.For .,21.20,2f-divergences , that the inequality characterizes the \u201cjoint range\u201d, that is, the range of the function We mention the work of Harremos and Vadja , in whicLemma\u00a02.For a \u03ba-convex f,Proof.\u00a0f. Thus, we may assume without loss of generality that f is Define a f about 1, Nielsen and Nock \u2248Theorem\u00a02.For measures P and Q, and a \u03ba convex divergence Proof.\u00a0By Lemma 2 and then Theorem 1,f-divergence inequalities.The proof of Lemma 2 uses a pointwise inequality between convex functions to derive an inequality between their respective divergences. This simple technique was shown to have useful implications by Sason and Verdu in , where iTheorem\u00a03.For divergences defined by g and f with Moreover, if (Sason\u2013Verdu ).For diCorollary\u00a01.For a smooth \u03ba-convex divergence f, the inequalityis sharp multiplicatively in the sense thatif f-divergence is defined as an f-divergence satisfying the normalization f-divergence that is 1-convex. In particular, the lower bound in Lemma 2 complimenting the estimate =1 (see ). Thus, estimate  is shownProof.\u00a0Without loss of generality, we assume that Thus,  follows.Proposition\u00a02.\u0398 such that \u0398, thenWhen In particular, when Proof.\u00a0Let ty givesDf(P||Q)\u2264To obtain the total variation bound, one needs only to apply Jensen\u2019s inequality,f-divergence from the set of distribution to their barycenter, by the mean square total variation of the set of distributions to the barycenter,Observe that, taking An alternative proof of this can be obtained by applying f strongly convex, Pinsker type inequalities can never be reversed,The next result shows that, for Proposition\u00a03.Given f strongly convex and Proof.\u00a0By f divergence, f-divergence can be bounded above by a constant multiple of a the total variation, if and only if In fact, building on the work of Basu-Shioya-Park  and Vadjf on f-divergences. The mapping If we denote f-divergences and leverage f-divergence inequalities in this section.Moreover, as mentioned in the Introduction, skewing imposes boundedness of the Radon\u2013Nikodym derivative f-divergence preserves its status as such. This guarantees that the generalized skew divergences of this section are indeed f-divergences. A proof is given in the The following appears as Theorem III.1 in the preprint . It statTheorem\u00a04.For is an f-divergence as well..For t,Definition\u00a04.For an f-divergence, its skew symmetrization,f Tops\u00f8e  providesDefinition\u00a05.When If one denotes the skew symmetrization of the ily from  that \u0394\u03c72Corollary\u00a02.For an f-divergence such that f is a \u03ba-convex on with equality when the Proof.\u00a0Applying Proposition 2When nce .For P Proof\u00a0of Theorem 4.If We recover the classical bound ,16 of thCorollary\u00a03.For probability measure P and Q,Proof.\u00a0 Since Proposition 4 gives a sharpening of Lemma 1 of Nielsen , who proDefinition\u00a06.For p and q densities with respect to a reference measure \u03bc, where (Nielsen ).For p Note that, when Theorem\u00a05.For p and q densities with respect to a reference measure \u03bc, where w average of the Note that, since e et al.  for the Theorem\u00a06.For where  thatProposition\u00a06.When Proof.\u00a0Since Information theoretic bounds to control the Bayes and minimax risk have an extensive literature  that 2nObserve that the f, quantified by the parameter f-divergence inequalities, and as a consequence achieve a sharpening of Pinsker\u2019s inequality.In this article, we begin a systematic study of strongly convex divergences, and how the strength of convexity of a divergence generator"}
+{"text": "Scientific Reportshttps://doi.org/10.1038/s41598-020-74770-x, published online 23 October 2020Correction to: The original version of this Article contained an error in the title of the paper, where the phrase \u201cDisease - associated\u201d was incorrectly given as \u201cDisease: associated\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Correction to: Molecular Psychiatry10.1038/s41380-018-0112-7\u00a0published online 14 August 2018Following publication, the authors noticed that \u2018Laura Cantwell\u2019, \u2018Otto Valladares\u2019, and \u2018Li-San Wang\u2019 were inadvertently omitted from the author list. These authors have now been added to the author list in 21st, 77th, and 79th position, respectively. This has been corrected in both the PDF and HTML versions of the article."}
+{"text": "Some studies have suggested that early-life exposure to these compounds could lead to increased body mass index (BMI) during childhood. Our aim was to assess whether children\u2019s exposure during the first 2 years of life is associated with BMI z-score in Japanese children at 42\u2009months of age.Children are exposed to n\u2009=\u2009290) of the Tohoku Study of Child Development. p,p\u2019-DDT and p,p\u2019-DDE levels were measured in breast milk samples collected 1 month after birth, and levels in children were estimated using a toxicokinetic model for three exposure periods . Associations between exposure estimates and BMI z-score at 42\u2009months of age were assessed using multivariate linear regression models.We used data from a birth cohort  for the 0\u20136\u2009months exposure period, 0.26  for the 6\u201312\u2009months exposure period, and 0.24  for the 12\u201324\u2009months exposure period.We found no significant association between levels of p,p\u2019-DDE levels were associated with increased BMI z-score at 42\u2009months of age, mostly in girls. These results are in line with previous studies supporting that early-life exposure to p,p\u2019-DDE may be associated with higher BMI during childhood.In this study of Japanese children, estimated postnatal  Although it was banned in most countries decades ago, it is still used in some countries for malaria vector control [p,p\u2019-DDT and its metabolites, such as p,p\u2019-dichlorodiphenyldichloroethylene , are widespread in the environment [ control . p,p\u2019-DDironment . Both ofironment \u20136.p,p\u2019-DDT and p,p\u2019-DDE through placental transfer and breastfeeding [p,p\u2019-DDT and p,p\u2019-DDE accumulate in the mother\u2019s adipose tissues [p,p\u2019-DDT and p,p\u2019-DDE mainly comes from diet [Children are exposed to tfeeding \u20139. Becau tissues . These c tissues . In mostrom diet . They arrom diet , the latp,p\u2019-DDT and p,p\u2019-DDE, there has been an increasing interest in their relationship to obesity. A systematic review and meta-analysis conducted by Cano-Sancho et al. [p,p\u2019-DDT and p,p\u2019-DDE and obesity. In vitro studies have shown that p,p\u2019-DDT can impair adipose tissue homoeostasis and induce endocrine disruptions; results on p,p\u2019-DDE were inconsistent. The in vivo studies found that perinatal exposure to p,p\u2019-DDT can induce thermogenesis and lipid metabolism disruptions, especially in female offspring [p,p\u2019-DDE exposure and higher BMI z-scores. Associations with other weight-related outcomes were less consistently reported, like associations between p,p\u2019-DDT and BMI z-scores. The authors expressed the need for more epidemiologic and experimental studies, and classified these contaminants as \u201cpresumed\u201d human obesogens.Among all the health impacts of o et al.  gatheredffspring , and traffspring . The metp,p\u2019-DDT and p,p\u2019-DDE with children\u2019s weight focused on prenatal exposure, little is known about the potential impacts of exposure through breast milk. We only identified three studies on lactational exposure to p,p\u2019-DDE and children\u2019s weight [p,p\u2019-DDE in seven European birth cohorts. They found an association between prenatal p,p\u2019-DDE exposure and increased infant growth, but no association with postnatal exposure estimates. Given the limitations of previous studies and the paucity of data the association between lactational exposure to p,p\u2019-DDT and p,p\u2019-DDE and children\u2019s weight, further investigation is warranted.Because most epidemiologic studies on the association of s weight , 16, 17.s weight  used bres weight  and Pan s weight \u201321 to esp,p\u2019-DDT and p,p\u2019-DDE, and BMI z-score in 42-month-olds participating in the Tohoku Study of Child Development. Because no postnatal exposure assessment was conducted in this study, we used a validated toxicokinetic model to estimate children\u2019s levels throughout their first two years of life.The aim of our study was to evaluate the association between measured breast milk levels and estimated children\u2019s postnatal levels of The Tohoku Study of Child Development is a prospective birth cohort study that comprises two birth cohorts from an urban area and a coastal area cohort of northeastern Japan. The protocol and research areas have been described previously , 23. ThePregnant women were recruited through their obstetrical units in two hospitals in the Sendai city . Women wn\u2009=\u200954), because they moved to another region (n\u2009=\u200918), or because they dropped out or weren\u2019t reachable (n\u2009=\u200916) [p,p\u2019-DDT and p,p\u2019-DDE, had data on total breastfeeding duration , and had data on child weight and height at 42\u2009months , leaving 290 mother-child pairs.Of the 1500 women who were met between January 2001 and September 2003, 687 gave their consent to participate in the study (participation rate: 46%). During their pregnancy, 88 women had to withdraw from the study, either because their baby did not meet the inclusion criteria ((n\u2009=\u200916) , 23. ThiAll the procedures of this study were approved by the Medical Ethics Committee of the Tohoku University Graduate School of Medicine and of the National Institute for Environmental Studies . In addiData on demographics, lifestyle, medical history, and fish consumption was obtained through questionnaires administered four days after delivery . BreastfMothers were asked to send a breast milk sample of more than 50\u2009ml in a clean glass bottle one month after delivery. Samples were aliquoted in 10\u2009ml centrifuge tubes and immediately frozen at \u2212\u200980\u2009\u00b0C until analyses.p,p\u2019-DDT and p,p\u2019-DDE were then measured using a gas chromatography/high-resolution mass spectrometry (HRGS/HRMS) system. The quality control was performed in accordance with the German external quality assessment scheme (G-EQUAS). The method limit of detection  was calculated using the Currie et al. method [All manipulations were made by IDEA Consultants, Inc. laboratory in Tokyo . A sampl. method . Becausep,p\u2019-DDT and p,p\u2019-DDE) developed by Verner et al. [p,p\u2019-DDT: \u2248 5\u2009years [p,p\u2019-DDE: 13\u2009years [p,p\u2019-DDT and p,p\u2019-DDE levels for each participating mother-child pair. For each pair, the model incorporated individual-specific data on mother\u2019s age at delivery, the total breastfeeding duration, mother\u2019s body weight before pregnancy and one month after delivery, weight gain during pregnancy, and child\u2019s sex. Available information did not allow estimating the duration of exclusive breastfeeding precisely. For that reason, only the total duration of breastfeeding was used, and daily breast milk intake was based on equations derived from studies including exclusively and partially breastfed children. For each pair and each chemical, iterative model simulations were performed to calibrate maternal lifetime daily oral intake until the breast milk level estimated with the model matched the breast milk level measured in the study. This maternal daily dose was then used in the model to estimate children\u2019s areas under the concentration vs. time curve (AUCs) for three periods: 0 to 6\u2009months, 6 to 12\u2009months, and 12 to 24\u2009months of age. Average children\u2019s levels during these periods were calculated by dividing AUCs by the integration period. We performed toxicokinetic model simulations using acslX .We used the toxicokinetic model of prenatal and lactational exposure to lipophilic persistent organic pollutants . Exposu13\u2009years , and fro13\u2009years  for the p-value <\u20090.05) but most of the chi-squared tests did not. Little\u2019s MCAR test showed statistical significance. Thus, we concluded that the missing data was not missing completely at random (MCAR), but was missing at random (MAR) as there might be systematic differences between the missing and observed values, but these can be entirely explained by other observed variables [Data was missing for 11% of the weight gain during pregnancy and 26% of the maternal weights one month after delivery. Missing data was due to non-response to the questionnaires. We tested the Missing at random assumption with t-tests for numeric variables, chi-squared test for categorical variables and an overall test of randomness (Little\u2019s MCAR test). Most results for t-tests showed statistical significance , an approach that reduces the degree of bias that can occur when measuring causal relationships between exposure and effect   to assess multicollinearity, and verified that the residual plots did not display unwanted patterns. Statistical analyses were performed in R, version 1.1.456 [We calculated sex and age-specific BMI z-scores using the World Health Organization\u2019s growth charts, which is an international standard taking into account children from different ethnic and cultural backgrounds . Summary 1.1.456 .p,p\u2019-DDT concentrations in breast milk in the excluded group made it impossible for us to assess the difference between included and excluded pairs for these variables.The median maternal age at delivery was 31 (range: 20\u201341) years, and the median total breastfeeding duration was 1.4 (range: 0.1\u20134.0) years  were estimated using the toxicokinetic model previously presented.Table p,p\u2019-DDT and p,p\u2019-DDE levels and BMI z-scores at 42\u2009months are shown in Table p,p\u2019-DDT levels were not significantly associated with higher BMI z-scores in either model. Only one significant association was found with p,p\u2019-DDE\u00a0when including boys and girls; BMI z-score was positively associated with estimated children\u2019s levels during the 12\u201324\u2009months period. Additional statistically significant associations were revealed with sex stratification, with p,p\u2019-DDE being associated with greater BMI z-score in girls for the three exposure periods in both Model 1 and Model 2. Overall, when significant associations were found, they were slightly stronger in Model 2. Beta coefficients for different time periods were similar, which may be related to the fact that exposure estimates were strongly correlated across periods, with correlation coefficients ranging from 0.87 to 0.98 for p,p\u2019-DDT and 0.90 to 0.99 for p,p\u2019-DDE. In all regression models, VIF values were below 1.2. Residuals were normally distributed, and showed no pattern indicative of non-linearity.Associations between p,p\u2019-DDT and p,p\u2019-DDE is associated with BMI z-score in 42-month-old children participating in the Tohoku Study of Child Development in Japan. We found associations between children\u2019s estimated p,p\u2019-DDE levels and higher BMI z-scores (mostly in girls), but none with p,p\u2019-DDT.In this study, we evaluated whether postnatal exposure to p,p\u2019-DDE. This difference between chemicals could be due to a stronger obesogenic potential of p,p\u2019-DDE than p,p\u2019-DDT. However, this could also be due to the fact that measured p,p\u2019-DDE levels of this contaminant were higher , and that toxicokinetic model predictions were more precise and accurate for p,p\u2019-DDE than p,p\u2019-DDT in this cohort [p,p\u2019-DDT and p,p\u2019-DDE on BMI increase remains uncertain. In vitro studies suggested that these chemicals may be endocrine disruptors [p,p\u2019-DDT and p,p\u2019-DDE on the endocrine system, as the former is an estrogen and androgen receptor antagonist, whereas the latter is an androgen and progesterone antagonist [p,p\u2019-DDT and p,p\u2019-DDE, the reasoning behind this phenomenon still remains uncertain.We selected BMI z-scores as our outcome because studies have shown that childhood obesity and/or overweight is associated with obesity, cardiometabolic morbidities and cancer in adulthood \u201342. Assos cohort . The mecsruptors , and thasruptors . In rat sruptors , and cousruptors . The diftagonist . Given tp,p\u2019-DDT and p,p\u2019-DDE levels during different time windows  and BMI z-score. Because the strength of the associations was similar from one time period to another, we weren\u2019t able to identify a specific critical exposure window. This could be interpreted as the lack of a specific window of vulnerability to the obesogenic impacts of these chemicals during the first two years of life. Another explanation could be that estimated exposure metrics, being highly correlated across periods, did not allow distinguishing time-specific differences in strength of exposure-outcome associations.In this study, we examined associations between estimated p,p\u2019-DDE. We found slightly stronger associations in Model 2 and with later exposure periods in general, although the differences were mostly negligible. In the meta-analysis, three studies stratified by sex to examine potential differences between boys and girls regarding associations with obesity indicators\u00a0[p,p\u2019-DDT and p,p\u2019-DDE and higher BMI z-score at nine years of age in boys [p,p\u2019-DDE and greater waist circumference and weight/height ratio in girls [Our effect estimates for postnatal exposure were slightly stronger than the meta-analytic effect estimate reported by Cano-Sancho et al. , but condicators\u00a0\u201347. One dicators\u00a0. Another in boys . The thip,p\u2019-DDT and p,p\u2019-DDE. Given the complex changes in physiology and exposure during infancy, spot measurements are unlikely to provide comprehensive information on children\u2019s exposure profile. Using our toxicokinetic model, we were able to reconstruct children\u2019s levels from birth to two years, and to estimate cumulative exposure over three different periods . This allowed us to assess exposure-outcome associations during different potential windows of vulnerability.Our study has some important strengths. First of all, the longitudinal study design is ideal when evaluating associations between risk factors and developmental outcomes. Anthropometric data were collected directly by trained physicians or research coordinators using a certified electronic scale, which reduces measurement error. Typically, epidemiologic studies rely on one or few blood or breast milk levels to assess children\u2019s early-life exposure to persistent organic pollutants like p,p\u2019-DDE and p,p\u2019-DDT levels due to analytical measurement error and intra- and inter-feed variability may have impacted precision in exposure estimates. Calculating BMI z-scores based on WHO data may not be optimal for the Japanese population [Some limitations are also worth mentioning. First of all, when stratifying by sex, our sample size was cut by more than half, going from 290 to 134 mother-child pairs for analyses in girls. Also, estimations using the toxicokinetic model are not perfectly precise, and the error in level estimates likely impacted the precision in exposure-outcome models. Precise information on exclusive breastfeeding duration data wasn\u2019t available, which could have potentially helped increase the precision of the estimates. Furthermore, uncertainty in measured breast milk pulation ; howeverp,p\u2019-DDE levels and higher BMI z-scores in girls. These results suggest that prenatal exposure may not be the only sensitive time window when looking at chemical exposures and weight-related outcomes later in life. The strength of our associations concurred with that of Cano-Sancho et al.\u2019s meta-analysis [Our study suggested an association between estimated children\u2019s analysis . PostnatAdditional file 1: Fig. S1. Directed acyclic graph (DAG) for the association between p,p\u2019-DDT/E exposure metrics and BMI z-score at 42\u2009months of age. Table S1. Correlations between breastfeeding duration and ln-transformed exposure metrics for p,p\u2019-DDT. Table S2. Correlations between breastfeeding duration and ln-transformed exposure metrics for p,p\u2019-DDE."}
+{"text": "Using the first characterization, we present all n-bit partial Boolean functions that depend on n bits and can be computed exactly by a 1-query quantum algorithm. Due to the second characterization, we construct a function F that maps any n-bit partial Boolean function to some integer, and if an n-bit partial Boolean function f depends on k bits and can be computed exactly by a 1-query quantum algorithm, then n-bit partial Boolean functions that depend on k bits and can be computed exactly by a 1-query quantum algorithm is not bigger than an upper bound depending on n and k. Most importantly, the upper bound is far less than the number of all n-bit partial Boolean functions for all efficiently big n.We provide two sufficient and necessary conditions to characterize any  In classical computation, a simplest model of computation is the decision tree . Corresum model . Roughlyf, quantum advantage can be investigated by comparing the exact quantum query complexity In quantum computation, the hope is to find out many problems whose computational complexity in quantum computer is less than the computational complexity in classical computer, i.e., finding out many problems that have the quantum advantage. For a function ity D(f) , where Dry model ,18,19,20ry model  proved tAmbainis , and theAmbainis  presentef can be computed exactly by a 1-query quantum algorithm if and only if f can be computed by the Deutsch-Jozsa algorithm [t queries. However, the result in [t-query quantum algorithms in terms of the unit ball of a space of degree-For any partial Boolean function, the best separation is still achieved by Deutsch-Jozsa algorithm ,17. And,lgorithm . In the lgorithm  showed algorithm  investigesult in   Boolean functions. Naturally, what is the characterization of partial Boolean functions with exact quantum query complexity 1?The partial Boolean functions can be regarded as a generalization of the total Boolean functions. Actually, Deutsch\u2019s algorithm  computesIn the field of quantum computation, it is a fundamental and interesting subject to evaluate the computational power of the 1-query quantum model, and is also critical for discovering quantum advantage. Specifically, the number of partial Boolean functions with exact quantum query complexity 1 shows the power and advantage of the exact 1-query quantum model. So, how many partial Boolean functions can be computed exactly by 1-query quantum algorithms?The rest of the paper is organized as follows. In In this section, we introduce some basic notations and recall some basic knowledge of partial Boolean functions and the exact quantum query model. For the details, we can refer to Refs. ,23,30,31D (or promised set) to denote a subset of x is denoted by S, the notation S and the notation S. For any finite set S, the notation S. For a complex matrix A, A, and A. Obviously, A. Furthermore, the notation a. In particular, As usual, notations f computed by Deutsch\u2019s algorithm [n-bit partial Boolean function f computed by Deutsch-Jozsa algorithm [In this paper, we mainly concern partial functions lgorithm  can be g),f(01),f,f(11))=xi ,30. In pxi ,30. Ier basis ,30. If axi ,30. I all x\u2208D . Unlike j is the auxiliary space. As a result, a t-query quantum algorithm can be determined by an initial state In the quantum query model, for every input fined byOx|i,j\u232a=n-bit partial Boolean function f, if some equations n-bit partial Boolean function n-bit partial Boolean function g defined byIf the exact quantum query complexity of an This subsection considers a special class of all partial Boolean functions using Theorem 1.First, we introduce the following definition ,31 A ba.Definition\u00a01.,31. An nn, the n-bit partial Boolean function computed by Deutsch-Jozsa algorithm [By Definition 1, the two-bit total Boolean function computed by Deutsch\u2019s algorithm  depends lgorithm  depends For partial Boolean functions depending on all bits, the result is stated in the following.Theorem\u00a02.For any n-bit partial Boolean function Proof.\u00a0n-bit partial Boolean function f can be written ask-th bit being flipped. With an argument, if f depends on n bits , then there must exist at least n input pairs k, if f depends on n bits).By Theorem 1, there exists a non-negative vector f can be given by The case n-bit partial Boolean functions into Since there are many partial Boolean functions with exact quantum query complexity 1, it is necessary to divide them into some classes. In 2015, Montanaro et al. ,24 studin-bit partial Boolean functions depending on 1 and 2 bits, the problem is trivial. For n-bit partial Boolean functions depending on n bits, the result is put into Theorem 2. By a trivial (not direct) argument, the statement that a partial Boolean function f depends on all n bits is consistent with previous definition. This is a key hint in the proof. Intuitively, this implication seems obvious. However, since the implication does not hold for For all n-bit total Boolean function depending on kk-bit total Boolean function depending on k bits. Therefore, Theorem 2 generalizes the result on total Boolean functions [n-bit partial Boolean functions depending on n bits is quite big. This fact is implied by the following lemma.Theorem 2 clarifies all partial Boolean functions that depend on all bits and can be computed exactly by a 1-query quantum algorithm. Observing the unique multilinear polynomial of any total Boolean function, any unctions  to partiLemma\u00a01.Let n-bit total Boolean functions  is 22n u et al. ,24) is 3n-bit partial Boolean functions depending on As a result, many This section introduces and proves the second characterization and two related results.f and Following the discussions of Lemma 7 and Theorem 17 in [First, the following lemma follows the discussions of Lemma 7 and Theorem 17 in .Lemma\u00a02.. If therIn order to give the second characterization, we introduce the following definition. This definition is also used in . More reDefinition\u00a02.,37,38,39hold, then the is called a degree-1 SOS complex representation matrix of f and Equation .S the column index. In a 1-query quantum algorithm, the number pair S traverses As we know, for the state By Definition 2 and the coefficient matrix, the second characterization is presented in the following.Theorem\u00a03.Any n-bit non-constant partial Boolean function Proof.\u00a0i-th block matrixf and According to Lemma 2 and Definition 2, the coefficient matrix Equation  holds.f and f can be determined by As a result, the three states f and In order to use Theorem 3, we need to find a pair of SOS real representations of unctions ,37,38,39t-query quantum algorithms in terms of the unit ball of a space of degree-To some extent, Theorem 3 provides a different style for the characterization of partial Boolean function with exact quantum query complexity 1. On one hand, similar to Ref.  =\u2211l=1tisfyingf(x)=\u2211l=1Equation  holds.n-bit partial Boolean function f with exact quantum query complexity 1, there exists an SOS complex representations matrix f and x such that On the other hand, by Theorem 3, for an Equation , we can Equation  for x suf given by the two-tuple The inverse direction of Theorem 4 is not always hold. For example, a three-bit partial Boolean function  of Ref. , QE(f)\u22652n-bit partial Boolean function depends on k bits and can be computed exactly by a 1-query quantum algorithm. That is, the function Theorem 4 gives a necessary condition on the case that an f is bigger than 1 by Theorem 4, then the result is exact.Compared with Theorem 1, Theorem 4 provides an approximate method on deciding the exact quantum query complexity of a partial Boolean function. Most importantly, the method in Theorem 4 is more efficient than Theorem 1. In order to construct the linear system in Theorem 1, we should observe at most n-bit partial Boolean functions which depend on k bits and can be computed exactly by a 1-query quantum algorithm.In this subsection, let us evaluate the number As a preparation, the following lemma is necessary.Lemma\u00a04.Let the vector function By Theorem 4, the fifth result is the following.Theorem\u00a05.Let Proof.\u00a0n-bit partial Boolean functions satisfying n-bit partial Boolean function can be determined using the following two steps.Recall that all columns in the matrix In the first step, we choose n-bit partial Boolean function f is determined as follows. x in the set x in the set In the second step, we add some other vectors Equation  and Lemmn-bit partial Boolean functions, as each n-bit partial Boolean function corresponds to a string n-bit partial Boolean function is in the set n-bit partial Boolean functions which depend on k bits and can be computed exactly by a j-query quantum algorithm. Thus, all n-bit partial Boolean functions with exact quantum query complexity 1 only make up a very tiny proportion of all n-bit partial Boolean functions.The most important contribution of Theorem 5 is to give an estimate on the number of partial Boolean functions with exact quantum 1-query complexity. This is the first non-trivial upper bound on this problem. In contrast, Furthermore, corresponding to Fact 1 in Ref. , the folf and g satisfying f can be computed exactly by a 1-query quantum algorithm, then g can also be computed exactly by this 1-query quantum algorithm.g defined byn, n-bit partial Boolean functions with exact quantum query complexity 1. In general, given an n-bit partial Boolean function with exact quantum query complexity 1, we can find out trivially at least As we know, the partial Boolean function computed by Deutsch-Jozsa algorithm can be written asFinally, the gap between the upper bound and the lower bound comes from the following two aspects. The first aspect is that the upper bound is obtained from a necessary condition  and an approximate counting argument. The second aspect is that there exist many unknown partial Boolean functions with exact quantum query complexity 1.n-bit partial Boolean functions with exact quantum query complexity 1, and one necessary condition for characterizing n-bit partial Boolean functions that depend on kn-bit partial Boolean functions that depend on n bits and can be computed exactly by a 1-query quantum algorithm  of the actual number of partial Boolean functions in this class is quite big. On the other hand, known non-trivial n-bit partial Boolean functions in this class are still fairly rare [Find all (or some) non-trivial rly rare ,22,23,24n-bit partial Boolean functions can be computed exactly (or with bounded-error) by k-query quantum algorithms for all k-query quantum model. In contrast, the result of Ambainis et al. [How many s et al.  is a qua"}
+{"text": "As of May 25, 2020, the novel coronavirus disease  spread to more than 185 countries/regions with more than 348,000 deaths and more than 5,550,000 confirmed cases. In the bioinformatics area, one of the crucial points is the analysis of the virus nucleotide sequences using approaches such as data stream techniques and algorithms. However, to make feasible this approach, it is necessary to transform the nucleotide sequences string to numerical stream representation. Thus, the dataset provides four kinds of data stream representation (DSR) of SARS-CoV-2 virus nucleotide sequences. The dataset provides the DSR of 1557 instances of SARS-CoV-2 virus, 11540 other instances of other viruses from the Virus-Host DB dataset, and three instances of Riboviria viruses from NCBI . With this, it is possible to use data stream algorithms.\u2022All researchers in bioinformatics, computing science, and computing engineering disciplines can benefit from these data because by using this numeric representation, they can apply several stream algorithms and techniques such as TEDA , TEDA-Cloud, TEDA-Cluster and Teda-Class in genomic information.\u2022Data experiments that use analytic stream techniques in SARS-CoV-2 virus genomic information can be used with this dataset.\u2022These data represent an simple way to evaluate the SARS-CoV-2 virus genome with stream algorithms.\u2022Differently of the conventional bioinformatics techniques in which are based on dynamic programming (such as BLAST and other), this approach allows the utilization of different techniques (techniques commons in other areas) to find similarities between genome sequences.1k-mers mapping (kMersM) and k-mers mapping with CGR (kMersM-CGR). k-mers is a frequency count metric used in Bioinformatics. Other k-mers datasets are presented in This work presents a dataset of data stream representation (DSR) of SARS-CoV-2 virus nucleotide sequences. The dataset contains two kinds of data, the raw data, and the processing data. The raw data is composed of the 1557 instances of the SARS-CoV-2 virus genome collected from the National Center for Biotechnology Information (NCBI) k-mers representation k-mers also can be used with a signature of the genome sequence. However, in this manuscript, the genome sequence is transformed into a linear stream data, and this type of transformation can be used with stream algorithms. Another important aspect of this dataset is associated with applied CGR not in all sequences but just in each k bases (with mers or not). This strategy maintains the statistical characteristics and reduces the size of the stream.In the Chaos Game Representation (CGR) \u2022k.mat\u201d;For DM, the DSR was generated for \u2022k.mat\u201d;For DM-CGR, the DSR was generated for \u2022k.mat\u201d;For kMersM, the DSR was generated for \u2022\u2022k.mat\u201d;In the directories \u201cOther viruses data\u201d and \u201cSARS-CoV-2 data\u201d, the DSR was generated for \u2022k.mat\u201d;In the \u201cVirus-Host DB data\u201d, the DSR was generated for For kMersM-CGR:The data is organized into three main directories: \u201cSARS-CoV-2 data\u201d, \u201cVirus-Host DB data\u201d and \u201cOther viruses data\u201d. Each main directory contains three files called \u201cRawDataTable.mat\u201d, \u201cRawData.mat\u201d and \u201cRawData.xlsx\u201d, and four sub-directories named \u201cDirectMapping\u201d, \u201cDirectMappingCGR\u201d, \u201ckmersMapping\u201d and \u201ckmersMappingCGR\u201d. \u201cRawDataTable.mat\u201d, \u201cRawData.mat\u201d and \u201cRawData.xlsx\u201d files store the raw data information from viruses database; they have the same information, however in the \u201cRawDataTable.mat\u201d the attributes are stored in Matlab table format (after 2013b version), in the \u201cRawData.mat\u201d the attributes are stored in Matlab cell arrays format, and in the \u201cRawData.xlsx\u201d the attributes are stored in a Microsoft Excel file. In the sub-directories \u201cDirectMapping\u201d, \u201cDirectMappingCGR\u201d, \u201ckmersMapping\u201d and \u201ckmersMappingCGR\u201d are stored the DM, DM-CGR, kMersM and kMersM-CGR data stream representation, respectively. Inside each sub-directory the files are called:i-th file is called \u201cPointsData_k_k=k.mat\u201d for sub-directory \u201cDirectMapping\u201d, \u201cPointsDataCGR_i_k=k.mat\u201d for DM-CGR, \u201cPointsDatakmers_i_k=k.mat\u201d for kMersM and \u201cPointsDatakmersCGR_i_k=k.mat\u201d for kMersM-CGR.For the main directory \u201cVirus-Host DB data\u201d, the values are stored in 10 files where each 2s, expressed asN is the length of sequence and ns is the nth nucleotide of the sequence.The streams were based in nucleotide sequence, s, are grouped in sub-sequences of the k bases. The group of sub-sequences can be expressed asi-th vector bi is a i-th group of the k nucleotides, that isFor DM and DM-CGR, the nucleotide sequence, B, are transformed in a sequence of the integer values expressed asc is the DM stream stored in dataset. The DM stream, c, calculus can be expressed asfmap(\u202f\u00b7\u202f) is the mapping function expressed byFor DM, the group of sup-sequences, stored in matrix a expressed asia is the i-th value of CGR. In CGR  is the mapping processing characterized by z expressed asiz is the i-th value of CGR. Each ith element iz is a bi-dimensional value expressed asH, that isFor kMersM and kMersM-CGR, the nucleotide sequence, x(\u00b7) see \u2013(14)) anThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper."}
+{"text": "We have read the article titled \u201eQuality of life 10\u00a0years after cardiac surgery in adults: a long-term follow-up study \u201c by Perrotti A. et al. published in your distinguished journal with great interest. Unfortunately, we found few errors in this article. Dear Editor,I am contacting you in the name of the group of authors who published \u201cHealth-related quality of life five years after coronary artery bypass graft surgery\u201d in the International Journal of Cardiology . We read"}
+{"text": "In the 1950s, Crick proposed the concept of so-called comma-free codes as an answer to the frame-shift problem that biologists have encountered when studying the process of translating a sequence of nucleotide bases into a protein. A little later it turned out that this proposal unfortunately does not correspond to biological reality. However, in the mid-90s, a weaker version of comma-free codes, so-called circular codes, was discovered in nature in J Theor Biol 182:45\u201358, 1996. Circular codes allow to retrieve the reading frame during the translational process in the ribosome and surprisingly the circular code discovered in nature is even circular in all three possible reading-frames ( Crick et\u00a0al.  proposedX\u2014had been found by extensive statistical investigations in large samples of genetic data of archaea, plasmids and viruses, in addition to bacteria and eukaryotes  or even 24  . As usual, v a prefix of w if v a suffix of w if i-th circular shift ofw for Let We recall a few classical definitions of codes as follows:l-letter code and X is k-circularl-letter code if for any l-tuple from X there is only one partition into l-tuple from X when read on a circle. In other words, for any a circular l-letter code if it is a k-circular l-letter code for all a strong comma-free code if no X. In other words, given any two non-necessarily distinct elements X, for every a comma-free code if for any two elements X, we have a maximalcircular l-letter code if it is not contained in a larger a maximumcircular l-letter code or, equivalently, code of maximal size if Y is a l-letter code over a Let l-letter code ((k-)circular, comma-free, strong comma-free), namely the maximal size of a 1-circular l-letter code over complete classes l. The number of such complete classes is given byl-letter codes over Obviously, any strong comma-free code is also comma-free and hence also circular. Moreover, a maximum code is certainly also maximal. There is a general upper bound for the size of a maximum l et\u00a0al.  that alll-letter code. We say that X is Let An interesting class of codes is also given by the so-called X are also circular.A circular code A stands for adenine, C stands for cytosine, G stands for guanine and T stands for thymine  if fixed point of a bijection We will also consider the so-called If the cardinality of G and a subset G, the centralizerS in G is the set of all elements of G that commute with all elements of S, i.e. normalizer of S in G is the set of all elements g of G that commute with S as a set but not necessarily point wise, i.e. We will need some further notations from general group theory -comma freeness and also the Letbe a finite alphabet anda circular . This representation had many implications on the study of these codes since the codes from the same equivalence class have the same error-detecting properties th rows for j)th columns for n of them will have the shape Without loss of generality we may assume thatWe would like to remark that there are alternative descriptions of the group (outer) semidirect product with respect to wreath product. It is an interesting investigation in itself to get involved with the group. However, this is outside the scope of the article.The group n and c. It was pointed out in \u201cc-self-complementarity. It is thus natural to define an equivalence relation on codes by settingX and X will be denoted by [X].  strong comma-free codes.Let us consider the class of maximal . Without loss of generality, assume that x starts with 0 and ends with 1. However, if X would also contain c(x) which starts with 1 and ends with 0\u2014contradiction to strong comma-freeness. Let c-self-complementary strong comma-free diletter codes over an alphabet of even cardinality:Before we continue our considerations about equivalence classes, we have to close a gap and count the number of maximal Letbe a finite alphabet withfor someand letbe the centralizerof some involutioncwithout fixed points. Then, there aredifferent maximal (=maximum)c-self-complementary strong comma-free diletter codes overc-self-complementary code, we have to ensure that for every x and c(x) belong to different sets. There are n pairs of complementary letters, thus, we have In Fimmel et\u00a0al. , the strIn general, it can be assumed that in the case of maximum strong comma-free codes, the equivalence classes can be smaller than Let l-letter  strong comma-free codes, some Letbe a finite alphabet withfor someand letbe the centralizer of some involutioncwithout fix points. Moreover, letThen, the action ofoninduces some equivalence classes of size strictly less thanwhereis one of the following classes of codes: The class of all maximal (=maximum) strong comma-freel-letter codes;The class of all maximal (=maximum)c-self-complementary strong comma-freel-letter codes forc as well as l be given as stated in the theorem. We start with the proof of (1), so let l-letter codes over For Let us now consider the case l et\u00a0al. , it is sLet us consider now the case  Note that partition means in particular that the sets By . Assume now that c-self-complementary strong comma-free 1-letter code, namely For c-self-complementary strong comma-free diletter codes over Let us now consider the case Let us consider now the case Again we fix c and hence For instance, if r odd equality above would imply that r is even, then equality would imply that X is also c-self-complementary. Therefore, we choose Orb(x) under c. So also K into two disjoint parts r-letter words and end with a code We proceed as in the proof of (1) in order to construct a code Let n in case (1). It is not clear if not all of the codes are invariant under some permutation.We would like to remark that the above proof certainly also works for c-self-complementary strong comma-free triletter codes:For The following example shows how the construction from Theorem We give an example how the construction in Theorem\u00a0Finally, one putsX is a strong comma-free code which is c-self-complementary and invariant under For However, the result of Theorem\u00a0X is not invariant under any permutation from X generates an equivalence class of size equal to the size of For X is 18 and it is strong comma-free since all triletters in X start with either A,\u00a0C or G,\u00a0T or A appears exactly nine times in the first position, C exactly six times and X invariant must fix these three letters and a similar argument on the last letters shows that it must also fix G,\u00a0T and We shortly give an argument why the code in the above Example is not invariant under any permutation from c-self-complementary) strong comma-free triletter codes, the negative result can also be obtained more easily. The numbers of maximum (c-self-complementary) strong comma-free triletter codes calculated in Fimmel et\u00a0al.  For The code In the following, we will only need the sufficient condition of Theorem\u00a0Letbe a finite alphabet witha triletter code overin that no initial diletter ever occurs as a final diletter. Then,Xis comma-free.X beginning with X is comma-free. Let Letbe the symmetric group acting on the elements of the alphabet\u00a0withan involutory bijection without fix points. Then, there is a maximum triletter comma-free codewith1. Casemis even ormis odd andIn this case, we choose m and because not all three positions Without loss of generality, we may assume thatThen, 2. Casemis odd and2.1There areIn this case, we choose 2.2For allc(xyz) has the same shape again and no initial diletter ever occurs as a final diletter.In this case, we choose The so constructed code xy with xy cannot appear as final diletter in every tuple from the first case, because m. The constellation m. In summary, in the constructed code, an initial diletter can never appear as the final diletter, so the code is comma-free.Let\u2019 us take a look at X is also maximum k is the smallest natural number s such that Let (ii)Since (iii)l-letter X or one of the X provided Any (iv)l-letter such that for some i we have x has only one pair of identical consecutive letters with the convention that x generates a complete equivalence class .If We now write i) to (iii) from above hold when considered on l-letter word from We try to prove the above theorem by showing that for any Case 1:k is even.In this case, let iv), it follows that x generates a complete equivalence class. Hence, we may assume without loss of generality that iii) , the word x generates a complete equivalence class , we may assume that x contradicting circularity of X.Let We now distinguish cases:Case 2:k is odd.l. l copies of x is a concatenation of k words of length l, say iii). Moreover, x gives X.Choose a) applies and yields a contradiction. Note that also in this case, the In this case, the same construction as in Case m copies of x generates a complete equivalence class and by (iii) we may assume that x and Let We need to distinguish cases again according to the size of A first corollary is immediate.Letbe a finite alphabet or even size 2nand letbe the class of allmaximumc-self-complementaryl-lettercodes for some natural numberlwhereis an involution without fix points. Then, the action ofinduces equally sized equivalence classes onFollows directly from Theorem\u00a0We would like to remark that it is an open question if maximum and Letbe the genetic alphabet andas well asLetbe the class of all maximalc-self-complementary trilettercodes. Then, the action ofinduces equally sized equivalence classes . It was speculated that nature may use this mechanism in order to encode not only one set of information in DNA but 8 (the size of L) or even 24  genetic code, the case of the binary alphabet is especially important for applications in signal processing. It proves to be a special case for classes of maximal strong comma-free and maximum self-complementary comma-free trinucleotide codes. Namely, only in this case, the corresponding equivalence classes all have the maximum possible size.Our results clarify completely the situation for several classes of codes showing the (non-) existence of equivalence classes of size |Moreover, the results of the present investigation suggest that the code properties responsible for the maximal size of equivalence classes are that the codes are maximally large and retain their error-detecting properties in all frames ("}
+{"text": "To enhance the utility of acceleration time (AcT) in the diagnosis of internal carotid artery (ICA) stenosis, we assessed the value of AcT measurements with different waveform patterns.Ninety-three patients with acute atherothrombotic cerebral infarction were enrolled, and they underwent both carotid ultrasonography and digital subtraction angiography (DSA). AcT was determined by a conventional procedure (using the first peak point or the bending point) and the peak systolic velocity (PSV) procedure. The AcT ratio was calculated as (AcT of ICA)/. We evaluated the correlation of stenosis rate as assessed by the North American Symptomatic Carotid Endarterectomy Trial method using DSA (DSA-NASCET) with the AcT of ICA (ICA-AcT), the AcT ratio measured by the conventional procedure , and the AcT ratio measured by the PSV procedure (PSV AcT ratio). The area under receiver operating characteristic curves (AUC) for DSA-NASCET was calculated based on the ICA-AcT and AcT ratio.r\u2009=\u20090.723), conventional ICA-AcT (r\u2009=\u20090.638), and PSV AcT ratio (r\u2009=\u20090.245). The corresponding AUCs for ICA stenosis \u2265\u200950% were 0.971, 0.886, and 0.572, respectively.Forty-five vessels had 50% or greater ICA stenosis. DSA-NASCET was positively correlated with the conventional AcT ratio (We demonstrated the usefulness of the conventional procedure for diagnosing stenosis of ICA origin using AcT and showed that the AcT ratio was a more beneficial parameter than AcT. Carotid artery ultrasonography is capable of noninvasive evaluation of the internal carotid artery (ICA). The peak systolic velocity (PSV) , 2, as wIn addition, the acceleration time (AcT) of the ICA, which can be measured by pulsed-wave Doppler, has been reported useful in cases, where measurement of the PSV of stenosis is difficult \u20138. The AThe systolic pulsed Doppler waveform is different in each case. The commonly observed waveform has a monomodal or bimodal peak pattern, where the time from minimum flow velocity, namely initiation of upstroke, to the PSV (time-to-PSV) is consistent with the acceleration time, and this time-to-PSV has often been defined as AT . HoweverThere is a study comparing digital subtraction angiography (DSA) with the ICA-AcT, in which the time from initiation of the upstroke to the first peak of the bimodal peak pattern was considered to be the AcT, and the time from initiation of the upstroke to the bending point in the monomodal peak pattern was considered to be the ICA-AcT . In the This is why it was considered easier to define the time-to-PSV as the AcT. Furthermore, there have been few reports looking at the relationship between stenosis rate on DSA and AcT , 8.In the present study, we evaluated the usefulness of the time-to-PSV, being defined as AcT, in the diagnosis of stenosis using DSA, and we compared it to previous methods.Our subjects were 93 consecutive patients  who were hospitalized in the Dokkyo Medical University Hospital for acute atherothrombotic cerebral infarction and evaluated by both carotid artery ultrasonography and DSA between April 1, 2015 and March 31, 2018.In 68 vessels, pulsed Doppler waveform patterns of the CCA and ipsilateral ICA were identical, showing a bimodal peak pattern without a bending point in which the initial peak of the wave coincides with the PSV. Therefore, only time-to-PSV was calculated as AcT, and those vessels were excluded. In addition, 20 vessels were excluded, because the ICA was obstructed at its origin. Ultimately, 98 vessels were retrospectively analyzed.KI, HT, AS, YT, HI, MO, and AI performed carotid artery ultrasonography using the SSA-770A , TUS-AI800, and TUS-A500 .Carotid artery ultrasonography was performed, while the subject was in the supine position, with the head turned away from the scanned side and the neck slightly extended.The pulsed Doppler waveform of the CCA was measured approximately 2\u00a0cm from the carotid sinus using a linear-array probe . The pulsed Doppler waveform of the ICA was measured approximately 3.5\u00a0cm (3.56\u2009\u00b1\u20091.00\u00a0cm) from the origin of the ICA using a convex-array probe .The sample volume of the pulsed-wave Doppler was set at 1/2 or 2/3 of the vessel diameter, and the Doppler insonation angle against the direction of blood flow was 60\u00b0 or smaller. Sweep speed was fixed at 43.8\u00a0mm/sec (SSA-770A and TUS-A500) and 60.0\u00a0mm/sec (TUS-AI800).The measurement was continued for five beats or more, until the same waveform was plotted by the pulsed-wave Doppler.The stenosis ratio of the ICA origin diagnosed via DSA was evaluated by DT, SK, and TN using the North American Symptomatic Carotid Endarterectomy Trial method (DSA-NASCET) .Type A) A bimodal peak pattern, where the initial peak of the wave coincides with the PSV;Type B) A waveform, where the second peak coincides with the PSV of the bimodal peak pattern;Type C) A waveform of a monomodal peak pattern and a clear bending point; andType D) A monomodal peak pattern without a clear bending point.Pulsed Doppler waveforms were classified into the following four types Fig.\u00a0:Fig.\u00a01MeWe measured \u201cconventional AcT\u201d of the CCA  and ICA  according to Takekawa\u2019s method . BrieflyThe AcT ratio, which is the ratio of the ICA-AcT to the CCA-AcT, was calculated.In other words, the \u201cconventional AcT ratio\u201d was derived from the \u201cconventional ICA-AcT\u201d/\u201cipsilateral conventional CCA-AcT\u201d. At the same time, the \u201cPSV AcT ratio\u201d was derived from the \u201cPSV ICA-AcT\u201d/ipsilateral \u201cPSV CCA-AcT\u201d.The AcT used an average of five heartbeats, and the AcT and AcT ratio were measured by KI, HT, and AI, without taking into account the DSA-NASCET results.We evaluated the correlation of the DSA-NASCET with the \u201cconventional ICA-AcT\u201d, \u201cPSV ICA-AcT\u201d, \u201cconventional AcT ratio\u201d, and \u201cPSV AcT ratio\u201d, using the Pearson correlation coefficient. Then, we evaluated whether the DSA-NASCET was predictable for each item, using single regression analysis. We also calculated the area under the curve (AUC) based on the \u201cconventional ICA-AcT\u201d, \u201cPSV ICA-AcT\u201d, \u201cconventional AcT ratio\u201d, and \u201cPSV AcT ratio\u201d, using a receiver operating characteristic (ROC) curve.We calculated the inter-rater reliability for the AcT and the DSA-NASCET of five vessels, using the intraclass correlation coefficients (ICC).p\u2009<\u20090.05 was considered statistically significant.IBM SPSS  was used for statistical processing and plotting, and HT, KS, and HK were involved in overseeing the entire study.The ICCs for the \u201cconventional ICA-AcT\u201d, \u201cPSV ICA-AcT\u201d, and DSA-NASCET were 0.714, 0.994, and 0.998, respectively.The CCA pulsed Doppler waveforms were Type A, 87 vessels; Type B, 8 vessels; Type C, 2 vessels; and Type D, one vessel. The ICA waveforms were Type B, 39 vessels; Type C, 41 vessels; and Type D, 18 vessels, and there was no Type A (Table\u00a0The median DSA-NASCET was 38.6% (range 0\u201385.2); stenosis \u2265\u200950% was identified in 45 subjects (45.9%), and of these, 29 subjects had stenosis of \u2265\u200970%.p\u2009<\u20090.0001), \u201cconventional AcT ratio\u201d (p\u2009<\u20090.0001), and \u201cPSV AcT ratio\u201d (p\u2009=\u20090.0150), but no correlation was identified for \u201cPSV ICA-AcT\u201d (p\u2009=\u20090.629).DSA-NASCET showed significant correlation with the \u201cconventional ICA-AcT\u201d , and six vessels (54.5%) were \u2265\u200950%.p\u2009=\u20090.00344), there was no correlation with the \u201cconventional ICA-AcT\u201d (p\u2009=\u20090.0722), \u201cPSV ICA-AcT\u201d (p\u2009=\u20090.101), and \u201cPSV AcT ratio\u201d (p\u2009=\u20090.903), whereas the correlation coefficient with the \u201cconventional AcT ratio\u201d was 0.795 and the AUC was 1.00.In relation to DSA-NASCET, although a significant correlation was seen with the \u201cconventional AcT ratio\u201d  pre\u201cPSV ICA-AcT\u201d and \u201cPSV AcT ratio\u201d may have low utility as the pulsed Doppler waveform changes under the influence of various factors, such as age, heart disease, and arteriosclerosis. The results of our study point to the possibility that the \u201cconventional AcT\u201d, especially \u201cconventional AcT ratio\u201d, is a useful indicator for diagnosing stenosis of ICA origin in patients in whom measurements of the PSV of the maximum stenosis point and ICA PSV/CCA PSV are difficult.Our study had several limitations. First, we excluded 68 vessels in which pulsed Doppler waveforms showed Type A patterns in both the CCA and ipsilateral ICA. Therefore, the usefulness of AcT in vessels that had identical patterns of \u201cconventional AcT\u201d and \u201cPSV ICA-AcT\u201d could not be evaluated. In addition, because only 11 vessels showed patterns of Type B, C, or D in the CCA, further evaluations for those patterns other than Type A are needed. Finally, pulsed Doppler waveforms were measured at a constant sweep speed, but a change in the sweep speed could result in different patterns in pulsed Doppler waveforms. Determining the optimal sweep speed for AcT measurements requires further studies.We studied the value of AcT measurement in stenosis of ICA origin. Our study demonstrated that the proper measurement method for AcT was the \u201cconventional AcT\u201d method, measuring the time from initiation of upstroke to the initial peak or to the bending point. According to our inferences, the \u201cconventional AcT ratio\u201d has a still greater utility compared with the \u201cconventional ICA-AcT\u201d. There are few reports, where DSA-NASCET and AcT are compared. Multicenter studies should be conducted in the future, where \u201cconventional AcT\u201d or the \u201cconventional AcT ratio\u201d and DSA-NASCET are studied. Guidelines for the diagnosis of stenosis of ICA origin need to be created based on the knowledge of its relationship to AcT or the AcT ratio."}
+{"text": "Labels are a way to add some information on a text, such as functional annotations such as genes on a DNA sequences. V(D)J recombinations are DNA recombinations involving two or three short genes in lymphocytes. Sequencing this short region (500 bp or less) produces labeled sequences and brings insight in the lymphocyte repertoire for onco-hematology or immunology studies.BW-index). Both indexes need a space related to the entropy of the labeled text.We present two indexes for a text with non-overlapping labels. They store the text in a Burrows\u2013Wheeler transform (BWT) and a compressed label sequence in a Wavelet Tree. The label sequence is taken in the order of the text (TL-index) or in the order of the BWT (TLBW-index has an overhead on simple label queries but is very efficient on combined pattern\u2013label queries. We implemented the indexes in C++ and compared them against a baseline solution on pseudo-random as well as on V(D)J labeled texts.These indexes allow efficient text\u2013label queries to count and find labeled patterns. The TLNew indexes such as the ones we proposed improve the way we index and query labeled texts as, for instance, lymphocyte repertoire for hematological and immunological studies. Labels are a way to add some information on a text, as the semantics of words on an English sentence or functional annotations such as genes on a DNA sequences. 1 in the positions 12\u201341 and the label L2 in the positions 56\u201396?Can we build an index that saves a labeled text like ACGCC\u2026TTGA (of size 96), which have the label L We consider here the case where a same label can be given to different (but similar) patterns and can occur several times in the text. We introduce two indexes which store a labeled text and answers to position\u2013label association queries. Those indexes share some ideas with the RL-FMI (BW-indexes (text\u2013label indexes) and their associated queries. The last section presents experimental results on simulated and real genomic data.e RL-FMI  which usT = t0t1 \u2026 tn \u2212 1 be a text of length n over an alphabet of size \u03c3. The text may be composed of several sequences, each sequence ending with the symbol $. Let L = {L0, L1 \u2026 Ll \u2212 1} be a set of labels. A labeled text  is here a text with non-overlapping labels: a letter should have at most one label. Each position i of the text is labeled by exactly one label ia \u2208 L \u222a {\u03b5}, where the special \u03b5 label is put on every letter without label. A = a0a1 \u2026 an \u2212 1 is the label string. Let bit vectorB = B[0]B[1] \u2026 B[n \u2212 1], where each B[i] is either 0 or 1, we define as B the vector B[i]B[i + 1] \u2026 B[j]. Let us call rank the number of times the bit b \u2208 {0, 1} appears in the prefix B and select  the position i of the jth appearance of the bit b in B. Such a bit vector B can be stored in nH0(B) + o(n) bits to support rank and select in O(1), where H0(B) is the zeroth order entropy of B (Given a opy of B .BWT (BWT(T), is the concatenation of the last letters of the lexicographically sorted rotations of the text. BWT(T) is easier to compress and can be stored using knH(T) + o(n) bits, where kH is the kth order empirical entropy of the text T. The FM-index  giving the number of occurrences of \u03b1 in BWT(T). The FM-index allows to efficiently search a pattern using backward search.The BWT  is a revFM-index  uses theWT  + o(a log l) bits when bit vectors are zero-order compressed (A WT  is a bina\u2309) time  and requmpressed .The usual full-text indexes such as the FM-index  or the Lnon-overlapping labels and look for ways to efficiently store such labels along with sequences as well as to query them. The basic idea is that consecutive labels in A are often the same: we will thus store compressed label sequences.We focus here on T, A), we define the TL-index as, using a FM-index built on a BWT U to index the text, a bit vector AB marking the positions in the text where the labels change, and a WT AW indexing a compressed label sequence , where Q is the set of nodes of AW and q0 \u2208 Q is the root node. Each node q \u2208 Q is q = , where q.label \u2208 L \u222a {\u03b5} is the label of q and q.parent is the parent node of q . Both q.left and q.right are child nodes in Q \u222a {\u22a5}. A leaf is a node q where q.right and q.left are \u22a5. Each leaf q is linked to a label q.label \u2208 L \u222a {\u03b5}. The l + 1 leaves are exactly the labels of L \u222a {\u03b5} and we define leaf (q.label) = q. On a leaf q, we have q.val = \u22a5. Let q be a non-leaf node: we have q.label = q.val is the bit vector rooted at q in the WT. We explain in \u201cShaping the WT for a Label Hierarchy\u201d how AW can be further shaped depending on a label hierarchy.AW is part of the index. This WT is used to answer efficiently bidimensional range queries where the labels and the label positions are the two dimensions  time. This is a classical query within a WT. Given a label xL \u2208 L, the function selectW\u3008xL, i\u3009 gives the position of the ith xL label in A\u2032 in O(log l) time. The accessor \u22121W\u3008xL\u3009 gives the list of positions in A\u2032 where a\u2032i = xL. It runs in O(log l \u00d7 occ) time, with occ the number of occurrences of xL in A\u2032.mensions . A balanU.The BWT tends to store text repetitions consecutively. As those repetitions may have the same labels, it would be interesting that the labels benefit from the BWT reordering. Hence, labels can also be stored in the order of T, A), the TLBW-index is defined as   . The BWTThe indexes allow the following classical queries.label(it) )\u2014Which label is on the letter it? This query is done is O(log l) time in the TL-index, and in O(log1+\u03b5n + log l) time in the TLBW-index since it has to convert positions in U order (see rder see .findP(P) P\u2014Which are the occurrences of a pattern P? It is solved with the FM-index alone (O(|P| + occ \u00d7 log1+\u03b5n) time in both indexes, where occ is the number of occurrences of P in T.ex alone . This qufindL(xL)\u2014Which text positions are labeled xL? The query runs in O(y \u00d7 log l) time in the TL-index, and in O(y(log l + log1+\u03b5n)) time in the TLBW-index, where Y = \u22121W\u3008xL\u3009 and y = |Y|. See The three previous queries are well known in text indexes. The two next queries search for a pattern and a label at the same time.countPL\u2014How many text positions are labeled xL and begin an occurrence of a pattern P? As in the findL(xL) query, the occurrences of P are found in U, in the positions from i to j.\u2013occ occurrences to have the corresponding positions in the text. For each of them, we run the query label(it). The total time is O(|P| + occ (log n1+\u03b5 + log l)).TL-index: We translate all these \u2013BW-index: See i and j correspond to the positions i\u2032 = rank and j\u2032 = rank in the root q0 of DW. We then use an accessor customized from the rangeLocate function of  time. This accessor first traverses the WT from the root to the leaf xL and then traverses it back to the root to find the positions in q0.val which match the label in the given range. For every position found, we find the corresponding positions in DB and expand them to the following 0-bits in DB. This query runs in O(|P| + |Z| \u00d7 log l) time.TLction of , simulatfindPL\u2014Which text positions are labeled xL and begin an occurrence of a pattern P?\u2013countPL.TL-index: This query is exactly the same as \u2013BW-index: We use the countPL query detailed in cnt with a list Y holding the matching positions in U. The positions are converted at the end in the text order. This query runs in O(|P| + |Z| \u00d7 log l + y \u00d7 log1+\u03b5n) time, with |Y| = y.TLZ| \u2264 y \u2264 occ, the countPL and the findPL queries may thus be faster on the TLBW-index, |Z| depending of the compression DB can do on Y.As |countPL query could be faster if the WT was directly built on the labels, without the intermediate bit vector DB (AB): the answer would be known while reaching the leaf of the WT in O(|P| + log l) time. We chose to favor the execution time of the findPL query, as well as the size of the structure (when A can be compressed).Note that the findPL can vary to find the patterns P which have the label Lx on the ith position of the pattern, or in any pattern\u2019s position. Adapting this queries is easy in the TL-index as we find the positions of the pattern in the BWT, translate them in the text order and then find the label of the ith position following each of them. In the TLBW-index, we find the patterns\u2019 positions in the BWT, access to the ith letter (we need to sample the BWT to read the patterns in the forward way), and find the label as usual. To have the label in any pattern\u2019s position, in the TL-index we need to find a label xL between the first and last letter of the pattern (with only two access in the WT) but in the TLBW-index, we look for the label of all the pattern\u2019s letters.The T, A) is of length n and is labeled with l unique labels. As defined above, the indexes store U in knH(T) + o(n) bits. The TL-index stores the bit vector with rank and select capabilities in nH0(AB) + o(n) bits. The size of AW depends on the compressed label sequence A\u2032, of length a. AW takes a H0(A\u2032) + o(a log l) bits. Similarly, the TLBW-index stores DB in nH0(DB) + o(n) bits and DW takes d H0(D\u2032) + o(d log l) bits, where d is the length of D\u2032. The BWT can be built in linear time while using little space (AB is built while reading A in O(n) time. To make DB, we need to read the labels in the order of the original data file in O(n) time. To make AW, we find the occurrence of each label, corresponding to a 1-bit in AB, in O(a) time. Then we form the shape of AW in O(l). The labels corresponding to a 1-bit are extracted to make the WT\u2019s root q0. For each node containing at least two labels, we separate them by following the shape previously calculated, in DW the same way. The TL-index has thus a size of knH(T) + nH0(AB) + a H0(A\u2032) + o(n log l) bits, assuming \u03c3 = O(l), and is built in BW-index has a size of knH(T) + d H0(D\u2032) + o(n log l) bits and is built in We recall that the text  will be shaped according to the hierarchy, and internal nodes q of W may have non-empty q.label values belonging to F. For example, in q1.label = L1, where L1 is the label family gathering L1.1, L1.2 and L1.3.Labels may be further organized into a families . Both TLfindL and findPL queries naturally extend to label families. With the hierarchy depicted in findL(L1) has to find the positions that have a label L1.1, L1.2 or L1.3. Such a query does not need to be iterated on every label of the family L1, but rather directly starts at the corresponding internal node (q1 on The de q1 on .W for a label hierarchy may increase the height w of the WT to O(l) in the worst case. To have a lower space consumption and a faster average query time, one can give a Huffman shape to W (H0(A\u2032) in the best case while in the worst case it could be O(l). If no label hierarchy is given, the average height w will be H0(A\u2032) (Shaping ape to W . A leaf e H0(A\u2032) .BW-indexes with a baseline solution called HT-index, indexing the text T with a BWT. The labels are stored in a map linking each label to the list of its  positions. We also store the labels in the text order with the compressed bit vector AB and, stored in plain form, A\u2032. This enables the findL(xL) query in O(y), where Y\u2032 is the list of pairs  which represent the occurrences and y = |Y\u2032|. Note that Y (in the TL-index) and Y\u2032 represent the same information as the labels are stored in the text order in both indexes. The label(it) query runs in O(1) time. This solution is not space-efficient with repeated labels: it needs knH(T) + nH0(AB) + a + l\u2032 + o(n) bits, where a is the size of A\u2032 and l\u2032 the number of labeled factors. The query times are summarized in We compared the TL- and TLO(n log n) time on small DNA sequences, as it is very efficient for storing and appending sequences corresponding to our projected application (O(log1+\u03b5n) steps, we use sequences of length 50, which is similar to the sampling distance usually chosen in practice. The real files have longer sequences, thus longer sampling distances. The queries relying on the BWT will be slower and therefore cannot be compared between real and simulated files. We build the AB (or DB) bit vectors, compress them using the rrr_vector class of SDSL-Lite, and finally build AW (or DW) using a shape we added in SDSL-Lite, which depends of the label hierarchy.The three indexes were implemented in C++. We used the SDSL-Lite library  to buildlication . As RopefindP(P) behaving similarly in all indexes and countPL being very similar to findPL. The three indexes were tested on various datasets of labeled texts, each with 100 M characters .Simulated files, with random sequences but fixed labels. Here a given label is associated to the same pattern, possibly with some variation, and we alter the proportion of labeled letters (5\u2013100%), the variation in the label\u2019s pattern , the number of unique labels , the length of the labels (5\u2013100 letters). The dataset has 546 files, two of those files are shown in Genomic sequences with immunologic labels. A person\u2019s immune system can be described with a set of labeled DNA sequences with V(D)J recombinations. The dataset, detailed below, uses 838 K labels from 355 unique labels, with d \u223c 0.26n.lymphocytes, are under maturation, their DNA undergo a recombination which allows several billions possibilities from a register of a thousand genes J recombinations . These sThe tested DNA sequences come from patients 09, 12, 14 and 63 from a public dataset on a study on acute lymphoblastic leukemia . They haIndex sizes. The U, B (either AB or DB) and W (either AW or DW) grows linearly with the number of indexed elements (data not shown). The TL-index is the smallest index, and the TLBW-index is generally slightly larger. The compression is directly related to a and d. The file with random labels (d = 0.77n) is hard to compress, whereas the files with a low d/n ratio give a 2\u00d7 to 7\u00d7 compression. T or in U, thus more 1-bits in B. Note that when there are more labeled letters, the text is more similar (as labels are placed on similar substrings), hence a decrease in the BWT size . W increases while the number of unique labels increases (D), the height of W increasing logarithmically with the number of unique labels.Build time. Most of the build time of TLBW-index is devoted to build D\u2032. For TL-index, the building of U takes most of the total time.Queries. The label query is faster on the HT-index. As expected, the TLBW-index needs more time for label and findL, as it needs to translate positions from the BWT back to the text. Note that locating the positions in the text takes about the same time as label(it) in the TL-index. However, for the complex findPL query, the TLBW-index is the fastest solution because the position translation is only done on the letters which have both the label and the pattern. For the TL-index and HT-index, the actual time of the findPL queries is more affected by the number of pattern occurrences than the number of final occurrences (between 0 and 100 K depending on the file).BW-index suffers here even more from the missing suffix array sampling of the implementation for queries label and findL. However, on the findPL query, the other indexes are penalized due to the sparsity of the sampling, bringing a more than 30\u00d7 difference with TLBW-index.On the genomic dataset, the sequences are longer: The TLBW-index store a labeled text and allow efficient queries. They can be constructed from files of some MB in a few seconds. Experiments confirm that the indexes stay small when the text is redundant , when each label describes a pattern with few variations , and when few letters are labeled . However, the TL-index and TLBW-index are robust even to non-redundant text with almost random labels everywhere. The TLBW-index needs more memory space than the TL-index but is more efficient in combined label/pattern queries. Those structures might be used on any labeled data, such as DNA sequences, but also on natural language texts or on music sheets with some semantic annotations.The TL-index and TLsd_vector bit vector instead of the rrr_vector bit vector which should improve space consumption when the bit vectors are very sparse. However, this would only minimally improve the global space consumption of the index. We plan to use one of the indexes in a clone database for hematological malignancies: It will allow comparison of V(D)J recombinations between different samples of a patient or between several patients.Perspectives include improvement of the implementation, with label families queries or parameterizing the distance between samples in the FM-index to offer a space-time trade off. Within SDSL we could use the 10.7717/peerj-cs.148/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj-cs.148/supp-2Supplemental Information 2Click here for additional data file."}
+{"text": "Scientific Reportshttps://doi.org/10.1038/s41598-020-64654-5, published online 15 May 2020Correction to: The original version of this Article contained multiple errors.The incorrect image was used for Figure\u00a013.Furthermore, there was a typographical error in the legend of Figure\u00a014.a) and in part (b\u2013i) the 2D distribution of the corresponding elements is represented.\u201d\u201cImages show a radiation-induced dissolution of complex precipitation. The HAADF image is represented in part (now reads:a) and in part (b\u2013c) the 2D distribution of the corresponding elements is represented.\u201d\u201cImages show a radiation-induced dissolution of complex precipitation. The HAADF image is represented in part (Finally, a Supplementary File containing Tables S1 and S2 was omitted from the original version of this Article.These errors have now been corrected in the HTML and PDF versions of the Article."}
+{"text": "X in terms of the p-th absolute moment of X. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds on the rate-distortion function and the channel capacity. Specifically, we study the rate-distortion function for log-concave sources and distortion measure r and the target distortion d. For mean-square error distortion, the difference is at most d. We also provide bounds on the capacity of memoryless additive noise channels when the noise is log-concave. We show that the difference between the capacity of such channels and the capacity of the Gaussian channel with the same noise power is at most X with possibly dependent coordinates. Our proof technique leverages tools from convex geometry.We derive a lower bound on the differential entropy of a log-concave random variable  It was es, thenN(X+Y)\u22644Nes, thenN(X+Y)\u22644Nquality (N(X\u2212Y)\u2264e2gated in . For furgated in . In Sectrelated,N(X+Y)\u2264\u03c0ed, the rate-distortion function r-th moment distortion measure is given byd, explicitly linking the storage requirements for X to the information content of X (measured by d. As shown in [The bound  on the der bound  states tiven by1RXd=infPXr bound [RXd\u2265RXd\u225ch (r=2), (RXd\u2265h(X)\u2212shown in ,17 underd is linked to the optimality of simple lattice quantizers [d, where The speed of convergence in  and its antizers , an insiantizers  showed td\u21930. Ziv  proved td, provided that the source density is log-concave: for mean-square error distortion , we havBesides leading to the reverse entropy power inequality and the reverse Shannon lower bound, the new bounds on the differential entropy allow us to bound the capacity of additive noise memoryless channels, provided that the noise follows a log-concave distribution.Z is given by (21)CZ(P)The rest of the paper is organized as follows. log-concave if f is log-concave if for every A function X in We say that a random vector Our first result is a lower bound on the differential entropy of symmetric log-concave random variable in terms of its moments.Theorem\u00a01.Let X be a symmetric log-concave random variable. Then, for every  holds with equality for uniform distribution in the limit Moreover, As we will see in Theorem 3, for he bound  tightensp) as e) \u2248 1.4 bits at The difference between the upper bound in  and the The next theorem, due to Karlin, Proschan and Barlow , shows tTheorem\u00a02.Let X be a symmetric log-concave random variable. Then, for every  with equality [Moreover, the Laplace distribution satisfies equality .p, we deduce that for every symmetric log-concave random variable X, for every Combining Theorem 2 with the well-known fact that X and a Gaussian X.Using Theorem 1 and , we immeCorollary\u00a01.Let X be a symmetric log-concave random variable. Then, for every where Remark\u00a01. in the limitThe uniform distribution achieves equality in Indeed, if U is uniformly distributed on a symmetric interval, thenand so, in the limit We next provide a lower bound for the differential entropy of log-concave random variables that are not necessarily symmetric.Theorem\u00a03.Let X be a log-concave random variable. Then, for every  tightens asMoreover, for The next proposition is an analog of Theorem 2 for log-concave random variables that are not necessarily symmetric.Proposition\u00a01.Let X be a log-concave random variable. Then, for every Remark\u00a02..Contrary to Theorem 2, we do not know whether there exists a distribution that realizes equality in X and a Gaussian X. Recall the definition of Using Theorem 3, we immediately obtain the following upper bound for the relative entropy of \u0394p in .Corollary\u00a02.Let X be a zero-mean, log-concave random variable. Then, for every where X, one can optimize over p to further tighten x+As \u03b3\u21920, , and thuudied in ,27.Since for fixed For example, extended Cauchy distributions, that is, distributions of the formX in We say that a random vector Theorem\u00a06.Let We derive the following lower bound on the differential entropy for one-dimensional symmetric Corollary\u00a04.Let Notice that  reduces Theorem\u00a07.Let X and Y be uncorrelated log-concave random variables. Then,As an application of Theorems 3 and 4, we establish in Theorems 7 and 8 below a reverse form of the entropy power inequality X in Rn,  side of . Here,\u2225he bound  on D=12,Fuce thatF(\u22121)=fX81). In the context of information theory, Lemma 1 has been previously applied to obtain reverse entropy power inequalities [Actually, the powerful and versatile result of Lemma 1, which implies ualities , as wellualities . In thisProof\u00a0of\u00a0Theorem\u00a02.The result follows by applying Lemma 1 to the values The proof leverages the ideas from .Proof\u00a0of Theorem 3.Y be an independent copy of X. Jensen\u2019s inequality yieldsLet equality  to X\u2212Y ty yieldsh(X)=\u2212\u222bfXo obtain1fX\u2212Y(0)\u2265o obtain1fX\u2212Y(0)\u2265Proof\u00a0of\u00a0Proposition\u00a01.Y be an independent copy of X. Since Let isotropic if X is symmetric and for all unit vectors X is isotropic if its covariance matrix isotropic constant of X.We say that a random vector hyperplane conjecture, asks whether the isotropic constant of an isotropic log-concave random vector is also bounded from above by a universal constant (independent of the dimension). This conjecture holds under additional assumptions, but, in full generality, Lemma\u00a02.Let X be an isotropic log-concave random vector in It is well known that imension . A long-eader to . We will[\u2113X  Let equality . Upper-b Let equa2\u03c0e,and  follows.If Z is independent of X and realizes the maximum differential entropy under the r-th moment constraint, Z is given by(2) Let fined in . Hence,If en, from , we obtaProof.\u00a0X is a symmetric log-concave random variable.Denote for brevity X. This choice of Assume that If en, from , we obtaRemark\u00a07.1) Let us explain the strategy in the proof of Theorems 9 and 10. By definition, To estimate or one can apply Jensen\u2019s inequality directly to get the bound provides a tighter bound over . This justifies choosing  in the proof of .A simple study shows that  , which leads the tightening of  for  , we bound r-th norm by second norm, and we note that by the independence of X and Z,To justify the choice of  provides a tighter bound over .A simple study shows that 2) Using Corollary 2, if , and wherewhere is the rate-distortion function of a Gaussian source with the same variance ee e.g.,  \u2264, using (RXcov(d)\u2212If Recall that the capacity of such a channel isWe compare the capacity Proof.\u00a0X such that The lower bound is well known, as mentioned in . To obtaombining , 141) a a(141)h\u2212h\u2212h\u03b3-concaveables in . Finallyables in  and 66)\u03b3-concaveUnder the Gaussian assumption, information-theoretic limits in many communication scenarios admit simple closed-form expressions. Our work demonstrates that, at least in three such scenarios , the information-theoretic limits admit a closed-form approximation with at most 1 bit of error if the Gaussian assumption is relaxed to the log-concave one. We hope that the approach will be useful in gaining insights into those communication and data processing scenarios in which the Gaussianity of the observed distributions is violated but the log-concavity is preserved."}
+{"text": "Nature Communications 10.1038/s41467-020-18739-4, published online 2 October 2020.Correction to: The original version of this Article contained an error in Fig.\u00a03, in which the types of tegmino-tegminal stridulation in Gryllidea and in Tettigonioidea shown on the right side of the phylogeny were reversed. The correct version of Fig.\u00a03 is:which replaces the previous incorrect version.The original version of this Article contained an error in the last sentence of the Fig.\u00a03 legend, which incorrectly read \u2018The common ancestor of Gryllidea evolved \u201cleft-over-right\u201d stridulation, the common ancestor of Hagloidea evolved \u201cambidextrous\u201d stridulation, and the common ancestor of Tettigonioidea evolved \u201cright-over-left\u201d stridulation\u2019. The correct version replaces this sentence with \u2018The common ancestor of Gryllidea evolved \u201cright-over-left\u201d stridulation, the common ancestor of Hagloidea evolved \u201cambidextrous\u201d stridulation, and the common ancestor of Tettigonioidea evolved \u201cleft-over-right\u201d stridulation\u2019.43\u2019. The correct version replaces this sentence with \u2018Crickets and mole crickets stridulate by moving the right forewing over the left, and katydids stridulate in the opposite way by moving the left forewing over the right43\u2019.The original version of this Article contained an error in the Discussion, which incorrectly read \u2018Crickets and mole crickets stridulate by moving the left forewing over the right, and katydids stridulate in the opposite way by moving the right forewing over the leftThis has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantees in a variety of inference tasks with statistical constraints on accuracy and privacy. While the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to a binary case, we derive closed form expressions for several bottleneck problems.Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems , and strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding, and dependence dilution. Leveraging these connections, we prove a new cardinality bound on the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed \u201cbottleneck problems\u201d, by replacing mutual information in IB and PF with other notions of mutual information, namely  Y is a target variable and X is an observable correlated variable with joint distribution T of X that is maximally \u201cinformative\u201d for inferring Y. The bottleneck variable T is assumed to be generated from X by applying a random function F to X, i.e., Y given X, that we denote byT using the mutual information T that solves the constrained optimization problemYXT.Optimization formulations that involve information-theoretic quantities  have been instrumental in a variety of learning problems found in machine learning. A notable example is the information bottleneck  method . SupposeX and Y. Wyner and Ziv )Once ion The result in  was provIn this section, we illustrate several information-theoretic settings which shed light on the operational interpretation of both tings in ,30. In p problem ,89 under problem . Here, w problem  and sour problem .X of a source of interest Y. She wishes to transmit a rate-constrained description from her observation  to Bob such that he can recover Y with small average distortion. More precisely, let n i.i.d. samples of n probability measures on T)Suppose Alice has access only to a noisy version Tsybakov , who shofined in . For morfunctionIt can bY^ as T)where R=erred to ,93. Notiuch thatlim supn\u2192essed in  for discently in  for any n i.i.d. samples Q, we wish to test whether Q is a product distribution. This task is formulated by the following hypothesis test:Y observations U\u03a6,\u03a8 and L\u03a6,\u03a8 as4L\u03a6,\u03a8U(\u03b2)\u2254We will apply this approach to analytically compute YXT, generates unique Let Definition\u00a01.Let U be a discrete and V be an arbitrary random variables supported on andMoreover, the multiplicative gain of the observation V in guessing U is defined as (the reason for \u221e in the notation becomes clear later)U with or without the observation V, respectively. Intuitively, V is in estimating U: If it is small, then it means it is nearly as hard for an adversary observing V to guess U as it is without V. This observation motivates the use of As the names suggest, T can only improve, we have Y and T; instead, it means T is useless in estimating Y. As an example, consider Y and T are clearly dependent; i.e., Y is uniform  is given in In the following theorem, we apply the technique delineated in Theorem\u00a011.For andwhere As described in T satisfying YXT and Y. Similarly, to prove  (see ) correspfined in , with reTheorem\u00a012.Let where Moreover,where X and Y connected through T forming YXT, we haveX with probability at lest Y) is to obfuscate the higher-likely event T such that By letting nnel see (62)PT\u2217| we havePc(X|T)\u2265\u03bb we havePc(X|T)\u2265\u03bbComputing Lemma\u00a09.For any pair of random variables andwhere The previous lemma can be directly applied to derive upper and lower bounds for In this section, we describe another instantiation of the general framework introduced in terms of functions Definition\u00a04.Let where vergence  between f, we have f-information is always non-negative. If, furthermore, f is strictly convex at 1, then equality holds if and only f-divergence in [f-divergence and f-information can be found in [f with the property f-information. Popular examples include T-information [f-information in the binary case for a certain function f, see [Due to convexity of gence in  and applfound in  and the ormation , and alsormation  for. It milar to ), then tn f, see  (Theoremf-information can be utilized in (Let lized in  and 41)\u223cPXYIn light of the discussion in f-divergence is sometimes called Hellinger divergence of order Y given T is lower bounded by Y can be reconstructed with small MMSE given an observation of T. This result serves a natural justification for Consider the function ee e.g., . Note thn et al.  and Asoon et al.  showed tUnfortunately, our approach described in fined in , for the)\u22121  when X is a Gaussian perturbation of Y. We also utilized the celebrated I-MMSE relationship [T is considered to be a Gaussian perturbation of X.Following the recent surge in the use of information bottleneck , we equality  and stroequality , we obtationship  to derivf-information [In the second part of the paper, we argue that the choice of (Shannon\u2019s) mutual information in both quations  that canquations . Neverthormation  or f-information . Invokinormation ,34, we a"}
+{"text": "Scientific reports, 10.1038/s41598-019-41819-5 published online 01 April 2019Correction to: The original version of this Article contained an error in the title of the paper, where the words \u201cdomain swapping\u201d were incorrectly presented without a space between the words, as \u201cdomainswapping\u201d. This has now been corrected in the PDF and HTML versions of the Article and in the accompanying Supplementary Information file."}
+{"text": "One characteristic of epilepsy is the variety of mechanisms leading to the epileptic state, which are still largely unknown. Refractory status epilepticus (RSE) and depolarization block (DB) are other pathological brain activities linked to epilepsy, whose patterns are different and whose mechanisms remain poorly understood. In epileptogenic network modeling, the Epileptor is a generic phenomenological model that has been recently developed to describe the dynamics of seizures. Here, we performed a detailed qualitative analysis of the Epileptor model based on dynamical systems theory and bifurcation analysis, and investigate the dynamic evolution of \u201cnormal\u201d activity toward seizures and to the pathological RSE and DB states. The mechanisms of the transition between states are called bifurcations. Our detailed analysis demonstrates that the generic model undergoes different bifurcation types at seizure offset, when varying some selected parameters. We show that the pathological and normal activities can coexist within the same model under some conditions, and demonstrate that there are many pathways leading to and away from these activities. We here archive systematically all behaviors and dynamic regimes of the Epileptor model to serve as a resource in the development of patient-specific brain network models, and more generally in epilepsy research. Epilepsy is characterized by patient-specific electrophysiological discharges. The range of mechanisms and pathways leading to the same type of seizure, however, is large. The Epileptor model has found many applications in epilepsy research and clinical applications, because it allows the classification and dynamic modeling of seizure types independent of the knowledge of its underlying biophysical mechanisms. It is based purely on the dynamic features of the seizure. We provide here a complete functional atlas of all possible behaviors of the Epileptor model, which serves as a useful resource in modeling brain networks in epilepsy. More, we explore the contribution of the Epileptor model to better understand the dynamics of the refractory status epilepticus and depolarization block phenomena, which are linked to epilepsy.Epilepsy is a condition of the nervous system in which neuronal populations manifest as repeated epileptic seizures lasting a few minutes. These seizures are spontaneous and commonly accompanied by fast abnormal discharges , after which the brain activity slowly returns to normal. Epileptic seizures may present in different forms, as well as transitions from and to these pathological states. Some seizures are controlled by medication, particularly antiepileptic drugs (AEDs). However, there are seizures that last >1 h without returning to baseline, and do not respond to AEDs (31-43%), resulting then in so-called refractory status epilepticus (RSE) . PatientOther neuroelectric phenomena are linked to epilepsy, among which spreading depression (SD) is the most prominent. SD is characterized by a slowly propagating depolarization wave [or depolarization block (DB)] in neuronal networks, followed by a shutdown of brain activity . DB is aThe mechanisms underlying the genesis of epilepsy, DB, and RSE are still largely unknown. In this article, we take an integrative approach toward the understanding of these neuroelectric phenomena. Our thinking is inspired by the wish to understand the underlying dynamic underpinnings rather than the biophysiological basis.In this context, a large number of experimental and computational models have been proposed to clarify the basic mechanisms of seizures and DB. Most computational models rely on biophysically realistic parameters, trying to reproduce experimental data . Althougwww.epinov.com; z, evolving on a very slow timescale called the permittivity variable  written in the following form:In what follows, unless otherwise stated, the values of the parameters are as follows:a =\u20091; b\u2009=\u20093; c\u2009= 1; d\u2009=\u20095; m\u2009=\u2009 0Subsystem 1: \u03b3 = 0.01Subsystem 2: z dynamics: r\u2009 = \u20090.00,035; s\u2009 = \u20094; x0 = \u22121.6.Slow x1 and y1 comprise the subsystem 1 responsible for fast discharges, and x2 and y2 the subsystem 2 involved in spike-wave events . e events . The thiAll stochastic simulations are performed with linear additive Gaussian white noise with a zero mean and a variance of 0.0025 using the Euler\u2013Maruyama method. Deterministic simulations are performed using the Runge-Kutta method with a maximal time step of 0.01.m and x0 parameters. The solutions are the vector equilibrium points. We first determine the equilibrium points of the whole system when the parameter x0 varies, for two values of the parameter m (m\u2009 = \u20090 and m\u2009 = \u20090.5). We determine the stability of the equilibrium points E by evaluating the eigenvalues of the Jacobian matrix J at the equilibrium point E, which is stable if all the real parts of the eigenvalues of J are negative  parameter space for equilibrium points, which consists of various areas, each of which is characterized by coexisting equilibrium points with different stability. Moreover, when the parameter We explore the stability of the coexisting equilibrium points for a range of z, x1) bifurcation diagram of the Epileptor for constant m, here m\u2009 = \u20090.5. The  bifurcation diagram comprises the equilibrium points of the Epileptor, where x1 is the first coordinate of the vector of equilibrium points that we determined with respect to z. All equilibrium point solutions were obtained using the Matlab solve symbolic solver, where only the  curve is divided into different branches, of which each is numerically continued separately representing a different stability type of the equilibrium points solutions. Bifurcations were identified at stability changes for given z-values and are indicated by dots in the corresponding visualizations. As the main parameters m and m and One important step in the analysis of a mathematical model is the geometrical analysis of bifurcations, which here was performed on the deterministic Epileptor model. First, we draw a  phase space below the SLE attractor shown in z equation of the Epileptor model  bifurcation diagram. Thus, we modify the z equation to stabilize the final state. We interpret graphically the divergence of the Epileptor by introducing the averaging method, which is used to locate the periodic orbits in the phase space. The periodic orbits are intersections of the z-nullcline and the z-nullcline is given by x1 for each z constant written in the following form:When using this We also determine the periodic orbits by using the Pontryagin\u2019s averaging technique . To illux0 varies in a  bifurcation diagram of periodic orbits. We determine the bifurcation that results in the appearance or disappearance of the periodic orbits. Second, we explore two parameter spaces of periodic orbits for where periodic orbits are the zeros of the x0 can change the stability of equilibrium points and then can control the Epileptor behavior. Using the fact that a trajectory moves around the equilibrium point when it is stable, we use the bifurcation analysis to find the values of x0 for which an equilibrium point is stable. There is a qualitative distinction between the stable equilibrium points, which we discuss in more detail later.The parameter m and x0.The Epileptor behavior depends on the stability of its equilibrium points. More, there is a pre-existing limit cycle (LC) attractor, which is a stable periodic orbit. In this case, the trajectory can have a behavior that is controlled by the stability of the equilibrium points or can jump to the limit cycle attractor. Thus, there is a coexistence of two attractors. We identify all coexisting attractors according to the values of the parameters We provide a detailed analysis of the subsystem 1 dynamics without coupling .z is constant  by solving the following equations:We analytically find the equilibrium points  between them. When z further increases, the stable limit cycle disappears through a homoclinic bifurcation, HB  bifurcation diagram and the z-nullcline, which is related to the parameter x0. We show how the z-nullcline moves in the bifurcation diagram when varying x0, and use the bifurcation diagram to find the equilibrium points of the fast-slow subsystem for each value of x0.We analytically find the equilibrium points by solving  of z\u02d9=0 . We detenegative . We grapAs follows from the Epileptor analysis, we determine the periodic orbits of the fast-slow subsystem as well as their stability by using the averaging method and the Pontryagin\u2019s averaging technique. The slow averaged nullcline is given by the following:z constant.x0 varies and determine the bifurcation leading to their appearance or disappearance.Here, we plot the graph of x0 for which an equilibrium point is stable. We show how stable equilibrium points can correspond to different states.Our approach to stabilizing the equilibrium points of the fast-slow subsystem is the same as that of the Epileptor model: analyze bifurcation diagrams of the fast-slow subsystem and then find the values of m and x0, which control the stability of the equilibrium point. We discuss the coexisting attractors when m and x0 have different values.The fast-slow subsystem exhibits a bistability of two attractors as the Epileptor model. The first attractor is the fast-slow limit cycle. The behavior of the second attractor depends on the parameters In this section, we analyze the dynamics of subsystem 2 (without coupling), which generates SWEs. We explore the equilibrium points, evaluating their stability and determining the bifurcation types.The subsystem 2 equations are given by the following:x2, y2) by solving the following equations:We analytically find the equilibrium points . State variables x2 and y2 are responsible for generating the SWEs with an intermediate timescale (\u03c82). We plot the Epileptor trajectory in a  phase space  diagram for m\u2009 = \u20090.5  parameter space of equilibrium points in The stability of equilibrium points changes when we vary m and x0 A,B. TrajThe parameter space comprises nine areas. The equilibrium point is an unstable focus in area 1, a stable node in area 5, and a saddle in area 4. The Epileptor model has three equilibrium points in areas 2, 3, 6, 7, 8, and 9. In area 2, a stable node, a saddle and an unstable focus coexist. In area 3, a stable focus, a saddle, and an unstable focus coexist. In area 6, three saddles coexist. In area 7, two saddles and one unstable focus coexist. In area 9, two unstable foci and one saddle coexist. In area 8, an unstable focus, an unstable node, and a saddle coexist.m, x0) parameter space of equilibrium points for We plot a  bifurcation diagram of the Epileptor model in m\u2009 = \u20090.5. x1 is the first component of the equilibrium points E. z acts as a control parameter (r\u2009 = \u20090). Z-shaped curve (Z-curve). Z-lower and Z-upper branches consist of stable nodes and unstable foci, respectively. The Z-middle branch separates Z-lower and Z-upper branches and consists of saddles. The Z-middle and Z-upper branches collide as z increases in a saddle-node bifurcation SN3  consists of unstable foci and another (dash-dotted) consists of saddles. The two sub-branches collide as z increases in a saddle-node bifurcation SN2. The equilibrium points E of the Epileptor model lie at the intersection of the z-nullcline and the curve of equilibrium points (z-nullcline (x0. The z-nullcline moves downward (x0 decreases) or upward (x0 increases) in the bifurcation diagram; hence, it intersects the curve of equilibrium points at different sites. When x0 = \u22121.6, then the z-nullcline intersects the Z-middle branch, which consists of saddles  occurs through a saddle-node bifurcation, SN1. The transition from ictal to normal states (second bifurcation) occurs though a homoclinic bifurcation, HB. The homoclinic bifurcation z(HB) corresponds to an offset threshold and the saddle-node bifurcation 1, HB].Moreover, there are two branches above the ed curve , inset. m points . The z-n saddles . Consistm in the dynamics of the Epileptor, we plot a  bifurcation diagram, when m decreases. Let m\u2009 = \u20090  bifurcation with Z-curve, the lower branch consists of saddles and the upper branch comprises two sub-branches (z decreases in a SNIC bifurcation. The second sub-branch (dash-dotted) consists of saddles. The two sub-branches collide as z increases in a saddle-node bifurcation SN2. We plot a trajectory in Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation SN1 and the trajectory switches to the Z-upper branch exhibiting an oscillatory solution, which terminates as z increases in a SNIC bifurcation (see inset). Then the trajectory is at the upper branch above the Z-curve, which consists of stable foci. The trajectory exhibits a nonoscillatory solution, which terminates as z increases in a saddle-node bifurcation SN2 and the trajectory switches to the Z-lower branch. The Z-lower branch corresponds to the normal state. The Z-upper branch and the upper branch above the Z-curve correspond to the ictal state (see inset). The transition from normal to ictal states (first bifurcation) occurs through a saddle-node bifurcation, SN1. The transition from ictal to normal states (second bifurcation) occurs through a saddle-node bifurcation, SN2. Fast discharges characterizing the ictal state correspond to the oscillatory solution, which disappears through a saddle-node on invariant circle bifurcation SNIC. Therefore, the transitions between ictal and normal states are said to be of a fold/circle bifurcation. The system is bistable on .The branches , inset. Z-shaped curve. Above, there are the following three branches: two branches consisting of saddles, and one branch consisting of stable foci for m\u2009\u2264\u20090 and unstable foci for m\u2009>\u20090. The Epileptor model undergoes a SNIC bifurcation for m\u2009\u2264\u20090 and an HB bifurcation for m\u2009>\u20090. The transitions between ictal and normal states occur through a fold/circle bifurcation for m\u2009\u2264\u20090 and through a fold/homoclinic bifurcation for m\u2009 >\u2009 0. The system is bistable on  for m\u2009 \u2264 \u20090 and on  for m\u2009>\u20090.We conclude that the bifurcation diagrams of the Epileptor model is a z, x1) bifurcation diagram for m\u2009 = \u20090 in Z-shaped curve. Z-lower, Z-middle, and Z-upper branches consist of stable nodes, saddles, and unstable foci, respectively. Decreasing z, Z-lower and Z-middle branches collide in a saddle-node bifurcation, SN1. Increasing z, Z-upper and Z-middle branches collide in another saddle-node bifurcation, SN2. The Z-upper branch terminates as z decreases in a saddle-node bifurcation SN4. Moreover, two branches appear as z decreases. The lower branch (dashed) consists of unstable foci, and the upper branch (dash-dotted) consists of saddles. Increasing z, lower and upper branches collide in a saddle-node bifurcation SN3. Decreasing z, the upper branch terminates in a saddle-node bifurcation SN4.We now analyze the bifurcation diagram when x0 = \u22121.6, the z-nullcline is at the Z-middle branch, then the equilibrium point is a saddle. We plot a trajectory in Z-lower and Z-upper branches. When a trajectory is at the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation, SN1, and the trajectory switches to the Z-upper branch, which consists of unstable foci. An unstable focus is surrounded by a stable periodic orbit  and Z-upper (dashed) branches correspond to normal and ictal states, respectively. The transition from normal to ictal states occurs through a saddle-node bifurcation SN1. The transition from ictal to normal states occurs through an HB. Thus, the transitions between ictal and normal states occur through a fold/homoclinic bifurcation. The system is bistable on .Let m = \u22120.5, we plot a  bifurcation diagram in Z-upper branch is divided into two sub-branches separated by a Hopf (H) bifurcation (z increases in a saddle-node bifurcation SN2. The second sub-branch (dashed) consists of unstable foci and terminates as z decreases in a saddle-node bifurcation SN4. An unstable focus is surrounded by a stable periodic orbit  exhibiting an oscillatory solution, which terminates as z increases in an H bifurcation. Then, the trajectory is at the Z-upper (solid) sub-branch exhibiting a nonoscillatory solution, which terminates as z increases in a saddle-node bifurcation SN2. Z-lower (solid) and Z-upper branches correspond to normal and ictal states, respectively. The oscillatory solution corresponds to fast discharges. The transition from normal to ictal states occurs through a saddle-node bifurcation, SN1. The transition from ictal to normal states occurs through a saddle-node bifurcation SN2. The oscillatory solution (fast discharges) terminates in an H bifurcation. The transitions between ictal and normal states are said to be of a fold/Hopf bifurcation. The system is bistable on .Let urcation . The firm = \u22121, we plot a  bifurcation diagram in Z-shaped curve. The Hopf bifurcation point H disappears, then the Z-upper branch consists of stable foci only, which is the equilibrium point of nonoscillatory state. Increasing z, the Z-upper (solid) branch terminates in a SNIC bifurcation  branch consists of saddles, and the lower (dashed) one consists of unstable foci. An unstable focus is surrounded by a stable periodic orbit  branch, which consists of stable foci, thereby exhibiting a nonoscillatory solution. Then, the stable focus disappears as z increases through a saddle-node bifurcation, SN2, and the trajectory switches to the Z-lower branch. The transition from Z-lower to Z-upper branches occurs through a saddle-node bifurcation, SN1, and the transition from Z-upper to Z-lower branches occurs through a saddle-node bifurcation, SN2. The transitions between Z-lower and Z-upper branches occur through a fold/fold bifurcation. The system is bistable on . Here, the SLE attractor reduces to a periodic switch between a nonoscillatory state and a NS.Let urcation . Below tZ-lower and Z-upper branches occur through a fold/homoclinic bifurcation, m = \u22120.5; and a fold/fold bifurcation, 1, SN2] for m\u2009<\u2009 0 and on  for m\u2009 \u2265\u2009 0. Moreover, the transitions between ictal and normal states occur through a fold/circle bifurcation when We conclude that when y1, \u03c8, z) phase space below the SLE attractor shown in z equation (i2 are on the left of the separatrix (S), which means that i2 are below the separatrix (S) and the SLE attractor in the phase space. To explain this divergence, we plot the z-nullcline and the z, x1) bifurcation diagram for m\u2009 = \u20090.5  branch. Then three equilibrium points coexist: two unstable foci and one saddle. The z-nullcline intersects the We consider  diagram . The z-nz, trajectories converge to LC and the amplitude of periodic orbits increases, leading to LC with a large amplitude. The intersection of the z-nullcline and the We plot the olutions \u20138. Decrex0 = \u22121.6, two periodic orbits exist for m\u2009 = \u20090.5 (m\u2009 = \u20090 (Let \u2009 = \u20090.5  and m\u2009 =(m\u2009 = \u20090 . We showz-nullcline moves downward (x0 decreases) or upward (x0 increases) in the bifurcation diagram, hence the existence of periodic orbits depends on x0. We find S and LC in a  bifurcation diagram of periodic orbits  markers and black dots correspond to LC and S, respectively. Only LC exists for large x0. Decreasing x0, LC and S coexist, and collide as x0 is further decreased in a saddle-node of periodic orbits bifurcation (SNPO), then fades.The c orbits A. x0 actm = \u221216) shows that for some x0, a third periodic orbit appears, which is labeled as blue top (+) markers. This periodic orbit is stable, and is localized above LC and S . SLC and LC are two stable limit cycles that coexist for some x0, and are separated by S. SLC exists after a SNPO bifurcation occurs when m = \u221216 and disappears when x0 is further decreased.LC and S B. Since m, x0) parameter spaces of periodic orbits: for We explore two  bifurcation diagram for m\u2009=\u20091 in z-nullcline is at the middle branch and the equilibrium point is a saddle. The z-nullcline intersects the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation SN1 and the trajectory switches to the Z-upper branch, which consists of unstable foci. Then the trajectory exhibits an oscillatory solution on the Z-upper branch and continues to SLC at which z stabilizes  bifurcation diagram for m = \u22122 in x0 = 0, the equilibrium point is an unstable focus. The z-nullcline intersects the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation SN1, and the trajectory switches to the Z-upper (solid) branch, which consists of stable foci. Increasing z, the trajectory exhibits a nonoscillatory solution on the Z-upper branch (solid), which terminates in a SNIC bifurcation  curve. Let Z-upper branch consists of unstable foci when m\u2009 = \u20090  bifurcation diagram for m = \u22128 (Z-shaped curve. Z-lower (solid), Z-middle (dash-dotted), and Z-upper (solid) branches consist of stable nodes, saddles, and stable nodes, respectively. The Z-upper branch terminates as z decreases in a SNIC bifurcation (Z-upper branch (m decreases to the Z-upper (solid) branch. The lower branch consists of unstable foci, and the upper branch consists of saddles. Increasing z, the lower and upper branches collide in a saddle-node bifurcation, SN3. Note that x0 = \u22121.6, the equilibrium point is a saddle. When a trajectory is at the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation, SN1, and the trajectory switches to the Z-upper branch, which consists of stable nodes. The trajectory exhibits a silent activity on the Z-upper branch, which terminates as z increases in a saddle-node bifurcation SN2. Then, the trajectory switches to the Z-lower branch. The transition between Z-lower and Z-upper branches occur through a fold/fold bifurcation. The system is bistable on . Time series of the Epileptor model \u03c8, subsystem 1 \u03c81, and subsystem 2 \u03c82 are plotted in m underlying a slow wave. This scenario corresponds to a depolarization block  bifurcation diagram for m = \u22128 (Z-shaped curve. Z-lower (solid), Z-middle (dash-dotted), and Z-upper (dashed) branches consist of stable nodes, saddles, and unstable foci, respectively. Above the Z-curve, lower branch consists of saddles and upper branch consists of stable nodes , and hence does not enter into a DB.The DB occurs when ion, SN2 A, and th1, SN2] interval, on which the Epileptor model is bistable. We determine the branches of the  curve existing on this interval . When x0 increases, the Epileptor stabilizes in the ictal (nonoscillatory) state, and when x0 decreases, the Epileptor model stabilizes in the normal state.The transitions between ictal and normal states of the SLE attractor occur when the equilibrium point is a saddle (m and x0 = \u22121.6), the Epileptor switches differently to the normal state according to the bifurcation type: homoclinic, SNIC, or Hopf. The Epileptor switches to the normal state just after a homoclinic bifurcation, and remains in the nonoscillatory state after SNIC and Hopf bifurcations, thereby exhibiting a nonoscillatory solution. The latter disappears as z increases through a saddle-node bifurcation, SN2, and then the Epileptor switches to the normal state. When increasing x0, the stability of the equilibrium point changes, and the Epileptor remains in the nonoscillatory state. We illustrate this scenario in During the ictal state, epileptiform fast discharges (oscillatory state) disappear through three bifurcation types depending on urcation , 6, a SNurcation , or a Hourcation . When thm\u2009 = \u20090 and x0 = \u22120.9  curve: lower and upper (solid) branches above the Z-curve, and the Z-upper (dashed) branch. The z-nullcline intersects the upper branch above Z at C. Then three equilibrium points coexist: an unstable focus, a saddle, and a stable focus (C). When a trajectory is at the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation, SN1, and the trajectory switches to the Z-upper branch exhibiting an oscillatory solution (fast discharges), which terminates as z increases in a SNIC bifurcation. Then, the trajectory exhibits a nonoscillatory solution at the upper (solid) branch above the Z-curve, and continues to C at which z stabilizes. Therefore, the transition to the Z-lower branch does not occur and the Epileptor remains in the nonoscillatory state. We plot this scenario in a  phase space  sub-branch at C which is a stable focus. When a trajectory is at the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation SN1 and the trajectory switches to the Z-upper (dashed) sub-branch exhibiting an oscillatory solution (fast discharges), which terminates as z increases in a Hopf bifurcation, H. Then, the trajectory exhibits a nonoscillatory solution at the Z-upper (solid) sub-branch, which consists of stable foci, and continues to C at which z stabilizes. The transition to the Z-lower branch does not occur, and the Epileptor remains in the nonoscillatory state. We plot this scenario in a  phase space  phase space (see C is responsible for the oscillations (2) around the stable focus. After a transient normal state, the Epileptor spirals into the equilibrium point of the nonoscillatory state exhibiting damped oscillations, and does not re-enter the normal state.Let urcation . When inm (x0 = \u22121.6). When increasing x0, the Epileptor model stabilizes its stable node, which corresponds to the equilibrium point of DB. To see this, we plot a  bifurcation diagram when x0 = \u22120.8 in z-nullcline intersects the Z-upper (solid) branch at C, which is a stable node. When a trajectory is at the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation SN1 and the trajectory switches to the Z-upper branch and enters into a DB. The trajectory continues as z increases to C at which z stabilizes. Thus, the transition to the Z-lower branch does not occur and the Epileptor remains in DB. We plot this scenario in a  phase space (see x0 = \u22121.6), the normal state of the SLE attractor disappears through a saddle-node bifurcation SN1. When decreasing x0, the Epileptor stabilizes its stable node, which is the equilibrium point of the normal state. To see this, we plot a  bifurcation diagram when x0 = \u22122.5 in z-nullcline intersects the Z-lower branch at C, which corresponds to the equilibrium point of the normal state. The ictal state (Z-upper branch) exists but not the equilibrium point, hence the Epileptor remains in the normal state, at C which is a stable node.When the equilibrium point is a saddle (m.m = 0.5 (Z-upper branch (dashed), the oscillatory solution terminates as z increases in an HB bifurcation and the trajectory switches to the Z-lower branch.m = 0.5 A: When am = 0 (Z-upper branch (dashed), the oscillatory solution terminates as z increases in a SNIC bifurcation, then the trajectory exhibits a nonoscillatory solution on the upper branch above the Z-curve, which terminates as z increases in a saddle-node bifurcation SN2. Then the trajectory switches to the Z-lower branch.m = 0 B: When aWhen m.m \u2265 0 (Z-upper (dashed) branch, which terminates as z increases in a homoclinic bifurcation HB, and then it switches to the Z-lower branch.For m \u2265 0 C: The trm = \u22120.5 (Z-upper sub-(dashed) branch, which terminates as z increases in a Hopf bifurcation H. Then the trajectory exhibits a nonoscillatory solution on the Z-upper (solid) sub-branch, which terminates as z increases in a saddle-node bifurcation SN2, and the trajectory switches to the Z-lower branch.For m = \u22120.5 D: The trm \u2264 \u22121, when a trajectory starts at i with Z-upper branch, which terminates as z increases in a saddle-node bifurcation, SN2. Then the trajectory switches to the Z-lower branch  bifurcation diagram for m\u2009 = \u20090.5 (x0 = \u22121.6). The behavior of the first trajectory (right) corresponds to SLEs, which occur through a fold/homoclinic bifurcation. The Z-middle branch acts as a separatrix between ictal and normal states. The second trajectory (left) converges to LC. The saddle periodic orbit (S) separates LC and the SLE attractor. We plot LC, SLEs, and S in a  phase space  phase space  bifurcation diagram (x0 = \u22121.6). The transitions between ictal and normal states occur through a fold/circle bifurcation. Then SLEs and LC coexist and are separated by a saddle periodic orbit (S). We plot LC, SLEs, and S in a  phase space ( diagram . The firse space A. SLEs aA fold/Hopf bifurcation:x0 = \u22121.6). Parameter settings in Y, X, z) phase space (se space A. SLEs am = \u22121 (x0 = \u22121.6). Parameter settings in Y, X, z) phase space  phase space  bifurcation diagram is plotted in m = \u22128  phase space . Let m\u2009 = \u20090, the equilibrium point is a stable node when x0 is below \u22122.1  phase space . Parameter settings in Y, X, z) phase space  is the equilibrium point of the nonoscillatory state. Y, X, z) phase space . LC (below) and the nonoscillatory state (above) coexist. The nonoscillatory state shown in A, A, and A is the same as that shown in space A, A, 30A.m, x0 and We identified seven types of coexisting attractors: a coexistence of SLE and LC \u201321, a courcation , 19, a furcation , or a fourcation .m, x0) parameter space of periodic orbits and equilibrium points in To characterize the different types of the coexisting attractors, we explore a  by using 32, which shows 18 (1\u201318) areas:For each area, the Epileptor model has different equilibrium points, depending on (I) LC: Area I in z-nullcline intersects the z-nullcline intersects the  curve at different equilibrium points. The equilibrium point is an unstable focus in area 1 and a saddle in area 14. The equilibrium points are one saddle and two unstable foci in area 7. The equilibrium points are one unstable focus and two saddles in area 9. The equilibrium points are three saddles in area 10. The equilibrium points are a saddle, an unstable focus, and an unstable node in area 8. Trajectories exhibit only a fast-slow cyclic behavior (LC), which is plotted in (II) LC and SLC: Area II in z-nullcline intersects the z-nullcline intersects the  curve at one equilibrium point, which is an unstable focus. LC and SLC coexist. The stable manifold of the saddle periodic orbit (S) separates the basin of attraction of LC and the basin of attraction of SLC. Trajectories exhibit two periodic solutions depending on initial conditions. The first solution corresponds to a fast-slow cyclic behavior (LC). The second solution corresponds to a periodic solution with a small amplitude (SLC).(III) SLC: Area III in z-nullcline intersects the z-nullcline intersects the  curve at one equilibrium point, which is an unstable focus. The trajectories exhibit only a periodic solution with a small amplitude (SLC).(IV) Nonoscillatory state: Area IV in z-nullcline and the z-nullcline intersects the  curve at different equilibrium points. The equilibrium points are a stable node, an unstable focus, and a saddle in area 4. Trajectories remain in the nonoscillatory state.(V) LC and a nonoscillatory state: Area V in z-nullcline intersects the z-nullcline intersects the  curve at different equilibrium points. The equilibrium points are a stable node, an unstable focus, and a saddle in area 5. The equilibrium points are a stable focus, an unstable focus, and a saddle in area 6. Trajectories either exhibit a fast-slow cyclic behavior (LC) or remain in the nonoscillatory state. The coexistence of LC and the nonoscillatory state is plotted in (VI) SLE with a fold/circle bifurcation: Area VI in z-nullcline and the z-nullcline intersects the Z-middle branch, which consists of saddles. Thus, a unique saddle equilibrium point exists. Since m\u2009\u2264\u2009 0, an SLE occurs through a fold/circle bifurcation.(VII) LC and SLE with a fold/circle bifurcation: Area VII in z-nullcline intersects the (VIII) LC and SLE with a fold/homoclinic bifurcation: Area VIII in z-nullcline intersects the (IX) NS: Area IX in z-nullcline and the z-nullcline intersects the  curve at the Z-lower branch, and then the equilibrium point is a stable node in area 17. The Epileptor remains in NS after a transient period, which is shown in (X) LC and NS: Area X in z-nullcline intersects the z-nullcline intersects the  curve at the Z-lower branch, which is a stable node in area 18. Then LC and NS coexist and are separated by a saddle periodic orbit (S). This coexistence is plotted in  LC and a chaotic state: Areas XI and XII in z-nullcline intersects the z-nullcline intersects the z-nullcline intersects the Z-middle branch which consists of saddles. An SLE occurs through a fold/homoclinic bifurcation in area 16. Then LC and SLE coexist in area 16. S acts as a separatrix between the basin of attraction of LC and the basin of attraction of SLE in area 16.x0 in m\u2009 = \u20091 and in m\u2009 = \u20091.5. The system is chaotic when the ISI is irregular. Therefore, LC and the chaotic state coexist in areas 15 and 16 and are separated by a saddle periodic orbit (S).We calculate the times between two successive spikes, which are referred to as the interspike intervals (ISIs) with respect to m, x0) parameter space of periodic orbits and equilibrium points in The parameter space of the Epileptor model includes attractors as LC, SLE, and normal state, but neither DB nor SLE with a fold/Hopf bifurcation. In fact, using bifurcation analysis, we demonstrated that DB and Hopf bifurcation appeared when decreasing The parameter space is divided into two parts, which are separated by a bold line (SNPO bifurcation) . Above tm and x0. To analyze this further, we determine the equilibrium points and the periodic orbits of each area (I-XIII) by using 35, which shows 20 (1\u201320) areas:For each area, the Epileptor model has different equilibrium points depending on (I) LC: Area (I) in z-nullcline intersects the z-nullcline intersects the  curve at different equilibrium points. The equilibrium point is an unstable focus in area 1 and a saddle in area 17. The equilibrium points are one saddle and two unstable foci in area 7. Trajectories exhibit only a fast-slow cyclic behavior (LC).(II) LC and SLC: Area (II) in z-nullcline intersects the z-nullcline intersects the  curve at one equilibrium point, which is an unstable focus in area 2 and a saddle in area 18. The trajectories exhibit two periodic solutions depending on the initial conditions. The first solution corresponds to a fast-slow cyclic behavior (LC). The second solution corresponds to a periodic solution with a small amplitude (SLC). Moreover, the SLC behavior depends on the stability of the equilibrium point. The SLC behavior is plotted in (III) SLC: Area III in z-nullcline intersects the z-nullcline intersects the  curve at one equilibrium point, which is an unstable focus. Trajectories exhibit only a periodic solution with a small amplitude (SLC). The SLC behavior is plotted in (IV) DB: Area IV in z-nullcline and the z-nullcline intersects the  curve at different equilibrium points. The equilibrium point is a stable node in area 8. The equilibrium points are a stable node, an unstable focus, and a saddle in area 4. The Epileptor remains in DB after a transient period, which is plotted in (V) LC and a DB: Area V in z-nullcline intersects the z-nullcline intersects the  curve at different equilibrium points. The equilibrium points are a stable node, an unstable focus, and a saddle in area 5. The equilibrium point is a stable node in area 9. Trajectories either exhibit a fast-slow cyclic behavior (LC) or enter into a DB. The coexistence of LC and DB is plotted in (VI) LC and a nonoscillatory state: Area VI in z-nullcline intersects the z-nullcline intersects the  curve at different equilibrium points. The equilibrium points are a stable focus, an unstable focus, and a saddle in area 6. The equilibrium point is a stable focus in area 10 and a stable node in area 11. Trajectories either exhibit a fast-slow cyclic behavior (LC) or remain in a nonoscillatory state. The coexistence of LC and the nonoscillatory state is plotted in (VII) Periodic switch between DB and NS: Area VII in z-nullcline and the z-nullcline intersects the Z-middle branch which consists of saddles. Then only a saddle equilibrium point exists in area 12. The ictal state of SLE reduces to DB with decreasing m. Periodic switch between DB and NS occurs through a fold/fold bifurcation, and is plotted in (VIII) LC and a periodic switch between DB and NS: Area VIII in z-nullcline intersects the m. Periodic switch between DB and NS occurs through a fold/fold bifurcation, and coexists with LC. Both are separated by a saddle periodic orbit (S). The coexistence of LC and periodic switch between DB and NS is plotted in (IX) LC and a periodic switch between nonoscillatory state and NS: Area IX in z-nullcline intersects the (X) LC and SLE with a fold/Hopf bifurcation: Area X in z-nullcline intersects the urcation . Then LC(XI) LC and SLE with a fold/homoclinic bifurcation: Area XI in z-nullcline intersects the  area 16 . Then LC(XII) A NS: Area XII in z-nullcline and the z-nullcline intersects the  curve at the Z-lower branch, and then the equilibrium point is a stable node in area 19. The Epileptor remains in NS after a transient period, which is shown in (XIII) LC and a NS: Area XIII in z-nullcline intersects the z-nullcline intersects the  curve at the Z-lower branch, and hence the equilibrium point is a stable node in area 20. Then LC and NS coexist and are separated by a saddle periodic orbit (S). This coexistence is plotted in m and x0 vary  by solving the following equations:x1 is a solution of:We analytically find the equilibrium points  exists if:X is a solution of We find J:To determine the equilibrium points stability, we analyze the eigenvalues of the following Jacobian matrix J is defined at the equilibrium point . To find the eigenvalues of J, we solve the characteristic equation:Tr(J) and Det(J) are the trace and the determinant of the matrix J, respectively.J are given by:The trace and the determinant of J (Tr(J) and Det(J) are negative and positive.An equilibrium point is stable if all the real parts of the eigenvalues of J are negative . We can J . We deteTr(J) are as follows:The roots of Det(J) are as follows:X is a solution of The roots of x1 (x1 \u2265 0) exists (see We conclude that an equilibrium point ists see  if:(49)m.We find the stability of equilibrium points x1- and y1-nullclines. The x1-nullcline . Trajectories i1 and i2 converge to one equilibrium point, which is a stable node. Trajectories i3 and i4 converge to one equilibrium point, which is a stable focus when m\u2009 = \u20090 (m\u2009 = \u20090). By increasing (m\u2009 = \u20091 and m\u2009 = \u20091.5), the stable focus loses its stability, and the equilibrium point is an unstable focus. Trajectories i3 and i4 converge to a stable limit cycle, which surrounds the unstable focus. The radius of the limit cycle increases as m increases (m\u2009 = \u20091 and m\u2009 = \u20091.5).When \u2212Iext1=0 A. We ploz\u2009 = \u20093.1, three equilibrium points coexist. The first one is a stable node and the second one is a stable or an unstable focus, depending on m. The third equilibrium point is a saddle. The stable manifold of the saddle corresponds to a separatrix between the first and second equilibrium point. The subsystem 1 undergoes a supercritical Andronov\u2013Hopf bifurcation, H, as m increases at m(H)\u2009 = \u20090.514  for large x0. Decreasing x0, S (black dotted squares) appears. Stable (LC) and saddle (S) periodic orbits approach each other as x0 decreases, collide in a saddle-node periodic orbit bifurcation, and then fades. LC and S disappear through a SNPO bifurcation  markers] appear. Hence, LC and SLC1 coexist and are separated by S. Decreasing x0, SLC1 disappears. Further decreasing x0, LC and S disappear through an SNPO bifurcation  bifurcation diagram the equilibrium points, labeled as dots  bifurcation diagram when m = \u22128 in Z-lower branch consists of stable nodes, which are the equilibrium points of the NS. The Z-upper branch consists of stable nodes (z-nullcline is at the Z-middle branch which consists of saddles (x0 = \u22121.6). When a trajectory is at the Z-lower branch, the stable node disappears as z decreases through a saddle-node bifurcation SN1 and then the trajectory enters into a depolarization block, which terminates as z increases in a saddle-node bifurcation, SN2. Thus, the transitions between the Z-lower and Z-upper branches are reduced to a periodic switch between a NS and a DB. Time series are plotted in When Z-lower and Z-upper branches occur when the equilibrium point is a saddle (x0 = \u22121.6). When x0 is increased, the fast-slow subsystem stabilizes the equilibrium point of the Z-upper branch, and when x0 is decreased, the fast-slow subsystem stabilizes the equilibrium point of the Z-lower branch .The transitions between x0 = \u22120.5. We plot a  bifurcation diagram when m\u2009 = \u20090 in z-nullcline is at the Z-upper branch which consists of a stable focus. Decreasing z, the stable node disappears through a saddle-node bifurcation SN1 and the fast-slow subsystem switches to the Z-upper branch (dashed) exhibiting an oscillatory solution, which terminates in a Hopf bifurcation, H. The fast-slow subsystem exhibits a nonoscillatory solution at the Z-upper branch (solid) and continues to C, at which z stabilizes. The imaginary part of the eigenvalues of C is responsible for the oscillations around the stable focus, which is the equilibrium point of the nonoscillatory state. Time series are plotted in Let x0 = \u22120.5. We plot a  bifurcation diagram when m = \u22128 in z-nullcline is at the Z-upper branch which consists of stable nodes. Decreasing z, the stable node disappears through a saddle-node bifurcation, SN1, then the fast-slow subsystem switches to the Z-upper branch (solid) exhibiting DB and continues to C, at which z stabilizes. The imaginary part of the eigenvalues of C goes to zero, and therefore the oscillations around C disappear. Here, the stable node (C) is the equilibrium point of DB. Time series are plotted in Let x0 = \u22122.4. We plot a  bifurcation diagram when m\u2009 = \u20090 in z-nullcline is at the Z-lower branch which consists of stable nodes. When a trajectory is at the Z-upper branch (dashed), it exhibits an oscillatory solution, which terminates as z increases in a Hopf bifurcation, H, and then a nonoscillatory solution on the Z-upper branch (solid), which terminates as z increases in a saddle-node bifurcation SN2. The fast-slow subsystem continues to C, at which z stabilizes. The stable node (C) is the equilibrium point of the NS. Time series are plotted in Let Case 1: Only LC exists. m\u2009 = \u20092 and x0 = \u22121.6, which is LC  acts as a separatrix between LC and SLE  parameter space of the fast-slow subsystem in m and x0 (area I) only LC exists. The adjacent area II shows bistability of LC and a stable focus. Both attractors are separated by a saddle periodic orbit. In the middle, LC coexists with the SLE attractor separated by a saddle periodic orbit. SLE occurs via a saddle-node/saddle-node bifurcation (area VI) and a saddle-node/homoclinic bifurcation (area VII). In area VIII, the homoclinic bifurcation HB is not completed and gives rise to another (coexisting) stable periodic orbit with a small amplitude, SLC1. In area V, DB coexists with LC. In area IX, normal brain activity and LC coexist. In area X, only normal activity exists.To characterize the coexisting attractors, we explore a ((I) LC: The z-nullcline intersects the z, x1) curve at different equilibrium points. The equilibrium point can be a stable focus, an unstable focus, or a saddle. All trajectories converge to LC. Time series are plotted in (II) Coexistence of LC and a stable focus: The z-nullcline intersects the  curve at one equilibrium point, which is a stable focus, and intersects the Z-lower branch, the stable node disappears through a saddle-node bifurcation SN1 and the trajectory switches to the Z-upper branch, which comprises a Hopf bifurcation point, H. If z decreases in a Hopf bifurcation, H. Then, the trajectory continues to the stable focus at which z stabilizes. If z decreases to the stable focus at which z stabilizes. The stable focus is the equilibrium point of the nonoscillatory state. The system is bistable on .If a trajectory is in the basin of attraction of the stable focus, then it exhibits a nonoscillatory solution following two scenarios. When the trajectory is at the m decreases to a stable node . Here, the stable node is the equilibrium point of the DB, and then DB is present in area II. LC and DB coexist as m decreases.Using analytic techniques, we observe that the stable focus reduces as (V) Coexistence of LC and a periodic switch between DB and NS: The z-nullcline intersects the  curve at one equilibrium point, which is a saddle, and intersects the H, exists for m\u2009\u2264\u20091  Coexistence of LC and SLE with a fold/fold bifurcation: Using numerical techniques, there is a saddle-node bifurcation at both offset and onset seizures. We can deduce that SLE occurs with a fold/fold bifurcation in area VI. The z-nullcline intersects the Z-upper branch consists of a stable focus, which is the equilibrium point of the nonoscillatory state. The SLE attractor reduces then to a periodic switch between nonoscillatory state and NS, which occurs through a fold/fold bifurcation, coexisting with LC. Time series are plotted in m increases, m increases through a fold/Hopf bifurcation in area VI, coexisting with LC. Time series are plotted in F1for LC.Using analytic techniques , we can (VII) Coexistence of LC and SLE with a fold/homoclinic bifurcation: The z-nullcline intersects the  curve at one equilibrium point, which is a saddle, and intersects the m\u2009>\u20091, then the transitions between Z-upper and Z-lower branches occur through a fold/homoclinic bifurcation. For m\u2009 = \u20091, a Hopf bifurcation point, H, exists such that Z-upper branch, then it exhibits an oscillatory solution, which touches the Z-middle branch before the Hopf bifurcation, H. Then the transitions between Z-upper and Z-lower branches occur through a fold/homoclinic bifurcation for m\u2009 = \u20091. LC and a fold/homoclinic bifurcation coexist and are separated by S. Time series are plotted in )>z(SN1) . When a 1:(VIII) Coexistence of LC and SLC The z-nullcline intersects the  curve at one equilibrium point, which is a saddle, and intersects the 1, and S. Then LC and SLC1 coexist and are separated by S. If a trajectory is in the basin of attraction of SLC1, then it exhibits a periodic solution with a small amplitude. When the trajectory is at the Z-lower branch, the stable node disappears through a saddle-node bifurcation, SN1, and the trajectory switches to the Z-upper branch. Then, the trajectory exhibits, as z increases, an oscillatory solution, which stabilizes at SLC1. Time series are plotted in 1 and in (IX) Coexistence of LC and a NS: The z-nullcline intersects the  curve at one equilibrium point which is a stable node, and intersects the m. We discuss these scenarios below in area X.In the following areas, LC and S disappear through a SNPO bifurcation.(III) DB: The z-nullcline intersects the  curve at one equilibrium point, which is a stable node <z(SN1) . When a (IV) Periodic switch between DB and NS: This area exhibits a periodic switch between DB and NS, like area V. In contrast, LC and S disappear through a SNPO bifurcation.Therefore, the fast-slow subsystem only switches between DB and NS.(X) NS: The z-nullcline intersects the  curve at one equilibrium point, which is a stable node. Time series of this solution are plotted in m.m < 1 (first scenario), a Hopf bifurcation point, H, exists. If a trajectory is at the Z-upper sub-branch, which consists of unstable foci, it exhibits an oscillatory solution that terminates as z increases in a Hopf bifurcation, H. Then, the trajectory exhibits a nonoscillatory solution on the Z-upper sub-branch, which consists of stable foci. The nonoscillatory solution terminates as z decreases in a saddle-node bifurcation SN2 and the trajectory switches to the Z-lower branch.For m = 1 (second scenario), a Hopf bifurcation point H exists. If a trajectory is at the Z-upper sub-branch, which consists of unstable foci, it exhibits an oscillatory solution, which touches the Z-middle branch before the Hopf bifurcation, H, as z increases. Then the trajectory switches to the Z-lower branch through an HB.For m > 1 (third scenario), a Hopf bifurcation point, H, does not exist. If a trajectory is at the Z-upper branch, which consists of unstable foci, then it exhibits an oscillatory solution, which terminates as z increases in a homoclinic bifurcation, and the trajectory switches to the Z-lower branch.For Z-lower branch consists of stable nodes, which are the equilibrium points of the normal state. At the Z-lower branch, the trajectory continues to a stable node, at which z stabilizes. Therefore, the fast-slow subsystem only remains in the normal state. Time series are plotted in The m increases.Note that the SNPO curve (bold line) decreases as m and x0. When LC coexists with an attractor and both are separated by S, the trajectories converge to LC or the attractor, depending on initial conditions. When S does not exist  bifurcation diagram for x0 = \u22120.1  by solving the following equations:We analytically determine the equilibrium points  by using the x2- and y2-nullclines, where the x2-nullcline corresponds to a cubic curve given by:y2-nullcline corresponds to two straight lines given by:We graphically determine the equilibrium points  bifurcation diagram of the subsystem 2 in x2) curve is an S-shaped curve, which comprises four branches. S-lower and S-upper branches consist of stable nodes and unstable foci, respectively. The S-middle branch consists of saddles and acts as a separatrix between the S-lower and S-upper branches. The S-upper branch is divided into two sub-branches: a stable limit cycle surrounds one sub-branch (red) but does not surround the other sub-branch (green). We call the red sub-branch a limit cycle branch, which is limited by S-middle and S-upper branches collide in a saddle-node bifurcation, SN. Increasing further S-middle and S-lower branches collide in a SNIC bifurcation  and z change the input z in z increases, then z decreases, then \u03c82; g(x1) and z.We now link the dynamics of subsystem 2 to its behavior  bursters as proposed by m, controls the Epileptor dynamics during the ictal period, and the second, x0, controls the equilibrium points of the Epileptor. Bifurcations that define how the Epileptor qualitatively changes its behavior were identified using the scaling behavior of frequency and amplitude during seizure onset and offset. A taxonomy of seizures (SLEs) assembles the bifurcations into 16 different classes , RSE, DB, and normal brain activity (NS) in the brain, under a variety of conditions. Furthermore, the model predicts the existence of different paths between these neuroelectric activities which may help to explain the mechanisms underlying their genesis, making progress in clinical and brain research."}
+{"text": "Since, in Einstein gravity, a massless scalar field with lightlike gradient behaves as a null dust, one could expect that it can act as the matter source of Vaidya geometries. We show that this is impossible because the Klein\u2013Gordon equation forces the null geodesic congruence tangent to the scalar field gradient to have zero expansion, contradicting a basic property of Vaidya solutions. By contrast, exact plane waves travelling at light speed and sourced by a scalar field acting as a null dust are possible. R is its trace, and e.g., [The Vaidya solutions of the Einstein equations , 21\\docuor)e.g., , 5). Thepp-waves [A null dust appears frequently in classical and quantum gravity, in Vaidya spacetimes , 2, pp-wpp-waves \u20138, Robinpp-waves , twistinpp-waves \u201311, in spp-waves \u201321, blacpp-waves \u201324, and pp-waves , 25. Colpp-waves , 27. A nu is a retarded null coordinate, m(u) is a regular mass function, and u. The stress-energy tensor of the null dust sourcing the Vaidya geometry isAn outgoing Vaidya solution , 2 It is well known \u201344 that  of view . However of view  has prop of view  for a diThere remains the case affinely-parametrized null geodesics.As noted in the previous section, since a null vector is defined up to a multiplicative (positive) factor, one could choose a different parametrization of the null dust in which its stress-energy tensor is instead written as ab=\u03c1\u2113a\u2113b . For a gNow consider the congruence of null geodesics tangent to the null vector geometry\u00a0, or ingogeometry\u00a0). Let usgeometry\u00a0 first: bgeometry\u00a0, their ev is the advanced null coordinate) sourced by a scalar field, that would have to be The same argument, adapted to the replacement f(u) is an arbitrary (but regular) function of u, k are constants, and [It is possible to obtain analytic solutions of the Einstein equations\u00a0 travelliy2,where 17\\documents, and 21\\documeVaidya geometries sourced by a massless scalar field mentclass2pt{minimane wave\u00a0 can be s"}
+{"text": "The Editors-in-Chief have retracted this article\u00a0(Antoine et al. All authors agree to this retraction."}
+{"text": "This method provides an effective alternative to metasurface bandwidth extension and can also be extended to higher bands such as THz and infrared frequencies.In this paper, we propose a method of designing ultra-wideband single-layer metasurfaces for cross-polarization conversion, via the introduction of Fano resonances. By adding sub-branches onto the unit cell structure, the induced surface currents are disturbed, leading to coexistence of both bright and dark modes at higher frequencies. Due to the strong interaction between the two modes, Fano resonance can be produced. In this way, five resonances in all are produced by the single-layer metasurface. The first four are conventional and are generated by electric and magnetic resonances, whereas the fifth one is caused by Fano resonance, which further extends the bandwidth. A prototype was designed, fabricated and measured to verify this method. Both the simulated and measured results show that a 1:4.4 bandwidth can be achieved for both  Metamaterials can achieve a mass of exotic physical effects, such as polarization conversion7, negative refraction8, perfect absorber10 and so on. In order to reduce bulky volume and be more suitable for application, a two-dimensional form of metamaterial is generated, called as metasurface, which is a planar array composed of sub-wavelength metamaterial units. In the past decade, study of polarization converter is quite familiar to scientific community, but it is still a key issue in electromagnetic (EM) wave. Many meaningful and excellent works have been proposed such as linear-to-linear, linear-to-circular and dual-band polarization15. If a facile structure can achieve more wideband and higher-efficiency simultaneously, it will further promote the development of various polarization manipulating devices such as high-efficient circularly polarized antennas17, more reduction of radar cross section (RCS)19, and even to construct more complex EM waves20.Metamaterials refer to artificial objects exhibiting intriguing properties which do not exist in nature22 and chiral metasurfaces24 have been accounted. However, these polarizers suffer from either the narrow bandwidth or the low-efficiency, which extremely limit their practical applications. One method to extend the bandwidth is to stack multilayers25, which will lead to bulky thickness and difficult preparation. The other method is to use multiple resonances. Chen et al.6 have indicated that an ultra-wideband metasurface can achieve a 1/4 3\u00a0dB bandwidth through four electric and magnetic Lorentzian resonances but the polarization conversion ratio (PCR) is only above 50%. Therefore, it is a priority for us to expand bandwidth under the condition of maintaining the high-efficiency.Many polarization converters based on anisotropic metasurfaces28. Fano resonances is viewed as a quantum interference between a discrete state and a continuum state in atomic physics30. The shape of Fano resonance is distinctively different from the most common observed spectral line shapes known as symmetric Lorentzian line shapes. It is characterized by an asymmetric spectral shape and have been achieved in various electromagnetic metamaterial structures31.Fano resonances have been research hotspots recently, due to their capability of providing ultra-narrow spectral linewidth and hence various potential applications such as sensing, slow light, and nano-lasing33. In this paper, we aim to further extend the bandwidth via the introduction of Fano resonance. To this end, we first give an optimized double-head arrow  that consist of one long straight cut-wire and two oblique V-shaped wires, according to multiple plasmon resonances of Chen et al.6. Next, two sub-branches are added to the unit 1, generating a composited structure . When combine them together, the canceling current will be formed between the branch and sub-branch, which can be regarded as dark mode, as shown in Fig.\u00a0x- and y-polarized waves, with almost all polarization conversion ratio (PCR) above 90%.At present, most wideband polarization rotators are created by increasing the number of Lorentzian resonances but seldom involve Fano resonances6 have indicated that the bandwidth can be broadened through multiple plasmon resonances. On the basis of it, we give the unit 1 shown in Fig.\u00a0e\u2009=\u200913.7\u00a0mm, f\u2009=\u20096.95\u00a0mm, g\u2009=\u20090.70\u00a0mm, m\u2009=\u20090.30\u00a0mm, r\u2009=\u20090.5\u00a0mm. Then, full-wave simulations are performed using the frequency domain solver in CST Microwave Studio with periodic boundary conditions in x- and y-directions and open conditions along the z-direction. The polarization conversion properties are studied by the reflection coefficients. y- (x-) polarized wave. As shown in Fig.\u00a0Chen et al.entclass1pt{minimax- and y-directions with a periodicity of p\u2009=\u200912.2\u00a0mm. Top layer is a 0.018\u00a0mm metal pattern, whose geometrical parameters are illustrated as follows: a\u2009=\u20096.95\u00a0mm, b\u2009=\u20092.82\u00a0mm, c\u2009=\u200913.7\u00a0mm, d\u2009=\u20090.5\u00a0mm, k\u2009=\u20090.7\u00a0mm, l\u2009=\u20092.51\u00a0mm, r\u2009=\u20090.5\u00a0mm. The second layer is F4B dielectric spacer with a thickness y-polarized and x-polarized incident waves. Compared with Fig.\u00a0On the other hand, hoping to get Fano resonance to broaden bandwidth of polarization conversion, two sub-branches are added to the unit 1, generating the unit 2 depicted in Fig.\u00a0The PCR is used to evaluate the performance of the polarization conversion, which is defined as entclass1pt{minimau- and v-coordinate system is introduced. The v-axis is along 45\u00b0 direction with respect to the y-axis and u-axis is perpendicular to v-axis, as shown in Fig.\u00a0y-axis. The electric field can be decomposed into two orthogonal components (directions u and v). Hence, the electric field of the incident EM wave can be expressed as u- and v-axes, respectively. The electric field of the reflected wave can be written as u- and v-axes, respectively. Due to the anisotropic characteristic of the metasurface, a different phase change x-direction. The incident polarization is rotated by 90\u00b0. To verify the polarization conversion performance of the unit 2, we carried out numerical simulations of reflection phase and amplitude characteristics. As displayed in Fig.\u00a0u- and v-polarized waves are basically equal and we get 180\u00b0\u221239\u00b0To better understand the principle of polarization conversion, entclass1pt{minimaentclass1pt{minimau- and v-axes can excite resonant eigen-modes. Figure\u00a0u-polarized EM waves while the other two eigen-modes (ii) and (iv) are excited by v-polarized EM waves. Thus, when the y-polarized waves are incident, five resonances can be excited simultaneously because the y-polarized waves have both u- and v-components. However, there is a special resonance, the eigen-mode (v). We find that co-polarization reflection in (v) is far less than others. It means the resonance in (v) is fundamentally different from the other resonances.The curve of Fano resonance is asymmetry, which is a typical feature different from that of conventional symmetric resonance curves. As shown in Fig.\u00a0In order to judge what type of each resonance, it is better to analyze surface current distributions. Therefore, we monitor the surface currents at each eigen-frequency as shown in Fig.\u00a035.Magnetic resonances are generated by anti-parallel currents coupling between top metal pattern and the background sheet. Electric resonances are generated by parallel currents. Fano resonance can be introduced by the strong interaction between bright and dark modes. More intuitively, Fano resonances can be caused by the interaction between the electric dipolesv-direction. Therefore, in Fig.\u00a0Aiming to make it more intuitive, the partial surface current is shown by the arrows painting in the Fig.\u00a0Besides, we also simulate the surface current distributions of unit 1 shown in Fig.\u00a037. From the Fig.\u00a0Fano resonances suggest a good approximation of constructive and destructive interference of discrete states and continuum states, which are viewed as dark modes and bright modes40. It can be seen from the Fig.\u00a0u- and v-direction of the surface current components in the ground sheet. In the v-direction of Fig.\u00a0u-direction, it is different for the surface currents between both sides of the cut-wire structure. From the color we can realize that the redder the color, the greater the current. Main surface currents are centralized on one side while there's almost nothing on the other side. Therefore, according to the vector synthesis principle, the main surface currents in v-direction are the two red arrows, which are parallel to v-direction surface current component in the ground sheet. Then, electrical resonances in the u-direction are formed. It is the interaction between the electric dipole and the quadrupole that causes Fano resonance with an asymmetrical spectrum. In conclusion, the first four resonances result in expansion of the operating frequency range because they are generated by electric and magnetic resonances. The fifth resonance is Fano resonance caused by interaction between dark modes and bright modes, which leads to further expansion of bandwidth.On the other hand, Fano resonances also can be intuitively explained by the coupled-mode theory of two classical Lorentzian oscillators with electromagnetic waves as driving force. In a case of two coupled oscillators, there are effectively two driving forces acting on the first oscillator, which are out of phase and cancel each otherb) is a critical factor affecting the bandwidth and the performance of Fano resonance. As exhibited in Fig.\u00a0b is 0, 1.5, 2.0, 2.3, 2.8, 3.3. Compared b\u2009=\u20091.5 with b\u2009=\u20090 in Fig.\u00a0b can almost independently change the frequency of Fano resonance, and the resonant frequency will decrease with the increase of parameter b while have almost no effect on the first four resonances. Although the Fano resonance has a characteristic of narrow band, it still can be regarded as a method to further expand bandwidth on the basis of an ultra-wideband polarization conversion metasurface. Hence, in the principle of ensuring high efficiency while maximizing bandwidth, we successfully connect the narrow band of the Fano resonance with the wide band caused by the first four Lorentz resonances by adjusting parameter b to 2.8, as shown in the green lines of Fig.\u00a0b\u2009=\u20092.8 does increase by a peak around 13.3\u00a0GHz compared with b\u2009=\u20090 and b\u2009=\u20091.5. Meanwhile, in the process of changing parameter b as shown in Fig.\u00a0It is worth mentioning that the length of oblique V-shaped wires  reduction by combining with its 90\u00b0, 180\u00b0 and 270\u00b0 rotated ones to create the destructive interferences cancellation. Meanwhile, the proposed structure is a potential candidate for many polarization control devices due to its ultra-wideband and high efficiency performance or ultrasensitive sensors because the energy of Fano resonances is strongly confined which is suitable for switching devices, sensors, isolators, etc. This work also provides a notable avenue to metasurface bandwidth extension using Fano resonances and can also be extended to higher bands such as THz and infrared frequencies."}
+{"text": "Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an earlier paper containing q-congruences for truncated basic hypergeometric series with the base being an odd power of q. We also give a number of related conjectures including q-congruences modulo the fifth power of a cyclotomic polynomial and a congruence for a truncated ordinary hypergeometric series modulo the seventh power of a prime greater than 3.We provide several new  In his first letter to Hardy from 1913, Ramanujan announced that function . During example, , 27, 31)example, , q-superq-notation: For an indeterminate q, letq-shifted factorial. For convenience, we compactly writeq-shifted factorials. Moreover,q-integer, which can be defined by n, including negative n, which in particular gives nth cyclotomic polynomial in q, which may be defined asnth primitive root of unity.Recently, the authors , the following identity:q-Gamma functionIndeed, by replacing ain from , after mq by q-analogue of Euler\u2019s identityq-series identities.Now, since 1- limit  becomes51 we get  while font}q2 in  and putt2/6. See  for receoddWe turn to discussing whether some of the results obtained in the paper can be further strengthened. We have proved Theorems\u00a0 side of  with oddNevertheless, we would like to give the following result being similar to Theorem\u00a0r be an even integer with Let The proof of Theorem\u00a0We can also prove the following refinement of  and 1.81.8. HoweLet We would like to propose the following three conjectures which are similar to Corollary\u00a0r be a positive integer and let p be a prime with Let r a positive integer, thenLet r a positive integer, thenLet q-analogues of (Conjectures\u00a0ogues of  as follon be an integer greater than 1. ThenLet p be a prime. ThenLet p) modulo It is clear that the  case of  reduces  case of  modulo \\ize that , while sq-analogue of (Finally, we give a partial and a complete logue of  as follon be an integer greater than 1. ThenLet p be a prime. ThenLet It is clear that the  case of  reduces uence in ."}
+{"text": "Q-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems. Relations are a suitable tool for describing correspondences between objects. In this study we introduce and discuss Q-neutrosophic soft relations, which can be discussed as a generalization of fuzzy soft relations, intuitionistic fuzzy soft relations, and neutrosophic soft relations. Q-neutrosophic soft relation is a sub Q-neutrosophic soft set of the Cartesian product of the Q-neutrosophic soft sets, in other words Q-neutrosophic soft relation is Q-neutrosophic soft sets in a Cartesian product of universes. We also present the notions of inverse, composition of Q-neutrosophic soft relations and functions along with some related theorems and properties. Reflexivity, symmetry, transitivity as well as equivalence relations and equivalence classes of Q-neutrosophic soft relations are also defined. Some properties of these concepts are presented and supported by real life examples. Finally, an algorithm to solve decision making problems using Q-neutrosophic soft relations is developed and verified by an example to show the efficiency of this method. The theory of neutrosophic set was firstly proposed by Smarandache  as a genAnother commonly used method in handling uncertainties and representing incomplete and unreliable data is soft set theory which was established by Molodtsov  as a genQ-fuzzy soft sets was established by Adam and Hassan ,21. The Since fuzzy set theory was introduced by Zadeh , it has The utilization of fuzzy relations  derived The relations between fuzzy sets, soft sets and their extensions have been widely studied. However, these relations do not encompass indeterminate information which appears in two dimensional universal sets. To overcome this, we introduce the Q-neutrosophic soft relation (Q-NSR), which represents the degree of presence, absence or indeterminacy of interaction between the elements of the Q-neutrosophic soft sets (Q-NSSs). Thus, it serves the indeterminacy and two-dimensionality of a data set at the same time, which cannot be served by fuzzy sets, soft sets and their extensions models. We present the concepts of inverse, functions and composition of Q-neutrosophic soft relations (Q-NSRs), some related theorems and properties. We define reflexivity, symmetry, transitivity as well as equivalence relations and equivalence classes of Q-neutrosophic soft relations (Q-NSRs). To show the ability of this model to solve decision making problems with two-dimensional indeterminate information, we developed an algorithm to solve decision making problems using Q-neutrosophic soft relations (Q-NSRs) and illustrate it by an example.In this section, we review the notions of soft sets, neutrosophic sets, neutrosophic soft sets with some of their properties which are pertinent to this work. The Q-neutrosophic soft sets (Q-NSSs) is also introduced.X.Soft set theory was first introduced by Molodtsov  as a parDefinition\u00a01A pair . A pairNeutrosophic set was established by Smarandache  as a genDefinition\u00a02\u0393 on the universe X is defined asA neutrosophic set and. A neutDefinition\u00a03\u0393 and \u03a8 be two neutrosophic sets, then we say that \u0393 is a subset of \u03a8 denoted by Let . Let \u0393 Maji  presenteDefinition\u00a04Let X be an initial universe set and E be a set of parameters. Consider . Let X We will now introduce the concept of Q-neutrosophic set to provide a way to deal with uncertain, indeterminate and inconsistent two-dimensional information. We also extend this concept to multi Q-neutrosophic set and Q-neutrosophic soft set (Q-NSS).Definition\u00a05.Let X be a universal set and Q be a nonempty set. A Q-neutrosophic set where Note that the set of all Q-neutrosophic sets over X will be denoted by Definition\u00a06.Let X be a universal set, Q be any nonempty set, l be any positive integer and I be a unit interval where where l is called the dimension of The set of all multi Q-neutrosophic sets of dimension l in X and Q is denoted by Definition\u00a07.Let X be a universal set, E be a set of parameters, and Q be a nonempty set. Let such that The set of all Q-neutrosophic soft sets (Q-NSSs) in X and Q is denoted by Definition\u00a08.Let The following example illustrates the above definition of the Q-NSS.Example\u00a01.Suppose we want to examine the attractiveness of houses that a person is considering purchasing. Suppose there are three houses in the universe The Q-NSS In this section, after introducing the Cartesian product of two Q-NSSs, we will characterize the idea of Q-NSR, and present two fundamental operations of Q-NSRs, namely inverse and composition with some essential properties.In the following we define the Cartesian product of two Q-NSSs followed by an illustrative example.Definition\u00a09.If X is an initial universal set, Q is a nonempty set, E is a set of parameters, where Example\u00a02.Suppose we have a set of students The Cartesian product of where elements will look likeNow, we introduce the relation between two Q-NSSs, followed by the definitions of the domain and the range of a Q-NSR with some illustrative examples.Definition\u00a010.If X is an initial universal set, Q is a nonempty set, E is a set of parameters, where for all If If Definition\u00a011.Let R be a Q-NSR from Example\u00a03.Reconsider Example 2 with a relation R from Then Definition\u00a012.The identity relation Example\u00a04.In Example 2, the relation Now, we introduce the operations of inverse and composition of two Q-NSRs followed by examples and relevant theorems.Definition\u00a013.If It is to be noted that the inverse of R is defined by reversing the order of every pair belonging to R.Example\u00a05.Reconsider R as in Example 3, where we would then have Theorem\u00a01.Suppose 1.\u00a02.\u00a0If Proof.\u00a0If Next, we will propose the definition of the composition of Q-NSRs along with an illustrative example, followed by related theorem.Definition\u00a014.If where for all Example\u00a06.Let Suppose that Define the Q-NSRs The relation The composition between the Q-NSRs The components Theorem\u00a02.If Proof.\u00a0If Similar results follow for the rest of the terms. This completes the proof.\u2003\u2610In this section, we will introduce various types of Q-NSRs, partitions and equivalence classes of Q-NSSs with some related theorems.Definition\u00a015.Let R be a relation on 1.\u00a02.\u00a03\u00a04\u00a0Example\u00a07.Consider a Q-NSS Consider a relation Definition\u00a016.Let Example\u00a08.Reconsider R as in Example 3, we would then have Lemma\u00a01.Let Proof.\u00a0Suppose Conversely, suppose Now, we define the partition of a Q-NSS followed by some related theorems.Definition\u00a017.A collection of nonempty Q-NS subsets 1.\u00a02.\u00a0Example\u00a09.Let Suppose Remark\u00a01.Elements of the partition are called a block of Corresponding to a partition Theorem\u00a03.Let Proof.\u00a0Reflexive: Let Symmetric: If Transitive: If Remark\u00a02.The equivalence Q-NSR defined in the above theorem is called an equivalence relation determined by the partition P. In the previous example the equivalence relation determined by the partition Theorem\u00a04.Corresponding to every equivalence relation defined on a Q-NSS Proof.\u00a0A corresponding to P of (i)(ii)If Let Since Now for the second part, let Remark\u00a03.The partition constructed in the above theorem consisting of all equivalence classes of In this section, we present the concept of Q-NS function and some special types of Q-neutrosophic soft functions with related theorems.Definition\u00a018.Let Example\u00a010.Reconsider Example 2. The Q-NSR f which consists of a science student with excellent GPA forms a Q-NS function from Definition\u00a019.Let 1.\u00a0f is injective (one to one) if 2.\u00a0f is surjective (onto) if 3.\u00a0f is bijective if it is both injective and surjective.4.\u00a0f is a constant function if all elements in 5.\u00a0f is an identity function if the identity Q-NS function I on a QNSS Theorem\u00a05.Let 1.\u00a02.\u00a03.\u00a0Proof.\u00a01. Let 2. Let This implies, Now, clearly 3. Let f is one to one. Conversely, suppose Definition\u00a020.Let Definition\u00a021.Let Now we will define and propose a few theorems on the composition of Q-neutrosophic soft functions.Theorem\u00a06.If Proof.\u00a0f is one to one, Let f is surjective, there exists a unique element Now Theorem\u00a07.Let Proof.\u00a0f and g are one to one we have Let g is onto. Again since f is onto there exists Let In this section, we present an application of Q-NSR in a decision-making problem.The problem we consider is as below.E be a set of parameters where Let Suppose the Q-NSS Step\u00a01.X, Construct two Q-NSSs over Step\u00a02.Construct a Q-NSR Step\u00a03.Compute the comparison table using the formula: Step\u00a04.Select the highest numerical grades for each column in the comparison table.Step\u00a05.Find the score table which shows the objects with highest numerical grades corresponding to every pair of parameters.Step\u00a06.Compute the score Step\u00a07.M where The decision is any one of the elements in Then we can select a car on the basis of their parameters using Q-NSR, by applying the following algorithm.To execute the above steps, we will use the Q-NSSs We obtain the Q-NSR We compute the comparison table as:The highest numerical grade for each column in The score of each object by taking the sum of these numerical grades are: d\u201d of color \u201cq\u201d, as the appropriate solution for selecting the most suitable car according to the basis of parameters Hence, This work established the notion of relations between Q-NSSs. It improved the concept of relations between fuzzy sets, soft sets and hybrid models of these two types of sets because the relations have been constructed based on the Q-NSSs model which has three independent two-dimensional membership functions for uncertainty, indeterminacy and falsity. It provided an adequate parametrization tool to deal with the aspects of two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems. The notions of inverse, composition of Q-NSRs and functions were also presented along with some related theorems and properties. The ideas of reflexive, symmetric, transitive and equivalence Q-NSRs were defined followed by the introduction of the associated properties with illustrative examples. An algorithm using Q-NSR was constructed and applied to a decision making problem. Q-NSS facilitates the way to numerous prospects for future research since it serves the two-dimensionality and indeterminacy simultaneously. Thus, it can be extended using the refined neutrosophic set , soft ex"}
+{"text": "Scientific Reports 10.1038/s41598-020-62298-z, published online 23 April 2020Correction to: The original version of this Article contained errors.All instances of \u2018San Juan Islands\u2019 now read \u2018Gulf Islands\u2019.rs,NIR in Eq. (1), where the first instance of a minus should have been a plus:Additionally, as a result of clerical error the wrong sign was used in the definition of R\u2032now reads:This has now been corrected in both PDF and HTML version of the Article."}
+{"text": "Scientific Reports 10.1038/s41598-019-41318-7, published online 20 March 2019Correction to: Nematus oligospilus\u201d was incorrectly given as \u201cNematus Oligospilus\u201d.The original version of this Article contained an error in the title, where \u201cIn addition, in Fig. 2, panel (b) was a duplication of part of panel (a).These errors have now been corrected in the PDF and HTML versions of the Article."}
+{"text": "D with quotient field K, we give an easy to verify graph-theoretic sufficient condition for an element to be absolutely irreducible and show a partial converse: the condition is necessary and sufficient for polynomials with square-free denominator.An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one  factorization into irreducibles. In the case of the ring  Let associated in R if there exists a unit r = us. We denote this by Two factorizations into irreducibles of the same element,essentially the same if n\u2009=\u2009m and, after a suitable re-indexing, essentially different.are called tions in  are callDefinition 1.1.R be a commutative ring with identity. An irreducible element absolutely irreducible , if for all natural numbers n, every factorization of nc is essentially the same as Let R that is called \u201cnot absolutely irreducible\u201d might not be irreducible at all, whereas a \u201cnon-absolutely irreducible\u201d element is assumed to be irreducible, but not absolutely irreducible.Note the following fine distinction: an element of We now concentrate on integer-valued polynomials over a principal ideal domain.D is a principal ideal domain, is called primitive if the greatest common divisor of its coefficients is 1.Recall that a polynomial in Definition 1.2.D be a principal ideal domain with quotient field K, and f asI a finite (possibly empty) set, and each ig primitive and irreducible in standard form of f.Let b as the denominator, to a as the constant factor, and to numerator of f, keeping in mind that each of them is well-defined and unique only up to multiplication by units of D.We refer to Definition 1.3.fixed divisor of f, denoted D generated by f(D).For image-primitive.An integer-valued polynomial D is a principal ideal domain, we may, by abuse of notation, write the generator for the ideal, as in When Remark 1.4.D be a principal ideal domain with quotient field K, and f is in b divides Let Remark 1.5.D be a principal ideal domain with quotient field K. Then any non-constant irreducible element of f.Let a\u2009=\u20091 and Furthermore, Definition 1.6.D be a principal ideal domain. For p a prime element in D, we letLet Remark 1.7.D up to multiplication by units.By the above definition,By the nature of the minimum function, the fixed divisor is not multiplicative:2.We refer to, for instance,  for the Definition 2.1.D be a principal ideal domain, ig is essential for p among the jg with w is then called a witness for ig being essential for p.We say that ig is quintessential for p among the jg with w is called a witness for ig being quintessential for p.We say that Let jg with We will omit saying \u201camong the Remark 2.2.ig with ig being essential  is an edge if and only if there exists a prime element p in D such that both ig and jg are essential for p among the kg with The quintessential graph of the indexed set of polynomials I, and in which  is an edge if and only if there exists a prime element p in D such that both ig and jg are quintessential for p among the kg with The Let Example 2.4.Let and setg is 15.w\u2009=\u20091, 2, 0, respectively, as witnesses, we see that g1 is not essential for 5 because a, also Taking w\u2009=\u20091, 0, 2 respectively, as witnesses, we see that g4 is quintessential for 3. The polynomial g3 is not essential for 3.Taking A quick check shows that the fixed divisor of Lemma 2.5.Let D be a principal ideal domain anda non-constant image-primitive integer-valued polynomial, written in standard form according to where T is a finite set of pairwise non-associated primes of D, and letEveryn can be written asdividing fwithforand uniquefor. Moreover, every such representation of h satisfies:Ifandj is quintessential for q among thesuch that g, thenj and gk are both quintessential for the same primeIn particular, whenever g, thenProof.nf is image-primitive, and, therefore, all polynomials in nf are image-primitive. Let h is written in standard form as in k. This is so because h and k are image-primitive; see We know jg is quintessential for q. Note that, by jg in the numerator of any factor of nf is unique.Now let Writing D.(i) follows from unique factorization in (ii) follows from unique factorization in w for jg being quintessential for q. Since f is image-primitive, To see (iii), consider a witness k instead of h).\u2013(iii) together imply Theorem 1.Let D be a principal ideal domain with quotient field K. Letbe a non-constant image-primitive integer-valued polynomial, written in standard form aswith, andi is primitive and irreducible in, where each gIf the essential graph ofis connected, then f is irreducible inProof.f is irreducible in If f can be expressed as a product of m non-units if is a constant, and that Now assume kh primitive in I into non-empty pairwise disjoint subsets Write i to j in the essential graph of p0 in D dividing b, p0. As ig is essential for p0, p0 cannot divide any kb with p0 divides b1. For any kg essential for p0 it follows that kp for which both kI, and, finally, that Select m\u2009=\u20091. \u25a1As Theorem 2.Let D be a principal ideal domain andbe non-constant and image-primitive, written in standard form aswhereis a finite set and foris primitive and irreducible inIf the quintessential graph G ofis connected, then f is absolutely irreducible.Proof.i, p, Supposet with tf is a power of f by showing that each ig with tf with the same exponent.Fix I, h, a prime element hp in T such that hp. By tf with the same exponent. Eventually, ig and jg occur in the numerator of tf with the same exponent, for arbitrary tf is a power of f. Since tf is irreducible, tf = f. \u25a1Let or as in  and, henExample 2.6.The binomial polynomialThe converse of f is square-free, as we now proceed to show, cf. There is, however, a converse to 3.D be a principal ideal domain with quotient field K. When we talk of the denominator of a polynomial in Let Remark 3.1.D be a principal ideal domain. Suppose the denominator of Let f is irreducible in ig is essential for some ig. This further implies Then, if Theorem 3.Let D be a principal ideal domain andbe non-constant and image-primitive, with square-free denominator, written in standard form aswhereis a finite set and foris primitive and irreducible inLet G be the quintessential graph of Then f is absolutely irreducible if and only if G is connected.Proof.G is connected. Now assume G is not connected. We show that f is not absolutely irreducible. If f is not even irreducible, we are done. So suppose f is irreducible. This implies G is not connected, I is a disjoint union of J1 and J2, both non-empty, such that there is no edge  with In view of Theorem 2, we only need to show necessity. If T as a disjoint union of T1 and T2 by assigning every T1, every T2, and assigning each ig is quintessential to T1 or T2 arbitrarily. , each oRemark 3.2.D be a principal ideal domain. The proof of Theorem 3 shows that any non-absolutely irreducible element nf already for n\u2009=\u20093.Let D is a principal ideal domain, p a prime of D and each f is an irreducible element of ig is essential for p, that is, for each each If An analogous statement relates absolutely irreducible integer-valued polynomials with prime denominator to quintessential irreducible factors of the numerator:Corollary 3.3.Let D be a principal ideal domain,a prime, anda finite set. For, letbe primitive and irreducible in. LetThen f is an absolutely irreducible element ofandi is quintessential for p among the gi withg, that is, for eachthere existssuch thatandfor alleach Proof.f is in f is, in particular, irreducible and therefore ig is quintessential for p. \u25a1If We conclude by an example of how to apply Example 3.4.The following polynomial This is so because the essential graph of"}
+{"text": "Nature Communications 10.1038/s41467-020-18279-x, published online 7 September 2020.Correction to: The original version of this Article contained errors in Fig. 1. The label \u2018a\u2019 was omitted for the left panel and the label \u2018b\u2019 was omitted for the right panel. In Fig. 1b, the right parenthesis was incorrectly positioned indicating a 4-carbon linker, rather than the correct 6-carbon linker. These errors have been corrected in both the PDF and HTML versions of the Article."}
+{"text": "The authors wish to make the following correction to this paper :p > 0.001) compared...\u201d. It should instead read \u201c...LC-HS extract was statistically less (p < 0.001) compared... \u201d. Furthermore, the last sentence of the same paragraph reads \u201cInterestingly, the differences observed in the reduction of fat mass showed the effectiveness of the HS-LC extract in reducing fat mass\u201d. It should instead read \u201cInterestingly, the differences observed in the reduction of fat mass showed the effectiveness of the LC-HS extract in reducing fat mass\u201d. In this respect, there are several parts of the manuscript which reads HS-LC, it should be read as LC-HS instead. This includes: page 2, paragraph 2; Figure 1; page 4, last paragraph.There are text errors in Section 4.3.2 Densitometry, third paragraph. The second sentence states that \u201c...LC-HS extract was statistically less (p < 0.003)\u201d.There is also a missing explanation in the same section, regarding the intergroup analysis of the results. At the end of the third paragraph, it should include the following sentence: \u201cIntergroup analysis revealed significant differences between both groups, where LC-HS significantly decreased body fat mass compared to placebo (p = 0.014)\u201d, should read \u201cInter-group analysis revealed that the LC-HS extract significantly decreased the body weight compared to placebo (p = 0.014)\u201d. In the same section, sentence \u201cTherefore, the diminution of BMI after the consumption of the placebo was shown to be less than that observed for the LC-HS extract (p = 0.013)\u201d, should read \u201cTherefore, intergroup analysis revealed that the BMI of the LC-HS group significantly decreased with respect to the placebo group (p = 0.013)\u201d.In Section 4.2 Weight and BMI, the sentence \u201cTherefore, it can be determined that the LC-HS extract significantly decreased the body weight of the subjects (Information is missing from It should be as follows:Information is missing on It should be as follows instead:These changes have no material impact on the conclusions of our paper. The authors would like to apologize for any inconvenience caused to the readers by these changes."}
+{"text": "N = 24 BN; N = 24 BED) in the analyses. Participants allocated to the food-specific, compared to the general intervention group, showed significantly greater reductions in reaction time to low energy-dense foods, compared to non-foods, by post-intervention. Commission errors significantly increased from baseline to post-intervention, regardless of stimulus type (food vs. non-food) and intervention group . There were no significant changes in omission errors. P3 amplitudes to \u201cno-go\u201d cues marginally, but non-significantly, decreased by post-intervention, but there was no significant interaction with stimulus type (high energy-dense food vs. non-food) or intervention group . There were no significant changes in N2 amplitudes to \u201cno-go\u201d cues, N2 amplitudes to \u201cgo\u201d cues, or P3 amplitudes to \u201cgo\u201d cues from baseline to post-intervention. Training effects were only marginally captured by these event-related potentials. We discuss limitations to the task paradigm, including its two-choice nature, ease of completion, and validity, and give recommendations for future research exploring ERPs using inhibitory control paradigms.In a feasibility trial comparing two forms of combined inhibitory control training and goal planning  among patients with bulimia nervosa (BN) and binge eating disorder (BED), we found evidence of symptomatic benefit, with stronger effects among participants receiving a food-specific intervention. The aim of the present study was to examine changes in behavioral outcomes and event-related potentials  from baseline to post-intervention that might suggest the mechanisms underpinning these effects. Fifty-five participants completed go/no-go tasks during two electroencephalography (EEG) sessions, at baseline and post-intervention. The go/no-go task included \u201cgo\u201d cues to low energy-dense foods and non-foods, and \u201cno-go\u201d cues to high energy-dense foods and non-foods. Datasets with poor signal quality and/or outliers were excluded, leaving 48 participants ( The number of individuals receiving an eating disorder diagnosis has been increasing since the 1980s . This isImpulsivity is considered to be a risk factor for binge eating . ReviewsAs a multidimensional construct, impulsivity is thought to consist of two main components: decreased inhibitory control and increased reward sensitivity . AccordiEvent-related potentials (ERPs), derived from EEG recordings, offer the possibility of exploring cognitive processes within neural circuits . The N2,P3a among participants with healthy, overweight, and obese BMIs, amplitudes were enhanced when the task involved inhibiting to high energy-dense, as opposed to low-energy dense foods  and changes in N2 and P3 amplitudes to high energy-dense foods. Since the timing and onset of N2 and P3 can vary as a function of processing speed and training, we explore their respective latencies too.Recent evidence from a feasibility trial in our laboratory has found that an intervention combining go/no-go training and implementation intentions is associated with reductions in binge eating frequency among individuals with bulimia nervosa and BED . AccordiWe hypothesized that reaction time and omission errors to \u201cgo\u201d cues  and commission errors to \u201cno-go\u201d cues  will decrease from baseline to post-intervention. These effects will be more pronounced for food cues, and among individuals receiving a food-specific intervention.In response to \u201cno-go\u201d cues, we hypothesized that mean \u201cno-go\u201d N2 amplitudes will increase from baseline to post-intervention, indicative of improved inhibitory control, and that mean \u201cno-go\u201d P3 amplitudes will decrease from baseline to post-intervention, indicative of reduced motivated attention. The opposite pattern is expected for \u201cgo\u201d cues. Again, these effects will be more pronounced to food cues, and among individuals receiving a food-specific intervention. Finally, we predict that the training effects on binge eating will correlate with \u201cno-go\u201d N2 and P3 amplitudes to high energy-dense foods.N = 40) and BED (N = 38) were recruited through eating disorder charity websites, social media, flyers, and participant identification centers that supported the study. They were then randomly allocated to a food-specific or general intervention, which included both go/no-go training and goal planning . Within this manuscript, only participants who attended and completed both baseline and post-intervention EEG sessions were included (N = 55).Participants with bulimia nervosa  of at least 18.5, were between the ages of 18 and 60, did not have a visual impairment that could not be repaired with eyewear, a neurological impairment, an alcohol or drug dependence, or psychosis.Eligibility required that participants met criteria for bulimia nervosa or BED according to the Eligibility clearance. The Structured Clinical Interview for DSM-V SCID-5; , a semi-Over the last 28 days, how many times have you eaten what other people would regard as an unusually large amount of food?).Binge eating frequency. Item 13 of the eating disorder examination questionnaire EDE-Q;  was usedFood-specific go/no-go task. The present study used the food-specific go/no-go task, as implemented by EEG was recorded continuously throughout the experimental tasks using BrainVision Recorder, and amplified with two 32-channel BrainAmp DC amplifiers  An actiCAP 64Ch standard cap was equipped after the 10\u201320 system . FCz wasOffline, EEG data pre-processing was done using EEGLab  and compPrimarily driven by previous EEG studies using the go/no-go task e.g., , we had Similarly, based on previous literature  and our Individuals who expressed interest in learning about the study procedures were sent an information sheet detailing the procedure. Next, they were contacted for a 15-min eligibility phone interview. Those who met criteria were sent a consent form indicating their rights as participants. After informed consent, an appointment was booked for the first EEG session and participants were sent a battery of questionnaires to complete via an online platform . Before entering the laboratory for the first EEG session, participants were instructed to withhold from food, caloric drinks, and nicotine for 2 h, as well as caffeinated drinks and alcohol for 24 h. During the laboratory session, participants were briefed about what the session will involve. They were then asked to sign a hard copy of the consent form, and their weight and head circumference were measured. After the appropriate EEG cap size was selected, the researcher put the cap on and applied electro-gel into the electrodes.Before completing computerized tasks during EEG recording, participants were instructed to rest with their eyes open for 3 min and to rest with their eyes closed for 3 min. The researcher then explained the task rules and participants completed a practice trial of the go/no-go task, which included only 36 of the 216 trials of the full-length version. The average duration of the session was 2 h and 30 min. After 30 \u00b1 2 days , the same procedure was followed for the second EEG session.All procedures were revised and approved by the London Westminster Research Ethics Committee and the Health Research Authority (IRAS Project ID: 209609).The study followed a mixed models design, with intervention  as the between subject variable and time (baseline vs. post-intervention) as the between subject variables.The inhibitory control training used was developed at the University of Exeter . ParticiImplementation intentions involved encouraging participants to identify an unhelpful habit, reflect on situations and motivations that are likely to precede the unhelpful behavior, and then design an alternative behavior that could replace the unhelpful behavior. Participants allocated to the food-specific intervention group were asked to select an unhelpful behavior that was related to food/eating, while those allocated to the general intervention group were asked to select an unhelpful behavior that was unrelated to food/eating . One example would be: \u201cIf I am home alone (situation) and feeling anxious (motivation), then I normally buy binge food (unhelpful eating-related habit),\u201d would be replaced with \u201cIf I am home alone and feeling anxious, then I will meditate for 10 min .\u201d Each participant was assigned a trained mentor who followed up with him/her weekly via email for 4 weeks.t-test was conducted to explore between-group differences in training task completion, and a chi-squared test was conduced to explore between group differences in implementation intention  engagement. Next, independent samples t-tests were conducted to ensure that the two interventional groups did not significantly differ on demographic and clinical characteristics.Statistical analyses were conducted using SPSS 24  for Mac.For behavioral data analysis, a repeated measures ANOVA was conducted to measure reaction time to \u201cgo\u201d cues at two time points, across two types of stimuli, and between two intervention groups. The same ANOVA structure was used to analyze commission and omission errors, separately. ANOVAs followed the structure: 2 (time: pre- vs. post- intervention) \u00d7 2 (type of stimulus: low/high energy-dense food vs. non-food) \u00d7 2 . \u201cNo-go\u201d analyses included high energy-dense foods and non-foods, while \u201cgo\u201d analyses included low energy-dense foods and non-foods.t-tests were used to compare N2 and P3 amplitudes to \u201cno-go\u201d and \u201cgo\u201d non-food cues.To ensure that ERP amplitudes reflected the expected task demands, two paired samples For the main analysis, two repeated measures ANOVAs (for P3 and N2 separately) were conducted to measure amplitudes to \u201cno-go\u201d cues at two time points, across two types of stimuli, and between two intervention groups. They followed the format: 2 (time: pre- vs. post- intervention) \u00d7 2 (type of stimulus: high energy-dense food vs. non-food) \u00d7 2 . This was repeated for \u201cgo\u201d cues, with the following format: 2 (time: pre- vs. post- intervention) \u00d7 2 (type of stimulus: low energy-dense food vs. non-food) \u00d7 2 . The main analyses were repeated for ERP latencies.minus post-intervention no-go N2 amplitudes to high energy-dense food, (2) Baseline minus post-intervention no-go P3 amplitudes to high energy-dense food, and (3) Baseline minus post-intervention binge eating frequency. This analysis structure was repeated for ERP latencies.Finally, two-tailed Pearson\u2019s correlations were used to assess the correlation between changes in binge eating frequency and changes in ERP amplitudes to high energy-dense foods across time. The variables were created using the following formulas: (1) Baseline p > 0.05; see SD = 6.79). There was no significant difference in the number of trainings completed between participants in the food-specific intervention group  and participants in the general intervention group . With regards to if-then planning, 50% of participants were minimally engaged at implementing their plan. There were no significant differences in engagement between participants in the food-specific vs. general intervention group .No significant differences in demographic and clinical characteristics were found between the two intervention groups  = 28.12, p < 0.001, \u03b72 = 0.379] and a significant interaction between time x type of stimulus x intervention group , indicating that participants in the food-specific intervention, compared to the general intervention group, showed a significantly greater reduction (training effect) in reaction time to low energy-dense foods, compared to non-foods, by post-intervention (see p > 0.05). Although there was a main effect of time on commission errors , the direction, indicating that participants made more errors by post-intervention, compared to baseline, was unexpected. No other significant main effects of interaction effects were significant  see There was a significant main effect of time on reaction time . Neither was there a time \u00d7 type of stimulus \u00d7 intervention group interaction effect . There was no significant main effect of time  and no time x type of stimulus x intervention group interaction effect  on \u201cno-go\u201d N2 latency.There was no main effect of time on \u201cno-go\u201d N2 amplitudes , but no significant time x type of stimulus x intervention group interaction . There was a significant main effect of time on \u201cno-go\u201d P3 latency , indicating that \u201cno-go\u201d P3 latency decreased from baseline to post-intervention regardless of stimulus type. There was no time x type of stimulus x intervention group interaction effect  on \u201cno-go\u201d P3 latency.There was a marginal, but non-significant, main effect of time on \u201cno-go\u201d P3 amplitudes . Moreover, the expected 3-way interaction was not significant . There was no significant main effect of time  and no time \u00d7 type of stimulus \u00d7 intervention group interaction effect  on \u201cgo\u201d N2 latency.There was no main effect of time on \u201cgo\u201d N2 amplitudes , and the expected 3-way interaction was not significant . There was a significant main effect of time on \u201cgo\u201d P3 latency , indicating that \u201cno-go\u201d P3 latency decreased from baseline to post-intervention regardless of stimulus type. There was no time x type of stimulus x intervention group interaction effect  on \u201cgo\u201d P3 latency.There was no main effect of time on \u201cgo\u201d P3 amplitudes [See SD = 10.28).Across all participants, the mean reduction in binge eating frequency was 3.95  or N2 latency to high energy-dense food . Moreover, there was no significant correlation between changes in binge eating frequency and changes in no-go P3 amplitude to high-energy dense food  or P3 latency to high energy-dense food .There was no significant correlation between changes in binge eating frequency and changes in no-go N2 amplitude to high energy-dense foods  and event-related potential  changes at baseline and at the end of an intervention designed to modify inhibitory control for bulimia nervosa and BED. The research aimed to explore whether changes would be present, whether they would be specific to food, and whether they would differ between the two intervention groups.In line with our hypothesis, individuals allocated to the food-specific intervention group, compared to the general intervention group, showed significantly greater reductions in reaction time to low-energy dense foods, compared to non-foods, from baseline to post-intervention. These indicate that successful stimulus-response learning to \u201cgo\u201d cues had taken place, which may have induced a beneficial attentional bias toward these foods. Participants in both intervention groups showed significant reductions in P3 latency over time, indicating a speeding of task-related information processing . ContrarAt baseline, \u201cno-go\u201d cues elicited larger N2 amplitudes and smaller P3 amplitudes compared to \u201cgo\u201d cues, suggesting that there was greater inhibition and less attention/salience toward \u201cno-go\u201d cues, lending evidence to the fundamental validity of the task and training.Despite this, no significant increases in \u201cno-go\u201d N2 amplitudes were found from baseline to post-intervention, and no significant differences were found between the two intervention groups. This was in line with findings from previous research, which reported no increase in N2 amplitude as a result of inhibitory control training . Such fiAlbeit marginally and non-significantly, P3 amplitudes to \u201cno-go\u201d cues descriptively decreased from baseline to post-intervention. Nonetheless, there was no significant interaction between time x type of stimulus x intervention group, and no significant correlation between changes in binge eating frequency and no-go P3 amplitudes to high energy-dense foods. These indicate that the marginal decrease in P3 to \u201cno-go\u201d cues may reflect a general depreciation that comes with repeated task completion. Given that the P3 amplitude is sensitive to the amount of attentional resources engaged , it is lOur hypotheses regarding changes in N2 to \u201cgo\u201d cues were not supported and no significant 3-way interaction was found. In addition, while we expected less negativity over time (suggestive of reduced inhibition), there was a non-significant trend in the opposite direction. These findings might have been influenced by the inclusion of a binary \u201cleft-right\u201d decision to the \u201cgo\u201d instruction . This additional attentiontal control may have slowed down the \u201cgo\u201d process and engaged inhibitory processes.In addition, no significant changes in P3 amplitudes to \u201cgo\u201d cues were found from baseline to post-intervention, and no significant 3-way interaction was found. While previous research using similar methodology had found enhanced P3 amplitudes in frontal electrodes over the course of training , the go/In light of these findings, we were unable to identify changes in neural components that correlate with changes in eating behavior over time. Therefore, while changes in binge eating frequency were found on a behavioral level , it remains unclear what change processes had occurred on a neural level. A consideration of limitations is essential. For instance, the negligible error rates during task completion may suggest that the task was not challenging and hence, did not recruit inhibitory circuits. This is consistent with the absence of a P3 in fronto-central electrodes . To incrThe present research shows that, while participants in the intervention showed reductions in binge eating frequency , the neural processes supporting this clinical effect could not be entirely uncovered. It remains unclear whether the null findings reflect an absence of change in neural activity over time, or an inability of the measures to detect change. It is advisable for future research to explore different task parameters, by potentially differing the ratio of \u201cgo\u201d to \u201cno-go\u201d trials and increasing the speed-accuracy trade-off.The datasets generated for this study are available on request to the corresponding author.The London Westminster Research Ethics Committee and the Health Research Authority reviewed and approved all the procedures involved in this study (IRAS Project ID: 209609). The patients/participants provided their written informed consent to participate in this study.RC has recruited participants and collected the data. GM has offered use of EEG equipment. RC and ML-M have pre-processed the data. KE has contributed to epoching the EEG data. JB has assisted in the creation of figures. RC has written the manuscript, with suggestions and corrections from JT, VC, ML-M, KE, GM, and JB.ML-M was employed by company CiberObn. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Reducing energy consumption has become a critical issue in today data centers. Reducing the number of required physical and Virtual Machines results in energy-efficiency. In this paper, to avoid the disadvantages of VM migration, a static VM placement algorithm is proposed which places VMs on hosts in a Worst-Fit-Decreasing (WFD) fashion. To reduce energy consumption further, the effect of job scheduling policy on the number of VMs needed for maintaining QoS requirements is studied. Each VM is modeled by an M/M/* queue in space-shared, time-shared, and hybrid job scheduling policies, and energy consumption of real-time as well as non-real-time applications is analyzed. Numerical results show that the hybrid policy outperforms space-shared and time-shared policies, in terms of energy consumption as well as Service Level Agreement (SLA) violations. Moreover, our non-migration method outperforms three different algorithms which use VM migration, in terms of reducing both energy consumption and SLA Violations. Ever-increasingly, companies move to the cloud to lower their budgets and reduce costs by benefiting from pooled hardware and software resources, delivered as IT services. These shared, on demand services are mainly offered in three forms: Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS). In the scope of IaaS clouds ), server virtualization is a key factor for elasticizing the data center by sharing computing resources between several users and simultaneously, isolating them from each other. Elasticity, the ability to expand and contract resources as workloads change, is an important aspect of IaaS clouds, which profits both cloud providers and users by removing the extra resources. Elasticity not only decreases green-house gasses and global warming by reducing the energy consumption of data centers, but also cuts the costs for cloud users, while providing sufficient resources to maintain QoS requirements. Server virtualization benefits IaaS datacenters, in fundamental different ways :Physical servers are usually too big for a single user. Virtual machines can divide them into smaller virtual servers, and assign each one to a different user.The Virtual Machine (VM) technology is capable of isolating different users and workloads from each other, while sharing hardware resources between them.Virtual servers are easier to manage because they are software-based and expose a uniform interface through standard abstractions.QoS requirements and obligations such as response time, reliability, availability, and security are summarized in Service Level Agreement (SLA), and a penalty is charged for any violation . In thisSome papers consider using VM migration to dynamically place as many VMs as possible on a server and reduce the number of active servers , 7. VM mIn this paper, we propose a method to place VMs on less number of servers statically in a Worst-Fit-Decreasing (WFD) fashion. WFD is a bin packing algorithm that according to our results performs better than other bin packing algorithms, namely, First-Fit-Decreasing (FFD) and Best-Fit-Decreasing (BFD) when placing VMs on servers. To further make our method more energy-efficient, we purpose a hybrid job scheduling algorithm using queuing theory that reduces the number of VMs by placing as many jobs as possible on a VM. By using less VMs, we utilize less servers and eventually reduce energy consumption.W + Ts)/Ts, where W is the job\u2019s waiting time and Ts is the expected service time), for the next slice, respectively. Feedback scheduling is another pre-emptive scheduling algorithm which concentrates on the time spent in execution so far, rather than the remaining time to execute. The hybrid mode includes algorithms such as co-operative scheduling and scheduling with Message Passing Interface (MPI). Detailed discussion of job scheduling disciplines is beyond the scope of this paper.Generally, Virtual Machines (VM) use two main scheduling policies, namely, space- and time-shared to assign resources to the jobs appointed to them. Additionally, hybrid algorithms, combine the two aforementioned policies. While in space-shared, which is non-preemptive, the processing space is shared among different jobs, in time-shared, which is pre-emptive, time is divided between them , 13. In Inspired with static VM allocation superiority, in this paper, we propose a non-migration method which does not necessarily need to predict the workload, when placing VMs on hosts in a WFD fashion. As an extension to our research and to reduce the energy consumption further, a novel queue-based algorithm is proposed to schedule jobs on fewer number of VMs by finding the right number of VMs required for each cloud user to maintain SLA conditions. By removing the extra VMs, we aim to utilize fewer number of servers and reduce energy consumption. Since a VM with space-share policy shares the processor space between jobs non-preemptively, it executes the jobs on different cores of the processor. Therefore, it is modeled by an M/M/m queue. Normally, all the cores of a processor are the same and have equal capacity. Furthermore, we make sure jobs are assigned to the VMs which have enough capacity for executing them. In such a situation, FCFS with backfilling, which performs very well  and even\u03bbmax of each VM is derived. By modeling SLA in terms of response times or latencies, both real-time and non-real-time applications are taken into consideration. Our findings show that there is a trade-off between server utilization and SLA violation: The busier a server gets, the more time is required for each job to be completed. Analyzing VM request queues, we balance those two metrics to design an energy-aware non-migration algorithm for placing VMs on servers in a WFD bin-packing fashion, as WFD is found in our work to have better performance in placing VMs on physical hosts compared with the other two algorithms, namely BFD and FFD bin-packing.In time-shared policy, since Processor Sharing (PS) discipline is a good approximation for RR algorithm, a VM is modeled by an M/M/1/PS queue. In hybrid mode, each core devotes a time slot to a different job in an RR manner. Therefore, it is modeled by an M/M/m/PS queue. In each scenario, the maximum request arrival rate To simulate our algorithm CloudSim  is interThe remainder of the paper is organized as follows. Related work is reviewed in Section 2. Section 3 and 4 describe our proposed model. Section 5 presents the experimental results. A conclusion is made in section 6.\u03bb. In order to satisfy QoS requirements, they define a limit on maximum waiting times, corresponding to deadlines. By Little\u2019s law, they transfer this limit to an upper bound on the queue\u2019s length. Using this upper bound, they adjust the number of VMs to reduce energy consumption.To reduce the power consumption, the proposed methods in  and 7]  7] decreThe reported works in \u201327 try tThe authors of  and 28]28] use FNone of the works explained above consider the VM\u2019s job scheduling policy, when rightsizing the allocated resources. Moreover, they do not bring real-time applications under consideration. EARH  proposesIn this paper, we propose an energy-aware non-migration VM placement algorithm which benefits real-time applications the most. We show that taking the job scheduling policy into consideration and adopting hybrid policy instead of space-shared or time-shared can remarkably reduce the energy consumption while maintaining SLA conditions. For this purpose, a resource-rightsizing algorithm for a space-shared policy with FCFS and a time-shared policy with RR discipline, and hybrid policy: the combination of space-shared and time-shared policies, are tested. We take both real-time and non-real-time applications into consideration. The results show that the hybrid policy excels space-shared and time-shared policies lower energy consumption and fewer SLA violations. In addition, the hybrid policy outperforms WFD, BFD, and FFD with VM migration, in terms of reducing both energy consumption and SLA violation. The next two sections explain our proposed model. The terminology used is summarized in According to what has been stated in the SLA, some minimum number of VMs are initially assigned to each cloud user. It has been shown in  and 31]31] that We aim to execute the jobs on minimum number of VMs possible, and therefore, reduce the number of active hosts. Since it takes considerable amount of time to turn on a server, a host whose all its VMs are idle will not be switched off, instead, it will be asleep. This is extremely useful for real-time applications. As depicted in \u03bbmax .In our method, when a job is executed and completed, the VM updates the maximum request arrival rate, \u03bbmax to the maximum number of jobs in the VM, Nmax (Nmax = 1 + \u03bbmax.waiting_time where \u03bbmax.waiting_time number of jobs are waiting for service and 1 job is being served). If the number of jobs that the VM is serving is smaller than Nmax, the VM reports to the job scheduler that it \u201ccan accept more jobs\u201d otherwise, it reports that it \u201ccannot accept more jobs\u201d.The job scheduler unit keeps a record for each VM, stating whether the VM can or cannot accept more jobs. The job scheduler uses this record to decide whether or not it should give a newly arrived job to a VM. Each time a new job is assigned to a VM, or completed and removed, the VM sends a report to the job scheduler unit and updates its record. Algorithm 1 shows a VM sending a report to the job scheduler unit upon a new job arriving, or a job departing. In this algorithm, the VM uses Little\u2019s law to convert the maximum request arrival rate Algorithm 1. VM Report Upon a New Job Arriving or a Job Departing\u03bbmax, the maximum request arrival rate the VM is allowed to have;Input: W, maximum waiting time.job_number: the number of jobs being served by this VM.Output: Report stating whether it can accept more jobs or not.Nmax = \u03bbmax.W + 1\u20031: jobnumber < Nmax then\u20032: if \u20033: report = can_accept_more_jobs\u20034: else\u20035: report = cannot_accept_more_jobs\u20036: send (report)When the service is entering busy hours, or the job request rate is increasing, the job scheduler unit might find that none of the active VMs are able to undertake the new job, therefore, a new VM should be activated or created. We designed the job scheduler unit to make a fair decision in the four following steps:If there are idle sleeping VMs on active hosts, activate the largest one and assign the new job to it. The host is already active and much of its energy is being consumed. By activating the largest VM, we make better use of the host and provide more processing capacity to the increasing number of arriving jobs.If there isn\u2019t any idle VM on the active hosts, but there is enough empty space on them, select the largest space and create the largest VM which fits in that space. Aside from making better use of active hosts and presenting biggest processing capacity possible to the increasing number of arriving jobs, this decision is the closest to WFD policy.If no VM can be activated or created on the active hosts, but there are idle VMs on sleeping hosts, select the smallest sleeping host and activate the largest VM on it. Since we are activating only one VM of a host, a great portion of the hosts\u2019 CPU capacity will be unused. With a larger host, which consumes more energy, more CPU capacity is unused and wasted. Additionally, the largest VM consumes a greater portion of hosts\u2019 processing capacity and provides greater processing capacity to the increasing number of arriving jobs.If no VM can be activated or created on the active hosts, and there is no idle VM on the sleeping ones, select the smallest host and create the largest VM on it. Other than the reason explained in the previous part, this decision is the closest to WFD policy.\u03bbmax.The job scheduler unit checks the VM reports in the order of VM creation. In other words, the VMs which were created earlier are checked sooner. This way, when the busy hours are over, or the job request rate is decreasing, new jobs are assigned to older VMs and the younger ones would gradually become idle and asleep in turn. A host can go to sleep as soon as all of its VMs are idle. Once a VM is created, we do not delete it anymore, because it is very likely that it would be needed again soon when the job request rate increases. With this paradigm, we place the VMs on servers in a WFD fashion, and reduce the number of servers used and the amount of energy consumed without migrating any VM. We elasticize the data center by adding and removing VMs from the service. In other words, we divided the VMs into two parts: (1) the minimum number of VMs which are almost always running, because the load seldom gets lower than the sum of their capacities, and (2) additional VMs, which are added to the service as the load increases, and removed again when the load decreases. The minimum number of VMs are created initially and located on the servers according to WFD algorithm. The additional VMs are located on the hosts later on in our aforementioned four steps with a policy very close to WFD. Algorithm 2 provides the code of the job scheduler unit. In the next section, we explain how VMs calculate their maximum request arrival rate Algorithm 2. The job scheduler unitVM, a list of all VMs in the order of their age, stating whether they can accept more jobs or not,Input: ctive_hosts, a list of active hosts,\u2003\u2003\u2003asleeping_hosts, a list of sleeping hosts.\u2003\u2003\u2003Output: A suitable VM for the new job.\u20031: selected_vm = nullfor each vm inVMdo\u20032: if report(vm) = = can_accept_more_jobs then\u20033: \u2003\u20034: \u2003\u2003selected_vm = vm\u20035: \u2003\u2003break;end if\u20036: \u2003end for\u20037: if selected_vm = = null then\u20038: \u20039: \u2003\u2003 largest_idle_vm = nullfor each host inactive_hostsdo\u200310: \u2003for each idle_vm in host do\u200311: \u2003\u2003if largest_idle_vm = = null or largest_idle_vm < idle_vm then\u200312: \u2003\u2003\u2003\u200313: \u2003\u2003\u2003\u2003largest_idle_vm = idle_vmend if\u200314: \u2003\u2003\u2003end for\u200315: \u2003\u2003end for\u200316: \u2003\u200317: \u2003selected_vm = largest_idle_vmend if\u200318: if selected_vm = = null then\u200319: \u200320: \u2003largest_idle_vm = nullfor each host insleeping_hostsdo\u200321: \u2003for each idle_vm in host do\u200322: \u2003\u2003if largest_idle_vm = = null or largest_idle_vm < idle_vm then\u200323: \u2003\u2003\u2003\u200324: \u2003\u2003\u2003\u2003largest_idle_vm = idle_vmend if\u200325: \u2003\u2003\u2003end for\u200326: \u2003\u2003end for\u200327: \u2003\u200328: \u2003selected_vm = largest_idle_vmend if\u200329: if selected_vm = = null then\u200330: \u200331: \u2003smallest_host = nullfor each host insleeping_hostsdo\u200332: \u2003if smallest_host = = null or smallest_host > host then\u200333: \u2003\u2003\u200334: \u2003\u2003\u2003smallest_host = hostend if\u200335: \u2003\u2003end for\u200336: \u2003\u200337: \u2003selected_vm = create_largest_vm end if\u200338: return selected_vm\u200339: We define a start time, an execution time, and a deadline for each job. Therefore, the waiting time is calculated by:W is as small as 100 (ms), but in non-real-time procedures, it can be greater [\u03bb. In fact, it is very common to assume the arrival time and service time of the jobs have an exponential distribution [\u03bb, increases, the VM gets busier and it takes more time for each job to complete. Our goal is to discover the maximum value of \u03bb, which keeps the time jobs spend in the VM lower than W and no SLA violation occurs. Taking t as a random variable denoting the time a job spends in the VM (sojourn time), we can find a lower bound on the probability In real-time applications,  greater . Since rribution \u201324. As tequality Pr. Thus, the utilization factor is \u03c1 = \u03bb/(m\u03bc) = \u03bbTs. According to t, which can be obtained for FCFS discipline by Eqs In space-shared policy the VM shares the CPU cores between jobs, non-preemptively . A VM wi\u03c0w is the probability of the number of requests waiting in the queue (n), being greater or equal to m. In other words, the probability that a request must wait for service, when it arrives.Where \u03c00 is the probability of no requests waiting in the queue. Hence, \u03c0w is Erlang\u2019s C formula. We want b, therefore by substituting Eqs And \u03c1 with maximum order 2m + 2. For m = 2, we findb is to 1, the higher is the possibility of roots being lower than 1. Once the roots of \u03c1 are found, the largest positive answer is chosen, and the maximum arrival rate \u03bbmax is obtained byWe solve this equation with Newton-Raphson\u2019s method . The clo\u03bbmax. We calculated the mean execution time (Ts = 1/(m\u03bc)) using the moving average method [That implies that in our algorithm, this VM is allowed to accept the coming jobs, as long as its arrival rate is not greater than e method .\u03b1\u03f5 is the smoothing factor, and i is the index of the job submitted to the VM. By experiment we found that the best results are obtained when \u03b1 = 0.2.Where \u03bb and mean service time Ts = 1/\u03bc. Therefore, the utilization factor is \u03c1 = \u03bb/\u03bc = \u03bbTs. In order to find \u03bbmax, we find a lower limit on In time-shared policy, in each time slot, the VM devotes all of its processing space to the selected job. Thus, it is modeled by an M/M/1/PS queue with arrival rate PS queue , 43:\u03bct=b for Again we consider a fixed lower limit \u03c1, which can be solved by Newton-Raphson\u2019s method [\u03bbmax by Ts is acquired by s method , and thr\u03bb and mean service time Ts = 1/(m\u03bc), and thus, the utilization factor is \u03c1 = \u03bb/(m\u03bc) = \u03bbTs. Again we need the mean and variance of the sojourn time to acquire a lower limit for M(1) and M(2) [m = 2 the variance of the sojourn time isIn the hybrid mode, in each time slot, the VM assigns each one of its cores to a different job and therefore serves more than one job in a time slot. This scenario, which is a combination of space-shared and time-shared policies, is modeled using an M/M/m/PS queue with arrival rate and M(2) . Accordin, the number of requests in the queue is zero. It has thoroughly been explained in [Where ained in  how M0 (see ) is solv(2)  + (1 \u2212 \u03b1).Ts\u20031: \u20032: ifroot = = \u03d5then\u20033: \u03bbmax = 0\u20034: \u2003else\u20035: \u20036: \u2003max = 0for each\u03c1 \u03f5 rootdo\u20037: \u2003if\u03c1 > maxthen\u20038: \u2003\u2003\u03c1\u20039: \u2003\u2003\u2003max = end if\u200310: \u2003\u2003end for\u200311: \u2003ifmax = = 0 then\u200312: \u2003\u03bbmax = 0\u200313: \u2003\u2003else\u200314: \u2003\u03bbmax = \u03c1/Ts\u200315: \u2003\u2003end if\u200316: \u2003end if\u200317: Based on experimental analysis, we found that our proposed queuing theory methods for finding the right number of jobs in a VM with space-shared, time-shared, and hybrid job scheduling policies have a small transition time and converge to steady state fast enough, so that sufficient number of VMs are activated on time.b = 0.99, 0.9, and 0.8 for our simulation. b = 0.99, 0.9, and 0.8.To simulate and evaluate our proposed model, we interfaced CloudSim with Matlab. We used Google cluster data  that wasIt t can be seen from the diagrams that as maximum waiting time increases, energy consumption and SLA violations are both reduced. This indicates that managing real-time jobs is much harder and more complicated than non-real-time jobs. Moreover, the diagrams indicate that the hybrid policy outperforms both space-shared and time-shared policies and has lower energy consumption and fewer SLA violations compared to space-shared and time-shared policies.b = 0.99 and b = 0.9.Next, our algorithm is compared with three different energy-aware VM placement algorithms which use VM migration. Initially, VMs are randomly placed on hosts. Every five seconds, VM placement is checked and optimized using WFD, BFD, and FFD algorithms. The diagrams show that our algorithm outperforms WFD, BFD, and FFD algorithms with VM migration. The reason is that our algorithm places VMs on physical machines in a WFD fashion without migration. VM migration prolongs the execution process and raises the probability of SLA violation. Even in live migration the jobs have to stop and wait until their essential codes and data stacks are moved, and then continue their execution. Moreover, VM migration introduces a burst to the network and causes even more latency. Thus, especially for real-time applications, VM migration brings about SLA violation. In addition, some additional amount of energy is consumed by the network to migrate the VMs. Therefore, the energy consumption and SLA violation of the three algorithms with VM migration degrades and our energy-aware non-migration VM placement excels them. Corresponding to any SLA violation level, the energy consumption of our method is better than that of dynamic FFD, BFD, and WFD methods. So, our hybrid algorithm presents lower energy consumptions and fewer SLA violations and outperforms the three dynamic algorithms. We also found that the energy consumption of the three dynamic algorithms is highly affected by the number of migrations. Therefore, since the number of migrations of the three dynamic algorithms does not noticeably change as the waiting time rises, in \u03bbmax by studying the sojourn time of the jobs. \u03bbmax was used to determine whether a VM can accept more jobs or not. An energy-aware non-migration algorithm was designed to place the VMs on servers in a WFD fashion.In this paper, an energy-aware non-migration VM placement and hybrid job scheduling policy was proposed to make the cloud elastic. Generally, job scheduling policies can be classified into two main groups, namely, space-shared and time-shared. Moreover, some algorithms, which we call hybrid, combine the two aforementioned algorithms. Proposed methods which completely avoid VM migration, usually require the workload to be predictable. However, in our approach, the workload do not necessarily need to be predictable. In addition, our method is applicable for both real-time and non-real-time applications. We showed in our paper that hybrid policy excels space-shared and time-shared policies in terms of reducing both energy consumption and SLA violation. We adjusted the resources allocated to each cloud user according to their QoS by modeling the VMs of a data center with a queuing theory technic. We applied our idea to space-shared, time-shared, and hybrid policies, developed different equations for each one, and obtained the maximum acceptable arrival rates We interfaced CloudSim with Matlab to simulate and evaluated our algorithm. The results show that as waiting time increases, both energy consumption and SLA violation decrease. This clearly shows that although real-time jobs are not minded in previous research deservedly, managing real-time jobs are much more complicated than non-real-time jobs. The experimental results indicate that the hybrid policy is superior to space-shared and time-shared policies in reducing both energy consumption and SLA violation. Moreover, we compared hybrid algorithm with three different algorithms, WFD, BFD, FFD with migration. The results show that our energy-aware non-migration VM placement algorithm with hybrid job scheduling policy outperforms all three in terms of reducing both energy consumption and SLA violation.S1 Data(ZIP)Click here for additional data file."}
+{"text": "To quantify coherence, two proper measures were introduced in the literature, the one is the relative entropy of coherence  Quantum computing utilizes the superposition and entanglement of quantum states to operate and process information. Its most significant advantage lies in the parallelism of operations ,2,3. To In 2014, Baumgratz et al.  proposedoherence , fidelitoherence , robustnoherence , geometroherence , coherenoherence , relativoherence , trace doherence ,23,24.In addition, some research related to quantum coherence have been developed, including quantum coherence and quantum correlations ,28,29,30In this paper, we discuss some inequalities on the measures of quantum coherence. The organization of this paper is as follows: In In this section, we give a review of some fundamental notions about quantification of coherence, such as incoherence states, incoherence operations, and measures of coherence.H be a d-dimensional Hilbert space, whose elements are denoted by the Dirac notations H. The adjoint operator of an operator T in H is denoted by I. We use H, whose elements are said to be the states of the quantum system S described by H. Fixed an orthonormal basis (ONB) H, a state S is said to be incoherent with respect to (w.r.t.) the basis e if coherent w.r.t. e. Let S that are incoherent w.r.t. e, that is,Let e if and only if e, i.e.,e if and only if it can not be written as a diagonal matrix under this basis.For every According to , a lineae-incoherent operation (IO) if it has Kraus operators A CPTP map e-incoherent Kraus operators of In this case, we call In order to measure coherence, Baumgratz et al.  presentee-incoherent operation e-incoherent operation e-incoherent Kraus operators It was proved in  that theNotably, for a bipartite quantum system Moreover, let quations  and 4),,\u03c1A:=trB,,\u03c1ABC satded that\u03bbS\u2265ows thatCr(\u03c1ABC)\u2264n-partite state As a generalization of inequalities  and 13)13), we cTheorem\u00a01.For any state where Proof.\u00a0To prove that the first inequality in Equation  holds, wN-partite state Next, let us prove that the second inequality in  holds byality in  holds foEquation , we knowEquation  is proveAs immediate application of Theorem 1, we have the following corollaries.Corollary\u00a01.Let Corollary\u00a02.Let It is remarkable that the equalities in Equation  may holdEquation  also becEquation  are tighIn this section, we discuss the relation between t state \u2264C\u21131 proved \u2264C\u21131Proposition\u00a01.Let \u03c1 be a state of S satisfying Equation  and let Proof.\u00a0The convexity of d-dimensional system, it holds thatRana et al. proved in (, Proposiived in (, Equation-partite quantum states In this paper, we have established lower and upper bounds for relative entropy of coherence"}
+{"text": "Tree stem density and basal area increases with elevation while species richness decreases. Stem density and species richness both decrease with latitude. Subtropical forests have distinct tree species composition compared to those in the tropical region. In addition, floristic similarity of subtropical plots is between 13 to 16% while similarity between tropical forest plots is between 3% to 9%. Overall, plots ~ 0.5-ha or larger may be preferred for describing patterns at regional scales in order to avoid plot size effects. We highlight the need to promote collaboration and capacity building among researchers in the Andean region  in order to generate and synthesize information at regional scale.Our knowledge about the structure and function of Andean forests at regional scales remains limited. Current initiatives to study forests over continental or global scales still have important geographical gaps, particularly in regions such as the tropical and subtropical Andes. In this study, we assessed patterns of structure and tree species diversity along ~ 4000 km of latitude and ~ 4000 m of elevation range in Andean forests. We used the Andean Forest Network (Red de Bosques Andinos,  The Tropical Andes have been identified as one of the most important hotspots of global biodiversity , 2. Inde2 total) of their cloud forests Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: YesReviewer #2: Partly**********2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: I Don't KnowReviewer #2: Yes**********3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data\u2014e.g. participant privacy or use of data from a third party\u2014those must be specified.The Reviewer #1: NoReviewer #2: Yes**********4. Is the manuscript presented in an intelligible fashion and written in standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes**********5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: General remarks:This paper reports on trends in stem number, basal area and species diversity patterns for trees in a series of plots spanning ~4000 km of latitude and 4000 m of elevation range. The results are a useful addition to the analysis of trends in the physical and biological structure of Andean forests. In general, I found the manuscript clearly written and not over-reaching in its conclusions.condesan.org/) database which, at 71 present, includes 491 forest plots  representing 72 a total of 86,964 tree stems \u2265 10 cm diameter at breast height belonging to 2341 identified 73 species, 584 genera and 133 botanical families.\u201dI believe that most last contribution of this manuscript would be the publication of the data upon which all the analyses were conducted. Unfortunately, it appears that this manuscript does not meet PLOS One standards of data availability. The authors state that \u201cAll relevant data are within the manuscript and its Supporting Information files.\u201d, and that \u201cWe used the Andean Forest 70 Network , but that led only to plot metadata, not to the actual data.In summary, even with a diligent effort I was unable to find the data on which this manuscript is based. If somehow the stem data are in fact publicly accessible without restriction somewhere, they are not easily findable even with reasonable effort. The authors should clearly show exactly where the individual stem data can be freely accessed with no restrictions.The authors state \u201cThe plot data that support the findings of this study are available from Andean 251 Forests Network upon reasonable request\u201d, so it appears to me that the data are not publicly available without restriction. PLoS ONE\u2019s data availability policy states: \u201cPLoS journals require authors to make all data necessary to replicate their study\u2019s findings publicly available without restriction at the time of publication.\u201d To replicate the study\u2019s findings requires access to the individual stem data. Unless public access without restriction is provided the manuscript is not acceptable according to PLoS ONE\u2019s standards.https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0183819#sec013. In their S1 Table those authors provide individual stem data for size, location and taxonomic identity of ~80,000 individual census measurements, which is a similar-size data set. I strongly encourage the authors to include the individual stem data as a table in Supporting Information so that the exact version of the dataset that they used to generate the paper is archived with the paper. Data in a dataset of this nature are constantly and very correctly changing as errors are detected and corrected and as taxonomic concepts evolve. It would be difficult in the future to recreate these analyses unless the version of the database at the time of these analyses is published. Such publication of the freely available base data is a PLoS ONE requirement for publication, and it is also best scientific practice.In the case of this manuscript complying with PLoS ONE\u2019s data policy is not an onerous requirement. Stem data for 87,000 individuals is not large dataset and the data could easily be easily be included as a table in the Supporting Information. An example from PLoS One is Clark et al. 2017 My pdf copy of the manuscript lost line numbering after line 274, so after that I use the page numbers of my pdf copy to reference comments.It is unclear how many individuals were analyzed. The Abstract states 86,944 stems, but on page 26 a total of 97,054 stems is mentioned. It is not clear if the 86,944 applies only to the analyses involving taxonomic identity. I assume that the total 97,054 stems were used in the analyses of basal area and stem number, there is no reason to discard individuals for these analyses. In any case the sample size for each set of analyses must be clarified.The authors are very aware of the issues of plot size and its effects on scaling to larger spatial scales. They are clear that they omitted many very small plots (<0.1 ha) from their analyses. However the analyzed plots are located in mountainous terrain, and are likely spatially biased towards rare flat areas. In addition, most  of the plots were subjectively sited  and may be subject to the \u201cmajestic forest\u201d bias. It would be useful for the authors to provide their opinion of the effects on non-random plot placements on these results.Other comments:I suggested deleting lines 230-241, this section is not directly relevant to the reported research.Table 1. Clarify if temperature and rainfall are annual averages. This table would be easier to read with vertical lines separating the variables, and \u201cMin\u201d and \u201cMax\u201d over each of those columns.Page 22. Spell out CHELSA. Rapid variation in environmental gradients is well known in tropical mountain area. Are there any site-specific data to check the accuracy of the predicted climate with actual climate on the ground?The whole paragraph on page 22 on climate data reads like climate was actually measured on the ground. In fact climate variables were predicted from remotely sensed data, with an unknown (or unreported) degree of uncertainty. All of these data should be labeled as \u201cestimated\u201d or \u201cpredicted\u201d to make clear that actual ground-measured data are not being reported. It\u2019s fine to report remotely sensed data, but the manuscript should be clear that is what\u2019s being reported. Based on this manuscript there is no way to know how good these estimates are at the plot level. If the authors in fact do know the accuracy of these predictions it would be useful to report that.Figure 3 caption, B, change \u201cclimate\u201d to \u201cestimated annual rainfall\u201d. What is the reason for the inverted scale on panel B? All the other scales are linear increasing, so this exception is confusing. I suggest plotting plot B like the other variables, both variables increasing from the origin.Figure 4. Move Elevation and Latitude to the top of each column rather than below .Table 2. Add units to the column headings were these are missing.Figure 4 is confusing. What is the difference between panels E and G? The text states that \u201cSpecies richness decreased with latitude \u201d but panel E is based on elevation, not latitude. Please clarify in the text and in the figure legend.Consider replacing \u201chump-shaped elevational pattern of tree species richness\u201d with \u201cmid-elevation peak in species diversity\u201d.Reviewer #2: I liked the manuscript and the overall approach. I also enjoy reading synthesis-based analyses that are based on field-plot data. I also think this particular plot network has an enormous potential for future work and research to support conservation and management of Andean forests. However, in its current form, this work requires more analytical thinking, especially to discuss the main findings and the causal mechanisms behind the patterns that were reported. See the attached file for detailed comments.**********what does this mean?). If published, this will include your full peer review and any attached files.6. PLOS authors have the option to publish the peer review history of their article  digital diagnostic tool, AttachmentPONE-D-19-30260_First_ReviewDec2019.pdfSubmitted filename: Click here for additional data file. 16 Mar 2020March 30th, 2020Dr. Joerg Heber, Editor-in-ChiefPLoS ONEDear Dr. Herber,I am writing to submit our revised manuscript (PONE-D-19-30260) entitled Elevation and latitude drives structure and tree species composition in Andean forests: results from a large-scale plot Network for consideration for publication in PLoS ONE. We are very thankful for your comments and those of the reviewers as they have allowed us to improve our manuscript. We have carefully considered each of them and addressed all of them. In this sense, we have made clear the point about data availability as well as we have improved the discussion concerning the major results. Please find below the detailed responses to each comment. Line and Page numbers referred correspond to the revised manuscript with track changes. With best regards,Dra. Agustina Malizia Instituto de Ecolog\u00eda Regional (IER) (CONICET-UNT)----------------------------------------------------------------------------------------------------------------------------------------Editor CommentsPlease seriously consider the concerns of the referees and make revisions according to their suggestions, especially you should pay attention to comments about data availability  and the discussions on the major results. Response: We have paid attention to all comments made by both reviewers, incorporated all of them in the manuscript, and responded to each one in detailed. Please, see below. Reviewers' comments:Reviewer's Responses to QuestionsComments to the Author1. Is the manuscript technically sound, and do the data support the conclusions?The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.Reviewer #1: YesReviewer #2: Partly ________________________________________2. Has the statistical analysis been performed appropriately and rigorously?Reviewer #1: I Don't KnowReviewer #2: Yes________________________________________3. Have the authors made all data underlying the findings in their manuscript fully available?The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data\u2014e.g. participant privacy or use of data from a third party\u2014those must be specified.Reviewer #1: NoReviewer #2: Yes________________________________________4. Is the manuscript presented in an intelligible fashion and written in Standard English?PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1: YesReviewer #2: Yes ________________________________________5. Review Comments to the AuthorPlease use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1: General remarks:This paper reports on trends in stem number, basal area and species diversity patterns for trees in a series of plots spanning ~4000 km of latitude and 4000 m of elevation range. The results are a useful addition to the analysis of trends in the physical and biological structure of Andean forests. In general, I found the manuscript clearly written and not over-reaching in its conclusions.condesan.org/) database which, at present, includes 491 forest plots  representing a total of 86,964 tree stems \u2265 10 cm diameter at breast height belonging to 2341 identified species, 584 genera and 133 botanical families.\u201dI believe that most last contribution of this manuscript would be the publication of the data upon which all the analyses were conducted. Unfortunately, it appears that this manuscript does not meet PLOS One standards of data availability. The authors state that \u201cAll relevant data are within the manuscript and its Supporting Information files.\u201d, and that \u201cWe used the Andean Forest Network , but that led only to plot metadata, not to the actual data.In summary, even with a diligent effort I was unable to find the data on which this manuscript is based. If somehow the stem data are in fact publicly accessible without restriction somewhere, they are not easily findable even with reasonable effort. The authors should clearly show exactly where the individual stem data can be freely accessed with no restrictions.https://redbosques.condesan.org/) is to check general information about the Network . Response: In Table S1 we included: i) number of stems, ii) basal area (both extrapolated to 1-ha) and iii) species richness for each of the 491 plots. Additionally, in Appendix 1 we reported the abundance of tree species per country. This information constitutes the primary input used in the analyses to describe the main structural and compositional trends across the Andean forests. Thus, we included the following text in the manuscript to make explicitly clear that the information upon which replicate the analyses is available in the supporting information: \u201cAll relevant data upon which all the presented results in this manuscript are based on is included in its Supporting Information files\u2026\u201d. . We also clarified that the link to Red de Bosques Andinos  number of stems, ii) basal area and iii) species richness for each of the 491 plots which, and as we stated previously, it is provided in the supporting files. To avoid confusion, we have deleted the sentence: \u201cThe plot data that support the findings of this study are available from Andean Forests Network upon reasonable request\u201d.https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0183819#sec013. In their S1 Table those authors provide individual stem data for size, location and taxonomic identity of ~80,000 individual census measurements, which is a similar-size data set. I strongly encourage the authors to include the individual stem data as a table in Supporting Information so that the exact version of the dataset that they used to generate the paper is archived with the paper. Data in a dataset of this nature are constantly and very correctly changing as errors are detected and corrected and as taxonomic concepts evolve. It would be difficult in the future to recreate these analyses unless the version of the database at the time of these analyses is published. Such publication of the freely available base data is a PLoS ONE requirement for publication, and it is also best scientific practice.In the case of this manuscript complying with PLoS ONE\u2019s data policy is not an onerous requirement. Stem data for 87,000 individuals is not large dataset and the data could easily be included as a table in the Supporting Information. An example from PLoS One is Clark et al. 2017 Response: We understand the reviewer's request; however, as explained above, the data required to replicate this research is available in the supporting information included in the manuscript. Also, the Andean Forest Network dataset belongs to the different research groups that are part of the Network. Currently, these research groups are implementing projects and research with master's and doctoral students based in part on the same information presented here. It is not our intention to hinder research initiatives that require an embargo of the data until the different research projects are complete, making the base information available.My pdf copy of the manuscript lost line numbering after line 274, so after that I use the page numbers of my pdf copy to reference comments.Response: We added line numbers until the end of the manuscript. Apparently, lines were missing after number 274 as the reviewer stated. We apologize for the inconveniences.It is unclear how many individuals were analyzed. The Abstract states 86,964 stems, but on page 26 a total of 97,054 stems is mentioned. It is not clear if the 86,964 applies only to the analyses involving taxonomic identity. I assume that the total 97,054 stems were used in the analyses of basal area and stem number, there is no reason to discard individuals for these analyses. In any case the sample size for each set of analyses must be clarified.Response: Corrected. We added a clarifying sentence: For calculations of stem density and basal area we used all stems \u226510 cm DBH  while for species richness we used stems \u226510 cm identified to species level  . We also clarified this in the abstract: \u201c\u2026representing a total of 86,964 identified stems \u2265 10 cm diameter\u2026\u201d .The authors are very aware of the issues of plot size and its effects on scaling to larger spatial scales. They are clear that they omitted many very small plots (<0.1 ha) from their analyses. However the analyzed plots are located in mountainous terrain, and are likely spatially biased towards rare flat areas. In addition, most  of the plots were subjectively sited  and may be subject to the \u201cmajestic forest\u201d bias. It would be useful for the authors to provide their opinion of the effects on non-random plot placements on these results.Response: Forest plots may not have been located strictly at random thus is challenging to guarantee that some of them were not subject to the majestic forest bias. However, forest plots setup were based on the combination of several factors: (1) accessibility, (2) sustainable over time to ensure long term monitoring for some plots, and (3) homogeneity in terms of forest type, topography, and disturbances in order to be representative of particular forest types. We clarified this in text . In this sense, we have stated that: \u201cThe majority of the plots are placed in mature forests, but the Network also includes several older secondary forests plots, i.e. > 30 years old as a result of human activities and the associated land-use changes\u201d (P13 279-281).Concerning the majestic forest bias, small plots may be subjected to this effect showing higher estimated values of basal area . In this sense, in the result section we have reported that \u201cPlot size had a significant effect on basal area, small plots of 0.1-ha tended to present higher basal area than 1-ha plots (Appendix 1) (P19 L396-397). However, taking into account the three variables combined, the variance explain is less than 10%, as we have stated: \u201cCombined, elevation, latitude and plot size explained 9.5% of the variation in basal area\u201d (P19 L398). Finally, in the discussion section we added: \u201c\u2026as well as majestic forest effect could be expected in these small plots (P24 L504-505). Phillips OL, Malhi Y, Vinceti B, Baker T, Lewis SL, Higuchi N, ... & Ferreira LV. (2002). Changes in growth of tropical forests: evaluating potential biases. Ecological Applications, 12(2), 576-587.Other comments:I suggested deleting lines 230-241, this section is not directly relevant to the reported research.Response: Agreed, we deleted it. Table 1. Clarify if temperature and rainfall are annual averages. This table would be easier to read with vertical lines separating the variables, and \u201cMin\u201d and \u201cMax\u201d over each of those columns.Response: Done. We clarify in the legend of Table 1  that we referred to total annual rainfall and mean annual temperature. Also, we added vertical lines in this table, and \u201cmin\u201d and \u201cmax\u201d as suggested. Additionally, in legend of Table S1 we also clarified that we referred to total annual rainfall and mean annual temperature. Page 22. Spell out CHELSA. Rapid variation in environmental gradients is well known in tropical mountain area. Are there any site-specific data to check the accuracy of the predicted climate with actual climate on the ground?Response: We spelled out CHELSA as \u201cClimatologies at high resolution for the Earth\u2019s land surface areas\u201d (P16 L318). We were not able to corroborate the accuracy of the predicted climate with actual climate on the ground. In this sense, Andean precipitation patterns are currently not yet well described, due to the high spatio-temporal variability and low density of rain gauges, thus we expect some underestimations and overestimations in precipitation values . Nevertheless, we believe we have used the best available climatic information to describe general climatic patterns across Andean forest plots. Buytaert, W., Vuille, M., Dewulf, A., Urrutia, R., Karmalkar, A. & C\u00e9lleri, R. (2010) Uncertainties in climate change projections and regional downscaling in the tropical Andes: implications for water resources management. Hydrol. Earth Syst. Sci., 14, 1247-1258The whole paragraph on page 22 on climate data reads like climate was actually measured on the ground. In fact climate variables were predicted from remotely sensed data, with an unknown (or unreported) degree of uncertainty. All of these data should be labeled as \u201cestimated\u201d or \u201cpredicted\u201d to make clear that actual ground-measured data are not being reported. It\u2019s fine to report remotely sensed data, but the manuscript should be clear that is what\u2019s being reported. Based on this manuscript there is no way to know how good these estimates are at the plot level. If the authors in fact do know the accuracy of these predictions it would be useful to report that.Response: We rephrased the information within this paragraph adding the word estimated and predicted in order to make clear that it was remotely sensed data information . Figure 3 caption, B, change \u201cclimate\u201d to \u201cestimated annual rainfall\u201d. What is the reason for the inverted scale on panel B? All the other scales are linear increasing, so this exception is confusing. I suggest plotting plot B like the other variables, both variables increasing from the origin. Response: We showed the inverted scale on Fig 3B (y axis = temperature) to emphasize illustratively the location of plots associated with elevation and temperature, i.e. higher plots are also the colder ones and are graphed in similar position in both panels . We also clarified it  in the legend of Fig 3 .Figure 4. Move Elevation and Latitude to the top of each column rather than below . Response: Done. We moved Axis X (Elevation and Latitude) above to the top of each columnTable 2. Add units to the column headings were these are missing. Response: Done. We added the symbol \u201c#\u201d (number) in two of the columns. Figure 4 is confusing. What is the difference between panels E and G? The text states that \u201cSpecies richness decreased with latitude \u201d but panel E is based on elevation, not latitude. Please clarify in the text and in the figure legend.Response: Done. We clarified that Fig 4F is the one that refers to latitude . Fig 4E does not distinguish between tropical and subtropical sections, while Fig 4G does distinguish between tropics and subtropics taking into account only 1ha-plots (n = 109). This is stated in text .Consider replacing \u201chump-shaped elevational pattern of tree species richness\u201d with \u201cmid-elevation peak in species diversity\u201d. Response: Done. We replaced as suggested.________________________________________6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose \u201cno\u201d, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #1: Yes: David B. ClarkReviewer #2: Nohttps://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, Reviewer #2: I liked the manuscript and the overall approach. I also enjoy reading synthesis-based analyses that are based on field-plot data. I also think this particular plot network has an enormous potential for future work and research to support conservation and management of Andean forests. However, in its current form, this work requires more analytical thinking, especially to discuss the main findings and the causal mechanisms behind the patterns that were reported. See the attached file for detailed comments.Manuscript Review PLOS ONE (PONE-D-19-30260)Structural and compositional trends along elevation and latitude gradients of Andean forests By Malizia et al\u2026General comments:This study is based on data collected from an impressive number of research sites, between temporary and permanent forest plots, located in different parts of the Andes in South America, an important biological hotspot that has received less attention compared to lowland forests. Broadly, this paper takes advantage of the wide and complex environmental range covered by the dataset to address the questions of the combined effects of elevation and latitude on the structure and tree species composition of Andean forests. By means of generalized models, the authors found that forest density (i.e. number of trees or stems per unit of area) increased with elevation with an opposite effect from latitude. The differences in species richness found between tropical and subtropical Andes are not surprising and are aligned with previous studies. However, the degree of similarity (or dissimilarity) in terms of species diversity in these two broad regions within the Andes was an interesting finding. The authors very well highlight the immense value that this Andean plot-network (i.e. Red de Bosques Andinos) has for strengthening scientific research in the region and promote collaboration. These are not \u2018novel\u2019 questions but given the amount of data used, especially compared to an earlier study from the same group , I find the paper of high interest for many scientists and forest ecologists, and readers of PLoS ONE. However, in its current form this manuscript remains largely descriptive and a better explanation of the causal mechanisms behind how elevation and/or latitude drives structure and composition is missing. The implications of the results to other aspects of forest structure (e.g. carbon) or dynamics (e.g. stem turnover) could be added too. I think the paper should be improved, especially in the discussion section, before being considered for publication. I am pointing out several comments, questions, and occasionally, a few suggestions, that could help moving this paper forward. Response: We appreciate the reviewer effort for improving the manuscript. We have incorporated all comments and addressed each one in detail below. Typesetting and formatting:I don\u2019t normally pay too much attention to these aspects at this stage. However, I strongly recommend the paper by checked for type setting errors, and the written structure of some paragraphs is reviewed to help the reader. Details are offered below indicating page and line numbers. Yet, as a direct note to the authors, in the pdf version I had access to there was no line number after page 13 of the document (after Table 1), and at line 275 (Table 1), the page number starts again with 1. For this section then I will be referring my comments using these numbers while trying to point out the paragraph number and a few words in the sentence to facilitate the review process.Response: Done. We added continuous line numbers after line 274, until the end of the manuscript.Title:I suggest the title to be more directly linked with the results (e.g. Elevation and latitude drives structure and tree species composition in Andean forests). As I will mention later, the manuscript includes in the discussion a long portion about the value of the plot network that I am not sure if is relevant. However, if the authors decide to keep it, maybe a change in the title should also reflect this .Response: We have changed the title as suggested. Abstract:This section needs to be modified a bit. In particular, the reader will benefit from having more specific results being mentioned in the abstract. For example, there is an important aspect of the study related to plot size and its effects on the results that is not mentioned here. Response: Agreed. We added a sentence to refer to plot size effect: Overall, plots ~ 0.5-ha or larger may be preferred for describing patterns at regional scales in order to avoid plot size effects . Page 4, Lines 68 - 69: \u201c\u2026Here, we assessed patterns of Andean forest tree structure and diversity along ~ 4000 km of latitude and ~ 4000 m of elevation range\u2026\u201d. Consider changing to: \u201c\u2026In this study, we assessed patterns of structure and tree species diversity across a wide altitudinal and latitudinal range in Andean forests\u2026\u201d Response: We changed it as suggested. Page 4, Line 75: \u201c\u2026Subtropical forests have distinct composition from tropical forests...\u201d Consider changing to: \u201c\u2026Subtropical forests have distinct tree species composition compared to those in the tropical region\u2026\u201dResponse: We changed it as suggested.Introduction:Page 4, L83: \u201cIndeed, the Tropical Andes\u2026\u201d. The region is already mentioned in the first sentence. Just start the line with something like \u201c\u2026Indeed, this region is one of the most diverse terrestrial hotspots on earth [1]\u2026\u201dResponse: We changed it as suggested.Page 5, L86: \u201c\u2026that have not been described yet\u2026\u201d Change to: \u201c\u2026that have not yet been described\u2026\u201d.Response: We changed it as suggested.P5 L87-90: There are two different sentences, with different citations too, that mention \u201cclimate regulation\u201d. Unify or combined these statements avoiding repetition. Response: We combined both sentences.P5 L92-95: Again, two sentences discuss similar aspects, specifically about social aspects . Consider simplifying this paragraph. Also, is not clear what \u201ccontrasting patterns of human population growth\u201d means? Please clarify. Response: We combined both sentences.P5 L96: \u201cChanges to Andean forests\u2026\u201d Changes in what? Forest cover? Structure? I don\u2019t think the word \u201cpatterns\u201d fits here. Consider something like: \u201c\u2026Changes in Andean forest cover includes both forest expansion, mostly frequent above 2000 masl) and deforestation that often dominates at lower elevations [12]\u2026\u201dResponse: We changed it as suggested.P5 L102: \u201c\u2026are already undergoing\u2026\u201d Change to: \u201c\u2026experiencing an apparent shift in species composition (i.e\u2026)\u201d Response: We changed as suggested. P5 L104: Are these predicted shifts for plant species, animal species? Please clarify.Response: Predicted shifts are for vascular plant species. We clarified it.P6 L109-114: I am not sure if this whole paragraph fits here. Are those \u201cknowledge gaps\u201d related to the study? I understand the importance of collaborative research networks but the next paragraph (L116) immediately start discussing the effects of elevation on tree density. Consider removing this paragraph or in any case a connecting sentence is needed before you jump to the density portion.Response: Knowledge gaps are related to the study. We clarified this, and rephrase the sentence adding connection to next paragraph (P6 L121-125). P6 L121 \u201c\u2026subtropical section of the Andes\u2026\u201d Just say\u201d \u201csubtropical Andes\u2026\u201d Response: We changed as suggested. P6 L128: \u201cSpecies richness\u2026\u201d All species? Plants? Response: We referred to plant species. We clarified it.Clarify. P7 L134: \u201c\u2026also showed\u2026\u201d -- > \u201c\u2026also shows the\u2026\u201d Response: We changed as suggested. P7 L135: \u201c\u2026being maximum\u2026\u201d -- > \u201c\u2026reaching a maximum at\u2026\u201d. Response: We changed as suggested. P7 L136: \u201c\u2026Argentina [38], decreasing\u2026\u201d -- > \u201c\u2026Argentina [38], while decreasing above\u2026\u201d. Response: We changed as suggested. P7 L138-140: I agree that long-term monitoring is needed, but the study do not use or report temporal trends so how is this relevant here? Consider moving to the conclusions. Response: We deleted as suggested.P7 L142: \u201c\u2026the main structural and diversity patterns\u2026\u201d -- > \u201c\u2026the main patterns of structure and tree species diversity in Andean forest communities\u2026\u201dResponse: We changed as suggested. P7 L144: Why consider species richness as a structural component? Response: Actually, we consider species richness within diversity patterns. We clarified this. P7 L148-150: \u201c\u2026This study\u2026\u201d This paragraph would fit better perhaps at the beginning of this section in L142. Also, is not clear what do you mean about \u201c\u2026at regional scales in global context...\u201d? Perhaps just say \u201c\u2026This study is one of the first attempts to describe and characterize regional patterns of forest structure and diversity in the Andes across (go to L143)\u2026\u201d Response: We moved the sentence to the beginning of the paragraph and changed as suggested. Two major points here: 1) I think is important to highlight how is this study different from the Baez et al study? I understand that in the 2015 paper there was no consideration about diversity and here you use a much higher number of plots. Thus, I see the need for making this point clear; 2) I think at the end of the introduction some general hypotheses would be useful. What were the patterns expected considered earlier evidences? Response: We added a sentence highlighting the progress of this analysis in relation to Baez et al 2015, as suggested . Also, we added a general hypothesis and two specific ones at the end of introduction section .Materials and Methods:P8 L155: \u201c\u2026Paleogene . Subsequent\u2026\u201d Change to \u201c\u2026Paleogene , and subsequent collisions\u2026\u201d. Response: We changed as suggested. P8 L156: The reference of Hoorn et al, 2010 does not follow PLoS guidelines (i.e. ). P8 L157: \u201c\u2026late middle\u2026\u201d -- > \u201c\u2026late mid Miocene\u2026\u201d Response: We changed as suggested. P8 L160: A citation is needed for this paragraph after \u201c\u2026Amazon ecosystems\u2026\u201d. We added citation. P8 L164: \u201c\u2026biodiversity and distribution\u2026\u201d -- > \u201c\u2026biodiversity and species distributions\u2026\u201d Response: We changed as suggested. P8 L169: \u201c\u2026vary gradually\u2026\u201d how? What does the word gradually means? I think the paragraph that starts later in L180 of page 9 with \u201c...The mountain forest ecosystem\u2026\u201d should be moved here in support of this initial statement. In relation to this, I liked Figure 1, but I also thinks it deserves a better explanation, either in the main text or at least as an expanded figure caption. Why these variations in forest architecture? Some lines on temperature and radiation effects would be useful. Response: We reorganized the paragraph, including suggestions for a better understanding (P9 L191-206). Also the paragraph includes lines on temperature and radiation. P9 L194: Consider using \u201cis\u201d instead of \u201chas been\u201d when referring to the objective of the network. Response: We changed as suggested. P9 L196-197: Delete \u201cthe\u201d before exchange, development, strengthening. Response: We deleted as suggested.P10 L205-212. This whole section and the next (L215 to 212) about the protocols can be combined, simplified and shortened. Response: We simplified, combined and shorten both sections as suggested. P11 L226: \u201c\u2026events and recorded and the DBH of marked trees are\u2026\u201d -- > \u201c\u2026events arerecorded and the DBH of marked trees is remeasured\u2026\u201d Response: We changed as suggested.P11 L230-241: I understand the importance of this section and I hugely support collaboration and networking. I am trying to find sections that could be simplified to allow for more space for discussion and I think this is definitely one of those parts. This paragraph here seems out of place. It could be shortened and added to the background section, used in a new appendix to fully describe the work of the Andean network or simply removed. As mentioned earlier when reviewing the title of the paper, if the goal is to highlight the value of the network a different approach would be useful, where a more in-depth discussion about research collaboration and networking is part of the manuscript. Response: We deleted this section as suggested by Reviewer 1.P12 L247: Are these values in precipitation 1901 \u00b1 903 refers to the mean and SD? Clarify. Response: We clarified as suggested. P12 L248: \u201c\u2026mature forest but the Network also includes a few older\u2026\u201d -- > \u201c\u2026mature forests but the network also includes several older\u2026 Response: We changed as suggested.P12 L250-252: This statement about the data being available is out of place. This should be part of the data availability statement that is one of the specific sections asked by PLoS. Also, with regards to this there are three different statements: In Data availability the authors express: Yes - all data are fully available without restriction Later, when answering the questions on where this data could be found the authors expressed \u201cAll relevant data are within the manuscript and its Supporting Information files\u2026\u201d. Delete the portion in the main text and unify these statements clearly. Response: We deleted the incorrect statement in text as suggested and clarified that: \u201cAll relevant data upon which all the presented results in this manuscript are based on is included in its Supporting Information files\u2026\u201d . In this sense, as mentioned before in Table S1 we included: i) number of stems, ii) basal area (both extrapolated to 1-ha) and iii) species richness for the 491 plots. Additionally, in Appendix 1 we reported the abundance of tree species per country. As stated before, this information constitutes the primary input used in the analyses to describe the main structural and compositional trends across the Andean forests. We clarified this in text .P12 L254: Again, the values in plot size refers to mean and SD? I don\u2019t understand 0.32 \u00b1 0.47 ha? How is this possible?. The same observation applies to the subsequent parts where plot size is mentioned. Also, I don\u2019t think is necessary to put \u00b1 0 whenever the plot size remains constant in some regions/countries. Response: We clarified that values in plot size refers to mean \u00b1 SD, and deleted \u00b1 0.P12 L261: \u201c\u2026being the longest subset\u2026\u201d -- > \u201c\u2026being the longest known subset\u2026\u201d ChangedP13 L270 or caption in Figure 2: Please clarify what do you mean when you say \u201c\u2026One (1) census refers to the establishment of a permanent plot\u201d? I understand a one census plot as that with only one measurement, whether temporal or permanent.Response: We deleted the phrase as it was confusing. Exactly, one census refer to one measurement, whether temporal or permanent. L275 Table 1 (No page number! We added page number): It is not clear to me that if the range shown for plot area also corresponds to the range in basal area. That is for example: Row 1 in the table (AR). A 0.16 ha plot accounts for 78 stems and 5 m2 in BA, while the 6-ha plot is linked to 1834 stems and 189.4 m2? Why not just simply express everything in 1 ha scale? I understand the issues of extrapolation, especially from really small plots, but yet you still perform the analysis later. Please clarify. Response: The range shown for plot area not necessary corresponds to the range in stems or basal area. In this table we prefer to show plot values, and not extrapolate to 1-ha in order to avoid the very large variability and dispersion when scaled to 1-ha . We discarded small plot for the analyses. We clarified this in text: \u201cTo analyze patterns in stem density, basal area and species richness, we considered those plots \u2265 0.1-ha (n = 236) where stems \u226510 cm DBH were measured. Due to high variability and dispersion when extrapolating basal area and stem density at a larger spatial scale we discarded plots of 0.01-ha, 0.04-ha, 0.05-ha and 0.08-ha \u201d . This was also stated in the discussion section . *** Starting here there is no line number, and page number is 2 for the section where \u201cData analyses\u201d subtitle is included. I\u2019m using these numbers and will add the \u201cp\u201d for paragraph.Response: We added line and page numbers. P2 paragraph 1: \u201c\u2026resolution that represents the\u2026\u201d -- > \u201c\u2026resolution covering the average\u2026\u201d Response: We changed as suggested.P2 p1: \u201c\u2026from 1 C for Ecuador\u2026\u201d -- > \u201cfrom 1 C in Ecuador\u2026\u201d Same for the rest of the sentences where a similar text is used (i.e. change \u201cfor\u201d to \u201cin\u201d). Response: We changed as suggested.Data Analyses P2 p2: Delete \u201cIn order to\u2026\u201d Just simply say \u201cTo analyze\u2026\u201d Changed\u201c\u2026(n = 236) and stems\u2026\u201d -- > \u201c\u2026(n = 236) where stems \u2265 10 cm DBH were measured. Due to high variability and dispersion when extrapolating basal area and stem density\u2026we discarded plots of 0.01 to 0.08 ha in size ...\u201dResponse: We changed as suggested.. Related to this part of the analytical approach, I am wondering how different are the extrapolations when you compare a 0.08 ha plot and a 0.1 one? You have discarded quite a lot of plots using this cut-off (which I am ok with) but I asked myself if maybe just 0.05 ha would have been enough?Response: In addition to the high variability and dispersion of data when extrapolating basal area and stem density of small plots at a larger spatial scale, we chose the 0.1 cut-off point as it is a standard minimum size for plots in forestry, thus for comparisons. Citation [55] should be placed after the (GLM) portion as this work refers to this modeling approach. Response: We changed as suggested. \u201cConsidering the nature of the response variables\u2026\u201d what is that nature? Statistical distribution? Did you perform a distribution test ahead of the GLMs? Please clarify. Response: We referred that: \u201cWe used a Quasi-Poisson distribution for stem density and species richness \u2026, and a Gaussian distribution with log-link function for basal \u00e1rea\u201d. This is clarified in text  with stems \u2265 10 cm DBH. To describe species composition, we applied a Non-Metric Multidimensional Scaling approach\u2026\u201d Response: We changed it as suggested. [\u2026[61] using latitudinal bands as random factor\u2026\u201d -- > \u201c\u2026as a random factor\u2026\u201d Response: We changed it as suggested. P4: Include citations for all R packages used.Response: R package used are cited in text: \u201cAll analyses were performed in R 3.4.3 [63], using AER to test overdispersion in GLM, vegan for ordination analysis, and lme4 for LMM\u201d (P18 L372-373).Results:P4 p2: \u201c\u2026 Mean annual air temperature and rainfall were positively correlated  \u2026\u201d I trust the numbers but the correlation in the figure seems to be driven by a few really wet points. Can you clarify this? Adding a trend line would be useful too. Using green and red dots here makes difficult to tease apart the countries. I suggest using an alternate color palette and perhaps different symbols for each country. Response: We have checked the correlation and it is correct. There are some plots that have between 2000 and 3000 mm of rainfall which also have around 25 degrees of temperature, but also some other plots with 4000 and 5000 mm of rainfall that also have around 23-24 degrees. We did not include a trend line as this is a correlation and no cause-effect is expected. P5 p1: Delete \u201cConsidering plots\u2026\u201d since is already mentioned in the methods. Just start with\u201cwe found that stem density\u2026\u201d Response: We changed as suggested.With regards to this section and Figure 4, the small-sized plots seem to be creating a lot of noise in the trends. Why not testing stem density and basal area for only 1-ha plots as shown for species richness in Fig 4G? Also discussed later, are the plots with higher stem density also showing high basal area? There is a brief mention in the discussion about this relationship, but a simple bivariate plot would help. Response: We tested stem density and basal area for only 1-ha plots and found that results and tendencies were very similar. Thus we kept small plots in order to have higher number of plots. Plots with higher stem density not necessary have higher basal area. P6 p2: \u201c\u2026we registered a total of 97,054 tree stems\u2019\u2026\u201d The abstract mentions 86,964 individuals (?). Also, are these all tree species? When authors say stems it might imply other life forms as palms or tree-ferns. Please clarify.Response: The number 97,054 referred to all stems \u226510 cm while 86,964 referred to identified stems \u2265 10 cm diameter to species level. We clarified this in abstract . We addressed the entire manuscript to trees but actually we included palms and ferns. P6 p2: \u201c\u2026was shared among all data sets\u2026\u201d -- > \u201c\u2026was shared among all plots\u2026\u201d Response: We changed as suggested. P6 p3: \u201cThe study plots tended to segregate along\u2026\u201d Use a different word for segregate:cluster, group. Response: We used the word \u201cgroup\u201d as suggested (P20 L426-438).P6 p3: \u201c\u2026Elevation and latitude correlated with both\u2026\u201d -- > \u201c\u2026correlated well with\u2026\u201d. Also, in Figure 5 could you explain what does each axis in the NMDS represent? Response: We changed as suggested. Discussion and conclusions: See in bold edits and suggestions.An overall recommendation here is that for every sentence/statement where the authors are highlighting a specific result, having a direct reference to the particular figure or table where the reader can refer to again would be quite useful. Also, I think authors can separate the conclusions here. P9 p1: \u201c\u2026it was less expected for rainfall as [5]\u2026\u201d Change the structure of the sentence and citation format to \u201c\u2026it was less expected for rainfall as Urrutia et al [5] reported for the Andes where rainfall did not covaried linearly with elevation\u2026\u201d. Also, this statement relates to an earlier observation about the need for some hypothesis statements. If you say \u201cit was less expected\u201d, what were your initial expectations? Response: Changed as suggested. Actually, we were referring that our findings were different from those of Urrutia et al. We rephrased the statement to avoid confusion . P9 p2: \u201cBoth stem density and basal area were related with the gradients addressed\u2026\u201d -- >\u201cBoth stem density and basal area were related to the gradients covered by our dataset\u2026\u201dResponse: Changed as suggested. \u201c\u2026patterns of stem density were more consistent with elevation and latitude than for basal area\u2026\u201dResponse: Changed as suggested. Here, authors repeat some sentences from the results section. \u201cStem density peaked at 10-15 latitude\u201d. Response: We rephrased the statement and differentiate it from the result section. \u201cThe observed increase in the mean values of the structural variables with elevation hasnot\u2026\u201dResponse: Changed as suggested. P10 p1: \u201c\u2026or maybe some local climate and topographic conditions\u2026\u201d This sounds vague. What other climate or topographic conditions might have influenced these results? Explain. Response: We refer to some slopes orientation which may imply wetter or drier conditions, for example. We explained it in text as suggested (P24 L495-496). Land-use history is briefly mentioned as a potential driver of stem density. Yet, the authors have some (limited) information on the time since disturbance for some of the plots. Why not discuss this better? Can you filter some of the results based on different disturbance periods? Very dense plots might be a reflection of recent (or not that recent) events. At least in the form of an Appendix this would add some support when contrasting such a wide range of sites and conditions. Response: We do not have this information that is why we did not reported it. Nevertheless, we discussed that for the secondary plots considered, it may have had some influence on stem density (P24 L497-498). P10 p1: Change \u201cborder effect\u201d for \u201cedge effect\u201d. Response: Changed as suggested.Also, briefly explain why these effects are more pronounced for small plots?. Why plots ~0.5 ha or larger might be preferred? This section discussing potential effects of plot size also needs some citations. See for example: Wagner et al. 2010 Biotropica, Volume 42 (6): 664-671 and some references therein.Response: We added the citation as suggested.P10 p2: I think only mentioning the main hypotheses (e.g. Janzen & Connel) is not enough here. How these hypotheses are related to the results found? Response: We explained in text as suggested. P11 p2: \u201c\u2026plots associated with low diversity of tree species\u2026\u201dResponse: We changed as suggested. P11 p2: Change the reference format for Kattan et al. 2004 accordingly. P11 p3: Delete \u201cAs well\u2026\u201d Response: We deleted as suggested. P12 p1: \u201c\u2026are unknown\u2026\u201d change to -- > \u201c are not clear [36]\u201dResponse: We changed as suggested. There is quite an abrupt change from this last paragraph to the next that discuss the importance of the Andean forest plot network. What are some of the potential implications of the findings? What does it mean that some forests in the Andes have higher density than others? More carbon? Less carbon? What about diversity? Are these forests well protected? I am not asking for a detailed analysis but just a brief consideration to potential links of the results to management or conservation aspects.Response: We added a brief consideration as suggested .P12 p2: The enumeration used in this long paragraph is confusing. There are two sections discussing different aspects, yet, some are redundant (e.g. #4 and #8 about models). Consider rewriting.Response: We re-wrote as suggested. P12 p2: \u201c\u2026improving the number of hectares per country\u2026\u201d -- > \u201c\u2026increasing the area covered per country\u2026\u201dResponse: We changed as suggested.AttachmentResponse to Reviewers. Malizia et al. FINAL.docxSubmitted filename: Click here for additional data file. 26 Mar 2020Elevation and latitude drives structure and tree species composition in Andean forests: results from a large-scale plot NetworkPONE-D-19-30260R1Dear Dr. Malizia,We are pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it complies with all outstanding technical requirements.Within one week, you will receive an e-mail containing information on the amendments required prior to publication. When all required modifications have been addressed, you will receive a formal acceptance letter and your manuscript will proceed to our production department and be scheduled for publication.https://www.editorialmanager.com/pone/, click the \"Update My Information\" link at the top of the page, and update your user information. 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For more information, please contact With kind regards,RunGuo ZangAcademic EditorPLOS ONEAdditional Editor Comments :Reviewers' comments: 30 Mar 2020PONE-D-19-30260R1 Elevation and latitude drives structure and tree species composition in Andean forests: results from a large-scale plot Network Dear Dr. Malizia:I am pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. onepress@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper at this point, to enable them to help maximize its impact. If they will be preparing press materials for this manuscript, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact plosone@plos.org. For any other questions or concerns, please email Thank you for submitting your work to PLOS ONE.With kind regards,PLOS ONE Editorial Office Staffon behalf ofProfessor RunGuo Zang Academic EditorPLOS ONE"}
+{"text": "SA, SB and SC of the three species, the spin-structures of the ground state can be classified into two types. In Type-I the three spins are either parallel or anti-parallel to each other, while in Type-II they point to different directions but remain to be coplanar. Moreover, according to the magnitudes of SA, SB and SC, the spin-structures can be further classified into four kinds, namely, p\u2009+\u2009p\u2009+\u2009p , one species in f (fully polarized) and two species in q (a mixture of polarized atoms and singlet-pairs), two in f and one in q, and f\u2009+\u2009f\u2009+\u2009f. Other combinations are not allowed. The scopes of the parameters that supports a specific spin-structure have been specified. A number of spin-structure-transitions have been found. For Type-I, the critical values at which a transition takes place are given by simple analytical formulae, therefore these values can be predict.We have performed a quantum mechanic calculation  together with an analytical analysis based on a classical model. Then, according to the relative orientations of the spins  For these systems, when the temperature is extremely low , the spatial degrees of freedom are nearly frozen and the spin degrees of freedom play essential roles3. Various spin-structures will emerge, and they are found to be sensitive to the very weak spin-dependent forces. Therefore, these systems might be ideal for realizing exquisite control.The study of the multi-species Bose-Einstein condensates (BEC) with atoms having nonzero spin is an attractive topicN spin-1 atoms, the polar phase (p-phase) and the ferromagnetic phase (f-phase) have been found in the ground state (g.s.)10. In the p-phase, the spins of atom are two-by-two coupled to zero to form the singlet pairs (s-pair), and the total spin of the condensate S\u2009=\u20090. In the f-phase, all the spins are fully polarized, i.e., lying along a common direction, and S\u2009=\u2009N. For 2-species BEC, it was found in23 that there are three types of spin-structures, namely, (i) the p\u2009+\u2009p spin-structure where both species are in p-phase; (ii) the f//f structure where both species are in f-phase, and the two total spins (each for a species) are lying either parallel or antiparallel to each other; and (iii) the f//q structure where one in f-phase and one in quasi-ferromagnetic phase .When the BEC contains only one kind of The above message from 2-species BEC attracts the exploration on the spin-structures of multi-species BEC. Note that, for 3-species BEC, the three intra-species and three inter-species spin-dependent interactions can be repulsive or attractive. Thus, the spin-structures are expected to be very rich. However, this interesting topic is scarcely studied before. This paper is a primary study on this topic. The aim is to clarify the variety of the spin-structures and the related critical phenomena, and the effects of the intra- and inter-species interactions. We believe that the knowledge extracted from 3-species BEC would be in general useful for understanding the spin-structures of many-body systems with multi-species.J\u2009=\u2009A, B, C) and N, while the interaction energy increases with N2, the relative importance of the kinetic terms is very weak when N is very large. Therefore, the TFA is applicable when the particle numbers are huge as usually in the experiments of BEC .From the experience of 2-species BEC, the spin-structures are seriously affected by the compactness of the spatial wave functions  calculation, a corresponding classical model has been proposed and solved analytically. The results from the model are checked via a comparison with those from QM calculation. This model helps greatly to understand the complicated 3-species spin-structures.We proceed in the following way:i-th atom of the J-species. The inter-species interaction is m and \u03c9, and use Let the mixture of three kinds of spin-1 atoms be trapped by isotropic and harmonic species-dependent potentials J-species where the spins are coupled to Z-component MJ. According to the theory given in27, SJ and MJ are fixed), and the set A- and B-species, in which SA and SB are coupled to Note that, in the ground state (g.s.), every particles of a kind will condense to a spatial state , as a reasonable approximation, the contribution of the former can be neglected. Then, we have Since the spin-dependent forces are in general two order weaker than the spin-independent forces  will occur at J to III) will occur at If a wave function . An example is given in Fig.\u00a01, Form I3, and empty, respectively.The spin-structures in multi-species BEC is caused by the inter-species interactions. Obviously, they would act more effectively when the three species are distributed closer to each other. Therefore, in the following examples, we take the miscible states into account, in which all the three species have nonzero distribution at the center , \\docummentclasspt{minima/\u03b3C (Eq. ). They g via Eq. . Then, tA at A can link with a Form IC at Nonetheless, the realization of the miscible state is based on a number of assumptions. First, it is assumed that all the wave functions are nonzero at the center, thus mentclass2pt{minimM can be neglected. Accordingly, a candidate of the g.s. can be expanded asMaking use of the spin basis-state, we define a set of basis-states for the g.s. asCarrying out the diagonalization of J-species. Similarly, we haveTo extract information on spin-structure from Examples are given below.Neglecting all spin-independent terms, the spin-dependent energy of the g.s. can be written asBased on Eq. , we propThe effect of the inter-species force is embodied by There are two types of spin-structures. When all pg.s. be the point where For Type-IJ. At the minimum the three equations pg.s. cannot locate inside the cuboid. It implies that the three species cannot all be in the q-phase.In this case P1 belong to the first kind, the other three containing Let a rectangle on the surface of the cuboid be denoted as pg.s. were located on pg.s. cannot be located on P1. It implies that the case with one or two species in P-phase is prohibited, while all species in P is possible. This fact coincides with the finding found in 2-species condensates, in which the P-phase is extremely fragile when it is accompanied by an f or a q. Therefore, the P\u2009+\u2009f or P\u2009+\u2009q structures do not exist, but the P\u2009+\u2009P structure is allowed23.If this case is realistic, the g.s. would have at least one species in pg.s. can only access P1 and the three rectangles of the second kind, but those edges each being a common edge of two rectangles belonging to two kinds should be excluded.With the prohibition of the above two cases, f//f//f. . The three inequalities f//f//f-structure. The energy of this structure f//f//f structure is the only choice for the g.s. When some species  is polar in nature , whereas QA and QB can be negative or weakly positive. If they are positive and large, the inter-species interaction should be even stronger to ensure that the inequalities hold. The equality for C-atoms arrive at a balance. The energy f//q//f (B-species in q) and q//f//f (A-species in q) can be similarly discussed. These three together are called the double-f-structure (double-f-str).When mentclass2pt{minimpg.s. is in the interior of f//q//q. The inequality C) are required. This leads to the constraint listed in the third row of Table\u00a0C-species are polar in nature, whereas f//q//q structure. The structures q//f//q and q//q//f can be similarly discussed. The three together are called the single-f-str.When mentclass2pt{minimp and the structure is therefore denoted as p\u2009+\u2009p\u2009+\u2009p. When f-str will be lower than p\u2009+\u2009p\u2009+\u2009p \u2192 single-f-str will occur.When all the three species are polar in nature  if f-phase. Starting from p\u2009+\u2009p\u2009+\u2009p to a single-f-str as mentioned above. Recall that the single-f-str must have p\u2009+\u2009p\u2009+\u2009p has f-strs  cannot both be satisfied Otherwise, two contradicting inequalities f-strs can survive. Therefore, p\u2009+\u2009p\u2009+\u2009p can only transit to a specific single-f-str depending on the parameters. Besides, the transitions among the three single-f-strs  are prohibited.We aim at the effect caused by the variation of the inter-species forces. Note that q-phase can be changed to a f-phase. Therefore, the single-f-str \u2192 double-f-str transition will occur (as shown below). One can prove that the three sets of constraints for the three double-f-strs do not compromise with each other as before. Thus, a single-f-str can only transit to a specific double-f-str depending on the parameters, and the transitions among the three double-f-strs are prohibited. When f//f//f structure.When p\u2009+\u2009p\u2009+\u2009p \u2192 single-f-str \u2192 double-f-str \u2192 f//f//f.With these in mind the increase of Two numerical examples of Type I are shown in Figs.\u00a0According to the model, when 23. Obviously, Eq.  is helpful to the transition \\documentThe two angles obtained in this way should ensure that the two second order derivatives given in Eqs.  and 47)47) are prom Eqs.  and (47)f\u2009+\u2009f\u2009+\u2009q. The constraints appear as (refer to the second row of Table\u00a0When mentclass2pt{minimf\u2009+\u2009q\u2009+\u2009f and q\u2009+\u2009f\u2009+\u2009f can be similarly discussed.The angles are subjected to the two coupled equations (refer to Eqs.  and 49)49))40\\dof\u2009+\u2009q\u2009+\u2009q. The constraint imposed on this structure is listed in the third row of Table\u00a0When mentclass2pt{minimp\u2009+\u2009p\u2009+\u2009p.When all A comparison of the results from the model and from the diagonalization of \u03c0. This supports the assumption of coplanar structure.Table\u00a0The structures can be described by the norms of the three spins The spin-structures not in entclass1pt{minimaThe spin-structures can be further classified according to the norms of the spin. In addition to Starting from the e-I Fig.\u00a0 the equae-I Fig.\u00a0, 34) an an\\docume-I Fig.\u00a0). Thus, e-I Fig.\u00a0, analytiK-species BEC  and is believed to hold also for K-species cannot all be in K-species BEC remain to be checked.Recall that, for 2-species BEC, the phases  to Eqs.  and 30)\\documentFeatures of the spin-structures of 3-species condensates with spin-1 atoms have been extracted from a model and have been checked via a QM calculation. Note that the effect of the spatial wave function is embodied in the factors"}
+{"text": "It has been suggested that scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the presence of a few highly connected hub nodes and a large number of small-degree nodes may provide alternate paths between any two nodes on average\u2014such robustness has been suggested in studies of metabolic networks, gene interaction networks and protein folding. A theoretical justification for why many networks appear to be scale-free has been provided by Barab\u00e1si and Albert, who argue that expanding networks, in which new nodes are preferentially attached to highly connected nodes, tend to be scale-free. In this paper, we provide the first efficient algorithm to compute the connectivity density function for the ensemble of all homopolymer secondary structures of a user-specified length\u2014a highly nontrivial result, since the exponential size of such networks precludes their enumeration. Since existent power-law fitting software, such as powerlaw, cannot be used to determine a power-law fit for our exponentially large RNA connectivity data, we also implement efficient code to compute the maximum likelihood estimate for the power-law scaling factor and associated Kolmogorov\u2013Smirnov p value. Hypothesis tests strongly indicate that homopolymer RNA secondary structure networks are not scale-free; moreover, this appears to be the case for real (non-homopolymer) RNA networks.A network is  A network is said to be scale-free if its connectivity function N(k), which represents the number of nodes having degree k, satisfies the property that power-law distribution, which by definition satisfies The 1 Newman . Scale-fpreferential attachment. In Barabasi and Albert (N(k) with which a node in the network interacts with k other nodes decays as a power-law, following Barabasi and Albert  analyzedd Albert , it was How scale-free are biological networks?not to be fit by a power-law distribution, despite published claims to the contrary. Estimating an optimal power-law scaling factor by maximum likelihood and using truncated power-law distribution. The data analyzed by the authors included data from protein\u2013protein interaction networks  [resp. p(k)] for secondary structure connectivity of a given homopolymer, which allows non-canonical base pairs. Section\u00a0The plan of the remaining paper is as follows. Section\u00a0K in the ensemble of all secondary structures with run time Section\u00a0nhomopolymer is a set s of base pairs , such that (1) there exist at least free energy of a homopolymer secondary structure s is defined to be s| of base pairs in s , computed the following simple recurrence relation from Stein and Waterman (O(n) space, hence is more efficient by a factor of n. In a similar fashion, the recurrence relations  is a base pair, then Z denote the number of secondary structures on the interval , for k neighbors, and for which there are exactly h unpaired positions (or holes) in either(i)i,\u00a0j] are all unpaired, or(ii) that (i), in which the rightmost (i)(i)Suppose that every hairpin loop is required to have at least the Eqs. \u201312 for Bi,\u00a0j] that have exactly k neighbors with respect to the k), so thatZ and n to indicate a length n homopolymer.Let mentclass2pt{minimi,\u00a0j] where i,\u00a0j] where i,\u00a0j] can be partitioned into structures having exactly degree k (i.e. kk structures that can be obtained by either adding or removing a single base pair). To support an inductive argument, in proceeding from interval  to k, which have a certain number h of positions that are visible , which can be paired with the last position not be base-paired with j in ; however, can be base-paired with j in h of holes (positions in j), we introduce the variable v to keep track of the number of visible positions in Z as defined in the Eqs.  denotes the number of secondary structures on the interval , for k neighbors, and for which there are exactly h unpaired positions (or holes) in i,\u00a0j]. When i,\u00a0j] are all unpaired.Let N denote the number of secondary structures on  for the homopolymer model, as computed by Eq. , since other potential base pairs would contain fewer than i,\u00a0j] is external to the base pair , so visibility parameters i,\u00a0j).Base Case B considers all structures on  where i,\u00a0j). The arrow is meant to indicate that the structure on the right is the only neighbor of that on the left, as depicted in Fig.\u00a0i,\u00a0j] is i,\u00a0j] is visible , Base Case C considers the converse situation, consisting of the empty structure on  where i,\u00a0j) many base pairs can be added to the empty structure. In Fig.\u00a0j.Base Case D considers the empty structure on  is visible , so visibility parameters Inductive Case A considers the case where left and right extremities Inductive Case A: For i,\u00a0j) base-paired in ,see Fig. .Fig. 5Sj base-pairs with the r, where j, since the corresponding hairpin loop would constain less than h holes  base-paired in  for some C(v) considers the case where position s of the format has k neighbors, provided the restriction of s to s to vh is due to the fact that since base pair holes are located in visible positions in s can be obtained by adding a base pair from any hole to any visible suffix position\u2014there are vh many such possible base pairs that can be added. Finally, the last term s can obtained by removing base pair C(v).For each value s in Eq. . Figure\u00a0Inductive Case C(v), fori,\u00a0j], for some i,\u00a0j],D considers the case where there are h holes, and positions D includes the addition requirement that position s satisfying Case D can be partitioned into subcases where the restriction of s to h holes in structure s in Case s to j, but not with s to j and j, s produced in this fashion is thus s to The term s be a structure that satisfies conditions of Case D with h holes and s to w visible positions. Then s has k neighbors provided that the restriction of s to The argument just given shows the following. Let mentclasspt{minimaInductive Case D: For i,\u00a0j], and v), when implemented, this requires a test that As in Case C, we describe the function m corresponds to the length i,\u00a0j].The algorithm described in Sect.\u00a0Base Case A: For Base Case B: For Base Case C: For Base Case D: For all Inductive Case A: For Inductive Case B: For Inductive Case C(v): For Inductive Case D: For h is strictly less than p value for Kolmogorov\u2013Smirnov goodness-of-fit, as described in Clauset et\u00a0al.  of secondary structures having degree k, for all k within a certain range. It follows that the likelihood Recall the definition of the function , as wellfunction , definedt et\u00a0al. 27\\documep value, following  p value for goodness-of-fit follows Sect.\u00a04.1 of Clauset et\u00a0al.  power-law distribution with scaling factor M synthetic data sets, each containing N sampled values, in time O(mNM); however, since N is the  number of all secondary structures having degrees in sequential method would require prohibitive run time. Instead, we implemented the much faster conditional method  is the proportion of structures having degree k. However, Table\u00a0p values for optimal power-law fis of connectivity data for homopolymers of lengths from 30 to 150.Since powerlaw requires input files of  connectivity degrees, when creating Table\u00a0entclass1pt{minimacut-off values n homopolymer has degree greater that dg(s) is redefined to be the number of structures t that can be obtained from s by adding, removing, or shifting a base pair in s. The so-called p value of 0.248. Since RNApowerlaw determined p value of 0.219, we can not reject the null hypothesis that a power-law distribution fits the tail of Figure\u00a0H. sapiens, M. musculus, D. melanogaster, C. elegans) those genes, which are enriched in exon shuffling events, displayed a higher connectivity degree on average in protein\u2013protein interaction (PPI) networks; i.e. such genes had a larger number of interacting partners. On similar grounds that nature should reuse and amplify successful metabolic networks, one might argue that metabolic networks should exhibit scale-free properties. However, rigorous statistical analysis has shown that metabolic networks fail a goodness-of-fit test for scale-free distribution, while PPI satisfy a goodness-of-fit test for scale-free distributions over a certain range of connectivity (Khanin and Wit Since the pioneering work of Zipf on the scale-free nature of natural languages Zipf , variousIndex of Complex Networks exhibit the \u201cstrongest level of direct evidence for scale-free structure\u201d. In a response to a preprint of Broido and Clauset (https://www.barabasilab.com/post/love-is-all-you-need, A.L. Barab\u00e1si argued against the conclusions of Broido and Clauset (Information and Control. For details, references, and a history of the power-law distribution, see Mitzenmacher (There appears to be a current polemic whether certain naturally occurring networks are scale-free. Broido and Clauset  provide  Clauset  dated Ma Clauset . Here, ienmacher .Fig. 13aK is a user-specified degree bound fruA. Figure\u00a0Klebsiella pneumoniae subsp. pneumoniae with EMBL accession code CP000647.1/1773227-1773291 and the 76 nt alanine transfer RNA from Mycoplasma mycoides with accession code tdbR00000006 from tRNAdb Juhling et\u00a0al. (fruA, Figure\u00a0Given the current interest in whether certain naturally occurring networks are scale-free, we have introduced a novel algorithm to compute the connectivity density function for a given RNA homopolymer. Our algorithm requires mentclasspt{minimag et\u00a0al.  (accessimentclasspt{minimahttp://bioinformatics.bc.edu/clotelab/RNAnetworks.Since (Day et\u00a0al. As an afternote, our personal opinion is that it doesn\u2019t much matter whether a naturally occurring network arising from physical phenomena is precisely scale-free or not. If network connectivity appears to follow a power-law distribution, even approximately, then by results of Barabasi and Albert , this su"}
+{"text": "Scientific Reports 10.1038/s41598-019-56662-x, published online 27 December 2019Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cExtracellular\u201d was incorrectly given as \u201cExtracellur\u201d. This has now been corrected in the PDF and HTML versions of the Article and in the accompanying Supplementary Information file."}
+{"text": "We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, \u201cformal balance,\u201d and the new notion of \u201ccycle balance\u201d are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic  proofs of a previous result , our main result , and a corresponding result in the setting of continuous-time Markov chains. Detailed balance and complex balance are important concepts in chemical reaction network theory (CRNT). Both principles have been proposed already in the 1870s and 1880s by Ludwig Boltzmann in the kinetic theory of gases \u00a0 mass-action systems display remarkably robust dynamics. If one positive equilibrium is CB, then so is every other equilibrium, which justifies calling the entire system CB. Moreover, there is exactly one positive equilibrium in every stoichiometric class (invariant set), and this equilibrium is asymptotically stable (implied by a strict Lyapunov function)\u00a0(Horn and Jackson r is the number of reversible reactions (pairs of edges), m is the number of complexes (vertices), s is the rank of the stoichiometric matrix. Schuster and Schuster consider \u201cgeneralized mass-action kinetics\u201d in the sense that the net reaction rate contains a mass-action factor (as for enzyme kinetics). They provide \u201cgeneralized Wegscheider\u2019s conditions\u201d on the equilibrium constants; in fact, they obtain For mass-action kinetics, complex balance has been characterized by Horn , and expFeinberg , and \\doph\u00a0Berge . That isIn this work, we provide new conditions on a complex-balanced equilibrium of a reversible chemical reaction network to be detailed-balanced. As just stated, a characterization has already been obtained in\u00a0Dickenstein and P\u00e9rez\u00a0Mill\u00e1n . On the The work is organized as follows. First, we present the elementary argument  that is common to all types of networks. Then, we apply it to different types of networks .mixed graph contains undirected and directed edges, in general, and that a simple mixed graph does not contain multiple edges (connecting two vertices) or loops (connecting a vertex to itself).The object of the study in this section is a simple mixed graph. Recall that a V, undirected edges\u00a0U, and directed edges\u00a0D). Explicitly, if two vertices Let path is a (finite or infinite) sequence of edges which connect a sequence of distinct vertices. For finite paths, the first and last vertex may be identical, in which case the path is a cycle. A path is called directed if it contains only directed edges and all edges have the same direction . In other words, a path connecting the vertices weakly directed if it contains a directed edge and all directed edges have the same direction.A balanced if it is undirected. A vertex is called balanced if the set of incident edges contains either only undirected edges or a pair of oppositely directed edges (with respect to the vertex). In other words, a vertex v is balanced if the existence of An edge is called G is called edge-balanced/vertex-balanced if every edge/vertex is balanced.An edge-balanced graph has only undirected edges and therefore is vertex-balanced and contains no directed cycle. In the following, we show the converse.G is vertex-balanced, but not edge-balanced, then it contains a directed cycle.Let G is vertex-balanced and that there exists a directed edge Assume that The main result used in the following section is the contrapositive of Proposition\u00a0G is vertex-balanced and contains no directed cycle, then it is edge-balanced.Let bi-infinite if it connects a bi-infinite sequence of vertices. Bi-infinite directed paths can be viewed as a \u201cdirected cycles of infinite length.\u201dA directed path is called G is vertex-balanced, but not edge-balanced, then it contains a directed cycle or a bi-infinite directed path.Let Analogous to the proof of Proposition\u00a0Again, as a main result, we state its contrapositive.G is vertex-balanced and contains no directed cycle or bi-infinite directed path, then it is edge-balanced.Let G is vertex-balanced and contains no directed cycle, then it cannot have a finite number of directed edges.As a consequence, if In the following, we denote the positive real numbers by chemical reaction network  is given by a finite, simple directed graph (complex)n chemical species which are the left- and right-hand sides of chemical reactions.A As an example, consider the \u201cnetwork\u201d consisting of the single reaction kinetic system  is given by a chemical reaction network , where (kinetics)A n chemical species) is defined asThe resulting dynamical system for the concentrations For \u201cgeneral kinetics,\u201d it is often assumed that reversible reaction networks, where the underlying graph G is symmetric, that is, ij for In the following, we consider detailed-balanced (DB) if, for every An equilibrium mentclass2pt{minimcomplex-balanced (CB) if, for every An equilibrium mentclass2pt{minimObviously, we have the implicationdirected cycle A formally balanced (FB) if, for every directed cycle A state mentclass2pt{minimUnder quite weak assumptions on the kinetics, formal balance is independent of the state: With every vertex Formal balance is defined by equations for directed cycles. We introduce two other variants of cycle balance which are defined by inequalities and which are weaker than formal balance.strongly cycle-balanced (sCycB) if, for every directed cycle cycle-balanced (CycB) if, for every directed cycle A state mentclass2pt{minimmentclass2pt{minimx is FB x is CycB\u201d is obvious if x is FB\u201d implies x is CycB.\u201d All other implications are obvious.The implication \u201cFor \u201cgeneral kinetics,\u201d where t}(\u2217) in  holds foi only. If j with To see this, first note that the sign of C), then also x is FB\u201d and \u201cx is sCycB.\u201d Otherwise, x is FB\u201d and \u201cx is sCycB.\u201dObviously, implication t}(\u2217) in  holds foAs stated above, the two new variants of cycle balance are weaker than formal balance, in general. They allow elementary graph-theoretic proofs of a previous result and of a new result which holds for arbitrary kinetics and boundary equilibria; see Theorem\u00a0Algorithmically, all variants of cycle balance  are equally costly: the most expensive step is the identification of all cycles in the underlying graph. For mass action  defined asGiven a reversible reaction network, defined by a finite, simple directed graph Let mentclass2pt{minimmentclass2pt{minimAs stated in the introduction, it was shown in Dickenstein and P\u00e9rez\u00a0Mill\u00e1n  that detx is CB and CycB, then it is DB.Let mentclass2pt{minimBy the implications  and TheoThe above result is new and stronger than the existing result: first, it holds for nce, see\u00a0. HoweverTo summarize, given complex balance, detailed balance is equivalent to all variants of cycle balance. The result holds for x is detailed-balanced (DB).x is formally balanced (FB).x is strongly cycle-balanced (sCycB).x is cycle-balanced (CycB).Let mentclass2pt{minimBy the implications  and Propweakly complex-balanced (wCB) if x is wCB Only the second implication in  is not aG, which contains two independent cycles; see the left diagram. Consider the reversible cyclic network G, have deficiency zero: Both networks, x, does not contain a (weakly) directed cycle, and the same holds when G; see below.For the isolated network G, there exists a complex-balanced equilibrium x is not detailed-balanced, in particular, that the mixed graph G and x, does not have x\u00a0is not cycle-balanced, that is, there exists a directed cycle in not a (weakly) directed cycle.  The only feasible subgraph For the full network Remarkably, all edges of the induced graph  can be determined without computing the complex-balanced equilibrium.The argument in Sect.\u00a0A continuous-time MC is a random process on a countable state space, where a measure  on the set of states is determined by the initial measure and the transition rates (via the Kolmogorov forward equations). For a formal definition, see, e.g., Norris . In a naV and the transition rate from state q. Further, we introduce the set of transitions (edges) We denote the set of states (vertices) by V assigns a nonnegative real or infinity to each subset of V. Here, we consider only stationary if, for all reversible  if, for all A measure induced graphGiven a MC with associated symmetric, simple, directed graph entclass1pt{minimaentclass1pt{minimaG be the graph associated with a continuous-time Markov chain, where Let Its contrapositive is useful to state. If a stationary measure is not reversible, then the induced graph contains a directed cycle or a bi-infinite directed path. See Examples stochastic mass-action kinetics. The corresponding rate constants are specified as edge labels in the graph below.  The (infinite) graph Consider again the reversible cyclic network For the deterministic system, n et\u00a0al. . Since tG, except for the trivial two cycles. A\u00a0stationary distribution on Let Since Since there exist two different stationary distributions Finally, we summarize similarities and dissimilarities in the settings of RNs and MCs in a table."}
+{"text": "Correction to: Inj Epidemiol 7, 29 (2020)https://doi.org/10.1186/s40621-020-00248-zAfter publication of this supplement article Lee , it was The sentence currently reads:Because our goal is not the \u201cmoon,\u201d but for our children to leave in a world that is Injury Free.The sentence should read:Because our goal is not the \u201cmoon,\u201d but for our children to live in a world that is Injury Free.This has now been included in this correction article."}
+{"text": "Scientific Reports 10.1038/s41598-019-51286-7, published online 30 October 2019Correction to: A supplementary file containing a \u2018dive bomb sound\u2019 was omitted from the original version of this Article. This has been corrected in the HTML version of the Article; the PDF version was correct at time of publication."}
+{"text": "Autism spectrum disorder (ASD) is a neurodevelopmental alteration characterized by social/communicative deficits, repetitive/stereotyped movements, and restricted/obsessive interests. However, there is not much information about whether movement alterations in ASD comprise modifications at the basic kinematic level, such as trajectory and velocity, which may contribute to the higher level of processing that allows the perception and interpretation of actions performed by others, and hence, impact social interaction. In order to further explore possible motor alterations in ASD, we analyzed movement parameters in the Valproate (VPA) animal model of autism. We found that VPA-treated rats displayed greater movement acceleration, reduced distance between stops, spent more time in the corner of the open-field arena, and executed a number of particular behaviors; for example, supported rearing and circling, with no major changes in distance and velocity. However, in the social interaction test, we found other alterations in the movement parameters. In addition to increased acceleration, VPA-rats displayed reduced velocity, increased stops, reduced distance/stop and lost the social/non-social area discrimination that is characteristic of control rats in acceleration and stops variables. Hence, even if prenatal VPA-treatment could have a minor effect in motor variables in a non-social context, it has a crucial effect in the capacity of the animals to adjust their kinematic variables when social/non-social context alternation is required. Autism spectrum disorder (ASD) is a multifactorial group of neurodevelopmental alterations of unknown etiology, in which genetic and environmental factors are involved . This coMotor alterations in ASD were described in the earliest studies of this pathology by Furthermore, animal models of autism have allowed us to explore the cellular and molecular underlying mechanisms and, to some extent, the associated motor alterations . In partIn order to explore possible motor alterations in the VPA-model related to independent free exploration or social interaction, we evaluated kinematic parameters in two habitually used behavioral tests for laboratory rats: the open field test (OFT) and the three-chamber social test (3C-ST). The first one is designed to evaluate locomotor activity and exploratory behavior without social demands and the second test specifically evaluates social interaction. In brief, the aim of our study was to determine whether the VPA autism model shows kinematic particularities and if they are influenced by social or non-social contexts.ad libitum access to food and water). On embryonic day 12.5 (E12.5) experimental rats received a single i.p. injection of Sodium Valproate , while the control group received a saline solution injection. On postnatal day 21 (PN21), the day of weaning, pups were separated from their dam and males were housed in groups of 3\u20134 littermates until P30, when behavioral tests were performed. We only used males in this study, considering that prenatal VPA treatment produces effects both in males and females, but with qualitative and quantitative differences , and a second batch composed of 8 control and 8 VPA-treated rats.A black OFT of 60 \u00d7 60 cm was used. At the beginning of the test, every animal was located at the center of the illuminated arena and allowed to freely explore; such behavior was recorded for 5 min. OFT was conducted in two batches of control and experimental rats. A first batch composed of 13 control and 7 VPA-treated rats (n = 8) and VPA treated (n = 11) rats. The apparatus consisted of three 30 \u00d7 22 cm adjoining chambers of transparent acrylic, connected by 10 \u00d7 10 cm doors. Because we used juvenile rats (PN30) we have used the apparatus dimensions for adult mice, which are similar in weight  to examine anxiety levels, as previously reported  in the s1 using the \u201cthreshold\u201d and \u201canalyze particles\u201d functions to obtain the Cartesian position coordinates  of the rat\u2019s \u201ccenter of mass\u201d in each video frame. For all analyzed video sequences, a visual verification of whole photograms was performed in order to correct the data, when necessary. Even though time consuming, this method guarantees no biases in point position data. Data were then transferred to an Excel worksheet  and each video data set was calibrated to the actual dimensions of the testing arenas. From these data sets we calculated the displacement between two consecutive frames and, using logical functions, extracted the frames in which the rats were moving and those in which the rats remained immobile. These two variables allowed us to obtain two parameters: \u201ctraveled distance,\u201d as the cumulative sum of frame to frame displacement, and \u201ceffective velocity,\u201d as the total distance divided by the time during which the rat was actually moving. We used the term \u201ceffective,\u201d rather than \u201cmean\u201d velocity because we calculated the velocity only when the animal moved (excluding the time when it remained immobile). \u201cMean acceleration\u201d was calculated as the mean value of frame to frame positive change of velocity, only counting the frames with displacements. The parameter \u201cstops\u201d corresponds to the number of times that a frame-series with displacements was interrupted by, at least, one frame of immobility, from another frame-series with displacements. The parameter \u201cdistance/stop\u201d was obtained, as the total distance divided by the total number of \u201cstops.\u201d These analyses were performed for both the OF and 3C-ST behavioral tests.All videos were recorded with a web video camera , converted to the grayscale AVI format, and then processed by ImageJ 1.52p software 1 using tSpecific behaviors, such as \u201csupported rearing\u201d . Multiple comparisons in minute-by-minute analysis from OFT and 3C-ST-habituation and social/non-social areas- were analyzed by two-way ANOVA, followed by Tukey  or Sidak  post hoc tests. In all cases, a p-value lower than 0.05 was considered as statistically significant.Statistical analyses were performed using GraphPad Prism 8.0.2 . The non-parametric two-tailed Mann-Whitney In order to analyze possible motor alterations in our VPA model, we decided to explore changes in kinematic parameters in two behavioral tests; one designed to evaluate locomotor activity (OFT), and another one usually chosen to evaluate social interaction (3C-ST).2), which was higher  than that of the control group (81.3 \u00b1 5.8 cm/s2)    . Our ana U-test) . The tot U-test) .p < 0.0001, F = 14.04], without an effect of the VPA treatment , or minute \u00d7 VPA interaction , thus evidencing a reduction of the same magnitude for both control and VPA-treated groups . Similarly, analysis in the VPA-group showed a \u201ctraveled distance\u201d in the first minute of 517.9 \u00b1 36.8 cm, which significantly decreased in the last minute, reaching 200.3 \u00b1 29.8 cm . Regarding the behavior of \u201ceffective velocity\u201d along the five minutes of the OFT, we did not observe significant effects by two-way ANOVA analysis for time , VPA treatment  nor interaction time \u00d7 VPA . Control and VPA-groups showed a nearly invariable \u201ceffective velocity\u201d along the trial period   = 3.643], VPA treatment  and time \u00d7 VPA interaction . \u201cMean acceleration\u201d significantly decreased  from the first minute (165.8 \u00b1 14.8 cm/s2) to the last minute (106.9 \u00b1 13.8 cm/s2), reaching values that were not statistically different from those of the control group in the last 2 min  to the end (minute 5). In fact, two-way ANOVA showed a significant main effect of time , no significant effect of VPA treatment  and significant time \u00d7 VPA interaction . Even if no statistically significant difference was found between the control and VPA-group at any minute, the first minute in the control was statistically different from minute five in the same control condition .As shown in p = 0.0002, F = 6.892], a significant effect of VPA treatment  and significant time \u00d7 VPA interaction . There was no statistically significant difference between the control and VPA-group in any minute, but the first minute in the control group was statistically different from minute five in the same control condition .On the other hand, minute-by-minute \u201cdistance/stop\u201d showed a profile inverse to that of stops, which was expected considering no changes in traveled distance . \u201cDistanThese data evidenced that prenatal VPA treatment specifically affects the acceleration of movements without influencing the \u201ctraveled distance\u201d and \u201ceffective velocity\u201d parameters. In addition, habituation to the OFT arena occurred normally at the level of \u201ctraveled distance\u201d and only the VPA-group showed an habituation-like behavior at the level of \u201cmean acceleration,\u201d suggesting that not all kinematic parameters show a similar variation as a function of time. Interestingly, the parameters \u201cstops\u201d and \u201cdistance/stop\u201d showed a constant behavior in the VPA-group, while the control group was able to modulate them along the time of the test, suggesting that VPA animals decrease in-time acceleration by decreasing the traveled distance but not increasing the stops.p < 0.01, Mann-Whitney U-test), without a significant effect on \u201creturns.\u201d Circling activity increased nearly three times in the total OFT arena (regardless of direction) in the VPA-group  and was more notorious in the OFT corners    lower time (2.41 \u00b1 1.9%) compared to control group (7.99 \u00b1 3%)  . In addi U-test) . Regardi99 \u00b1 3%) .p = 0.43, Mann-Whitney U-Test)  . A remarp < 0.05, Mann-Whitney U-Test) demonstrating a higher level of anxiety in VPA-treated rats.Since anxiety is a fundamental sign in ASD individuals and in animal models of autism, we conducted the EPM test in order to corroborate this characteristic. 2) significantly increased in the VPA group (126 \u00b1 18.5 cm/s2)   .p < 0.01, Mann-Whitney U-test)   . Inverse U-test) .p < 0.0001, F = 19.25], without an effect of VPA treatment  or time \u00d7 VPA interaction . We observed a statistically significant gradual decline for \u201ctraveled distance\u201d from the first to the last minute in control and VPA groups  = 22.02], no effect of VPA treatment , and significant minute \u00d7 treatment interaction . There were no statistical differences between the control and VPA groups in each minute, but a statistically significant decline in the control group  and the VPA-group   . This be minute) .p < 0.0001, F = 11.97], VPA treatment  and time \u00d7 VPA interaction . \u201cMean acceleration\u201d was relatively stable during the 5 min of the 3C-ST habituation stage in the control group. On the other hand, the VPA-group showed a statistically significant decline  from the first minute (147.9 \u00b1 18.8 cm/s2) to the last minute (98.1 \u00b1 16.8 cm/s2), reaching values that were not statistically different from that of the last minute in the control group  = 2.009], a significant effect of VPA treatment  and a significant time \u00d7 VPA interaction . Minute five of the VPA-group was significantly lower than the first minute in the same group .Regarding the behavior of \u201cstops\u201d during the 3C-ST habituation stage, we observed that the stops increased in the VPA-group compared to the control group in the first minute and a gradual decline to converge to control values was produced in minute five . Two-wayp = 0.1117, F = 2.009], a significant effect of VPA treatment  and a significant time \u00d7 VPA interaction . The differences between the first minute and the last minute in control and VPA groups was statistically significant .The \u201cdistance/stop\u201d parameter showed an inverse pattern respect to the \u201cstops.\u201d We observed decreased \u201cdistance/stop\u201d in the VPA-group compared to the control group in the first minute and a gradual decline -also observed in controls-, to converge to control values in minute five . Two-wayIn general, the results obtained in the habituation stage of 3C-ST validate our analysis performed with the OFT, and show that prenatally VPA-treated rats do not display considerable differences in their kinematic characteristics (such as distance and velocity). However, a general increase in mean acceleration was present in all conditions, along with increased halts during trajectories and reduced distance between stops, more or less evident depending on the behavioral test used. In fact, increased \u201cstops\u201d and reduced \u201cdistance/stop\u201d were more evident in the beginning of the OFT and habituation stage of the 3C-ST.p < 0.001; Mann-Whitney U-test)  . Hence, p = 0.064; Mann-Whitney U-test, p < 0.05; Mann-Whitney U-test, U-test); from 116.3 \u00b1 3.8 cm/s2 in the control group to 197.7 \u00b1 20.5 cm/s2 in the VPA-group   . These rp = 0.4944, F = 0.4923], but a significant effect of treatment , without area \u00d7 treatment interaction . The VPA-group showed a reduced \u201ctraveled distance\u201d in the social area compared to the control group , while no significant difference was found in the non-social area   or VPA groups . These results suggest that VPA-treated rats reduce their locomotor activity in the new condition; however, this parameter did not differentiate between social and non-social areas, in both control and VPA groups.Furthermore, the analysis of kinematic parameters to separate social from non-social areas showed a differential effect of VPA treatment. First, two-way ANOVA analysis of \u201ctraveled distance\u201d showed no effect for area  and VPA treatment , without area \u00d7 treatment interaction . A statistically significant reduction was observed in the VPA-group in social (p = 0.0153) and in non-social (p = 0.0004) areas, in relation to the control group (Sidak post hoc test) , while the VPA group showed an \u201ceffective velocity\u201d of 8.05 \u00b1 1.8 cm/s in the social area and 13.42 \u00b1 2.34 cm/s in the non-social area . Therefore, \u201ceffective velocity,\u201d in contrast to \u201ctraveled distance\u201d is a parameter that discriminates between social and non-social contexts in both control and VPA-treated rats.In relation to \u201ceffective velocity,\u201d two-way ANOVA analysis showed a significant main effect of area  and VPA treatment , without area \u00d7 VPA interaction . A statistically significant increase of \u201cmean acceleration\u201d was observed in the VPA-group in both social (p < 0.01) and non-social (p < 0.05) areas, in relation to the respective areas in the control group (Sidak post hoc test) , but not in the VPA-group (p = 0.8200) . Two-way ANOVA analysis indicated a main effect of area , no effect of VPA-treatment  and a significant area \u00d7 VPA interaction  (p = 0.0007), but not in the VPA group . However, no significant difference was observed between control and VPA groups in social (p = 0.1368) or in non-social (p = 0.0944) areas (Sidak post hoc test). This result suggests that the control group is able to discriminate social from non-social areas in this parameter, while the VPA-group loses that ability.\u201cStops\u201d in social and non-social areas also showed a differential behavior between control and VPA groups. Two-way ANOVA analysis of stops indicated a main effect of area [= 8.326] . A statip < 0.0001, F = 32.29] and VPA treatment  and a significant area \u00d7 VPA interaction  (p < 0.0001), but not for the VPA-group . No significant difference of distance/stop was observed in the social (p = 0.0940) area, but a significant difference was found in the non-social area when comparing the control with the VPA-group , suggesting that this parameter discriminates social from non-social areas in controls, but not in VPA treated rats.On the other hand, two-way ANOVA analysis of \u201cdistance/stop\u201d showed a main effect of area [= 10.55] . The difp = 0.16; Mann-Whitney U-test, p = 0.64; Mann-Whitney U-test, p < 0.05; Mann-Whitney U-test, p = 0.030, Mann-Whitney U-test), suggesting that controls discriminate by context, an ability lost in the VPA-group. Regarding \u201cdistance/stop,\u201d no statistical difference was found between control and VPA groups   .The results obtained in the social stage of the 3C-ST corroborated increased acceleration in the VPA group and suggests that control animals reduce their movement acceleration and increase their halts when they move in the social chamber, while VPA-treatment abolishes the ability to modulate acceleration and halts when the rats face social or non-social contexts.We have studied basic kinematic parameters in the juvenile rat VPA-model of autism using two behavioral tests (OFT and 3C-ST), which represent two different contexts. The most remarkable observation of our work was evidenced in the social stage of the 3C-ST, where, according to the \u201cmean acceleration\u201d and \u201cstops\u201d parameters, the social/non-social context discrimination was lost in the VPA-group, whereas distance does not discriminate a social context, while velocity does in both groups. In addition, we showed that VPA treatment produced consistent increases in \u201cmean acceleration\u201d and reduced \u201cdistance/stop,\u201d with almost null effect on \u201ctraveled distance\u201d and \u201ceffective velocity\u201d in the OFT, an effect corroborated during the habituation stage of the 3C-ST. However, in the last case, we observed additionally increased \u201cstops.\u201d These results suggest that in a socially neutral context, the motor alterations in ASD may specifically affect certain kinematic parameters; i.e., acceleration and related variables as \u201cstops\u201d and \u201cdistance/stop,\u201d without evidently affecting distance and velocity. Moreover, in a condition where there is an alternation of social vs. non-social contexts, velocity is also affected and more importantly, we evidenced an effect in the ability to dynamically change \u201cmean acceleration\u201d and \u201cstops\u201d parameters between social and non-social contexts. To our knowledge, this is the first report in an animal model of autism that shows this type of discriminative behavior for acceleration and stops variables in control rats, and its loss in VPA-treated rats.In the OFT, control and VPA-treated rats exhibited similar kinematic characteristics, such as total displacement and velocity. In addition, according to the \u201ctraveled distance\u201d parameter, both groups seemed to equally habituate to the arena. In order to obtain a real parameter of movement velocity in general, but not associated with a particular type of movement , we calculated \u201ceffective velocity\u201d as the mean velocity, considering only the time in which the animal showed a displacement of its center of mass, respect to the precedent video frame. Furthermore, despite the similarity displayed by control and VPA groups in these two basic kinematic parameters, we found an important difference in movement acceleration, measured as \u201cmean acceleration.\u201d Nonetheless, it is important to mention that we cannot infer whether these differences are associated with a particular movement characteristic; in other words, related to increased acceleration, which might represent less smooth movements or faster movement initiation. Even though a more precise kinematic study is necessary to clear this point out, we can conclude that the observed differences represent an intrinsic characteristic of the animal movements affected by the VPA treatment. A previous report in which kinematic parameters were studied in different strains of control mice has indicated that the acceleration-influenced parameter \u201cvelocity/stops,\u201d may differentiate mice strains, and this parameter was associated with \u201cdarting behavior,\u201d which can reflect vulnerability to stress, anxiety or jitteriness . In factOf note, VPA-treated animals normally habituate the \u201ctraveled distance\u201d parameter in the OFT and the 3C-ST, while \u201cmean acceleration\u201d reflects a habituation-like behavior only in VPA animals. In addition, velocity showed a habituation-like behavior in both control and VPA rats in the little arena of habituation stage of 3C-ST. We suggest that acceleration is a more sensitive parameter for detecting anxiety in VPA animals. In fact, Since our kinematic parameters did not characterize any particular type of movement, we also evaluated walking, rearing, turns and circling behavior. When comparing control and VPA rats, we did not find any differences in walking velocity, but we had difficulties in finding video sequences in which VPA rats walked in a straight line, reflecting their propensity to perform circling behavior, especially in the corners of the arena test, where they also spent more time in comparison to controls. Increased circling behavior and supported rearing may suggest anxious behavior but, considering that standing upright is a normal behavior , we cannpostmortem encephalic tissue from ASD individuals , located in the upper brainstem, is fundamental in defining walking velocity , althougividuals . Moreoveividuals .Based on the exploratory component of our behavioral tests and taking into account the particular exploratory behavior displayed by VPA-treated rats in the OFT arena, basal ganglia circuits may be interesting regions in which the neurobiological underpinnings of the kinematic alterations observed in ASD could be further investigated. In fact, multiple alterations have been described in basal ganglia circuits in ASD individuals and animal models of autism . This coKinematic studies in ASD are scarce but, an interesting work showed a characteristic kinematic signature regarding micro-movements during a reaching task in ASD . The autAn interesting recent report of On the other hand, studies in the VPA-model do not normally address kinematic parameters, such as velocity and acceleration. Only a recent report evaluated velocity in control and postnatally VPA-treated rats in a context of empathy-like pro-social behavior, evaluating the willingness of rats to open a restrainer where a conspecific was trapped . InteresOn the other hand, atypical kinematics has been evidenced in ASD individuals by studying a simple sinusoidal arm movement and, importantly, the degree of such atypicality correlates with the ADOS score and the difficulty to interpret biological movement . Neverthbona-fide\u201d model of autism- on the social/non-social context discrimination by the kinematic variables, acceleration and stops, suggesting that these specific parameters may reflect behavioral inflexibility, a fundamental alteration of ASD, pervasive even at the most basic levels of motor control.Finally, we provide, for the first time, evidence of the effect of prenatal exposition to VPA -a \u201cealiaga@ucm.cl.The datasets presented in this article are not readily available because data sharing is not applicable to this article as no new data were created in this study. Requests to access the datasets should be directed to EA, The animal study was reviewed and approved by the Ethic Committee of the Chilean Science and Technology National Commission (CONICYT).EA and JF designed the study, analyzed and interpreted the data, and wrote the article. NQ, SS-O, and FP performed the experiments, analyzed the data, and participated in the final correction of the article. FA, KM-G, and CM-R participated in the analysis and interpretation of data and editing of the article. All authors gave approval of the final version to be published and agreed to be accountable for all aspects of the work.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "The Editors-in-Chief have retracted this article\u00a0(Yang et al. All authors agree to this retraction."}
+{"text": "Scientific Reports 10.1038/s41598-020-74174-x, published online 14 October 2020Correction to: The Supplementary Information published with this Article contains errors.The degree of Takashi Oka, \u201cPhD., DMSc\u201d, is incorrectly given as \u201cPhD\u201d.In addition, the excitation wavelength measurements within the \u201cSupplemental materials and methods\u201d section is omitted.Lastly, the explanation of the Figures given in the legend of Figures The correct Supplementary Information file is linked to this correction notice.Supplementary Information"}
+{"text": "THIS ARTICLE USES WORDS OR LANGUAGE THAT IS CONSIDERED PROFANE, VULGAR, OR OFFENSIVE BY SOME READERS. The presence of a significant amount of harassment in user-generated content and its negative impact calls for robust automatic detection approaches. This requires the identification of different types of harassment. Earlier work has classified harassing language in terms of hurtfulness, abusiveness, sentiment, and profanity. However, to identify and understand harassment more accurately, it is essential to determine the contextual type that captures the interrelated conditions in which harassing language occurs. In this paper we introduce the notion of contextual type in harassment by distinguishing between five contextual types: (i) sexual, (ii) racial, (iii) appearance-related, (iv) intellectual and (v) political. We utilize an annotated corpus from Twitter distinguishing these types of harassment. We study the context of each kind to shed light on the linguistic meaning, interpretation, and distribution, with results from two lines of investigation: an extensive linguistic analysis, and the statistical distribution of uni-grams. We then build type- aware classifiers to automate the identification of type-specific harassment. Our experiments demonstrate that these classifiers provide competitive accuracy for identifying and analyzing harassment on social media. We present extensive discussion and significant observations about the effectiveness of type-aware classifiers using a detailed comparison setup, providing insight into the role of type-dependent features. Disclaimer: This article uses words or language that is considered profane, vulgar, or offensive by some readers. Owing to the topic studied in this article, quoting offensive language is academically justified but neither we nor PLOS in any way endorse the use of these words or the content of the quotes. Likewise, the quotes do not represent our opinions or the opinions of PLOS, and we condemn online harassment and offensive language.Although social media has enabled people to connect and interact with each other, it has also made people vulnerable to insults, humiliation, hate, bullying\u2013facing threats from individuals who are either known  or unknown . Please note that in this work, cyberbullying and harassment are used interchangeably. A Pew research study reports  that oneHate speech is \u201cspeech that denigrates a person because of their innate and protected characteristics\u201d . Th. Thone gficient)  metric wficient) . Convent\u201cI\u201d is prevalent in the sexually non-harassing corpus with e = \u22121.2, which is highly significant, e.g., i\u2019m le***an kiss. Furthermore, the feature \u201cMONEY\u201d is prevalent in the harassing corpus with e = 2.9. E.g., send me free money b**ch h*es i won\u2019t give you anything to dance to you h*e a*s industry b*t*h d*cks**king p*r*star people.The pronoun \u201cYOU\u201d is prevalent in the harassing corpus with e = 0.9, e.g., Vishalp sikanda, Quideazam hahahaha u p**i can block u cant debat u p**i I***an. The \u201cCOMPARATIVE\u201d feature is prevalent in racial non-harassing corpus with e = \u22120.84, e.g., save block p**i like po yung comment ni richard fronda (the word \u2018like\u2019 is an indicator of comparison in LIWC). Thus, these features can be used to discriminate between harassing and non-harassing tweets.The pronoun \u201cSHE\u201d and \u201cHE\u201d with e = \u22120.9 and the pronoun \u201cWE\u201d with e = \u22120.8 are prevalent in the non-harassing corpus, e.g., realdonaldtrump putin a**hat just like word can express displeasure leader god help us (us indicates the pronoun \u2018WE\u2019). The \u201cRISK\u201d feature is significant in non-harassing with e = \u22121.9, e.g., f*** wrong democratic senators. The word \u2018wrong\u2019 represents a risk feature in LIWC dictionary. Other sample risk related words are \u2018danger\u2019, \u2018doubt\u2019, etc. Furthermore, the \u201cANXIETY\u201d feature with e = \u22120.92 is significant in the non-harassing corpus. E.g., well i\u2019m true dumb f*** democrat wouldn\u2019t doubt.The pronoun \u201cNEGATION\u201d with e = 2.3 is prevalent in the harassing corpus (probably because of the negative language used for referring to the body and appearance-related subjects). E.g., Taylor swift cant shake c**el toe. The other significant feature in the harassing corpus is the \u201cPAST TENSE\u201d. E.g., Ugli a** didn\u2019t go run yesterday get work f*t**s. Furthermore, the \u201cCOMPARATIVE\u201d feature is prevalent in appearance-related harassing corpus with e = 0.63. E.g., hey lardass notice your look pizza perhaps like f*** salad a**hole. The word \u2018like\u2019 indicates a comparative feature.\u201cFEMALE REFERENCE\u201d feature with e = 2.3 is highly significant in intellectual harassing corpus  E.g., She is dumb f***.The \u201cDISCREPANCY\u201d with e = \u22121.5 is prevalent in the non-harassing corpus e.g., boss brought drunken sugar cook explain there alcohol just sh**face.Q1: whether or not offensive words are observed as frequent words, Q2: whether or not the frequent words in harassing corpora differ from those in non-harassing corpora, and Q3: whether or not frequent words are type-sensitive, in other words, whether the frequent words vary with type of context. We investigate the relationship between the offensive words employed in collecting our corpora and the specific lexical items in the crawled corpora. We determine Regarding Q1, as expected, we observed that offensive words are commonplace in both harassing and non-harassing corpora across types cf. Figs  and 4. Iper se is not necessarily harassing.To reply quantitatively to Q3, we ran an annotation task on the top-15 most frequent words for each type of harassing corpus as well as the corresponding non-harassing corpus. The description of this task is as follows: we asked the human annotators  to determine whether or not a given frequent word is related to the associated type either explicitly or implicitly. E.g., the words \u201ceat\u201d or \u201cfood\u201d are implicitly related to appearance while they seem far from the type racial. The results of this exercise appear in One caveat is that the most frequent words appearing in the sub-corpus associated with each type are predominantly stop-words or curse words, as our initial seed terms are biased to an offensive lexicon. Ignoring these words, whose presence cuts across different types of harassment, revealed that the following prominent word groups are associated with various harassment types, shedding light on the possible features that may elicit harassment: (i) In the appearance-related harassment corpus, target words such as \u201ceat\u201d, \u201cugly\u201d, \u201cfat\u201d, \u201cgym\u201d, and \u201cweight\u201d, are present. (ii) In the intellectual harassment corpus, target words such as \u201cdumb\u201d, \u201cstupid\u201d, \u201cwork\u201d, and \u201chead\u201d, are present. (iii) In the political harassment corpus, the target words such as \u201crealdonaldtrump\u201d, \u201clibtard\u201d, \u201cdumb\u201d, \u201ctouch bag\u201d, \u201cstupid\u201d, and \u201ccnn\u201d, are present. (iv) In the racial harassment corpus, target words such as \u201cm*ki\u201d, \u201cn**ger\u201d, \u201cb**ner\u201d, \u201cch**k\u201d, \u201cmuslim\u201d, \u201ci**ian\u201d, \u201cmoron\u201d, and \u201cjew\u201d, are present. (iv) In the sexual harassment corpus, target words such as \u201chump\u201d, \u201chussy\u201d, \u201cl**k\u201d, and \u201cgrab\u201d, are present.We aim to develop effective supervised learning methods to detect harassing language automatically and distinguish it from non-harassing language for each contextual type. The state-of-the-art contains various approaches for detecting harassing content from non-harassing content but not for discriminating the type of harassment. We approach this gap in two ways. The first is to build individual binary classifiers that identify a particular type of harassment, e.g., a binary classifier that identifies only racial content or a binary classifier that classifies just offensive political content. The second approach uses the state-of-the-art methods to detect harassing language; after such recognition, we can employ a type-aware classifier to predict the associated type for that harassment incident. We implemented both approaches. Initially, we trained the individual classifiers for each type. In another approach, we built up a binary classifier that differentiates harassing content from non-harassing content regardless of their type. Note that any classifier from the state-of-the-art can substitute for this part. Then, we built up a multi-class classifier that predicts the type of harassment incident. The results of our experiments for both approaches reveal high accuracy. Furthermore, to verify the effectiveness of our classifier, we apply transfer learning by running our classifier on the Golbeck corpus and assess its performance for how successfully it predicts the type of harassment. In the following, we present the details of our experiments.We utilized four approaches for transforming tweets to numerical representations : (i) the conventional vectorization approach TFIDF, (ii) word2vec, (iii) fastText and (iv) a LIWC vector. We feed our classifiers with each of these individual vectors or a combination of them.We use this approach  to transwk (i.e. context word) appearing in the neighborhood of the context word wi (i.e. target word), Distributional semantics   play a v Corpora  leveragi Corpora  as the u Corpora , 57. OurThe vector obtained by running the LIWC tool is denoted by L.As the number of harassing tweets is not equal to the number of non-harassing ones in our corpus\u2014in fact, it varies for each type\u2014we prepared balanced datasets for training the classifier. We prepared five type-aware training data sets using an under-sampling approach taking all of the harassing tweets with an equal number of non-harassing (randomly sampled). Also, we prepared a combined training data set considering all of the harassing tweets regardless of their type and an equal number of non-harassing tweets. Support Vector Machine (SVM) [K-Nearest Neighbors (KNN) [Gradient Boosting Machine (GBM) [Naive Bayes (NB) [In our experimental study, we trained four types of classifiers, using (i) ne (SVM) , (ii) K-rs (KNN) , (iii) Gne (GBM) , and (ivyes (NB) . We relyTo gain insight over the effectiveness of various features, we feed the GBM classifier with various feature settings. The fine-grained results of our experiment are listed in We also trained a binary classifier on our combined corpus where it can differentiate the harassing language from non-harassing regardless of the contextual type. In situations that the type of harassment does not play a role, or type detection must occur after the harassment detection, using such a generic classifier is necessary. Apart from building binary classifiers for predicting types, we trained a multi-class classifier to predict the type of harassment incidents. We trained several multi-class classifiers, among them the GBM classifier outperformed others. Herein we report the result for GBM classifier only. We used W(S)+F(S) vectorization approach as the input feature. Then, we trained this classifier on a corpus containing all of the sub-corpora from the previous step. This corpus has samples with six various labels where five labels indicate a particular type of harassment and the last label indicates \u201cnon-harassing\u201d implying there is no harassing language. Since this work was the first to introduce contextual type for harassment, comparison to the state-of-the-art that relies only on two or three variants of harassment, is unfair. However, to verify the effectiveness of our type-oriented multi-class classifier, we tested it on the harassing tweets from the Golbeck corpus  that is a publicly available state-of-the-art harassment-related corpus . This co@usr you deserved to be raped by a thousand Muslims in your c**t a**hole, our classifier classified that as sexual harassment and not racial because of the word \u2018rape\u2019. Similarly, the tweet @usr @usr lol it\u2019s not against women. It\u2019s against f***ing feminist c***s like you. #feminazi #womenagainstfeminism was classified as sexual. Such cases are ambiguous because even manual annotation is highly subjective. In other words, categorizing harassment is highly subjective and the boundary between types is not rigid. In majority of the overlapping cases , the tweets were classified as sexual rather than racial. We also analyzed errors in political tweets and concluded that harassment signal can be: (i) implicit, e.g., John Boehner blames Democrats for #shutdown. He better stop drinking cuz a few more drinks and he starts blaming the J*ws f, (ii) ambiguous ??? You\u2019re a wh*** to the telecom industry, i hope your constituents vote you out., (iii) unreliable, e.g., It\u2019s going to be a republican government in the US next term. Democrats can kiss their presidency bid goodbye. Let the J*ws rule!, (iv) poorly captured through annotation, e.g., the tweet @TrueNugget @FeministPeriod @OregonState Man college is becoming more and more a mistake. in the Golbeck corpus. Our classifier misses them as they are weak cases of harassment.To make sense of classifier errors, we examined a couple of tweets classified as sexual. E.g., for Our project involves analysis of Twitter data that is publicly available and that has been anonymized. It does not involve any direct interaction with any individuals or their personally identifiable data. So our work does not meet the Federal definition for human subjects research, specifically, \u201ca systematic investigation designed to contribute to generalizable knowledge\u201d and \u201cresearch involving interaction with the individual or obtains personally identifiable private information about an individual\u201d. Thus, this study was reviewed by the Wright State University IRB and received an exemption determination.In this paper, we introduced five contextual types for harassment, namely, (i) sexual, (ii) racial, (iii) intellectual, (iv) appearance-related and (v) political. We presented experiments with a type-aware tweets corpus to analyze, learn, and understand harassing language for each type. Our contribution lies in providing a systematic and comparative approach to assessing harassing language from linguistic and statistical perspectives. Furthermore, we built type-specific classifiers, and the results of our experiments show the importance of considering the contextual type for identifying and analyzing harassment on social media.In general, a single tweet identified as \u201charassing\u201d may not provoke the same intense negative feeling that we associate with that word in the real-world scenario. However, in practice, \u201cconversational\u201d exchanges containing a sequence of such tweets can rise to the level of harassment causing mental and psychological anguish, and fear of physical harm. Nevertheless, our current Twitter dataset is limited to annotating single tweets in isolation for harassment. Furthermore, the reliable assessment of the type of harassment is a difficult problem because it requires significant knowledge of current events and common-sense. We plan to extend this work by learning the language of harassers as well as victims, and further study the contribution of non-verbal cues  for identifying online harassment activities, particularly on social media."}
+{"text": "Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps in understanding and handling traffic problems, optimizing traffic regulations and adapting the traffic management in real time for unexpected disaster events. A mathematically rigorous stochastic model that can be used for traffic analysis was proposed earlier by other researchers which is based on an interplay between graph and Markov chain theories. This model provides a transition probability matrix which describes the traffic\u2019s dynamic with its unique stationary distribution of the vehicles on the road network. In this paper, a new parametrization is presented for this model by introducing the concept of two-dimensional stationary distribution which can handle the traffic\u2019s dynamic together with the vehicles\u2019 distribution. In addition, the weighted least squares estimation method is applied for estimating this new parameter matrix using trajectory data. In a case study, we apply our method on the Taxi Trajectory Prediction dataset and road network data from the OpenStreetMap project, both available publicly. To test our approach, we have implemented the proposed model in software. We have run simulations in medium and large scales and both the model and estimation procedure, based on artificial and real datasets, have been proved satisfactory and superior to the frequency based maximum likelihood method. In a real application, we have unfolded a stationary distribution on the map graph of Porto, based on the dataset. The approach described here combines techniques which, when used together to analyze traffic on large road networks, has not previously been reported. In the past decade, research and development of smart city applications have become an active topic , 2. ThesRobocar City Emulator (RCE). We extract geographical information from OpenStreetMap (OSM) and transform this data into a routing map graph. The simulation takes place on a rectangular part of the OSM. The traffic simulation model of the RCE is based on the Nagel-Schreckenberg cellular automata model 63].V is the vector \u03c0 \u2254 (\u03c0v)v\u2208V where \u03c0v \u2265 0 for all v \u2208 V and \u2211v\u2208V\u03c0v = 1. That is a p.d. \u03c0 is a normalized \u03c0v as the proportion of the number of vehicles which drive through the crossing v with respect to the whole number of vehicles in the city at a fixed time period. A Markov kernel or transition probability matrix on V is defined as a real kernel P \u2254 (puv)u,v\u2208V such that puv \u2265 0 for all u, v \u2208 V and \u2211v\u2208Vpuv = 1 for all u \u2208 V, i.e., pu \u2254 (puv)v\u2208V is a p.d. on V for all u \u2208 V. The quantity puv \u2208  is called the transition probability from vertex u to vertex v. The kernel P is said to be G-subordinated if puv > 0 for a pair u, v \u2208 V implies  \u2208 E or u = v, i.e., P as a matrix on V is G-subordinated in the weak sense. It is well known, see [P on V, an associated digraph GP =  can be introduced in the following way: for a pair u, v \u2208 V   \u2208 EP if and only if puv > 0. Thus, P is G-subordinated if and only if EP \u2286 E \u222a S, i.e., GP is the subgraph of the digraph G extended with its loops S. In other words, a G-subordinated Markov kernel P is a stochastic matrix on V with support E \u222a S. Then, the sum condition for a G-subordinated Markov kernel P can be rewritten as:p00 = 0).A probability distribution (p.d.) on own, see , that fo\u03c0 on V is a stationary distribution (s.d.) of the kernel P if \u2211u\u2208V\u03c0upuv = \u03c0v for all v \u2208 V. For a G-subordinated Markov kernel P this formula, the so-called global balance equation, can be expressed as:A p.d. The stationary distribution can be derived by solving the linear P on V and the strongly connected property of the physical road network G if the Markov and graph structures are compatible with each other. The Markov kernel P on V is called G-compatible if, for any u, v \u2208 V such that u \u2260 v, puv > 0 if and only if  \u2208 E. Note that the G-compatibility implies the weak G-subordination for a Markov kernel P, however the converse is not true.We show that there is a direct connection between the uniqueness of s.d. of a Markov kernel P is G-compatible then the strong connectivity of G implies that the associated graph GP to the Markov kernel P is also strongly connected. In this case, the Markov kernel (the transition matrix) P is called irreducible. Thus, by Theorem 1 in [Clearly, if rem 1 in , see alsrem 1 in  the follTheorem 1. If a road network G is strongly connected then there is a unique stationary distribution \u03c0 to any G-compatible Markov kernel P. Moreover, this distribution satisfies \u03c0v > 0 for all v \u2208 V.The main consequence of this theorem is that, in case of any physical road network augmented by the ideal vertex 0, all of the Markov kernels defined on the road network that has positive transition probability on all roads have unique stationary distribution. Thus, it is reasonable to suppose that a real traffic which follows a Markovian dynamic has a local unique stationary distribution in a short time period that can be explored by observing the traffic.V-valued random variable (r.v.) is a X: \u03a9 \u2192 V measurable function, i.e., v \u2208 V. In this case, X is a random function on the set V of vertices. For example, X can be the random position of a vehicle on the road network G, where the position refers to the actual vertex which the vehicle belongs to. Then, v \u2208 V. By v \u2208 V, a r.v. X induces a p.d. \u03c0X on V.Let V-valued r.v.\u2019s is a Markov chain on the state space V if the Markov property holds:v0, \u2026, vt \u2208 V. If X, X\u2032 are V-valued r.v.\u2019s then for the conditional distribution P = (pvv\u2032)v,v\u2032\u2208V, v, v\u2032 \u2208 V, we shall also use the notation X|X\u2032. Clearly, X|X\u2032 is a Markov kernel on V.A sequence The main concepts of this paper are the Markov random walk and the Markov traffic defined in the following way.Definition 2. Let the road network G be strongly connected and let P be a G-compatible Markov kernel on V with unique s.d. \u03c0. Moreover, let V such that Xt|Xt\u22121 \u223c P for all Markov random walk on the road network G with Markov kernel P.k .The set \u03c0 of fv = 1 for a fix v \u2208 V and 0 otherwise, see page 75 in [k mutually independent Markov random walks its s.d. becomes the k-fold convolution \u03c0k* on \u03c0k* fulfillsv\u2208Vfv = k. In this case, f can be considered as traffic configuration where fv counts the vehicles at vertex v. In fact, \u03c0k* corresponds to the multinomial distribution with parameters k and \u03c0, see Chapter 35 in [k and \u03c0v for all v \u2208 V, respectively. Note that the process v in the Markov traffic.The s.d. ge 75 in . Since ter 35 in . MoreoveP is the uniform Markov kernel on G then we obtain the standard random walk of the graph theory, see the survey [A similar model to Markov random walk is proposed in  where bie survey .k = 1 in the sense that it describes the movement of a random vehicle which follows the stochastic rules defined by the Markov kernel. On the other hand, the Markov traffic provides a mathematical model for describing the traffic of k vehicles on a road network. Note that the independence assumption seems reasonable and not too strong because the vehicle controls are working separately form each other. For a pair u, v \u2208 V the notation u \u21d2 v will mean that  \u2208 E \u222a S, i.e., either u \u2192 v or u = v. If X1, X2 are random functions on V then X1 \u21d2 X2 means that the two-dimensional distribution of  is concentrated on E \u222a S. Clearly, for any Markov random walk Xt \u21d2 Xt+1 \u21d2 \u2026 \u21d2 Xt+n for all t and u to vertex v with probability puv. The second-order Markov random walk (traffic) on the line road network, where the vehicles move from edge to edge, can also be defined similarly, see [A Markov random walk is an individual Markov traffic with rly, see .Q = (quv) on V \u00d7 V as quv \u2254 \u03c0upuv, u, v \u2208 V. Then, Q is a two-dimensional s.d. on G in the following sense:Using the concept of two-dimensional s.d. a Markov traffic can be reparametrized in the following way. Introduce the two-dimensional distribution Definition 3. A matrix Q = (quv)u,v\u2208V is called two-dimensional stationary distribution on G if (i) quv \u2265 0 for all u, v \u2208 V and quv = 0 for all u, v \u2208 V such that  \u2209 E \u222a S ; (ii) \u2211u,v\u2208Vquv = 1 ; and (iii) \u2211v\u2208Vquv = \u2211v\u2208Vqvu for all u \u2208 V .Q on G is called (strictly) positive if quv > 0 for all u, v \u2208 V such that (u \u21d2 v) u \u2192 v.A two-dimensional s.d. G coincide with each other. Clearly, for a Markov traffic, Q defined above is a positive two-dimensional distribution on G. Q can also be considered as a p.d. on the state space E \u222a S, i.e., if we extend the set V\u2032 of vertices of L(G) as V\u2032 = E \u222a S, on the line digraph. Thus, Q can be interpreted as the distribution of the vehicles on the edges of the road network, i.e., on the line digraph, see formula (11) in [Q can also be visualized on the edges, see, Xt, Xt+1), Q.Property (iii) states that the two (row-wise and column-wise) marginal distributions of a two-dimensional s.d. on  11) in . The dis1 in . ThG. One can easily see that Denote by P = (puv) defines a G-compatible Markov kernel with s.d. \u03c0 = (\u03c0u) on G. Thus, a Markov traffic defined by the quadruple  can be introduced by an equivalent way through the triplet . However, it will turn out later that, from a statistical point of view, the parameter matrix Q can be estimated in a computationally more efficient way than the pair of transition matrix P and its s.d. \u03c0.Conversely, for a positive The simulation method proposed in this paper is based on the ergodicity of Markov traffic which follows from the ergodic theory of finite Markov chains.\u03c00 be an initial distribution on V and define the n-th absolute p.d. \u03c0n by the recursion P and Q on V is defined as (PQ)uw \u2254 \u2211v\u2208Vpuvqvw, u, w \u2208 V. If G is strongly connected and we start from the unique s.d. \u03c00 = \u03c0 of P, see Theorem 1, then \u03c0n \u2192 \u03c0 as n \u2192 \u221e. However, in general, the sequence \u03c00 even if the s.d. is unique. However, if we consider the average of the n-th absolute p.d.\u2019s in time, we have the convergence to the unique s.d. The Markov kernel which satisfies this property is called ergodic.Let G is strongly connected then any G-compatible Markov kernel P is ergodic and the average Markov kernel An converges, i.e.,n \u2192 \u221e, where \u03c0 is the unique s.d. of P. Moreover, the limiting probabilities of the time averages of the absolute p.d.\u2019s satisfyn \u2192 \u221e for all initial p.d. \u03c00.The following result is based on Theorem 4.1 in Chapter 3 of . If a rof(\u03c0) \u2254 \u2211v\u2208Vfv\u03c0v of p.d. \u03c0, where n \u2192 \u221e, see Theorem 4.1 of [In applications, along absolute p.d.\u2019s, we may also be interested in some functionals of these distributions, e.g., the number of vehicles in a region of the road network. Define the functional F. Then,  can be em 4.1 of .n-th absolute p.d.\u2019s we need the additional assumption of aperodicity for G, see Theorem 2.1 in Chapter 4 of [G is an aperiodic, strongly connected road network and P is a G-compatible Markov kernel on it, then the sequence of Markov kernels Pn, \u03a0. Moreover, the limit of the sequence of n-th absolute p.d. \u03c0n is the unique s.d. \u03c0 to the Markov kernel P which is independent of the initial p.d. \u03c00. For any functional F we also have that F(\u03c0n) converges to F(\u03c0) as n \u2192 \u221e on an aperiodic, strongly connected road network.Instead of time averages, in order to achieve the convergence of ter 4 of . If G isG-compatible Markov kernel is derived in the same way. Let n-th absolute p.d., respectively, for the ith vehicle, i = 1, \u2026, k. Then, the ergodic property of Markov traffic, similarly to .The ergodicity of Markov traffic with any larly to , can be in)(f)\u2192\u03c0vas n \u2192 \u221eG-compatible Markov kernel can be approximated and thus explored by long run behavior of the traffic flow on the road network. A visualization of the convergence of Markov traffic simulation to its s.d. is presented in Fig 10.The convergence results  and 7)  7) guaraContains complete trajectories, i.e., the availability of only the start and end points is not sufficient, intermediate trajectory points must also be available.The trajectory points must be sampled at a high enough frequency, so that the distance between consecutive points should not be too large, .The dataset is sufficiently large. It should cover a long enough period of time, preferably uniformly. The number of trajectories per day should be of the order of thousands.Trajectories should cover a relatively small geographic area, e.g., a city or a district.Vehicles should not follow a fixed route, e.g., public transport bus trajectories are not suitable.Publicly available for research purposes.For our experiments, we needed a dataset of real-life traffic trajectory data. In our terminology, a trajectory is a sequence of data that provides information about the path of a vehicle moving from a start to an end point, associating geographic coordinates with timestamps. We required a dataset that satisfies the following criteria:These requirements were satisfied by the Taxi Trajectory Prediction (TTP) dataset from Kaggle. The dataset covers a period of one year from July 1, 2013 to June 30, 2014. It is split into a training and a test set, the former contains 1,710,670 trajectories, and the latter contains 320. The trajectories were collected in the city of Porto, Portugal, with a sampling rate of 15 seconds. First, we created a subset of the dataset, filtered to coordinates between W8.6518, W8.5771, N41.1129, N41.1756, see http://wiki.openstreetmap.org/wiki/API. OSM uses two formats for exporting map data, namely OSM XML and PBF. Software libraries for parsing and working with OSM data are available for several programming languages, see https://wiki.openstreetmap.org/wiki/Frameworks.OpenStreetMap (OSM) is a community project to build a free map of the world to which anyone can contribute. Data is available under the Open Data Commons Open Database License (ODbL). The representation and storing of map data is based on a simple but powerful model, that uses only three modeling primitives, namely, nodes, ways, and relations: 1. A node represents a geographical entity with GPS coordinates. 2. A way is an ordered list of at least two nodes. 3. A relation is an ordered list of nodes, ways, and/or relations. All of these modeling elements can have associated key-value pairs called tags that describe and refine the meaning of the element to which they belong. Users can export map data at the OSM web site manually, selecting a rectangular region of the map. Alternatively, map data can be extracted via web services, see We started our processing by building a graph from the OSM map of Porto, with the same bounding box as the filtered dataset. Specific nodes of the OSM file become the nodes in the graph. Because we only need those nodes that can be reached via vehicles, we had to filter the OSM file and collect only specific types of way nodes. In the OSM file, a way is a sequence of OSM nodes, so naturally, the nodes of ways become nodes in the graph. For every node we store the node\u2019s OSM ID, and its coordinates. We also insert an edge into the graph between every nodes in way. The weight of an edge is given by the squared distance between the nodes, which we calculate from the OSM file\u2019s data. We used pyosmium library for processing the OSM files and the NetworkX Python library for building the graph.After building the graph we process the list of trajectories. Because the trajectories are given in GPS coordinates, we first have to translate those coordinates into OSM node IDs. For every coordinate in a trajectory, we search for the closest way node\u2019s coordinates in the built graph, so the result nodes have the same domain as the built graph\u2019s nodes. Obviously, the original trajectories made up of GPS coordinates does not have the same scaling as the OSM map. The coordinates in the trajectory are sampled in regular, but larger time intervals than the OSM, so they are not aligned. In order to match a trajectory to a way in our graph, we had to perform an interpolation on the result list of node IDs, so we ran a Dijkstra\u2019s shortest path algorithm on our graph between every node IDs for every trajectory. Because the OSM database contains errors, it can happen that in real life a route exists between two given places, but in the OSM database, there are no existing routes between those nodes that are representing the given places. In this case, we cut the faulty trajectories into pieces. The result of this process is an aperiodic strongly connected road network augmented by the ideal vertex 0, with a set of trajectories on the road network.G, P, \u03c0, k) or the triplet  using observed data. To estimate G we have to explore the road system under study by identifying the set V of vertices and the set E of directed road segments. Fortunately, this exploring has already been done by a few organizations, see, e.g., the Google Maps and the OpenStreetMap. However, we should note that, in case of GPS-based trajectory data, we have to fit the data to the applied map system which is not an evident task at all. In the present paper, we propose a method for estimating the two-dimensional stationary distribution Q immediately instead of the pair  of a transition matrix and its stationary distribution using mobile sensor data which may be gathered by vehicles, passengers etc. In this case, we have trajectories data which consists of the sequences of consecutive vertices, like in the TTP dataset. By   pairs in the i-th trajectory. One can see that since {Xi} is a proper Markov random walk we have u, v)\u2209E \u222a S. Thus, the support of the two-dimensional frequency matrices N \u2254 (nuv)u,v\u2208V, i = 1, \u2026, k, is a subset of E \u222a S, i.e., they are weakly G-subordinated matrices. Clearly, n \u2212 k is the corrected sample size. Introducev \u2208 V, i.e., sv denotes the number of trajectories which start at vertex v and ev denotes the number of trajectories which terminate at vertex v, respectively. Denote the one-dimensional marginal frequencies of N by nv+ \u2254 \u2211u\u2208Vnvu and nv+ \u2254 \u2211u\u2208Vnuv, v \u2208 V. We obtain thatv \u2208 V, where nv denotes the number of vertex v in all trajectories. Finally,s and e on V as s \u2254 (sv)v\u2208V and e \u2254 (ev)v\u2208V, respectively. Then, (1\u22a4(e \u2212 s) = 0, i.e., the vectors e \u2212 s and 1 are orthogonal.Suppose that, for a Markov traffic, we observed a random sample of trajectories {\u2211v\u2208Vev=k.Define tP is given by the maximization of the conditional loglikelihoodpuv, u, v \u2208 V such that u \u21d2 v, under the constraints pu+ = 1 for all u \u2208 V. A solution of this constrained optimization problem is u, v \u2208 V if nu+ > 0 and nu+ = 0 where \u03b4 denotes the Kronecker delta. The maximum likelihood estimator \u03c0 is derived by the solution of the global balance equation \u03c0. Thus, the maximum likelihood estimator Q is given by u, v \u2208 V. In the sequel, a direct method is proposed for estimating the two-dimensional stationary distribution Q.The traditional maximum likelihood (ML) estimator Q based on the two-dimensional consecutive empirical frequency matrix N is V, satisfies the properties (i) and (ii) of Definition 3. However, the problem with this na\u00eeve estimator is that its row and column marginals are not necessarily equal, i.e., in general, it does not satisfy the asumption (iii) of Definition 3. Hence, we have to introduce a new estimator A na\u00eeve estimator for the two-dimensional stationary distribution G. Let A = (auv)u,v\u2208V and B = (buv)u,v\u2208V such that auv = buv = 0 for all u, v \u2208 V where A and B be weakly G-subordinated matrices. The distance between A and B is defined asG is the Frobenius norm of the matrices of dimension |V| \u00d7 |V| which vanish on the entries outside of E \u222a S.The optimality of the proposed estimator is defined by means of the least squares distance between matrices over M = (muv) denote a non-negative parameter matrix on G which satisfies assumptions (i) and (iii) of Definition 3, i.e., M is weakly G-subordinated and \u2211v\u2208Vmuv = \u2211v\u2208Vmvu for all u \u2208 V. Then, one can easily derive a two-dimensional stationary distribution Q from M by its normalization defining as Q \u2254 (1\u22a4M1)\u22121M.To formulate the objective function for estimating the two-dimensional stationary distribution it is convenient to weaken the assumptions of Definition 3 by leaving the normalizing assumption (ii). In the sequel, let k number of trajectories, using the Frobenius norm, the optimality criterion is defined as the weighted sum of squared errors (SSE):M is a non-negative parameter matrix satisfying assumptions (i) and (iii) of Definition 3, w = (wi)i=1,\u2026,k are non-negative unknown weights, with N \u2254 (Ni)i=1,\u2026,k denotes the data, where Ni is the two-dimensional consecutive empirical frequency matrix for the ith trajectory, see (M and w deriving the weighted least squares (WLS) estimators Q is defined as neff gives the equivalent sample size related to the independent case which may be thought of as the information content of the observed data. Note that neff is not necessarily an integer and is different from n and n \u2212 k. Finally, wi gives the importance of the ith trajectory in the sample. One can see that longer trajectory implies higher weight.Based on ory, see . The staL of a digraph G is defined asA denotes the adjacency matrix of G and D \u2254 diag{d+ + d\u2212} is a diagonal matrix. Note that for the road graph G, since there is no loop, we have lvv = dvv = deg+(v) + deg\u2212(v) for all v \u2208 V. The main theorem of this paper is the following.To formulate our result on WLS estimation of Markov traffic we need some basic facts on the spectral theory of directed graphs, see  for detaTheorem 2. There is a unique pair i = 1, \u2026, k, andL\u03bb = s \u2212 e which satisfies the constraint 1\u22a4\u03bb = 0  and \u2218 denotes the entrywise (Hadamard) product of matrices.fined in . These Wneff depends only on the graph structure of the road network, which is independent of the data, the traffic direction vector s \u2212 e, and the corrected sample size. However, it does not depend on the data which are inside the trajectories.Based on the previous theorem, by , the effith trajectory, i = 1, \u2026, k. The parameters of the objective function MSE are the effective sample sizes Q. The heuristic explanation of the need to use weights in formulas  likelihood estimators for Markov chains, see . The comformulas  and 14)MSE\u2254neff\u2212ni, i = 1, \u2026, k} are bounded, where k is large or tends to infinity. In our example, for the TTP dataset, the number of trajectories is above 80K with the mean length 40 and maximum length 2K, see s \u2212 e while The estimation theory of finite Markov chains goes back for a long time, see . In the The fundamental statement of Theorem 2, as one of the main result of this paper, is that the estimator \u03bb in Theorem 2. This can be performed in a numerically effective manner by the eigenvalues-eigenvectors decomposition of the symmetric unnormalized  graph Laplacian matrix, see Proposition 1 and 2 in [The computationally intensive part of WLS estimator is the numerical solution of sparse linear equation system given for the Lagrange vector and 2 in . Remark and 2 in ), a lineQ as a parameter is defined by https://pypi.org/project/PyDTMC/). The codes and datasets of our simulation are available upon request.To evaluate the performance of the proposed WLS estimation method by comparing it to the traditional ML one discussed above, a simple simulation study was conducted at different sample sizes for small and medium road network. In the simulations, in order to mimic the real traffic, we tried to keep the length of trajectories low and the number of trajectories high compared to the size of the road network, similarly to the Porto example. The absolute bias of an investigated estimator https://github.com/rbesenczi/Crowd-sourced-Traffic-Simulator/blob/master/model-sources/Markovkernel/example_graph.py). The simulation parameters were k = 100, 200, 500, and 1000 number of trajectories with n = 3, 5, and 10 length. The absolute bias and its standard error do not depend on the length n and they are decreasing as k is increasing for both estimation methods. The latter is an expected result. Moreover, while for relatively small k the performance of the WLS and ML methods are similar, in the case of relatively large number of trajectories the ML estimator outperforms the WLS one a little bit. This phenomenon could be due to the asymptotic optimality of the ML estimator because the parameter k is enough large (1000) compared to the size of the road graph (5).k = 1000, 3000, and 5000 with n = 3, 5, and 10. In this scenario, the absolute bias and its standard error depend also only on k and are independent of the length n. However, there are significant differences between the performances of the two estimation methods (ML and WLS) related to the parameter k. On the one hand, the absolute bias of ML estimator is decreasing as k is increasing while it is constant for WLS estimator. On the other hand, the WLS estimator is better than the ML one in case of k = 1000 but worse in case of k = 5000. Since the former parameter setting is closer to the real traffic, this simulation corroborates the superiority of WLS method based on two-dimensional s.d. against the traditional maximum likelihood. Finally, in this scenario, the scale of the SE\u2019s indicates that the WLS estimator is more stable than the ML one See In the second simulation scenario, a strongly connected subgraph, which contains 1000 vertices, of Porto\u2019s road network was chosen . The entries of Markov kernel were generated randomly. The simulation parameters were We have also implemented the model in the OOCWC system in order to apply our simulation method for real large-scale problems. First, we have filtered the TTP dataset. Then, we have created the Markov kernel from the filtered dataset, so all nodes of the simulation graph will have the corresponding transition probability vector. We should note, however, that not all nodes can be found in the Markov kernel, because it can happen that the dataset does not completely cover the whole map, i.e., not all nodes are part of a trajectory. In this case, we set uniform distribution for the corresponding node. Finally, we had to modify the basic operation of the simulation algorithm. In the original implementation, the cars are moving on the map quite randomly. Now, a car selects the next node based on the transition probability vector of the current node. For this, we use the pseudo-random number generation engine from the Boost Random library that is based on the method presented in paper .Let\u2019s consider an example. We are at the graph vertex (or intersection) of OSM node ID 1110673569 . The total transitions of this node  in the dataset is 1,649. The transitions to the neighbor nodes are shown in k = 5, 000, 10, 000, 20, 000, 30, 000 and 50, 000 units. The simulation starts when all simulation units are added to the map. The initialization phase of the simulation adds traffic units to the map. Each unit is placed to an OSM node, i.e., on a vertex of the simulation graph. There exist two ways to do this, one is following a prescribed distribution (e.g. uniform), the other is following measured data. In our test case, we initialized simulations with fictional measured data. We put units only to the streets Rua de Antero de Quental, Rua da Constitui\u00e7\u00e3o and Rua da Boavista , i.e., the simulation starts from the traffic configuration which is concentrated on three nodes of the road graph. In addition, we can set the number of the simulation units. We run simulations with The RCE produces a logfile that contains the position of every simulation unit in every simulation step. From this file, we calculate the number of cars by streets in every minute, so we can observe the change of distribution of the cars. In addition, we calculated the s.d. of cars for streets in the city of Porto, see To obtain a quantitative measure that describes the \u201cgoodness\u201d of our simulation algorithm, we applied the Pearson\u2019s chi-squared test. We expect, by the ergodicity of the Markov traffic, that during the simulation, independently from the initial distribution, within a certain time period, the distribution of the cars become close to the previously calculated stationary distribution. Finally, we should note some implementation details and possible drawbacks of this model that may have an impact on the model\u2019s overall performance.\u03c0, namely, negative values may present in the results. We need to handle this problem when we calculate the Pearson\u2019s chi-squared test. We chose to shift every value of \u03c0 until we get a sum of 1 for \u03c0.In small and medium graphs, the proposed algorithm and its implementation performs as it is expected. But in the case of our Porto example, where the graph has 33,961 nodes and 53,126 edges and the TP matrix is very sparse, numerical problems may occur. One problem can occur when we calculate the Some minor issues can occur with the map database and the differences between the Porto dataset and the OSM data. In some cases, we could not calculate a route between two consecutive trajectory points using OSM data. This can happen because of the imperfection of the OSM data or false GPS measurement. We handle this case by splitting the trajectory into pieces.\u03c0 for a subgraph of the whole map. During the simulation the units can traverse the whole map graph, so, it can happen that a traffic unit reaches an edge which is not part of the subgraph where we know the s.d. \u03c0. During the calculation of the Pearson\u2019s chi-squared test, we consider only those cars that are present on the road network, where the s.d. \u03c0 is known.Another minor issue arises in the calculation of the Pearson\u2019s chi-squared test. Since the OSM Porto map and the trajectory dataset do not cover each other perfectly, we only know the s.d. In this paper, we have described our traffic simulation model that is called \u201cMarkov traffic\u201d based on tools from graph theory and Markov modeling. The aim was to provide a simulation method that is able to keep the distribution of the cars on the map in a steady-state on a large scale road network. We have proven that, under general assumptions, the stationary distribution (s.d.) is unique for any Markov transition mechanism on a wide class of road networks. An explicit formula has also been derived for the s.d. and the ergodicity of Markov traffic has also been proved.We have shown that the s.d., with the related transition mechanism, can be explored from observed data based on sample trajectories. We have provided a statistical method and proved its optimality by simulation with which we can create the Markov kernel necessary to obtain a Markov traffic on a given road graph. Using this kernel, we can initiate traffic simulations that provide a s.d. of the cars on the map.To provide an example for creating this kernel file, we have used a publicly available dataset, namely the Taxi Trajectory Prediction dataset. Our simulation uses OpenStreetMap, a free map database.https://github.com/rbesenczi/Crowd-sourced-Traffic-Simulator/blob/master/justine/install.txt). Some simulation video is available at the YouTube channel of the first author at http://bit.ly/2FRpPxL.To test our theories, we have implemented the proposed model in our simulation program (RCE). We have run simulations and it has been proved to provide a s.d. on the map graph of Porto, Portugal. The whole project (including the RCE) is available for download Click here for additional data file."}
+{"text": "Scientific Reports 10.1038/s41598-020-76726-7, published online 12 November 2020Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cbiofunctionalized\u201d was incorrectly given as \u201cbiofunctionalaized\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "ENORA and NSGA-II have been adapted to optimize the performance of the classifier based on three different machine learning metrics: accuracy, area under the ROC curve, and root mean square error. We have extensively compared the generated classifiers using our proposed method with classifiers generated using classical methods such as PART, JRip, OneR and ZeroR. The experiments have been conducted in full training mode, in 10-fold cross-validation mode, and in train/test splitting mode. To make results reproducible, we have used the well-known and publicly available datasets Breast Cancer, Monk\u2019s Problem 2, Tic-Tac-Toe-Endgame, Car, kr-vs-kp and Nursery. After performing an exhaustive statistical test on our results, we conclude that the proposed method is able to generate highly accurate and easy to interpret classification models.The ease of interpretation of a classification model is essential for the task of validating it. Sometimes it is required to clearly explain the classification process of a model\u2019s predictions. Models which are inherently easier to interpret can be effortlessly related to the context of the problem, and their predictions can be, if necessary, ethically and legally evaluated. In this paper, we propose a novel method to generate rule-based classifiers from categorical data that can be readily interpreted. Classifiers are generated using a multi-objective optimization approach focusing on two main objectives: maximizing the performance of the learned classifier and minimizing its number of rules. The multi-objective evolutionary algorithms  Supervised Learning\u00a0is the branch of Machine Learning (ML)\u00a0[Artificial Neural Networks (ANN)\u00a0[Deep Learning Neural Networks (DLNN)\u00a0[Support Vector Machines (SVM)\u00a0[Instance-based Learning (IBL)\u00a0[DLNN, for example, is a large mesh of ordered nodes arranged in a hierarchical manner and composed of a huge number of variables. DLNNs are capable of modeling very complex behaviors, but it is extremely difficult to understand the logic behind their predictions, and similar considerations can be drawn for SVNs and IBLs, although the underlying principles are different. These models are known as black-box methods. While there are applications in which knowing the ratio behind a prediction is not necessarily relevant, , there are other situations where the interpretability of a model plays a key role.ing (ML)\u00a0 focused ing (ML)\u00a0. The besks (ANN)\u00a0, and, mos (DLNN)\u00a0, as welles (SVM)\u00a0, and Insng (IBL)\u00a0 are archinterpretability of classification systems refers to the ability they have to explain their behavior in a way that is easily understandable by a user\u00a0[accuracy, area under the ROC curve, and root mean square error), there is no universally accepted metric to measure the interpretability of the models. Nor is there an ideal balance between the interpretability and performance of classification systems but this depends on the specific application domain. However, the rule of thumb says that the simpler a classification system is, the easier it is to interpret. Rule-based Classifiers (RBC)\u00a0[RBC as the number of its rules or as the number of axioms that the rules have. These metrics tend to reward models with fewer rules as simple as possible\u00a0[RBCs are classification learning systems that achieve a high level of interpretability because they are based on a human-like logic. Rules follow a very simple schema:RBCs are so natural in some applications that they are used to interpret other classification models such as Decision Trees (DT)\u00a0[RBCs constitute the basis of more complex classification systems based on fuzzy logic\u00a0[LogitBoost or AdaBoost\u00a0[The y a user\u00a0. In others (RBC)\u00a0,9 are ampossible\u00a0,11. In gees (DT)\u00a0. RBCs cozy logic\u00a0 such as AdaBoost\u00a0.multi-objective optimization problem. We define a solution as a set of rules , and establish two objectives to be maximized: interpretability and accuracy. We decided to solve this problem by applying multi-objective evolutionary algorithms (MOEA)\u00a0[NSGA-II\u00a0[ENORA\u00a0[NSGA-II is very well-known and has the advantage of being available in many implementations, while ENORA generally has a higher performance. In the current literature, MOEAs are mainly used for learning RBCs based on fuzzy logic\u00a0[Fuzzy RBCs are designed for numerical data, from which fuzzy sets are constructed and represented by linguistic labels. In this paper, on the contrary, we\u00a0are interested in RBCs for categorical data, for which a novel approach is necessary.Our approach investigates the conflict between accuracy and interpretability as a s (MOEA)\u00a0,16 as me[NSGA-II\u00a0 and ENORI\u00a0[ENORA\u00a0. They arI\u00a0[ENORA\u00a0,19,20. Nzy logic\u00a0,24,25,26ENORA and NSGA-II, and the well-known rule-based classifier learning systems PART, JRip, OneR and ZeroR. In RBC for categorical data, and we propose the use of multi-objective optimization for the task of learning a classifier. In Breast Cancer, Monk\u2019s Problem 2, Tic-Tac-Toe-Endgame, Car, kr-vs-kp and Nursery. The experiments allow a comparison among the performance of the classifiers learned by our technique against those of classifiers learned by PART, JRip, OneR and ZeroR, as well as a comparison between ENORA and NSGA-II for the purposes of this task. In This paper is organized as follows. In optimization\u00a0[Mathematical programming\u00a0[multi-objective constrained optimization problems\u00a0[l objectives and m constraints, as follows:objectives) and combinatorial, and those with continuous variables. In combinatorial problems, we are looking for objects from a finite, or countably infinite, set The term mization\u00a0 refers tgramming\u00a0 deals wiproblems\u00a0, which c follows:Min./Max.non-dominated set . A solution non-dominated if there is no other solution dominatesi . When a problem\u00a0. A non-lgorithms\u00a0 are typiMOEA ENORA\u00a0[NSGA-II\u00a0[binary tournament selection (Algorithm 2) and a rank function based on Pareto fronts and crowding (Algorithms 3 and 4). The difference between NSGA-II and ENORA is how the calculation of the ranking of the individuals in the population is performed. In\u00a0ENORA, each individual belongs to a slot , therefore, the time complexity of ENORA is The EA ENORA\u00a0 and NSGA[NSGA-II\u00a0 use a \u03bc+ished in\u00a0) of the  sorting . It comp O(l\u00b7N2) . HoweverAlgorithm 1Require:Require:\u00a01:P with N individualsInitialize \u00a02:PEvaluate all individuals of \u00a03:\u00a04:whiledo\u00a05:\u2003\u00a06:\u2003\u00a07:whiledo\u2003\u00a08:Parent1\u2190 Binary tournament selection from P\u2003\u2003\u00a09:Parent2\u2190 Binary tournament selection from P\u2003\u200310:Child1, Child2\u2190Crossover\u2003\u200311:Offspring1\u2190Mutation(Child1)\u2003\u200312:Offspring2\u2190Mutation(Child2)\u2003\u200313:Offspring1\u2003\u2003Evaluate 14:Offspring2\u2003\u2003Evaluate 15:\u2003\u200316:\u2003\u200317:end while\u200318:\u200319:N best individuals from R according to the rank-crowding function in population R\u200320:\u200321:end while22:return Non-dominated individuals from PAlgorithm 2 Binary tournament selection.Require:P {Population}\u00a01:P\u00a02:P\u00a03:ifI is better than J according to the rank-crowding function in population Pthen\u00a04:returnI\u2003\u00a05:else\u00a06:returnJ\u2003\u00a07:end ifAlgorithm 3 Rank-crowding function.Require:P {Population}Require:\u00a01:ifthen\u00a02:return\u2003\u00a03:end if\u00a04:ifthen\u00a05:return\u2003\u00a06:end if\u00a07:returnENORA and NSGA-II behave differently is as follows. NSGA-II never selects the individual dominated by the other in the binary tournament, while, in ENORA, the individual dominated by the other may be the winner of the tournament. B and C are selected for a binary tournament with NSGA-II, individual B beats C because B dominates C. Conversely, individual C beats B with ENORA because individual C has a better rank in his slot than individual B. In this way, ENORA allows the individuals in each slot to evolve towards the Pareto front encouraging diversity. Even though in ENORA the individuals of each slot may not be the best of the total individuals, this approach generates a better hypervolume than that of NSGA-II throughout the evolution process.The main reason ENORA is our MOEA, on which we are intensively working over the last decade. We have applied ENORA to constrained real-parameter optimization [NSGA-II algorithm was designed by Deb et al. and has been proved to be a very powerful and fast algorithm in multi-objective optimization contexts of all kinds. Most researchers in multi-objective evolutionary computation use NSGA-II as a baseline to compare the performance of their own algorithms. Although NSGA-II was developed in 2002 and remains a state-of-the-art algorithm, it is still a challenge to improve on it. There is a recently updated improved version for many-objective optimization problems called NSGA-III [mization , fuzzy omization , fuzzy cmization , featuremization  and featmization . In thisNSGA-III .Algorithm 4 Crowding_distance function.Require:P {Population}Require:P {Population}Require:I {Individual}Require:l {Number of objectives}\u00a01:forldo\u00a02:\u2003\u00a03:\u2003\u00a04:jth objective for the individual higher adjacent in the jth objective to the individual I\u2003\u00a05:jth objective for the individual lower adjacent in the jth objective to the individual I\u2003\u00a06:end for\u00a07:forldo\u00a08:ifthen\u2003\u00a09:return \u221e\u2003\u200310:end if\u200311:end for12:13:forldo14:\u200315:end for16:returnPART  is a wiT Method\u00a0. Experimstrategy\u00a0 typical lgorithm\u00a0), and thJRip is a fast and optimized implementation in Weka of the famous RIPPER  algorithm\u00a0[RIPPER was proposed in\u00a0[IREP) rule learner developed in\u00a0[IREP and RIPPER work in a similar manner. They begin with a default rule and, using a training dataset, attempt to learn rules that predict exceptions to the default. Each rule learned is a conjunction of propositional literals. Each literal corresponds to a split of the data based on the value of a single feature. This family of algorithms, similar to decision trees, has the advantage of being easy to interpret, and experiments show that JRip is particularly efficient in large datasets. RIPPER and IREP use a strategy based on the separate-and-conquer method to generate an ordered set of rules that are extracted directly from the dataset. The classes are examined one by one, prioritizing those that have more elements. These algorithms are based on four basic steps  applied repetitively to each class until a stopping condition is met\u00a0[Weka implementation, the procedure selects the condition with the highest information gain). In the pruning phase redundancy is eliminated and long rules are reduced. In the optimization phase, the rules generated in the previous steps are improved (if possible) by adding new attributes or by adding new rules. Finally, in the selection phase, the best rules are selected and the others discarded.lgorithm\u00a0. RIPPER posed in\u00a0 as a morloped in\u00a0. IREP ann is met\u00a0. These sOneR (One Rule) is a very simple, while reasonably accurate, classifier based on a frequency table. First, OneR generates a set of rules for each attribute of the dataset, and, then, it selects only one rule from that set\u2014the one with the lowest error rate\u00a0[ror rate\u00a0. The setZeroR  is a clRBC specifically designed for categorical data. Then, we propose and describe a multi-objective optimization solution to obtain optimal categorical RBCs.In this section, we propose a general schema for an M rules, where each rule antecedent) takes values in a set consequent) takes values in maximum matching as reasoning method, where the compatibility degree of the rule Let association degree for the example c, that is:The classification (or output) of the classifier Therefore, the K instances with p categorical input attributes, j can take a category Let w is the number of classes of the output attribute and In the problem (Equation ), the fuon trees ,48. FiguENORA and NSGA-II have been adapted to solve the problem described in Equation .All individuals contain at least one rule for any output class between 1 and The initial population (Algorithm 5) is randomly generated with the following conditions:Algorithm 5 Initialize population.Require:Require:Require:Require:Require:Require:Require:\u00a01:\u00a02:forNdo\u00a03:\u2003\u00a04:ifthen\u2003\u00a05:\u2003\u2003\u00a06:else\u2003\u00a07:Random\u2003\u2003\u200320:end if\u2003\u200321:end for\u200322:\u2003{Random integer values for adaptive variation}23:Random. The seself-adaptive crossover and mutation, which means that the selection of the operators is made by means of an adaptive technique. As we have explained , the prENORA and NSGA-II have been implemented with two crossover operators, rule crossover (Algorithm 9) and rule incremental crossover (Algorithm 10), and two mutation operators: rule incremental mutation (Algorithm 11) and integer mutation (Algorithm 12). Rule crossover randomly exchanges two rules selected from the parents, and rule incremental crossover adds to each parent a rule randomly selected from the other parent if its number of rules is less than the maximum number of rules. On\u00a0the other hand, rule incremental mutation adds a new rule to the individual if the number of rules of the individual is less than the maximum number of rules, while integer mutation carries out a uniform mutation of a random antecedent belonging to a randomly selected rule.Both Algorithm 6 Variation.Require:\u00a01:\u00a02:\u00a03:Self-adaptive crossover \u00a04:Self-adaptive mutation \u00a05:Self-adaptive mutation \u00a06:returnAlgorithm 7 Self-adaptive crossover.Require:I, J {Individuals for crossing}Require:Require:\u00a01:if a random Bernoulli variable with probability then\u00a02:Random\u00a03:Random, and have been used as a comparison for many algorithms on several occasions. In particular, in [AQ17-DCI, AQ17-HCI, AQ17-FCLS, AQ14-NT, AQ15-GA, Assistant Professional, mFOIL, ID5R, IDL, ID5R-hat, TDIDT, ID3, AQR, CN2, WEB CLASS, ECOBWEB, PRISM, Backpropagation, and Cascade Correlation. For our research, we have used the Monk\u2019s Problem 2, which contains six categorical input attributes and a binary output attribute, summarized in Monk\u2019s Problem 2 is the binary outcome of the logical formula:In July 1991, the monks of ular, in , they haaccuracy:K is the number of instances of the dataset i in ith instance in area under the ROC curve:ROC curve obtained with the classifier ROC (Receiver Operating Characteristic) curve [sensitivity versus the specificity index for a classifier varying the discrimination threshold value. Such a curve can be used to generate statistics that summarize the performance of a classifier, and it has been shown in [ROC curve can be computed as follows [sensitivity) is the proportion of positive instances classified as positive by the classifier specificity) is the proportion of negative instances classified as negative by t is the discrimination threshold. Finally, our third constrained optimization model is based on the root mean square error (RMSE):mean square error obtained with a classifier ith instance for the classifier ROC curve, and root mean square error are all well-accepted measures used to evaluate the performance of a classifier. Therefore, it is natural to use such measures as fitting functions. In this way, we can establish which one behaves better in the optimization phase, and we can compare the results with those in the literature.We have conducted different experiments with different optimization models to calculate the overall performance of our proposed technique and to see the effect of optimizing different objectives for the same problem. First, we have designed a multi-objective constrained optimization model based on the nstances  obtainedc) curve  is a grashown in  to be a  follows :AUCD(\u0393)=ENORA and NSGA-II as metaheuristics in this particular optimization task, we use the hypervolume metric [error ratio, the generational distance, the maximum Pareto-optimal front error, the spread, the maximum spread, or the chi-square-like deviation, is that it can be computed without an optimal population, which is not always known [P, and is formulated as:P, and i. Subsequently, the hypervolume ratio (HVR) is defined as the ratio of the volume of the non-dominated search space over the volume of the entire search space, and is formulated as follows:HVR requires reference points that identify the maximum and minimum values for each objective. For RBC optimization, as proposed in this work, the following minimum :FDlo:FDloENORENORA, and three driven by NSGA-II), over both datasets, has been designed for the purpose of showing the aspect of the final Pareto front, and compare the hypervolume ratio of the models. The results of this single execution, with population size equal to 50 and 20,000 generations , are shown in A first single execution of all six models , we have executed again the six models in full training mode.To perform an initial comparison between the performance of the classifiers obtained with the proposed method and the ones obtained with classical methods (Breast Cancer dataset (this case), while, for the Monk\u2019s Problem 2, it was set to 9. Observe that, since Breast Cancer dataset. In fact, after the preliminary experiments were run, it turned out that the classical classifier learning systems tend to return very small, although not very precise, set of rules on Breast Cancer, and that justifies our choice. On the other hand, executing the classical rule learners on Monk\u2019s Problem 2 returns more diverse sets of rules, which justifies choosing a higher Monk\u2019s Problem 2, that individual has seven rules. The comparison is shown in number of rules, percent correct, true positive rate, false positive rate, precision, recall, F-measure, Matthews correlation coefficient, area under the ROC curve, area under precision-recall curve, and root mean square error. As for the Breast Cancer dataset (observe that the best result emerged from the proposed method), in the optimization model driven by NSGA-II, with root mean square error as the first objective , excepting the tive see , only PArror see . The expcross-validated experiment for the Breast Cancer dataset, in which we iterated three times a 10-fold cross-validation learning process [percent correct, area under the ROC curve, and serialized model size of all results. Second, we designed a train/test percentage split experiment for the Monk\u2019s Problem 2 dataset, in which we iterated ten times a 66% (training) versus 33% (testing) split and considered, again, the average result of the same metrics. Finally, we performed a statistical test over on results, to understand if they show any statistically significant difference. An execution of our methodology, and of standard classical learners, has been performed to obtain the models to be tested precisely under the same conditions of the experiment To test the capabilities of our methodology in a more significant way, we proceeded as follows. First, we designed a  process  and conspercent correct, area under the ROC curve and serialized model size. We proceeded as follows. First, we checked normality and sphericity of each sample by means of the Shapiro\u2013Wilk normality test. Then, if normality and sphericity conditions were met, we applied one way repeated measures ANOVA; otherwise, we applied the Friedman test. In the latter case, when statistically significant differences were detected, we applied the Nemenyi post-hoc test to locate where these differences were. Breast Cancer dataset for each of the three metrics, and Monk\u2019s Problem 2 dataset.The statistical tests aim to verify if there are significant differences among the means of each metric: Monk\u2019s problem 2 dataset and for the following four other datasets:Tic-Tac-Toe-Endgame dataset, with 9 input attributes, 958 instances, and binary class  (kr-vs-kp), with 36 input attributes, 3196 instances, and binary class .From the statistical tests  between precision and interpretability than the rest of the classifiers. For the rest of the analyzed datasets, the accuracy obtained using ENORA is substantially higher. For example, for the Tic-Tac-Toe-Endgame dataset, ENORA obtains a PART obtains JRip obtains Car, kr-vs-kp and Nursery, we want to comment that better success percentage can be obtained if the maximum number of evaluations is increased. However, better success percentages imply a greater number of rules, which is to the detriment of the interpretability of the models.We would like to highlight that both the Breast Cancer  and Monk\u2019s Problem 2 , using two different evolutionary algorithms, namely ENORA and NSGA-II, and three different choices as a performance metric, i.e., accuracy, the area under the ROC curve, and the root mean square error. Additionally, we have shown the results of the evaluation in 10-fold cross-validation of the publicly available Tic-Tac-Toe-Endgame, Car, kr-vs-kp and Nursery datasets.In this paper, we have proposed a novel technique for categorical classifier learning. Our proposal is based on defining the problem of learning a classifier as a multi-objective optimization problem, and solving it by suitably adapting an evolutionary algorithm to this task; our two objectives are minimizing the number of rules (for a better interpretability of the classifier) and maximizing a metric of performance. Depending on the particular metric that is chosen, (slightly) different optimization models arise. We have tested our proposal, in a first instance, on two different publicly available datasets, PART and JRip, but only indirectly. Finally, the idea underlying our approach is that multiple classifiers are explored at the same time in the same execution, and this allows us to choose the best compromise between the performance and the interpretability of a classifier a posteriori.Our initial motivation was to design a classifier learning system that produces interpretable, yet accurate, classifiers: since interpretability is a direct function of the number of rules, we conclude that such an objective has been achieved. As an aside, observe that our approach allows the user to decide, beforehand, a maximum number of rules; this can also be done in embedded future selection mechanism. In fact, all attributes are  used in every rule of a classifier learned by our optimization model. By simply relaxing such a constraint, and by suitably re-defining the first objective in the optimization model , the resulting classifiers will naturally present rules that use more features as well as rules that use less . Although this approach does not follow the classical definition of feature selection mechanisms (in which a subset of features is selected that reduces the dataset over which a classifier is learned), it is natural to imagine that it may produce even more accurate classifiers, and more interpretable at the same time.As a future work, we envisage that our methodology can benefit from an multi-objective differential evolution (MODE) for rule-based classification for inclusion in the Weka Open Source Software issued under the GNU General Public License. The implementation of other algorithms, such as MOEA/D, their adaptation in the Weka development platform and subsequent analysis and comparison are planned for future work.Currently, we are implementing our own version of"}
+{"text": "Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems can be solved via Approximate Bayesian Computation (ABC). However, an optimal alternative for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose an adjusted population-based MCMC ABC method by re-defining the standard ABC parameters to discrete ones and by introducing a novel Markov kernel that is inspired by differential evolution. We first assess the proposed Markov kernel on a likelihood-based inference problem, namely discovering the underlying diseases based on a QMR-DTnetwork and, subsequently, the entire method on three likelihood-free inference problems: (i) the QMR-DT network with the unknown likelihood function, (ii) the learning binary neural network, and (iii) neural architecture search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel. In various scientific domains, an accurate simulation model can be designed, yet formulating the corresponding likelihood function remains a challenge. In\u00a0other words, there is a simulator of a process available that, when provided an input, returns an output, but\u00a0the inner workings of the process are not analytically available ,2,3,4,5.Commonly, likelihood-free inference problems for continuous data are solved via a group of methods known under the term Approximate Bayesian Computation (ABC) ,7. The\u00a0m biology ,9, and s biology , Sequent biology , and\u00a0neu biology ,13. In\u00a0t biology  for disc biology . Thus, tOur main focus is on optimal proposal distribution design as there is no \u201cnatural\u201d notion of the search direction and scale for discrete data spaces. Hence, the\u00a0presented solution is inspired by Differential Evolution (DE) , which hThe contribution of the present paper is as follows. First, we introduce an alternative version of the MCMC-ABC algorithm, namely a\u00a0population-based MCMC-ABC method, that is applicable to likelihood-free inference tasks with discrete random variables. Second, we propose a novel Markov kernel for likelihood-based inference methods in a discrete state space. Third, we present the utility of the proposed approach on three binary\u00a0problems.y, x and\u00a0Let x while only a simulator is available, then it is considered as an Approximate Bayesian Computation (ABC) problem, meaning that In many practical applications, the\u00a0likelihood function is unknown, but\u00a0it is possible to obtain (approximate) samples from nference  or a blanference . If\u00a0the Typically, a\u00a0likelihood-free inference problem or an ABC problem is solved through sampling. One of the most well-known sampling methods is the Metropolis\u2013Hastings algorithm , where tGiven a population of chains, a\u00a0question of interest is what is the best proposal distribution for an efficient sampling convergence. One approach is parallel tempering. It introduces an additional temperature parameter and\u00a0initializes each chain at a different temperature ,24. HoweReversibility is met, because\u00a0the suggested proposal could be inverted to obtain Reference  successfAperiodicity is met, because\u00a0the Markov chain follows a random walk.Irreducibility is solved by applying the noise.Furthermore, the\u00a0created Markov chain is ergodic, as\u00a0the following two conditions are\u00a0met:Hence, the\u00a0resulting Markov chain has a unique stationary distribution. The\u00a0results presented by  indicateIn this paper, we focus on binary variables, because\u00a0categorical variables could always be transformed to a binary representation. Hence, the\u00a0most straightforward proposal for binary variables is the independent sampler that utilizes the product of Bernoulli:x is represented by a string of bits, xoroperator between two bits We propose to utilize the ideas outlined by , but\u00a0in ollowing , we propction in . Next, wm q(\u03b4|C):xnew=xi\u2297\u03b4Remark\u00a01.The proposal defined in  fulfillsProof.\u00a0Reversibility is met, as\u00a0 side of . Aperiod side of  is determut) operation:The missing property of  could bermulated  as in PrProposition\u00a01.The proposal defined as a mixture fined by  and\u00a0qxorfined by , is a prProof.\u00a0mut proposal assures that there is a positive transition probability across the entire search space. \u00a0\u00a0\u00a0\u25a1Reversibility and aperiodicity were shown in Proposition 1. The\u00a0irreducibility is met, because\u00a0the mut+xor. First, it introduces another hyperparameter, However, we notice that there are two potential issues with the mixture proposal mut operation in .We refer to this new Markov kernel for discrete random variables as the discrete differential evolution Markov chain  . See theAlgorithm 1 Population-MCMC-ABC.1:Given 2:mut+xor or dde-mc.\u25b9 Either , mut+xor3:Simulate 4:ifthen5:\u00a0\u00a0\u00a0\u00a06:\u00a0\u00a0\u00a0\u00a07:ifthen\u00a0\u00a0\u00a0\u00a08:\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a09:returnxA single step of the population-MCMC-ABC algorithm is presented in Algorithm 1. Notice that in Line 5, we take advantage of the symmetricity of all the proposal. Moreover, in\u00a0the procedure, we skip an outer loop over all chains for clarity. Without\u00a0loss of generality, we assume a simulator to be a probabilistic program denoted by dde-mc, on a problem when the likelihood is known.QMR-DT network (likelihood-based case): First, we validate the novel proposal, QMR-DT network (likelihood-free case): Second, we verify the performance of the presented proposal by modifying the first test-bed as a likelihood-free problem.Binarized Neural Network Learning: Third, we investigate the performance of the proposed approach on a high-dimensional problem, namely learning binary neural networks.Neural architecture search: Lastly, we consider a problem of Neural Network Architecture Search (NAS).In order to verify our proposed approach, we use four test-beds:https://github.com/IlzeAmandaA/ABCdiscrete (accessed on 5 March 2021).With each test-bed, we increase the complexity of the problem. Hence, the number of iterations chosen varies per experiment. The code of the methods and all experiments is available at the following link: x) and findings (y):y and l and finding i, i.e., the probability that the disease l alone could cause the finding i to have a positive outcome. For a complete inference, the prior l.The overall setup was designed as described by , i.e., wDT model . qil is  made by  that thedde-mc kernel to the mut proposal, the mut-xor proposal, the mut+crx proposal (see [ind-samp) as in  as in  with sam work by , it was x and the most probable values found by the population-MCMC with different proposals. The number of diseases was set to In this experiment, we used the error that is defined as the average Hamming distance between the real values of dde-mc and mut+xor, are superior to kernels stemming from genetic algorithms or random search, i.e., mut+crx, mut, and ind-samp , while the time complexity of ind-samp is O(1).DE-inspired proposals, ind-samp . In partdde-mc, mut+xor, and ind-samp as a baseline. mut+crx and mut were not selected due to to their very slow convergence with high-dimensional problems.Based on the obtained results, the subsequent experiments were carried out only with In this test-bed, the QMR-DT network is redefined as a simulator model, i.e., the likelihood is assumed to be intractable. The Hamming distance is selected as the distance metric, but due to its equivocal nature for high-dimensional data, the dimensionality of the problem is reduced. In particular, the number of diseases and observations  are decreased to 10 and 20, respectively, while the probabilities of the network are sampled from a beta distribution, dde-mc converged faster and to a better  optimum than mut+xor. However, this effect could be explained by a lower dimensionality of the problem compared to the first experiment. Second, utilizing the exponential distribution had a profound positive effect on the convergence rate of both dde-mc and mut+xor  with a single fully-connected hidden layer on the image dataset of ten handwritten digits (MNIST ). We usex inspired by the work of [D denotes the dimensionality of x. As a result, the prior distribution acts as a regularization term as it favors parameter settings with fewer active weights. The distribution is independent of the data y thus, the partition function For the Metropolis acceptance rule, we define a Boltzmann distribution over the prior distribution of the weights  work of :(14)p(x)The original dataset consists of 60,000 training examples and 10,000 test examples. For our experiment, we selected the digits 0 and 1; hence, the dataset size was reduced to 12,665 training and 2115 test examples. Different tolerance values were investigated to obtain the best convergence, ranging from 0.03 to 0.2, and each experiment was run for at least 200,000 iterations. All experiments were cross-evaluated five times. Lastly, we evaluated the performance by computing both the minimum test error obtained by the final population, as well as the test error obtained by using a Bayesian approach, i.e., we computed the true predictive distribution via majority voting by utilizing an ensemble of models. In particular, we selected the five last updated populations, resulting in 5 \u00d7 24 \u00d7 5 = 600 models per run, and we repeated this with different seeds 10 times.Because the classification error function in  is non-dmut+xor proposal converged the fastest towards the optimal solution in the search space  was better for dde-mc and mut+xor compared to ind-samp  . The cordde-mc, for a population-based MCMC-ABC algorithm. The obtained results suggest that the newly designed proposal is a promising and effective solution for intractable problems in a discrete space.In this paper, we note that there is a gap in the available methods for likelihood-free inference on discrete problems. We propose to utilize ideas known from evolutionary computing similarly to , in ordeind-samp. This is accounted for by the fact that for high dimensions, it takes more time for the entire population to converge.Furthermore, Markov kernels based on differential evolution are also effective to traverse a discrete search space. Nonetheless, great attention has to be paid to the choice of the tolerance threshold for the MCMC-ABC methods. In other words, if the tolerance is set too high, then the performance of the DE-based proposals drops to that of an independent sampler, i.e., the error of the Markov chain is high. For high-dimensional problems, the proposed kernel seems to be most promising; however, its population error becomes similar to that of Alternative ABC algorithms like SMC should be further investigated.In this work, we focused on calculating distances in the data space. However, utilizing summary statistics is almost an obvious direction for future work.As the whole algorithm is based on logical operators and the input variables are also binary, the algorithm could be encoded using only bits, thus saving considerable amounts of memory storage. Consequently, any matrix multiplication could be replaced by an XNORoperation followed by a sum, thus reducing the computation costs and possibly allowing implementing the algorithm on relatively simple devices. Therefore, a natural consequence of this work would be a direct hardware implementation of the proposed methods.In this paper, we outline a number of potential applications of the presented methodology and indicate that the obtained results are of great practical potential. From the optimization perspective, a discrete ABC gives an opportunity to solve a problem in a principled manner. This is extremely important for applications associated with deep learning, e.g., NAS ,35, neurIn conclusion, we would like to highlight that the present work offers new research directions:"}
+{"text": "We present uncertainty relations based on Wigner\u2013Yanase\u2013Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. It is shown that the lower bounds contain two terms: one characterizes the degree of compatibility of two measurements, and the other is the quantum correlation between the measured system and the quantum memory. Detailed examples are given for product, separable and entangled states. R and S, where R. Schr\u00f6dinger gave a further improved uncertainty relation [d-dimensional Hilbert space H, and H. The number c is the largest overlap among all R and S. Berta et al. [R and S in the presence of quantum memory B:d is the dimension of the subsystem A. The term A and the quantum memory B. The bound of Berta et al. has been further improved [h, \u03a6) entropies [The uncertainty principle is an essential feature of quantum mechanics, characterizing the experimental measurement incompatibility of non-commuting quantum mechanical observables in the preparation of quantum states. Heisenberg first introduced variance-based uncertainty . Later, relation :VV:(1)I\u03b1 wR, S and For a quantum state ty holds :3)U\u03b1 , and theA and B satisfy Theorem 1 gives a product form of the uncertainty relation. Comparing the results (Equation ) withoutEquation , while iEquation , even ifTheorem\u00a02.Let Proof\u00a0of\u00a0Theorem\u00a02.By definition and taking into account the fact that \u2265I\u03b1 , we haveEquation . By usinEquation .\u2003\u2610Corresponding to the product form of the uncertainty relation, we can also derive the sum form of the uncertainty relation:We note that Equation  reduces eorem in .B. It is shown that the lower bound contains two terms: one is the quantum correlation From Theorems 1 and 2, we obtain uncertainty relations in the form of the product and sum of skew information, which are different from the uncertainty of , which orelation .Example\u00a01.We consider the 2-qubit Werner state Equation  are giveandrespectively; see .Similarly, we can obtain the values of the left- and right-hand sides of Equation :andrespectively; see .Here we see explicitly that, just as for the Shannon entropy, R\u00e9nyi entropy, Tsallis entropy, Equation , the casquations  and 7)   enExample\u00a02.Consider a separable bipartite state, .We still choose Equation  are zeroEquation  is zero.Equation  are 12 aEquation  are zero.Example\u00a03.For the Werner state .We have the values of the left- and right-hand sides of Equation , respectandSee .We can also obtain the values of the left- and right-hand sides of Equation :andrespectively; see .Moreover, when .We have investigated the uncertainty relations both in product and summation forms in terms of the Wigner\u2013Yanase\u2013Dyson skew information with quantum memory. It has been shown that the lower bounds contain two terms: one is the quantum correlation"}
+{"text": "An analysis of low birth weight (LBW) births in ten contaminated prefectures of Japan, 1995\u20132018, finds a statistically significant increase in the LBW proportion in 2012\u20132013, but no increase after 2013. In the rest of Japan (37 prefectures), no increase in LBW births was found after the Fukushima accident. The effect was greater in area 1  than in area 2 , and not statistically significant in area 3 .In their recent article, Scherb et al.  investighttps://www.r-project.org/); the option family\u2009=\u2009quasibinomial was applied to adjust the variances for overdispersion. This means that F-tests were used instead of chi-square tests.Since the numbers of live births and LBW births for all three areas were provided in Table 1 of [p-value 0.074. A fifth-degree polynomial for the temporal trend, however, fitted the data better  than a fourth-degree polynomial . Now, the odds ratio for the level shift decreased to OR\u2009=\u20091.009 , p-value 0.347. Similarly, the regressions of the data for the three sub-areas yielded non-significant level shifts when a fifth-degree polynomial was applied: area 1: OR\u2009=\u20091.039 , p-value 0.152; area 2: OR\u2009=\u20091.013 , p-value 0.244; area 3: OR\u2009=\u20091.004 , p-value 0.730). For all three data sets, a fifth-degree polynomial yielded a better fit than a fourth-degree polynomial.With a fourth-degree polynomial for the time trend as applied in , the estp-value 0.152. No notable level shift was detected in the control region .To increase the statistical power, I pooled the data from areas 1 and 2 and termed them the study region; area 3 was used as the control region. The odds ratio of the level shift in the study region was 1.019 , p-value 0.041). The deviance was 40.2 (df\u2009=\u200917), considerably smaller than deviance\u2009=\u200945.9 (df\u2009=\u200917) obtained with model 1. A similar regression for the control region with model 2 yielded OR\u2009=\u20090.998 . The trend of LBW proportions in the study region and the regression lines for the two competing models are shown in Fig.\u00a0A plot of the data shows an increase in LBW-proportions in 2012\u20132013. Therefore an additional regression analysis was carried out with a model that allowed for a short term increase in 2012\u20132013 (model 2) instead of a level shift in 2012\u20132018 (model 1). The estimate of the odds ratio in 2012\u20132013 was 1.016 , p-value 0.018) and model 2 , p-value 0.002), but model 2 fitted the data better  than model 1 . As the data showed no overdispersion, a chi-square test was applied for testing the significance of the odds ratios. The test for a possible level shift in addition to the effect in 2012\u20132013 yielded OR\u2009=\u20091.00 . Thus, the significant result for the shift in LBW proportion obtained with model 1 is driven by the peak in 2012\u20132013.A considerable improvement of the fit was obtained when 2002 was chosen as the beginning of the study period. Logistic regression with a fourth-degree polynomial turned out to be the best choice for the long-term trend. The results were statistically significant for both regression model 1 , To conclude, my re-analysis of the data shows that there was an increase in LBW proportion in the first 2 years after Fukushima, but no increase after 2013. Thus, the claim by Scherb et al. that their result is evidence of a genetic radiation effect is challenged by the present analysis."}
+{"text": "For n-coalescents, this has been explicitly shown for only a limited subclass of n-coalescents and exponentially growing populations. This article gives a more general construction of time-changed n-coalescents as limits of specific Cannings models with rather arbitrary time changes.Multiple-merger coalescents, e.g.  As a more realistic alternative, multiple-merger coalescents, especially n-coalescents, introduced by Pitman  limit of genealogies from samples of size n taken from Cannings models. The limit is reached as population size N goes to infinity and time is rescaled, see M\u00f6hle and Sagitov  timescale. Such changes are featured in coalescent simulators as ms  transformed. However, size changes too extreme can yield a non-bifurcating (multiple merger) genealogy, see Birkner et al.  from Eldon and Wakeley  with changed time scale have been recently discussed and applied as models of genealogies, see Spence et\u00a0al. , where ancestors of different sets are different. For The terminology from M\u00f6hle  is used ee M\u00f6hle  for detaN Cannings models for each n-coalescent n-coalescents. For this, we need some assumptions. Most importantly, an asymptotically infinite sum needs to be controlled. For this, we introduce a concept of o-terms: A sequence Consider a sequence of fixed-N leading to a well-defined population size profile in coalescent time, i.e. Population size changes of order The first class of Cannings models used to construct time-changed n-coalescents are modified Moran models. In a modified Moran model, only a single individual has more than one offspring (and may have many offspring). Following Huillet and M\u00f6hle , Matuszewski et\u00a0al. -n-coalescent. In the discrete model, additional individuals can be added in any way so that the resulting model is still a modified Moran model.Let ying Eq.\u00a0 for \\docn-coalescents. For instance, if one only allows certain population size changes, one can also use the modified Moran model used in Theorem\u00a0The specific models used in each of the two theorems are not the only possibilities of modified Moran models with variable population sizes to converge to entclass1pt{miniman-coalescent. In the discrete model, additional individuals can be added in any way so that the resulting model is still a modified Moran model.Let ying Eq.\u00a0 for \\docFinally, for the classic Moran model, i.e. the modified Moran model with  via Eq.\u00a0 for \\docFor the standard Moran model and a population size profile d by Eq.\u00a0 so that n-coalescents, N Cannings models introduced in Schweinsberg  lets each individual in any generation r produce a number of  offspring X with N offspring are chosen to form the next generation. If less than N offspring are produced, the missing next generation individuals are arbitrarily associated with parents. Here, this is done by randomly choosing a parent, which preserves exchangeability and makes the model a Cannings model. The genealogies of a sample of size n converge as n-coalescent, see Schweinsberg  with growth rate n-coalescent with exponential growth, waiting times for coalescence events follow a Gompertz distribution, e.g. see Slatkin and Hudson , Eq.  appeared\u03c1t), Eq. .t in the continuous time limit. The approach of this study was to build on existing Cannings models that converge for fixed population size to the n-coalescent and just change the population sizes gradually from generation to generation, which includes adjusting parent-offspring allocation between generations. This raises the question whether the used Cannings models and the adjustment of ancestral relationships have biological interpretations and are a reasonable model for at least some real populations.As for the Wright\u2013Fisher model, genealogies of samples taken from (haploid) modified Moran and other Cannings models can be approximated by a time-change of their limit coalescent process, when the population sizes of the discrete models are fluctuating, but are always of the same order of size. As for models with fixed population size, time intervals of n-coalescent with N): On top of a standard Moran model choice of one parent M with two offspring and one individual in the parent generation with no offpring, there is a random probability X for each other individual in the parent generation to not have offspring in the next generation. X is drawn from M reproduce once, and M replaces itself and all non-reproducing individuals by its offspring. These models capture the concept of sweepstake reproduction . Both models lead to the same Dirac coalescent limit and have the same time rescaling order X, a fixed number of X, similar models also appear in Hartmann and Huillet . Ad. Ad5). Af is regularly varying \\document1 in Eq.\u00a0 yields14Now, we establish an easy-to-verify variant of M\u00f6hle , N satisfyondition , \\documer for n-coalescent as the fixed-size model. Eq.\u00a0 Markovian process. This has an implication for modelling of real populations: The genealogy of a sudden population expansion, happening at a specific generation, where a single genotype/individual is responsible for the population growth, is not given by a time-changed continuous-time n-coalescent.Depending on the magnitude of a population size increase, adding individuals as further offspring of the multiplying parent from the fixed-size modified Moran model can strongly increase coalescence probabilities. For instance, for a population expansion of size N modified Moran models.We recall some properties of fixed-(i)As (ii)n coalescent if If (iii)If (i) from Huillet and M\u00f6hle ,\u00a0Eq.\u00a010 n-coalescent after a suitable time change.The following proposition provides criteria for genealogies in modified Moran models with fluctuating population sizes to converge to a N modified Moran model so that r. If Consider a fixed-and that  holds fohat Eqs.\u00a0 and 13)N modifieBased on the fixed-size modified Moran model and n-coalescent limit for the fixed-N modified Moran model.Then, This is shown by applying Lemma\u00a0s are Stirling numbers of the first kind. From Eq.\u00a0 is a logarithm, we have, using d Tavare , we can ince Eq.\u00a0 ensures n-coalescents.The integral representation of the time change is a deterministic version of the coalescent intensity from Kaj and Krone -coalescents for To prove the Corollaries\u00a0n-coalescents are covered by Theorem\u00a0From Eq.\u00a0, it follentclass1pt{minimaentclass1pt{minimaN case, again  model satisfies B is the Beta function, see Schweinsberg : for a us, only  needs toentclass1pt{minimat, since  holds,\\dentclass1pt{minima"}
+{"text": "In this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation. In 1965, Lotfi A Zadeh  introducIn our literature review, we have seen that the neutrosophic precalculus and neutrosophic calculus were first studied by Smarandache , which iNeutrosophic integral calculus plays very important role in the field of neutrosophic calculus. Neutrosophic integral is the extension of fuzzy integral, which was first introduced by Smarandache . In the Before discussing about neutrosophic differential equation, we should know about fuzzy differential equation which may be modified or generalized for neutrosophic environment. The theory of fuzzy differential equation was first introduced by Kaleva , which hi et al.  proposedi et al.  studied i et al. \u201343. Now,In the recent time, researcher is also working on neutrosophic differential equation. Sumanthi et al.  proposedIn our literature review, we have been seen that there are few works have been done on neutrosophic differential equation. However, there are almost no work have been done on neutrosophic boundary-value problem and neutrosophic initial value problem. Therefore, there is a big scope and opportunity to work in these area. Since there is not much work which have been done, then we must develop the basic properties and results which are needed for the proper development of this topic. Now, a proper development of basic differential equation already have been done in crisp and fuzzy environment which motivates us to think about the similar types of development and modification in neutrosophic environment. In the future, this article may help the other researcher for the further development of this topic.To build a theory of neutrosophic differential equation, the second-order neutrosophic boundary-value problem is developed in this article.To present some properties of neutrosophic number.To prove the neutrosophic derivative  and genen,\u00a0m)-types differentiability of neutrosophic-valued function.To present  system, where To define two-point neutrosophic boundary-value problem in different -system.To solve two-point neutrosophic boundary-value problem and investigate the solutions in different .When H is an interval, then the definition written as:Then, it can be written as: Let \\docLet Proof of this proposition is trivial and it can be done using extension principle . \\documeLet Since Let Moi et al.  found sof(x) at  Let \\docNow, type-1 first-order derivative is denoted by f(x). Now, type-3 derivative if type-4 derivative if type-5 derivative if type-6 derivative if type-7 derivative if type-8 derivative if However, we will use only type-1 and type-2 derivative of f(x) in the rest of this article.In the similar way, we can define another types of derivative of Let I. If f is type-1 differentiable, then f is generalized neutrosophic differentiable function of type-1. Again, if f is type-2 differentiable function, then,f is generalized neutrosophic differentiable function of type-2. Therefore, Definition Since Let f is type-2 differentiable. If If This completes the proof. F, f(x) at It is said to be type-1 derivative if Let nth-order derivative of a neutrosophic-valued function.By this similar process, we can define the f(x) is said to be -type differentiable at f(x) at Let If If If If Let If If The proof the third and fourth part of the theorem is similar to the second and first part, respectively. f(x) is type-1 differentiable function and g(x) is type-2 differentiable function on I. Then, I and Let f is type-1 differentiable, then we have:g is type-2 differentiable, then there exists Since From Eq. Now, multiplying Eq. f is type-2 and g is type-1 differentiable. By similar process, we can show the same result when f and g are second-order generalized neutrosophic differentiable function on I, such that f is -type and g is -type differentiable function or f is -type and g is -type differentiable function or f is -type and g is -type differentiable function or f is -type and g is -type differentiable function on I. Then, I and:Let f is -type differentiable and g is -type differentiable. Then, by the above Theorem For the first case, g is type-1 differentiable, then f.g is type-1 differentiable and If g is type-2 differentiable, then f.g is type-2 differentiable and If Let Subcase 1: Let g is type-1 differentiable, then: Subcase 2: Let There are two subcases. Subcase 1: Let g is type-2 differentiable, then: Subcase 2: Let There are two subcases. This completes the proof. a and b are neutrosophic number, and Let us consider the second-order neutrosophic boundary-value problem as follows:y is said to be -solution of Eq. Let To find the solution of the neutrosophic boundary-value problem Therefore, there are four types of possible system of boundary-value problem. System :where Here, Since there is no derivative involve in the boundary conditions. Therefore, for all remaining system, the boundary conditions will be same as above. Only the equation will be change. System :Here,  System :Here,  System :Here, y be the -solution of the boundary-value problem Let F.where In this section, we shall discuss some test problems and their numerical results. The Tables are calculated using Wolfram Mathematica 9.0 and the figures have been drawn using MATLAB R2018a. The Matlab code for the figures has been given below.Matlab code :x=k; %Choose k, where plot(hold on.plot(hold off.xlabel(\u2019x\u2019); %For x-axis.ylabel(\u2019y\u2019); %For y-axis.Let us consider second-order neutrosophic boundary-value problem as follows: Systemy is a  solution for the boundary-value problem, then:If entclass1pt{minimay is  differentiable for y gives a  solution of the neutrosophic boundary-value problem on Then, the type-1 derivative of the solution is: SystemThe solution of the boundary-value problem for 2,2) system is:,2 systemy is type-2 differentiable. Then, type-2 derivative of y is:y is type-2 differentiable. Then, we have:y gives a  solution on For  Systemy is:y gives a  solution on The solution of the boundary-value problem for 1,2) system is: system i System :y is:y gives a  solution on The solution of the boundary-value problem for 2,1) system is:,1 systemTherefore, the boundary-value problem gives -solution on In Fig.\u00a0entclass1pt{minimaentclass1pt{minimaentclass1pt{minimax\\in 0,1/$$\\end{doLet us consider second-order neutrosophic boundary-value problem as follows: SystemThe solution of the boundary-value problem for -system is: System-solution of the boundary-value problem is: System-solution for this boundary-value problem does not exist. Because, if -solution exists, then the solution can be written in the form as follows: SystemBy similar argument, we can show that -solution does not exist.In Figs.\u00a0entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaLet us consider second-order neutrosophic boundary-value problem as follows: Systemy, The solution of the boundary-value problem for -system is: systemThe solution for  system is:By this similar process, we can show that for  system and  system, From Fig.\u00a0n,\u00a0m) differentiability of neutrosophic-valued function, where In this article, mainly, we have focused on the development of neutrosophic differential equation. Some properties of neutrosophic number have been presented here. In Definition n,\u00a0m) system, where x.Here, we have considered different types of derivatives in the form of different (mentclass2pt{minimmentclass2pt{minim"}
+{"text": "Patent data is an established source of information for both scientific research and corporate intelligence. Yet, most patent-based technology indicators fail to consider firm-level dynamics regarding their technological quality and technological activity. Accordingly, these indicators are unlikely to deliver an unbiased view on the current state of firm-level innovation and are thus incomplete tools for researchers and corporate intelligence practitioners. In this paper, we develop DynaPTI, an indicator that tackles this particular shortcoming of existing patent-based measures. Our proposed framework extends the literature by incorporating a dynamic component and is built upon an index-based comparison of firms. Furthermore, we use machine-learning techniques to enrich our indicator with textual information from patent texts. Together, these features allow our proposed framework to provide precise and up-to-date assessments about firm-level innovation activities. To present an exemplary implementation of the framework, we provide an empirical application to companies from the wind energy sector and compare our results to alternatives. Our corresponding findings suggest that our approach can generate valuable insights that are complementary to existing approaches, particularly regarding the identification of recently emerging, innovation-overperformers in a particular technological field. Heat waves, droughts or melting glaciers in different parts of the world underline the need for a rapid green transition to mitigate the implications and to approach the challenges of climate change. While this involves structural changes across all sectors of today's society, the invention of new green technologies and their adoption by businesses play a key role for achieving a sustainable green transformation  provides an indication of the patent's technological importance, since these citations depict the extent to which other patents are making use and build upon its underlying invention. Notwithstanding this very appealing feature of patent citations, they are also subject to several distorting factors. For example, the citation intensity of patents varies over time and across technological fields and patent offices , which allows to investigate firms' technological strength and innovative quality using a dynamic perspective. This dynamic perspective is the core of our proposed framework, as it thereby extends the prior literature that typically uses static indicators  and additionally represent their corresponding average values (2a and 2b). Moreover, the sub-measures are characterized by the following two properties:First, the four sub-measures are all index-based, which means that their calculation steps take the patents of other companies from the same index as a benchmark into account. This allows to automatically mitigate distorting factors such as a company's size, geographical location, or technological area  the firms forming a stock index, e.g., the Nasdaq-100 for US firms, where c =100, (2) the firms assigned to a specific technology field, (3) the firms headquartered in a selected country, (4) the firms listed in a fund or firms active in an ESG technology.i represents end of year i, e.g., if i refers to 2022, it represents the end of the year 2022, i-1 then represents the end of the year 2021 etc. This means that the duration from due time (i\u2013x) to (i-x + n) is n years. At due time i, only active patent publications are accounted for, and the same holds true for i-1, i-2, and so on.To derive the index-based metrics, we consider a set of patents denoted by This definitions and assignment processes allow all subsequent investigations to be index-specific.Although several approaches are possible to depict a patent's technological quality, it is typically approximated by a patent's citations it received from patent offices. Our framework follows this approach but can also be flexibly adapted to other quality definitions. Hence, the following describes our concept to approximate patents' technological quality in very general terms, so it can be identically applied to any other kind of quality measure at the patent level.As a starting point, recall that existing patent quality indicators typically leverage information from patent citations. The idea behind this approach is simple: When an arbitrary patent A  is cited by a subsequently applied patent B filed at some patent office, its disclosed technology is somehow related to patent B. Often patent A is relevant to novelty for one or more claims in patent B which define the scope of the invention in patent B.However, using patent A's raw number of received citations as a proxy for its technological quality can be problematic, since received citations can vary greatly due to several reasons. On the one hand, the patent office's examiner may have made a misjudgment, or the quoted text passages from patent A do not relate to the core of the invention of patent A. In addition, examiners may be biased and prefer to cite patents from their own geographic area and possibly from specific companies. It is also conceivable that once cited patents appear in later citation analyses, they are cited more frequently than patents that have not yet been cited, but which describe the same or at least very similar technical content. Patent A can also be too young to appear in a citation, although it is technologically located in a highly competitive and highly valued technology-environment.technology micro cluster (tmc) comes into play: instead of simply counting the number of citations of patent A and calculating a quality score based on that number, we derive a tmc formed by y patents describing the technology that is closest to the one codified in patent A. We then use this tmc's average technological quality and adjust it for the patents that are assigned to the company of patent A. In our case, the quality of the tmc is derived based on the citation frequency of the patents in the tmc, which is then assigned to patent A . However, as stated above, alternative quality definitions are possible as well. We identify the closest patents to patent A and define its tmc based on machine learning process, because machine learning approaches are particularly well suited to calculate the textual similarity between patent texts  based on the set of all patents described by N, i\u03b1, N, i-1\u03b1, N, i-2\u03b1\u2026 N, i-y\u03b1, plus patent A itself, adjusted by the patents publications of firm fNf, \u03b1, i, Nf, \u03b1, i-1, Nf, \u03b1, i-2\u2026 Nf, \u03b1, i-y for the index \u03b1 and the period i, i-1, i-2 \u2026i-y yielding the set Ntmc (patent A):Following this logic, we calculate the tmc for patent A  is then defined as the mean value of the quality values (indicted by a bar over the q) of the Ntmb(patent A) patents:maxM, i\u03b1, M, i-1\u03b1, M, i-2\u03b1\u2026 M, i-n\u03b1 that forms the index alpha does not necessarily have to match the set of patents N, i\u03b1, N, i-1\u03b1, N, i-2\u03b1\u2026 N, i-y\u03b1 that is used to calculate the tmc. However, it is advisable to select patents for which a quality can be derived. For example, if the citation frequency is the method of choice, the selected patents N, i\u03b1, N, i-1\u03b1, N, i-2\u03b1\u2026 N, i-y\u03b1 should be of a certain age to have received any citations at all.At this point it should be noted that the set of patents Having outlined our chosen approach to approximate a patent's technological quality, we can now describe in more detail how we operationalize our 4 measures that define the DynaPTI indicator.Mf, \u03b1, i is the number of patents published in year i corresponding to firm f in the index \u03b1. The mean value of the technological quality q of these patents yields Qf, \u03b1, i = mean(q). Correspondingly, the technological quality of firm f assigned to the patents Mf, \u03b1, i-1, Mf, \u03b1, i-2\u2026 Mf, \u03b1, i-n is given by Qf, \u03b1, i-1, Qf, \u03b1, i-2\u2026 Qf, \u03b1, i-n. To calculate the technological quality change rate (sub-measure 1a), we first calculate the growth, i.e., the slope \u03b2 = \u03b2 of the linear regression line fitting the values Qf, \u03b1, i, Qf, \u03b1, i-1, Qf, \u03b1, i-2\u2026 Qf, \u03b1, i-n. The slope of the regression line is calculated based on the least squares method according towith the arithmetic mean value of the qualityand the arithmetic mean value of the due date yearsQf, \u03b1, i, n) represents the absolute growth and hence the absolute change of the technological quality of firm f assigned to the index \u03b1 with the patent portfolios Mf, \u03b1, i, Mf, \u03b1, i-1, Mf, \u03b1, i-2\u2026 Mf, \u03b1, i-n. To calculate the relative growth \u03b3 of the technological quality, we divide the absolute growth by the arithmetic mean value according to\u03b2, the mean value of the relative growth of the technological quality of all firms forming the index \u03b1, is calculated according toTo relate firm dQ,\u03b1,i,n is given byThe standard deviation f in the time period i, i-1, i-2\u2026i-n according to the standard scoreWe can then use these calculations to derive an index-based change rate for the technological quality of firm f assigned to patents Mf, \u03b1, i, Mf, \u03b1, i-1, \u2026 Mf, \u03b1, i-n is given by Mf,\u03b1, i, Mf,\u03b1, i-1\u2026Mf,\u03b1, i-n itself: The number of patents published in the corresponding year. To calculate the change rate of the activity (sub-measure 1b), we first calculate again the growth, i.e., slope \u03b2 = \u03b2 of the linear regression line fitting the values Mf,\u03b1, i, Mf,\u03b1, i-1, Mf,\u03b1, i-2\u2026Mf, \u03b1, i-n. The slope of the regression line is calculated based on the least squares method according toThe technological activity change rate related to the index \u03b1 is calculated in the same way as the technological quality change rate. The technological activity of firm with the activity's arithmetic mean valueMf, \u03b1, i, n) represents the absolute growth and the absolute change of the activity of firm f assigned to the index \u03b1 with patents Mf,\u03b1, i, Mf,\u03b1, i-1\u2026Mf,\u03b1, i-n.and Mf, \u03b1, i, n) is calculated by dividing the absolute growth by the arithmetic mean value according toThe information value of absolute changes must be considered as rather limited since this sub-measure can be biased in favor of firms with higher patenting activity. Hence, it is expected that firms with large patent portfolios tend to have larger absolute growth rates when referring to the change of the absolute number of active patent families. To account for this distorting size effect, the activity's relative growth \u03b3, the mean value of the relative growth of the technological activity of all firms forming the index \u03b1 according toTo relate the relative growth regarding the technological activity determined by the patent portfolio dM,\u03b1,i,n is given byThe corresponding standard deviation f in the time duration i, i-1, i-2\u2026i-n is then given byEquivalent to the calculations for the technological quality, the index-based change rate of the technological activity for firm f forming the index \u03b1 is calculated according toTo consider the mean value of the technological quality (sub-measure 2a) in a consistent manner with the change rates of the quality and activity, the mean value of the quality (equation 4) over the time duration i, i-1, i-2\u2026i-n for all firms The standard deviation f in the time period i, i-1, i-2\u2026i-n according to the standard scoreThe formulas above yield the index-based mean value of the technological quality of firm i, i-1, i-2\u2026i-m for all firms f is calculated according toThe average value of the technological activity (sub-measure 2b) is derived equivalently to the corresponding calculations for the technological quality. The mean value of the technological activity (equation 11) over the time duration And the standard deviation f in the time period i, i-1, i-2\u2026i-m according to the standard scoreThe formulas above yield the index-based mean value of the technological activity of firm m instead of n years like the other sub-measures. Of course, m can be set to n, but in practice the current technological activity  of a company is often considered instead of a longer time period, so in many cases m<n.Note that the mean value of the technological activity is given here for f, \u03b1, i, n, m, is calculated by simply adding the four sub-measures up. That is, the index-based change rate of firm f 's technological quality, \u03b4Q, f, \u03b1, i, n, the index-based change rate of its technological activity \u03b4M, f, \u03b1, i, n, the index-based mean value of its technological quality, The final value of DynaPTI, \u03b4f, \u03b1, i, n, mis 0:Due to the method of standard score, the mean value of \u03b4f can achieve a high indicator value if it has (i) a high technological quality (ii) a high technological activity (iii) an increasing technological quality, (iv) an increasing technological activity. Firms with an indicator value, \u03b4f, \u03b1, i,n,m > 0, are above average according to the DynaPTI measure, whilst firms with \u03b4f, \u03b1, i, n, m < 0 are below average. We next provide an illustration of this framework to demonstrate its implementation and main benefits.Firm In what follows, we demonstrate an application of the DynaPTI framework to present how it can be implemented and operationalized. We perform this application exercise for firms that are active inventors in over the recent past the technology field of wind energy. Although the primary goal of this application is to present an example implementation and not an assessment of a technology field, this selection to firms active in wind energy allows us to highlight how our proposed indicator can be used for corporate intelligence in a technology field that is highly important for the green transformation.In order to do this, the first step is to define an index \u03b1 of firms from the technology field of wind energy and to extract their corresponding patents for a given time window. We identify such firms and their patents based on data and a definition of wind energy patents provided by EconSight AG.y in equations (1) and (2) is set to y = 5. The DynaPTI for innovators in wind energy is then derived according to the specifications in the previous section and calculated using a Python script. The corresponding results can be seen in We then set the following restrictions and use the following parameters to calibrate the framework: First, to keep our analysis concise, we require that all patents we use for any kind of calculation must be assigned to EconSight's wind energy technology field. Second, we want to focus on relevant players in this area. To ensure this, we restrict our selection of patents to those from firms that have published at least 5 patents in the time period 2020\u20132022, and have at least 1% of their patents in the field of wind energy. Third, we aim to focus on the very recent past to have an up-to date evaluation. Hence, we restrict the selection of patents to wind energy patents published in the 3 years' time period 2020\u20132022 for the calculation of our 4 sub-indicators. Instead, the set of patents for calculating the tmc is formed by all patents in the field of wind energy, which were published in the time period 2015\u20132018, and is not restricted to any set of firms. Again, with regard to the tmc, the number of patents to calculate the parameter Global X Wind Energy ETF (if they are included in the fund).In According to our results, the two companies Siemens Energy AG and Vestas Wind Systems AS show particularly high DynaPTI values. Both companies have a very high sub-measure 2b and thus a particularly high patent activity in the technology field wind energy. Compared to the other companies in the index, Vestas Wind Systems AS also has the highest sub-measure 1a and thus the highest dynamic in the development of patent quality.Another interesting case is Vinci SA, which has a particularly high sub-measure 1b. This indicates that its patent activity has increased significantly in the last 3 years compared to the other companies. Moreover, the company Holcim Ltd has a particularly high sub-measure 2a and thus a particularly high average patent quality compared to the other companies. This means that the companies Holcim Ltd and Vinci SA are also rated very highly in the DynaPTI even though they only have a relatively small proportion of their overall patents in the wind energy sector (see column F).Turning to a comparison with alternative measures, let us first focus on column (G), where we have included the Patent Asset Index (PAI) scores from PatentSight, which is an established patent-based indicator for corporate intelligence that although lacks a dynamic component.Global X Wind Energy ETF if they are present in the fund. The two top-performing companies according to DynaPTI are also included in the ETF and have relatively high portfolio weights. However, several green innovation over-performers, such as Vinci, ThyssenKrupp or Holcim are not reflected in this ETF. This may be due to their relatively low specialization in wind energy. Yet, despite their relatively low overall specialization our dynamic patent technology indicator suggests that they may be important innovators in wind energy and could make significant new contributions to this technology field. Thus, our approach can possibly offer investors a data-driven framework to identify companies that may be neglected due to their size or specialization. Conversely, it might also be a tool to detect potential greenwashing from companies pretending to innovate in an ESG-related field but not showing significant performance based on our framework.A second main advantage of our indicator can be seen from column (H), where we report companies' portfolio weights in the Patent data has become an established source of information for both scientific research and corporate intelligence. However, most patent-based indicators fail to consider firm-level dynamics regarding technological quality and technological activity. Especially in rather dynamic technological areas that are particularly relevant for the green transition, this limitation can distort company assessments that are based on existing patent-based measures. In this paper, we have developed a framework to build a novel indicator, which we call DynaPTI, that tackles this particular shortcoming. Its main strength is that it provides researchers and practitioners a tool that is more reliable for up-to-date assessments about firm-level innovation activities.Our proposed approach is complementary to prior work and is based on three main building blocks: First, it focuses on index-based comparisons to mitigate distorting effects such as the technological area. Second, it uses a transformer-based approach to leverage textual information contained in patents. This procedure allows to approximate the technological quality of firms' innovation pipelines and to correct for distorting factors related to the patent examination process. Third, the indicator consists of four different sub-measures that capture technological quality and activity, as well as their corresponding dynamics over a specific time window. We operationalize these sub-measures using patent citations and patent applications as approximations for the technological quality and activity of firms, respectively. Note however that our proposed indicator is relatively generic and can be flexibly specified. Researchers and practitioners could thus easily adapt its empirical ingredients as long as there is corresponding temporal data available. For example, one may use patent claims instead of patent citations as a technological quality proxy.Yet, the main advantage of our proposed indicator is that it incorporates a dynamic perspective. This seems particularly useful for investigating companies in technological areas that are characterized by rapid changes, which is the case, for example, for several technology domains that are highly relevant for a successful green transition. We demonstrate this by providing an application of our framework to the wind energy sector. In doing so, we assess the strength of companies' innovation pipelines that are active in this domain based on different measures, including our own. Taken together, the results from this application exercise highlight the following: DynaPTI may be viewed as a tool that can uncover recently emerging innovation-overperformers in a particular technological field and is less biased in favor of large incumbents compared to existing patent-based indicators.Patent Asset Index. This is because DynaPTI puts less to no emphasis on innovations from the relatively distant past compared to static patent-based innovation indicators , how strongly is the calculation of the tmc influenced by the selected machine learning model. These parameter choices may depend on the underlying technology or the selected index: the faster a technology develops, the shorter the period should be defined. The period can also depend on the context in which the relevant index calculations are carried out: longer periods may have to be chosen for political decisions, i.e., for decisions at the economic management level. Ultimately, one must also consider that for patents with a completely new technological approach, the tmc calculation may lead to nonsensical outcomes, since such a patent would not have any semantically close counterparts.Hence, future research in the area of patent-based technology indicators may primarily focus on evaluating our measure's performance and those of other dynamic approaches in alternative settings. Another direction for future research would be to examine the parameter space of the model and, if necessary, identify meaningful values depending on the scenario. Furthermore, since our proposed framework is rather generic, it would be interesting to specify and calibrate DynaPTI based on alternative parameters  and data , and subsequently evaluate corresponding results. In principle, DynaPTI can even be expanded beyond patent data. Due to its index-based calculation and the method of the statistical standard score, parameters can be omitted or added at will. For example, it would be possible to include financial key figures such as sales and profits. With this regard, DynaPTI could also be interpreted and tested as an extension tool for classical financial analyses. Taken together, we believe that all of these open issues are interesting and important avenues for future research to improve patent-based indicators for scientific research and corporate intelligence.michael.freunek@econsight.ch.The data analyzed in this study is subject to the following licenses/restrictions: data is proprietary. Requests to access these datasets should be directed to MF: conceptual idea, methodological approach and calculation, empirical estimation, and conclusions. MN: literature, motivation, methodological evaluation, empirical evaluation, and conclusions. Both authors contributed to the article and approved the submitted version."}
+{"text": "The methodological design was quasi-experimental with a duration of 8\u2009weeks. The data were collected three times: pretest, posttest, and follow-up. The results showed differences favoring the experimental group compared to the control group after the implementation of the intervention program in the following variables: team identification (p <\u20090.001), role clarity (p <\u20090.001), intra-team communication , group cohesion (p <\u20090.05), social conflict (p =\u20090.001), commitment to the team (p <\u20090.001), inside sacrifice (p <\u20090.001), transactive memory systems , collective efficacy (p =\u20090.02) and team performance (p =\u20090.001). Consequently, the application of team-building strategies incorporated into specific technical-tactical training tasks in football seems to improve group dynamics in sports teams.The study aimed to analyze the effects of an intervention program based on team building developed in technical-tactical training tasks in football. Specifically, it examined the benefits of the intervention in variables related to the conceptual model of team building: role clarity, team identification, intra-team communication, cohesion, intra-group conflict, commitment to the team, inside sacrifice, transactive memory systems, collective efficacy, and perceived performance. The participants were 51 young elite footballers divided into an experimental group ( Within 1.1.This conceptual framework has served as a reference to develop interventions focused on the construction of sports teams . These iSecondly, the professional in charge of carrying out the intervention can be a key figure to develop the established strategies optimally. Previous studies have chosen two methods: (a) a direct method, in which the sports psychology specialist works directly with the players, or (b) an indirect method, in which the sport psychology specialist works exclusively with the coach, who is the one who implements the intervention . ResearcThird, the type of intervention focused on variables of the environment, structure, or processes of the team can also determine the program\u2019s efficacy. Overall, interventions focusing on goal setting  or teamwAnother relevant aspect of team training interventions is the consequences analyzed. In general, improvements have been studied in different measures of performance  and psyc1.2.Taking into account the existing scientific literature on the creation of interventions to improve group dynamics, this research seeks to develop an intervention program: (a) intervening on the inputs ; and team processes  of the model of Therefore, the main objective of the study was to analyze the effects of an intervention with team-building strategies integrated into training tasks with technical-tactical objectives within the team\u2019s game model to improve group dynamics and team performance. Accordingly, the central hypothesis of the study is that the intervention program developed will favor role clarity, improve team identification, optimize intra-group communication, increase group cohesion and commitment to the team, reduce intra-group conflict, increase teammate inside sacrifice and coordination in game situations, increase the levels of collective efficacy, and improve perceived performance.2.2.1.To develop the research, we followed the ethical guidelines of the Regarding the intervention program, a group of experts in sports psychology and football training was in charge of analyzing, relating, and integrating the technical-tactical objectives of the team , with the psychosocial variables of the model of The team-building strategies were carried out in 32 football training tasks  related to the main objective of each session and associated with the team\u2019s technical-tactical contents . The control and experimental groups both performed the same training sessions, except for the modifications proposed in the specific tasks in the experimental group.2.2.age =M 16.54, SD\u2009= 1.23; years of seniority in the club: years =M 7.87, SD\u2009=\u20091.31), and 24 players from the under-16 elite team in the control group . The intervention was carried out with four coaches  between 34 and 42\u2009years old , with a coaching license and experience of at least 5\u2009years in training categories. Sample selection was intentional by clusters, considering the geographical proximity of the teams and the working group\u2019s possibilities to access and monitor the sample.In the present study, participants were 51 male training footballers belonging to two teams of different categories but the same professional football club of the Argentine first division. Specifically, there were 27 players from the under-17 elite team in the experimental group (2.3.2.3.1.strongly disagree) to 9 (strongly agree).To evaluate role clarity, we used the Spanish version validated by 2.3.2.completely disagree) to 5 (completely agree).Team identification was assessed with five items  used in previous research . Items a2.3.3.almost never) to 7 .Intra-team communication was analyzed with the Spanish version of the SECTS-2 . This sc2.3.4.strongly disagree) to 9 (strongly agree).The Spanish version of the Group Environment Questionnaire developed by 2.3.5.never) to 7 .The Spanish adaptation of the Intra-Group Conflict Scale elaborated by 2.3.6.strongly disagree) to 5 (strongly agree).To measure players\u2019 perceptions of commitment to the team in the season, we used the Spanish version of the KUT Objective Scale KUT: . This sc2.3.7.totally disagree) to 9 .Players\u2019 perceptions of inside sacrifice were measured with the Group Sacrifice Scale (GSS), originally designed by 2.3.8.strongly disagree) to 5 (strongly agree).The Scale of Transactive Memory Systems in Sport (TMMS-S) developed by 2.3.9.bad) to 5 (excellent).This variable was analyzed with the instrument developed by 2.3.10.poor) to 10 (excellent) was used to evaluate the responses. This way of analyzing team performance seems to be ecologically valid and reliable  was used to test group differences in the dependent variables before starting the study. When significant group differences were observed in the pretest measures, they were included as covariates. Mixed-design ANOVAs  were used to check the effect of the intervention. If this analysis yielded a significant interaction effect, the main effect of time was calculated for each condition. The changes were considered significant when the value of p was less than p\u2009<\u20090.05.The data were analyzed with the SPSS 25.0 statistical program. First, means and standard deviations were calculated. Second, the normality of the data was checked with the Shapiro\u2013Wilk test. The data had a normal distribution, so parametric tests were used. Third, one-way analysis of variance (3.p\u2009=\u20090.133), ERP (p\u2009=\u20090.079), personal inside sacrifice (p\u2009=\u20090.485), or team performance (p\u2009=\u20090.265). On the contrary, However, there were significant pretest group differences in RR (p\u2009=\u20090.007), team identification (p\u2009<\u20090.001), distinctiveness (p\u2009<\u20090.001), positive conflict (p\u2009<\u20090.001), acceptance (p\u2009<\u20090.001), negative conflict (p\u2009<\u20090.001), IG-T (p\u2009=\u20090.035), ATG-T (p\u2009<\u20090.001), IG-S (p\u2009=\u20090.003), ATG-S (p\u2009<\u20090.001), social conflict (p\u2009<\u20090.001), task conflict (p\u2009<\u20090.001), commitment to the team (p\u2009=\u20090.001), teammate inside sacrifice (p\u2009=\u20090.003), specialization (p\u2009<\u20090.001), credibility (p\u2009<\u20090.001), coordination (p\u2009=\u20090.002), collective efficacy (p\u2009<\u20090.001), and individual performance (p\u2009=\u20090.007).Before staring the intervention, there were no significant group differences in SR&B (p\u2009<\u20090.001). Pairwise comparisons revealed that the control group decrease  from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009=\u20090.001). There was also a significant Condition x Time interaction for ERP (p\u2009<\u20090.001). Pairwise comparison showed that the control group decrease from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009=\u20090.001). There was a significant Condition x Time interaction for RR (p\u2009<\u20090.001). The experimental group showed an increase in this variable from pretest to follow-up (p\u2009=\u20090.009), whereas the control group showed an increase from pretest to posttest (p\u2009=\u20090.006) with a decrease from posttest to follow-up (p\u2009=\u20090.008). Finally, there was a significant Condition x Time interaction for team identification (p\u2009<\u20090.001). The experimental group showed an increase from pretest to posttest (p\u2009=\u20090.013) and from pretest to follow-up (p\u2009=\u20090.043), whereas the control group showed a decrease from pretest to posttest (p\u2009=\u20090.020) and follow-up (p\u2009<\u20090.001), and from posttest to follow-up (p\u2009<\u20090.001).p\u2009=\u20090.029). Pairwise comparisons showed an increase in this variable from pretest to follow-up (p\u2009=\u20090.004) and from posttest to follow-up (p\u2009=\u20090.001) in the control group. There was also a significant Condition x Time interaction for positive conflict (p\u2009<\u20090.001). The control group showed a decrease from pretest to posttest (p\u2009=\u20090.049), from pretest to follow-up (p\u2009=\u20090.004), and from posttest to follow-up (p\u2009<\u20090.001), whereas the experimental group showed an increase in positive conflict from pretest to posttest (p\u2009<\u20090.001) and from pretest to follow-up (p\u2009=\u20090.007). There was a significant Condition x Time interaction for acceptance (p\u2009<\u20090.001). Pairwise comparison showed decreases in the control group from pretest to follow-up (p\u2009=\u20090.004) and from posttest to follow-up (p\u2009<\u20090.001), whereas experimental group showed an increase from pretest to follow-up (p\u2009<\u20090.001), and from posttest to follow-up (p\u2009<\u20090.001). Finally, there was a significant Condition x Time interaction for negative conflict (p\u2009<\u20090.001). Pairwise comparison showed decreases in the experimental group from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009<\u20090.001).p\u2009=\u20090.001). Pairwise comparisons showed a significant increase from pretest to posttest (p\u2009=\u20090.001) but also a decrease from posttest to follow-up (p\u2009=\u2009<0.001) in the control group, whereas an increase from pretest to follow-up was observed in the experimental group (p\u2009=\u20090.005). Also, there was a significant Condition x Time interaction for ATG-T (p\u2009=\u20090.005). Pairwise comparisons showed significant decreases from pretest to posttest (p\u2009<\u20090.001), from pretest to follow-up (p\u2009=\u2009<0.001), and from posttest to follow-up (p\u2009<\u20090.001) in the control group. In contrast, the experimental group showed increases from pretest to posttest (p\u2009<\u20090.001), from pretest to follow-up (p\u2009<\u20090.001), and from posttest to follow-up (p\u2009<\u20090.001). Regarding social cohesion, there was a significant Condition x Time interaction for IG-S (p\u2009<\u20090.001). Pairwise comparisons showed decreases from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009<\u20090.001) in the control group. Likewise, there was a significant Condition x Time interaction for ATG-S (p\u2009=\u20090.038). Pairwise comparisons showed that the control group decreased this variable from pretest to follow-up (p\u2009< 0.001) and from posttest to follow-up (p\u2009<\u20090.001), whereas the experimental group showed an increase from pretest to posttest (p\u2009=\u20090.048), and also an increase from pretest to follow-up (p\u2009<\u20090.001). By contrast, there was no significant Condition x Time interaction for task conflict (p\u2009=\u20090.066), but there was a significant interaction for social conflict (p\u2009=\u20090.001). Pairwise comparisons showed that the control group increased this social conflict from pretest to follow-up (p\u2009< 0.001), whereas the experimental group showed decrease from pretest to posttest (p\u2009=\u20090.001) and also an increase from posttest to follow-up (p\u2009<\u20090.001).p\u2009<\u20090.001). Pairwise comparisons showed an increase from pretest to posttest (p\u2009<\u20090.001) and from pretest to follow-up (p\u2009=\u20090.015), but a decrease from posttest to follow-up (p\u2009<\u20090.001) in the control group, whereas the experimental group showed increases from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009<\u20090.001). Secondly, there was also a significant Condition x Time interaction for personal inside sacrifice (p\u2009<\u20090.001). Pairwise comparisons showed a decrease in this variable from pretest to posttest (p\u2009<\u20090.001) and from pretest to follow-up (p\u2009<\u20090.001) in the control group. Thirdly, there was a significant Condition x time Interaction for teammate inside sacrifice (p\u2009<\u20090.001). Pairwise comparison showed decreases in the control group from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009<\u20090.001), whereas increases were observed from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009<\u20090.001) in the experimental group.Analyzing commitment to the team and inside sacrifice, firstly, the results showed a significant Condition \u00d7 Time interaction for commitment to the team (p\u2009=\u20090.008). Pairwise comparison showed decreases from pretest to follow-up (p\u2009<\u20090.001) and from posttest to follow-up (p\u2009<\u20090.001) in the control group, whereas increases were observed from pretest to posttest (p\u2009=\u20090.001), from pretest to follow-up (p\u2009<\u20090.001), and from posttest to follow-up (p\u2009=\u20090.016) in the experimental group. There was a significant Condition x Time interaction for credibility (p\u2009<\u20090.001). Pairwise comparison showed a decrease from pretest to follow-up (p\u2009<\u20090.01) and an increase from posttest to follow-up (p\u2009=\u2009<0.01) in the control group, whereas increases were observed from pretest to posttest (p\u2009=\u20090.001). By contrast, there was not a significant Condition x Time interaction for coordination factor (p\u2009=\u20090.535).In relation to the TMS factors, there was a significant Condition x Time interaction for specialization (p\u2009=\u20090.021). Pairwise comparison showed a decrease from posttest to follow-up (p\u2009=\u20090.310) in the control group, whereas increases were observed from pretest to posttest (p\u2009=\u20090.020) and from posttest to follow-up (p\u2009=\u20090.03) in the experimental group. On the contrary, there was no significant Condition x Time interaction for individual performance (p\u2009=\u20090.092), but there was a significant Condition x Time interaction for team performance (p\u2009=\u20090.001). Pairwise comparison showed a decrease from pretest to follow-up in the control group (p\u2009=\u20090.045), whereas increases were observed from pretest to posttest (p\u2009=\u20090.003) and from pretest to follow-up (p\u2009=\u20090.012) in the experimental group.Regarding collective efficacy and performance, there was a significant Condition x Time interaction for collective efficacy  and at follow-up . Previous correlational studies have revealed the importance of roles  and teamConcerning the team processes, the different communication factors presented a similar line of results, with increases in the positive dimensions in the experimental group, mainly at follow-up , and a decrease in the negative dimension . On the other hand, the control group showed a decrease in the positive variables and an increase in the negative dimension at follow-up. In this sense, intra-team communication had already been identified as a key process that facilitates a better performance of group members . TherefoConcerning the model\u2019s outcomes, in the dimensions of group cohesion and team conflict, the experimental group showed an improvement over the control group in group cohesion but not in team conflict. Two relevant aspects can be extracted from the results: (a) on the one hand, tactical training tasks seem to improve both task and social dimensions in the team, which had not been achieved previously ; (b) on Continuing with the analysis of the remaining variables, after the intervention, commitment to the team and inside sacrifice presented group differences, with a positive trend in the experimental group compared with the control group. Given the previously found relationship between the two variables with team performance , this stConcerning the TMS, coordination improved in both groups without differences. The reason for this may be that, as the competition progresses, coordination improves, if only because of the training and matches played by the players. However, the dimensions of specialization and credibility did present differences, with a positive trend in the experimental group compared with the control group. In this sense, it has been proven that the creation and development of shared memory systems , specifiFinally, collective efficacy and team performance presented group differences, with a positive trend in the experimental group after the intervention program. Similar results were found by other intervention programs that integrated strategies with tactical training tasks , as coop4.1.Despite the contribution of the study, there are several limitations that must be taken into account for future work. Firstly, the study was conducted in a specific sport with players in training, so caution is recommended when applying some of the strategies in other collective sports or population groups. It would be interesting to analyze other age groups and other collective sports, which could develop team-building strategies associated with tactical training due to their similar characteristics. Secondly, it should be noted that many psychosocial variables linked to the intervention were analyzed, but there was no assessment of the technical-tactical components trained. Therefore, developing an analysis of behaviors related to technical-tactical aspects in training and competitions would be essential. Another limitation of this study is that it used quantitative assessments exclusively, and the involved agents did not assess the intervention program itself through a qualitative approach, which could provide relevant information to perfect the program development. Finally, it should be noted that the number of participants and teams was reduced, so it would be relevant to develop this training program with more sports teams to corroborate the positive results of this intervention.5.The main conclusion of the present study is that the intervention program with strategies based on team-building implemented in the experimental group\u2019s tactical training tasks improved almost all analyzed variables compared with the control group . Therefore, this study provides new knowledge on the development of intervention programs based on team building, mainly the integration of strategies from the model of The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by Bioethics Committee of the University of the first author (Protocol number: 239/2019). Written informed consent to participate in this study was provided by the participants\u2019 legal guardian/next of kin.JT and TG-C designed and performed the study, acquired and interpreted the data, and drafted the first version of the manuscript. JD-G interpreted the data and improved the manuscript. ML-G and FL designed the study, interpreted the data, had overall responsibility for the study, and improved the manuscript. All authors contributed to the article and approved the submitted version.Financial support provided by the European Regional Development Fund (ERDF) and the Government of Extremadura (GR18KA20).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher."}
+{"text": "Commonly used minimizer orders select more k-mers than necessary and therefore provide limited improvement in runtime and memory usage of downstream analysis tasks. The recently introduced universal k-mer hitting sets produce minimizer orders with fewer selected k-mers. Generating compact universal k-mer hitting sets is currently infeasible for k > 13, and thus, they cannot help in the many applications that require minimizer orders for larger k. Here, we close the gap of efficient minimizer orders for large values of k by introducing decycling-set-based minimizer orders: new minimizer orders based on minimum decycling sets. We show that in practice these new minimizer orders select a number of k-mers comparable to that of minimizer orders based on universal k-mer hitting sets and can also scale to a larger k. Furthermore, we developed a method that computes the minimizers in a sequence on the fly without keeping the k-mers of a decycling set in memory. This enables the use of these minimizer orders for any value of k. We expect the new orders to improve the runtime and memory usage of algorithms and data structures in high-throughput DNA sequencing analysis.Minimizers are ubiquitously used in data structures and algorithms for efficient searching, mapping, and indexing of high-throughput DNA sequencing data. Minimizer schemes select a minimum  A key parameter for evaluating and comparing sketching schemes is density   any L-long sequence. In terms of a complete de Bruijn graph (dBG) of order k, a minimum UHS is a minimum set of nodes whose removal leaves no path of length L \u2212 k + 1 nodes in the graph. Heuristic algorithms for finding a compact UHS include DOCKS  . A UHS ide DOCKS  and PASHde DOCKS , both ofdBG size .k, and currently, compact UHSs are available only for k \u2264 13. As a result, UHS-based minimizer orders could not be used in many applications that require larger values of k, such as long-read mapping . Polar-set-based sequence-specific minimizers achieved very low density for k \u2264 25  for alphabet \u03a3. Moreover, the same order is used for all L and a given k, unlike DOCKS and PASHA, which need to compute a UHS for every combination of k and L. Furthermore, the longest remaining path in a complete dBG after removal of an MDS was recently shown to be bounded by O(k3)  , so for k, precomputing, storing, and querying it become infeasible for large k. We overcome this limitation by presenting an efficient method to test in O(k) time if a k-mer belongs to the MDS, which enables computing the minimizers in a sequence according to our MDS-based order on the fly. Thus, the minimizer orders that we defined provide, for the first time, universal orders with low density that easily scale to any value of k and to any desired window length.As the MDS size grows exponentially in We begin by providing definitions and theoretical background and describing relevant related work  iff o(x1) < o(x2).A de Bruijn graph (dBG) of order k is a directed graph in which every node is labeled with a distinct k-mer, and there is a directed edge from node a to b iff the (k \u2212 1)-long suffix of a is the same as the (k \u2212 1)-long prefix of b. The edge is labeled with the (k + 1)-long merge of the two labels. A complete dBG has a node for every possible k-mer and an edge for every possible (k + 1)-mer. Paths in a dBG of order k represent sequences, and a path of w nodes represents a sequence of w overlapping k-mers.A minimizer scheme is a function fk,w,o:\u03a3w+k\u22121 \u2192 {0, \u2026, w \u2212 1}. Function f returns the position of the minimum k-mer under o in a given window of w overlapping k-mers . By convention, ties are broken by choosing the leftmost k-mer. The minimizers of a string S, denoted as L-long windows of S.A expected density of a minimizer scheme is the expected fraction of k-mer positions that will be selected as minimizers over an infinitely long random i.i.d. sequence. The particular density of a minimizer scheme on a specific sequence S  is the fraction of k-mer positions selected by the scheme on that sequence. The expected (particular) density factor is the expected (particular) density multiplied by (w + 1).The k \u2192 \u221e or w \u2192 \u221e and prove a general lower bound of The expected density factor of a random minimizer is two . Mar\u00e7aisk, k-mer order h, we say that minimizer order oh\u03a0, is compatible with \u03a0 and h if for i = j, then Given an ordered partition of \u03a3decycling set of a graph G =  is a set of nodes whose removal results in an acyclic graph. Finding an MDS  in an arbitrary graph is NP-hard (k. Mykkeltveit (k). A pure cycle is a set of nodes corresponding to all the cyclic rotations of some k-mer  (x is positive (negative) if x) > 0 (<0). All positive (negative) rotations of a k-mer are consecutive, and either all rotations have x) = 0 or the two blocks of consecutive positive and negative rotations are separated by at most one rotation with x) = 0 on either side (x) = 0, any arbitrary k-mer from the cycle can be selected.To determine which of the cyclic rotations of a , T = 3) . We say her side . The MDShttps://www-cs-faculty.stanford.edu/~knuth/programs/unavoidable2.w). This implementation uses the FKM algorithm  = 0 for all k-mer rotations, the lexicographically smallest k-mer is included in the decycling set. An MDS consists of \u0398(|\u03a3|k/k) k-mers.Mykkeltveit's algorithm has an efficient implementation owing to Knuth  k-mers such that any L-long string contains at least one k-mer from k-mer from w = L \u2212 k + 1 overlapping k-mers, and thus, the nodes represented by w-long paths in a complete dBG of order k |\u03a3|k+1L) for p iterations of node removal. Using DOCKS, small UHSs have been constructed only for k \u2264 11. Minimizer orders compatible with these UHSs were shown to have lower density than random orders  time and compared to determine if x is the first positive counterclockwise rotation. If x) = x\u2032) = 0, then the algorithm determines whether x is a lexicographically smallest rotation in O(k) time.For large values of Proposition 1in time O(k).Algorithm 1:Input: k-mer xOutput: Membership in the MDS fori \u2208  doci = sin(2\u03c0i/k)1:\u20032:\u2003x\u2032 = xk\u22121x0x1..xk\u221223:\u20034:\u2003ifx) > 0 thenx is the first rotation with x) > 05:\u2003ifx\u2032) \u2264 0 then return true6:\u2003\u2003else ifx) = 0 then7:\u2003ifx\u2032) = 0 thenx is the lexico. smallest rotation8:\u2003\u2003i \u2190 09:\u2003\u2003\u2003\u2003forj \u2208  do10:\u2003\u2003ifthen return false11:\u2003\u2003\u2003\u2003iftheni = 012:\u2003\u2003\u2003\u2003elsei \u2190 i + 113:\u2003\u2003\u2003\u2003ifthen return true14:\u2003\u2003\u2003\u200315:\u2003return falseProof.k-mer x is positive, negative, or nonpositive if x) > 0, < 0, or \u22640, respectively. Recall that a k-mer k-mers in the conjugacy class have x) = 0 and x is a lexicographically smallest rotation.The proof follows from the definition of k-mer x is the first positive counterclockwise rotation in its conjugacy class; that is, x has x) > 0, and the one-letter clockwise rotation of x, denoted x\u2032, has x\u2032) \u2264 0.For 1 above, line 6 returns true iff the input k-mer x, x\u2032 have x) = x\u2032) = 0 (lines 7\u20138), then all k-mers in that conjugacy class have zero embedding by x and returns false if there is a k-mer that is lexicographically smaller than x (line 11). Otherwise, it returns true if either all possible rotations are lexicographically larger than x  or x is a lexicographically smallest rotation but is identical to another rotation .For 2 above, note that if two consecutive rotations of a O(k) time. The loop beginning on line 10 can run for at most 2k times and performs constant time computations per iteration for a total running time of O(k).The embedding computations  take k-mer x in each conjugacy class rather than the first positive one. We refer to this set as the symmetric decycling set By symmetry, Mykkeltveit's construction can be used to create an MDS using the first counterclockwise negative Theorem 1 (remaining path partition).In any remaining path in a complete dBG after removing, all the positive nodes  precede all the nonpositive nodes.positive part, containing only positive k-mers, followed by a nonpositive part consisting of only nonpositive k-mers. The proof relies on two lemmas:In other words, a remaining path must consist of two distinct parts: a Lemma 1.The k-mers associated with all incoming neighbors of a node x in a dBG have the samex).Proof.y of x differ only in y0 and have embedding with All incoming neighbors Lemma 2.The pure cycles factor a complete dBG; namely, every k-mer belongs to exactly one of the pure cycles.Proof.k-mer is on some pure cycle corresponding to its rotations. Assume the contrary that k-mer x is on two distinct pure cycles, C1 and C2. Let y be the last common node in the path in x. Then, the edges out of y in the two cycles are distinct, contradicting the fact that both correspond to the cyclic rotation of y.Every Proof (Theorem 1).xi be the first nonpositive node in a remaining path x1, \u2026, xt and assume the contrary that there exists a positive xj for j > i. W.l.o.g. assume xj is the first with that property in the path. Let C be the pure cycle that contains xj. C exists, and it is well defined by y be the node preceding xj in C. By xj\u22121) = y). Because y is nonpositive, xj should be in C, a contradiction.Let double decycling set consisting of k-mers.By a similar argument, in a remaining path after removing We define a partition-compatible minimizer order based on double decycling sets with k and L values. Miniception uses lexicographic order by default, which was shown to have worse performance than random order. To be fair, here we modified Miniception to use the same random hash as our implementations and ran it with the recommended parameters.We compared the performance of our new MDS-based minimizer orders to random orders and to orders based on DOCKS, PASHA, and Miniception , across k-mer order. We calculated particular density factors on 10 randomly selected 10 million\u2013nt segments from Chromosome X of the CHM13 telomere-to-telomere human genome assembly  combination.UHSs for L, and the relative improvement of UHS- and MDS-based orders compared with random orders increases with k. Conversely, as L grows for fixed k, the density factors of the different methods tend to perform similarly to random because longer windows are more likely to contain multiple k-mers from the sets defining the order (UHS or MDS), and the k-mers within the set are ordered randomly. MDS-based orders have much lower standard errors than the others, likely because the decycling-set k-mers remain the same for all repeated runs regardless of the random seed.The MDS-based orders consistently perform similarly or better than UHS-based orders. As hypothesized, the double decycling-set order has lower density than the decycling-set order. Miniception performs better than random and worse than the UHS-based orders, as was previously shown . As expek-mer usage is not uniformly distributed in real genomic sequences. However, the overall shape of the density curves and the performance ranking among the methods remain the same.The particular density factors are presented in k greater than those that are feasible to run with DOCKS and PASHA. k = 20, 50, and 100 on random segments of the human X Chromosome. Average density factors over the repeated runs are shown without error bars for visual clarity. The same plots with error bars as well as the expected density factors for k = 20, 50, and 100 are in We compared the MDS-based orders to the random baseline order and to Miniception for values of k grows, the advantage of the MDS-based orders becomes even more pronounced, and the double decycling-set-based order improves more significantly over the decycling-set-based order. This is true in particular for smaller L, with the differences between the decycling-set-based and double decycling-set-based orders beginning to diminish as L > 2k. The advantage compared to Miniception is maintained for large values of k across most L values, and the MDS-based minimizer orders achieve density factors that are up to 20% lower than Miniception-based orders. Miniception-based orders achieve lower density for small L as MDS-based orders are similar to random in that regime because most windows do not contain a member of the MDS. In contrast, Miniception approaches its theoretical density factor of 1.67 while L \u2264 2k and converges to (but remains below) the performance of random for larger L. In most cases, the particular density factor is slightly higher than the expected density factor, but the overall shape of the performance curves and the relative performance of the methods are the same for both particular and expected density.As L increases, whereas the MDS-based orders converge to two. Interestingly, the shape of the density factor curves is similar to the lower bound with a minimum around L = 2k.There exists a consistent gap between the theoretical lower bound for forward schemes, which is not known to be tight for minimizers and converges to 1.5 as k < 20, the MDS is precomputed and stored as a boolean vector. Thus, k-mer set membership is determined with an O(1) lookup. The exponential growth of the MDS makes it impossible to precompute or store in memory for even moderately larger k. Instead, we compute k-mer set membership on the fly for every k-mer in O(k) time using k-mers are represented using two bits per nucleotide, our implementation in C++ can use CPU-supported 128-bit operations for k \u2264 63 . We used the GMP library (https://gmplib.org/) to support operations for k > 63. As a result, the process is an order of magnitude slower than CPU-supported operations. We report runtimes to compute minimizers of a random 10 million\u2013nt sequence for all methods and three values of k representing the different regimes in We report runtime measurements under three regimes of our MDS-compatible minimizer scheme implementations. For k and L values. The lookup and comparison used by the precomputed decycling set and UHS methods are also fast but limited to relatively small k. k. Our implementation's runtime increases by one to two orders of magnitude for k > 63. However, even the slowest double decycling order processes 10 million nucleotides in less than half a minute for k = 100, achieving much lower density than a random order. Miniception is implemented in Python and has a consistent runtime across all values of k but is much slower than other methods in two of the three regimes and achieves higher density than MDS-based orders.We implemented the pseudorandom order by a simple XOR operation and a comparison of the resulting integers. Thus, the random order is extremely fast for all kk-mers in a boolean vector. In contrast, the memory overhead of the random and MDS-based orders computed on the fly is negligible, and the memory usage is dominated by the sequence being processed. For the lookup-based methods, memory grows exponentially with k, and for a 10 million\u2013nt sequence, the memory needed to store the set begins to dominate the memory for the sequence starting at k = 14. The memory usage, measured as the maximum resident set size, for k = 19 reaches 33.6 GB and is prohibitively large for k = 20.The implementation of lookup-based methods for the precomputed MDS-based order and UHS-based orders represents all 4k. A major limitation of minimizer orders based on UHSs was the need to create and store the whole set in advance. Instead, we based our new order only on an MDS, avoiding the need to add k-mers to make the set universal. This bypasses the costliest steps in DOCKS and PASHA and generates minimizer orders that are even better in terms of their density factors. Furthermore, this approach enables calculating the minimizers in a sequence efficiently on the fly, without the need to store the set. We showed that based on Mykkeltveit's algorithm, we can determine in O(k) if a k-mer belongs to the MDS, and thus, MDS membership can be checked for all k-mers in a sequence. The resulting new orders are comparable or better in their density than UHS-based minimizer orders, thus achieving good performance while avoiding escalating runtime and memory usage with the increase of k.In this study, we developed a method to generate highly effective minimizer orders for any k and L \u2264 2k, the double decycling-set-based orders yielded much lower density than the decycling-set-based orders . In adde window .There are also open theoretical and technical questions arising from our study. It is necessary to explain why the densities of the MDS-based minimizer orders match the shape of the theoretical lower bound for the more general forward sequence sketching schemes. The gap observed between the MDS-based order and the lower bound should be studied, and hopefully, a tighter lower bound for minimizer schemes can be found. Performance analysis of our new minimizer orders in terms of other criteria, including maximum bin load  and consk > 63 to speed up runtimes for very large k. In addition, the implementations using precomputed UHS or MDS could use more efficient data structures to store the set, for example, Bloom filters  and as All code developed under this project is publicly available at GitHub (Supplement 1Supplement 2"}
+{"text": "H, its reciprocal degree distance is defined asH and H. The goal of this paper is to establish some sufficient conditions to judge that a graph to be \u0127-hamiltonian, \u0127-path-coverable or \u0127-edge-hamiltonian by employing the reciprocal degree distance.Given a connected graph  We call the sequence degree sequence for the network topology H. Throughout this paper we can assume that H from the symbols in the following.In this paper, we are only concerned with simple graphs . We assume these graphs are undirected, connected and finite. Let join (resp. union) of two graphs p vertices.We use H is \u0127-hamiltonian. Therefore 0-hamiltonian is similar to that of hamiltonian. A hamiltonian path of a graph H is nothing but a sequence of incident edges covering exactly all vertices in the graph H. At this moment, we call H traceable. In general, a graph H is \u0127-path-coverable if we can cover the vertex set by no more than \u0127 paths which do not have any two identical vertices. These paths are called vertex-disjoint in graph theory. Especially, 1-path-coverable is similar to that of traceable. We call a connected graph H \u0127-edge-hamiltonian (\u0127 is a positive integer) under the following condition: If we choose a group of vertex-disjoint paths which have less than or equal to \u0127 edges totally, the group must form a subgraph of some hamiltonian cycle of H. Standard graph theory terminology, see e.g., If the subgraph induced by Molecular structure descriptors are also referred to as topological indices. These indices form an important part of the theoretical and mathematical chemistry, which are used to describe the characteristics of chemical compounds H is connected, then we define the reciprocal degree distanceadditively weighted Harary index because this invariant is regarded as an additively weighted variant of the Harary index. The present name for If Denote In graph theory, it is often interesting and challenging to determine whether a graph has some kind of important graph property. For example, it is NP-complete to decide whether a given graph is hamiltonian \u0127-hamiltonian, \u0127-path-coverable and \u0127-edge-hamiltonian by using the reciprocal degree distance are given respectively in this paper. The following theorems are verified.Motivated by Theorem 1.1Letbe a graph withvertices. Ifthen H is \u0127-hamiltonian.Theorem 1.2Letbe a graph withvertices. Letandbe two integers.i) Foris even and, oris odd andor, ifthen H is \u0127-path-coverable. Ifthen \u03c0 enforces \u0127-hamiltonian.(b) Ifthen \u03c0 enforces \u0127-edge-hamiltonian., there exists an integer x is an integer, we haveAssume to the contrary that Case 1.H is \u0127-hamiltonian.Case 2.Case\u20091, and we are done for this case.\u00a0\u25a1Proof of Theorem 1.2H is not \u0127-path-coverable. Therefore according to k with x is an integer, we obtainAssume to the contrary that Case 1.Since Subcase 1.1.H is \u0127-path-coverable.Subcase 1.2.H is \u0127-path-coverable.Case 2.Since Subcase 2.1.Subcase\u20091.1, and we are done for this case.Subcase 2.2.H is \u0127-path-coverable.\u00a0\u25a1Proof of Theorem 1.3H is not \u0127-edge-hamiltonian. Thus by b), there exists an integer x is an integer, we haveAssume to the contrary that Case 1.H is \u0127-edge-hamiltonian.Since Case 2.Case\u20091, and we are done for this case.\u00a0\u25a1Since 4k-connectivity and \u03b2-deficiency of graphs are mainly studied in \u0127-hamiltonian, \u0127-path-coverable or \u0127-edge-hamiltonian by means of RDD. In this paper, these problems are completely solved. Compared with the previous research, we improved the proof method and assisted matlab to solve the problems.In the previous relevant research literature, Mingqiang An, Yinan Zhang: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper. Kinkar Chandra Das, Yilun Shang: Performed the experiments; Analyzed and interpreted the data; Wrote the paperThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper."}
+{"text": "The situation concerning adolescent mental health is a global public health concern, and the concept includes the ability to cope with problems of everyday life. A person\u2019s approach and attitude towards themselves, i.e., their self-esteem, affects mental health. The study aimed to appraise and deepen the scientific understanding of adolescents\u2019 self-reported self-esteem at age 12\u221213 from a resource perspective and test its ability to predict subsequent perceived mental well-being at age 17.n\u2009=\u2009654) were analysed using ANCOVA. The outcome variable, perceived mental well-being (MWB), covers the aspects of mental well-being inspired by the \u201cMental Health Continuum,\u201d representing positive mental health. Covariates were self-esteem (SE) and reported initially perceived MWB at age 12\u221213. Other independent explanatory variables were gender, the family\u2019s economy, and the mother\u2019s educational level.Data from the Longitudinal Research on Development in Adolescence (LoRDIA) prospective follow-up study of adolescents aged 12\u221213, and 17 . There was a significant but inverted U \u2013 shaped association between SE at age 12\u201313 and perceived MWB at age 17 [F \u2009=\u200919.02, \u03b2-0.057; CI -0.08\u2212-0.03, Eta\u2009=\u20090.03, Good self-esteem in early adolescence increases the likelihood of an unchanged favourable development of self-esteem and the probability of good perceived mental well-being. SE explained 18 per cent of the variation of MWB, and even more among girls. However, normal SE rather than high SE at 12 and 13 years is predictive of later mental well-being. Girls reported low self-esteem more often. Therefore, supporting self-esteem early in life can promote mental well-being in adolescence.The online version contains supplementary material available at 10.1186/s40359-023-01450-6. Adolescent mental health is a global public health concern and needs prioritisation . BesidesSelf-esteem involves an approach and attitude towards oneself that is either global or more specific . Global The theoretical base for the variable of mental well-being is the mental health continuum , consistAdolescence is the period in life when most developmental changes take place within a relatively short period. During this period, self-esteem generally fluctuates to a low level in childhood but increases throughout adolescence and young adulthood . TherefoWell-being as a concept relates to mental health. Mental health as well as self-esteem shows a gender bias: girls tend to report more emotional problems  and lowen\u2009=\u20091884) consisted of almost equal shares of boys  and girls . The research team visited the four municipalities to distribute and collect the survey responses in class.The Longitudinal Research in Development in Adolescence (LoRDIA) study started in 2013, following adolescents aged 12\u221213 to 17 in four municipalities in Southwestern Sweden and inviting the total population of sixth- and seventh-grade adolescents to participate. The participants (Data collection started in 2013 (Wave 1\u2009=\u2009W1); adolescents aged 12 and 13 agreed to participate, a total of 1515 children. At 17 years of age, the fifth wave of LoRDIA was collected, and 949 children participated. A total of 654 individuals responded to both waves for this particular study\u2019s relevant waves. A published report describes the LoRDIA planning and participants on p. 44\u201345 .A scientifically well-known and frequently used instrument  validateA variable assessing perceived mental well-being was created to test the relationship between positive mental health and self-esteem. The scale for perceived mental well-being (MWB) comprises a sum score from three questions: \u201cHow healthy do you think you are?\u201d, \u201cHow do you feel about life right now?\u201d, and \u201cI think my life has purpose and meaning.\u201d In W1, the response scale was a 3-grade rating scale from \u201cvery healthy to not healthy at all\u201d, but in W5, a 4-grade rating scale ranging from \u201ctotally healthy, quite healthy, not particularly healthy, and not healthy at all\u201d was used. For the second question: \u201chow do you feel about life right now?\u201c in W1, the response scale started from \u201cvery good and ranged to not particularly good\u201d. In W5, the response scale varied from \u201cvery good, pretty good, not particularly good, and not good at all\u201d. For the third question \u201cI think my life has purpose and meaning\u201d, the response scale in W1 ranged from \u201cyes to no\u201d and finally in W5 as follows: \u201ctotally agree, partially agree, takes a partial distance, and takes distance completely\u201d. When adding the three questions as a sum score, Cronbach\u2019s \u03b1 was .715 in W1 and .719 in W5, indicating high internal consistency in measuring positive mental health. The variables were recoded into high and low MWB in W1 as follows: 1\u2009=\u2009very healthy, 0\u2009=\u2009quite healthy, and not healthy. Corresponding for W5 was: 1\u2009=\u2009very healthy, and 0\u2009=\u2009all other alternatives. By handling each question this way, the sum score for MWB using the three questions varied from 0 to 3, indicating low, normal, or high positive mental health. Higher scores stand for better mental health. Categories described the groups, but the total sum was used in the forthcoming ANCOVA analyses as the outcome. In Wave 1, the range of the total sum was 0\u22126, and in Wave 5, 0\u22129.Gender, the mother and father\u2019s educational levels (secondary vs. post-secondary education), and the family\u2019s economy are relevant background variables. The variable of the family\u2019s economy comprised three questions: \u201cThe family\u2019s income in comparison with other families\u201d, \u201cThe family\u2019s income in comparison to other classmates\u201d, and \u201cI can afford things that are expensive to me.\u201d To every question, three levels of answers were applicable: \u201cworse\u201d, \u201cmedium\u201d, or \u201chigh\u201d (0\u20132). The Cronbach\u2019s \u03b1 for the sum score of the family\u2019s economy was .617, its range was 0\u20136, and it was divided into three categories: worse (0\u20132), medium (3\u20134), and high (5\u20136). All of these variables are fixed factors in the ANCOVA.Self-rated SE and perceived MWB at 12\u201313 and 17 years of age were tested using an independent t-test between groups divided into gender and a paired sample t-test for the dependent association over time. Categorical descriptions were made using Chi-square and cross-tables, and gender differences in the MWB and SE categories were investigated.p\u2009=\u2009.098) and using a random independent sample were fulfilled. The association was also checked for independent background variables, such as gender, the mother\u2019s educational level, and the family\u2019s economy.A general linear analysis of Covariance (ANCOVA) was conducted using the continuous variable self-esteem (SE) at age 17 as the outcome and concomitantly including the continuous sum scores SE and perceived MWB as covariates at age 12\u201313. The criteria for modelling normality and homogeneity via Levene\u2019s test (p\u2009=\u2009.319), and using a random independent sample were fulfilled. Background variables  which were gender, mother\u2019s educational level, and family\u00b4s economy, were used as categorical variables at age 12\u221213, chosen from previous research [p\u2009<\u2009.05.To analyse the relation between SE and subsequent perceived MWB, a general linear model, ANCOVA was used in several steps. The dependent continuous variable perceived MWB at 17 years as an outcome. First (a), the association of initial perceived MWB at age 12\u221213 (W1) with the outcome of MWB four years later (W5) was calculated in a univariate model. In a second univariate model (b), initial perceived MWB was replaced with initial SE at age 12\u221213 (W1) as a continuous variable. In a third model (c), these two covariates (SE and perceived MWB at age 12\u221213) were used in a multivariable model. The criteria for conducting the variance models, ANCOVA, normality, homogeneity of variance via Levene\u2019s test p\u2009=\u2009.3, and usiresearch . The datn\u2009=\u20091472, vs. those participating in both waves, n\u2009=\u2009936, and perceived MWB with the corresponding figures n\u2009=\u20091414 vs. n\u2009=\u2009948 was compared. No significant difference was detected when comparing the mean values using an independent t-test for those participating in one versus two waves. The results are presented using descriptive statistics and variance models, including the \u03b2 and F-values. SPSS version 27 was used for all statistical analyses.SE in those participating only in Wave 1, n\u2009=\u2009654, 57% girls), indicating significantly more attrition in boys. Both SE and perceived MWB were stable over time. However, there was a slight and significant decrease in SE .The correlation between SE at 12\u221213 and 17 years) showed a stable trend during adolescence  at age 17 (W5), separately for girls and boys.Re-analysing the hierarchical ANCOVA separately for boys and girls showed differences between girls and boys. The outcome of MWB at the age of 17 depended more for girls on their mother\u2019s education than for boys. For boys, a difference was present regarding SE as the sole covariate with a significant association for families\u2019 economy, which was in line with results from the total sample in the ANCOVA models a and b (see Table\u00a0The study aimed to appraise and deepen the scientific understanding of adolescents\u2019 self-reported self-esteem (SE) at age 12\u221213 from a resource perspective and test its ability to predict subsequent perceived mental well-being (MWB) at age 17. SE was significantly negatively associated with perceived MWB, explaining 18 per cent of the variance in a hierarchical ANCOVA model, including initial MWB as a covariate. For every additional point on the SE scale at age 12\u221213, adolescents rated their MWB at 17 years by 0.06 units less. Arguably, normal SE rather than high SE at 12\u221213 years is predictive of later mental well-being. The negative correlation may also be connected to girls\u2019 lower initial SE than boys. The association was not surprising, though earlier research has reported associations between self-esteem and mental disorders [Girls often report more internalising mental health problems, and gender differences have previously been shown . In thisMental well-being is important for boys as well. In a school-based survey in Norway, a similar result was found regarding self-esteem, gender, and life satisfaction, where girls reported lower SE and boys had higher quality of life . In our In this study, self-esteem was stable with a slight decrease, while previous research has indicated that self-esteem increases with age . HoweverThirty per cent of the adolescents with high self-esteem reported good mental well-being, while 16 per cent had low mental well-being. However, most had good mental well-being when looking at those with low self-esteem. However, in another study, boys seemed to have a higher mental well-being in both the young and older age groups . A revien\u2009=\u200974501) following students aged 12 to 19, Romano et al. [Global self-esteem is connected to psychological well-being , and thio et al.  found a o et al. , arguingo et al.  which ago et al.  with betA mother\u2019s educational level was significantly associated with initial SE and MWB for girls, which aligns with  findingsp\u2009=\u2009.269 vs. p\u2009=\u2009.346) could be detected, pointing at a random dropout.In all longitudinal studies, participant drop-out is an almost inevitable event, and at the same time, a longitudinal study design is a strength. In this study, the total population of 12\u221213-year-olds from four municipalities was invited, and the majority participated. However, in senior high school, at age 17, adolescents were more spread out and more difficult to contact, increasing the dropout rate. While 1472 participated in the first wave, only 779 participated in the fifth regarding SE vs. 1414 in the first wave and 746 in the fifth regarding mental well-being. Of these, only 654 responded to both waves and questionnaires. Looking at those participating in Wave 1 but not in Wave 5 vs. those participating in both, we see a somewhat higher attrition rate among boys. Regarding SE and MWB, a slight non-significant difference in the mean scores . The strength of obtaining ready-collected longitudinal data is hampered by what variables were included and when the data related to them were collected. An outcome variable had to be developed, which was not validated as a scale in other studies. Theoretically and also according to a statistical evaluation, these variables fit together. The questionnaire lacked a specific item measuring social well-being as the third aspect of the mental health continuum, which may, besides the regression to the mean phenomenon, have impacted the negative association between initial self-esteem and subsequent mental well-being in the ANCOVA models. However, when creating the variable, the aim was to assess similar content, as is the case concerning the well-validated scale health continuum created by Westerhof and Keyes . AnotherGood self-esteem in early adolescence predicts a continuation of a favourable situation and increases the probability of subsequent good mental well-being. Adolescents\u2019 mental well-being explains their self-esteem by 18 per cent, especially among girls. This highlights the question of sophisticated measuring instruments from a gender and resource perspective. Other researchers have also focused on these methodological aspects, which supports further research on handling the complex mental health situation. Accordingly, supporting self-esteem early in life can promote mental well-being.Additional file 1. Table of Flowchart within LoRDIA regarding self-esteem (SE) and mental well-being (MWB)"}
+{"text": "R-modules to finitely generated R-modules, for any commutative ring R whose spectrum is Noetherian. As Erman\u2013Sam\u2013Snowden pointed out, when applying this with R-module\u00a0M we associate a topological space, which we show is Noetherian when In a previous paper, the third author proved that finite-degree polynomial functors over infinite fields are topologically Noetherian. In this paper, we prove that the same holds for polynomial functors from free  K is a functor P from the category of finite-dimensional K-vector spaces to itself such that for any two finite-dimensional vector spaces V,\u00a0W the map P is a polynomial functor and U a constant vector space, then the functor V the vector space P has finite degree, which we will always require, then\u2014much like a univariate polynomial and its shift by a constant\u2014P and A polynomial functor over an infinite field P is a rule X that assigns to a vector space V a Zariski-closed subset X(V) of P(V) in such a manner that for each X(U) into X(V). In earlier work   is that if R has a Noetherian spectrum, then so does the polynomial ring R[x]. This special case, a topological version of Hilbert\u2019s basis theorem, is easy and well-known; e.g., it also follows from -module.Let K yields that Note that tensoring with K replaced by R[1/r] for some nonzero r.The vector space R-module M. Then for each R such thatR[1/r] since their images in K. It follows that R[1/r]-module spanned by v is a linear combination of the first m basis elements and the basis elements do not satisfy any linear relation there. Hence To see this, extend M,\u00a0N be R-modules. Denote by R-algebras.We follow  is just the subring of R[N] consisting of all polynomials that are constant on fibres of the projection When R is Noetherian and M is finitely generated, R[M] need not be Noetherian.The following example shows that, even when K is a field of characteristic zero, and let R-module generated by a single element R[M] is the subring of R[x] spanned by all homogeneous polynomials R[M] is the vector space over K spanned by R[M] is not Noetherian, since the ideal R[M] by its ideal of nilpotent elements is K.Let M is finitely generated, then a certain topological space R[M] is also Noetherian. In Example\u00a0However, we will see later that if K of characteristic 2 and set oddi can only be in c is in (t). But for eveni, R[M] regardless of R[M] is the K-vector space with basisNow consider a field B is an R-algebra, then the base change functor from Definition\u00a0R-algebra homomorphism B-algebra homomorphism If R[M] is the subring of R[x] spanned by all homogeneous univariate polynomials f such that Let B is a localisation of a domain R, then the map is an isomorphism:However, when R is a domain. Let M be a finitely generated R-module and let S be a multiplicative subset of R not containing 0. Set Suppose that M and embed R[M] as a graded R-subalgebra\u00a0A of B of O be the kernel of the R-module homomorphism s gives R is a domain, the same holds over R and hence R-module M. Hence The first and last isomorphisms are standard. For the middle isomorphism, we choose generators Like in ordinary algebraic geometry, the coordinate ring of a direct sum is the tensor product of the coordinate rings.M,\u00a0N be finitely generated R-modules. ThenLet R[M] and R[N] induce elements of R-linear map R-algebras. Denote by R-submodule of d,\u00a0e). It suffices to show that M,\u00a0N are free. In this case, we get R-linear maps from finitely generated free R-modules. Then we see thatElements of M is free. In that case, by Lemma\u00a0R[M] is just a polynomial ring over R.Example\u00a0M a finitely generated R-module. To be precise, R-domains with R-algebra monomorphisms, in the sense of the following definition.We now construct the topological space element of F is an element of F(C) for some subset of F is a subfunctor of X that assigns to each X(C) into X(D) for all morphisms topological space overF is a functor as above and F including the subsets Let C to the set F(C) with the collection We note that all definitions that can be stated in terms of elements and (closed) subsets of a topological space carry over to topological spaces over \u201cinjections\" to refer to R-algebra monomorphisms.In what follows, we use the term X that assigns to each X(D) of X(D) into X(E) for all injections closed if Define D is an R-domain, then we can make R) on D is a domain. For any R-algebra homomorphism R-domains (not necessarily injective), the induced map If M. Note that in the definition of closed subsets of S to be independent of\u00a0D, i.e., not every rule assigning to We think of Base change). If B is an R-algebra, and D is a B-domain, then B, coming from closed sets defined by subsets of R. If X is a closed subset of B-domain D to X(D).. Clearly, the inclusion X of A closed subset This follows from the previous proposition since The proof of Theorem\u00a0R be a ring with Noetherian spectrum and r an element of R. Let R/(r). Then two closed subsets Let K be an R-field and let r in K is zero, then K is a r in K is nonzero, then K naturally is an R[1/r]-field. In this case, we have Suppose that Let The extension R be a ring.We now prove Proposition\u00a0If This is an application of  define the same closed subset in not define the same closed subset in If two ideals M be a finitely generated R-module. Is R[M] to closed subsets of Suppose that R be a domain, let M be a finitely generated R-module and let X be a closed subset of Let R[1/r], the R[1/r]-module M is free, say of rank m, and so X is a closed subset of monic polynomials in r such that f in the latter ideal whose leading monomial is not divisible by any of the leading monomials of the f we would find that By Lemma\u00a0R be a domain, M a finitely generated R-module, and X a closed subset of f vanishes identically on f vanishes identically on Let M is free of rank m. Let X. This time, for each nonzero monic polynomials in some power of which lies in r such that g be the image of f in g reduces to zero modulo g vanishes identically on As in the previous proof, it suffices to prove the statement in the case that R-modules into either For reasons that will become clear later, we will only be interested in polynomial functors from the category  commutes for every P has finite degree, i.e., there is a uniform bound U,\u00a0V the polynomial law d.A polynomial functor R-linear map  commutes for all U,\u00a0V. Note that post-composing with R-linear maps and hence, indeed, (linear) polynomial laws.Polynomial functors R-algebra A and R-modules U,\u00a0V,\u00a0W, let A-bilinear extension of the R-bilinear composition maps R-algebras A and For every R-modules U,\u00a0V, there is a natural A-linear mapA\u201d. Viewing  commutes; here A-linear extension of A is a polynomial ring over R, the mapRecall that for all mentclass2pt{minimP,\u00a0Q be polynomial functors. We define a polynomial transformationR-algebras A and Let R-module homomorphisms, and the latter are precisely the linear polynomial laws, polynomial transformations generalise morphisms of polynomial laws, and the latter are precisely the linear polynomial transformations.Just like polynomial laws generalise R is an infinite field, then a polynomial functorR-vector spaces to itself such that for all R is a field but not necessarily infinite, then a polynomial functor If et-up in . If R isr\u2013Suslin .Many of our proofs will involve passing to the case of (infinite) fields and invoking arguments from . This isBase change). Let B be an R-algebra and let P induces a polynomial functor B-module U fix a B-module isomorphism R-module of the same R-rank as the B-rank of U. Then, set B-algebra A, we need to assign to every  and the outermost Let P has the same degree as P and will play a role in Sect.\u00a0P takes values in P.The dual functor U be a finitely generated free R-module.Let shift of P by U.We define the shift functor P.The composition R is an infinite field) carries over to the current more general setting. The proof in -modules for all R[1/r]-module.Let R[1/r].Note that we do not claim that the complement is itself the evaluation of another subobject; i.e., P. If P has degree 0, then so does S and then the statement is just Lemma\u00a0P is d.Again, we proceed by induction on the degree of n we havem, P,\u00a0S. By Lemma\u00a0Schur Algebras. To introduce these, let R-modules, we obtain a mapR-module. Indeed, if U is free with basis The Friedlander\u2013Suslin lemma relates polynomial functors of bounded degree to representations of certain associative algebras called R-module Schur algebra of degreeonU, and (given a basis of U), the basis distinguished basis.The The Schur algebra is associative  naturally carries the structure of an P(U) via U.Now suppose that :A-algebra A-module\u00a0To conclude this section, we observe that Schur algebras behave well under base change: if R be a domain and let R. Recall that the base change functor yields a polynomial functor Let K and assume that Q of P in the category of polynomial functors Let Q is a functor into R is not a Noetherian ring.Note that we don\u2019t require that In order to prove this proposition, we use the following lemma.A be a (not necessarily commutative) associative R-algebra and N an A-module that is, as an R-module, finitely generated and free. Suppose that Let R-basis of N. For each structure constants determined byR whose set of k-dimensional k consider the J are a R and whose other entries are variables R on which the coordinates are precisely these Let k-dimensional k and any k-set Let R  M.So let R[1/r]-module with basis R equal to R[1/r] and A equal to By Lemma\u00a0P is a fixed polynomial functor Closed subsets of a polynomial functors play the role of affine varieties in finite-dimensional algebraic geometry. In this subsection, For any P. A subset of X that assigns to each X(U) of closed if X(U) is a closed subset of\u00a0closure of X is the closed subset U for all We define U,\u00a0V be finitely generated free R-modules, let D be an R-domain and let X(V)(D). In the particular case where X(U) is preserved under the polynomial action of X be a subset of Q. Then P.It is worth spelling out what this means. Let X to be the rule assigning U for all R-algebra over the category For Base change). If B is an R-algebra, then we obtain a closed subset R-module such that (We will use the following lemmas very frequently in our proof of Theorem\u00a0R be a ring with Noetherian spectrum and r an element of R. Let R/(r). Then two closed subsets Let X(U),\u00a0Y(U) for every This follows from Lemma\u00a0Let X(U),\u00a0Y(U) for every This follows from Lemma\u00a0R-domains D defines a closed subset Y is the biggest closed subset of g is in the ideal of Y(U).Let Y(V) is a subset of Y is a subset of Y is a closed subset of Y(V) is a closed subset of\u00a0It is easy to check that R-algebra A, consider the mapD be an R-domain and take p as an element of D, we find thatLet p while the left hand side also has the requirement that D-domain E. So It is not true in general thatR-algebra R[P(U)] has two natural gradings: first, the ordinary grading that each coordinate ring R[M] of a module M has ] is the tensor product of the i and use these to define a grading on R[P(U)], called the standard grading. The standard grading has an alternative characterisation, as follows: j if f of standard degree j.Let For any closed subset D be an R-domain. Thenf are also contained in Take R be a ring whose spectrum is Noetherian and let In this section we prove Theorem\u00a0R has finitely many minimal primes R is a domain, we write Since We will prove the following stronger statement which clearly implies Theorem\u00a0R,\u00a0P,\u00a0X) be a triple consisting of a domain R with Noetherian spectrum, a polynomial functor R,\u00a0P,\u00a0X) satisfies the following conditions: X eventually stabilises.Every descending chain f vanishes identically on There exists a nonzero Let (Condition (2) of the theorem means that P, Noetherian induction on X\u2014for details, see below.The proof of Theorem R,\u00a0P,\u00a0X), we denote conditions (1) and (2) of Theorem\u00a0For any fixed triple R; or(ii)R[1/r] of\u00a0R, e such that the homogeneous parts In both cases, we write R,\u00a0P). The reflexive and transitive closure of the relation To prove the theorem for The partial order on Suppose that we had an infinite sequenceEach step Let By Lemma\u00a0R/(r). Assume that Let R,\u00a0P,\u00a0X) follows from condition (1) for R,\u00a0P,\u00a0X) follows from condition (2) for By Lemma R,\u00a0P,\u00a0X) by Combining this lemma with our induction hypothesis, we see that in order to prove R with Noetherian spectrum. Recall that K is the fraction field of R.Now let R-module, there exists a nonzero R,\u00a0P,\u00a0X) by d times, we may assume that the base change P.Suppose first that the base change  Theorem\u00a0, we thenM of the top-degree part P whose base change with M exists after passing from R to a suitable finite extension of one of its localisations.We want a polynomial subfunctor R[1/r] of R and a polynomial subfunctor M of the top-degree part of the polynomial functor There exist a finite extension N of\u00a0K of R. Let R[1/r] of R since the R[1/r]. Consider the submodule M of The R,\u00a0P,\u00a0X) by R. We now prove a version of Lemma\u00a0Let Assume that R,\u00a0P,\u00a0X). Let R. Pick any nonzero R,\u00a0P,\u00a0X) with this particular r.By Lemma\u00a0f be an element of f is naturally induces an element of f vanishes on R, for any r, then the prime ideal f vanishes identically on Indeed, let R,\u00a0P,\u00a0X) by M of the top-degree part P such that the base change We replace (R-module P(U) is the direct sum of a finitely generated free R-module and the  R-module M(U). In particular, both P and Proposition R by a further localisation R[1/r] which ensures that, if Let P(U) is the direct sum of the R-modules M(U) and X(U) but does not lie in the vanishing ideal of the pre-image in R[M(U)] have positive degree, so that a degree-0 homogeneous element of R[P(U)] that lies in the ideal of X(U) is an element of X(U) is the Cartesian product of U. We order closed subsets of We perform the same inner induction as in , \u00a72.9. LY of X, we have R,\u00a0P,\u00a0X). Condition (2) for  follows from condition (2) for f as a polynomial in the coordinates on M(U) with coefficients in First suppose that X(U) but not on the preimage in f as a polynomial in the coordinates on R[M(U)] with coefficients in f does not vanish identically on the pre-image of R-basis of M(U) and extend this with R-basis of P(U), inducing an isomorphism t turns this expression intoNext, suppose that P(U), we may write K so that R[1/r] containing all R by R by R-domains D. Define Y to be the biggest closed subset of\u00a0X where\u00a0h does vanish.Let R-domains D.We haveY is the intersection of X with the biggest closed subset of\u00a0h vanishes. So the lemma follows from Lemma\u00a0The closed subset X. Since Y stabilise. This settles part of condition (1) of Y. This will afterwards be used to settle both condition (2) for Let M(V) is a submodule of R-modules M(V) and N(V) does not depend on the choice of section.In , gives that then V. Recall that the degree of the polynomial functor R by the localisation R[1/r] and may henceforth assume that We now replace P,\u00a0R,\u00a0X), we will first prove an analogous statement for the localised shift.To establish condition (2) for  with coefficients in Z be the closure of the projection of g and V, one concludes that g itself, vanish identically on Assume that Now we can establish condition (2) of g vanishes identically on There exists a nonzero V, such an r exists by Proposition\u00a0r\u2019s, the same applies to a finite number of V\u2019s, so we may restrict our attention to all V of sufficiently large rank; we will do this in the proof.For each fixed R by a localisation R[1/r], we know that if By the inner induction hypothesis, after replacing V has rank at least that of U. Hence we may replace V by For any g that vanishes identically on R by a localisation that does not depend on g or V), g also vanishes identically on g then vanishes identically on Such a Y, the Z defined in the proof is not a subset of X in the sense of Definition\u00a0Note that, unlike X. Recall from Sect.\u00a0Y stabilise. Now, consider again the projection P, we have Noetherianity for Finally, we prove condition (1) of Let Since X is the following result.By the lemma, the fact that the sequence of The sequence m be the rank of U. As in equation Let t}(\u2217) in , \u00a72.9, wmentclass2pt{minimX is Noetherian. This concludes the proof of condition (1) for  and hence the proof of Theorem\u00a0Since both the sequence of entclass1pt{minimaTo illustrate that the proof method for Theorem\u00a0n with integral coefficients for all For each (Proof sketch) Both statements follow by inductions identical to the one for Theorem\u00a0X be the closed subset defined as the image closure of the polynomial transformation n for n for Take"}
+{"text": "The union-closed sets conjecture states that, in any nonempty union-closed family  For that purpose, every set A and denote i among all sets in Let Conjecture\u00a01\u00a0(Frankl Union-Closed Sets Conjecture). This conjecture equivalently states that, for any union-closed family e, e.g., ,4,5. We e, e.g.,  for moreearchers ,9,10,11.earchers  further earchers ,13,14. Bearchers  showed tgiven in .The present paper further develops Gilmer\u2019s (or Sawin\u2019s) technique to derive new constants (or bounds) in the optimization form for the union-closed sets conjecture. These bounds include Sawin\u2019s improvement as a special case. By providing cardinality bounds on auxiliary random variables, we make Sawin\u2019s improvement computable and then evaluate it numerically which yields a bound approximately x. That is, the PMF of this measure takes the value 1 at x and takes the value 0 at other points.To state our result, we need to introduce some notations. Since we only consider distributions on finite alphabets, we do not distinguish between the terms \u201cdistributions\u201d and \u201cprobability mass functions\u201d. For a pair of distributions For a joint distribution e, e.g., . ClearlyA. We regard the set in >1}.If we choose bound in  since, fby Sawin , we can Substituting Proposition\u00a01.\u00a0For where the infimum is taken over all distributions and 1 at 0 at other points).with As a consequence of the two results above, we have the following corollary.Corollary\u00a01.\u00a0If The proof of Corollary 1 is given in https://leiyudotscholar.wordpress.com/ (accessed on 1 May 2023.) More decimal places of Sawin\u2019s bound . i-th distribution i-th objective function For a conditional distribution  follows j in the last line is the optimal i attaining the minimum in HB be a finite subset of Let  in  and 7)..B be a fTherefore,f a,b in ). \u25a1A a.s. The union-closed sets conjecture states that such a code exists if and only if The breakthrough made by Gilmer  shows thduced in ). It is Furthermore, as an intermediate result, it has been shown that given in , expressFor simplicity, in this paper, we only consider the maximal correlation coefficient as the constraint function. In fact, the maximal correlation coefficient used here can be replaced by other functionals. The key property of the maximal correlation coefficient we used in this paper is the \u201ctensorization\u201d property, i.e.,  in fact was usedons, see ,21,22. (\u0393n(t) in  (i.e., i"}
+{"text": "M,\u00a0g) with horizon boundary M,\u00a0g) has non-negative scalar curvature, and the boundary M,\u00a0g) that increase the scalar curvature. As a consequence, we show that equality holds in the above inequality if and only if the exterior region of  is isometric to a Schwarzschild half-space. Previously, these results were only known in the case where Building on previous works of Bray, of Miao, and of Almaraz, Barbosa, and de Lima, we develop a doubling procedure for asymptotically flat half-spaces ( M,\u00a0g) be a connected, complete Riemannian manifold of dimension R(g) and non-compact boundary M.Let  is an asymptotically flat half-space if there is a number M whose complement is diffeomorphic to We say that  satisfies suitable energy conditions. As noted in [Escobar has studied asymptotically flat half-spaces in the context of the Yamabe problem for compact Riemannian manifolds with boundary; see  and alsothe work  of Schoethe work . AlmarazM,\u00a0g) be an asymptotically flat half-space of dimension M,\u00a0g) is isometric to ([R(g) across As explained in , \u00a72, thesee also , p.\u00a0207.Theorem  Bray in  in the c Bray in  in the cAlmaraz, de Lima, and Mari  have stuTo describe recent results in this direction, we recall the following definitions from ; see FigM,\u00a0g) has horizon boundary The connected components of Every minimal free boundary hypersurfaces or minimal closed hypersurfaces in We say that an asymptotically flat half-space  of dimension The proof of [The region entclass1pt{minima-2}; see , \u00a72.The second-named author has recently proved the following Riemannian Penrose-type inequality for asymptotically flat half-spaces whose horizon boundary is a connected free boundary hypersurface.M,\u00a0g) be an asymptotically flat half-space of dimension Then be an asymptotically flat half-space of dimension Let Let  be an asymptotically flat half-space of dimension ThenLet  can be locally perturbed to increase the scalar curvature near non-umbilical points of the boundary The approximation argument used to prove Corollary  and Yau  to charaM,\u00a0g) be an asymptotically flat half-space of dimension Assume thatLet  be an asymptotically flat half-space with horizon boundary M,\u00a0g) obtained by reflection across Let  unless R(g), preserves the condition m(g) nor To prove Theorem ality in  holds, tmentclasspt{minimaM,\u00a0g) is an asymptotically flat half-space of dimension M,\u00a0g) has horizon boundary In this section, we assume that , and  holds.i is sufficiently large. We consider the class of all embedded hypersurfaces of g in g in By , there iM,\u00a0g) is an asymptotically flat half-space of dimension M,\u00a0g) is conformally flat outside of a compact set. by reflection across In this section, we assume that  is conformally flat at infinity, that The assertions follow from the above construction, using that  be an asymptotically flat half-space of dimension Let , Proposition n and a sequence The assertion follows. Using Proposition M,\u00a0g) be an asymptotically flat half-space of dimension Let . By  such that M whereLet Next, we compute the linearization of t led to  also shoThere holds M from Lemma Suppose, for a contradiction, that there is entclass1pt{minimaentclass1pt{minimaOn the one hand, using that The assertion follows. M,\u00a0g) is an asymptotically flat half-space with horizon boundary m(g). Suppose that  and  of the pld space  with maslf-space  of mass In this section, we give an argument alternative to that in  to show For the statement of Theorem Let ld space .Following the argument given in , \u00a76, we andThe argument presented in Lemma"}
+{"text": "Nature Neuroscience 10.1038/s41593-023-01452-y, published online 5 October 2023.Correction to: In the version of this article initially published, there was an error in the title: \u201cchanges in amygdala GABAergic inhibition\u201d first appeared as \u201cchanges in gene amygdala GABAergic inhibition\u201d. The error has been corrected in the HTML and PDF versions of the article."}
+{"text": "Directed Feedback Arc Set, Directed Cutwidth and Optimal Linear Arrangement, also admit such algorithms on digraphs of bounded independence number. Towards this, we rely on the generic approach of Fomin and Pilipczuk , where to get the desired algorithms, it is enough to bound the number of k-cuts in digraphs of bounded independence number by a sub-exponential FPT function (Fomin and Pilipczuk bounded the number of k-cuts in transitive tournaments). Specifically, our main technical contribution is a combinatorial result that proves that the yes-instances of the problems (defined above) have a sub-exponential number of k-cuts. We prove this bound by using a combination of chromatic coding, inductive reasoning and exploiting the structural properties of these digraphs.Fradkin and Seymour  defined the class of digraphs of bounded independence number as a generalization of the class of tournaments. They argued that the class of digraphs of bounded independence number is structured enough to be exploited algorithmically. In this paper, we further strengthen this belief by showing that several cut problems that admit sub-exponential time parameterized algorithms  on tournaments, including  Directed Feedback Vertex Set (DFVS) and Directed Feedback Arc Set (DFAS).Tournaments form one of the most well studied families of digraphs, both algorithmically and structurally. In particular, whenever we try to generalize results that hold for undirected graphs to digraphs, arguably, one of the first families to consider is that of tournaments. Indeed, this has been the case when designing parameterized algorithms or approximation algorithms. Two problems that have been extensively studied on tournaments are DFVS admits a 7/2-approximation algorithm on tournaments , we denote the directed subgraph induced by the vertices of X. A set independent set of D if for any X is an independent set in the underlying undirected graph of D. The independence number of a digraph is equal to the size of the maximum independent set it contains. A directed Hamiltonian path in D is a directed simple path on all vertices in D. For a set of vertices ith vertex of the ordering.For any k-cuts in any digraph on n vertices with bounded independence number is k-cut in a directed graph D is a partition of the vertex set of D into two parts, D is a partition  of the vertex set V(D) such that there are no arcs from R to L in D.In this section, we prove that the number of k-cuts is easier. This simple observation is then exploited to its fullest using two main tools - (1) the Gallai-Milgram\u2019s Theorem and (2) chromatic coding. Let us state them formally. We begin by stating this key observation, followed by formally defining both these ideas.At the heart of the proof of Lemma\u00a0D be a digraph and V(D). For any k-cuts in k-cuts in D is at most Let k-cut  in D, there exists k-cuts k-cut in L,\u00a0R) is not a k-cut in D. To prove the lemma, observe that, it is enough to prove that for any D into o(k) parts such that it is \u201ceasier\u201d to bound the number of k-cuts in each of these parts, then we are done. At a high level, we will first partition the vertex set of D using chromatic coding, and then further partition each part of this partition using Gallai-Milgram\u2019s Theorem. We will then conclude by proving that the number of k-cuts in each of the sub-parts is linear in the number of vertices. We now state the Gallai-Milgram\u2019s Theorem formally.Thus, if we can partition the vertex set of -coloring family and then state the known results about the existence of such a families of bounded size. This result is called the chromatic coding lemma. For any graph G, a proper vertex coloring of G is a function Next, we state the technique of chromatic coding in its derandomized form. To this end, we first define Universal -Coloring Family) For integers n, k and r, a family n] to [r] is called a universal -coloring family, if for any graph G on the vertex set [n] with at most k edges, there exists an G. into at most k-cut  in D, there exists a partition u,\u00a0v) of , there exists for any For any digraph V(D) from the family i, Let entclass1pt{minimaL,\u00a0R) be some k-cut in D. Consider the digraph, say D with only the cut-arcs of . Note that h is a proper vertex coloring of h is a proper coloring of L,\u00a0R) are in u,\u00a0v) of , We will now show that D and integer k. For any arc  of a digraph and a partition u,\u00a0v) goes across the parts of this partitionifandFor any partitionof the vertex set of the digraphD, we say that ak-cut  inDrespectsL,\u00a0R) go across the parts of k-cuts in D is at most the sum of the number of k-cuts that respect a partition k-cuts that respect an arbitrary partition in D, an integer k and k-cuts in D that respect For the rest of this section, let mentclass2pt{minimk-cuts in D is at most The total number of k-cut  in D, there exists L,\u00a0R) respects To prove the lemma, we need to prove that for any mentclass2pt{minimk-cuts in D that respect k-cuts in D, it is sufficient to bound the number of k-cuts in k-cuts in D that respect Henceforth, let us fix D, let D. For any k-cuts in D that respect For any digraph k-cut  of D that respects L,\u00a0R) be some k-cut in D that respects u,\u00a0v), such that L,\u00a0R) respects Observe that to prove the lemma it is enough to prove that for any k-cuts that we want to bound. More precisely, we are now interested in bounding the number of 0-cuts in Thus, we have further narrowed down the class of D be a digraph on n vertices that has a directed Hamiltonian path. Then the number of 0-cuts in D is at most Let D has a directed Hamiltonian path, let D such that for each L,\u00a0R) in D. Let i be the smallest integer such that i, for all D. Since L,\u00a0R), which contradicts that  is a 0-cut.Since D where D, either does not contain any vertex in its right part (there is only one such cut) or contains some vertex, the total number of 0-cuts in D is at most Thus, for any We are now ready to prove Lemma\u00a0N be the total number of k-cuts in D. Consider the family D and integer k. From Corollary\u00a0k-cuts in D that respect Let mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimD is said to be d-out-degenerate, if for every subgraph H of D, there exists a vertex Dd-out degenerate if and only if it has a d-out-degeneracy sequence.In this section we give the proof of Lemma\u00a0D is a digraph on n vertices and d-out-degeneracy sequence of D. For any k-cut  in D is of type-i, if k-cut  in D is of type-0 if i cuts for all k-cuts. Observe that there is exactly 1 type-0 cut in any digraph.Throughout this section, k-cuts in D of type-i. Then the number of k-cuts in D is at most For any k-cuts in D of type-i, for an arbitrary D, then to bound the number of k-cuts in D, it is enough to bound the number of k-cuts in each D, where the number of parts of this partition is 4, compared to o(k) in Lemma\u00a0Henceforth, our goal is to bound the number of k, for any fixed If k-cut  in D of type-i, For any k-cut  in D of type-i, For any For a digraph D can be partitioned into 4 parts with the following properties. The digraph induced on the first part is either empty or belongs to k-cuts in such a digraph we will use an induction on second part of this partition, we prove that for any k-cut  of type-i, all the vertices of this part belong to L. Similarly, for the third part of this partition, we prove that for any k-cut  of type-i, all the vertices of this part belong to R. Therefore, there is a unique k-cut of type-i in the digraph induced by the second and third part. The last part of the partition has the property that the number of vertices in this part is \u201csmall\u201d. For the digraph induced by this part, we will get the desired bound by using Lemma\u00a01.4 on this digraph.Lemma\u00a0k-cuts of type-i in the digraph induced on each part of the partition, thereby bounding the number of k-cuts in D because of Observation\u00a0The proof of Lemma\u00a0mentclass2pt{minimk-cuts in c is the absolute constant hidden in the k-cuts in D for any digraph n vertices. We claim that for any positive integers n,\u00a0d and k-cuts in D.We prove the lemma using induction on entclass1pt{miniman and d, D is 1, then from Lemma\u00a0D such that for any k-cut  in D of type-i, k-cuts of type-i in D is at most the number of k-cuts in D, the independence number of k-cuts in D of type-i is at most k-cuts in D is at most Let us first prove that for any positive integers mentclass2pt{minimn,\u00a0d and for all k-cuts in any digraph n vertices is k-cuts in the digraph k-cut  in D of type-i, k-cuts of type-i in D is at most the product of the number of k-cuts in k-cuts in k-cuts in k-cuts in k-cuts of type-i in D is at most k-cuts in D is at most By induction hypothesis, let us assume that for any positive integers mentclass2pt{minimProof of Partitioning Lemma. We start by a lemma that gives an upper bound on the size of a digraph in k, if for all For any digraph Let G and integer r, if G does not contain a clique of size G be the underlying undirected graph of D. Let G. Since G, G is the underlying undirected graph of D, To prove the above-mentioned claim, we invoke Turan\u2019s Theorem , which Intuitive Ideas for the proof Lemmad-out-degeneracy sequence of D. Also recall that, the aim of proving Lemma\u00a0k-cuts in D of type-i. Consider any k-cut in D of type-i. By definition, D. Thus, they go to d-out-degeneracy sequence of D, the number of out-neighbors of d. This set of neighbors goes to the set X, of vertices that appear before D[X], then there are at least v to D. Thus, such a vertex v should always belong to same part as k-cut. Thus, such vertices goes to X has out-degree at most k. By Lemma\u00a0d-out-degeneracy sequence of D. Consider the partition of V(D) into three parts: Let D is a tournament, D and X, of size D of size D is bounded by i cut, for any k-cut  of type-i in D, L,\u00a0R) is a k-cut in D and i cut, i cut .d-out-degeneracy sequence of D, D, This concludes the proof. We now claim that the desired partition entclass1pt{minimaDFAS, Directed Cutwidth and Optimal Linear Arrangement when the input graph belongs to first is observing that the digraphs that are Yes-instances of these problems have sub-exponential FPT many k-cuts. The proofs for DFAS and Directed Cutwidth are based on showing that the digraph in the Yes-instances of the problems are k-out-degenerate, and hence, the bounds follow from Lemma\u00a0OLA, we show that if there is an ordering of the vertex set of a digraph of cost at most k then the cutwidth of this digraph is Directed Cutwidth, the number of k-cuts in the Yes-instances of OLA is also bounded. The second step is a procedure to enumerate all k-cuts of the input digraph. And the third is to do some dynamic programming procedure over these enumerated cuts to solve the respective problems. The last part of the algorithm (doing dynamic programming over k-cuts) is standard and is identical to the algorithm given by Fomin and Pilipczuk  has a dfas of size i, and L witnessing that D[L] has a dfas of size i, and We now prove that for any D[L] has a dfas of size at most i.Since D[L] has a dfas of size at most i and We will now prove that if D be a digraph. For an ordering V(D), the width of this ordering is cutwidth of D, denoted by V(D).Let k-cuts in the Yes-instances of DFAS.Next we bound the number of D,\u00a0k) is a Yes-instance of Directed Cutwidth and k-cuts in D is at most c is a fixed absolute constant.If  is a Yes-instance of DFAS, then there is an ordering, say V(D) of width at most k. Recall that, the width of an ordering D is k-out-degenerate. Thus, the bound follows from Lemma\u00a0If  is a No-instance of Directed Cutwidth. Otherwise, from Lemma\u00a0k-cuts in D. Let us denote this set by Directed Cutwidth problem by doing a dynamic programming over the set k-cuts. Let T be the dynamic programming table indexed by a k-cut T) to store the following information.T) for any Using the algorithm of Lemma\u00a0L, say L, say L, say L, for all We now prove that for any L, say We will now prove that if there exists an ordering of D be a digraph. For an ordering V(D), the cost of Let The following proposition gives an alternate definition of the cost of an ordering.D and an ordering V(D), the cost of this ordering is equal to  For a diLemma\u00a0D, if there is an ordering say V(D), of cost at most k, then For any digraph k, from Proposition\u00a0r, the number of arcs of length exactly r with tail in r. Thus, for any r, the total number of arcs of length at most r, with tail in Since k-cuts in the Yes-instances of OLA.Next we bound the number of D,\u00a0k) is a Yes-instance of OLA and k-cuts in D is at most c is a fixed absolute constant.If  is a No-instance of OLA. Otherwise, from Lemma\u00a0k-cuts in D. Let us denote this set by k-cuts. Let T be the dynamic programming table indexed by a k-cut T,\u00a0i) to store the following information.D has an ordering of cost at most k. We now describe how we compute T,\u00a0i) for any Using the algorithm of Lemma\u00a0L, say L, say L, say L, say L, We now prove that for any L, say i-cut in D. Since We will now prove that if there exists an ordering of DFAS, Directed Cutwidth and OLA on digraphs of bounded independence number. We thus significantly generalized known results for the restricted case of input digraphs that are tournaments. Towards this, we obtained an upper bound on the number of k-cuts in digraphs in DFAS, Directed Cutwidth and OLA admit polynomial kernels\u00a0on\u00a0In this paper, we designed sub-exponential time parameterized algorithms for"}
+{"text": "Cell Death Discovery 10.1038/s41420-023-01298-0, published online 25 January 2023Correction to: The original version of this article contained a mistake. Due to a typesetting error in the \u201cIntroduction\u201d section the references are out of order. We apologize for the error. The original article has been corrected."}
+{"text": "The proposed solution is scaled and allows the use of many trusted status authorities that issue explicit short-term certificates confirming the validity of explicit long-term certificates. Furthermore, we demonstrate that our signature scheme has a short-term non-repudiation property for the shell validity model.This paper addresses the certificate revocation problem and proposes the first revocable pairing-based signature scheme with implicit and explicit certificates (IE-RCBS-kCAA). We should no longer discuss whether to revoke certificates but how to do it effectively, ensuring both the scalability of the revocation operation and the non-repudiation of the signature in the short or long term. Under the computational difficulty assumptions of the modified collusion attack algorithm with  Digital signatures are a critical component that ensure the integrity, authenticity and non-repudiation of electronic documents. In public key cryptography (PKC), a digital signature is considered valid if it is mathematically correct and a related certificate is valid. The certificates are issued for a limited period , they can be revoked  and in most cases, a user certificate is issued by an intermediate CA (certificate authority), and other certificates are issued by another intermediate CA or by a root CA with a self-signed certificate. The root CA is considered a trust anchor. All certificates between an end-entity certificate and a trust anchor certificate form the trusted certificate path. The validation of this chain is a challenging task.shell model, the certificate is valid as long as all the certificates in the certification path are valid when the signature is verified. The second one is the modified shell model. In this model, the signing time is the basis for decision making about the signature validity (this requires a timestamp). The third model is the chain model: once a signature is valid at signing time, it remains valid all the time. The chain model can only provide non-repudiation of property over a long period of time [Three models for certificate validation exist . In the  of time ,2.The purpose of certificate validation is to confirm the authenticity of the public key, i.e., to provide proof that the public key belongs to the signer and that the associated private key was under the sole control of an owner at the moment of signature creation. The process of verifying certificates for signatures that need to be valid for a long period of time is one of the main difficulties when implementing and managing a public key infrastructure. The authenticity of a public key in a public key cryptosystem can be achieved in two ways: either explicitly or implicitly. During explicit authentication, the public key authenticity can be verified directly using the certificate issued by a CA. In implicit authentication, the secret certificate issued by a CA  can be verified indirectly during signature verification or decryption operation. Combining both approaches and obtaining cryptographic schemes based on explicit and implicit certificates is another possible solution .It seemed that the certificate validation problem had been solved in 1984 when Shamir [The great interest shown in the ID-PKC, CL-PKC and IC-PKC schemes is because they eliminate explicit certificates from the encryption or signature schemes and allow the need to manage the status of certificates to be dispensed with. In practice, this is not the case, as the problem of certificate status management is shifted to the user identity management level ,6. In adThe digital signature schemes must include a revocation mechanism to support non-repudiation and achieve Girault trust level 3 . The reIn the online mediator  technique ,9, a useIn 2001, Boneh and Franklin  proposedIn 2014, Sun et al.  proposedIn 2017, Jia et al.  proposedmodified k-CAA problem and the discrete logarithm (DL) problem. When an explicit long-term certificate is revoked, its status information (in the form of an explicit short-term certificate) is available online at the moment of signature generation. The method used for revoking and providing certificate status is similar to that presented by Yum et al. [This paper proposes a new revocable signature IE-RCBS-kCAA scheme with implicit and two explicit (short- and long-term) certificates, which is secure in the random oracle model under the hardness assumption of the m et al. .The implicit and short-term explicit certificates are two components of the signature key that can be used to sign documents. A signatory who wishes to reject the signatures he or she has generated may intentionally compromise his or her signature key and falsely claim that the signatures have been forged by someone else. Such a scenario is impossible with an explicit short-term certificate because the signer cannot revoke the explicit short-term certificate used as part of the full signature key.Using explicit short-term certificates ensures that revocation latency  is irrelevant, as the digital signature is valid only until the associated short-term explicit certificate expires. Because of the proposed signature validation approach based on the certificate validation shell model see , the accIn our approach, a user\u2019s private key consists of a secret value, a long-term partial private key and a short-term explicit certificate (a time key). The first two partial keys are kept secret by the user, and their authenticity is confirmed by a long-term certificate issued by the trusted authority (TA). An explicit short-term certificate is periodically updated and sent over a public channel. To perform such an operation  problem, kCAA problem, k-mCAA problem) can be found in Hyla et al.  and MitsThe architecture framework of the IE-RCBS-kCAA signature scheme is shown in t by a trusted authority, TA, is denoted Next, the TA issues the partial secret key for each registered user using its master system key. The TSA is an authentication service that decides the validity of an explicit long-term certificate at the current time and issues an explicit short-term certificate if the TSA answer is positive. Therefore, on request, the TSA checks the signer\u2019s long-term explicit certificate status according to the signed revocation list from the TA. The revocation list issued at time The trust model (understood as building trust relationships between cryptographic keys and their owner\u2019s identity) with the TSA, and separating its role from the TA role, allows various business models to be obtained that can provide certificate issuing services (explicit or implicit) and determine their status. In a particular case, the TSA may act as an independent third party and provide certificate status verification services to multiple TA authorities. This type of scenario aligns with the model that has long been used in PKI systems: CAs issue certificates, and the OCSP server issues certificates of their status .Let us assume that the earlier mentioned trust authorities and trusted status authorities are part of the trust model based on a common set of system parameters. These parameters may include, among others, the same algebraic groups The IE-RCBS-kCAA consists of eleven polynomial-time algorithms : the syDefinition\u00a01\u00a0(IE-RCBS-kCAA scheme).An implicit and explicit certificates-based signature against k-traitors collusion attack scheme consists of the following eleven polynomial-time algorithms:TA-Setup The TA runs the algorithm and, in secret, keeps the master private key s, while the TSA-Setup Create-User Implicit-Cert-Gen LongTerm-Explicit-Cert-Gen ShortTerm-Explicit-Cert-Gen Set-Private-Key Set-Public-Key Cert-Revoke Sign\u00a0algorithm that generates a signature \u03c3 for the given input: the Sign Verify m, m, It is required that if Remark\u00a01.Implicit-Cert-Gen and Explicit-Cert-Gen algorithms are successful when the TA positively verifies the identity and certificate information of The security proof of the proposed IE-RCBS-kCAA signature scheme is based on the commonly accepted standard security notion EUF-CMA . The EUF-CMA notation guarantees the highest security level of the signature scheme and thus the resistance of the signature scheme against the strongest attacks of the adversary.The security proofs is a claim made within the random oracle model, where a hash function finally replaces the random oracle. It is easy to see that the last step is heuristic in nature. In practice, the heuristics are successfully used for problem solving An adversary does not know the TA and TSA master keys;(b)An adversary knows the TA and TSA master keys;(c)An adversary knows the TA master private key and does not know the TSA master private status key;(d)An adversary does not know the TA master private key TA and knows the TSA master private status key TSA.For the IE-RCBS-kCAA signature scheme, four cases of access or lack of access by an adversary to TA and TSA master keys should be considered:Access to or lack of access to TA and TSA keys may depend on the adversary\u2019s knowledge or ignorance of different user keys. Consequently, this allows us to define five different types of adversaries, the capabilities of which are shown in Note that even if the A thorough analysis of the adversary types and their capabilities in n et al.  and Y. Hn et al. ).C and adversary A, assuming that the adversary chooses which game to play. In all cases, adversary Based on the above comments, the security model of the proposed IE-RCBS-kCAA scheme, from now on referred to as EUF-IERCBS-kCAA-CMA, is defined by three games between challenger A=A1,A2,A is tryine, e.g.,  and Y. He, e.g.,  that is e, e.g.,  and thei, et al. ,41,42 an, et al. ): NormalDefinition\u00a02.An implicit and explicit certificate revocable signature scheme IE-RCBS-kCAA has existential unforgeability against chosen message attacks (EUF-IERCBS-kCAA-CMA) if no probabilistic polynomial-time adversary has a non-negligible probability of winning Game I, Game II and Game III.The IE-RCBS-kCAA scheme consists of eleven polynomial-time algorithms: TA-Setup, TSA-Setup, Create-User, Implicit-Cert-Gen, LongTerm-Explicit-Cert-Gen, Set-Private-Key, Cert-Revoke, Get-Cert-Status, Sign and Verify. The algorithms are as follows.1.TA-Setup: The system parameters are p, P, Q, k is the system security number), 2.TSA-Setup (3.Create-User (4.Implicit-Cert-Gen ((a)Randomly selects (b)Composes the user\u2019s certificate information (c)For (d)Generates S\u2019s partial private key (an implicit certificate):5.LongTerm-Explicit-Cert-Gen\u00a0Implicit-Cert-Gen algorithm:(a)The TA creates the explicit certificate that links S\u2019s identity with the public key components:(b)The TA sends 6.ShortTerm-Explicit-Cert-Gen ((a)Randomly selects secret key (b)Composes the certificate status information (c)For (d)S via a public (open) channel; in addition, the TSA sends Generates the explicit short-term certificate (the certificate status evidence) as:7.Set-Private-Key\u00a0quations  and 4)))Set-Priv8.Set-Public-Key\u00a09.Cert-Revoke\u00a0(10.Sign\u00a0S performs the following steps:(a)Picks two random numbers (b)Computes the hash value (c)Generates a short-term explicit certificate by calling the ShortTerm-Explicit-Cert-Gen ((d)Generates the signature (e)If in  k1h+sIDsNote. Each time a signature is generated, a fresh short-term explicit certificate is retrieved from the TSA .11.Verify\u00a0(a)Computes Equation ) and the(b)Computes Equation );(c)accept, otherwise reject.If the status of the certificate rect and  is validRemark\u00a02.Note that during the indirect signature verification, the long- and short-term explicit certificates are validated (If the conditions formulated in Equations \u20139) are  are 9) aSuppose we use a shell model and the verifier received the signature at time (a)\u00a0(b)\u00a0When the above conditions are successful, the signature will be accepted as valid short-period non-repudiation evidence in whole period Remark\u00a03.Based on the properties of the asymmetric bilinear map groups:LongTerm-Explicit-Cert-Gen\u00a0algorithm can be entrusted to the signatory S, who, after receiving the implicit certificate from the TA will use Equation  problem with non-negligible probability. To this end, we used a general forking lemma (Bellare and Neven ), similaC with the help of adversary In both cases, after creating a valid forged signature, the adversaries Lemma\u00a01.Suppose the hash functions where e is the base of the natural logarithm, Proof.\u00a0k-mCAA problem to be\u00a0obtained.(sketch) According to the approach given in  (b)else, (a)(b)i.if ii.C = else, if else, (c)c, C, c as the answer.(a)if the query is made explicitly by (b)i.if ii.otherwise, if otherwise, (c)t, t is output as the answer.U, c. For each request made on c, Public-Key-Replacement-Query(a)(b)Else, Corruption-Query (ID). Implicit-Cert-Gen-Query ((a)Implicit-Cert-Gen-Query for On the running (b)i.failure i.Implicit-Cert-Gen algorithm in creates ii.runs Otherwise, LongTerm-Explicit-Cert-Gen-Query ((a)(b)i.failure Otherwise, ShortTerm-Explicit-Cert-Gen-Query ((a)(b)t, i.failure i.ShortTerm-Explicit-Cert-Gen algorithm in composes a certificate status information ii.runs Otherwise, Super-Sign-Query (Else:(a)if there is no a tuple (b)t, if tuple (c)failure i.sets ii.selects iii.calculates iv.v.vi.otherwise Super-Sign oracle.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Output. A successful adversary returns a valid forgery U = Create-User-Query. Moreover, ShortTerm-Explicit-Cert-Gen-Query or Super-Sign-Query queries, respectively.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Let C, U, C, \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Note that side output U, C,  and the tuple \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0When an adversary returns an invalid forgery, failure .Now we can show how to build a reduction algorithm Algorithm 2\u00a03R(if (b == 0) then return 0 // Event E3 3.Correctness of the k-mCAA Problem SolutionC, failure  with a single thread. The scheme was implemented using an IAIK ECCelerate library for Java. Type 2 asymmetric pairing (ate pairing) based on the Barreto\u2013Naehrig curve was used with different field sizes . The results . In The run times of the  results  average In the IE-RCBS-kCAA scheme, a trusted status authority (TSA) directly performs the revocation procedure and, as a result, alleviates the load of the trusted authority (TA). Moreover, the architecture framework proposed in this paper can contain many TSA authorities, effectively solving the scalability problem. This property is unique and is not available in other similar solutions. Unlike other proposals, e.g., Jia et al. , obtainik-mCAA and the We also formalize the security model for an adversary that can obtain a valid signature in the super sign query phase relevant to the public key selected by itself without providing the corresponding secret key. This security model proves that our IE-RCBS-kCAA signature scheme is semantically secure against Super Type I/II/III attackers under the The digital signature schemes must include a revocation mechanism to support non-repudiation and achieve Girault trust level 3. In order to achieve such properties, the paper proposes an architecture framework adapted to the needs of the IE-RCBS-kCAA scheme. In this scheme, an important role from the point of view of practical applications is played by the trusted status authority TSA, see , which pSign and Verify algorithms are significantly below one second. The signature size in our scheme is approximately 1 KB. Such a size will be too large a value for some practical applications, e.g., the transmission of short messages from IoT sensors. However, this value will be within an acceptable range for large documents and for signing transactions that are sent over high-speed internet connections. The performance analysis shows that the scheme is suitable for further practical work when signing large documents is needed. In this case, the signature is always decidedly shorter than the message. In other practical applications, one must carefully analyse if the signature size is acceptable.The performance comparisons with two other revocable signature schemes show that our signature scheme has a similar number of time-intensive operations. The empirical execution times of the Future research includes deploying the signature scheme with the certificates to be validated according to the chain model see . Such a"}
+{"text": "Nature Genetics 10.1038/s41588-023-01343-9. Published online 3 April 2023.Correction to: y-axis units shown below 0, where \u201c10\u201d and \u201c20\u201d were shown as negative numbers. The errors have been corrected in the HTML and PDF versions of the article.In the version of this article originally published, the surname of author Stefan Johansson was misspelled as Johanson. In the abstract and \u201cGenome-wide association analyses\u201d section of the Results, the number of loci associated with preterm birth was shown as six instead of seven. In addition, there was a production error in the Figure 1a"}
+{"text": "Correction to: Graefe\u2019s Archive for Clinical and Experimental Ophthalmology10.1007/s00417-023-05979-5In the published version of this article, the given name of the second author has been misspelled.Shengtao Liu\u201d.The correct author name should be \u201cThis is being corrected in this publication."}
+{"text": "T < 360 K; 0 < P < 100 MPa), density and self-diffusion obey a special type of dynamic scaling, similar to the \u201c\u03c4TV\u201d scaling of Casalini and Roland, but with the negative exponent \u03b3. The model predictions are consistent with experimental data. The new equation of state can be used for various process models and generalized to include multicomponent mixtures.Water is one of the most important compounds on Earth, yet its material properties are still poorly understood. Here, we use a recently developed two-state, two-(time)scale (TS2) dynamic mean-field model combined with the two-state Sanchez\u2013Lacombe (SL) thermodynamic theory in order to describe the equation of state (density as a function of temperature and pressure) and diffusivity of liquid water. In particular, it is shown that in a relatively wide temperature and pressure range (160 K <  Water is one of the most anomalous substances on Earth ,2 as welT \u2248 277 K), often understood in terms of competition between two or more competing local environments with different density and symmetry whose relative concentration is indeed determined by thermodynamic conditions ..SH,H=SH,XT) is a decreasing function of pressure, while in most conventional glass-formers the glass transition temperature (gT) and the melting temperature (mT) are increasing functions of pressure. This anomaly is connected to the fact that the L-state has a lower density and the H-state has a higher density; thus, increasing the pressure makes the H-state more favorable (at constant temperature) and causes the L-H transition to shift towards lower temperatures. The scaling exponent g is estimated to be ~(\u22121.7), while for most other materials obeying the \u201c\u03c4TV\u201d scaling, g is usually positive. There are several theories relating g to the effective interaction between the molecules or clusters; however, those theories apply for positive values of g. A consistent molecular-theory-based understanding of the \u201c\u03c4TV\u201d scaling for water is still a task for future research.We also demonstrated that water exhibits dynamic scaling, similar to the \u201c\u03c4TV\u201d scaling described by Casalini, Roland, and other authors for multiple glass-forming materials. One interesting distinction for water is as follows: The transition temperature from the low-T state to the high-T state  ,17,20\u2014thg/TXT , it would be very close to 1 for polymers and organics, but only ~0.5\u20130.6 for water.It is important to note that while SL-TS2 was originally proposed to describe the glass transition in amorphous polymers and organics, here it is applied to events that are well separated from the \u201ctrue\u201d glass transition (~130\u2013150 K for water). This is due to the low activation energy of the low-temperature state of water (~20\u201330 kJ/mol) as compared to polymers (~100\u2013300 kJ/mol). Thus, if we consider the ratio Finally, we should emphasize that the Casalini\u2013Roland-type scaling (Equation (15) in the Overall, the proposed simple model successfully describes both the equation of state and the transport properties of liquid water in a wide temperature (~180\u2013360 K) and pressure (~0 to 100 MPa) range. The framework, in principle, is flexible enough to allow the model to be extended to higher pressures closer to the LLCP. Another, more challenging problem is extending the proposed approach to integrate the crystalline phase (\u201cice\u201d), at least in its most common form. These will be topics for future research. N clusters, including X being in the L-state and (N-X) being in the H-state, is written as follows:We adopted the two-state SL-TS2 formalism that combines the description of the density and relaxation time of an amorphous liquid or glassy material . L\u03c6 is the volume fraction of the L-clusters, H\u03c6 is the volume fraction of the H-clusters, and V\u03c6 is the volume fraction of the voids or empty spaces  represents the van der Waals energies between the neighboring sites. The \u201cinternal\u201d entropy of an L-cluster is labeled H,LS, and that of an H-cluster is labeled H,HS; the first index \u201cH\u201d refers to the origin of this entropy term as arising from the combinatorics of hydrogen bonds within the cluster . Finally, It is convenient to rewrite the free energy in a non-dimensional way, as follows:\u03c8 and \u03bd leads to the following equations:Minimizing the free energy with respect to H < rLr; this means that the parameter Equations (7) through (12) are similar to Equations (6) and (7) in Ref.  (the indgT~130\u2013160 K) [T and P after solving Equations (7) and (8) for y and \u03bd. Given that the glass transition temperature of water is fairly low (0\u2013160 K) ,38,40,68\u03b1-relaxation time is given byHE is the activation energy for the H-state, and LE is the activation energy for the L-state. Similar to the case of conventional (non-hydrogen-bonding) amorphous materials, LE > HE.Within the TS2 framework (similar to the Shi-Tanaka-Russo model ), the \u03b1-a0 is some characteristic length that is assumed to be temperature-independent but pressure-dependent. Strictly speaking, there is a linear temperature dependence of D on T in addition to the Arrhenius or super-Arrhenius dependence built into the relaxation time, but here we neglect this weaker dependence. Thus, log(D) and \u2212log(\u03b1\u03c4) differ only by an additive constant, to be determined if both the diffusion coefficient and relaxation time are known at any given temperature.The diffusion coefficient can be estimated as follows:f(x) is some material-specific monotonic function. This scaling indicates that the relaxation time depends not on T and P separately, but on some \u201cstate variable\u201d Z. The exponent \u03b3 is usually a positive number, ranging from ~0.5 to ~9 [P, at least within some reasonably broad range. For water, however, this scaling obviously fails because of the non-monotonic temperature dependence of the specific volume at constant pressure. One can imagine two different temperatures T1 and T2 such that the right-hand sides are the same, but the left-hand sides are drastically different. The question is whether the corresponding states concept applies to water at all.It has been shown that for many amorphous materials, there is a relationship between the relaxation times for various \u201ccorresponding states\u201d, described by the following formula:.5 to ~9 ,50,51,52*, EH, EL\u03b5) depend on the pressure, as follows:Y == , and \u03a4\u03b1 =1/PT0, [Recently, it was demonstrated that the Casalini-Roland scaling (Equation (15)) emerges naturally within the SL-TS2 framework (at least within some reasonably broad pressure range) ,48. Herer\u03b1 =1/P0,v is the isothermal compressibility. Finally, we further hypothesize thatD\u03b1. Here, and below, we set a0(0) = 0.14 nm = 1.4 \u00c5.Next, we consider the density scale and assume thatXT is defined as the temperature for which \u03c8 = 0.5 . The pressure dependence of XT is given by Equation (16), such that XT decreases as P is increased. The state variables y and \u03bd then depend on the combined variable X(P)T/T\u2014not on T and P independently.The \u201ccorresponding states\u201d hypothesis can be expressed as follows:T < 373 K, from Price et al. [T < 298 K, and from Xu et al. [T < 262 K. The first three works consider the nuclear magnetic resonance (NMR) pulsed-field-gradient spin-echo method, allowing the evaluation of the self-diffusion coefficient from the trend of the spin-echo decay as a function of the intensity (or duration) of the perturbing magnetic gradient pulse [T > 273 K) measured by Weing\u00e4rtner [To test our models, we used the published experimental data from multiple sources; these data were collected using standard techniques and instruments and were found to reproduce one another fairly well when the measurements were done under similar environmental conditions . The self-diffusion data were obtained from a series of different experiments from the literature. In detail, at atmospheric pressure, we considered data from Yoshida et al.  in the 3e et al.  for 238 u et al.  for 180 nt pulse  used a pnt pulse . At highnt pulse , including\u00e4rtner  and by Tng\u00e4rtner . All of T < 423 K, from Kell and Whalley [T < 373 K, from Hare and Sorensen [T < 260 K, and from Erko et al. [T < 220 K (the latter two were measured in a confining environment to prevent the water from freezing). In detail, Grindley et al. measured the water\u2019s specific volume by means of a piezometer [The density data were also obtained from different experiments; in particular, we considered atmospheric-pressure data from Grindley et al.  for 298  Whalley  for 273 Sorensen  in the 2Sorensen  for 183 o et al.  for 170 ezometer ; the datezometer  measuredezometer  were obtezometer  were obtezometer ) at the ezometer  and Grinezometer  at the hezometer , and we We applied the \u201ctwo-state, two-(time)scale\u201d Sanchez\u2013Lacombe model (SL-TS2) to describe the equation of state and diffusion coefficient of both equilibrium and supercooled liquid water. The model showed a good agreement with the experimental data for the ambient-pressure measurements in a broad temperature range (180\u2013360 K). We also discovered non-trivial scaling rules similar to the Casalini-Roland \u201c\u03c4TV\u201d scaling in \u201cconventional\u201d glass-formers; using this scaling, we successfully described the density and diffusion coefficient at multiple pressures (0\u2013100 MPa). The results could provide a new description of both the equilibrium and transport properties of liquid water and, thus, may be of interest in many applications in the chemical and other industries."}
+{"text": "Designing reasonable MAC scheduling strategies is an important means to ensure transmission quality in wireless sensor networks (WSNs). When there exist multiple available routes from the source to the destination, it is necessary to combine a data traffic allocation mechanism and design a multi-path MAC scheduling scheme in order to ensure QoS. This paper develops a multi-path resource allocation method for multi-channel wireless sensor networks, which uses random-access technology to complete MAC scheduling and selects the transmission path for each packet according to the probability. Through theoretical analysis and simulation experiments, it can be found that the proposed strategy can provide a reliable throughput capacity region. Meanwhile, due to the use of random-access technology, the computational complexity of the proposed algorithm can be independent of the number of links and channels. In wireless sensor networks (WSNs), the use of scheduling policies as the MAC layer protocol can bring better QoS than the traditional competition-based CSMA/CD protocol . AccordiIn a single-hop or single-route network scenario, the MAC scheduling algorithm determines whether each link queue transmits packets in the current time slot. In actual network scenarios, if there exist multiple alternative paths available between the source node and the destination node, it is necessary to allocate data traffic  to different paths reasonably based on MAC scheduling, so as to better balance the network load and obtain better transmission performance . In a muResearchers have made a series of research progress in addressing the distributed MAC scheduling problem. We organize and summarize the current research status from two aspects: single-channel scheduling and multi-channel scheduling and introduce the ideas and innovations of this paper.With regard to the distributed MAC scheduling problem in single-channel networks, some researchers have proposed a maximal scheduling (MS) strategy for various interference models ,5 and deIn wireless networks, wireless spectrum resources can be divided into multiple different channels, each occupying a certain frequency range. Wireless network nodes can choose a certain channel to transmit data on their own. Thus, links within the same interference area can transmit data without interference by using different channels, which increases throughput and bandwidth . If multFor distributed MAC scheduling in multi-channel networks, due to capacity differences between different channels, directly extending the single-channel MAC scheduling strategies to a multi-channel scenario may result in extremely poor throughput performance ,13. FollL| links and |C| channels, performing a complete maximal match requires at least O(|L||C|) iterations  is located within a certain region \u03a9, then the region \u03a9 is named as the maximum throughput capacity region. In the multi-path scenario used in this paper, the maximum throughput capacity region \u03a9 can be defined as a set of all input loads  that meet the following conditions:k\u03a9, then the strategy is called throughput guaranteed, and the efficiency ratio is k (0 \u2264 k \u2264 1). Obviously, a larger value of k means that the MAC scheduling strategy has better throughput performance. The multi-path MAC scheduling scheme proposed in this paper is throughput guaranteed. Moreover, the implementation complexity of the proposed scheme is independent of the network size. The following sections will provide a detailed explanation and analysis of the execution process and the performance of the proposed algorithm.In practical network systems, queue-stable is an important state measuring network throughput performance, which refers to the network being able to bear the current input load. If there exists a MAC scheduling strategy that can maintain the queue-stable state of the network when the input load vector . Such a proportion vector indicates the proportion of data packets sent by the source node to each path and its calculation is completed by solving the following maximum value problem:s\u03d5 and \u03bd are positive constants. After solving the problem of (4), the vector sT(n) can be obtained. In detail, the element in the vector sT(n) represents the probability of the source node sending a data packet to the corresponding path. For example, if siT(n) = 0.2, the source node s sends data to path i with a probability of 20% in time slot n. In this way, sA(n)siT(n) represents the total number of data packets sent to path i by source node s in time slot n.Step 1: Data traffic allocation. In each time slot n into two parts: a calculation time slot and a transmission time slot, as shown in P mini time slots. Within time slot n, each link selects one of the P mini-time-slots according to the mechanism proposed in step 3 as the starting time for data transmission.Step 2: Time slot segmentation. In order to make the implementation complexity of the MAC scheduling strategy independent of the network size, it is necessary to divide the time length of each time slot n, each link l selects a certain mini time slot in the set {1, \u2026, P + 1} with probability:lY denotes the mini time slot picked by link l, and the parameter l\u03c8 is calculated using the following formula:\u03b1 = ln P. When link l picks P + 1, it means that it will not send data in the current time slot. If two neighboring links that interfere with each other (interference may come from a shared channel or interface conflict) choose the same mini time slot, then both will not send data in this time slot. Meanwhile, if link l detects other links in its interference set sending data when it is about to start sending, it will remain silent during this time slot. From Formula (6), it can be seen that the calculation of parameter l\u03c8 requires the neighbor queue information of link l, which can be assisted by using the RTS/CTS mechanism in the MAC protocol.Step 3: Scheduling. In each time slot The performance of the M-Scheduler scheme is analyzed here from two aspects: throughput and complexity. With regard to throughput performance, we demonstrate that the proposed M-Scheduler is throughput guaranteed, and the throughput efficiency ratio of the algorithm is further obtained. In terms of complexity, we will explain that the implementation complexity of M-Scheduler is independent of the network size. Based on this characteristic, the M-Scheduler strategy has significant advantages in complexity compared with the existing maximal-matching-based multi-path MAC scheduling schemes.For the purpose of achieving the throughput performance of M-Scheduler, the following lemma is needed.Lemma\u00a01.0 > 0 such that when \u03c4 \u2265 \u03c40, we have:For any positive constant \u03bc > 0, there exists \u03c4Proof of Lemma\u00a01.j regarding link j, denoted as:jb is 0 j \u2264\u2264 b 1. At the same time, it can be found that there must be a link j in the network that makes jb = 1. Without loss of generality, let b1 = 1. Hence, if the following inequality holds for every jb (j \u2208 L and j \u2260 1), Lemma 1 is then obtained:\u03c4 > 0, if jb \u2265 e\u03bc\u2212, we have (jb)\u03c41+ \u2265 (jb)\u03c4 e\u03bc\u2212; if j \u2264 e\u2212\u03bcb, then we have (jb)\u03c41+ \u2265 0. Hence, by combining the two cases, the following inequality can be obtained:L| denotes the cardinality of the set L. Hence, when the parameter \u03bc > 0 is given, we can appropriately choose a positive number \u03c40 to make 1 \u2212 (|L| \u2212 1) e\u03bc(1+\u2212\u03c40) \u2264 e\u03bc\u2212. Thus, for arbitrary \u03c4 > \u03c40, it is not difficult to deduce (9). Therefore, Lemma 1 was proven. After obtaining Lemma 1, the following theorem is given to describe the throughput performance of M-Scheduler. \u25a1Firstly, define a parameter bTheorem\u00a01.\u03bb =  satisfiesEmploying the M-Scheduler strategy, for any \u03bc > 0, if the input load vector denoted by then the network system can maintain a queue-stable state.Proof of Theorem\u00a01.lx(n) and j\u03a5 as:E[\u00b7] represents the mathematical expectation. Due to E[sA(n)siT(n)] = sTsi\u03bb(n), it can be then obtained that:q(n) = , lZ indicates the event that link l is scheduled, and o[\u00b7] denotes the higher order infinitesimal. Furthermore, according to Equations (5) and (6), it is not difficult to obtain:j. Thus, according to Lemma 1, for any positive constant \u03bc, there exists \u03c40 > 0 such that when \u03c4 \u2265 \u03c40, we have:Firstly, construct the following Lyapunov function:tability , and The\u03bb meeting:j [\u03bc is small enough and P is large enough, the right half of inequality Equation (12) approaches 1, i.e.:It should be emphasized that if the interference degree of the entire network is K, then the maximum throughput capacity region \u03a9 can be denoted by the set of all input load vectors h link j . Hence, \u03bb \u2208 \u03a9/K. Thus, the proposed scheme is throughput guaranteed. According to the above analysis, the larger the number of mini time slots P, the closer the throughput efficiency ratio of M-Scheduler is to 1/K. In the future, the hardware performance of the communication terminal can be improved to ensure that the value of P is large enough. In theory, one can compare the throughput performance of M-Scheduler with other existing comparable strategies. The MP algorithm proposed in [ER) of the three schemes has a relationship of ERM-Scheduler > ERLDCS > ERMP. Among them, LDCS adopts a relay-forwarding mechanism in the process of traffic allocation, which brings better throughput performance than the MP algorithm. Furthermore, M-Scheduler utilizes the tuple-based model to virtualize multi-channel networks into single-channel networks, which improves the transmission performance significantly. Therefore, the efficiency ratio of M-Scheduler is greater than that of LDCS. In By comparing Inequalities (12) and 21), it can be concluded that the throughput efficiency ratio of the M-Scheduler strategy is close to 1/K. That is to say, M-Scheduler can ensure the queue-stable state of the network system when posed in  and the , it can L| links and |C| channels, the MAC scheduling based on the maximal matching method needs to perform O(|L||C|) iterations in each time slot. Obviously, such implementation complexity is not conducive to the deployment of the corresponding scheduling strategies in large-scale dense wireless networks. Under the proposed M-Scheduler policy, each link selects its own data transmission timestamp based on probability in each time slot. Therefore, the implementation complexity of M-Scheduler does not increase with the number of available channels and links in the network. Hence, it is said that the complexity of M-Scheduler is independent of the network scale and can be better applied to large-scale dense wireless networks.From the execution process of M-Scheduler, it can be seen that it adopts a distributed implementation mechanism. Compared to centralized implementation, distributed implementation has lower complexity and is easier to deploy in distributed networks such as WSNs. Meanwhile, compared to existing multi-path distributed MAC scheduling schemes applied to wireless multi-channel networks, M-Scheduler does not need to execute the maximal matching processes and does not require iterative operations. The research shows that if the multi-channel network contains |P = 103. The simulation results in this scenario are shown in P = 105. The simulation results of scenario 2 are shown in To verify the effectiveness of the multi-path MAC scheduling strategy proposed in this paper in practical network scenarios, the throughput performance of M-Scheduler is compared with the existing MP and LDCS schemes using the NS-2.31 tool. We use a grid topology as shown in As shown in Moreover, by comparing This paper put forward a novel MAC scheduling scheme for wireless multi-channel networks, named M-Scheduler. The scheme adopts a mathematical model based on tuples, which models nodes, interfaces, and channels as tuple nodes and models the link between a pair of tuple nodes as a tuple link. In this way, a multi-interface multi-channel network can be modeled as a single-channel network. At the same time, when there are multiple transmission paths from the source to the destination in the network, the proposed M-Scheduler first allocates the data traffic to each path reasonably in each time slot and adopts a random-access-based scheduling strategy to complete packet forwarding during the MAC scheduling stage. The theoretical basis for designing a data-traffic-allocation algorithm and random-access probabilities is to ensure the throughput performance of M-Scheduler. By using the Lyapunov analysis method, we have demonstrated that M-Scheduler can achieve a stable throughput capacity region. When the input load is located within the capacity region, the network system maintains a queue-stable state. In addition, due to the utilization of random-access technology to complete MAC scheduling, the implementation complexity of M-Scheduler is independent of the network size. Such a feature makes M-Scheduler perform better in terms of complexity than the existing multi-path MAC scheduling schemes and also enhances its applicability in practical networks.It should be noted that other types of distributed networks (such as Ad hoc) can also consider using the solution proposed in this paper. The difference lies in the relatively fixed position of nodes in WSNs and, hence, our proposed algorithm is easier to promote and apply in WSNs. In future work, we plan to transplant the M-Scheduler algorithm to the communication protocol stack of WSN terminals and collaborate with IoT companies to conduct practical experiments to verify the effectiveness of M-Scheduler and gradually promote its application in new products."}
+{"text": "Studies have documented that utilizing peer feedback can enhance students\u2019 English academic writing skills. Little is known, however, about the effects of incorporating peer feedback to enhance English as a second language (L2) medical students\u2019 academic writing performance.n\u2009=\u2009124).This longitudinal interventional study examines Chinese medical students\u2019 English academic writing skills development via peer feedback in four parallel classes over an 18-week semester between the experimental and control groups , and the effects were retained in the delayed post-test 6\u00a0weeks later . Little improvement was found in the control group in the post-test  or the delayed post-test . Between-group comparisons indicate that the experimental group outperformed the control group in the post- and the delayed post-tests, as shown in their overall score and scores on the four components.Significant increases in the experimental group\u2019s performance in the post-test were found after 18-week instructions (pre- vs. post-test: overall score, Incorporating peer feedback into process-oriented medical English writing classroom teaching can effectively enhance Chinese medical students\u2019 English academic writing skills over time, while the traditional product-oriented writing instructions had little help in improving Chinese medical students\u2019 academic writing skills. This longitudinal intervention study develops our understanding of the effectiveness of peer feedback in L2 academic writing pedagogy. It offers instructional implications for L2 writing teachers to teach English academic writing among medical students in China and beyond. Limitations and suggestions for future studies are discussed. Researchers have proposed several approaches for teaching writing, e.g., the product- and process-oriented approaches , 39. ThePeer feedback, a commonly used peer-supported positive learning strategy in the writing process, refers to a process where learners provide feedback on their peers\u2019 work in oral or written forms and learners also receive feedback from other peers see , 45, 47), 4745, 4n\u2009=\u2009198) in a Chinese university [Given the advantages of peer feedback above and the potential of utilizing peer feedback for English writing instructions, previous studies have incorporated peer feedback activities into the process-oriented approach for improving students\u2019 writing performance e.g., , 42, 45), 4542, 4iversity . They deiversity  investigiversity . Additioiversity , 46), whiversity .RQ1: Does the use of peer feedback improve Chinese medical students\u2019 English academic writing development over time?RQ2: Is there any difference in the effects of peer feedback and traditional writing instructions on Chinese medical students\u2019 English academic writing development?To address some of the existing research gaps, the current study applies a longitudinal intervention design to investigate the effects of peer feedback on L2 medical students\u2019 academic writing skills development over time. Specifically, this study is guided by the following two research questions (RQ):n\u2009=\u200962) and the control group (CG\u2009=\u200962). Students in the experimental group were 10 males and 52 females between 18 and 19 . Similarly, students in the control group were 9 males and 53 females between 18 and 19 . Regarding their past English learning experience, they started to learn English in the first year of primary school. In addition, the homogeneity tests were run to ensure students\u2019 writing abilities were homogenous in the pre-test. The results illustrated that students\u2019 writing skills in overall scores and the five subscores were similar at the pre-test  degrees in English language education and have taught English writing for 15\u00a0years. Four key genres  were chosen as the teaching target for both groups. Although the English writing tasks involved various topics such as education, career, and culture, most of the writing topics were health-related due to their medical major.Peer feedback activities were implemented in the experimental group and the writing course design. The writing teachers for the experimental group  incorporated peer feedback activities, while the teachers for the control group  applied the conventional product-oriented approach.In the experimental group, students received feedback on different writing dimensions from peers, and eventually completed a revised draft each week. To help students provide effective peer feedback, the Department of English of the university arranged weekly peer feedback workshops to teach students how to use a rubric to offer feedback on each dimension of their peers\u2019 work. Specifically, the details of each dimension on the rubrics were explained in the weekly workshops. Writing samples for different score ranges were also presented, and teachers explained how to use the rubric to provide feedback to these writing samples, which could ensure the inter-rater reliability and the uniformity of the marking process to a large extent. Furthermore, when they experienced difficulties in giving feedback to their peers, they could immediately raise their hands and seek help from the teacher in writing classes. The rubric used in this study was adapted from the rubric for marking writing sections of College English Test-6 (CET-6) , which iTo alleviate external factors affecting learners\u2019 writing performance, weekly pre-class teaching training sessions were organized with the two teachers for the experimental group to guide them to implement the same teaching procedures, and the two teachers for the control group attended other sessions for the same purpose. The first author observed the actual writing classes to ensure that teachers teach English academic writing in a planned manner.At the pre-test stage, a mock writing test for CET-6 was arranged by the Department of English at this university, and students should finish the writing section in the classroom. The writing samples were collected to obtain baseline data from the experimental and control groups. Then, 18-week writing instructions were carried out in the experimental group. At the post-test stage, another mock writing test was conducted again immediately after the interventions. In addition, to investigate the follow-up effects, we conducted a delayed post-test 6\u00a0weeks after the intervention was completed. The topics of the mock writing test for pre-, post-, and delayed post-tests were adapted from the writing section of the CET-6 test, which requires students to write an essay with around 200 words within 30\u00a0minutes. Three experienced English writing teachers were consulted to ensure the comparability and feasibility of the two writing topics. And then, students from another parallel class were invited to finish the two tasks to guarantee that the difficulty of the two topics was moderate for freshmen medical students.A double-blinded expert (two teachers) assessment mechanism was applied to score students\u2019 writings. The 9-point scoring rubric was used to rate all\u00a0essays from four dimensions with equal weight: task response, coherence and cohesion, lexical resource, and grammatical range and accuracy. Two teachers were invited to an academic seminar to guarantee acceptable inter-rater reliability and the uniformity of marking criteria. At first, twenty compositions were given to the two writing teachers, and they scored the compositions individually. Then, they went to check whether they could give the same mark on the same compositions. If not, they were asked to have a communication to explain why they scored this mark. During this process, they can agree on the scoring standard, and then they were allowed to evaluate the rest of the compositions independently. Finally, Cronbach\u2019s Alpha was calculated and reported at 0.802 in pre-tests, 0.855 in post-tests, and 0.875 in delayed post-tests, which indicated their scoring has good reliability.\u03b7\u03c12) was used for measuring the effect sizes for mixed ANOVAs. Cohen\u2019d was calculated for the t-tests, and r was calculated for Wilcoxon and Mann\u2013Whitney tests. The interpretation of the results was based on Cohen\u2019s (1992) classification that \u03b7\u03c12 values of 0.01, 0.06, 0.14; d values of 0.20, 0.50, and 0.80; and r values of 0.10, 0.30, and 0.50 were considered small, medium, and large, respectively.The assumptions of the statistical tests were checked via standard diagnostic tests and procedures. The visual inspection of histograms, normal Q-Q, normal P-P, box plots, skewness and kurtosis, and the Shapiro-Wilk tests were used to check the normality of distribution, Levene\u2019s test was used for homogeneity of variance, and Mauchily\u2019s test was used for sphericity of the data. Then, 2\u2009\u00d7\u20093 mixed factorials analysis of variance (ANOVAs) and Friedman test were conducted to investigate the effects of peer feedback on L2 students\u2019 writing skills. Besides, simple effect analysis and Wilcoxon signed-ranks tests were used as the posthoc test within groups. Where there were multiple comparisons, Bonferroni corrections were used to avoid Type I errors. Partial eta squared .Given that the assumptions of normal distribution, homogeneity, and sphericity were met, mixed ANOVAs were conducted for the overall writing scores and subscores including task response, coherence and cohesion, and lexical resource. Friedman test was conducted as an alternative analysis for grammatical range and accuracy scores since the scores were not normally distributed. The results of the baseline test illustrate that students\u2019 writing skills in overall scores and the five subscores were similar at the pre-test \u2009=\u200931.85, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.15, a significant main effect of group, F \u2009=\u200934.60, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.09, and a significant interaction effect for time\u2009\u00d7\u2009group, F \u2009=\u200918.61, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.09, on students\u2019 overall writing scores.As shown in Table p\u2009<\u20090.001; pre- vs. delayed post-test, p\u2009<\u20090.001), and the effect was retained in the delayed post-test . Nevertheless, the overall writing score of students in the comparison group did not improve significantly across the three tests .Then, a simple effect analysis was used to explain the time\u2009\u00d7\u2009group interaction effect further. Within-subject comparisons (see Table p\u2009=\u20090.115), while the experimental group significantly outperformed the comparison group in the post-test, p\u2009<\u20090.001, with large effect size, d\u2009=\u20091.02, and in the delayed post-test, p\u2009<\u20090.001, with large effect size, d\u2009=\u20091.04.Further, between-group comparisons \u2009=\u200912.69, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.07, a significant main effect of group, F \u2009=\u200912.95, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.03, and a significant interactive effect of time\u2009\u00d7\u2009group, F \u2009=\u20096.08, p\u2009=\u20090.003, \u03b7\u03c12\u2009=\u20090.03, with respect to the task response score. Furthermore, a significant main effect of time, F \u2009=\u200922.74, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.11, a significant main effect of group, F \u2009=\u200925.43, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.07, and a significant interactive effect of time\u2009\u00d7\u2009group, F\u2009=\u200914.64, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.07 were found in terms of the coherence and cohesion score. The mixed-design ANOVA results also showed that there was a significant main effect of time on lexical resource, F \u2009=\u200917.75, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.09, a significant main effect of group, F\u2009=\u200921.36, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.06, and a significant interactive effect of time\u2009\u00d7\u2009group, F\u2009=\u20099.61, p\u2009<\u20090.001, \u03b7\u03c12\u2009=\u20090.05.The results of 2\u2009\u00d7\u20093 mixed factorials analysis of variance (ANOVAs) suggested that there was a significant main effect of time, p\u2009<\u20090.001; pre- vs. delayed post-test, p\u2009<\u20090.001), and the effect was maintained in the delayed post-test , whereas the score for the control group did not improve over time . Moreover, a simple effect analysis revealed that peer feedback enhanced the coherence and cohesion scores for students in the intervention group, and the effect was retained in the delayed post-test . However, no significant improvement was found for the comparison group over the three-time points . Simple effect analysis also shows that the lexical resource scores improved significantly for the experimental group , and the effect was retained in the delayed post-test . However, for the control group, no significant improvement was found over time .As shown in Table p\u2009=\u20090.444), while students in the experimental group performed much better than those in the control group in the post-test (p\u2009<\u20090.001) and in the delayed post-test (p\u2009<\u20090.001), with medium effect sizes, d\u2009=\u20090.62 and d\u2009=\u20090.68, respectively. Between-group comparisons (see Table p\u2009=\u20090.135). However, the experimental group showed better performance regarding coherence and cohesion than the control group in the post-test, p\u2009<\u20090.001, with a large effect size (d\u2009=\u20090.93), and in the delayed post-test, p\u2009<\u20090.001, with a large effect size (d\u2009=\u20090.83). Between-group comparisons revealed that no significant difference was found between the two groups in lexical resource scores in the pre-test (p\u2009=\u20090.367). However, the experimental group showed better performance regarding lexical resource scores than the control group in the post-test, p\u2009<\u20090.001, with a medium effect size d\u2009=\u20090.74), and in the delayed post-test, p\u2009<\u20090.001, with a large effect size, d\u2009=\u20090.84.Additionally, the task response scores of the two groups in the pre-test showed no significant difference p\u2009=\u20090.44, while\u03c72\u2009=\u200943.33, p\u2009<\u20090.001), and had no effects on that of the control group across time .Given that the scores were not normally distributed, the Friedman test examined the differences in grammatical range and accuracy scores over the three tests. Table p\u2009<\u20090.017 (0.05/3\u22480.017). There was a statistically significant improvement in the grammatical range and accuracy scores in the experimental group in the pre-test vs. the post-test , the pre-test vs. the delayed post-test . And no significant difference was found for the experimental group in the post-test vs. the delayed post-test , meaning that the effect was retained in the delayed post-test. However, no significant difference was found in the grammatical range and accuracy scores in the control group in the pre-test vs. the post-test , the pre-test vs. the delayed post-test , and the post-test vs. the delayed post-test , indicating that the traditional product-oriented approach had little effects on students\u2019 grammatical range and accuracy scores. Additionally, Mann-Whitney U tests were conducted to compare the differences between the two groups at the three tests. The results showed that students in the experimental group and the control group in the pre-test were quite similar concerning the grammatical range and accuracy scores , whereas statistically significant differences were found in the grammatical range and accuracy scores between the experimental group and the control group in the post-test  and the delayed post-test .Post-hoc analysis with Wilcoxon signed-rank test was conducted with a Bonferroni correction applied, resulting in a significant level set as task response, coherence and cohesion, lexical resource, and grammatical range and accuracy) for the experimental group and the control group were compared at both pre- and post-test stages.The current study aimed to investigate the effects of peer feedback on enhancing medical students\u2019 English writing skills development over time at a university in China. Peer feedback (see Table task response and coherence and cohesion). The current study extended previous studies and suggested that peer feedback in process writing instructional framework, although not conclusively, can improve medical students\u2019 English writing performance in terms of task response, and coherence and cohesion.The research question concerns testing the effects of peer feedback on developing students\u2019 writing performance over time. This study has shown that students in the experimental group performed better at the post-test stage in the overall writing score and its four dimensions after processing writing instructions for 18\u00a0weeks. This was in line with the findings of other studies e.g., , 28, 44), 4428, 4\u201cAs the medical science continues to develop, people have no choice but to learn new knowledge\u2026\u201d and \u201cWith the development of the Internet, a wide range of amusements have filled our life\u201d. Although these sentences had no problems concerning grammatical accuracy, it can be easily recognized that these sentences do not have direct relations with the writing topic the importance of reading ability, or the way to improve it. In contrast, in the post-tests, this phenomenon did not occur in most students in the experimental group.The improvement in task response for students in the experimental group has suggested that students had realized the importance of presenting relevant and well-supported opinions, and their ability to answer the writing requirements can be improved through the teacher\u2019s instructions on model texts and brainstorming activities in the planning stage. Therefore, they could address the issues with relevant and persuasive statements. This can be supported by the analysis of students\u2019 essays. For example, in the pre-tests, many students tend to write some sentences that did not have a direct relationship with the writing topic such as lexical resource, which echoes the findings of several recent studies , 28lexicMuncie\u2019s  study. Tcoherence and cohesion after the peer feedback intervention. Compared with teacher feedback, a significant benefit of peer feedback is that it put great emphasis on providing feedback at the meaning level [coherence and cohesion. Based on the analysis of students\u2019 written texts in the experimental group, one of the most apparent changes happened in the use of conjunctions. In the pre-tests, we found that some students might not have realized the necessity to use conjunctions to organize their sentences logically. Consequently, students wrote sentences like \u201cI am keen on the ancient history regarding China, it offers me the opportunities to enjoy ancient cultures.\u201d and \u201cPractice makes perfect, you should read authentic books regularly.\u201d. However, our analysis of students\u2019 writing samples in the post-tests has shown that a wide range of conjunctions like \u201cbecause\u201d, \u201cso\u201d \u201csince\u201d \u201cwhile\u201d and \u201cbut\u201d were accurately used to organize their sentences. This may be because they have understood the logical relationship  between simple sentences and were able to use specific conjunctions to present their ideas.Students in the experimental group also made great achievements in ng level , 38. Thagrammatical range and accuracy, which confirms the empirical findings that peer feedback could significantly develop the grammatical accuracy of learners\u2019 English writing . Fu. Fugrammg , 4527, 4To conclude, this longitudinal interventional study examined the effects of peer feedback on Chinese medical students\u2019 English writing performance over time. Compared with prior studies using the conventional product-oriented writing approach, the finding of the current study suggests that incorporating peer feedback into L2 writing teaching can effectively enhance medical students\u2019 overall writing performance and performance in various aspects, including task response, coherence and cohesion, lexical resource, and grammatical range and accuracy."}
+{"text": "X-ray microtomography is a nondestructive, three-dimensional inspection technique applied across a vast range of fields and disciplines, ranging from research to industrial, encompassing engineering, biology, and medical research. Phase-contrast imaging extends the domain of application of x-ray microtomography to classes of samples that exhibit weak attenuation, thus appearing with poor contrast in standard x-ray imaging. Notable examples are low-atomic-number materials, like carbon-fiber composites, soft matter, and biological soft tissues. We report on a compact and cost-effective system for x-ray phase-contrast microtomography. The system features high sensitivity to phase gradients and high resolution, requires a low-power sealed x-ray tube, a single optical element, and fits in a small footprint. It is compatible with standard x-ray detector technologies: in our experiments, we have observed that single-photon counting offered higher angular sensitivity, whereas flat panels provided a larger field of view. The system is benchmarked against known-material phantoms, and its potential for soft-tissue three-dimensional imaging is demonstrated on small-animal organs: a piglet esophagus and a rat heart. We believe that the simplicity of the setup we are proposing, combined with its robustness and sensitivity, will facilitate accessing quantitative x-ray phase-contrast microtomography as a research tool across disciplines, including tissue engineering, materials science, and nondestructive testing in general. DespiThe technology for x-ray phase-contrast imaging is more demanding in comparison to what is needed for conventional x-ray imaging, specifically in terms of the required spatial and temporal coherence of the radiation . While sIn this context, we have identified a solution for lab-XPC\u00b5T that has minimum requirements on the experimental setup. Our approach is based on a low-power, fixed target and sealed x-ray tube; it requires a single optical element (modulator), and it is compatible with flat-panel detectors as well as with single-photon counters. All of these components are readily available and require a minimal amount of maintenance. The modulator is fabricated through laser ablation of a tungsten foil and requires positioning accuracy of approximately 5\u201310\u00a0\u00b5m. The total length of the system is less than 1\u00a0m, making it one of the most compact for lab-XPC\u00b5T. Our approach shares similarities with a Shack\u2013Hartmann wavefront sensor and in our work, it evolved from one-directional to two-directional sensitivity of beam tracking ,38. It c2.A.The core element of the imaging system  is the sWhen a sample is in place, the intensity distribution of each probe is attenuated and shifted by the local properties of the sample, e object . The tralgorithm . These dBy linking the two refraction images to the orthogonal gradients of the phase shift   can be o follows : (7)F[A better signal-to-noise ratio can be seen by direct visual comparison with the attenuation-image contrast of the same phantom . The retB.The x-ray system features a fixed W-target microfocus Hamamatsu x-ray source (L12161-07), which we run at 40 kVp and 10\u00a0W. The modulators were manufactured with a laser ablation procedure from readily available 100-\u00b5m-thick tungsten foils (Goodfellow). Two pitches, 50 and 100\u00a0\u00b5m, were tested. The apertures have a conical shape with diameters of Three detectors were tested: i) Pixirad-2/PIXIE-III photon counter with a 650\u00a0\u00b5m CdTe sensor (98% detection efficiency up to 50\u00a0keV), 62\u00a0\u00b5m pixel pitch and a The geometry was defined as follows: To characterize the system and fine-tune the quantitative retrieval algorithm, a test phantom consisting of a poly(methyl methacrylate) (PMMA) calibration sphere  embedded in wax and polyethylene foam. Images were acquired at n angles , nine diThe ability of the system to measure The performance of the system for soft-tissue imaging was demonstrated with two animal-derived small organs; a heart and an esophagus, extracted from a 300\u00a0g Sprague\u2013Dawley rat and a 3\u00a0kg piglet, respectively. The heart sample was obtained from the UCL Biological Services Unit (BSU), while the esophagus from piglets was procured from JSR Genetics Ltd, a Home Office-approved supplier. Animals were euthanized via Schedule 1 methods, and sample sizing has been implemented following the NC3R principles. The organs were prepared for imaging through paraformaldehyde (PFA) fixation, followed by critical point drying (as described in previous work ). For thAll reconstructions were performed using the Feldkamp\u2013Davis\u2013Kress algorithm implementation in CUDA of the Astra Toolbox . The vol3.The angular sensitivity depends on the exposure time and closely follows the trend expected from the Poisson statistics, proportional to the power of \u22121/2 . This inTomographic reconstructions of ted ones  in Tableexpected ; howeverLab-XPC\u00b5T of the animal-derived small organs are presented in For the piglet esophagus , we idenat heart , lab-XPC4.We presented a compact and cost-effective system for performing XPC\u00b5T in a laboratory setting. The system is based on a single modulator and a low-power sealed x-ray tube and is compatible with a range of readily available detectors. We report submicrometer angular sensitivity starting at 2\u00a0s of exposure time at 50\u00a0\u00b5m spatial resolution and 32\u00a0s at 16\u00a0\u00b5m spatial resolution, and a maximum angular sensitivity of 220 nrad in 64\u00a0s at 50\u00a0\u00b5m spatial resolution. These results are compatible with the state of the art and were achieved with a simple and compact setup. The proposed approach is quantitative, as validated through a phantom composed of known materials, and flexible in terms of spatial resolution and sampling. By introducing the amplitude modulator, sampling and resolution are driven by the structure of the illumination and can be tuned to the requirement of the sample by adapting the data acquisition strategy. The potential of the system for soft-tissue imaging was demonstrated on two biological specimens prepared without staining: five different tissue layers were identified in a piglet esophagus, and the orientation of microfibers within the myocardium of a rat heart was visualized. We believe that the concurrent simplicity, sensitivity, robustness, compactness, and efficiency of our approach will be instrumental in making XPC\u00b5T more accessible and available to a wider community."}
+{"text": "Nature Communications 10.1038/s41467-022-29506-y, published online 20 April 2022Correction to: In the original version of the manuscript, the image shown in Figure 4c, third row down for the condition \u201cWT SCD\u201d was incorrect. This image incorrectly showed the same sample as shown in Figure 4a, top row for the condition \u201cWT DMSO\u201d. This has been corrected in the PDF and HTML versions of the article. The correct version of Figure 4 is as follows:"}
+{"text": "In our prior studies, human participants were required to generate long sequences of targeted hand movement when task difficulty varied between conditions, and where full vision of the hand and target was always available. The movement amplitude\u2014that is, the actual distance travelled\u2014for each movement was measured; consecutive movement amplitude values were formed into time series; then, the time series were submitted to spectral analysis. As task difficulty increased, there was a pink-to-white-noise shift in movement amplitude time-series structure. Those changes could be attributed to a difficulty-induced increase in the need to engage visual feedback processes, which maintain accurate guidance of the hand to the target. The current study was designed to provide a more direct test of the hypothesis that difficulty-induced increases in visual feedback processing modulate movement amplitude time-series structure. To that end, we examined cyclical aiming performance under four unique conditions created from the crossing of two index of difficulty (2 and 5 bits) and two visual feedback  conditions. That allowed us to examine how variations in visual feedback quality might influence difficulty-induced changes in time-series structure. In the visual feedback condition, we predicted that the increase in difficulty should result in a pink-to-white-noise shift in time-series structure. If that expected shift resulted from increased engagement of visual feedback processing, then in the no-visual feedback condition\u2014where visual feedback processing was disabled\u2014we should observe a strengthened pink-noise time-series structure that does not change with the increase in difficulty. The current results confirmed those predictions. That provides further support for the hypothesis that engagement of closed-loop visual feedback processing modulates movement amplitude time-series structure. Traditionally, the control of manual aiming has been understood in terms of two types of information processes: Feedforward and feedback control e.g., \u20135. FeedfOur research has shown that when participants are required to generate long sequences of cyclical aiming movements under conditions of full vision and movement amplitude\u2014the target-to-target travel distance\u2014is recorded, movement amplitude time-series structure increases in complexity\u2014shifting from pink to white noise\u2014as task difficulty increases ,7. Fig 12(2A/W), where ID is the index of difficulty expressed in binary units (bits), A is the amplitude or distance between target centers, and W is the target width [In addition, in that research ,7 we defet width . We hypoet width \u20135,10\u201313.et width ,7. In adet width .Although it is reasonable to infer that pink-to-white-noise shifts in time-series structure reflect a transition from feedforward to feedback control, our aforementioned studies did not directly manipulate visual feedback availability. A manipulation of visual feedback would provide a more direct test of the hypothesis that shifts in time-series structure under visual feedback conditions reflect shifts in closed-loop motor control processes. For example, if increased closed-loop visual feedback processing is responsible for the ID-induced pink-to-white-noise shift in movement amplitude time series, then blocking visual feedback processing through the removal of visual feedback should result in increased dominance of feedforward control and a strengthened pink-noise time-series structure that remains constant across increases in the ID.We are aware of one study that examined manual aiming movement amplitude time-series structure under both visual feedback and no-visual feedback conditions: In Miyazaki et al. , long seIn the current experiment, participants performed in a cyclical aiming task under two ID levels\u20142 and 5 bits\u2014and two visual feedback conditions\u2014visual feedback and no-visual feedback, during which closed-loop visual feedback processing was enabled or disabled, respectively. Following our prior findings, under the visual feedback condition we predict a pink-to-white-noise shift in movement amplitude time-series structure with the increase in ID ,7,17. IfThirty healthy individuals, 19 of whom were female, and whose mean age was 23.933 years (SD = 3.523), served as participants. All participants reported that they were right-hand dominant, had no prior history of neurological disease or damage, and had normal or corrected-to-normal vision. They responded to advertisements for healthy right-hand dominant volunteers between the ages of 18 and 2(2A/W)\u2014we created two target displays, one that had an ID value of 2 bits  and one that had an ID value of 5 bits . With the increase in ID, there was an eight-fold increase in A while W was held constant. During the experiment itself, participants performed under both levels of ID twice, once under the visual feedback condition and once under the no-visual feedback condition. Thus, each participant performed in four unique experimental conditions. Each condition required the production of 500 consecutive cyclical aiming movements. The same apparatus and customized software reported in detail by Slifkin and Eder ,21 was ucursor on the video monitor would correspond to the position of the mouse on the graphics tablet. They were told to move back and forth between the two targets, being as fast and accurate as possible\u2014where the instruction to be fast was of equal importance to the instruction to be accurate\u2014and that a target hit would register if the cursor \u201clanded\u201d anywhere within the target region at the time of a mouse-button press. For each movement, a crosshairs marker appeared at the center of the currently active target; when the mouse button was pressed to indicate the end of the action, the marker moved to the opposite target to mark it as the newly active target. Any button press occurring when the cursor was outside of the target was classified as a target miss and resulted in a \u201cbeep\u201d sounded by the computer. The mouse cursor, targets, target marker, and error beep were active during the first 100 movements of all four experimental conditions , which translates to instantaneous acquisition rates of either 66.67 or 62.50 Hz (M \u2248 64.52 Hz), respectively. The spatial resolution of each sample was 0.1 mm. In addition, during data acquisition we recorded the x-dimension movement-trajectory position at the moment of each mouse-button press.All data presented in this report came from the x-axis distance between consecutive mouse-button press positions. We did not analyze the initial 200 movements of the time series in any experimental condition. That excluded the initial 100-movement calibration period (movements 1\u2013100) and the first 100 movements following the transition (movements 101\u2013200). The latter was meant to exclude any transient adjustments that may have been present following the transition. The remaining 300 movements in each condition (movements 201\u2013500) for each participant were submitted to data analyses. The main analysis involved spectral analysis of time series of consecutive movement amplitude measurements, where each movement amplitude measurement was the While analysis of movement amplitude time-series structure via spectral analysis was the primary focus of the current study, we also present an analysis of mean movement amplitude and mean movement time; the latter was the average time from one mouse-button press to the next. Analysis of those variables allowed an assessment of whether the ID manipulation was effective, which should be evident in between-ID differences for movement amplitude and movement time. For example, the analysis of mean movement amplitude allowed a determination of the scaling of movement amplitude to the different amplitude requirements imposed under ID 2 and ID 5. Following Fitts\u2019 law, its numerous replications, and our prior research, it was expected, at least under visual feedback conditions, that movement time would increase with the increase in ID e.g., ,13,14,21The average movement amplitude and movement time were calculated for each participant\u2019s time series under each of the four unique conditions. Separate two-way ID (2) by visual feedback (2) ANOVAs, with repeated measures on both factors, were used to test the reliability of the change in mean movement amplitude and mean movement time with the change in ID and visual feedback conditions.pwelch function. We chose pwelch parameter values that allowed each series to be analyzed as a single segment (window) of 300 data points.  Then, the 300-point segment was multiplied by a Hamming window followed by the calculation of the power spectral density. The power spectrum from each time series was divided into 150 bins of equal width where the frequencies associated with the upper limits of the lowest and highest frequency bins were 0.0033 and 0.5000 cycles per movement (Hz), which translates to 300 and 2 movements per cycle, respectively. Each frequency bin spanned a 0.0033 Hz range. The amount of power in each frequency bin was related to the magnitude of the movement amplitude oscillations within that bin\u2019s frequency range.Assessments of movement amplitude time-series structure were made through spectral analysis. Prior to spectral analysis, each 300-point movement amplitude time series was linearly detrended e.g., . The det\u03b2 from the power spectrum. That involved a log10 transformation of both the spectral power and frequency of each participant\u2019s power spectrum in each condition. Then, linear regression\u2014y = bx + a\u2014was used to describe changes in log10 power as a function of log10 frequency (see 10 transformation) was removed from the analysis. That step was taken because the aforementioned linear time-series detrending procedure has been shown to attenuate power in the lowest frequency bin, which may bias estimates of \u03b2 [see 10 transformation\u2014to the frequency bin with an upper limit of 0.1000 Hz\u2014or \u22121.0000 Hz after the log10 transformation. The reason for imposing a \u22121.0000 Hz upper limit is that a common feature of human performance time-series data exhibiting long-range correlations (including the current data) is a linear reduction in power across the lower frequencies until about \u22121.0000 Hz, after which there is a flattening, a sharp downturn, or a sharp upturn in power across the higher frequencies [e.g., see Our main measure of movement amplitude time-series structure was an estimate of b describing the relation between log10 frequency and log10 power is equivalent to the exponent \u03b2 in the equation for the power function S(f) = 1/f\u03b2. In that equation, S(f) is the spectral power at each frequency, 1/f is the inverse of frequency, and \u03b2 specifies the degree of proportionality between S(f) and 1/f [e.g., see b has a value of \u22121, then the power function \u03b2 has a value of 1. If \u03b2 = 1, then the fall-off of power is inversely proportional to the increase in frequency, which is the signature of a pink-noise time-series structure  For each dependent variable\u2014mean movement amplitude, mean movement time, and \u03b2\u2014the Tukey HSD post-hoc test was used to compare pairs of group means, which allowed us to investigate the locus of any significant main effects or interactions. All results reported as \u201csignificant\u201d had p values less than .05. Exact p values were reported, unless the p value was less than .0001; in that case, p < .0001 was reported. All statistical analyses were performed using Statistica v.13.3.A two-way ID (2) by visual feedback (2) ANOVA, with repeated measures on both factors, was used to examine changes in the group-mean \u03b2 values with an average across the remaining participants within the relevant condition. When separate two-way ANOVAs based on the two solutions were compared, the between-ANOVA statistical outcomes  were the same for each dependent variable\u2019s main effects and interaction. Furthermore, the two analyses applied to each dependent variable yielded essentially identical patterns of group means. Here, we report the results based on the missing data replacement procedure. Before reporting the statistical analyses of our results, we present representative time series from each condition.For three participants, data from 1 of the 4 experimental conditions was incomplete or missing. In two cases, the data files were corrupted. In the third case, one of the four conditions was run twice, which resulted in the absence of data for one condition. Two solutions were considered: The first solution entailed removing all data of the three participants from all analyses; the second solution entailed replacing the missing mean movement amplitude, mean movement time, and As with all data submitted to spectral analysis in the study, each panel in As shown in the time series and as highlighted by the polynomial regression functions, the contribution of low-frequency oscillations appears to be similar across the ID-2 no-visual feedback (top left panel), ID-5 no-visual feedback (top right panel), and ID-2 visual feedback (bottom left panel) conditions, but at the ID-5 visual feedback condition (bottom right panel) the polynomial regression function has flattened. In particular, at ID 2 a similar low-frequency-dominant time-series structure can be seen either when visual feedback was absent or present (cf. top left panel and bottom left panel). However, at ID 5 the low-frequency-dominant structure was attenuated when visual feedback was added (cf. top right panel and bottom right panel). It is at ID 5 where the control of manual aiming should require greater reliance on visual feedback processing and there should be increased time-series whitening. While the main results of this study will focus on further analyses of movement amplitude time-series structure , prior to that presentation we provide an analysis of the group-mean movement amplitude and the group-mean movement time.F = 634.297, p < .0001, \u03b7p2 = .956. When averaged across ID levels within each visual feedback condition, the group-mean movement amplitude was 69.892 mm and 70.466 mm in the visual feedback and no-visual feedback conditions, respectively. Those values were nearly identical, resulting in the absence of a significant main effect of visual feedback, F = 0.014, p = .907, \u03b7p2 = .0005. As seen in F = 0.552, p = .464, \u03b7p2 = .019.As shown in p = .0002) and from ID-2 no-visual feedback to ID-5 no-visual feedback (p = .0002). Differences between group means were not significant for either the ID-2-visual-feedback vs. ID-2-no-visual-feedback comparison (p = .924) or the ID-5-visual-feedback vs. ID-5-no-visual-feedback comparison (p = .973).  The pattern of Tukey HSD results reflects both the ANOVA results and the pattern of group means depicted in According to the Tukey HSD post-hoc test, there was a significant increase in the group-mean movement amplitude both from ID-2 visual feedback to ID-5 visual feedback  = 273.108, p < .0001, \u03b7p2 = .904. When averaged across ID levels within each visual feedback condition, movement time under visual feedback and no-visual feedback was 780.100 ms and 653.696 ms, respectively. The reduction in movement time with the removal of visual feedback resulted in a significant main effect of visual feedback, F = 11.326, p = .002, \u03b7p2 = .281. However, the magnitude of that effect differed at the different ID levels  = 17.163, p = .0003, \u03b7p2 = .372.As shown in vels see : At ID 2p = .0002) and from ID-2 no-visual feedback to ID-5 no-visual feedback (p = .0002). While a statistically significant difference between ID-2 visual feedback and ID-2 no-visual feedback was absent (p = 0.999), there was a significant increase of the ID-5-visual-feedback movement time over the ID-5-no-visual-feedback movement time (p = .0002). That provides further confirmation of the larger ID-induced increase in movement time under visual feedback as compared with no-visual feedback.  The pattern of Tukey HSD results reflects both the ANOVA results and the pattern of group means depicted in According to the Tukey HSD post-hoc test, there was a significant increase in the group-mean movement time both from ID-2 visual feedback to ID-5 visual feedback  of the regression line is negative at ID 2 and clearly flattens to a near-zero value at ID 5. In contrast, under no-visual feedback, the regression bs are negative and parallel for the ID-2 and ID-5 power spectra. That pattern of regression b results based on the group-mean power spectra matched the pattern of group-mean \u03b2 coefficients plotted in \u03b2 was reduced from 0.521 to \u22120.004 with the change from ID 2 to ID 5; thus, the distribution of power was in the pink-noise range at ID 2 and clearly whitened at ID 5. However, under no-visual feedback, \u03b2 was essentially unchanged with the increase in ID, that is, \u03b2 at ID 2 and ID 5 was 0.846 and 0.842, respectively; thus, in the absence of visual feedback, the distribution of power exhibited a strengthened pink-noise structure that persisted with the change in ID level.\u03b2 declined from 0.684 at ID 2 to 0.419 at ID 5. The overall ID-induced decline in \u03b2 was reflected by a significant main effect of ID, F = 9.807, p = .004, \u03b7p2 = .253. When averaged across ID levels within each visual feedback condition, \u03b2 increased from 0.259 under visual feedback to 0.844 under no-visual feedback, which yielded a significant main effect of visual feedback, F = 38.164, p < .0001, \u03b7p2 = .568. The differential influence of the visual feedback manipulation on the ID-induced change in \u03b2\u2014that is, the ID-2-to-ID-5 reduction in \u03b2 under visual feedback and the absence of an ID-induced change in \u03b2 under no-visual feedback\u2014resulted in a significant ID by visual feedback interaction, F = 6.323, p = .018, \u03b7p2 = .179. Under visual feedback, the ID-induced change from pink to white noise closely replicates our prior findings: In the current study , but the very small difference between ID-2 no-visual feedback and ID-5 no-visual feedback was not significant (p = 0.999). In addition, the reduction in the group-mean \u03b2 from ID-2 no-visual feedback to ID-2 visual feedback was not significant (p = .143), whereas the reduction from ID-5 no-visual feedback to ID-5 visual feedback was significant (p = .0002).  The pattern of Tukey HSD results reflects both the ANOVA results and the pattern of group means depicted in The Tukey HSD post-hoc test confirmed, namely, that the reduction in the group-mean Our earlier research showed that movement amplitude time-series structure in a cyclical aiming task shifted from pink to white noise with increases in the ID ,7. In thThe current study provided a more direct test of the hypothesis that increased whitening of movement amplitude time series reflects increased engagement of closed-loop visual feedback processes ,7,17. If\u03b2 values for the no-visual feedback and visual feedback conditions were in the pink-noise range and did not differ statistically. That finding is consistent with the idea that at low-ID levels there is little if any need to engage closed-loop visual feedback processing, even when visual feedback is available [e.g., When viewing the results as changes across visual feedback conditions within each ID level, we also found confirmation of our predictions: Within ID 2, the group-mean le e.g., . In contle e.g., ). That sle e.g., .As might be predicted by Fitts\u2019 law and its numerous replications e.g., ,13, we fFurthermore, the current pattern of movement time results is consonant with the findings of Wu et al. . They exAs shown in \u03b2 values to the absence of visual feedback  under visual feedback. Thus, while movement time was always sensitive to variations in ID, \u03b2 was only sensitive to variations in ID when visual feedback was available and there was an ID-induced need to engage closed-loop visual feedback processing. How can those findings be explained in terms of our model of movement amplitude time-series structure [\u03b2\u2019s insensitivity to the increase in ID in the absence of visual feedback\u2014when visual feedback processing was disabled\u2014and 2) \u03b2\u2019s sensitivity to the increase in ID in the presence of visual feedback\u2014when visual feedback processing was enabled.In contrast, there was no ID-induced change in tructure ,7? Accor\u03b2. In turn, there was a strong relation between variations of \u03b2 and variations of movement time, r2 = .981 [\u03b2 must reflect \u03b2\u2019s dependence on closed-loop visual feedback processing too [\u03b2 from the four conditions of the current experiment was examined, the r2 value was more than halved, r2 = .413, compared to the same relation examined in Slifkin and Eder [r2 = .981. The reduction in the current r2 value occurred because, although under visual feedback the increase in movement time was related to a decrease in \u03b2, under no-visual feedback the increase in movement time was related to no change in \u03b2  and under a set of large-scale  target displays [scale doubled. We found that with the increase in the ID, movement time increased and \u03b2 changed from pink-to-white-noise values (those outcomes were observed in the visual feedback condition in the current study too [see Figs \u03b2 there were no statistically significant differences between scale levels within either the 2-bit or 5-bit ID level [\u03b2 [Would the current results have differed if the 2-to-5-bit increase in the ID was achieved through a reduction in target width while the movement amplitude requirement was held constant? In our prior research, under conditions of visual feedback we examined changes in movement time and displays . Within \u03b2 would have been expected. That expectation follows from our previous results where we found a systematic reduction of \u03b2 over the ID levels of 2, 3, 4, and 5 bits [\u03b2 values. We would not expect different \u03b2 values at intermediate ID levels. Thus, adding more ID levels should result in a similar pattern of results as that of the current study: Namely, we would still expect a reliable ID by visual feedback interaction like that shown in One might also wonder whether including additional levels of the ID would have changed the main findings of the current study. Our interest has been in determining whether ID-induced increases in visual feedback processing are related to changes in time-series structure ,7,17. ThWhile including conditions where an increase in the ID was achieved through a reduction in target width, including variations in target display scale, and including additional ID levels would provide more detail about the influence of the ID and visual feedback conditions on movement amplitude time-series structure, doing so would come at a cost: Reliable time-series analyses require lengthy time series, which increase both the duration of experimental sessions and the likelihood of participant fatigue . Consequ\u03b2 is uniquely sensitive to closed-loop visual feedback processing. Future research with the goal of quantifying the degree of closed-loop visual feedback engagement may benefit from assessments of motor-event time-series structure via \u03b2: Variations in \u03b2 might predict the degree of closed-loop visual feedback processing in a similar fashion as variations in time-series structure predict neurological disease severity [The original motivation for this study was to test the possibility that the proximal, direct cause of increased movement amplitude time-series whitening with increases in ID was the ID-induced need to engage the available visual feedback through closed-loop processing. The current findings provided support for that hypothesis. Furthermore, the results suggest that Last, the current study adds to other attempts to understand the processes and mechanisms underlying the structure of long sequences of discrete motor events e.g., ,34\u201336. I"}
+{"text": "Recent success stories in reinforcement learning have demonstrated that leveraging structural properties of the underlying environment is key in devising viable methods capable of solving complex tasks. We study off-policy learning in discounted reinforcement learning, where some equivalence relation in the environment exists. We introduce a new model-free algorithm, called QL-ES , which is a variant of (asynchronous) Q-learning tailored to exploit the equivalence structure in the MDP. We report a non-asymptotic PAC-type sample complexity bound for QL-ES, thereby establishing its sample efficiency. This bound also allows us to quantify the superiority of QL-ES over Q-learning analytically, which shows that the theoretical gain in some domains can be massive. We report extensive numerical experiments demonstrating that QL-ES converges significantly faster than (structure-oblivious) Q-learning empirically. They imply that the empirical performance gain obtained by exploiting the equivalence structure could be massive, even in simple domains. To the best of our knowledge, QL-ES is the first provably efficient model-free algorithm to exploit the equivalence structure in finite MDPs. Reinforcement learning (RL) aims to develop computer systems with the ability to learn how to behave optimally, or nearly so, in an unknown dynamic environment. An RL task typically involves an agent interacting with the environment, which is often modeled as a Markov decision process (MDP), and the agent\u2019s goal is to find a policy maximizing some notion of reward. In most settings in RL, the MDP is initially unknown beyond its state and action spaces. Hence, the agent aims to learn a near-optimal policy using the experiences collected from the environment.behavior or logging policy. Perhaps the most famous off-policy learning algorithm is the celebrated Q-learning algorithm )Assumption\u00a0A2.The agent knows the reward function R.In this section, we present a variant of Q-learning that exploits the equivalence structure in the environment to speed up the learning of the optimal Q-function. We call this algorithm QL-ES, which is short for \u2018Q-learning with equivalence structure\u2019.t to update potentially multiple entries of t, the agent can construct samples for all other pairs in counterfactual next-state for QL-ES follows the same machinery of QL but is also built on the idea that the knowledge on Algorithm 2 QL-ESInput: dataset T, learning rates Initialization:\u00a0for\u00a0do\u00a0\u00a0\u00a0\u00a0Sample action \u00a0\u00a0\u00a0\u00a0Find for\u00a0do\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Compute +1 using end for\u00a0\u00a0\u00a0end forThe agent thus uses st,at,st+ to updatWhen the underlying MDP admits some equivalence structure, QL-ES performs multiple updates of Q-function at any slot, in contrast to structure-oblivious Q-learning that updates only the Q-function of the current state\u2013action pair. Thus, we expect learning the optimal Q-function under QL-ES to be faster than Q-learning; this will be corroborated by the numerical experiments in Remark\u00a01.The multiple updates used in QL-ES can be straightforwardly combined with many other variants of Q-learning, such as Speedy Q-learning  and UCB-f is some suitable function f satisfying the Robbins\u2013Monro conditions, e.g., We finally remark that some works in the literature on Q-learning use learning rates of the form T time steps. A relevant notion of deviation often studied in the literature  is tfirst time step such that all state\u2013action pairs are visited at least once with probability at least M and the behavior policy M. Further, we have Let us first recall the classic definition of cover time ariants) ,38,39. LNext, we introduce a notion of cover time for equivalence classes, which is relevant to the performance analysis of QL-ES. We believe it can be of independent interest.Definition\u00a03.Let M be a finite MDP and The following theorem provides a non-asymptotic sample complexity for QL-ES. It concerns constant learning rates, i.e., Theorem\u00a01.There exist some universal constants A proof of this theorem is provided in Comparison with sample complexity of Q-learning. Theorem 1 tells us that the number of steps to have rem 2 in ) revealsM and M and M, the ratio M appears to be complicated and tedious, if possible at all. Nonetheless, it is possible to construct simple problem instances, where one can derive analytical bounds on This ratio S but on C, the number of classes in We refer the reader to the results in This section is devoted to reporting numerical experiments conducted to examine the performance of QL-ES against the (structure-oblivious) Q-learning algorithm. First, we present the considered evaluation metrics and environments. Then we present numerical assessment of (i)Max-norm Q-value Error defined as (ii)Total Policy Error defined as s.We consider two evaluation metrics in the experiments:t. Equivalently, we may compute the metric (ii) viaThe metric (i), which is in line with the definition of sample complexity studied in Working with  is prefeRiverSwim and GridWorld. These are classical MDPs widely used in the RL literature. Both render suitability to demonstrate the numerical performance of QL-ES since each allows us to define a family of MDPs with progressive difficulty levels.We consider two environments: RiverSwim and variants. A generic RiverSwim MDP with L states is shown in L of states, the more exploration is required. The L-state RiverSwim , the state\u2013action space is of size 84 , while the number of classes remains 8 in both. In S of states grows. Specifically, we consider RiverSwim, Perturbed RiverSwim , These results reveal that We now turn to reporting experimental results for QL-ES and Q-learning in RiverSwim and GridWorld. In the following figures, QL indicates the standard Q-learning algorithm (Algorithm 1). We used a constant learning rate To demonstrate the scalability of QL-ES, in We now turn to the results for GridWorld MDPs. As in RiverSwim MDPs, QL-ES significantly outperforms Q-learning in the grid-world environments. For Q-learning, the Q-value error remains considerable, even for Modified RiverSwim and Modified GridWorld defined as follows. The Modified RiverSwim is identical to 6-state RiverSwim  and QLES(6) manage to find optimal actions significantly faster than Q-learning. In addition, QLES(10) is far superior to QLES(6) because of the quite smaller Q-value error and total policy error. The results show that algorithms with a suitable number of equivalent pairs are sufficient to learn an optimal policy in most states reasonably fast.S, the size of the state space. Through extensive numerical experiments in standard domains, we demonstrated that QL-ES significantly improves over (structure-oblivious) Q-learning. These results revealed that exploiting state\u2013action equivalence favors faster convergence of the Q-function and policy learning in large MDPs. A limitation of our approach is the need for the prior knowledge on the structure. To the best of our knowledge, existing methods for learning the equivalence structure are all model-based. Hence, an interesting question is whether it is possible to exploit the equivalence structure without prior knowledge on the structure using only model-free algorithms. Devising such model-free algorithms (or otherwise establishing an impossibility result) is an interesting yet challenging topic for future work. Another interesting direction for future work is to investigate ways to combine the knowledge of the equivalence structure with function approximation methods. Finally, another avenue for future work is to study model-free algorithms for the regret minimization setting in average-reward MDPs ..S, the s"}
+{"text": "X of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization that cannot be captured by trees. A variety of classes of such networks have been discussed in the literature, including phylogenetic, level-1, tree-child, tree-based, galled tree, regular, or normal networks as models of different types of evolutionary processes. Clusters arise in models of phylogeny as the sets v. The clustering system N conveys key information on N itself. In the special case of rooted phylogenetic trees, T is uniquely determined by its clustering system N and N is a network of type N of type Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set  X of vertices without descendants (the leaves of the network) represents the extant taxa, while the remaining vertices model their ancestors.Networks used to model phylogenetic relationships typically are directed acyclic graphs (DAGs) with a single root, i.e., a unique vertex from which all other vertices can be reached from. As usual in phylogenetics, the subset a and b are more closely related with each other than with c  Dress ; on the T and hierarchies T is uniquely determined by N for a given clustering system T, the Hasse diagram T are isomorphic. For general networks, however, the situation is much more complicated  such that In section\u201cN whenever x and y. These are closely related to weak hierarchies.In \u201cA very prominent role in phylogenetics is played by level-1 networks. Section\u00a0\u201cX is denoted by A and B overlap if The power set of a given set G is undirected if E is a subset of the set of two-element subsets of V and G is directed if G are of the form degree of a vertex G, denoted by v. If G is directed, we furthermore distinguish the indegree H is a subgraph of G, in symbols induced by some subset We consider graphs P in an undirected (resp. directed) graph G is a subgraph consisting of G is undirected, G is directed, the existence of a undirected path for a subgraph P of a directed graph G that has vertices forward arcbackward arcP are the endpoints of P and all other vertices (in P) are its inner vertices. A path P with vertices induced (in G) if A path K in a directed graph G is a subgraph with vertices undirected cycleK in a directed graph G is a subgraph with K.A directed cycle bipartite if there is a partition of V into subsets W and G connects one vertex in W to one vertex in G is complete bipartite.An undirected graph connected if, for every two vertices u and v. A directed graph is connected if its underlying undirected graph is connected. A connected component of G is a maximal induced subgraph that is connected. A vertex v is a cut vertex in a graph G if G. Similarly, a directed or undirected arc  is a cut arc in G if the graph G.An undirected graph is biconnected if it contains no vertex whose removal disconnects the graph. A block of an undirected or a directed graph is a maximal biconnected subgraph  cycle. Equivalently, a block is non-trivial if it is not a single vertex or a single arc. An arc that is at the same time a  block is a cut arc. For later reference, we state here the following observations that are immediate consequences of the fact that two distinct blocks in a graph share at most one vertex  cycle in B.Any two vertices of a non-trivial block The following well-known result will also be useful throughout:H be a biconnected subgraph of G and P be a path in G that only shares its endpoints with H. Then, the subgraph obtained by adding P to H is again biconnected. contains at least one forward and one backward arc. In a DAG G, a vertex ancestor of v a descendant of u, in symbols G from u to v. We write u and v are comparable and otherwise, incomparable. Moreover, if u is a parent of v, v is a child of u, v that is B a terminal vertex (of B). Note that every terminal vertex v of a non-trivial block B must always have indegree at least 2 since, by Corollary\u00a0v lies on some undirected cycle in B and, by v in B, its two incident vertices on this cycle must both be in-neighbors. Below we will consider DAGs in which terminal vertices are a type of so-called hybrid vertices.A directed graph r et\u00a0al. , we callmentclass2pt{minimu,\u00a0w) in a DAG G is a shortcut if there is a vertex u,\u00a0w) of N is a shortcut if G has a directed path from u to w avoiding   networks here as a slightly more general class of DAGs than what is customarily considered in most of the literature on the topic.(rooted) network is a directed acyclic graph (N1)root of N, with There is a unique vertex  A network is phylogenetic if (N2)There is no vertex  A vertex with leaf if hybrid vertex if tree vertex if X.A We emphasize that all networks considered here are rooted and thus we always use the term \u201cnetwork\u201d instead of \u201crooted network.\u201dtrees. The set of inner vertices of a network N is strict descendant of x contains v. In contrast to the even more general definition  ofNrooted atv, is the network obtained from the subgraph N[W] induced by the vertices in w if it has indegree 0 and outdegree 1 in N[W] or hybrid vertices of N that have in- and outdegree 1 in N[W].For a vertex N with leaf set X is often called a network onX. Two networks X are graph isomorphic, in symbols graph isomorphism betweenandX, we say that isomorphic in symbols N on X is unique w.r.t. some property (or some set of properties), if A network Many studies into phylogenetic networks require that reticulation events and speciation events are separated, i.e., separated if all its hybrid vertices have outdegree 1.A network is In particular, all leaves have indegree 1 in a separated network (or indegree zero if the network consists of a single vertex).phylogenetic and separated are part of the definition of networks in many publications in the field, see, e.g., Jetten and van Iersel  by Create a new vertex As mentioned above, often only separated networks are considered, stipulating that 1) leaves, i.e., vertices  leaves, u,\u00a0v) for all v,\u00a0w) for all Replace arcs  The notation The operation entclass1pt{minimacf. Fig.\u00a0A.Fig. 3CWe are now in the position to define least-resolved networks:N is least-resolved  such that Repeatedly apply In many applications, phylogenetic networks are considered. However, Apply Now, contraction of an arc The term \u201cancestor-preserving\u201d\u2014which is rigorously defined below\u2014has been used in particular for mappings between certain network  in N results in a network X and N and Let N be a network on X and  be a shortcut in N. Since  is a shortcut, there is a P in N. Since N is acyclic and u is not a vertex in P since otherwise w has indegree larger than 1 in N. In particular, there is a uw-path P. Since removal of  only decreases the indegree of w and Let N. Clearly, removal of arcs changes nothing about this and thus N. If u,\u00a0w), then u,\u00a0w) by the uw-path Now, let X and we have By the latter arguments, Note that deletion of a shortcut from a phylogenetic network does not necessarily result in a phylogenetic network.N is shortcut-free and has no vertex of outdegree 1, then for every vertex v and w are N is phylogenetic.If a network N is shortcut-free, siblings w if and only if Since N be a network on X and N results in a network X or w.In particular, v and Let The proof is rather lengthy and technical and is, therefore, placed to \u201cN be a network on X and X and Let N be a network on X and X or w is the only out-neighbor of u, we do not add any out-neighbors for w. Hence, X.Let X and we have w is the unique out-neighbor of u, one can easily verify that By the latter argument, As an immediate consequence of Lemma\u00a0N is shortcut-free and does not contain vertices v with Every least-resolved network N be a network and N by applying N and N is phylogenetic, then w is a hybrid vertex and Let N be a network on X. We show first that w is the only vertex in N whose in-neighborhood changes and it has the new vertex w has at least one in-neighbor in N, which becomes an in-neighbor of N and thus w no longer has indegree 0, K comprising the vertices K are in N, then K is a directed cycle in N, a contradiction. If K contains an arc that is not in N, then K must contain the new vertex w and exactly the vertices of K at most once, K that are incident with K are also arcs in N. In particular, there is a N. Together with the fact that N contains a directed cycle, a contradiction. Therefore, Let N creates a network w is the unique out-neighbor of N is recovered from N and The operation N is phylogenetic. Assume first that w is a hybrid vertex and w is replaced by an out-neighbor N is phylogenetic, the latter arguments imply that there is no vertex w is a not hybrid vertex or w is not a hybrid vertex, then w does not change. In addition, w in w is a hybrid vertex and Suppose now that X. The newly created vertex w. The statement \u201cN is recovered from By the latter arguments, The following result shows that the expansion operation does not introduce shortcuts and is an immediate consequence of Lemma\u00a0N be a network and N by applying N is shortcut-free if and only if Let We remark that an analogue of Corollary\u00a0N will play a key role in the following. We first establish several technical results that will allow us efficiently reason about the block structure of a network.The blocks of N be a network and u and v are connected by an undirected path P that contains at least 3 vertices and of which all inner vertices w satisfy w.Let u and v, respectively. Let u and v would be u and v, respectively. By construction, P that is the union of the underlying undirected version of P contains at least the three vertices u, v, and w satisfy v and u are There are directed paths u and v are called \u201cup-down-paths\u201d in Bordewich and Semple . Thus, suppose B is a non-trivial block. Suppose, for contradiction, there is a vertex w in P w and all of its parents are contained in a non-trivial block B and w and u. By Observation\u00a0(1)w and all of its (at least two) parents are contained in B, then clearly (3) mentclass2pt{minimw is contained in a block B but not properly contained, then it must hold k networks:As a consequence, if a hybrid vertex N is level-k if each block B of N contains at most k hybrid vertices distinct from A network N is level-k if each block B of N properly contains at most k hybrid vertices. In Choy et\u00a0al.  for which As we shall see in Lemma\u00a0X and a subset closure operator as the map For a clustering system closed if, for all non-emptyA clustering system The following result is well known in the clustering literature.A clustering system For completeness, a proof is provided in \u201cWe continue with three simple observations concerning the clusters of networks.N be a network. Then, Let v lies on a directed path from the root x. Furthermore, w lies on a directed path from v. By (N1) and since N is a DAG, there is directed path from x that contains w, and thus By construction, v is a hybrid vertex with unique child w, we have N in Fig.\u00a0P connecting u or v. However, it requires that u and v have at least one descendant leaf in common, i.e., that We note in passing that the converse of Lemma\u00a0N be a network and u and v are connected by an undirected path (i)(ii)In particular, P satisfy P is a subgraph of a non-trivial block.Let u and v, respectively, to the leaf x. Let x is contained in both paths. It must hold that u and v would be u and v, respectively, to P satisfies all of the desired properties. Two see that P is a subgraph of a non-trivial block B, observe that, by Lemma\u00a0u and v are connected by an undirected path P and u and v are connected by two distinct paths that both have at least 3 vertices and that only have the endpoints u and v in common. Hence, u and v lie on a cycle K and thus in a common block B of N. In particular, P is a subgraph of K and thus of B. There are directed paths N be a network and u and v are B of N.Let u and v are u and v are contained in a common non-trivial block B of N. Since B. Thus, neither u nor v is a terminal vertex. In summary, Let w are redundant in the sense that every directed path from w to one of its descendant leaves necessarily passes through the unique child v of w. Thus, we have Clusters of outdegree 1 vertices N be a network. If v is the unique child of w in N, then Let N be a network, B a block in N and H be the set of hybrid vertices h that are properly contained in B and satisfy Let u and v are u and v are connected by an undirected path P which contains a hybrid vertex N. Since B and u and v, Observation\u00a0h must be properly contained in B by Lemma\u00a0It suffices to show that mentclass2pt{minimNote that Hasse diagramX as its unique root. The singletons The X. Then, every non-singleton set Let C to some singleton set C and C has a child C has a child C satisfies Let X with corresponding Hasse diagram Let X is the unique cluster in X is the root in Clearly, C is a singleton, and For a given a clustering system C does not overlap any other set. Then, there is no undirected cycle in C is a cut vertex in Let C does not overlap with any other cluster. If K in K cannot intersect both. Now, assume that C is neither a singleton nor X, both C is disconnected and thus C is a cut vertex. In particular, every undirected path connecting a cluster in C and thus the second statement of the lemma follows as an immediate consequence. Suppose that T is isomorphic to the Hasse diagram of its clustering systems Every phylogenetic tree nd Steel . Figure\u00a0nd Steel ; Baroni nd Steel ; Willsonnd Steel .regular if the map N and (ii)N is shortcut-free.A network N is regular if and only if the following three conditions hold: (a) v to u, i.e., u and v, then neither path consists of a single arc, i.e.,  is not a shortcut. Clearly, conditions\u00a0(ii) and\u00a0(c) are equivalent. It therefore suffices to show that condition\u00a0(i) holds if and only if conditions\u00a0(a) and\u00a0(b) are satisfied. Together, (a), (b) and Lemma\u00a0Proposition\u00a04.1 in Baroni et\u00a0al.  states tProposition\u00a0N with For every clustering system Every regular network is least-resolved.N is not least-resolved, i.e., there is a network N by a non-empty sequence of shortcut removals and application of N is shortcut-free and, therefore, the operation that is applied first must be a contraction. Therefore, and since no new vertices are introduced, it must hold N is regular, it holds Suppose, for contradiction, that the regular network N is shortcut-free and satisfies N. Hence, we obtainThe converse of Corollary\u00a0Not every least-resolved network is regular.Nevertheless, for level-1 networks the terms least-resolved and regular coincide as shown in Corollary\u00a0A clustering system X is a hierarchy if and only if N is a phylogenetic tree if and only if A clustering system The 1-to-1 correspondence of hierarchies and phylogenetic trees is well known, see, e.g.,  in Proposition\u00a0Regularity as characterized in Proposition\u00a0N has the path-cluster-comparability (PCC) property if it satisfies, for all (PCC)u and v are A network Definition\u00a0N with For every clustering system u and v.We emphasize that (PCC) is a quite restrictive property. For instance, the rooted N be a network satisfying (PCC) and Let u and v are Suppose N be a network. Then, Let vw-path which passes through some child Since Property (PCC) still allows that distinct vertices are associated with the same clusters. It requires, however, that such vertices lie along a common directed path.semi-regular if it is shortcut-free and satisfies (PCC).A network is We introduce the term \u201csemi-regular\u201d because, as we shall see in Theorem\u00a0N be a semi-regular network and let N is phylogenetic, then u is the unique child of v in this case.Let u be the unique child of v. Thus, it holds w and N being shortcut-free imply w is the unique child of v.Suppose first that N is phylogenetic and assume, for contradiction, that w has a unique child. Therefore, and since N is phylogenetic, there must be a vertex v and N being shortcut-free imply v. Now, suppose, in addition, that As a consequence of Lemmas\u00a0N be a semi-regular network and let Let N be a semi-regular network, Q(u) are pairwise N. Moreover, if Q(u) is contained in a non-trivial block, or adjacent pairs of vertices in Q(u) form a trivial block.Let Q(u) are pairwise Q(u) forms a directed path in N and there are unique N is acyclic and shortcut-free, this path must be an induced subgraph.By (PCC), u is a hybrid vertex and suppose there is u has a parent in Q(u). Then, there is v and N is shortcut-free, v and Q(u). By similar argument, only P formed by Q(u) have degree 2. Therefore, if one arc in P is contained in an undirected cycle, then all arcs in P are contained in this cycle, in which case Q(u) is contained in a non-trivial block. Otherwise Q(u) consists of a sequence of consecutive cut-arcs. Now, suppose The examples in Fig.\u00a0A network is regular if and only if it is semi-regular and there is no vertex with outdegree 1.N is regular, it is in particular also semi-regular and thus satisfies (PCC). Furthermore, then u,\u00a0v satisfying N is semi-regular (and thus shortcut-free) and suppose there is not vertex with outdegree 1. Then, Lemma\u00a0u,\u00a0v with N is regular. If N be a network on X. Then, N is regular.Let N is shortcut-free, satisfies (PCC), and has no vertex with outdegree 1  would be a shortcut, contradicting that N is semi-regular, and an arc  would imply A with a vertex in D cannot exist. Since B is a non-trivial block, a and d lie on an undirected cycle K in B. In particular, they are connected by two undirected paths that do not share any inner vertices. Thus, there is an undirected path u. Let P such that A. Since P does not contain u and u and v are N since otherwise u and v are u and v are v is not a terminal vertex since Suppose We note that semi-regularity cannot be omitted in Lemma\u00a0We continue by showing that whenever (PCC) is satisfied, least-resolved networks are precisely the regular network, To this end, we consider first the implications given by the operations N be a network, N by applying N satisfies (PCC) if and only if Let N and w is the unique child of By Lemma\u00a0u and v are N also satisfies (PCC), consider u and v are u and v are also u and v are Suppose first N satisfies (PCC). By similar argument as above, it holds, for all u and v are v and v and w are v and w is the unique child of v and w are w in v and v and w are Now, suppose u,\u00a0w) where Corollary\u00a0N be a network, N by applying N is semi-regular if and only if Let N be a network satisfying (PCC). The unique regular network N by repeatedly executing one of the following operations (1) and (2) until neither of them is possible: u,\u00a0w), andremove a shortcut  with apply Let X and that, for all Let mentclass2pt{minimmentclass2pt{minimN satisfies (PCC), i.e., for all u and v are u and v are u and v are also u and v are v with By assumption, entclass1pt{minimaN be a least-resolved network satisfying (PCC). Then, N is uniquely determined by Let N is shortcut-free  and contains no vertex with outdegree 1. By Theorem\u00a0N is regular. By Corollary\u00a0As a consequence of Corollary\u00a0N is regular if and only if N is least-resolved and satisfies (PCC).A network N is separated if all hybrid vertices have outdegree 1. We have already seen above that the Hasse diagrams of the clustering systems cannot produce separated networks with hybrid vertices because u is the only child of v. By Theorem\u00a0vice versa.Recall that a network entclass1pt{minimaCluster-popping algorithm (Huson and Rupp cluster network (Huson and Rupp The N is a cluster network if (i) it satisfies (PCC), and, for all (b)v is a hybrid vertex and parent of u or vice versa,(c)u is a child of v, then there exists no node w with if (d)v has exactly one child, which is a tree node.every hybrid vertex A network (i\u2019) However, this contradicts the existence of hybrid vertices v, which are required to have exactly one child u by (iv). To see this, observe that We note that the definition of cluster networks usually is expressed using the following condition instead of (PCC): We can rephrase conditions\u00a0(i)-(iv), and thus the definition of cluster networks, as follows:N is a cluster network if and only if it is semi-regular, separated, and phylogenetic.A network N is a cluster network, i.e., it satisfies conditions\u00a0(i)-(iv) in Definition\u00a0N satisfies (PCC) and is separated. Hence, it remains to show that N is shortcut-free and phylogenetic. Suppose, for contradiction, that  is a shortcut in N. Then, there is v is a hybrid vertex with exactly one child, a contradiction. Therefore, u is a tree node, contradicting that N must be shortcut-free and thus semi-regular. Suppose, for contradiction, that N is not phylogenetic. Hence, there is a vertex v with exactly one child u and v must be a hybrid vertex by\u00a0(ii), a contradiction.Suppose first that N is semi-regular, separated, and phylogenetic. Hence, N satisfies\u00a0(PCC), i.e., condition\u00a0(i). Condition\u00a0(iii) must be satisfied since an arc  with u is the unique child of v. Since N is phylogenetic, v must be a hybrid vertex. Conversely, a hybrid vertex v in a separated network has exactly one child u implying N is separated, it remains to show that the unique child u of a hybrid vertex v is a tree node. Suppose for contradiction that u is a hybrid node. Then, u again has a unique child w. Hence, we have v,\u00a0w) is an arc in N and, in particular, a shortcut, a contradiction. Therefore, condition\u00a0(iv) is also satisfied. Conversely, suppose We shall see in Theorem\u00a0N be a semi-regular phylogenetic network. Then, the multiplicity of each cluster Let N satisfies (PCC) and is shortcut-free. Let u is the unique child of v. Suppose, for contradiction, there is a third vertex w is the unique child of v, a contradiction. If v and u are both the unique child of w, which is not possible since u and v are adjacent in both cases. Recall that a semi-regular network As we shall see in Theorem\u00a0N and (i)N with cluster C such that sort the (ii)k vertices in C such that sort the (iii)set Let C in N to C in In other words, we map the N and V(N) and X. Writing v is a leaf if and only if Let C in N and k vertices with cluster C in V(N) and X and satisfies v is a leaf if and only if Since N be a semi-regular network. Then, N is the unique semi-regular network whose cluster multiset is Let N and N and X. In the following, we write v,\u00a0u) must be a shortcut in N, a contradiction. Therefore, X and thus N is the unique semi-regular network whose cluster multiset is Suppose We emphasize that none of the two conditions (PCC) and shortcut-free that define semi-regular networks can be omitted in Theorem\u00a0N (as any other network for which the property of being phylogenetic has been left out) are not determined by their clustering systems N in Fig.\u00a0It is an easy task to verify that semi-regular networks N be a cluster network with clustering system C has indegree at least 2 in u and v are adjacent in N.Let N is phylogenetic, separated, and semi-regular, i.e., it satisfies (PCC) and is shortcut-free. By Lemma\u00a0C has indegree at least 2 in By Theorem\u00a0u must be the unique child of v. Since N is phylogenetic, this implies that v. Since N is shortcut-free and by Observation\u00a0C in C in C has indegree at least 2 in Suppose C has at least two distinct parents v, N. Let v has a parent in each of v is a hybrid vertex. Since moreover N is separated, v has a unique child u. By Observation\u00a0C in N with cluster C. Conversely, suppose N with N is the unique semi-regular separated phylogenetic network with clustering system For every clustering system N be the network obtained from N is a phylogenetic network that satisfies N is semi-regular. In particular, by construction, all hybrid vertices in N have outdegree 1, i.e., N is separated. By Theorem\u00a0N is a cluster network.By Theorem\u00a0mentclasspt{minimaN is the unique cluster network with clustering system N and C has multiplicity 2 in C has indegree at least 2 in C has multiplicity 2 in N is the unique cluster network. In particular, by Theorem\u00a0N is the unique semi-regular separated phylogenetic network with clustering system It remains to show that reticulate networks in , and hence (b) is satisfied trivially. Since N is separated, every hybrid vertex v has exactly one child u. By Obs\u00a0u is also a hybrid vertex, i.e., there is N is shortcut-free, v and v and N also satisfies condition\u00a0(a). In summary, every cluster network is reticulate. By Theorem\u00a0N has the tree-child property if, for every .N be a tree-child network and u and v are Let The converse is not true. Figure\u00a0normal if it is tree-child and shortcut-free.A network is X comprises not only the leaves in our sense but also the root and all vertices with outdegree 1. Under this assumption, regular networks that are not normal, see Fig.\u00a01 of Willson  and alsoNot every semi-regular network, and in particular not every cluster network, is normal.N with N is unique w.r.t. these properties. In particular, N is the unique cluster network with Let N is phylogenetic, separated, and normal and satisfies N is semi-regular and thus, by Theorem\u00a0N is unique. Suppose From Proposition\u00a0N be a binary normal network. Then, N is the unique binary normal network whose cluster set is N is a cluster network.Let The following result appears to be well known, see, e.g., Murakami et\u00a0al. . An arguEvery phylogenetic level-1 network is tree-child.N be a phylogenetic level-1 network. If v is a hybrid vertex, then, by Lemma\u00a0v and all its parents. Suppose, for contradiction, there is a non-leaf vertex v whose children are all hybrid vertices. Suppose first that N is phylogenetic, this implies that v is hybrid vertex. Let u be the unique child of v, which is a hybrid vertex by assumption. The hybrid vertices u and v are contained in a common non-trivial block N is level-1. Now, suppose that v and N is level-1. Otherwise, there is at least one N is acyclic, there is N is level-1. Let v with a hybrid child v,\u00a0u) creates a new tree vertex u as its only child. The modified network is still level-1 but no longer tree-child.Note that \u201cphylogenetic\u201d cannot be omitted in Proposition\u00a0Next we consider the overlapping clusters in tree-child networks in some more detail:N be a tree-child network and suppose u and v are Let N satisfies (PCC) and thus either u,\u00a0v are contained in a common non-trivial block B. Set H of hybrid vertices. Since A is non-empty and, by assumption, h, we must have H. Since N is tree-child, there is a leaf x that is reachable from w along a path consisting entirely of tree vertices and thus cannot be a descendant of any hybrid vertex By Corollary\u00a0N is not necessarily closed.In particular, the case N be a tree-child network with clustering system Let Another class of networks that has received considerable attention in the last decade are tree-based networks  subdividing the arcs of T by introducing vertices with in- and outdegree 1 , and (b) adding arcs  between pairs of vertices, so that N remains acyclic.A network This definition further generalizes the original one for non-binary tree-based networks in Jetten and van Iersel  in the sN on X is tree-based if and only if there is a rooted (not necessarily phylogenetic) spanning tree T with leaf set X, i.e., there are no dummy leaves in T that correspond to inner vertices in N. Clearly, the unique incoming arc  of a tree vertex v must be contained in every rooted spanning tree T of a network N and thus u cannot be a dummy leaf in T. As an immediate consequence, the well-known fact that tree-child network are always tree-based  since the two vertices highlighted in orange correspond to the same cluster but are U of all inner vertices whose children are all hybrid vertices, called omnians in Jetten and van Iersel . Moreover, there are cluster networks and thus phylogenetic separated networks that do not satisfy (PCC).least common ancestor (LCA) of a subset N is an ancestor of all vertices in Y that is Bender et\u00a0al.  A least N, an LCA does not necessarily exist for a given vertex set. Moreover, an LCA is not unique in general. We write Y. In a (phylogenetic) network N, the root V(N), and thus, a least common ancestor exists for all In general DAGs N be a network and Let y is also an ancestor of all vertices in Z and thus there is a Z, i.e., Consider u only, we write Y exists and is uniquely determined. We leave Y with If u are defined in terms of the fact that no child of u is an ancestor of all vertices in Y. These definitions are equivalent:In Huber and Scholz , least cN be a network and Y if and only if u is an ancestor of all vertices in Y but there is no Y.Let Y if it is ancestor of all vertices in Y and only if-part of the statement follows immediately. Conversely, suppose u is an ancestor of all vertices in Y but there is no u is an ancestor of all vertices in Y but u is a least common ancestor of Y. By definition, We will in particular be concerned here with LCAs of leaves, i.e., the sets v with Suppose N be a network, (i)v with (ii)A.(iii)Let In much of the literature on least common ancestors in DAGs, only pairwise LCAs are considered. Networks with unique pairwise LCAs are of interest because of a close connection with so-called binary clustering systems  if (CL)For every A network N has property (CL). Then, for all Suppose v or one of its descendants. The second statement now follows directly from the definition. If In Lemma\u00a0N be a network satisfying (CL). Then, (i) Q(u) has a unique w is contained in a directed path from u to v, then Let q is the unique The second statement in Lemma\u00a0N satisfies (PCC), then it satisfies (CL).If a network N satisfies (PCC). Given a cluster W are pairwise Suppose that Figure\u00a0N with For every clustering system Since a normal network is tree-child, it satisfies (PCC) by Corollary\u00a0N satisfies (CL).Every normal network Property (CL), however, does not imply that N is an lca-network if A network From Observation\u00a0N is an lca-network and Every lca-network satisfies (CL). Moreover, if N be an lca-network on X and Let N satisfies (CL). Hence, we can apply Lemma\u00a0Since Every lca-network has a closed clustering system.N be an lca-network. We show that u with A. By analogous arguments, A. Since N is an lca-network. Therefore, Let N is a network with a closed clustering system N satisfies (PCC), then it is an lca-network.If A with two distinct vertices u,\u00a0v are Assume, for contradiction, that there is some set N be a network satisfying (PCC). Then, N is an lca-network if and only if its clustering system Let N be an lca-network satisfying (PCC). By Lemma\u00a0Let The example in Fig.\u00a0N is an lca-network if and only if its clustering system A semi-regular network Since every tree-child network satisfies (PCC) we also obtainN is an lca-network if and only if its clustering system A tree-child network Moreover, we haveN with A clustering system N and a unique cluster network N and N with N with Let entclass1pt{minimaentclass1pt{minimaAs in the case of trees, there is a simple connection of the LCA with the closure operator:N be an lca-network with clustering system Let Y. Let u be a vertex in N such that Y, this implies Let entclass1pt{minima) by Eq.\u00a0 follows Next we show that two sets have the same LCA whenever their LCAs are associated with the same cluster.N be an lca-network on X and let Let Since In this section, we consider an interesting subclass of lca-networks.N on X is a strong lca-network if it is an lca-network and, for every non-empty subset A network Figure\u00a0We shall see below that strong lca-networks are intimately connected with well-studied types of clustering systems.X isweak hierarchy if a binary if it is pre-binary and, for every C is the unique inclusion-minimal cluster containing x and y.A clustering system Weak hierarchies were introduced in Bandelt and Dress  and subsN be an lca-network. Then, the following conditions are equivalent: (i)For all (ii)Let N is an lca-network, it is in particular pre-binary  in Lemma\u00a0X is a weak hierarchy if and only if for every non-empty subset . Then, N is a strong lca-network if and only if Let N be a network satisfying (PCC). By Theorem\u00a0N is an lca-network if and only if N is a strong lca-network precisely if and only if Let Furthermore, we can use the same arguments in the proof of Proposition\u00a0A clustering system We start by showing that all phylogenetic level-1 networks have the path-cluster-comparability property (PCC).Every phylogenetic level-1 network satisfies (PCC).N is a phylogenetic level-1 network, then it is tree-child by Proposition\u00a0If N in Fig.\u00a0We note that \u201cphylogenetic\u201d cannot be dropped in Lemma\u00a0N be a level-1 network. Then, N is least-resolved if and only if N is regular.Let By Corollary\u00a0N for a given clustering system We emphasize, however, that there can exist least-resolved networks n be a positive integer. Then, there is no phylogenetic, shortcut-free level-1 network N on n leaves that is not a tree and where Let N be a phylogenetic, shortcut-free level-1 that is not a tree. By Lemma\u00a0N satisfies (PCC). Since, in addition, N is shortcut-free, N is semi-regular. Since N is not a tree, it must contain a non-trivial block B. By Lemma\u00a0u and v such that Let As an immediate consequence of Theorem\u00a0A phylogenetic level-1 network is semi-regular if and only if it is shortcut-free. Furthermore, a level-1 network is regular if and only if it is shortcut-free and has no vertex with outdegree 1.N be a phylogenetic level-1 network and v be a hybrid vertex of N. Then, Let N be a phylogenetic level-1 network and v be a hybrid vertex of N. By Lemma\u00a0v and all of its (at least two) parents are contained in a common non-trivial block B. Hence, consider first one of the parents v such that v and B and N is level-1, N is phylogenetic, we have N satisfies (PCC), and thus, v and Let v, which together with the arc v, and B and thus equals B. But then B contains two hybrid vertices v and In Case\u00a0(a), the arc v has a parent B and Lemma\u00a0V(N) being finite. The latter together with the fact that w of v that is distinct from v. Since v is a hybrid vertex, it has another parent B and satisfies Now, consider Case\u00a0(b), i.e., w is a parent of v. This together with Lemma w is a parent of v. Finally note that N be a level-1 network. Then, every block B has a unique B is not a single vertex or arc, B and B.Let B follows from Lemma\u00a0B is acyclic, a u in B does not have an out-neighbor along the cycle, and therefore, u has at least two in-neighbors that are contained in B. Thus, u is a hybrid vertex and, by Lemma\u00a0u is properly contained in B. By definition of level-1, there is at most one such vertex in B. The statement is trivial for a block that consists only of a single vertex or arc. Uniqueness of the As an immediate consequence, we haveN be a level-1 network and B a block of N. For every Let B . Thus, it is semi-regular, which allows us to use Corollary\u00a0u of v. Hence, u of v. Moreover, by Corollary\u00a0w in which case, N is strong lca-network by Lemma\u00a0Suppose that v has a child N is shortcut-free, u, w, and u and B and u and w and v does have a child v is the unique least common ancestor of Now, suppose N be a shortcut-free level-1 network on X and u,\u00a0w of v if and only if v is the N.Let u,\u00a0w of v. Since N is shortcut-free, u and w must be u and w are connected by an undirected path P whose inner vertices x satisfy P and the two arcs  and  form an undirected cycle whose v. Conversely, suppose v is the K in N. Hence, the two vertices v in K are children of v. In particular, v, N is shortcut-free. Therefore, we can apply Lemma\u00a0Suppose In many applications, vertex- or arc-labeled networks are considered as a scaffold to explain genomic sequence data  one of the Cases\u00a0(i) or\u00a0(ii) as specified in Lemma\u00a0Assume first that x and z as well as y and z, i.e., we have z and v as well. Hence, we have\u00a0(i) N. For both cases, we have Assume that Case\u00a0(i) holds for both x and z. In this case, y and z. Hence, neither of the Cases\u00a0(i) or\u00a0(ii) as specified in Lemma\u00a0x and z (resp. y and z), a contradiction. Therefore, Assume now that Case\u00a0(ii) is satisfied for z and Assume now that In Case\u00a0(a), v in N, the case N, we must have In Case\u00a0(b), suppose first, for contradiction, that z and z and c becomes a child of v in In Case\u00a0(c), In summary, neither of Cases\u00a0(a), (b), and\u00a0(c) is possible. Therefore, N be a level-1 network with clustering system Let B, and w with w and w and u are w are located in a common block Let N contains a non-trivial block and thus a hybrid vertex. In particular, therefore, if N is a rooted tree, then Inspection of the proof of Lemma\u00a0Lemma\u00a0(Property (L)) A clustering system For later reference, we record an equivalent way of expressing property (L):A clustering system Let N satisfies property (L).The clustering system Let A clustering system If one of the three sets C is not the intersection of two overlapping clusters. In particular, we haveIn order to show that closed clustering systems with property (L) define level-1 networks, we first demonstrate that one can identify the non-trivial blocks directly in a clustering system provided it satisfies (L). We start by introducing subsets of clusters with a given overlap: For a given clustering system T with Let T be phylogenetic tree with T is a tree, we have First, let T such that Assume now that Let D overlap. If D overlap, then (L) implies D. Now, (L) implies Consider a cluster C does not overlap with any cluster in Let D does not overlap with C in any of the three cases. If, on the other hand, D and C also do not overlap. If Alternative (iii) in Lemma\u00a0Let U(C). To see the \u201cif\u201d direction, note first that D, which is impossible because U(C), and thus also D, contains at least one set overlapping The \u201conly if statement\u201d follows directly from the definition of As a consequence we can use the condition C of a closed clustering system In general, Let X. Since Let Although U(C) does not overlap any cluster Let D cannot overlap since in this case (L) implies D does not overlap U. Let C. To see that C. Clearly, these two supersets overlap with C and So far, If C. Hence, If Lemma\u00a0Let D satisfies one of the alternatives: (i) Let As an immediate consequence of Corollary\u00a0Let Furthermore, the sets Let D and D overlap. By (L), Suppose that C in Let C. Hence, D and D and C in C has indegree zero if and only if C has exactly one in-neighbor D and C. Both of these paths must pass through if-direction must also hold. Suppose Lemmas\u00a0Let C. The statement is trivially true for all C.Let C. It is now easy to verify the graph obtained from (i) a rooted tree whose root has at least two children and (ii) connecting its leaves to an additional vertex is biconnected. Hence, C, and any two vertices lie along a common \u201cundirected\u201d cycle (which necessarily passes through C). By Corollary\u00a0D in the Hasse diagram (i)D is the unique in-neighbor of (ii)(iii)if Let D is contained in D, i.e., D is its unique in-neighbor.We start with showing Property (i). By Corollary\u00a0D are adjacent in We continue with showing Property (ii). Since D is the unique in-neighbor of Finally, we show Property (iii). Suppose that Let C, K exists. Since K contains at least one arc of P of K on at least two vertices and where all vertices of P are contained in P are both incident with one cluster in P must be distinct from P that is adjacent to K. Therefore, it suffices to consider the two mutually exclusive cases (a) C overlaps with some cluster C does not overlap any cluster. Furthermore, by Lemma\u00a0C are contained in C and thus K containing (cf. Eq. ). SupposD is the unique in-neighbor of K, it must be adjacent to another vertex K. Since D is the unique in-neighbor of K in D has at least one child F such that C does not overlap with any cluster in C and C does not overlap with any other cluster. Hence, U as child of U in D. In U does not overlap any set in U is a cut vertex in UD, there is no cycle in By Lemma\u00a0mentclass2pt{minimX satisfying (L). If Let C does not overlap any cluster. By Lemma\u00a0C in C. Clearly, We show that the arc We summarize Lemmas\u00a0X satisfying (L) and with Hasse diagram B is a block of B is a trivial block and, otherwise, in Case (i) a non-trivial one.Let If B is a trivial block of C or the single arc C overlaps with some cluster C and C does not overlap any cluster. Suppose now that B is a non-trivial block of B contains an undirected cycle K on at least 3 clusters. Since K contains at least one cluster C with two in-neighbors K .X satisfying (L). Then, the Hasse diagram Let B of B is a trivial block consisting of a single arc or, if B is a non-trivial block, and thus, by Proposition\u00a0C is a hybrid vertex. From Corollary\u00a0C is the only hybrid vertex in By Lemma\u00a0X that satisfies (L), there is a level-1 phylogenetic network N such that For every closed clustering system N for N is also a level-1 phylogenetic network. By Proposition\u00a0We summarize Corollary\u00a0N such that Let N is regular if N can easily be edited into a level-1 network We emphasize, however, that there is no 1-to-1 correspondence between level-1 networks and clustering systems. Recall that a network entclass1pt{minimaN, the regular network N by repeatedly removing shortcuts and contracting arcs  with N in this way.For every level-1 network N be a level-1 network. By Theorem\u00a0N by repeatedly (1) removing a shortcut and (2) applying u,\u00a0w) with N does not matter. By Corollary\u00a0u,\u00a0w) with N by repeatedly removing shortcuts and contracting arcs  with Let mentclasspt{minimaentclass1pt{minimaentclass1pt{minimaAs a direct consequence of Theorem\u00a0N such that Let N with v with N is regular and least-resolved.Let N with N is shortcut-free and contains no vertex v with N is phylogenetic. Now, let N be a shortcut-free phylogenetic level-1 network with v with N is a regular network, which is unique by Proposition\u00a0N is least-resolved. By Corollary\u00a0entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaMost publications on phylogenetic networks assume that leaves always have indegree 1, see, e.g., Huson et\u00a0al. .N with v with Let x with N is a phylogenetic network, Corollary\u00a0N is shortcut-free, Lemma\u00a0N is level-1 and Lemma\u00a0N satisfies N has indegree 1 by construction and all vertices with outdegree 1 must be adjacent to leaves.By Corollary\u00a0N is unique w.r.t. these properties. Let v with v with outdegree 1, we obtain a phylogenetic level-1 network N from N is the unique network with the desired properties. It remains to show that As an immediate consequence, we obtain a characterization of the level-1 networks that are completely determined by the least common ancestor function, and equivalently by their clusters.N be a level-1 network without shortcuts. Then, the following statements are equivalent: (i)(ii)For every Let N is regular, i.e., w. Moreover, assume for contradiction that there leaves If with Eq.\u00a0, i.e., tFinally, we show that every closed clustering system satisfying (L) is represented by a unique \u201cminimal\u201d separated level-1 network. More precisely, we haveN with N is obtained from the unique regular network Let N with N is also level-1. Since N is semi-regular, it is shortcut-free. Hence, a network with the desired properties exists. To see that N is unique, let By Corollary\u00a0N has property N a compatible w.r.t.networks if there is N on X such that A frequent task in phylogenetics is the construction of networks based on partial information of putative networks, e.g., subtrees  is a hereditary property, it suffices to show that if X such that N can be constructed in Let The proof  is rather lengthy and technical and is, therefore, placed to Sect.\u00a0There is a  level-1 network with For every clustering system If Statement (1) is satisfied, then the network computed with Check-L1-Compatibility is a network with B is highly constrained if the unique terminal vertex v of B has only two parents In level-1 networks, the structure a block N be a level-1 network. Then, every non-trivial block is an (undirected) cycle if and only if every hybrid vertex v in N satisfies Let k networks with We note that a similar result does not hold for level-N is a level-1 network and every hybrid vertex v in N satisfies N is outerplanar.If N is a cycle. Therefore, the underlying undirected graph of N does not contain a subdivision of the graph N is outerplanar. By Observation\u00a0d Harary , N is ougalled trees were introduced as phylogenetic networks in which all cycles are vertex disjoint. Here, we consider a more general version, where cycles are allowed to share a cut vertex and the network is not required to be phylogenetic. More constrained types of networks will be discussed in the subsequent sections.In Gusfield et\u00a0al. , galled galled tree is a network in which every non-trivial block is an (undirected) cycle.A Every galled tree is level-1.N be a galled tree. Every trivial block B contains at most one hybrid vertex distinct from B and assume, for contradiction, that B properly contains two hybrid vertices h and B is a cycle, the two vertices in B that are adjacent with h must exactly be the two in-neighbors of h. The same holds for h. It is now easy to see that the two path in B that connect h and B are out-neighbors. Hence, these two distinct vertices are B, which contradicts the uniqueness of Let Lemma\u00a0v.A network is a galled tree if and only if it is level-1 and satisfies B that is distinct from B.In a galled tree, every non-trivial block consists of two internally vertex disjoint paths connecting As we shall see below, this implies that its clustering system satisfies the following property:(N3O)If N with N is level-1 by Lemma\u00a0B. Clearly, B from v in v in v is a hybrid vertex in B and clearly distinct from i and j were chosen arbitrarily, the paths N has a non-trivial block that is not an undirected cycle. Hence, N is not a galled tree, a contradiction. Suppose there is a galled tree The converse of Lemma\u00a0N is the clustering system of a shortcut-free galled tree. By Lemma\u00a0N is level-1, and thus, it is closed and L), and does not contain three pairwise overlapping clusters. By Corollary\u00a0N is not a galled tree, i.e., it contains a non-trivial block, that is not an undirected cycle. By Observation\u00a0N is shortcut-free, N must be a galled tree. Suppose first that tisfies NO. Now, spre-pyramidal if there exists a total order X such that, for every Diday ; Bertran(WP)If  Taken together, (L) and (WP) imply (N3O). More precisely, we haveA necessary condition Nebesk\u00fd  for \\docLet Assume, for contradiction, that Pre-pyramidal set systems are also known as \u201cinterval hypergraphs.\u201d A characterization in terms of an infinite series of forbidden subhypergraphs has been developed in Tucker ; TrotterLet Starting from Duchet  and (N30).N with Let N is, in particular, a phylogenetic level-1 network (cf. Lemma\u00a0N satisfies (PCC). By definition, every non-trivial block contains at least 3 vertices. If a block B would contain exactly three vertices, then one easily sees that N contains the shortcut N contains at least 4 vertices. Assume, for contradiction, that N contains a non-trivial block B with at least B refers to an (undirected) cycle in N. Hence, there are two internal vertex disjoint paths in B connecting N is shortcut-free and v and the other path contains vertices B is an undirected cycle, one easily verifies that v and v and v and v and Suppose first that N with v, N. In particular, we have B contains at least five pairwise distinct vertices v, Assume now that there is a shortcut-free phylogenetic galled tree k networks N that are not level-It is worth noting that for paired hierarchies, and in particular also for hierarchies, mentclasspt{minimaThe literature on phylogenetic networks often stipulates that the leaves n et\u00a0al. . FurtherN is conventional if (i) all leaves have indegree at most 1 and (ii) every hybrid vertex is contained in a unique non-trivial block.A network N is conventional, while We remark that if X satisfying (L). Then, Let B and By Lemma\u00a0mentclass2pt{minimN is separated, then N is conventional.If N separated. Then, all leaves in N must have indegree at most 1 since they have outdegree 0 and, by definition, hybrid vertices have outdegree 1. By Lemma\u00a0v that is contained in two non-trivial blocks B and v is hybrid vertex in a separated network, we have v that is contained in two non-trivial blocks cannot exist. Hence, N is conventional. Suppose binary if it is phylogenetic, separated, and all vertices have in- and outdegree at most 2. Equivalently, in a binary network, every tree vertex is either a leaf or has exactly two children, and every hybrid vertex has exactly two parents and one child. As an immediate consequence of the definition, Proposition\u00a0Recall that a network is Binary level-1 networks are always phylogenetic, separated, conventional, tree-child, galled trees.N be a binary level-1 network. Then, N is a tree.Let N be a binary level-1 network. By definition, N is phylogenetic. If N is a tree, then N is not a tree and thus, N contains hybrid vertices all with outdegree 1 in N. However, Proposition\u00a0Let Hence, (2-Inc) A clustering system N be a binary network that satisfies (PCC). Then, Let N be a binary network on X with clustering system Let v has at least one but at most two parents in N since N is binary and N with v has at most two parents, at least two of w of v in N. W.l.o.g. assume that v is Assume first that there are (at least) three inclusion-minimal clusters C cannot be a singleton. Since C is not a singleton and N is binary, we can conclude that v has at least one but at most two children in N. Let N with v has at most two children, at least two of w of v in N. Since v is Assume now that there are (at least) three inclusion-maximal clusters X. Then, there is a binary level-1 network N with Let N by applying N is binary. Moreover, since N is a level-1 network. Hence, a binary level-1 network N with N is a binary level-1 network. Conversely, suppose that N is a binary level-1 network on X with N satisfies (PCC) and thus, by Lemma\u00a0Assume first that Since a phylogenetic level-1 network satisfies (PCC) by Lemma\u00a0N be a phylogenetic level-1 network. Then, N is a cluster network if and only if it is shortcut-free and separated.Let Observation\u00a0N be a binary level-1 network. Then, N is a cluster network if and only if it is shortcut-free.Let We finally consider the problem as whether a clustering system w in A given clustering system N be such a network with w in w in N is a galled tree. Hence, by Theorem\u00a0Assume first that w in n leaves such that each inner vertex has exactly two children and the subgraph induced by the inner vertices is a directed path with the root B, B. Let v be vertex in v as follows: If v. Otherwise, v is a tree vertex. In this case, let B in v that are not contained in some v by a caterpillar n leaves of the caterpillar and the elements in B. We therefore re-attach, for each block B as children of the leaf of the caterpillar that corresponds to B. Note that this construction is well defined since, by Lemma\u00a0N with Assume now that Using Check-L1-Compatibility and the results in Theorem\u00a0Determining if a clustering system N whose hybrid vertices w have For all phylogenetic level-1 networks w in N have N is a galled tree by Observation\u00a0w in If all hybrid vertices N for which there is a binary level-1 network w with B such that N that is obtained from N is still phylogenetic and level-1 and by Lemma\u00a0The converse of Corollary\u00a0In this part, we focus on a particular subclass of networks:N is a quasi-binary if B in N.A network We note that, in particular, all binary networks are quasi-binary. Moreover, quasi-binary networks are separated. Therefore and by Corollary\u00a0Quasi-binary level-1 networks are separated galled trees.N is a phylogenetic quasi-binary level-1 network. In this case, we obtain Property (PCC) as an immediate consequence of Lemma\u00a0Theorem\u00a0all networks N for which either precisely one or at least one of the following conditions hold: N is level-k, N does not satisfy (PCC);N is not quasi-binary;N is not shortcut-free;N is not phylogenetic.Then, no network Let N be a phylogenetic quasi-binary level-1 network. Then, N is the unique phylogenetic quasi-binary level-1 network tree whose cluster multiset is Let N and N and V(N) and X. In the following, we write v is a leaf if and only if N and Suppose that both N is acyclic and finite, we can assume w.l.o.g. that v,\u00a0u) is a shortcut in N. In particular, u is a hybrid vertex and, since by definition the non-trivial blocks in the galled tree N correspond to the undirected cycles, B of N whose unique hybrid vertex is It remains to show that, for all N is quasi-binary, the hybrid vertex u has a unique child c. By the v,\u00a0u), there is an arc c is the only child of u) such that N is phylogenetic, u), or at least two children. By the choice of , the images of these vertices are adjacent with We continue with showing that z be the parent of the hybrid vertex u that is not v and observe that u must have a parent N is acyclic, it holds that z and v are the only two parents of u in N. Therefore, Let B consists of two paths that have only v and u in common and which do not contain additional hybrid vertices and since v and z are the unique two parents of u, it holds that Now, let Case\u00a0(a)q is also contained in B. In particular, q is a tree vertex. Since N is a galled tree, B is exactly the undirected cycle that is formed by the shortcut  and the directed path from q as an inner vertex). Hence, q has exactly one child B and, since N is phylogenetic, at least one child that is not in B. Consider an arbitrary such child B. Since all vertices of B lie on a directed path and N is level-1. The vertices N is a level-1 network whose non-trivial blocks correspond to undirected cycles, N contains a non-trivial block q to B and q and N. Since they are q of the tree vertex q is a N correspond to undirected cycles, we have q in N), a contradiction to the construction of mentclass2pt{minimCase\u00a0(b)N and X and thus N is the unique phylogenetic quasi-binary level-1 network whose cluster multiset is In summary, therefore, N. It utilizes the concepts of cherries and reticulated cherries that have been used extensively in the literature, see, e.g., Bordewich and Semple  are\u00a0between hierarchies and weak hierarchies (Bertrand and Diatta"}
+{"text": "Scientific Reports 10.1038/s41598-023-44957-z, published online 25 October 2023Correction to: The original HTML version of this Article contained a display error\u00a0in Equation\u00a02.This error has now been corrected in the HTML version of the Article; the PDF version was correct from the time of publication."}
+{"text": "X is called absolutely -closed if for any homomorphism h[X] is closed in Y. Let X is absolutely X is absolutely X is chain-finite, bounded, group-finite and Clifford\u00a0+\u00a0finite. On the other hand, a commutative semigroup X is absolutely X is finite. Also, for a given absolutely X we detect absolutely X.Let  X is complete if and only if X is closed in any metric space containing X as a subspace. A uniform space X is complete if and only if X is closed in any uniform space containing X as a uniform subspace. A topological group G is Ra\u012dkov complete if and only if it is closed in any topological group containing G as a subgroup.In many cases, completeness properties of various objects of General Topology or Topological Algebra can be characterized externally as closedness in ambient objects. For example, a metric space On the other hand, for topological semigroups there are no reasonable notions of (inner) completeness. Nonetheless we can define many completeness properties of semigroups via their closedness in ambient topological semigroups.topological semigroup is a topological space X endowed with a continuous associative binary operation A X is calledclosed if for any isomorphic topological embedding h[X] is closed in Y;injectively-closed if for any injective continuous homomorphism h[X] is closed in Y;absolutely-closed if for any continuous homomorphism h[X] is closed in Y.Let For any topological semigroup we have the implications:X is defined to be  closed if X endowed with the discrete topology has the corresponding closedness property.A semigroup A topological space satisfies the separation axiom zero-dimensional if it has a base of the topology consisting of clopen (=\u00a0closed-and-open) sets. It is well-known (and easy to see) that every zero-dimensional We will be interested in the  Since H-closed spaces ;complete topological groups ;absolutely maximal topological semigroups ;absolutely H-closed semilattices ;h-complete topological groups ;categorically compact topological groups ;sealed topological groups .Similar complete objects in different classes have been investigated under different names. For instance:mentclass2pt{minimgated in , 45, 51.gated in , 73; \\dogated in , 43, 63.gated in , 38, 50.gated in , 68, 71.gated in , 13 provX is calledchain-finite if any infinite set singular if there exists an infinite set AA is a singleton;periodic if for every bounded if there exists n-th power group-finite if every subgroup of X is finite;group-bounded if every subgroup of X is bounded;group-commutative if every subgroup of X is commutative.The following theorem (proved in  is a discrete subspace of Y;topologizable if X is not projectively -discrete if for every homomorphism h[X] is a discrete subspace of Y.Let The study of topologizable and nontopologizable semigroups is a classical topic in Topological Algebra that traces its history back to Markov\u2019s problem  of topolIn Propositions 3.2 and 3.3 of  the follX is X is injectively X is projectively absolutely (Banakh\u2013Bardyla) A semigroup The following two theorems characterizing absolutely X the following conditions are equivalent: X is absolutely X is projectively X is projectively X is finite.For a commutative semigroup X the following conditions are equivalent: X is absolutely X is ideally X is ideally X is chain-finite, bounded, group-finite and Clifford\u00a0+\u00a0finite.Let Theorems\u00a0Let G without elements of order 2 is a subgroup of an absolutely X. If the group G has infinite center, then G is not injectively G is a subgroup of the absolutely X. This example also shows that the equivalences Corollary\u00a0X letcenter of X, andideal center of X. Every commutative semigroup X has For a semigroup The following theorem proved in , Sect. 5X be a semigroup. X is Z(X) is chain-finite, periodic and nonsingular.If X is Z(X) is group-finite.If X is ideally Z(X) is group-bounded.If (Banakh\u2013Bardyla) Let In  it was pX, its ideal center (Banakh\u2013Bardyla) Let Theorem\u00a0X absolutely Let The \u201cideal\u201d version of Problem\u00a0X has absolutely Let Z-viable semigroups.The \u201cnon-ideal\u201d version of Problem\u00a0Xviable if for any Following Putcha and Weissglass  we call e in a semigroup X is defined to be viable if the setcoideal in X in the sense that X. By X.An idempotent X is viable if and only if each idempotent of X is viable if and only if for every X with By Theorem\u00a03.2 of , a semigFor ideally (absolutely) e be a viable idempotent of a semigroup X and e in X. X is ideally If X is absolutely If (Banakh\u2013Bardyla) Let X is called Z-viable if X is viable. It is clear that each viable semigroup is Z-viable. On the other hand, there exist semigroups which are not Z-viable, see Remark\u00a0A semigroup A of semigroup X letB of a semigroup X is called bounded if For a subset X is ideally (Banakh\u2013Bardyla) If a semigroup The following theorem gives a partial answer to Problem\u00a0X is absolutely Z-viable), then the set Z(X) is absolutely If a semigroup For classes X be an absolutely X, one of the following conditions is satisfied: Ce of for every C is countable;Ce of Ce of Then the set X is absolutely Let The cardinal xiom. By , 7.13, tZ(X) of any E(X) endowed with the natural partial order E(X) and also on the partial order of the semilattice reflection X.By Theorem\u00a0X is called a semilattice congruence if the quotient semigroup semilattice, i.e., a commutative semigroup of idempotents. The intersection X is called the smallest semilattice congruence on X and the quotient semigroup semilattice reflection of X. The smallest semilattice congruence was studied in the monographs  is discrete in Y). Since C is a prime coideal in X, the mapX to the 0-extension Y, endowed with the topology X, the image C is absolutely (resp. projectively) Assume that a semigroup e of a semigroup X is viable if the subsemigroup X. By X.We recall that an idempotent The following lemma was proved in , 2.5.X we have For any semigroup The inclusion E(X): by  or 20]  \\documenX we study the order properties of the posets In this section, for any semigroup X be a semigroup and Let X. Then the map Given two viable idempotents In the following four lemmas we prove the statements of Theorem\u00a0X, the posets For any ideally X, so it suffices to prove that the poset Y is not well-founded, we can find a strictly decreasing sequence Y. For every Y. Consequently, its preimage X.By Proposition\u00a0X and the complement X. Consider the semigroup S with the topology P. Since X is not ideally It is easy to see that X, the posets For any projectively X onto its semilattice reflection. If the semigroup X is projectively Let X is projectively If a semigroup X onto its semilattice reflection. Consider the set H of all homomorphisms from Let Theorem\u00a0X, the sets For any absolutely In this section we establish some properties of absolutely X we have implications X is finite;X is absolutely X is projectively X is projectively X is projectively Z(X) is periodic and If X is commutative, then the conditions (1)\u2013(6) are equivalent.For any semigroup The implication X is projectively Z(X) is periodic and group-finite. Then for every Z(X). In both cases, the set To prove that X is projectively Z(X) is periodic. By Theorem\u00a0To prove that X is commutative, we shall prove that Z(X) is periodic and X is viable and hence Z(X) implies that Now assuming that Z-viable semigroup is absolutely Z(X) is finite and hence If a Z-viability of X yields Z(X) is periodic and hence The In this section we shall prove a sufficient condition of the absolute (Stepp) Every chain-finite semilattice is absolutely X is called E-commutative if A semigroup E-commutative semigroup X is absolutely Each chain-finite group-finite bounded Clifford\u00a0+\u00a0finite X is absolutely Y. We should prove that the semigroup h[X] is closed in Y. Replacing Y by h[X] is dense in Y. Since X is bounded, there exists h is a homomorphism, we conclude that Y contains the dense set h[X] and hence coincides with Y. Therefore, To show that X is a chain-finite E-commutative semigroup, the set E(X) is a chain-finite subsemilattice of X. By Theorem\u00a0E(X) is absolutely h[E(X)] is closed in the Hausdorff topological semigroup Y. The continuity of the map n implies that X is Clifford\u00a0+\u00a0finite, the set Y, the set Y and contains the set Since h[X] is not closed in Y, take any point E(X) is chain-finite, we can apply Theorem\u00a0E(Y). By Theorem\u00a0L is closed in E(Y). Then its complement E(Y) and its preimage y in Y. Since E(X) is chain-finite, the nonempty subsemilattice X is group-finite, the maximal subgroup y in Y such that Assuming that h[X] is closed in Y. SinceX, we characterize subsets X. We recall that a subset bounded if In this section, given an absolutely The following notion plays a crucial role in our subsequent results.X is defined to be A-centrobounded over a set A semigroup antichain if In the following theorem we endow the set X be an absolutely X;X;X is B-centrobounded over every countable infinite antichain Let X by its 1-extension X contains a two-sided unit 1. By Theorem\u00a0Z(X) is chain-finite, periodic, nonsingular, and group-finite.Replacing the semigroup n witnesses that X is B-centrobounded over any set Z(X) and the choice of n, we haveThe equivalence It remains to prove the implication There exists a sequence X, for every u and hence the set Z(X) is periodic and group-finite). By the Pigeonhole Principle, for any Z(X) is chain-finite. Therefore, E(Z(X)). Write the infinite set Since the set X onto its semilattice reflection.Let Z(X) imply that the idempotent X and moreover, Let  2.15 in .X is absolutely X, the quotient semigroup X/I is absolutely Since the semigroup I is not empty and the element X/I is well-defined.For convenience, by 0 we denote the element Now we introduce a 0-discrete Hausdorff semigroup topology Q is nonempty, as X contains a unit exactly to omit the easier case Fix any free ultrafilter Q is a subsemilattice of Q. Thus, the semilattice Q contains the smallest element s. Since For any s. ThenThe inclusion Y, we need the following notations. For a real number r by r. For each A implies that Y. On the semigroup To introduce the topology To see that the topology It remains to prove that In each of these cases, So, it remains to consider three cases: (1) Assume that If (2) The case a and b do not belong to the same subgroup (3) If X, is itself Note that Y generated by the base Y. Also, since Let For any The claim is obvious if There exists X is Since m ensures that We claim that for every Y to the set T by the formula:T which satisfies the following conditions:if Let T is Hausdorff and zero-dimensional.The topology V in First we show that the topological space u is an isolated point of Y and T. So, we can take u in 1. If 2. If V is closed in t such that t is disjoint with V. If V. Finally assume that V is clopen.3. If Therefore the topology ab. We must find neighborhoods a,\u00a0b such that To check the continuity of the semigroup operation in So, it remains to consider three cases:1. (1a) (1b) (1c) 2. 3. Y is a dense subsemigroup of T. Thus, X. The obtained contradiction completes the proof of the implication Observe that the continuity of the binary operation in In this section we shall find some sufficient conditions for centroboundedness, which will be combined with Theorem\u00a0The following theorem is the main result of this section.X be a semigroup, X, the group X is A-centrobounded if one of the following conditions is satisfied: X is projectively Ce of h[C] is polyfinite;the semigroup X is projectively h[C] is countable;X is absolutely X is absolutely Ce of Let A is countable and hence admits an injective function ath coordinate projection. The definition of the homomorphism h implies that By our assumption, the set X is projectively Ce of C of X is projectively h[C]. By Theorem\u00a0H. By Theorem\u00a0h[C] is bounded. Then there exists X is A-centrobounded.1. Assume that h[C] is polyfinite. Then there exist X is A-centrobounded, it suffices to check that for any 2. Assume that the semigroup n and F, there exists a semigroup polynomial For every X is projectively h[C] is countable. By Lemma\u00a0C in X is projectively h[C]. Being h[C] is zero-closed, see Lemma\u00a0h[C] is polybounded and by Lemma\u00a0h[C] is polyfinite. By the preceding statement, the semigroup X is A-centrobounded.3. Assume that the semigroup X is absolutely h[C] of the metric group C is absolutely h[C]. By the absolute h[C], the semigroup h[C] is zero-closed and also h[C] is closed in the zero-dimensional topological group H. Then the metric h[C] is a Polish space.4. Assume that the semigroup h[C] is polybounded. If h[C] is countable, see [h[C] is polybounded. If h[C] is polybounded by Theorem\u00a0h[C] is polybounded. By Lemma\u00a0h[C] is polyfinite. By the second statement of this theorem, the semigroup X is A-centrobounded.We claim that ble, see , 6.5. ByX is bounded. For a bounded subset least common multiple of numbers in the set F.5. Assume that X is not A-centrobounded. Writing down the negation of the A-centroboundedness, we obtain sequences (i)(ii)Consider the group n-th coordinate projection. Endow the group C of the absolutely X is absolutely To derive a contradiction, assume that the semigroup Recall that For every m. Let Let For every It follows from X be an absolutely Ce of for every h[C] is polyfinite;the semigroup h[C] is countable;Ce of Then the set X is absolutely Let X. By Theorem\u00a0S implies that S is Clifford\u00a0+\u00a0finite. By Lemma\u00a0S is absolutely By Theorems\u00a0X is absolutely If a semigroup Z(X) is chain-finite, group-finite, periodic, and nonsingular. By Lemma\u00a0X and so is its subset For every Therefore, the commutative semigroup Let X is absolutely X is absolutely Z(X) is periodic and henceGiven an absolutely If X, we shall prove the equivalence of the assertions (1)\u2013(4) of the theorem.Given a class X.The implication The implication"}
+{"text": "Numerical simulations show that the reflection phase difference \u0394\u03c6uv of the polarization converter is very close to +90\u00b0 in two separated frequency ranges, so the polarization converter can achieve high-efficiency and dual-band CP-to-LP polarization conversion, it can convert right-handed circular-polarized (RHCP) and left-handed circular-polarized (LHCP) waves into y-polarized and x-polarized waves respectively in the two separated frequency bands of 8.08\u20139.27 GHz and 13.80\u201327.11 GHz; moreover, its polarization conversion rate (PCR) is kept larger than 99.7% in the two frequency bands. Finally, to validate the design, a prototype is manufactured and measured, the measured results are in good agreement with the simulated ones.In this paper, to achieve circular-to-linear polarization conversion, a novel polarization converter based on an anisotropic metasurface is proposed. Because the polarization converter is an orthotropic anisotropic structure with a pair of mutually perpendicular symmetric axes  The polarization of electromagnetic (EM) wave refers to the characteristics of the direction and amplitude of the electric field in the EM wave changing with time. For various planar EM waves, the spatial trajectory of the endpoint of the time-varying electric field vector at any spatial-point may be a straight line, a circle or an ellipse, so the polarization of EM wave can be divided into the following three basic types: linear polarization (LP), circular polarization (CP) and elliptical polarization (EM). Different polarized EM waves have different propagation characteristics, a suitable polarization should be chosen for EM waves propagating in different propagation environments, so it is of great significance to effectively modulate the polarization of various electromagnetic waves in real time. At present, the LP and CP waves are both widely used, in order to realize the interconversion of LP and CP waves, many LP-to-CP polarization converter based on various metasurfaces have been proposed, these polarization converters can convert LP wave into CP wave in a certain frequency band through reflection or transmission \u201316; howey- and x-polarized ones respectively in two separated frequency bands. Moreover, for the CP-to-LP polarization conversion, a detailed theoretical analysis is carried out, in which a new type of CP-to-LP reflection coefficients is proposed, the theoretical analysis shows that magnitudes of the CP-to-LP reflection coefficients of the polarization converter can be completely decided by the reflection phase difference \u0394\u03c6uv under u-polarized and v-polarized incidences; if the reflection phase difference \u0394\u03c6uv can be close to \u00b190\u00b0, the CP-to-LP polarization conversion can be realized.In this work, a novel CP-to-LP polarization converter is proposed based on an anisotropic metasurface, the polarization converter can achieve high-efficiency and dual-band CP-to-LP polarization conversion under both right-handed circular-polarized (RHCP) and left-handed circular-polarized (LHCP) incidences, the RHCP and LHCP incident waves will be converted to u and v along \u00b145\u00b0 directions with respect to the vertical y axis. In addition, the geometrical parameters of the unit cell structure are shown in P = 8.00 mm, a = 2.744 mm, b = 2.616 mm, d1 = 0.25mm, w1 = 0.20mm, d2 = 0.20 mm, w2 = 0.20 mm and h1 = 2.50mm and h2 = 2.90 mm; moreover, the two dielectric layers are both chosen as a Polytetrafluoroethylene (PTFE) with a relative permittivity of \u03b5r = 1.80 and a loss tangent of tan \u03b4 = 0.0008.The proposed dual-band CP-to-LP polarization converter is based on a reflective metasurface, which is a two-dimensional periodic structure, one of its unit cells is shown in u and v axes, so no cross-polarized reflection components will exist when it is under the incidence of u- and v-polarized waves, and its reflection matrix Rlin in the U-V coordinate system can be expressed as follows:The proposed CP-to-LP polarization converter is symmetrical with respect to both When the incident wave of the CP-to-LP polarization converter is assumed as a RHCP or LHCP one, the incident wave can be expressed as:Rlin, the total reflected wave under the RHCP and LHCP incidences can be expressed as:Thus, based on the above reflection matrix u and v are along \u00b145\u00b0 directions with respect to the y-axis, as shown in y- and x-polarized unit waves can be expressed as For the symmetric axes ruu and rvv in the reflection matrix Rlin will both be very close to 1.0, but the phases will be different, thus, when we regard the polarization converter as a lossless structure, the following equation is established:\u03c6uv = Arg(ruu) \u2212 Arg(rvv) \u2264 +180\u00b0. In this way, the CP-to-LP reflection coefficients in In addition, the CP-to-LP polarization converter can be regarded as a lossless structure because the loss tangent of its two dielectric layers is only 0.0008, the magnitudes of According to \u03c6uv is equal to +90\u00b0, the magnitude of ry\u2212RHCP and rx\u2212LHCP will be equal to 1.0, the reflected wave under RHCP incidence will be converted to a y-polarized one, and the reflected wave under LHCP incidence will be a x-polarized one; in addition, if \u0394\u03c6uv = \u221290\u00b0, the magnitude of rx\u2212RHCP and ry\u2212LHCP will be 1.0, the reflected waves under RHCP and LHCP incidences will be converted to x-polarized and y-polarized ones, respectively. However, if \u0394\u03c6uv \u2260 \u00b190\u00b0, the prefect CP-to-LP polarization conversion can\u2019t be achieved, the reflected wave will be an elliptically polarized one, ry\u2212RHCP(rx\u2212LHCP) and rx\u2212RHCP(ry\u2212LHCP) is a pure imaginary number, which means that the phase difference between them will be just \u00b190\u00b0, thus, the AR of the reflected wave can be expressed as:u- and v-polarized incidences, the simulation result, the phase difference \u0394\u03c6uv between ruu and rvv, is shown in \u03c6uv is very close to +90\u00b0 in the two frequency ranges of 8\u20139.5 GHz and 13.5\u201327.5 GHz. Thus, according to the above theoretical prediction, it is known that the polarization converter can achieve CP-to-LP polarization conversion in the two separated frequency ranges, and its reflected waves under RHCP and LHCP incidences will be converted to y-polarized and x-polarized ones, respectively. To show this, according to \u0394\u03c6uv in rx\u2212RHCP| and |ry\u2212LHCP| is kept less than \u201325 dB and the AR is always larger than 25.0 dB in the two separated frequency bands of 8.08\u20139.27 GHz and 13.80\u201327.11 GHz, which shows that the proposed CP-to-LP polarization converter can achieve dual-band CP-to-LP polarization conversion in the two frequency bands. In addition, for To numerically investigate the performance of the proposed CP-to-LP polarization converter, we have carried out numerous numerical simulations using Ansoft HFSS. Firstly, the polarization converter was simulated under Based on the CP-to-LP reflection coefficients and AR shown in Furthermore, to validate the above theoretical prediction, the proposed dual-band CP-to-LP polarization converter has been simulated directly under RHCP and LHCP incidences. The simulation was performed using the commercial software Ansoft HFSS. In the simulation, when the excitation was assumed as a CP plane incident wave, the commonly used Floquet Port could not be available, the excitation must be changed as an incident wave. In this way, in order to analyze the performance of the polarization converter in a certain frequency band, these frequencies must be swept in a discrete manner, thus, the amount of simulation calculation was increased by a little, however, the AR of the reflected wave under the CP plane-wave incidence was directly obtained through far-field report. The simulated results are presented in u- and v-polarized incidences because no ultra-wideband CP antenna exists in common microwave experimental equipment. The measured result, the phase difference \u0394\u03c6uv between ruu and rvv, is shown in \u03c6uv is close to +90\u00b0 in the two frequency ranges of 8\u20139.5 GHz and 13.5\u201327.5 GHz, which reasonably agrees with the above simulated results in \u03c6uv, the calculated magnitudes of the CP-to-LP reflection coefficients, together with the calculated AR of the reflected wave, are basically the same with the above predicted values, as shown in In order to experimentally validate the performance of the proposed CP-to-LP polarization converter, an experimental sample was fabricated and measured. The grounded dielectric substrate of the experimental sample is shown in u and v, and the reflection phase difference \u0394\u03c6uv under u- and v-polarized incidences is very close to +90\u00b0 in two separated frequency ranges, the polarization converter can convert RHCP wave into y-polarized one and convert LHCP wave into x-polarized one with a PCR greater than 99.7% in the two separated frequency bands of 8.08\u20139.27 GHz and 13.80\u201327.11 GHz. The performance of the CP-to-LP polarization converter has been verified by both simulations and experiment. In summary, the proposed polarization converter can achieve CP-to-LP polarization conversion, moreover, it is not only dual band, but also highly efficient, so it is of great application value to modulate the polarization of various EM waves.In this paper, a high-efficiency and dual-band CP-to-LP polarization converter was proposed based on an anisotropic metasurface. Because the proposed polarization converter is an orthotropic anisotropic structure with a pair of mutually perpendicular symmetric axes S1 Dataset(RAR)Click here for additional data file."}
+{"text": "Nature Communications 10.1038/s41467-023-43000-z, published online 11 November 2023Correction to: The original version of this Article contained an error in the Abstract. The correct version states \u201cuntapped reservoir\u201d in place of \u201cuntapped reservo)ir\u201d. The original version of this Article also contained an error in the Methods section. The correct version states \u201cSNV, Pangenome analysis of SMAG\u201d in place of \u201cSNV, Pangenome analysis of SAMG\u201d. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "For genotype and haplotype inference, typically, sequencing reads aligned to a reference genome are used. The alignments identify the genomic origin of the reads and help to infer the absence or presence of sequence variants in the genome. Since long sequencing reads often come with high rates of systematic sequencing errors, single nucleotides in the reads are not always correctly aligned to the reference genome, which can thus lead to wrong conclusions about the allele carried by a sequencing read at the variant site. Thus, allele detection is not a trivial task, especially for single-nucleotide polymorphisms and indels.k-merald, improves allele detection accuracy leading to better genotyping performance as compared to the existing WhatsHap implementation using edit-distance-based\u00a0allele detection, with a decrease of 18% and 24% in error rate\u00a0for high-coverage Oxford Nanopore and PacBio CLR sequencing reads for sample HG002, respectively. We additionally observed a prominent improvement in genotyping performance for sequencing data with low coverage. For 3To learn the characteristics of sequencing errors, we introduce a method to create an error model in non-variant regions of the genome. This information is later used to distinguish sequencing errors from alternative alleles in variant regions. We show that our method, https://github.com/whatshap/whatshap. Genotyping is a process used for detecting the genotypes of an individual, which further helps in the detection of haplotypes, a task termed as phasing. These processes are widely used in studying the genetic aspects of different diseases and genetic relationships among species. Both genotyping and phasing typically use the alignment between sequencing reads and a reference genome. Thus, prior to genotyping, it is important to determine for each read, whether it carries the reference allele \u201c0\u201d or alternative allele \u201c1\u201d at each of the variant positions it overlaps. Most commonly, short sequencing reads from second-generation sequencing technologies, e.g. Illumina, are used for this purpose because long reads obtained using third-generation sequencing technologies, e.g. Oxford Nanopore technology (ONT) and Pacific BioSciences (PacBio), tend to be more prone to sequencing errors . These k-mer pairs include cases where the two k-mers match, indicating an error-free position, or where they mismatch, indicating a sequencing error. The counts of k-mer pairs are then used to determine the probability for observing each reference-read k-mer pair across the whole genome. We introduce a new approach for global sequence alignment in k-mer space. The read, reference, and alternative sequences in each variant window (excluded during the training phase) are split into k-mers and the strings of k-mers are then aligned. Instead of using a fixed cost value, k-mer mismatches are penalized using the learned error model, i.e. k-mer mismatches that represent common sequencing errors can be allowed in the alignment at a low cost. The sequencing read is then assigned to the allele with the lowest alignment cost. k-merald has been incorporated into the existing WhatsHap implementation and is available as an alternative to the edit-distance-based\u00a0allele detection.In this study, we propose a new approach, F be the reference sequence excluding all variant windows, where each variant window, v and a flanking region of a fixed number of w base pairs on each side. The training data consists of F and the set of sequencing reads aligned to it, D. Suppose f denotes a k-mer belonging to F, while, d denotes a k-mer belonging to a sequencing read from D. During model training, described in F is traversed from left to right while maintaining, for each f, the count of each mapping d using the mapping positions from the input read alignments. For extracting the reference-read k-mer combinations k-mer AC-GTCT is aligned to the reference k-mer ACTGTCT, the respective * is the nucleotide following ACGTCT in the read sequence. These counts of k-mer combinations k-mer, to obtain a unique matrix M with reference k-mers f shown in columns (j) and read k-mers d represented in rows (i). An entry k-mer k-mer F. Although there are k-mer of length k, many of these combinations are not observed. The F are each given a pseudocount value k-mer combinations can theoretically exist, but have a low probability of occurrence based on our training data. For each reference k-mer f, we define k-mers d aligned to f, i.e. the pair M. The sum of individual counts over all of these pairs is denoted by M, is then converted into a matrix P, storing the probability of observing each possible reference-read k-mer pair k-mer combination As input, we expect a list of candidate variants. In the first step, as shown in learn\u201d module in WhatsHap.Algorithm 1. Model trainingInput:R1: The complete reference sequence, B2: Aligned sequencing reads, V3: Variants for which allele detection is to be performed, Output:\u2002M4: 5: whiledo6: ifthen7: \u20038: \u2003\u2003do nothingelse ifthen9: \u200310: \u2003\u200311: \u2003\u2003else12: \u200313: \u2003\u2003fordo14: \u2003\u2003R[i]15: \u2003\u2003\u200316: \u2003\u2003\u2003end for17: \u2003\u2003end if18: \u200319: \u2003end while20: return\u2002M21: Problem 1V be a set of all variant positions across the reference genome, let v. Determine b at position v.(Allele detection). Let Definition 1b sequence from the window around variant v and let v and v. If x and y, thenb at position v.. Let P, which represents our model of sequencing errors, to define an alignment cost k-mer-based comparisons  haplotagging, the process to label each read with a haplotype of origin, (ii) genotyping, and (iii) phasing.In summary, by design, the algorithm ensures that a read carrying a sequencing error aligns to the reference with a cost lower than to the alternative allele, thus minimizing the risk of a sequencing error being mistaken for a variant allele. The read is assigned the allele resulting in lowest alignment cost. However, equal alignment costs indicate that the algorithm was unable to make an allele detection based on the alignment. In case of multiallelic variants, the alignment is performed using each alternative sequence. Algorithm 2.k-mer alignmentInput:k-mers from the target sequence, 1: List of k-mers from the query sequence, 2: List of 3: Gap penalty, P4: Output: Optimal cost for aligning fordo5: 6: \u2003end for7: fordo8: 9: \u2003end for10: fordo11: fordo12: \u200313: \u2003\u200314: \u2003\u200315: \u2003\u200316: \u2003\u2003end for17: \u2003end for18: return19: k\u2009=\u20097 and w\u2009=\u200925. The error rate for each reference k-mer represents the sum of probabilities of observing each k-mer pair k-mers for ONT, PacBio CLR, and PacBio HiFi, each, reveals that the nature of erroneous k-mers also differs across the sequencing technologies  samples, HG001 (NA12878) and HG002 (NA24385). We used k-mer value of k\u2009=\u20097, variant window w\u2009=\u200925 and k is shown in k-merald for allele detection shows an improved performance in comparison to WhatsHap\u2019s genotyping results based on the conventional edit-distance-based\u00a0allele detection approach. For 54F1 score values also depict this improvement  and homoploymers  above 200 are more strongly enriched for correct genotypes when using Our training procedure exploits the similarity of a sequenced sample and the reference genome by using variant-free regions for training. In this way, our model can be readily retrained even on a single dataset, which potentially allows it to adapt to subtle differences such as version of the sequencing chemistry and other batch effects. Because the learning procedure is technology agnostic, we anticipate that our method can readily be applied to future long read data types.vbad149_Supplementary_DataClick here for additional data file."}
+{"text": "The heights obtained during the countermovement jump and drop jump tests have been measured by numerous studies using different calculation methods and pieces of equipment. However, the differences in calculation methods and equipment used have resulted in discrepancies in jump height being reported.The aim of this systematic review was to examine the available literature pertaining to the different calculation methods to estimate the jump height during the countermovement jump and drop jump.A systematic review of the literature was undertaken using the SPORTDiscus, MEDLINE, CINAHL, and PubMed electronic databases, with all articles required to meet specified criteria based on a quality scoring system.Twenty-one articles met the inclusion criteria, relating various calculation methods and equipment employed when measuring jump height in either of these two tests. The flight time and jump-and-reach methods provide practitioners with jump height data in the shortest time, but their accuracy is affected by factors such as participant conditions or equipment sensitivity. The motion capture systems and the double integration method measure the jump height from the centre of mass height at the initial flat foot standing to the apex of jumping, where the centre of mass displacement generated by the ankle plantarflexion is known. The impulse-momentum and flight time methods could only measure the jump height from the centre of mass height at the instant of take-off to the apex of jumping, thus, providing statistically significantly lower jump height values compared with the former two methods. However, further research is warranted to investigate the reliability of each calculation method when using different equipment settings.Our findings indicate that using the impulse-momentum method via a force platform is the most appropriate way for the jump height from the instant of take-off to the apex of jumping to be measured. Alternatively, the double integration method via a force platform is preferred to quantify the jump height from the initial flat foot standing to the apex of jumping. Jumping is commonly performed during competitive sports, which is an action requiring the coordination of multiple joints and muscles , 2. DuriThere are numerous pieces of equipment available to measure parameters required for JH calculations during both of these jump tasks. For example, force\u2013time data is recorded by force platforms (FP), or the position-time data is recorded by three-dimensional (3D) motion capture systems . SubsequA number of different methods are available to calculate JH , 32, 34.The primary aim of this systematic review was to examine the available literature pertaining to the different calculation methods to estimate JH during the CMJ and DJ tests. More specifically, we sought to critically evaluate the reliability, equipment selections, and the strengths and weaknesses of each method.This systematic review was conducted under the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) statement in 2020 . A revieOriginal and review journal articles were searched from SPORTDiscus, MEDLINE, CINAHL and PubMed electronic databases (publication date from 2000 to 2022). Figure\u00a0Studies were included if they met the following criteria: (1) implemented at least two or more calculation methods or pieces of equipment in the outcome measure; (2) clearly described equations of each calculation method, equipment information (i.e. type and sampling frequency) and jump actions (i.e. CMJ or DJ); included healthy adult participants (i.e. aged\u2009\u2265\u200918\u00a0years\u00a0old); (3) presented full data (mean and standard deviation) and statistical significance in results; (4) the drafts were written in English and were published in a peer-reviewed journal. For the purpose of this systematic review, the included articles were required to describe methods used to measure JH during CMJ and/or DJ. As such, articles that simply measured JH in their experimental designs were excluded.The quality scoring system used in the present study was adapted and modified from Bishop et al. . Each stA total of 6557 articles were initially returned with an additional four articles included from other sources , 35, 36.Of the 21 articles included in the final analysis  via a single piece of equipment (i.e. the FP) in four studies , 39, 42.The aim of this systematic review was to critically evaluate the available literature relating to different calculation methods to estimate JH during the CMJ and DJ. When collecting data in applied settings, the equipment and the calculation methods employed may have a significant effect on the outcome measure of JH. Given that a variety of equipment is available to collect FT data, the first sub-section will briefly compare the JH-2 values derived from different pieces of equipment, followed by the explanation of why the FT method over- or under-estimated the JH-2 compared to other calculation methods. The subsequent four subsections critically discuss the advantages and disadvantages of the IM method, the double integration method, the jump-and-reach method and the motion capture systems. Thus, the information in this systemic review makes suggestions for how to standardise procedures and use equipment, and which calculation method to use when assessing JH during the CMJ and DJ tests.u equals the initial velocity that is 0\u00a0m/s, t is the duration between the take-off and landing instants, where the FT should be half of the t, and a represents the absolute value of gravitational acceleration (\u2212\u20099.81\u00a0m. s\u22122) [The FT method measures the time intervals between the instant of take-off and landing during vertical jumping JH-2). This time is then used in the following equation of uniform acceleration, as shown in Eq.\u00a0. This ti\u00a0m. s\u22122) . As show\u00a0m. s\u22122) , 25.\u22122) [From the equipment selection perspective, Brooks et al.  used a F\u22122) ; thus, e\u22122) .p\u2009<\u20090.05) and ErgoJump Plus  photocell mats using the FT method. In terms of these two devices, the ErgoJump Plus showed a statistically significantly lower JH-2 compared with the FP along with poor\u00a0to\u00a0moderate reliability . In contrast, the SportJump System Pro photocell mat showed high reliability  compared to the reference FP . The under-estimation of the optical measurement systems could be because these systems were placed at a small height off the ground , where z et al. , 44. If z et al. . Accordiz et al. . Researcz et al. , 30. In p\u2009<\u20090.001). Reeve and Tyler [p\u2009<\u20090.001). Supported further by Moir [Compared to other calculation methods, the FT method has several limitations, which numerous studies have acknowledged , 34, 36.nd Tyler  suggeste by Moir , JH-2 cap\u2009<\u20090.001) and motion capture systems . In addition, a statistically significantly lower JH-2 was measured by the FT method using the jump mat (38.6\u2009\u00b1\u20096.5\u00a0cm) compared to the JH-1 measured by the double integration method using the FP  in the study by Buckthorpe et al. [p\u2009<\u20090.001) and DJ (p\u2009<\u20090.001). Thus, the rise in height generated by plantarflexion of the ankles prior to the take-off instant largely explains the higher JH-1 values calculated by the double integration method and motion capture systems [p\u2009=\u20090.972). Noting that Leard et al. [p\u2009>\u20090.001 and p\u2009>\u20090.05, respectively). Thus, the FT method provides similar outcomes to the motion capture systems, but only if measuring JH-2 where the take-off height is not considered [The FT method calculates the JH-2 via the time interval from the plantar-flexed take-off to landing on the force\u2013time data, where the take-off height of the jumper is not included in the calculation process. Consequently, this makes the FT method under-estimate JH-2 compared with the double integration method and motion capture systems i.e., JH-1) , 36. Diae et al. . Researc systems , 36, 41. systems  revealedd et al.  did not d et al.  may not d et al.  and S\u0142omd et al.  used the , 36. Dinsidered , 26. Onensidered  recruiteAlthough the accuracy of the FT method is primarily determined by the aforementioned factors, this method is still suitable for various sports testing environments because of its simple operation, fewer data processing and abundant equipment available  . If the J is the net impulse, and tstart and ttake-off are the time at instant of the propulsion phase and take-off, respectively. The vstart (v\u2009=\u20090) and vtake-off are the velocity at tstart and ttake-off, respectively. The FvGRF and Fg are the vGRF and the body mass of the participant, respectively. Finally, the vtake-off is extracted from Eq.\u00a0vtake-off is subsequently used for the calculation of JH-2 via Eq.\u00a0g represents the acceleration of gravity (\u2212\u20099.81\u00a0m. s\u22122).The IM method is based on Newtonian mechanics and related mechanical laws. Specifically, the IM relation is derived from Newton\u2019s law of acceleration, which is also connected to the law of conservation of energy . Accordip\u2009<\u20090.001), along with the accelerometer showing poor reliability (ICC\u2009=\u20090.47) [As previously mentioned, the accelerometer provides reliable but inaccurate JH-2 compared to the FP using the FT method . Not sur\u2009=\u20090.47) . Althoug\u2009=\u20090.47) , 43, 49.\u2009=\u20090.47) .p\u2009>\u20090.05), and both methods presented excellent reliability . To investigate which method is suitable to evaluate the loaded CMJ, P\u00e9rez-Castilla et al. [From the calculation method perspective, an early study by Moir et al.  confirmea et al.  recruitea et al. . Resultsa et al. . Althouga et al. , 50. In a et al. , 51. Moia et al.  found tha et al. . Thus, ia et al. , 39, thep\u2009<\u20090.01) and double integration method . Similarly, the JH-2 measured by the IM method (29.8\u2009\u00b1\u20098.9\u00a0cm) was found to be statistically significantly lower than the JH-1 measured by the double integration method  in a study by Chiu and D\u00e6hlin [Nevertheless, like the FT method, the IM method calculates the JH between the COM position at the take-off and the apex of the jump i.e. JH-2), and only accounts for a fraction of the work performed during the jump , 5, 15. , and onld D\u00e6hlin , and reqd D\u00e6hlin . Second,d D\u00e6hlin . Otherwid D\u00e6hlin , 48. Whed D\u00e6hlin , 36, lesd D\u00e6hlin , less thd D\u00e6hlin . Therefod D\u00e6hlin . The 0.3d D\u00e6hlin . This med D\u00e6hlin . Chavda d D\u00e6hlin  in additd D\u00e6hlin , 54.Furthermore, it would be possible to obtain the displacement\u2013time data by twice integrating the force\u2013time data from initial standing still to landing , and thetstart and tlanding are the time at instant of countermovement (or drop movement in DJ) and landing, respectively. The FvGRF and Fg are the vGRF and the body mass of the participant, respectively. The h0 in CMJ is the COM height of jumpers during initial standing still (i.e. h0\u2009=\u20090\u00a0m), and the h0 in DJ is the drop height. It is worth noticing that the DJ measures via the above equation are applicable only when the two-adjacent FP are available [Given that the FT method calculated JH-2 according to the time intervals from take-off to landing , 34, thevailable .p\u2009<\u20090.01). Like the IM method, the double integration also relies on the reading of vGRF from the FP and involves the numerical integration process [p\u2009=\u20090.079 and p\u2009>\u20090.01, respectively). Similarly using the FP with 1000\u00a0Hz, JH-1 was not statistically significantly different between the double integration method (0.432\u2009\u00b1\u20090.15\u00a0m) and the motion capture systems  [p\u2009<\u20090.01) was observed [n\u2009=\u200921), and authors in only four studies measured the JH-1 values using the double integration method concurrently with the motion capture systems [From the calculation method perspective, previous studies like Concei\u00e7\u00e3o et al. , Wank an process , where t process  and Wank process  revealedthod 0.43\u2009\u00b1\u20090.15\u00a0method 0.4\u2009\u00b1\u20090.15\u00a0mthod 0.43\u2009\u00b1\u20090.15\u00a0method 0.4\u2009\u00b1\u20090.15\u00a0m systems . It woulthod 0.43\u2009\u00b1\u20090.15\u00a0mp\u2009=\u20091.000) when measuring JH-1 via FP. Further to this, no statistically significantly different JH-1 between IM\u2009+\u2009S method and the motion capture systems  was found by Wade et al. [The double integration method is considered reliable during CMJ measures because this method starts the twice integration prior to the movement initiation of CMJ (i.e. standing with flat feet), where the initial standing height is a constant value, and a \u2018truly\u2019 zero acceleration is achieved, which is the requirement for accurate integrations , 32, 36.h0) equals zero as the jumpers have landed, so applying the integration process in reverse makes the calculation of drop height in the forward integration process unnecessary [As proposed by Baca , the douecessary , 36. Notecessary , 58, 59.ecessary , 32, 36,ecessary , and thiecessary , 55. Howecessary . Thus, iecessary , 32, 36,The jump-and-reach method via the vertical jump devices has been proposed to make the JH measurement more convenient for various tests in the field because the method needs less equipment and provides the outcome directly . Practitp\u2009<\u20090.05, p\u2009<\u20090.05 and p\u2009<\u20090.001, respectively). Given that the Vertec device is calibrated using flat feet standing on the floor, the jump-and-reach method (which measures JH-1) involves the positive vertical COM displacement generated by the ankle plantarflexion prior to take-off [p\u2009<\u20090.05). Furthermore, the intersession reliability measures in this study indicated that in female participants, the jump-and-reach method  was less reliable as opposed to the FT method ; in male participants, a higher intersession reliability was found with the jump-and-reach method  rather than the FT method  [p\u2009>\u20090.01). Whitmer et al. [p\u2009\u2264\u20090.01) [When comparing the difference in JH between methods, authors in six studies adopted the jump-and-reach method, and existing results again appeared to be somewhat inconsistent. Bui et al. , Brooks take-off . In conttake-off , 28. In take-off , 60. Thitake-off  required\u2009=\u20090.84) . Of note\u2009=\u20090.84) . Althoug\u2009=\u20090.84) , a lack \u2009=\u20090.84) , they dir et al.  estimate\u2009\u2264\u20090.01) . However\u2009\u2264\u20090.01) , 41.Despite the appeal of the jump-and-reach method, factors that influence the accuracy of the jump-and-reach method should not be ignored. First, the accuracy depends on the timing of the touch, which is the ability of jumpers to displace the vane or touch the wall at the peak height of jumping. If touching of the device does not appear during the peak height, the measured JH-1 via the jump-and-reach method will be under-estimated , 29. SecIn addition, it is not surprising to see the JH difference between the jump-and-reach method and other calculation methods (e.g. the FT method), as they measured disparate biomechanical constructs, i.e. the reaching height difference versus the FT, which the latter variable is associated with the jumpers\u2019 COM displacement . ConsequThe motion capture systems typically involve high-speed cameras or multiple 3D cameras. The 3D motion capture system acquires the position-time data by tracking the reflective markers placed on the trunk, pelvic and lower extremities , the lefp\u2009>\u20090.01). Similar results have been noted in Concei\u00e7\u00e3o et al. [p\u2009=\u20090.079). Although the difference is relatively minor, factors that affect the COM estimation and accuracy of the motion capture systems should be highlighted. For example, researchers in some studies only model parts of the total body for the COM estimation  , 63, whiThe cumulative body of literature indicates that the measured JH is influenced by the calculation methods and equipment employed. For measuring the JH from the COM height at the initial flat feet standing to the apex of jumping (i.e. JH-1), the double integration method via the FP is encouraged for practitioners, as this method measures the most comparable JH-1 values compared to the motion capture systems. Of note as well, when two-adjacent FP are unavailable in the DJ measurement, the double integration method is unable to calculate the initial standing height, and the integration process must be processed reversely. The motion capture systems are not preferred, given that this method requires accurate COM estimations and is primarily determined by the equipment availability. For measuring the JH from the COM height at the instant of take-off to the apex of jumping i.e. JH-2), we recommended that practitioners use the IM method via the FP when estimating JH-2 values in both CMJ and DJ, where the COM displacement before the take-off is ignored. The IM method requires a simpler integration process than the double integration method and shows excellent reliability. The FT method may be of use because of its simple calculative process and an abundant equipment selection enables practitioners to conduct the test when working with large groups of athletes. However, some factors such as the take-off and landing positions reduce the accuracy of the FT method, and practitioners should be aware of this. Similarly, the jump-and-reach method is the most convenient approach to estimate the JH-1 and the maximum jump-and-reach height when testing jumpers in a big squad, despite this method showing lower reliability in some studies. Therefore, if the jump-and-reach method is the only option to quantify JH-1, practitioners are suggested to minimise factors such as the coordination of the jump and arm swing or the timing of touch that affects the accuracy of the jump-and-reach method before conducting the data collection. The findings of this systematic review emphasise the strengths and weaknesses of each calculation method during the calculation of JH in CMJ and DJ (as shown in both Table , we reco"}
+{"text": "Understanding both the epidemiological and evolutionary dynamics of antimicrobial resistance is a major public health concern. In this paper, we propose a nested model, explicitly linking the within- and between-host scales, in which the level of resistance of the bacterial population is viewed as a continuous quantitative trait. The within-host dynamics is based on integro-differential equations structured by the resistance level, while the between-host scale is additionally structured by the time since infection. This model simultaneously captures the dynamics of the bacteria population, the evolutionary transient dynamics which lead to the emergence of resistance, and the epidemic dynamics of the host population. Moreover, we precisely analyze the model proposed by particularly performing the uniform persistence and global asymptotic results. Finally, we discuss the impact of the treatment rate of the host population in controlling both the epidemic outbreak and the average level of resistance, either if the within-host scale therapy is a success or failure. We also explore how transitions between infected populations (treated and untreated) can impact the average level of resistance, particularly in a scenario where the treatment is successful at the within-host scale. The level of resistance to a given antimicrobial is then a continuous trait by nature referred to as antimicrobial quantitative resistance (qAMR), at least at the population level, and qAMR is key to better understanding the evolutionary dynamics of AMR  resistance are generally based on the dynamical interaction between two parasite strains resulting in a discrete and finite formulation of MICs  is one of the major challenges we face in the modern area  model explicitly linking the within- and between-host evolutionary dynamics. Such a nested structure is particularly important because, over the past few decades, it is clear that ecological and evolutionary dynamics are influenced by processes operating across scales  is the bacterial intrinsic growth rate, and y to mutate towards a level x during the reproduction process. Therefore, the total number of bacteria produced at time x is quantified by x, either by the immune system (k). Thus, t, an individual\u2014with the immune system\u2019s response level An integro-differential equation is used to model the within-host dynamics of the bacterial population. Such a within model formulation is previously proposed in Djidjou-Demasse et\u00a0al. . Each hoIndividual transmission and loss rates at the between-host scale, t is then given byThe force of infection induced by infected individuals at time The dynamics of newly infected individuals (i.e. hin-host  and betwmentclass2pt{minimmentclass2pt{minimhin-host  are prechin-host . Therefohin-host \u20131.5).Fi.Fi\\documThe rest of this work is organized as follows. In Sect.\u00a0This section is devoted to the main results of the nested model \u20131.5). S. S1.5). First of all, for biological feasibility of the nested model \u20131.5), w, w1.5), k, p are always positive on p is a bounded function on Functions J is bounded and integrable on x.The mutation kernel J decays rather rapidly towards infinity in the sense that The mutation kernel Furthermore, the between-host model\u2019s parameters satisfy the following assumption.Recruitment rate The treatment rates The rates Parameters The transmission rates The dynamical properties of the within-host model  have beeThere exists a unique global solution +1(R) of  with \\doThe semi-flow defined by The semi-flow Let Assumption\u00a0x, within an individual with immune system level i, is calculated asThe basic reproduction number of Model  is stronWhen of Model .When \u03d1, Model  has a unof Model  with iniThe bacteria-free equilibrium of Model  is asympWhen Let We recall that the within-host model  is precist model   re re\\documi, is given byUsing the next-generation operator approach , t, t\\documLet Assumptions\u00a0n system \u20131.5) ha ha\\documTherefore, the threshold dynamics of Model \u20131.5) is is1.5) i(i)If f system -1.5) is is\\docum(ii)If f system -1.5) is is\\documLet Assumptions\u00a0x can be classically referred to as \u201csensitive\u201d, \u201cintermediate\u201d, or \u201cresistant\u201d depending on whether Here, we present a series of numerical simulations employing semi-explicit finite difference numerical schemes. We refer to Djidjou-Demasse  for an e Theorem\u00a0. The pro of type . SpecifiWithin-host parameterization The antimicrobial killing rate function x such that, p is p and k and p can be found in <1 Fig.\u00a0C. In suc)<1 Fig.\u00a0A, while )<1 Fig.\u00a0B. At the)<1 Fig.\u00a0F\u2013H. Moreize Fig.\u00a0F\u2013H, withion Fig.\u00a0E.Fig. 3DIn the second scenario, the treatment is assumed unsuccessful at the within-host level, i.e., the basic reproduction number of treated individuals )>1 Fig.\u00a0C. In suc)>1 Fig.\u00a0A,B. Inde)>1 Fig.\u00a0A, at the\u2217>0 Fig.\u00a0C. In con\u2217>0 Fig.\u00a0, increaseak Fig.\u00a0F\u2013H. In fium Fig.\u00a0E, where ium Fig.\u00a0E, the avOptimizing the treatment rate in the host population is key to controlling both the epidemic outbreak and the average level of resistance Increasing the treatment rate in the host population contributes to reducing the epidemic size at the between-host scale, although the effect is quite marginal in the treatment failure scenario at the within-host scale  wh whi. We We establish the existence of a positive global solution of the system . We firs, system  becomes5f system  are provLet ation of , and wheFor all The semiflow rated by  is boundThere exists a unique strongly continuous semiflow ution of . That isA is a Hille-Yosida operator. Then standard results apply to provide the existence and uniqueness of a mild solution to (ii)(iii)(iv)By  holds. We have for iii) holds, and then the second claim holds.Now, we show that condition  is nonnegative with its global minimum point By Theorem\u00a0Step 1: Differentiating Step 2: Note thatStep 3: Finally, combining k, f system  and usinBy using , we obtaby using  and (5.8s, using  and (6.9"}
+{"text": "Correction to: Journal of Cancer Research and Clinical Oncology 10.1007/s00432-022-04418-yIn Fig.\u00a05 of this article, there were two errors in Fig.\u00a05c, right panel. Firstly, the title of the graph (in the right panel) that had read \u201cTarget tumour\u201d should have read \u201cOff-target tumour\u201d. In addition, the graph had presented the raw tumour volume data, and it should have presented the % tumour volume increase data. Asterisks that depict the level of significance had also been missing;The Fig."}
+{"text": "However, along the other two directions, i.e., x2 and x3, their properties are constant. The effects of the size of a microstructure (the microstructure effect) on the behaviour of the composites can play a significant role. This effect can be described using the tolerance modelling method. This method allows us to derive model equations with slowly varying coefficients. Some of these terms can depend on the size of the microstructure. These governing equations of the tolerance model make it possible to determine formulas describing not only fundamental lower-order vibrations related to the macrostructure of these composite solids, but also higher-order vibrations related to the microstructure. Here, the application of the tolerance modelling procedure is shown to lead to equations of the tolerance model that can be used for non-periodically laminated solids. Then, these model equations are mainly used to analyse a simple example of vibrations for functionally graded composites with non-periodically laminated microstructure (FGL). Similar problems were investigated in the framework of the homogenised  model ; the resulting equations neglect the microstructure effect.Dynamic problems of elastic non-periodically laminated solids are considered in this paper. It is assumed that these laminates have a functionally graded structure on the macrolevel along the  Therefthe tolerance modelling method (or the tolerance method), to the monographs  can be investigated by applying an alternative approach, named erzbicki , Wo\u017aniakerzbicki ,65). ThiVarious mechanical problems of different periodic media were considered in many works using the tolerance method. Fluid-saturated micro-periodic grounds were analysed in . CertainThe tolerance method is also a good tool for modelling and analysing the functionally of structures with tolerance-periodic microheterogeneity. Various aspects of the elastic responses of laminates with functional gradation of properties were shown in the works ,90,91. TThe above-mentioned papers do not cover the full range of problems analysed by the authors using the tolerance method for various media with a periodic or tolerance-periodic structure. They also do not constitute a complete list of such literature.the tolerance model for functionally graded laminates (FGL) and then to show an application of these equations in the analysis of a simple dynamical problem for a special example of functionally graded laminates. The example has been selected in such a way as to obtain simple analytical solutions and to show the extension of the tolerance model in relation to the asymptotic model.The aim of this paper is to present equations of This paper consists of six sections.Introduction includes a short description of a problem under consideration and a review of some papers related to different objects with microstructure.Modelling preliminaries, basic denotations of a classical model of an elastic medium used for laminates are introduced. The known equation of such media is formulated.In Modelling technique includes some basic concepts of the tolerance modelling method, with the reminded definitions of the averaging operator, the tolerance-periodic function, the slowly-varying function, the fluctuation shape function. In the second section, two basic assumptions of the method -the micro-macro decomposition, the tolerance averaging approximation are formulated. The third section has a short description of the tolerance modelling procedure.Model equations, two subsections show the governing equations of the models\u2014the system of equations of the tolerance model of functionally graded laminates (FGL) with tolerance-periodic microstructure, and the asymptotic model of functionally graded laminates (FGL) with tolerance-periodic microstructure.In the An example: vibrations of a special laminated layer consists of three subsections. In the first section, an example under consideration of a laminated functionally graded layer on the undeformable base is described. Some basic assumptions for this example are also introduced. Vibration equations of both the models are shown in the second subsection. Equations of the tolerance model for the considered layer in the first approximation are decoupled on two equations\u2014for the macro- and the micro-vibrations. The third section consists of three points. In the first point, it is assumed that the cell distribution functions and the properties distribution functions are defined. Equations for the macro- and the micro-vibrations are written with the boundary conditions on the upper and the bottom boundaries of the layer, and the new denotations and some additional assumptions in the second point of this subsection. Then these equations with the boundary conditions are rewritten in the non-dimensional form. In the third point, formulas of non-dimensional solutions of the macro- and the micro-vibrations are obtained. Results from these formulas are shown in the form of diagrams.Remarks, general and some detailed remarks of the proposed model for FGL layer and obtained numerical results of the example are formulated.In Ox1x2.For the sake of simplicity, but without losing the generality of the analysis, further considerations are limited to a plane problem of composites in the orthogonal Cartesian coordinate system h1, h1) \u00d7  be the region of the considered laminate, where 2h1 is the dimension of the region along the x1 axis; h2 is the dimension along the x2 axis. Introduce also denotations: x \u2261 ; and t for a time coordinate. Then denote x \u2261 x1, z \u2261 x2. Let \u2207 \u2261 , \u2202 \u2261  and 2) denote derivatives of x, x and z, respectively. It is assumed that a distribution of laminas thicknesses is extrapolated by smooth function of cells distribution \u03bb(x), being slowly varying. Let us define a closed subset \u2206 of the region \u03a9 as \u2206 \u2261  \u00d7 {0} and the region \u2206(x), x\u2208\u03a9, as \u2206(x) \u2261 x + \u2206, such that \u03a9 = {x\u2208\u03a9: \u2206(x)\u2282\u03a9}. The subset \u2206 can be called the \u201cbasic cell\u201d and the region \u2206(x)\u2014\u201cthe cell with a centre at point x\u201d. Introduce also a set of centres of cells \u2206(x) defined as \u03a9\u2206 =  \u00d7 .Let \u03a9 = (\u2212x), \u03bd\u2033(x), satisfying the condition \u03bd\u2032(x) + \u03bd\u2033(x) = 1. Moreover, the non-dimensional function x. It is also assumed that planes x\u03b1 = const, \u03b1 = 1, 2, are material symmetry planes, .The laminate under consideration is made of two linear-elastic materials that occupy regions \u03a9\u2032, \u03a9\u2033, and where \u0393 is the system of contact planes between the components. These components are distributed in laminas with varying thicknesses. Every lamina consisted of two sub-laminas made of isotropic homogeneous materials with mass densities \u03c1\u2019, \u03c1\u201d and elastic tensors unctions ,89,90,91w = w and a vector of external forces by f, the differential equation of the composite under consideration can be written ast. It is assumed that the vector of displacements w and the stress tensor T = C:\u2207w satisfy regular conditions, and the condition of continuity for the stresses on contact planes between laminas \u0393, i.e., ETFn = 0, where ETF, x \u2208 \u0393, is a jump of the stress tensor; n is a unit normal vector.Denoting a vector of displacements by The above Equation (1), describing dynamical problems of laminates with functionally graded properties (FGL), has non-periodic (tolerance-periodic), non-continuous functional coefficients. In this form, the equation is not a good tool to consider the special problems of these laminates. Hence, Equation (1) can be replaced by a system of differential equations with slowly varying, continuous functional coefficients, using the tolerance modelling method.SV, tolerance-periodic function TP, and fluctuation shape function FS. They were also shown and applied in different papers, e.g., in  , byDefine f is a slowly varying function in x, but this value is constant for periodic function.The averaged value obtained from (2) for a tolerance-periodic function the tolerance-periodic function, \u03d5\u2208TP; if for every x\u2208\u03a9\u2206, there exists a function \u03d5x such that the functions \u03d5 and \u03d5x are indistinguishable within a certain tolerance, determined by the tolerance parameter \u03b4. The function \u03d5x can be named a periodic approximation of the function \u03d5 in the region \u2206(x).Function \u03d5, integrable and bounded in the region \u03a9, is called the slowly varying function, \u03c8\u2208SV, if, and only if, the following condition is satisfied: the tolerance parameter, \u03b4 << 1, related to the considered problems.Function \u03c8, TP, defined in \u03a9, having a partly continuous derivative of the order 1.Let us introduce a tolerance-periodic, bounded function \u03c6, \u03c6\u2208the fluctuation shape function, \u03c6\u2208FSF, depending on the parameter \u03bb and satisfies the conditions \u03bb\u2202\u03c6\u2208O(\u03bb) and <\u03c6>(x) \u2248 0 (for every x\u2208\u03a9\u2206).Function \u03c6 is called x. It is assumed in the following form:In the laminates under consideration, this function is a continuous, linear function along the thickness of every sub-lamina, dependent only on the argument x) \u2248 0  \u2248 0 for every x\u2208\u03a9\u0394, where \u03c1 > 0 is a certain tolerance-periodic function).Because the distribution function of non-homogeneity \u03bd is slowly varying, it can be shown that the averaged value of the function \u03c6 is equal to zero in every lamina, <\u03c6> \u2245 \u03c8 can be used, according to which quantities of the order O(\u03b4) are negligibly small compared to 1.In the second assumption, called The tolerance modelling procedure was proposed in different forms ,64,65.r(\u00b7) within the macro-dynamics, which is defined in the formHere, it is applied similarly to that shown in . The firthe residual orthogonality condition is formulated; it is assumed that the residual field r(\u00b7) has to satisfy the following conditions:In the next step, u and the fluctuation amplitude v can be obtained.Then, in applying the conditions (7), combined together with the modelling assumptions, a system of governing equations for the macro-displacement u and v are derived:From the use of the residual orthogonality condition (7) with the tolerance modelling assumptions, the averaged equations of the laminates under consideration for the tolerance model of functionally graded laminates (FGL) with tolerance-periodic microstructure. The above equations have coefficients, being slowly varying functions in x. Moreover, some of the coefficients, underlined here, depend on the parameter \u03bb, determining the thickness of laminas. Hence, the microstructure effect is described by Equation (8) on the overall dynamic behaviour of the considered laminates. Equation (8) is the system of differential equations for the basic unknown factors: the macro-displacement u and the fluctuation amplitude v, which have to be slowly varying functions in x. It can be observed that boundary conditions should be formulated at x = \u00b1h1 only for the macro-displacement u, but on all other edges (at z = const) for every unknown: the macro-displacement u and the fluctuation amplitude v.Equation (8) with the decomposition (5) stands the system of equations of the asymptotic model of functionally graded laminates (FGL) with tolerance-periodic microstructure, omitting the microstructure effect on the overall behaviour of the laminated composites. The above equations have coefficients being slowly-varying functions in x, similarly to Equation (8) for the tolerance model, in the contrast to Equation (1), which have highly oscillating, tolerance-periodic non-continuous, functional coefficients.Results obtained in the framework of the above model derived using the tolerance modelling method can be evaluated by results from the approximate model. Equations of this approximate model neglect the microstructure effect. These equations can be derived using the proper asymptotic modelling procedure . Howeverh2 along the z-axis (z = x2), loaded on the upper boundary by p and rested on the undeformable base are considered. The layer has the length 2h1 along the x-axis (x = x1) and is non-periodically reinforced along this axis. It is made of two components, f = 0.As an example, vibrations of a layer with the thickness u1 and the fluctuation amplitude v1, the following boundary conditions on the boundaries x = \u00b1h1:u1, v1 are equal to zero.Assuming for components of the macro-displacement vector x, i.e.,:Let us assume other components as independent of the argument The tolerance modelUnder assumptions and denotations from - macro-vibrations equation- micro-vibrations equationu describing only macro-vibrations, and one (11) for the fluctuation amplitude v describing only micro-vibrations.The asymptotic modelIt can be observed that for the considered problem of vibrations for FGL layer, Equation (8) can be written as two independent equations\u2014one (10) for the macro-displacement u and has a form identical as Equation (10). Hence, the obtained Equation (12) describes only the macro-vibrations.Under assumptions and denotations from Let us assume the following parameters:- the cell distribution function- for which the properties distribution functions can be written in the form:x, called the macro-loading amplitude, the micro-loading amplitude, respectively; R(x) is an oscillating function.- the loading on the upper boundary:U(z) is the amplitude of the macro-displacement, called the macro-deflection, and V(z) is the amplitude of the fluctuation amplitude, called the fluctuation variable.The basic unknowns in Equations (10) and (11) are assumed asLet us introduce some denotations:the macro-vibrations equationThen let us assume the loadings amplitudes on the upper boundary as- on the upper boundary:- on the bottom boundary:the micro-vibrations equation- on the upper boundary:- on the bottom boundary:Now, the equations of vibrations (23) and (26) with the boundary conditions can be transformed to the non-dimensional form.Introduce non-dimensional parameters:Defining the non-dimensional unknowns asthe non-dimensional macro-vibrations equationthe equations of vibrations (23) and (26) take the following non-dimensional form:the non-dimensional micro-vibrations equationwith the boundary conditions:For the macro-vibrations described by Equation (31) the following solutions are obtained:2 = 0:- the linearly decaying solution for \u03a92 > 0:- the oscillating solution for \u03a9- the resonance for:For the micro-vibrations described by Equation (33), the following solutions are obtained:2 < 0, \u03bc2 = \u2212\u03b32 = 12\u03c7/\u03b72 \u2212 \u03a92:- the decaying solution for \u03b32 = 0:- the linearly decaying solution for \u03b32 > 0:- the oscillating solution for \u03b3- the resonance for:z/h2.Some results calculated from Formulas (35), (36) and (38)\u2013(40) are presented in From the solutions (35) and (36) and the above figure it can be observed that for the problem of vibrations for the FGL layer under consideration there is one linearly decaying solution of the non-dimensional macro-deflection (for \u03a9 = 0); and are many solutions, which are decaying and oscillating , and are also many solutions, which are decaying and oscillating (for \u03b32 > 0). Moreover, for higher values of \u03bc, e.g., \u03bc = 5, the solutions become strongly decaying, and for higher values of \u03b3, e.g., \u03b3 = 5, the solutions become strongly oscillating. The results shown in Results calculated from the solutions (38)\u2013(40), and presented in The tolerance modelling method applied to the known differential equation of composites replaced this equation with tolerance-periodic (non-periodic), non-continuous coefficients by the system of governing differential equations with continuous, smooth, slowly-varying coefficients.In this paper, vibrations of functionally graded laminated (FGL) composites with tolerance-periodic (non-periodic) microstructures have been considered. The microstructure effect is taken into account in the obtained averaged tolerance model equations on the overall dynamic behaviour of the composites under consideration. Thus, in these problems, this effect can be studied both at the macro and microlevels within the tolerance model.The asymptotic model has been also introduced to evaluate the obtained results within the tolerance model. The governing equations of this approximate model could be derived using the asymptotic modelling procedure. This model, omitting the microstructure effect, allows the investigation of vibration problems only at the macrolevel.u2 = u and the fluctuation amplitude v2 = v), are independent of x1 = x coordinate.In the example, it has been determined that the property distribution function in the FGL layer loaded on the upper boundary, under the condition, and the basic unknowns (the macro-displacement It has been shown that only the tolerance model makes it possible to investigate the effect of the micro-oscillations of the boundary loading, and also the effect of macro-oscillations.The asymptotic model allows for the analysis of only the effects of the macro-oscillations of the loading.Introduced various additional assumptions and restrictions make it possible to obtain the analytical formulas of solutions.It can be observed that the solutions of macro-vibrations can decay linearly, decay and oscillate, or they not exist.Solutions of micro-vibrations can decay exponentially, decay linearly, decay and oscillate, or they not exist.From the example, some specific remarks can be formulated.Other more complicated and interesting problems will be investigated using the tolerance model equations of the considered FGL composites in forthcoming papers."}
+{"text": "Games have a long history as benchmarks for progress in artificial intelligence. Approaches using search and learning produced strong performance across many perfect information games, and approaches using game-theoretic reasoning and learning demonstrated strong performance for specific imperfect information poker variants. We introduce Student of Games, a general-purpose algorithm that unifies previous approaches, combining guided search, self-play learning, and game-theoretic reasoning. Student of Games achieves strong empirical performance in large perfect and imperfect information games\u2014an important step toward truly general algorithms for arbitrary environments. We prove that Student of Games is sound, converging to perfect play as available computation and approximation capacity increases. Student of Games reaches strong performance in chess and Go, beats the strongest openly available agent in heads-up no-limit Texas hold\u2019em poker, and defeats the state-of-the-art agent in Scotland Yard, an imperfect information game that illustrates the value of guided search, learning, and game-theoretic reasoning. Student of Games combines search, learning, and game-theoretic reasoning to play chess, go, poker, and Scotland Yard. In the 1950s, Arthur L.\u00a0Samuel developed a checkers-playing program that used what is now called minimax search  and \u201crote learning\u201d to improve its evaluation function via self-play , an algorithm that generalizes the class of games in which strong performance can be achieved using self-play learning, search, and game-theoretic reasoning. SoG uses growing-tree counterfactual regret minimization (GT-CFR): an anytime local search that builds subgames nonuniformly, expanding the tree toward the most relevant future states while iteratively refining values and policies. In addition, SoG uses sound self-play: a learning procedure that trains value-and-policy networks using both game outcomes and recursive sub-searches applied to situations that arose in previous searches.SoG achieves strong performance in multiple challenge domains with both perfect and imperfect information\u2014an important step toward truly general algorithms that can learn in arbitrary environments. Applications of traditional search suffer well-known problems in imperfect information games  \u00d7 \u0394[\ud835\udcae2(spub)] is a pair of distributions over possible information states for both players representing the beliefs over information states in spub. A basic depiction of the various components of a public belief state is depicted in Imperfect information games introduce additional complexity, as \ud835\udcae1, \u03c02). Denote the expected utility to player to player i as iu and \u2212i as the opponent of player i. A best response to a specific opponent policy \u03c0i\u2212 is any policy i\u2212: i\u2223iu = maxi\u2032\u03c0iu}. A policy profile \u03c0 is a Nash equilibrium if and only if \u03c01 is a best response to \u03c02 and \u03c02 is a best response to \u03c01. There are also approximate equilibria: \u03c0 is an \u025b-Nash equilibrium if and only if i.Suppose players use a policy profile \u03c0 = , Exploitability(\u03c0) = [max1\u2032\u03c0u1 + max2\u2032\u03c0u2]/2. Also, equilibrium strategies in two-player zero-sum games are interchangeable: If \u03c0A and \u03c0B are Nash equilibria, then . Here, we focus on the two-player zero-sum setting. To put SoG in context, we begin with a high-level description of several techniques that have been dominant in this setting, and then contrast SoG with existing work.tw, along with a heuristic evaluation function to estimate the value of states beyond the depth limit, h(wt + d), and game-theoretic reasoning to back up values  can be easily beaten by another playing the best response . The Nash equilibrium plays each action with equal probability, which minimizes the benefit of any particular counter-strategy. Similarly, in poker, knowing the opponent\u2019s cards or their strategy could yield substantially higher expected reward, and in Scotland Yard, players have a higher chance of catching the evader if their current location is known. In these examples, players can exploit any knowledge of hidden information to play the counter-strategy resulting in higher reward. Hence, to avoid being exploited, players must act in a way that does not reveal their own private information. We call this general behavior game-theoretic reasoning because it emerges as the result of computing (approximate) minimax-optimal strategies. Game-theoretic reasoning has been paramount to the success of competitive poker AI over the last 20 years.s, \u00b7) \u2208 \u0394(\ud835\udc9c) for each player i at each of their information states s in a way that minimizes long-term average regret. As a result, the (appropriately weighted) average policy over all T iterations t, counterfactual values s, a) are computed for each action a \u2208 \ud835\udc9c(s) and immediate regrets for not playing a, tr = s, a) \u2212 \u2211a\u2208\ud835\udc9c(s)\u03c0ts, a), are computed and tabulated in a cumulative regret table storing TR = tr. A new policy is computed using regret-matching , if \u2211a[tR]+ > 0, or the uniform distribution otherwise.One algorithm for computing approximate optimal strategies is counterfactual regret minimization (CFR)  = [Qt\u22121 + tr]+ and \u03c0t+1 = tQ/\u2211btQ.CFR+) is one that traverses the public tree of public states, rather than the classical extensive-form game tree of world states (and information states). Quantities required to compute counterfactual values, such as each player\u2019s probabilities of reaching each information state under their policy , are maintained as beliefs. Finally, leaf nodes can be evaluated directly using the ranges, chance probabilities, and utilities } as well as the currently active policy {\u03c0CFR[is(h)]} from search: iv normalized by the sum of the opponent\u2019s reach probability at is to resemble state-conditional action values, and the prior policy p obtained from the queries. The second is simply CFR\u2019s average policy at is(h). As soon as the simulation encounters an information state is \u2208 spub such that spub is added to \u2112, and visit counts are updated along nodes visited during the trajectory. Similarly to AlphaZero . Optimal policies in perfect information games can be deterministic, and expanding a single action/node is a good way to avoid unneeded computation after unpromising actions. MCTS methods are sound as long as the best action has been added, which is always true in the limit as the tree is completely filled out. In imperfect information games, optimal policies might be stochastic, having nonzero probability over multiple actions. Rather than expanding a single action, SoG thus expands the top spub. In hold\u2019em poker, players generally take turns making actions, and a depth-limited search tree for a re-solving auxiliary game can always be deep enough to contain a state for the opponent\u2019s action. All player actions are fully visible to both players, so the opponent\u2019s maximum counterfactual value in the previous search tree can be used for the next re-solving auxiliary game, no matter what opponent action we are responding to. By working within the single, fixed domain of poker, these properties let DeepStack and Libratus simply retrieve the re-solving summary information from its previous search.The continual re-solving method used by DeepStack rprev. As with DeepStack, this regularization toward the previous opponent policy empirically improves the performance, and we used \u03b1 = 0.5.Finally, like DeepStack, the gadget for the re-solving auxiliary game is modified by mixing in the opponent\u2019s range from the previous search. As introduced in  be the interior of the tree: all nonleaf, nonterminal public states where GT-CFR generates a policy. Let \u2131(\u2112) be the frontier of \u2112, containing the nonterminal leaves where GT-CFR uses \u025b-noisy estimates of counterfactual values. Let U be the maximum difference in counterfactual value between any two strategies, at any information state, and A be the maximum number of actions at any information state. Then, the regret at iteration T for player i is bounded:RT,full in Theorem 1 is the gap in performance between GT-CFR iterations and the highest-value strategy. Theorem 1 shows that the average policy returned by GT-CFR converges toward a Nash equilibrium at a rate of The regret Theorem 2. Assume we have played a game using continual re-solving, with one initial solve and D re-solving steps. Each solving or re-solving step finds an approximate Nash equilibrium through T iterations of GT-CFR using an \u025b-noisy value function, public states are never removed from the search tree, the maximum interior size \u2211spub\u2208\ud835\udca9(\u2112T)\u2223\ud835\udcaei(spub)\u2223 of the tree is always bounded by N, the frontier size of the tree is always bounded by F, the maximum number of actions at any information states is A, and the maximum difference in values between any two strategies is U. The exploitability of the final strategy is then bounded by Theorem 2 is similar to Theorem 1 of (T iterations expanding k children is \ud835\udcaa(kT2) public states visited and CVPN network calls. In the special case of perfect information games, the number of network calls can be reduced to \ud835\udcaa(T).The computational complexity of a GT-CFR re-solving step with t, in the expansion phase, GT-CFR will traverse a single trajectory through the tree to expand a leaf, and use the CVPN to evaluate the newly expanded children. This requires k network calls and a worst case of \u2223t\u2112\u2223 states visited or \u2308logb\u2223t\u2112\u2223\u2309 states visited in a balanced b-ary tree.At every iteration t\u2112 and uses the CVPN to evaluate every leaf of the tree. Because k child states are added to the tree at each iteration, \u2223t\u2112\u2223 \u2264 \ud835\udcaa(kt), giving the stated bounds.In the regret update phase, GT-CFR visits every state in k = 1, each player range is a single number, and we only need to evaluate a state once because the optimal policy does not depend on the player ranges. If a state is evaluated once with a range of 1 for both players and then stored, any other belief state can by evaluated by scaling the stored result by the opponent\u2019s ranges.In perfect information games, h0 corresponding to the start of the game and produces a sequence of histories . At time t, the agent runs a local search and then selects an action ta, and the next history ht+1 is obtained from the environment by taking action ta at th. Data for training the CVPN are collected via resulting trajectories and the individual searches.SoG generates episodes of data in self-play by running searches at each decision point. Each episode starts at the initial history \u03b8 and with searches made at previous public states along the same trajectory . This is a critical requirement for sound search  generated by sound self-play described in the \u201cData generation via sound self-play\u201d section. Specifically, they are the output policies for all information states within the root public state, computed in the regret update phase of GT-CFR.T iterations of GT-CFR for all the information states within the public state that initiated the search. The specific way that the different value targets are assigned is described by the pseudocode in Supplementary Text and determined by a hyperparameter noted in table S2.Value targets are obtained in two different ways. First, the outcome of the game is used as a [TD(1)] value target for states along the main line of episodes generated by sound self-play. Second, value targets are also obtained by bootstrapping: running an instance of GT-CFR from subgames rooted at input queries. In principle, any solver could be used because any subgame rooted at \u03b2 has well-defined values. Thus, this step acts much like a policy improvement operator via decomposition described in the \u201cImperfect information search, decomposition, and re-solving\u201d section. Specifically, the value targets are the final counterfactual values after While the solver is computing targets for a query, it is also generating more queries itself by running GT-CFR. Some of these recursive queries are also added to the buffer for future solving so that the CVPN can produce reasonable answers for all leaves in a search, not just those on the self-play lines. As a result, at any given time, the buffer may include queries generated by search in the main self-play game or by solver-generated queries off the main line. To ensure that the buffer is not dominated by recursive queries, we set the probability of adding a new recursive query to less than 1 .T \u2192 \u221e and with very large  memory.One natural question is whether, or under what circumstances, the training process could ensure convergence to the optimal values? The answer is positive: The training process converges to the optimal values, asymptotically, as f(\u03b2) that can simply memorize the values and policy for the particular \u03b2 similar to a tabular value or policy iteration algorithm except with continuous keys. For any subgame rooted at some \u03b2 with a depth of 1 , the values and policies can be computed and stored for \u03b2 after T iterations of the solver. This can then be applied inductively: Since CFR is deterministic, for any subgame on the first iteration of GT-CFR, a finite number of queries will be generated. Each of these queries will be solved using GT-CFR. Eventually, the query will be a specific one that is one step from the terminal state whose values can be computed exactly and stored in f(\u03b2). As this value was generated in self-play or by a query solver, and CFR is deterministic, it will produce another self-play game with the identical query, except it will load the solved value from f(\u03b2), and inductively the values will get propagated from the bottom up. Since CFR is deterministic and T is finite, these ensure that the memory requirement is not infinite despite the continuous-valued keys. Practically, the success of the training process will depend on the representational capacity and training efficacy of the function approximation .Informally, imagine an oracle function For a fully detailed description of the algorithm, including hyperparameter values and specific descriptions of each process described above, see Supplementary Text."}
+{"text": "International Journal of Impotence Research 10.1038/s41443-021-00503-x, published online 2 December 2021Correction to: For this article parts of the text have been converted to footnotes. They read as follows:The Brussels Collaboration on Bodily Integrity [10] defines \u2018medically necessary\u2019 in the following way: \u2018(1) the bodily state poses a serious, time-sensitive threat to the person\u2019s well-being, typically due to a functional impairment in an associated somatic process, and (2) the intervention, as performed without delay, is the least harmful feasible means of changing the bodily state to one that alleviates the threat\u2019.By \u2018our\u2019, \u2018we\u2019, and \u2018us\u2019, I mean all embodied people."}
+{"text": "Conventional scenarios assume that K+ ions are tightly bound in the SF, and, thus, they are displaced from their energy well by ion\u2013ion repulsion with an incoming ion. This tight coupling between entering and exiting ions has been called the \u201cknock-on\u201d mechanism. However, this paradigm is contradicted by experimental data measuring the water\u2013ion flux coupling ratio, demonstrating fewer ion occupancies. Here, the results of molecular dynamics simulations of permeation through the KcsA potassium channel revealed an alternative mechanism. In the aligned ions in the SF (an ion queue), the outermost K+ was readily and spontaneously released toward the extracellular space, and the affinity of the relevant ion was\u2009~\u200950\u00a0mM. Based on this low-affinity regime, a simple queueing mechanism described by loose coupling of entering and exiting ions is proposed.The mechanism underlying ion permeation through potassium channels still remains controversial. KThe online version of this article (10.1007/s12576-019-00706-4) contains supplementary material, which is available to authorized users. The CRw-i metric provides the ion and water permeation pattern in the SF, and the failure of the canonical  mode at low [K+] (<\u20090.01\u00a0M) cannot be overlooked since this may threaten the present \u201cknock-on\u201d and \u201chigh-affinity\u201d paradigm.In the knock-on process, the alternating array mode , raising questions as to the fundamental assumption about the permeation process \u2009=\u20090.15\u00a0M). Color traces, denoting individual ions, reveal the progression of ions from the intracellular space (IS) into the nanocavity (NC), followed by progression through the successive sites within the SF before being released into the extracellular space (ES). K+ ions frequently access the entrance of the NC, but only a fraction of them enter the NC. Thus, a water-filled NC is mostly empty of ions and transiently holds up to one K+ ion  , thus warranting further examination of the microscopic details of the permeation process.To examine the concentration-dependent changes in + ion into the SF from the NC  , and two other ions, which previously underwent SF-in and remained in the SF, are denoted as I1 (blue) and I2 (green). The trajectories of the water molecules are drawn in light blue. A snapshot taken at the SF-in moment of I0 (\u0394t\u2009=\u20090) . Occasionally, zero or two water molecules are intercalated  Fig.\u00a0c 48]. I. I+ ion I0, I1, and I2 are strongly coupled . The uppermost and lowermost panels represent the distributions at two successive SF-in moments, and the middle panels show the distribution at the \u201crelaxed\u201d state and the next NC-in moment. The number labeling each peak represents the fractional number of the corresponding ion  at the relevant site.The permeation process is quantitatively evaluated by analyzing the time-lapse distributions of ions and water molecules. Figure\u00a0+]\u2009=\u20090.15\u00a0M  and water molecules upstream from I1 are mostly located at S4, where the number of water molecules is 0.86. In single-file permeation, water molecules upstream of I1 are intercalated between I1 and I0 upon the SF-in of I0. The cumulative sum of water-molecule distributions upstream from I1 at S4 and S3 is counted as Nwater\u2009=\u20090.86\u2009+\u20090.30\u2009=\u20091.16 at the SF-in moment. This number of water molecules is driven by the ion flux along the channel, leading to alternating (1:1) ion and water distributions within the SF. Thus, the microscopically observed Nwater at the SF-in corresponds to the overall number of water and ion flux ratio during the whole simulation time (CRw\u2013i\u2009=\u20090.99) as well as to the experimentally measured CRw\u2013i values . Thus, the alternating array mode predominates above the [K+] of 0.15\u00a0M.At the SF-in moment at [K+] (=\u20090.05\u00a0M) , which is consistent with the experimental CRw\u2013i value. More water molecules were intercalated because I1 shifted outward such that more than half of I1 was located at S2 or S1 (57%\u2009=\u200950%\u2009+\u20097%). Why was I1 shifted further downward at low [K+]? We found that nearly half of I2 had already been released out to the ES (49%) before the SF-in, retaining only one K+ in the SF. In this case, permeation proceeded without passing through the three-ion-occupied knock-on intermediate, posing a question as to the prerequisite role of the transition intermediate for permeation. After the SF-in, two ions (I0 and I1) shifted gradually until the relaxed state, during which half of I1 was spontaneously released . Although this affinity represents an attribute of the outermost ion in the two-ion-occupied state rather than an attribute of a specific site in the SF, this value is consistent with the experimental Kd values of 0.009\u20130.050\u00a0M . From the collection of the trajectories, the elapsed time from the SF-in to the release of either I2 (upper panel) or I1 (lower panel) was plotted as dots , and this de-queueing time is invariable for different concentrations. This immediate alleviation from the transient three-ion-occupied intermediate was expected to be a knock-on scenario, while the time course was first elucidated in this simulation. Another type of de-queueing is spontaneous release (2\u2009\u2192\u20091: lower right panel), which is significant here for the sparse array mode to proceed. This de-queueing occurs long after the en-queueing (SF-in), with an elapsed time of 16,000\u00a0ps at 0.05\u00a0M, which is in dramatic contrast with the de-queueing time for the 3\u2009\u2192\u20092 transition. Hence, such long-overdue time for de-queueing is poorly expressed as the coupling between en-queueing and de-queueing, and the exit process of 2\u2009\u2192\u20091 is accordingly called the spontaneous release process. During the period of spontaneous release, I0 advances deeper and more water molecules follow, providing higher Nwater or CRw\u2013i values. This mode is frequently seen at the lower concentration of 0.05\u00a0M, occurring as high as in half of the cases (51%). Even at high concentrations, the sparse array mode was observed, though infrequently (5% at 1\u00a0M).Now, a quantitative evaluation of the MD-simulated trajectories was performed. First, the exit (de-queueing) time was quantified , which are the inverse of the current amplitudes. The en-queueing times for 1\u2009\u2192\u20092 seemed to be similar to those for 2\u2009\u2192\u20093 because the arrival time of the ion at the SF was independent of whether the SF occupied either one or two ions.Next, the arrival (en-queueing) time was considered (left panels). The en-queueing occurred upon the SF-in event, and, thus, the en-queueing time could be read with the elapsed time from the less ion-occupied state to the SF-in, which is shown as dots and as the kernel density estimation . The average time for en-queueing of 2\u2009\u2192\u20093 (upper left panel) gradually prolonged as   the affinity of the outermost ion in the SF is low, and, thus, dynamic equilibrium with respect to the ES governs the occupancy of that ion Fig.\u00a0b; (ii) t+] Fig.\u00a0b; (iii) +] Fig.\u00a0b, c;  because of the geometrical length limit. At low [K+], ion arrival is infrequent and queueing processing in the SF (or de-queueing) is rapid  enough to maintain a short queue. As the frequency of arrival ions increases, a fraction of arriving ions are not allowed to enter the channel because of the limited queue capacity. When the queue elongates up to three ions, the processing rate of the queue is accelerated.Under the framework of the general queueing theory , 54, per+ concentration, whereas the de-queueing rate was constant. In this study, we found that the de-queueing rate of 2\u2009\u2192\u20091 was high (red line) and the affinity of K+ was deduced as 0.05\u00a0M at the intersection of the en-queueing and de-queueing rates. This value is consistent with the experimental values (0.009\u20130.050\u00a0M) [+] below the Kd value, de-queueing (2\u2009\u2192\u20091) occurs earlier than en-queueing, which occurs long afterward (1\u2009\u2192\u20092), giving rise to the sparse array mode. At [K+] above the Kd value, en-queueing precedes de-queueing. Once en-queuing (2\u2009\u2192\u20093) occurs, it immediately de-queues (3\u2009\u2192\u20092), yielding the predominant alternative array mode. Here, the rate of 3\u2009\u2192\u20092 deduced from Fig.\u00a0To characterize the queueing mechanism in comparison to the conventional knock-on mechanism, we expanded Fig.\u00a00.050\u00a0M) \u201352, 55. + binding (<\u20090.001\u00a0M) is implicitly assumed to be much below the physiological extracellular [K+] (0.003\u20130.005\u00a0M), from which the de-queueing rate is estimated as the intersection with the en-queueing rate , using the same potential and channel species as the ones we used, although the driving force was imposed by the concentration gradient. A recent paper by Kopec et al. showed that the CRw\u2013i value through the MthK channel was also 0 at 220\u2013280\u00a0mV, and was\u2009\u223c\u20090.1 at\u2009\u223c\u2009900\u00a0mV  across the membrane, more fractions (>\u200915%) of permeation should occur via the sparse mode.The + affinity \u2009=\u20090.15\u00a0M was composed of one KcsA channel, 119 dioleoylphosphatidylcholine (DOPC) lipids, 30\u00a0K+, 22 Cl\u2212, and 10,520 water molecules. First, the DOPC bilayer was equilibrated with the surrounding KCl solution for 10\u00a0ns. MD simulation was performed using the NPT ensemble  with a Berendsen\u2019s barostat [2)]. Simulation of the equilibration using the NVT ensemble (310\u00a0K) with a Berendsen\u2019s thermostat [+ and Cl\u2212; the system was then equilibrated.The system at [Kbarostat . The arebarostat . The DOPbarostat . H25, E1barostat . The resbarostat , 61. An ermostat  continue+ ions, and Siu model for the lipids [+\u2013w\u2013K+\u2013w, w-K+\u2013w\u2013K+, K+\u2013w\u2013w\u2013K+, and K+\u2013V\u2013K+\u2013w, where V stands for vacancy) were generated as initial configurations. The initial equilibrium runs, including the ion and water molecule permeation events in the process, were omitted from the analyses.The following empirical potentials were used: the TIP3P model for water, ff94 force field for the channel, Dang model for the Ke lipids , 62\u201364. e lipids , 66. Ten3) and a constant temperature (310\u00a0K) using the Berendsen\u2019s thermostat [MD simulations were performed at a constant volume Supplementary material 2 (MP4 7421\u00a0kb)Below is the link to the electronic supplementary material."}
+{"text": "This research proposes a deep-learning paradigm, termed functional learning (FL), to physically train a loose neuron array, a group of non-handcrafted, non-differentiable, and loosely connected physical neurons whose connections and gradients are beyond explicit expression. The paradigm targets training non-differentiable hardware, and therefore solves many interdisciplinary challenges at once: the precise modeling and control of high-dimensional systems, the on-site calibration of multimodal hardware imperfectness, and the end-to-end training of non-differentiable and modeless physical neurons through implicit gradient propagation. It offers a methodology to build hardware without handcrafted design, strict fabrication, and precise assembling, thus forging paths for hardware design, chip manufacturing, physical neuron training, and system control. In addition, the functional learning paradigm is numerically and physically verified with an original light field neural network (LFNN). It realizes a programmable incoherent optical neural network, a well-known challenge that delivers light-speed, high-bandwidth, and power-efficient neural network inference via processing parallel visible light signals in the free space. As a promising supplement to existing power- and bandwidth-constrained digital neural networks, light field neural network has various potential applications: brain-inspired optical computation, high-bandwidth power-efficient neural network inference, and light-speed programmable lens/displays/detectors that operate in visible light. Here the authors have realized a programmable incoherent optical neural network that delivers light-speed, high-bandwidth, and power-efficient neural network inference via processing parallel visible light signals in the free space. Its primary process is to train multiple layers of artificial neural networks to find abstractions in domain-specific datasets. The universal approximation theorem states that a feed-forward network with a single hidden layer containing a finite number of neurons can approximate continuous functions on compact subsets of Rn under mild assumptions pertaining to the activation function3.Deep learning has recently experienced tremendous success in delivering impressive results in various domains, including computer vision, medical analysis, natural language processing, and automatic vehicles7. However, building a programmable ONN using electronically controlled optical components remains an open problem. Note that while electronically controlled optical components are commonly modeled as perfect surfaces, they actually have inconsistently unmeasurable micro-structures and materials, creating unpredictable inter-reflections and interference. In addition to the optics, the electronic circuit and physical environment also introduce unpredictable bias and variance. As such, existing approaches can no longer properly simulate or train programmable ONNs.Modern electronic devices offer strong computing capabilities for the processing of laborious matrix multiplications and memory references, leading to the development of advanced networks with ever-growing amounts of neuron connections. However, the stringent constraints on power and bandwidth hinder the broader applications of deep learning in mobile devices, embedded systems, wireless wearable devices, and robots. The optical neural network (ONN) is a promising alternative mechanism for high-bandwidth, low-latency, and power-efficient neural network inferenceIn this work, we conceive the concept of practically training loose neuron arrays for practical tasks. It is a physical counterpart of the artificial neural network and enables the transformation from handcrafted hardware designs to non-handcrafted designs. One of the most important recent discoveries is that merely connecting many artificial neurons in a non-handcrafted way outperforms sophisticated handcrafted algorithms in a large number of tasks. While connecting artificial neurons is very handy in computers, there is no trivial way to connect and train arbitrary physical neurons because the actual design, material, structure, manufacture, fabrication, and run-time environment are far from ideal models. On the other hand, enabling the connection and training of arbitrary physical neurons releases us from such constraints. It reveals possibilities for hardware design, chip manufacturing, and system control.This concept is instantiated for the realization of incoherent programmable ONNs. We numerically verify the feasibility of various neuron arrays with liquid-crystal (LC) hardware to form programmable ONNs Fig.\u00a0. The neuWe physically implement a regular-2 array with off-the-shelf optical components, e.g., liquid-crystal display (LCD) panels, polarizers, and a camera, without fine calibration. We call such a programmable incoherent ONN design a light field neural network  is the optics of the LFNN hardware, p is the hardware control parameters, x is the input, and y is the expected output. At a specific inference task, once p is applied to the hardware, the incoherent light signal passing through the device is passively modulated to the target output.Instead, we propose the FL paradigm to control such an uncalibrated optical system. Given the input signals and expected targets as the training set, the parameters of the system are trained as trainable neurons to undertake inference on the input signal:f has no explicit mathematical formulation, we introduce a functional neural network  is an FNN, z denotes the functional space coefficients, p is the primary parameter as trainable neurons, and the two terms are iteratively optimized by p\u2009\u2212\u2009learning and z\u2009\u2212\u2009learning through the FL paradigm.Because 2. The function basis block reflects the physical structure of the device in which each input neuron has a potential impact, i.e., light propagation, to each output neural, forming a four-dimensional light field with numerous connections, whose cardinality is equal to input neural size times output neural sizes. The pixels of the LC panel, represented as control parameters, can potentially attenuate arbitrary input-to-output connection and are represented mathematically by multiplication to the input-to-output data flow. In order to depict features in various resolutions, we downsample the inputs and LC control parameters half and merge the results through trainable parameters. More details are in\u00a0The FNN consists of a physically-inspired function basis block and the following nonlinear combination through five layers of convolutional neural network (CNN) with 3\u2009\u00d7\u20093\u2009\u00d7\u200964 kernel and rectifier linear unit (ReLU)8 to train and test a 1-layer LFNN. The input of the device is a 28\u2009\u00d7\u200928 grayscale image, and the output is the predicted classification probability distribution of the input image, calculated by accumulating the sum of RGB channels at the output plane. Because the viewing angle of our backlight is too narrow to make the contribution of an input neuron cover the entire output plane, we train the probability distribution layout of different classes on the output plane to adapt to the uneven energy distribution. For example, the sum of the intensities in some dispersed areas represents the probability of one class  of every input neuron to the output plane. Then we measure and model the impact of every LC neuron on every input neuron\u2019s PSF as a linear function by switching on and off the corresponding neurons and recording the change on the output plane. In addition, we build look-up tables to calibrate the linearity of input and LC neurons by measuring the system output of the quantized control signal. Training the LFNN with the forward model achieves a 23.50% prediction accuracy. The limitation of this paradigm is that accurately measuring and modeling the tremendous amount of states of the LFNN, i.e., a high-dimensional, non-differentiable, non-linear, and correlated physical system, is beyond reality.In the MNIST test set, the LFNN achieves a 91.02% prediction accuracy, and the FNN predicted accuracy is 91.39%. As a reference, one fully connected digital dense layer running in a computer achieves 92.71% accuracy. In comparison, existing training paradigms have a hard time training a large number of parameters of a high-dimensional system as the LFNN. Using the forward analytical model6 and genetic algorithm11 may work well for a small number of parameters, but are still hard to train a large number of parameters. The finite difference paradigm captures the difference quotient as gradients to optimize the parameters. While facing thousands of parameters, it has to measure the finite difference of every parameter, which requires capturing 6,144 output images from the LFNN for one input image. In contrast, our FNN paradigm captures 1024 output images to implicitly evaluate the gradients for 60,000 images at each epoch. As a result, using finite difference yields an 8.594% prediction accuracy within equal training time. Genetic algorithm faces a similar problem for large-scale optimization. While converging efficiently with a small number of parameters, stochastically exploring a high-dimensional space without gradients is futile. We leverage the scikit-opt genetic algorithm to test training the LFNN. The metric of evaluating an offspring is calculated by randomly drawing 128 images and capturing the outputs. Within equal training time, the genetic algorithm trains the LFNN to achieve a 14.06% prediction accuracy. Table\u00a0Alternative stochastic training paradigms like finite difference12, followed by the third operation, a simple amplitude filter integrated into the driver of the input plane that clamps the impulse between zero and one. We connected multiple FNNs to train the multi-layer LFNN with the adaption of the single-layer training scheme to multiple layers. More discussion is given in the\u00a0We also test multi-layer optical neural networks by cyclically feeding the captured outputs onto the input plane. This electronic cycling also conducts energy redistribution and nonlinear activation. We apply three neuron-wise activation operations. We refer to the first operation as X-activation, where the captured output is subtracted from its 180-degree rotated image. X-activation effectively enables consistent value distributions between layers, nonlinearities, and deactivation, i.e., negative operations that are non-trivial in incoherent optical systems. Furthermore, its design uses only simple logic and operators that can be implemented by non-digital hardware in the future to match the activation to speed-of-light processing. The second operation is common neuron-wise batch normalizationWith the 2-layer LFNN, the MNIST classification task shows a 94.35% prediction accuracy, and its FNN counterpart shows 94.52% accuracy. As a reference, a 2-layer digital dense neural network, connected by the ReLU activation function achieves 98.32% accuracy.13, to evaluate a 3-layer LFNN. The FNN predicted accuracy is 46.19%, and the LFNN captured accuracy is 45.62%. As a reference, a 3-layer digital dense neural network achieves 53.52% accuracy. In the neuron array simulation, increasing the LC neuron size can significantly increase the accuracy of ONNs, nearly matching that of the digital dense neural network  to implement the LFNN prototype, the average training time is 4 minutes per epoch. For example, it takes around 400 minutes to train the 100 epochs  has no explicit formulation, we cannot mathematically solve the original problem of Equation  is an implicit function that can be represented by a functional neural network (FNN) as an instance with a learnable functional space. We then approximate the original problem with two sub-problems,gN(\u2009\u22c5\u2009) is a FNN , z is the functional space coefficients, and p is the primary parameter, i.e., the hardware parameter in our case. However, both sub-problems are under-determined if we simultaneously optimize the functional space and the parameters that alter the mapping between input and output. Therefore we reformulate the equation as the following, by decoupling the variables to make each sub-problem solvable:p0 and z0 are auxiliary variables. In this formulation, the problem can be solved by alternating minimization, which has shown convergence for non-convex problems30, of each sub-problem. Specifically, at each epoch k, we update p0\u2009\u2190\u2009pk and z0\u2009\u2190\u2009zk+1. The update rules can be then simplified as follows:The optimization of the parameters of a model-free system is challenging. In order to train the hardware parameters of the LFNN, we propose a deep-learning paradigm, functional learning. Specifically, we generalize the learning problem asz-learning and p-learning, respectively.We propose different deep learning schemes to minimize sub-problems of Equation  and EquaFunctional Learning (FL) Paradigm.functionFunctional Learning1: 2:z and p \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u22b3 Initialize.3: \u2003Initialize p-optimizer and z-optimizer using gN4: \u2003Initialize p-data\u2009\u2190\u20095: \u2003k\u2009\u2190\u200916: \u20037:whilek\u2009<\u2009 maximum epoch do8: \u2003u\u2009\u2190\u2009p-data.\u2009DrawSample(x)9: \u2009\u2009\u2003v\u2009\u2190\u2009LFNN.\u2009Capture(u)10: \u2003z-data\u2009\u2190\u2009 \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u22b3 Update z-data.11: \u2009\u2003z-optimizer.\u2009TrainNetwork \u2003\u22b3 Conduct z-learning.12: \u2003p-optimizer.\u2009TrainNetwork \u2003\u22b3 Conduct p-learning.13: \u2003k\u2009\u2190\u2009k\u2009+\u2009114: \u2003end while15: \u200316:end function17: p-variable. The orange lines and the variables of convolutional layers, termed z-variable, are trainable functional space coefficients trained to replace the hidden function f. The p- and z-variables are iteratively updated through p-learning and z-learning. P-learning accepts task-related data sets, e.g., CIFAR10, to optimize the primary parameter. Z-learning dynamically gathers z-data by sending impulses to the LFNN device to capture ground truth (GT) responses. The gradients are computed through backpropagation algorithms, and the variables are updated using the Adam optimizer31 in the PyTorch framework.The FL paradigm departs from existing deep learning paradigms in several ways. The FNN has two sets of trainable variables indicated here in blue and orange Fig.\u00a0a. The blz-learning and p-learning. Each learning procedure has independent loss functions, optimizers (z-optimizer and p-optimizer), trainable variables (z-variablez and p-variablep), and data set (z-data and p-data). First, we uniformly randomize the variables z and p in . Through the FNN gN, p-optimizer calculates the gradients of p using backpropagation and updates the variables p using the Adam algorithm in the p-learning stage, and z-optimizer is the counterpart for z. At each epoch, z-learning and p-learning are conducted once. The z-data used for z-learning is updated at each epoch by randomly drawing certain input samples from p-data and capturing the corresponding responses of the LFNN device.Algorithm 1 shows the pseudocode of the FL paradigm. Functional learning (FL) uses a weaved learning scheme, which iteratively conducts P-learning. p-learning trains the parameter neurons p, i.e., the hardware parameters for the LFNN device, to optimize the mapping from x to y in a specific function defined by the frozen functional space variables z. The training data set p\u2009\u2212\u2009data and the loss function depend on the chosen inference task. We use the Adam optimizer with a 0.001 learning rate.Z-learning. z-learning trains the functional space variables z to approximate the unknown function f with gN(z) given a fixed p. Different from classic deep learning, the training data set z-data is updated at each epoch. We give some input signals to the unknown function f, i.e., the LFNN device in our case, and capture its responses. The input signals and output responses constitute the inputs and targets of z-data. Because we use an off-the-shelf low-speed camera to implement our LFNN prototype, capturing the responses of all x of p-data is time-consuming, we only randomly draw a subset with 1024 samples (line 9 of Algorithm 1) every epoch and repeatedly train such a subset ten times while shuffling. This acceleration scheme works well experimentally across the training process. We use the L1 loss and the Adam optimizer with a 0.001 learning rate for z-learning.n-layer LFNN, Equation  Paradigm.functionMulti-Layer Functional Learning1: 2:zi} and {pi} for 1 \u2264 i \u2264 n \u22b3 Initialize.3: \u2003Initialize {p-optimizer and {z-optimizeri} using gN for 1 \u2264 i \u2264 n4: \u2003Initialize p-data\u2009\u2190\u20095: \u2003k\u2009\u2190\u200916: \u20037:whilek\u2009<\u2009maximum epoch do8: \u2003forj\u2009\u2190\u20091 to ndo9: \u2003\u2003if j = 1 then10: \u2003\u2003\u2003uj\u2009\u2190\u2009p-data.\u2009DrawSample(x)11: \u2003\u2003\u2003\u2003else12: \u2003\u2003\u2003uj\u2009\u2190\u2009vj\u2212113: \u2003\u2003\u2003\u2003end if14: \u2003\u2003\u2003vj\u2009\u2190\u2009LFNN.\u2009Capture(uj)15: \u2003\u2003\u2003z-dataj\u2009\u2190\u2009 \u22b3 Update z-data.16: \u2003\u2003\u2003z-optimizerj.\u2009TrainNetwork \u22b3 Conduct z-learning.17: \u2003\u2003\u2003p-optimizer.\u2009TrainNetwork \u22b3 Conduct p-learning.18: \u2003\u2003\u2009\u2009\u2009k\u2009\u2190\u2009k\u2009+\u2009119: \u2003\u2003\u2009\u2009end for20: \u2003\u2009\u2009end while21: \u2009\u2009\u2009\u200922:end function23: p-variable, orange represents the functional space variables, z-variable, and black represents fixed connections or neurons that gather inputs with specified operators. z-variable and p-variable are iteratively updated by z-learning and p-learning, respectively.Figure\u00a0p-variable that represents the hardware parameter of the input plane\u2019s neuron-wise gain, and z-variable that is trained to optimize the functional space. An LC neuron may affect the connection between an input neuron and an output neuron. Thus, we connect every LC neuron to the connections of the light field between the input and output plane  with a 3\u2009\u00d7\u20093\u2009\u00d7\u200964 kernel and the rectifier linear unit (ReLU)2. The function is to non-linearly combine the functional basis block for fitting the non-linear part of the actual hardware. In addition, the output neurons are also weighted by the hardware parameter of the output plane\u2019s neuron-wise gain. The intuition is similar to that of an attention mechanism.The functional basis block consists of various neurons inspired by the light field relationship between the input, LC, and output neurons. An input neuron can make a possible contribution to every output neuron and thus is connected to every output neuron to form a light field Fig.\u00a0b. The coane Fig.\u00a0c. The coz-variable.Because the signal passes through some relatively dim and noisy connections, we merge nearby neurons\u2019 connections to build stronger connections with less noise. As shown in Fig.\u00a0In practice, many connections of LC neurons, especially at the finest resolution, are very weak and therefore can be approximated by connections at coarser resolutions. Removing those connections from the FNN can save memory and accelerate the training. We measure the impacts of connections by alternating the LC neuron parameter between 0 and 1 and capturing the energy change on the output plane. If the energy change of a connection between an input and output neuron pair w.r.t. an LC neuron is below a threshold, we remove that LC neuron\u2019s connection to that pair. For the finest resolution, we experimentally set the threshold to 20% of the maximum energy of valid input and output neuron connections. For the second finest resolution, we experimentally set the threshold to 10%. For the coarsest resolution, we keep all connections.Because there are billions of connections to test and conducting a one-by-one test is time-consuming, we build quad-trees in the neurons of an LC plane and hierarchically perform the test. Figure\u00a0In summary, this sparsification scheme prunes 99.96% of the LC neuron connections for our LFNN implementation.12. Finally, a simple amplitude filter integrated into the driver of the input plane clamps the impulse between zero and one and also introduces non-linearity.In order to capture multiple-layer LFNN results, we cycle the captured output to the input of the next LFNN layer and conduct certain activation functions with the signal. These activation functions are currently performed on a computer but can be implemented by all-optical or non-digital photoelectric hardware in the future. First, we design a special activation, termed X-activation, to enhance the inference capability of the multi-layer ONN. Specifically, the captured output is subtracted by its 180-degree rotated image. The subsequent X-activation is a common neuron-wise batch normalization methodThis design of X-activation aims for four different targets. First, it enables the deactivation in optical neural networks. The data flow of common artificial neuron networks contains both positive and negative values, but there is no negative light in an incoherent optical system. By introducing X-activation, a neuron can either activate or deactivate an arbitrary subsequent neuron with different LC neuron parameters Fig.\u00a0c. SecondWe physically prototype a loose neuron array, termed light field neural network (LFNN), to realize the regular-2 array and Bernoulli array by randomly disabling neurons. We use off-the-shelf components, e.g., liquid crystal display (LCD) panels, polarizers, and a machine vision camera, without tedious calibration. As a result, the actual LFNN is not exactly the same as the regular-2 array.\u03bcm, the resolution of 1600\u2009\u00d7\u20091200, and the bit depth 12 bit. The focal length and F-number of the camera are 12.5 mm and 1.6, respectively. Because the device is not fine-tuned and the planes have different valid areas, we use the pixels in the center areas of these planes as neurons. Specifically, 15\u2009\u00d7\u200913 pixels in the input plane, liquid crystal 1 (LC1), and liquid crystal 2 (LC2) are jointly controlled as one input neuron and LC neurons. 12\u2009\u00d7\u200915 pixels in the camera\u2019s image plane are read together as one output neuron.The applied LCD panels are expected to show a high transmittance and good linearity between the applied voltage and the polarization rotation angle. Among available LCD panels, we use Chimei Innolux AT070TN83 as the optical layer. The photograph of our prototype is shown in Fig.\u00a0In our experiment, we use two standard classification datasets. The MNIST dataset contains 60,000 training images and 10,000 test images belonging to 10 classes of handwritten digits. From 0 to 9, each class contains 5,923(980), 6,742, 5,958, 6,131, 5,842(982), 5,421(892), 5,918(958), 6,265, 5,851(974), and 5,949 training(test) samples, respectively. The CIFAR10 dataset consists of 60,000 32\u2009\u00d7\u200932 color images in 10 classes of real-world objects, with 6,000 images per class. There are 5,000 training images and 1,000 test images in each class. The classes include airplane, automobile, bird, cat, deer, dog, frog, horse, ship, and truck.Supplementary DocumentPeer review file"}
+{"text": "Left-to-right readers classify faster past events with motor responses on the left side of space and future events with responses on the right side. This suggests a left-to-right spatial organization in the mental representation of time. Here, we show that the significance and reliability of this representation are linked to the joint use of temporal and spatial codes in the task at hand. In a first unimanual Go/No-Go Implicit Association Test (IAT), attending selectively to \u201cpast\u201d or to \u201cfuture\u201d words did not activate corresponding \u201cleft\u201d or \u201cright\u201d spatial concepts and vice versa. In a second IAT, attending to both temporal  words and spatial targets  pointing arrows produced faster responses for congruent rather than incongruent combinations of temporal and spatial concepts in task instructions . This effect increased markedly in a STEARC task where spatial codes defined the selection between \u201cleft-side\u201d and \u201cright-side\u201d button presses that were associated with \u201cpast\u201d and \u201cfuture\u201d words. Two control experiments showed only partial or unreliable space\u2013time congruency effects when (a) participants attended to superordinate semantic codes that included both spatial \u201cleft\u201d/\u201dright\u201d or temporal \u201cpast/future\u201d subordinate codes; (b) a primary speeded response was assigned to one dimension  and a nonspeeded one to the other dimension . These results help to define the conditions that trigger a stable and reliable spatial representation of time-related concepts.The online version contains supplementary material available at 10.3758/s13414-023-02746-w. People use space to think and talk about the flow of time , to represent the flow of time  and corresponding temporal concepts , then in an IAT, the mere and selective activation of one spatial concept  should consistently and reliably facilitate the activation and classification of the associated \u201cpast\u201d temporal concept. Alternatively, if the positioning of \u201cpast\u201d and \u201cfuture\u201d temporal concepts on the left and right side of an MTL depends on the simultaneous presence of contrasting \u201cleft vs. right\u201d response codes in the task at hand, then a significant and reliable STA should be found only in (a) IATs that require discriminating, in different trials of the same task, both the \u201cleft vs. right\u201d direction of arrow targets and classifying \u201cpast vs. future\u201d word targets; (b) conventional STEARC tasks where contrasting \u201cleft vs. right\u201d spatial response codes are associated to contrasting \u201cpast vs. future\u201d temporal stimulus codes.f(U) = 0.4388 derived from the previous study of Santiago et al. . To avoid \u201ccarryover\u201d effects that can take place in within-participants designs, the order of tasks administration followed that of the increasing complexity of task instructions. As an example, in the first experiment (see below), in different blocks of trials, unimanual responses were regulated by the consideration of a \u201csingle\u201d time or space code . In the second experiment, unimanual responses were regulated by the \u201cjoint\u201d association of a space code with a time code . Finally, in the third experiment, the \u201cjoint\u201d association of a space with a time code determined the selection of a left vs. right side motor response . It is clear, for example, that performing the second \u201cjoint\u201d experiment first would activate the explicit association between a space and a time code and that this association can be \u201ccarried over\u201d to the performance of the first \u201csingle\u201d code experiment, that is aimed at testing whether the activation of a single space or time codes produces the implicit activation of a corresponding and congruent time or space code, respectively. Vice versa, performing first the single code experiment does not activate the conceptual space\u2013time association and does not produce corresponding carryover effects on the performance of the second \u201cjoint\u201d code experiment. Following the same line of reasoning, we point out that the STEARC effect that in the present study was tested in the third final experiment is a very consolidated and replicated finding and that, therefore, the replication of this effect can hardly be attributed to the previous performance of the second unimanual experiment with the joint use of space and time codes.Based on this preliminary analysis, we tested 28 healthy adult participants. Each participant performed three different experiments included in the study  in the first three experiments.https://osdoc.cogsci.nl/3.3/; Math\u00f4t al., https://www.jatos.org/). Participants accessed the experiment using a General Multiple Worker link. Participants were instructed to run the experiment in a quiet and isolated room and wear in-ear plug headphones to reduce environmental noise sources. They were also asked to keep their head positioned at a viewing distance of 60 cm from the screen. All participants had a normal or corrected-to-normal vision and were na\u00efve to the aim of the study. Instructions for all experiments were provided during individual audio/video calls with one of the experimenters. A training block that included 24 trials was administered before the experimental session and always corresponded to a shortened version of the first experimental block.Due to COVID pandemic restrictions, experiments were administered through the open-source software OpenSesame , participants responded to targets according to instructions that required the discrimination of the left/right direction of arrows without requiring the discrimination of the past/future temporal targets or vice versa, the discrimination of the past/future temporal targets without requiring the discrimination of the left/right direction of arrows. The aim of the experiment was to test whether the selective activation of one  out of two contrasting spatial codes  determined the activation of the activation of a corresponding temporal code  and vice versa.https://www.trainingcognitivo.it/GC/nonparole/) and were equivalent in length and in the number of syllables to target word stimuli . In addition, past and future words have the same frequency of use in Italian  and an equivalent length . Similarly, in the time-to-space condition, in different trials, arrow targets were alternated with white circle no-go nontargets to promote the full processing of go left- and right-pointing arrows. Each block included 200 trials, with 40 repetitions for each stimulus category.In four different blocks of trials, participants had to (a) go only to left-pointing arrows and to words; (b) go only to right-pointing arrows and to words; (c) go only to past words and to arrows; (d) go only to future words and to arrows. Conditions \u201ca\u201d and \u201cb\u201d qualify the influence of space coding on time coding . Vice versa, conditions \u201cc\u201d and \u201cd\u201d qualify the influence of time coding on space coding . In the space-to-time condition, go temporal targets were intermixed with nonwords no-go nontargets to avoid participants responding to \u201call\u201d word stimuli without full processing. Nonwords were generated using an online nonword generator  and trials in which responses were above and below two standard deviations from the mean of each experimental condition were excluded from the analyses. Following these criteria, 3.56% of trials were excluded from analyses.The space-to-time congruency effect was analyzed by entering RTs in congruent trials (past words of condition \u201ca\u201d and future words of condition \u201cb\u201d) and RTs in incongruent trials (past words of condition \u201cb\u201d and future words of condition \u201ca\u201d) in a 2 \u00d7 2 repeated-measures ANOVA, with time (past vs. future) and congruency (congruent vs. incongruent) as within-subjects factors.The time-to-space congruency effects were analyzed by entering RTs in congruent trials (left arrow of condition \u201cc\u201d and right arrow of condition \u201cd\u201d) and RTs in incongruent trials (right arrow of condition \u201cd\u201d and left arrow of condition \u201cc\u201d) in 2 \u00d7 2 repeated-measures ANOVA, with arrow direction (left vs. right) and congruency (congruent vs. incongruent) as within-subjects factors.r1, 2). Besides, we used the corrected Spearman\u2013Brown correlation between the RTs advantages in the odd-numbered and even-numbered halves of trials as the reliability index (coefficient: rtt). To further assess the reliability of Congruency effects, the split-half test was also applied to 10,000 permutations of RTs .The reliability of congruency effects was examined using the split-half method. We first divided each experimental condition data into odd and even responses. Then we calculated the RTs advantages produced in the congruent respect to the incongruent condition (dRTs = RTs in the incongruent condition minus RTs in the congruent condition) for the odd-numbered and the even-numbered items. We then evaluated the correlation between the RTs advantages for odd and even-numbered items  = 0.336, p = .566, \u03b7p2 = 0.012, or Time \u00d7 Congruency interaction, F = 0.144, p = .70, \u03b7p2 = 0.005; see Fig. The ANOVA highlighted no significant main effect of congruency (congruent vs. incongruent), F1, 7 = 0.336F = 5.071, p = .032, \u03b7p2 = 0.158 . The same comparison with Left-pointing arrows was not statistically significant (p > .562). The reliability test showed inconsistent time-to-space congruency effect . This result was confirmed when 10,000 random halves were computed through a permutation method (see Supplementary File).The ANOVA revealed a significant Congruency \u00d7 Arrow Direction interaction, F1, 7 = 5.071Based on the null results of the SC task in Experiment In four different conditions/blocks of trials, participants had to respond (a) only to left-pointing arrows and past words; (b) only to right-pointing arrows and future words; (c) only to left-pointing arrows and future words; (d) only to right-pointing arrows and past words. In conditions \u201ca\u201d and \u201cb\u201d spatial and temporal codes are congruent, while in conditions \u201cc\u201d and \u201cd\u201d they are Incongruent. RTs to temporal-target trials qualified the influence of spatial coding on temporal coding (space-to-time). Vice versa, RTs to arrow-direction trials qualified the influence of temporal coding on spatial coding (time-to-space). Each block consisted of 160 trials, 80 with temporal targets and 80 with arrow targets . Following the same exclusion criteria adopted in Experiment The space-to-time congruency effects were analyzed by entering RTs of congruent temporal-target trials (past words in condition \u201ca\u201d and future words in condition \u201cb\u201d) and incongruent temporal-target trials (past words in condition \u201cc\u201d and future words in condition \u201cd\u201d) in a 2 \u00d7 2 repeated-measures ANOVA, with Time (past vs. future) \u00d7 Congruency (congruent vs. incongruent) as within-subjects factors.The time-to-space congruency effects were analyzed by entering RTs of congruent arrow direction-target trials (left arrows in condition \u201ca\u201d and right arrows in condition \u201cb\u201d) and incongruent arrow direction-target trials (left arrows in condition \u201cc\u201d and right arrows in condition \u201cd\u201d) in a 2 \u00d7 2 repeated-measures ANOVA, with arrow direction (left vs. right) and congruency (congruent vs. incongruent) as within-subjects factors for the investigation of the time-to-space congruency effect.The reliability of congruency effects was examined using the same procedure as in Experiment F = 7.403, p = .011, \u03b7p2 = .215, with faster RTs in the congruent (745 ms) than in the incongruent (772 ms) condition. There was also a significant Congruency \u00d7 Time interaction, F = 17.284, p < .001, \u03b7p2 = .390. Bonferroni planned comparisons showed faster responses to congruent future targets (729 ms) versus incongruent future targets . The reliability test showed that the space-to-time congruency effect was consistent  = 7.899, p = .009, \u03b7p2 = .226, with RTs being faster in the congruent (472 ms) than in the incongruent condition (493 ms). Reliability test showed that the time-to-space effect was consistent  in the \u201ccongruent\u201d condition, they were asked to respond to past words with the left hand/button and future words with the right hand/button; (b) in the \u201cincongruent\u201d condition, vice versa, they were asked to respond to past words with the right hand/button and future words with the left hand/button. Each block consisted of 80 trials, 40 for each past/future condition. The order of blocks was counterbalanced among participants. In this experiment, 4.38% of trials were excluded from analyses due to the exclusion criteria adopted in Experiments Individual RTs of the congruent (past-words/left hand-button and future-words/right-hand-button) and incongruent (past-words/right-hand-button and future-words/left-hand-button) conditions were entered in a Time (past vs. future) \u00d7 Congruency (congruent vs. incongruent) repeated-measures ANOVA.F = 50.560, p < .001, \u03b7p2 = .651, with faster RTs to congruent (759 ms) than to incongruent targets (873 ms). The reliability analysis confirmed the consistency of the congruency effect  measured in the three tasks. Preliminary analyses were run to test the presence of multivariate normality in the data set  = 31.060, p < .001, \u03b7p2 = .534. Bonferroni planned comparison showed a significant difference between Experiment ps < .001; see Fig. The ANOVA pointed out the main effect of task, F, 54 = 31p < .001). Other correlations were not significant .Pearson\u2019s correlation  were asked to perform a modified version of the single code experiment. In each condition of the original single code experiment, participants were asked to put in contrast one conceptual dichotomy , while the remaining dichotomy was not activated by task instructions . In contrast, in this new version of the task, one conceptual code dichotomy was fully activated by task instructions, while the remaining dichotomy was only implicitly activated through its corresponding superordinate semantic code. For example, in the case of spatial codes, \u201chorizontal\u201d is superordinate to \u201cleft\u201d and \u201cright.\u201d In the case of temporal codes, \u201cnot present-tense\u201d is superordinate to \u201cpast\u201d and\u201d future\u201d . Therefore, in different blocks of trials, participants had to respond (a) only to left-pointing arrows and not present-tense words (where past and future words targets were intermixed with present-tense nontargets words); (b) only to right-pointing arrows and not present-tense words; (c) only to past words and horizontal arrows ; (d) only to future words and horizontal arrows. Conditions \u201ca\u201d and \u201cb\u201d qualify the investigations of space-to-time congruency effects  triggers the activation of a corresponding temporal code . Vice versa, conditions \u201cc\u201d and \u201cd\u201d qualify the investigation of time-to-space congruency effects  that is not explicitly activated by the task instructions. The procedure of the superordinate category task was similar to that of the single code experiment except that, in this case, vertical up or down pointing arrows for conditions \u201ca\u201d and \u201cb\u201d and present-tense words were also for condition \u201cc\u201d and \u201cd\u201d presented as no-go nontargets. Each block included 200 trials, with 40 repetitions for each category of stimuli. Participants were tested in a quiet and isolated room. They wore in-ear plug headphones to reduce environmental noise. The head position was restrained with a chin rest at a viewing distance of 57.7 cm from the screen. All participants had a normal or corrected-to-normal vision and were naive to the aim of the study.Thirty-two right-handed Italian native speakers participants  and RTs in incongruent temporal trials (past words of condition \u201cb\u201d and future words of condition \u201ca\u201d) in a 2 \u00d7 2 repeated-measures ANOVA, with time (past vs. future) and congruency (congruent vs. incongruent) as within-subjects factors.The time-to-space congruency effects were analyzed by entering RTs in congruent spatial trials (left arrow of condition \u201cc\u201d and right arrow of condition \u201cd\u201d) and RTs in Incongruent spatial trials (right arrow of condition \u201cd\u201d and left arrow of condition \u201cc\u201d) in 2 \u00d7 2 repeated-measures ANOVA, with arrow direction (left vs. right) and congruency (congruent vs. incongruent) as within-subjects factors.The reliability of congruency effects was examined using the same procedure as in Experiment F = 12.939, p = 0.001, \u03b7p2 = 0.294, with faster RTs to congruent trials (654 ms) than to incongruent ones (664 ms). Nonetheless, the reliability test showed this effect was inconsistent [split-half reliability: r1,2 = \u2212.2563, rtt = \u2212.407, p = .156; see Fig. The ANOVA pointed out a significant main effect of congruency (congruent vs. incongruent), t trials 54 ms thaF = 29.175, p < .001, \u03b7p2 = 0. 484. Also, in this case, RTs were faster in the congruent (488 ms) than in the incongruent condition (514 ms). The reliability test showed that this effect was consistent , The single code task of Experiment SD = 2.55. In different experimental conditions, participants were asked to (a) \u201cgo\u201d as fast as possible only to left-pointing arrows and to all words and then indicate, without time pressure, whether the word was a \u201cpast\u201d or a \u201cfuture\u201d one by pressing the \u201cgreen\u201d or the \u201corange\u201d button, respectively; (b) \u201cgo\u201d as fast as possible only to right-pointing arrows and to all words, and then indicate, without time pressure, whether the word was a \u201cpast\u201d or a \u201cfuture\u201d one by pressing the \u201cgreen\u201d or the \u201corange\u201d button, respectively; (c) \u201cgo\u201d as fast as possible only to past words and to all arrows and then indicate, without time pressure, whether the arrow was a left- or a right-pointing one by pressing by pressing the \u201cgreen\u201d or the \u201corange\u201d button, respectively; (c) \u201cgo\u201d as fast as possible only to future words and to all arrows and then indicate, without time pressure, whether the arrow was a left- or a right-pointing one by pressing the \u201cgreen\u201d or the \u201corange\u201d button, respectively. Like in the other experiments, the central space bar was used for the primary speeded task. Buttons \u201cB\u201d and \u201cY\u201d were used for the secondary nonspeeded task: These buttons are vertically arranged one above the other on the computer keyboard and were chosen not to include or suggest the implicit use of left versus right spatial response codes. Half of the participants had the \u201cB\u201d button covered with a green plastic button and the \u201cY\u201d button with an orange plastic button, while for the other half of participants the position of green and orange buttons was reversed. Conditions \u201ca\u201d and \u201cb\u201d qualify space-to-time congruency effects, while conditions \u201cc\u201d and \u201cd\u201d qualify time-to-space congruency effects. The procedure and stimuli were as in Experiment In this second control experiment we tested 28 right-handed Italian native speakers  and RTs in Incongruent temporal trials (past words of condition \u201cb\u201d and future words of condition \u201ca\u201d) in a 2 \u00d7 2 repeated-measures ANOVA, with time (past vs. future) and congruency (congruent vs. incongruent) as within-subjects factors.The time-to-space congruency effects were analyzed by entering RTs in congruent spatial trials (left arrow of condition \u201cc\u201d and right arrow of condition \u201cd\u201d) and RTs in Incongruent spatial trials (right arrow of condition \u201cd\u201d and left arrow of condition \u201cc\u201d) in 2 \u00d7 2 repeated-measures ANOVA, with arrow direction (left vs. right) and congruency (congruent vs. incongruent) as within-subjects factors.The reliability of congruency effects was examined using the same procedure as in Experiment F = 0.057, p = .813, \u03b7p2 = 0.002 , F = 10.477, p = 0.003, \u03b7p2 = 0. 279. RTs were faster in the congruent (558 ms) than in the incongruent condition (573 ms). Nonetheless, the reliability test showed that this effect was inconsistent , gruent 55 ms than The main results of our study are as follows. First, in a single code task  shows that the STEARC arises at the response-related stage  gestures can be spontaneously adopted during the interpersonal communication of temporal information  while the contrast in the remaining dimension was only implicitly activated through a superordinate semantic code . In this case, we found significant congruency effects in the Space-to-Time and Time-to-Space directions .Current research mainly focuses on qualifying the types and the set of sensorimotor and cultural experiences that shape the spatial representation of abstract concepts like time and number. For example, Pitt and Casasanto  have sugIn the domain of space-number association, recent investigations have suggested that interindividual variations in scanning habits, finger counting style and spatial imagery can significantly affect the ability to generate and use mental spatial representations of numerical magnitudes Below is the link to the electronic supplementary material."}
+{"text": "Nature Communications 10.1038/s41467-023-38850-6, published online 12 June 2023Correction to: M\u2019 was incorrectly presented as mutation probability \u2018zM\u2019. These have been corrected in both the HTML and PDF versions of the Article.In the original version of this Article, in the third paragraph of the Discussion the equation \u2018"}
+{"text": "However, it is often the case in practice that the input keys have intrinsic relationships that we can exploit to lower the bit complexity of f. For example, consider a string and the set of all its distinct k-mers as input keys: since two consecutive k-mers share an overlap of f to map consecutive k-mers to consecutive addresses, as to also preserve as much as possible their relationship in the codomain. This is a useful feature in practice as it guarantees a certain degree of locality of reference for f, resulting in a better evaluation time when querying consecutive k-mers.Minimal perfect hashing is the problem of mapping a static set of k-mers extracted consecutively from a collection of strings. We design a construction whose space usage decreases for growing k and discuss experiments with a practical implementation of the method: in practice, the functions built with our method can be several times smaller and even faster to query than the most efficient MPHFs in the literature.Motivated by these premises, we initiate the study of a new type of locality-preserving MPHF designed for  U, a function f maps each key of S into a distinct integer in [n]. The function is allowed to return any value in [n] for a key Given a universe set or |U|\u226bn . Minimalor |U|\u226bn  to databor |U|\u226bn , as wellor |U|\u226bn , compileor |U|\u226bn ,b.f act less randomly on S. This, in turn, would permit to achieve a lower space complexity for f.In its simplicity and versatility, the minimal perfect hashing problem does not take into account specific types of inputs, nor the intrinsic relationships between the input keys. Each key S are all the distinct sub-strings of length k, for some S are called k-mers. The crucial point is that any two consecutive k-mers in a string of k-mers as to reduce the randomness of f, thus lowering its bit complexity and evaluation time.We therefore consider in this article the following special setting of the minimal perfect hashing problem: the elements of Q, if k-mer f to hash k-mer following x in Q , or contig identifiers (e.g. unitigs) in a de Bruijn graph. Consecutive k-mers tend to have very similar\u2014if not identical\u2014satellite values, hence hashing consecutive k-mers to consecutive identifiers induce a natural clustering of the associated satellite values which is amenable to effective compression. The second important reason is, clearly, faster evaluation time when querying for consecutive k-mers in a sequence. This streaming query modality is the query modality employed by k-mer-based applications  which allows a more parsimonious memory layout. The space of the proposed solution decreases for growing k and the data structure is built in linear time in the size of the input (number of distinct k-mers). In Section 4 we present experiments across a breadth of datasets to show that the construction is practical too: the functions can be several times smaller and even faster to query than the most efficient, albeit \u201cgeneral-purpose\u201d, MPHFs. We conclude in Section 5 where we also sketch some promising future directions. Our C++ implementation of the method is publicly available at https://github.com/jermp/lphash.We formalize the notion of locality-preserving MPHF along with other preliminary definitions in Section 2. We show how to obtain a locality-preserving MPHF in very compact space in Section 3. To achieve this result, we make use of two algorithmic tools: random minimizers  and a nok of a string k-mer of S.Definition 1The k-mer spectrum of\u2002is the set of all distinct k-mers of the strings in\u2002. Formally:\u2002(Spectrum). Definition 2A spectrum-preserving string set (or SPSS)\u2002of\u2002is a set of strings such that (i) each string of\u2002has length at least k, and (ii)\u2002(Spectrum-Preserving String Set). Let k-mers in a SPSS, we are interested in a SPSS k-mer is seen only once, i.e. for each k-mer x appears once. We assume that no k-mer appearing at the end of a string shares an overlap of k-mer of another string, otherwise we could reduce the number of strings in Since our goal is to build a MPHF for the see e.g. .k-mers. Without loss of generality, we index k-mers based on their positions in i-th k-mer in The input for our problem is therefore a SPSS n distinct k-mers in k-mers from a string of f as well as its evaluation time when querying k-mers in sequence.We want to build a MPHF Definition 3Let\u2002be a MPHF forand A be the set\u2002. The function f is\u2002-locality-preserving for\u2002if\u2002(LP-MPHF). We define a locality-preserving MPHF, or LP-MPHF, for Intuitively, the \u201cbest\u201d LP-MPHF for k-mers is a very desirable property as motivated in Section 1. A different definition of locality-preservation could instead be given if we were considering generic input keys. Second, we did not use the term \u201corder-preserving\u201d to stress the distinction from classic order-preserving functions in the literature . Two more considerations are in order. First, it should be clear that the way we define locality-preservation in Definition 3 is only pertinent to SPSSs where having consecutive hash codes for consecutive terature  that makk-mers in k-mers do not share any overlap .From Definitions 3 and 4, it is easy to see that k-mers that will be one of the main ingredients used in Section 3.Definition 5k-mer). Given a k-mer x and a random hash function h, the minimizer of x is any m-mer\u2002such that\u2002for any other m-mer y of x, for some\u2002 Since h is a random hash function . Given a string S, a super-k-mer g is a maximal sub-string of S where each k-mer has the same minimizer\u2002and\u2002appears only once in g.. Let p be the start position of x. We can use this positional information p to compute Now, suppose we are given a query if x cannot possibly be in g and, hence, indexed by f.otherwise .Lemma 1.The strategy in for any\u2002Our strategy is to compute Proof. For k-mer of g, k-mers inside a super-k-mer.To sum up, the position of the minimizer in the first k-mers of g into k-mer g. We proceed as follows.Algorithm 1.f, given the k-mer x. The helper function x and the starting position p of x.Evaluation algorithm for function\u2002f(x):1: 2: \u20033: \u2003return4: \u2003From Layout. Let k-mer g is the only super-k-mer having minimizer k-mers have the same minimizer in Section 3.3.) We allocate an array L, that is, k-mers before those in g .Definition 7Let g be a super-k-mer. The first/last (FL) rule is as follows:(FL rule). Depending on the starting position of the minimizer in the first and last if\u2002and\u2002, then g is left-right-max; elseif\u2002and\u2002, then g is left-max; elseif\u2002and\u2002, then g is right-max; elseif\u2002and\u2002, then g is non-max.See Layout. Based on the FL-rule above, we derive a partitioned layout as follows. We store the type of each super-k-mer in an array k-mers to improve the space bound of Theorem 1 because:k-mers, we do not store L nor P;for all left-right-max super-k-mers, we only store L\u2014precisely, two arrays k-mers, respectively;for all left/right-max super-k-mers, i.e. non-max, we store both L and P as explained before\u2014let us indicate them with for all the other super-R: the result of this query is the number of super-k-mers that have type t in the prefix R[1.i]. If k-mer associated to t, we either do not perform any array access or access the j-th position of either Addressing the arrays d Pn see .R that also supports R in A succinct representation of let tree . In our Lookup.f. The complexity of the algorithm is still R) and a rank query as explained above but, on the other hand, it permits to save 2 array accesses in the left-right-max case or 1 in the left/right-max case compared to L and one to P). Hence, the overall number of array accesses performed by Algorithm 2.f. The quantities k-mers of Evaluation algorithm for a partitioned representation of function\u2002f(x):1: 2: \u20033: \u20034: \u20035: \u20036: \u2003switch(t):7: \u2003case left-right-max:8: \u2003\u2003\u20099: \u2003\u2003\u2003 \u2009break10: \u2003\u2003\u2003case left-max:11: \u2003\u200312: \u2003\u2003\u2003break13: \u2003\u2003\u2003case right-max:14: \u2003\u200315: \u2003\u2003\u2003break16: \u2003\u2003\u2003case non-max:17: \u2003\u200318: \u2003\u2003\u2003break19: \u2003\u2003\u2003return20: \u2003Compression. Intuitively, if the fraction of left-right-max super-k-mers and that of left/right-max super-k-mers is sufficiently high, we can save significant space compared to the data structure in Section 3.1 that stores both L and P for all minimizers. We therefore need to compute the proportions of the different types of super-k-mers as given by the FL rule. For ease of notation, let k-mer g.Remark 1.The FL rule is a partitioning rule, i.e.\u2002for any super-k-mer.k (k-mer length) and m (minimizer length). To achieve this goal we propose a simple model based on a (discrete-time) Markov chain.Our objective is to derive the expression for the probabilities k-mer. The corresponding Markov chain is illustrated in X, i.e. with each value in k-mer if, from state w we transition to state w which corresponds to the event that the right-most m-mer (that coming next to the right) is the new minimizer. If the chain reaches state 1, instead, we know that we are always going to see a new minimizer next. If h used by u Lemma 2.and\u2002We give the following lemma to prove Theorem 2. , the fastest MPHF in the literature, and the popular BBHash , 64 GB of RAM, and running the Linux 5.13.0 operating system. The whole code (LPHash and competitors) was compiled with gcc 11.2.0, using the flags -O3 and -march=native.Datasets. We use datasets of increasing size in terms of number of distinct k-mers; namely, the whole-genomes of: Saccharomyces cerevisiae , Caenorhabditis elegans , Gadus morhua , Falco tinnunculus , and Homo sapiens . For each dataset, we obtain the corresponding SPSS by first building the compacted de Bruijn graph using BCALM2 . A suitable value of m should clearly be not too small , nor too large  and Theorem 3 (partitioned) for b parameter models the number of bits per key spent by a MPHF of choice for the representation of the minimizer MPHF and the fallback MPHF. , LPHash still retains 2.3\u20133.7\u00d7 better space.To make a concrete example, partitioned LPHash for We remark that, however, PTHash and BBHash are \u201cgeneral-purpose\u201d MPHFs that can work with arbitrary keys, whereas the applicability of LPHash is restricted to spectrum-preserving string sets.k-mers read from the Human chromosome 13, for a total of Q, we query for each k-mer read \u201cconsecutively\u201d from Q, that is, for Q[1.k], k-mers very cheap, as consecutive k-mers are likely to be part of the same super-k-mer.We distinguish between streaming and random queries (lookups) for LPHash. Given a query string k: while the streaming one slightly decreases for the better locality, the random one increases instead, for the more expensive hash calculations.Considering the result in LPHash is as fast as PTHash-v1 (fastest configuration) for streaming queries on the smaller Yeast dataset, but actually up to 1.4\u20132\u00d7 faster on the larger datasets Elegans, Cod, Kestrel, and Human. Instead, it is up to k-mers . However, we do not regard this as a serious limitation since, as we already motivated, the streaming query modality is the one used in Bioinformatics tasks involving k-mers . We alsoWe now consider building time which is reported in k-mers since it builds two smaller PTHash functions  3\u2009bits/k-mer and 100\u2013200 nanoseconds per lookup. This work shows that it is possible to do significantly better than this when the k-mers come from a spectrum-preserving string set: for example, less than 0.6\u20130.9\u2009bits/k-mer and 30\u201360 nanoseconds per lookup. Our code is open-source.We show that a concrete implementation of the method is practical as well. Before this paper, one used to build a BBHash function over the Miniception (As future work, we plan to further engineer the current implementation to accelerate construction and streaming queries. Other strategies for sampling the strings could be used other than random minimizers ; for exaiception  achievinbtad219_Supplementary_DataClick here for additional data file."}
+{"text": "CRISPR/Cas9  is a popular and effective two-component technology used for targeted genetic manipulation. It is currently the most versatile and accurate method of gene and genome editing, which benefits from a large variety of practical applications. For example, in biomedicine, it has been used in research related to cancer, virus infections, pathogen detection, and genetic diseases. Current CRISPR/Cas9 research is based on data-driven models for on- and off-target prediction as a cleavage may occur at non-target sequence locations. Nowadays, conventional machine learning and deep learning methods are applied on a regular basis to accurately predict on-target knockout efficacy and off-target profile of given single-guide RNAs (sgRNAs). In this paper, we present an overview and a comparative analysis of traditional machine learning and deep learning models used in CRISPR/Cas9. We highlight the key research challenges and directions associated with target activity prediction. We discuss recent advances in the sgRNA\u2013DNA sequence encoding used in state-of-the-art on- and off-target prediction models. Furthermore, we present the most popular deep learning neural network architectures used in CRISPR/Cas9 prediction models. Finally, we summarize the existing challenges and discuss possible future investigations in the field of on- and off-target prediction. Our paper provides valuable support for academic and industrial researchers interested in the application of machine learning methods in the field of CRISPR/Cas9 genome editing. Advances in the area of genome editing  in the 2010s revolutionized molecular biology, genetics, and biomedicine. Genome editing techniques allow precise manipulation, deletion, and insertion of sequence fragments within the DNA of living organisms. In recent years, three effective types of genome editing toolsets, called Zinc Finger Nucleases (ZFNs) .Highly effective CRISPR/Cas9 gene editing system, co-invented in 2012 by Emmanuelle Charpentier and Jennifer Doudna , has beeThe CRISPR/Cas9 genetic engineering system is an adapted version of the bacterial CRISPR-Cas9 antiviral defense system. CRISPR is a family of DNA sequences present in prokaryotic genomes that stems from DNA fragments of bacteriophages, which had infected prokaryotic genomes in the past. These DNAs are used as antiviral defense elements to recognize and eliminate DNA from similar bacteriophages during eventual infections . Cas9 isin vivo [In the CRISPR/Cas9 editing system, the Cas9 nuclease combined with a guide RNA (gRNA) is delivered into a cell, allowing the cell\u2019s genome to be cut in a specific location, some targeted genes to be removed from it, and some other added to it, in vivo . Guide Rin vivo .The CRISPR/Cas9 system is nonetheless prone to unintended off-targets: a cleavage may occur at non-target locations . Thus, tOver the last few years, data-driven machine learning methods emerged as a new modeling approach which outperforms the common scoring prediction methods, such as MIT CRISPR Design Tool2 , CCTop aet\u00a0al. [et\u00a0al. [et\u00a0al., only one employs deep learning. Chen et\u00a0al. [et\u00a0al. [in silico off-target prediction tools in order to evaluate their genome-wide CRISPR performances, and introduced an integrated Genome-Wide Off-target cleavage Search (iGWOS) platform designed for optimal genome-wide off-target predictions. The main goal of the study by Yaish et\u00a0al. [et\u00a0al. introduced predictive off-target in cellula models based on gradient boosting (i.e. the XGBoost decision tree-based ensemble learning framework was implemented by these authors) and compared them with state-of-the-art off-target prediction methods. The paper of O\u2019Brien et\u00a0al. [in silico optimization can successfully replace in vitro CRISPR-Cas9 designs. Thus, algorithmic solutions can be used for maximizing gRNA editing efficiency and minimizing gRNA specificity. Finally, a recent review of Konstantakos et\u00a0al. [et\u00a0al. assessed the performances of 10 deep learning and one conventional machine learning methods on six benchmark data sets, and provided recommendations for their use. The authors pointed out that the existing on-target prediction approaches still have some flaws, including their sensitivity to data heterogeneity, unclear decision making mechanism, and inability to produce general gRNA design rules.Among recent reviews and comparative studies discussing the use of computational methods for evaluating gRNA efficiency and predicting gRNA specificity, we need to mention the following works. Wang et\u00a0al.  highligh [et\u00a0al.  providedn et\u00a0al.  first br [et\u00a0al.  comparedh et\u00a0al.  was to sn et\u00a0al.  presentss et\u00a0al.  addresseIn this review paper, we provide a summary of studies that have examined the effectiveness of artificial intelligence (AI) methods for on- and off-target activity prediction related to CRISPR/Cas9. In contrast to some previous reviews , 37\u201342, Our main contributions are as follows:To the best of our knowledge, this is the first comprehensive review of both traditional machine learning and deep learning methods, used for both on-target (guide efficiency) and off-target (guide specificity) outcome prediction in CRISPR/Cas9 genome editing;A description of the benchmark data sets used for on- and off-target prediction in CRISPR/Cas9 is provided. Most of the discussed data sets were curated and made available for researchers on our GitHub repository;The main sequence encoding techniques used in CRISPR/Cas9, applying to both traditional machine learning and deep learning methods, are discussed along with their intrinsic properties;The main deep learning models used for on- and off-target prediction in CRISPR/Cas9 are presented and their advantages and limitations are highlighted;Research challenges and avenues of future investigation regarding the application of traditional machine learning and deep learning methods in the field of CRISPR/Cas9 genome editing are discussed.In this section, we present the most popular CRISPR/Cas9 benchmark data sets used in the literature for on- and off-target prediction. These data sets can be divided into three categories: data sets including off-targets only, on-targets only, and both off- and on-targets.et\u00a0al. [in vitro Reporting of CLeavage Effects by sequencing) screening strategy introduced by Tsai et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [in vitro Cas9 genome-wide nuclease activity data set. CHANGE-seq was carried out to analyze 110 sgRNA targets across 13 therapeutically relevant loci in human primary T cells. A total of 201 934 off-target sites were identified with variable numbers of off-target sites, ranging from 19 to 61 415, for an individual sgRNA.The first group of benchmark data sets consists of off-targets. GUIDE-seq was one of the first off-target data repositories, based on the results of the GUIDE-seq technique developed by Tsai et\u00a0al. . It can i et\u00a0al.  was used [et\u00a0al.  proposed [et\u00a0al.  collecte [et\u00a0al. , 47,  [et\u00a0al. data set [et\u00a0al. data set (4239 guides targeting 829 genes in Human Hct116 cells) [et\u00a0al. data set (1234 guides targeting Human 293T cells) [et\u00a0al. data set (50 guides targeting different genes in Caenorhabditis elegans genome) [et\u00a0al. [crispor.org) that is intended to design, evaluate and clone guide sequences for the CRISPR/Cas9 system. This web tool incorporates several on- and off-target scoring algorithms. It also displays pre-calculated results for all human exons from the UCSC Genome Browser tracks. On the first page of crispor.org, the user enters three pieces of information: (i) a single genomic sequence, typically an exon under 2300 bp; (ii) a genome ; (iii) a PAM motif. The main output of CRISPOR is a web page that shows the annotated input sequence and the list of possible guides in this sequence. Furthermore, CRISPOR also generates a list of primers related to a selected guide. The related GitHub data repository organized by Haeussler comprises direct links to 22 experimental data sets along with some necessary data conversion scripts written in Python. Munoz et\u00a0al. [et\u00a0al. [The third group of benchmark data sets considered in the literature includes data containing both off- and on-target information. First, we need to mention the RESistance assays (RES) data set, i.e. Doench V2, made available by Doench et\u00a0al. . It cons [et\u00a0al.  aggregat0 cells) , 61, Koidata set , Doench data set , 59, Har6 cells) , Z_fish 6 cells) , Z_fish 6 cells) , Z_fish 6 cells) , Drosoph6 cells) , Chari eT cells) , Ciona dT cells) , and Far genome) . Moreovez et\u00a0al.  designed [et\u00a0al.  includeshttps://github.com/dagrate/public_data_crisprCas9. Moreover, several data sets presented here have been one-hot encoded and prepared for use in machine learning and deep learning experiments. The related Python scripts have been also made available to the scientific community.In Table In conclusion, we think that using the latest benchmark data containing large amounts of samples and features is likely to facilitate future work in CRISPR/Cas9, since such data can provide wide and complete coverage of intrinsic properties of both off- and on-targets under study, and thus be effectively exploited by state-of-the-art machine learning and deep learning methods.Before building AI models intended for on- and off-target prediction, the sgRNA\u2013DNA sequence data must be pre-processed to be used as input. Data pre-processing, or data encoding, allows converting the sgRNA\u2013DNA sequences of letters into sequences of numbers that AI models can read and interpret to build their predictions. Data pre-processing is an important milestone when trying to boost the predictive performance of AI models. The two most popular encoding techniques used in CRISPR-Cas9 are: (a) One-hot encoding and (b) Word embedding. Figure Word2Vec . This naet\u00a0al., Wang et\u00a0al., and Charlier et\u00a0al. [It is worth noting that most of the sequence encoding schemes discussed in this section apply to both traditional machine learning and deep learning models. For example, the recent works of Lin r et\u00a0al. , 73\u201375 uet\u00a0al. [et\u00a0al. is of size et\u00a0al. [et\u00a0al. [et\u00a0al. combined a et\u00a0al. [et\u00a0al. [et\u00a0al. the created seven-bit-long features allow one to take into account all possible correspondences existing between the original sgRNA\u2013DNA pairs of features taking the values  technique, called word embedding. The idea of applying word embedding on sgRNAs is that off-targets are encoded closer to each other in the vector space than are on-targets. Liu et\u00a0al.  combined [et\u00a0al.  proposed [et\u00a0al. , designe [et\u00a0al.  proposed [et\u00a0al. . The encet\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al.[et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al., which are also known as thermodynamic properties, included Minimum Free Energy, the most favorable thermodynamic RNA\u2013RNA interaction energy, local pair probabilities and specific sgRNA heat parameters. In their CRISPRO experiments, Schoonenberg et\u00a0al. [et\u00a0al. include the PROVEAN  deletion score of the targeted amino acids 1 and 2, position in the gene, predicted disorder score of amino acids 1 and 2, GC content of the 20-mer guide, length of the targeted exon, and off-target score of the gRNA. Chen et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [One-hot encoding and word embedding are not the only ways to represent a sequence in machine learning models. The majority of conventional machine learning (ML) models used in CRISPR-Cas9 consider additional sequence features such as position-specific features, different counts, and structural/thermodynamic characteristics to best capture sequence information . Positi [et\u00a0al. . Rahman  [et\u00a0al.  considerg et\u00a0al.  considern et\u00a0al.  used two [et\u00a0al.  proposed [et\u00a0al.  explored [et\u00a0al.  used seqe et\u00a0al.  demonstrIn conclusion, we need to point out that feature comparison between different experiential CRISPR-Cas9 data sets uncover substantial discordance and that further research is warranted to identify the most significant generic predictors (i.e. explanatory features) in case of both guide efficiency (i.e. on-target activity) and guide specificity (i.e. off-target effects).In this section, we present different conventional machine learning models for on- and off-target prediction found in the genome editing literature related to CRISPR/Cas9. The presentation is organized based on the target categories: (1) off-target prediction only, (2) on-target prediction only, and finally (3) both on- and off-target prediction. Within each category, the works follow chronological order.et\u00a0al. [et\u00a0al. [et\u00a0al. opened new directions for data aggregation in the field of genome editing. Chen et\u00a0al. [et\u00a0al. [et\u00a0al. demonstrated that the ensemble-based AdaBoost algorithm was able to outperform the other predictive algorithms in terms of the area under the precision recall curve (AUPRC) and the area under the receiver operating characteristic curve (AUROC) metrics. Lazzarotto et\u00a0al. [in vitro activity. Their CHANGE-Seq model was designed to better understand the specificity of genome editors. In their experiments, Lazzarotto et\u00a0al. used the encoded one-dimensional vectors to train a gradient tree boosting model to predict off-target activities. The authors highlighted the importance of the protospacer and the PAM position to ensure accurate off-target predictions. Moreover, they showed that CHANGE-Seq generally outperforms the well-known GUIDE-seq [First, we discuss papers dealing with off-target activity prediction. Abadi et\u00a0al.  proposed [et\u00a0al.  were amo [et\u00a0al. , GUIDE-s [et\u00a0al. , HTGTS [ [et\u00a0al. , CIRCLE- [et\u00a0al. , and mul [et\u00a0al. . The autn et\u00a0al.  generaten et\u00a0al. , and rann et\u00a0al. , as well [et\u00a0al.  explored [et\u00a0al. , MIT Web [et\u00a0al. , CFD [54 [et\u00a0al. , and Cro [et\u00a0al. , as well [et\u00a0al. , random  [et\u00a0al. , SVM, an [et\u00a0al. . In theio et\u00a0al.  proposedUIDE-seq  and CIRCUIDE-seq  models.et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [in silico predictions of sgRNA on-target activity. CRISPRpred is capable to extract relevant features in order to use them in an SVM-based machine learning framework. The work of Rahman et\u00a0al. emphasizes the importance of feature engineering in boosting the predictive performance of sgRNA on-target prediction models. Furthermore, Rafid et\u00a0al. [et\u00a0al. [in silico design of sgRNAs. Konstantakos et\u00a0al. [et\u00a0al. evaluated the performance of CRISPRedict, comparing it with state-of-the-art gRNAs design tools, including some deep learning models, and concluded that despite its simplicity, CRISPRedict provides interpretable efficiency predictions with comparable performance. Zarate et\u00a0al. [Second, we present a summary of recent papers addressing the problem of machine learning prediction of on-target activities. Wang et\u00a0al.  were amo [et\u00a0al.  trained  [et\u00a0al.  applied  [et\u00a0al.  investig [et\u00a0al.  introducd et\u00a0al.  demonstrd et\u00a0al.  based on [et\u00a0al.  proposeds et\u00a0al.  introduce et\u00a0al.  developeet\u00a0al. [et\u00a0al. [Finally, we discuss papers addressing the problem of both on- and off-target activity prediction by means of conventional machine learning models. Doench et\u00a0al.  designed [et\u00a0al.  proposedAlthough the use of traditional machine learning algorithms, whose main advantages are their relative simplicity and fast training, led to some impressive on- and off-target activity prediction results, recent studies conducted using deep learning methods (see the next section) often demonstrated a superior performance. We are convinced that, in general, deep learning models are better suited for both on- and off-target activity prediction than conventional machine learning models, since modern CRISPR/Cas9 data sets contain hundreds of thousands, and sometimes millions, of samples, and state-of-the-art deep learning algorithms can be effectively used on such huge volumes of data encompassing complex non-linear patterns. However, for benchmark purpose, the results provided by deep learning algorithms should be always compared with those yielded by some well-performing traditional machine learning methods such as SVM, random forest and XGBoost, as well as their ensemble frameworks, which are capable of increasing the accuracy of individual methods.Table Deep learning applications across all research fields have recently gained popularity due to easier access to data, boosted computing power, and recent theoretical progress in supervised learning. DNNs are at the core of deep learning. They are capable of learning complex patterns from the data using multiple layers of interconnected neurons. Nonetheless, their training and optimization are still very challenging problems. This section is divided into two parts. First, we present the main properties of existing deep learning network architectures. Second, we discuss their applications in CRISPR/Cas9.In this section, we describe succinctly the three main types of DNNs used for on- and off-target activity prediction in CRISPR/Cas9. They are FNNs, CNNs, and RNNs. Figure FNNs are one of the most popular DNN models . In a stet\u00a0al. [CNNs, introduced by Lecun et\u00a0al. , rely, aet\u00a0al. ).RNNs are another type of neural networks that can be used effectively for on- and off-target prediction in CRISPR/Cas9. In contrast to FNNs and CNNs, the information in RNNs does not always move forward; it can also move backward. The aim of RNNs is to replicate a memory process through a recurrent learning mechanism. RNNs aggregate information of the past inputs and that of the current input in order to produce the current output. An example of an RNN architecture used for off-target prediction in CRISPR/Cas9 is presented in Figure  follows : where For all deep learning network architectures presented here, the neurons rely on an activation function that is used to determine whether a given neuron should be activated or not. Thus, the activation function being used determines whether the neuron\u2019s contribution to the network is important or not in the prediction process. An activation function allows the model to transform the weighted sum of the neuron\u2019s input signals into an output signal. Table DNNs, by their nature, have a large number of parameters to fine-tune during their training. Special attention must be given to the problem of overfitting in the model\u2019s training. Overfitting occurs when the model learns patterns only present in the training set and cannot generalize its predictive performance on the test set. Different techniques exist to limit the overfitting while training DNNs. The most important of them are early-stopping, network-reduction, regularization, and dropout , 128. WeThis section includes four thematic subsections. First, we discuss the studies emphasizing the use of novel sequence encoding strategies along with deep learning models. Second, we present works using different feature engineering approaches. Third, we highlight the papers applying class rebalancing techniques prior to carrying out deep learning algorithms. Forth, we describe some recent works relying on the use of attention mechanism. Within each category, the works follow the off-target, on-target and both on- and off-target prediction order.et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. compared the prediction performance of different FNN, CNN, and RNN network architectures  auto-encoder to learn the underlying representation of sgRNAs. The unsupervised deep representation learning approach was then used to transfer the encoded data to a hybrid DNN. The proposed network included a softmax activation function and an identity function for the classification and regression tasks, respectively. DeepCRISPR provided good prediction results in terms of both AUPRC and AUCROC, compared with the CFD prediction method [Concerning the prediction of both on- and off-targets, we need to mention the work of Chuai et\u00a0al. , who wern method .Most of the aforementioned studies demonstrated impressive prediction results using novel sgRNA\u2013DNA one-hot sequence encoding schemes combined with deep learning models. We think, however, that further prediction improvements will not anymore result from the use of sophisticated data encoding schemes, nor from the models complexity, but rather from an effective use of additional biological or physical features as well as from the application of the feature engineering and class rebalancing techniques.In addition to conventional nucleotide sequence data, some plausible biological and physical features, such as gene melting temperature, molecular weight or microhomology features, can be also used as input of CRISPR/Cas9 predictive models. Moreover, some new informative features can be created, or reengineered, from the existing ones. Feature engineering has proven to be an important milestone when developing and optimizing predictive models .et\u00a0al. [et\u00a0al. [et\u00a0al. demonstrated the importance of both the sequence context and the chromatin accessibility for effective cleavage prediction. Niu et. al. [et\u00a0al. [As regards the off-target prediction, Liu et\u00a0al.  introducet\u00a0al.  to extra [et\u00a0al.  introduc [et\u00a0al. . In thei et. al.  proposednd ReLUs  in the c [et\u00a0al.  introducet\u00a0al. [et\u00a0al. [et\u00a0al. demonstrated that the RNN that received as input the sequence data with added biological features was able to outperform the other competing models. Their second best-performing model was the RNN that received as input sequence data only. Furthermore, Wang et\u00a0al. developed a DeepHF website to ease the access to WT-SpCas9, eSpCas9(1.1), and SpCas9-HF1 indel data. The authors also applied SHAP with XGBoost and RNNs to assess the feature importance of the sequence input. Moreover, they used the Deep SHAP algorithm [et\u00a0al., we can conclude that additional biological information and plausible reengineered features increase the predictive performance of deep learning models, leaving opportunities for future model enhancement. Elkayam and Orenstein [et\u00a0al. [Concerning the on-target prediction, Shrawgi et\u00a0al.  introduc [et\u00a0al. , who com [et\u00a0al.  that com [et\u00a0al.  with thelgorithm  to estimrenstein  proposedrenstein . It is b [et\u00a0al. .et\u00a0al. [Finally, the CRISPRon and CRISPRoff deep learning models, based on CNN and gradient boosting regression trees, and the related interactive webserver were developed by Xiang et\u00a0al. . For theFeature engineering has proven to be essential in many research fields involving machine learning predictions. We think that this aspect has not yet been fully explored in CRISPR/Cas9 and that future investigations should contribute to higher classification performance of both traditional machine learning and deep learning models applied to predict on- and off-target activities.Training deep learning models with real-world CRISPR-Cas9 data is challenging because of a large natural imbalance existing between positive and negative samples. This leads to an imbalanced data classification problem with a much larger majority class and a much smaller minority class. Thus, the predictive models observe and learn more from samples of the majority class and, as a consequence, can fail to identify accurately samples from the minority class. This can negatively impact their overall predictive performance. In CRISPR/Cas9, the problem of data imbalance mainly applies to the task of off-target prediction.et\u00a0al. [in vitro and cell-based experiments) to increase the size of the positive class samples (i.e. off-targets), and thus improve the model\u2019s competency. Precisely, Zhang et\u00a0al. proposed to increase synthetically the number of positive samples by rotating the sgRNA\u2013DNA encoded images by 90, 180, and 270 degrees, respectively. Hence, the number of positive samples in the data set was quadrupled. The data were then passed to a four-layer CNN to perform the off-target prediction. The main finding of this work was that data augmentation was a critical step for improving the predictive performance of DL-CRISPR. Class rebalancing and data augmentation are still fast evolving domains. Alleviating data imbalance should boost the predictive performance of off-target prediction models as class imbalance remains one of the intrinsic properties of CRISPR-Cas9 data.In this context, we need to mention the work of Zhang et\u00a0al.  and theiRecent progress in the development of deep learning models using attention mechanism  has triget\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. introduced a third model, called seqCrispr, which harbors an LSTM component and a CNN component in parallel to provide accurate on-target efficiency predictions. Finally, Zhang et\u00a0al. [Recently, Zhang et\u00a0al.  have imp [et\u00a0al.  designed [et\u00a0al.  analyzedg et\u00a0al.  proposedWe are confident that future promising methods involving attention mechanism and deep learning should soon emerge in the field.Table AI methods have emerged as state-of-the-art approach in the field of genome editing. We reviewed recent applications of traditional machine learning and deep learning algorithms for prediction of on- and off-target activity in CRISPR/Cas9. We believe that our review paper can serve as a guideline for CRISPR/Cas9 practitioners willing to apply AI methods in genome editing.The main conclusions of our study are as follows:First, we highlighted the importance of sequence encoding for sgRNA\u2013DNA on- and off-target prediction. Initial models implied straightforward one-hot sequence encoding of the sgRNA\u2013DNA sequence pairs . SubsequSecond, some recent works have demonstrated that the ensemble ML methods have generally outperformed non-ensemble ML methods , 95. ForThird, recent studies have highlighted the importance of feature selection and feature engineering for accurate activity prediction in CRISPR/Cas9. New methodologies have been introduced to incorporate sequence information, such as gene melting temperature, molecular weight, or microhomology features, into the model's input . Some woFourth, we observed that most of publicly available data sets have incomparable numbers of positive and negative samples, thus leading to a class imbalance problem that has a negative impact on the performance of both traditional ML and DL models, especially when predicting off-targets. Recent papers propose to use data augmentation to increase the number of samples of the minority class  or to apFifth, for sufficiently large data sets, DNNs have demonstrated their superior predictive performance in comparison with both scoring methods and conventional ML algorithms such as SVM, random forest, and XGBoost , 73\u201375. Sixth, attention-based DL models have been extensively used in some recent works in the field , 138. ThResearch gaps and future research directions related to the application of AI methods in genome editing include:et\u00a0al. and Charlier et\u00a0al. [Powerful deep learning models have a huge number of parameters that need to be tuned in the training process. Thus, to be effective, these models require large amounts of input data. Transfer learning started to be used in the field to leverage the problem of deep learning training on data sets with insufficient amount of training samples. For instance, Lin r et\u00a0al. , 75 haveDNNs usually stack several layers of different types, each of which often containing dozens of neurons. Thus, designing efficient deep learning network architectures and finding optimal sets of hyperparameters remain extremely important and challenging tasks , 161. VaExplainability and interpretability of DNNs have been a topic of interest for the past few years , 162. ReAs we pointed out, some recent works in the field have focused on the use of features engineering to boost the predictive performance of machine learning models , 84. Infet\u00a0al. [Uncertainty quantification is a key technique to improve the trustworthiness of predictions made by a trained network. This technique has become popular for evaluating uncertainty in various research fields . There aet\u00a0al.  have recActive learning is a semi-supervised technique in which a learning algorithm is used to label unlabeled data. An active learning algorithm uses an initial subset of labeled data for training. The algorithm then predicts the most appropriate labels for unlabeled data. This technique is of particular interest in biology because obtaining labeled data is often costly and time-consuming . Active We reviewed current knowledge regarding the use of supervised machine learning methods for on- and off-target prediction in CRISPR/Cas9.We highlighted the importance of the data pre-processing step including encoding of the sgRNA\u2013DNA sequence pairs without any information loss, embedding supplementary data with different channels reflecting insertions, deletions and mismatches, and considering some additional sequence information such as gene melting temperature, molecular weight, or microhomology features.Most of CRISPR/Cas9 data sets have incomparable numbers of positive and negative samples, thus leading to a class imbalance situation that should be mitigated using either data augmentation or data re-sampling techniques, especially in the case of off-target prediction.When training data sets were large enough, DNNs have demonstrated their superior predictive performance in comparison with scoring methods and traditional machine learning algorithms. However, for benchmark purpose, the results obtained using state-of-the-art deep learning methods should be compared with those provided by some effective conventional machine learning algorithms, such as SVM, random forest, and XGBoost.We emphasized the importance of feature selection for accurate on- and off-target prediction in CRISPR/Cas9. Thus, the automated feature learning and automated feature engineering techniques should be used to boost the performance of deep learning models."}
+{"text": "Feedback oscillators, consisting of an amplifier whose output is partially fed back to its input, provide stable references for standardization and synchronization. Notably, the laser is such an oscillator whose performance can be limited by quantum fluctuations. The resulting frequency instability, quantified by the Schawlow-Townes formula, sets a limit to laser linewidth. Here, we show that the Schawlow-Townes formula applies universally to feedback oscillators beyond lasers. This is because it arises from quantum noise added by the amplifier and out-coupler in the feedback loop. Tracing the precise origin of quantum noise in an oscillator informs techniques to systematically evade it: we show how squeezing and entanglement can enable sub-Schawlow-Townes linewidth feedback oscillators. Our analysis clarifies the quantum limits to the stability of feedback oscillators in general, derives a standard quantum limit (SQL) for all such devices, and quantifies the efficacy of quantum strategies in realizing sub-SQL oscillators. Feedback oscillators are a fundamental tool in science and engineering. Here, Loughlin and Sudhir provide a generalized Schawlow-Townes-like formula for quantum-limited feedback oscillators, thus giving a general model to study the fundamental output noise of these devices and techniques to reduce their noise further. Frequency fluctuations of oscillators limit measurements of distance\u2014using a radar6, lidar7, or for gravitational-wave detection10\u2014and of time using optical atomic clocks11. The performance of information processors\u2014classical14 or quantum16\u2014and communication systems19 are also limited by the stability of their clocks. So is our sensitivity to new physics\u2014at low energy20 or using high-energy colliders21; and of our planet23, or the universe25. Even modern economic practice is beholden to the ticks of a clock26.Feedback oscillators28. Its frequency noise is given by the (modified) Schawlow-Townes (ST) formula33,0. Here, P0\u2009=\u2009\u210f\u03a90\u2223\u03b1\u22232 is the oscillator\u2019s mean output power and \u03b1 is the amplitude of the mean photon flux. In a laser, the feedback element is a cavity, whose round-trip time is \u03c4, average thermal occupation is \u03b7, equivalent to the cavity linewidth 34, nth\u2009=\u20090 .A paradigmatic example of a feedback oscillator whose stability is well understood is the laser37 to oscillators, and establish a bridge between the classical electronic theory of feedback oscillators and the quantum electronics of a laser. Based on these insights, we then consider methods of evading the ST bound by manipulating the oscillators\u2019 quantum states. We find that squeezing, entanglement, and phase-sensitive amplification in feedback oscillators allow us to achieve stability beyond the Schawlow-Townes limit, providing a new avenue toward realizing ultra-stable oscillators.In this work, we show that the Schawlow-Townes limit applies to a much larger class of feedback oscillators: those that are constructed by positive feedback of the output of a broadband amplifier. In doing so, we precisely identify the origin of the ST limit, extend the well-known theory of quantum noise in amplifiersG embedded in a feedback loop of time delay \u03c4, whose output, because of the no-cloning theorem38, is extracted from the loop using a beam-splitter. Clearly, the mode We consider, in Fig.\u00a037 is that the classical input-output relation i,\u2009j\u2009\u2208\u2009{in,\u2009out})39.In the absence of the feedback loop, the observation of Haus-Caves41. We will now resolve these issues and show that a proper account of the saturation behavior leads to the threshold condition for oscillation: \u201cgain = loss\u201d, while a proper imposition of the commutation relation gives the correct quantum noise of the oscillator.These observations do not apply when the feedback loop is closed. First, positive feedback will lead to a large mean field at the input of the amplifier, which will saturate its output due to the intrinsic nonlinearity of the amplifier. Note that nonlinearity in the response is a fundamental requirement of any physical amplifier since its gain arises from an external source whose energy density has to be finite; it is precisely this nonlinearity that will determine the amplitude of the oscillating output field (as discussed below). Second, the commutation relations in eq.  only appi\u2009\u2208\u2009{in,\u2009out}) is the mean amplitude, and G0, such that this gain is larger than the loss via the out-coupler, parametrized by x for which The nonlinear input-output behavior of the (memoryless) amplifier can be cast as42. Small signal analysis shows that this oscillatory state is stable if the in-loop field amplitude, \u03b1ss, satisfiesThe output of the amplifier ns, eqs.  and 6),,\\documenG is the linear gain of the amplifier, the ancillary mode Around the steady state, the (Heisenberg-picture) operators representing the quantum fluctuations satisfy the set of linear equations:\u03b7\u2009<\u20091) need not coincide with those in open-loop operation (\u03b7\u2009=\u20090)43. In the closed-loop configuration, since the ancillary mode is not freely propagating, it need not satisfy the commutation relations \u03c0/\u03c4 (for some integer n) at which these spectra are singular are the poles of the transfer functions H0,\u2009HG, and are therefore the frequencies of steady-state oscillations of the closed loop. Physically, they correspond to constructive interference after subsequent traversals of the feedback loop. In a practical oscillator, the gain G[\u03a9] is typically engineered to sustain only one steady state at, say, frequency \u03a90 as in Fig.\u00a0\u03c9 from the carrier, i.e., \u03a9\u2009=\u2009\u03a90\u2009+\u2009\u03c9 where \u03c9\u03c4\u2009\u226a\u20091, the phase quadrature spectrum in eq. . Thus the frequency spectrum of the output around the carrier is \u03b7\u2009\u2248\u20091, in which case eqs.  \u2264 \u2223z\u2223 for any complex number z. In the first line of eq. . Gaussian state techniques allow the resulting output spectra to be derived  amplifiers and linear out-couplers but with the injection of squeezed or entangled states into the feedback loop. Recent workAn alternative method of reducing the oscillator\u2019s output amplitude and phase spectra is to modify the feedback loop itself by replacing the phase-insensitive amplifier with a phase-sensitive amplifier as depicted in Fig.\u00a0G\u2009=\u20091 in eq. (In the extreme case where the in-loop amplifier is purely phase-sensitive (1 in eq. ), i.e., 52 and pump noise in the squeezer will contaminate its output, precluding the zero phase noise around the carrier predicted by eq.  We define the cross-correlation between the two general (not necessarily hermitian and not necessarily commuting) operators ion [eq. ] of the For weak-stationary operators, i.e., those that pair-wise satisfy The spectrum of a weak-stationary (but not necessarily hermitian) operator is positive; i.e.,pi \u2265 0,\u2009\u2211ipi\u2009=\u20091, and \u2329\u03c8i\u2223\u03c8j\u232a\u2009=\u2009\u03b4ij, the expectation value may be written as,Since ary, eq. , togetheary, eq. , impliesc,(Uncertainty principle for spectra) For weak-stationary hermitian operators \u03b1j, it requires that the eigenvalues of the matrix with elements Let used eq. . SplittiConsider now the case where Equation  then reqives eq. . \u25a1\u03b1i} are classical field amplitudes and \u03b10(t) sources the classical field that circulates in the loop. In reality, the input represented by \u03b10 is pure noise, in the ideal case, just vacuum noise.Here, we analyze the classical steady-state behavior of the saturating feedback oscillator shown in Fig.\u00a0\u03b10 represents infinitesimally small fluctuations. In order to understand how the loop starts, consider that \u03b10(0) is a small random value and zero for t\u2009>\u20090. Let this produce a small amplitude \u03b10(0) produces a steady state amplitude, it must satisfy\u03b1ss of eq.  is satisfied. We haveSimilarly, we can show that the operating point where all amplitudes are zero is unstable. That is, any initial fluctuation will drive the loop to its steady state eq. . Now, le\u03b1ss and a linearized gain ofIn sum, the loop will reach a steady state with a large circulating classical field with amplitude \u03b1ss circulating in the loop. This oscillating field is the fundamental feature of a positive feedback oscillator. Second, at this equilibrium point, the gain medium is linear for small perturbations around the large field, with a gain given by the requirement for the system to conserve round-trip power in steady-state, i.e., We emphasize two key points of this classical analysis of saturating feedback oscillators. First, any small initial fluctuation will be amplified, eventually reaching a stable equilibrium with a large-amplitude output field G is coupled back into its input after attenuation by a factor \u03c4. The remaining fraction of the signal is coupled out of the loop to derive the out-of-loop field aout.Consider the positive feedback amplifier configuration shown in Fig.\u00a037.The equations of motion for the system are obtained by going around the loop in Fig.\u00a0H0,G are the corresponding linear response transfer functions. In steady state, \u03b7 and the delay \u03c4; soEquation  can be sIn this section, we show that a quantum-limited phase-sensitive amplifier can always be decomposed into an ideal phase-insensitive amplifier followed by an ideal single-mode squeezer.Consider a phase-sensitive amplifier that amplifies the input see Fig.\u00a0A. We can prove this by explicit computation. In the case of the phase-sensitive amplifier, the output mode The primary benefit of this decomposition is that it clarifies the extent to which a phase-sensitive amplifier must add noise: only the phase-insensitive component in its decomposition adds noise, while the squeezer is noiseless.Supplementary InformationPeer Review File"}
+{"text": "Nature Communications 10.1038/s41467-022-32838-4, published online 19 September 2022Correction to: The original version of this article contained an error in Fig. 2E, in which the labels on the x-axis of \u201cLeukocyte proliferation regulation\u201d and \u201cT cell proliferation regulation\u201d were inadvertently swapped. This has been corrected in both the PDF and HTML versions of the article.The original version of the\u00a0Updated Supplementary Information"}
+{"text": "Nature Communications 10.1038/s41467-023-37648-w, published online 18 April 2023Correction to: The original version of this article contained an error in the spelling of the author \u2018Joseph N. Paulson\u2019, which was incorrectly given as \u2018Joe Paulson\u2019.y axis was labeled \u2018Cum Progression-free Survival\u2019 rather than \u2018Cum Survival\u2019.The original version of this article contained an error in Figure 1d, in which the These errors have now been corrected in both the PDF and HTML versions of the article."}
+{"text": "In this article, we propose adjusting this minimum Bayes factor with the information to approximate an exact Bayes factor, not only when p is a p-value but also when p is a pseudo-p-value. Additionally, we develop a version of the adjustment for linear models using the recent refinement of the Prior-Based BIC.Minimum Bayes factors are commonly used to transform two-sided  So p-values, and particularly the threshold of p-value. It is known that the evidence of a p-value against a point null hypothesis depends on the sample size. In [p-values in linear models and propose new monotonic minimum Bayes factors that depend on the sample size and converge to p-value increases with decreasing sample size. There are several proposals in the literature, and most do not depend on the sample size, while those that do continue to be Robust Lower Bounds; however, neither behaves like a real Bayes factor. In this article, we propose to adjust the Robust Lower Bound p-values are only pseudo-p-values [p-values. The effect of adjusting this minimum Bayes factor with the sample size is shown in a simulation in By now, it is well known by practitioners that p\u00b7log(p)  and (ii)\u03b1*=0.005 . These ssize. In , they cop-values  (p. 397)p-values using the p-value definition of [p-values in The outline of the article is as follows: In ition of  p. 397)ition of  and the ition of ; in bothition of p-values are well known to have Uniform; in [Under the null hypotheses, , 1); in  (p.\u00a0397)Definition\u00a01.\u00a0A p-value\u00a0is a statistic satisfying\u00a0xfor every sample point . Small values of give evidence that\u00a0is true, where\u00a0is some subset of the parameter space and\u00a0is its complement. A p-value is valid if, for every\u00a0and every\u00a0p-values that are Uniformly Distributed in , that is,Based on this definition, we can say that there are valid Remark\u00a01.\u00a0We consider any valid p-value complying with  a pseudoThe \u201cRobust Lower Bound\u201d  has been appropriately chosen so that large values of Note that this calibration has already been proposed in . Another=1\u2212p see .p-value under p-value.In contrast with Remark\u00a01, if we consider lly \u03b1  \u03b1 in (7)uated in  or (7), p in . Therefore, the approximate Bayes factor for this test calculated with 11) to prSince for any Bayes factor Equation\u00a0, BFG theEquation\u00a0, and BFLEquation\u00a0.Consider comparing two normal means via the testSo, for Assuming priors:The Bayes factor ist-statistic with degrees of freedom On the other hand, considering +n2; see .r data points from each of the two normal distributions, K times. For all K simulations, K replicates, we test the hypotheses p-values lie between p-values would be considered sufficient to reject p-values obtained from samples where We now present a simulation that shows how our adjustment, or calibration, to p-values coming from samples, where p-values behaved K replicates. quations ), and whquations ) is usedp-value is a pseudo-p-value (see the example 8.3.30 in [This is an example where the .3.30 in ). Let S1p be the common value of p-value isUnder Remark\u00a02.\u00a0It does not seem to be simple to estimate the appropriate value in , in FiguIt is important to note that in Bayesian tests with a point null hypothesis, it is not possible to use continuous prior densities, because these distributions (as well as posterior distributions) will grant zero probability to So,Now, if we take p-value and not a pseudo-p-value.Consider comparing two nested linear models http://academic.uprm.edu/eacuna/datos.html (accessed on 13 January 2022). We want to predict the average mileage per gallon (denoted by mpg) of a set of As an example, we analyze a data set taken from , which cp-value of the F test is Through the Bayes factors Consider the following simple linear model Yi=1i\u00b7\u03b8+mony. In , the incn grows and n is fixed and Here, we show through the posterior probabilities of the null hypothesis that the Bayes factor 1.p-value, which it should, but it is static, not a function of the sample size n. This limitation makes the bound of little use for moderate to large sample sizes, where it is arguably the correction to p-values more\u00a0needed.Lower bounds have been an important development to give practitioners alternatives to classical testing with fixed 2.p-values, and sample size has a distinct advantage over other approximations, such as BIC, in that it is a valid approximation for any sample size.The approximation develops here as a function of 3.p-value Bayes factors of hypothesis tests. In this article, we extended the validity of the approximation for \u201cpseudo-p-values,\u201d which are ubiquitous in statistical practice. We hope that this development will give tools to the practice of statistics to make the posterior probability of hypotheses closer to everyday statistical practice, on which p-values  are calculated routinely. This allows an immediate and useful comparison between raw-p-values and (approximate) posterior odds.The (approximate) Bayes factors  and 11)11) are s"}
+{"text": "In medical imaging, images are usually treated as deterministic, while their uncertainties are largely underexplored.This work aims at using deep learning to efficiently estimate posterior distributions of imaging parameters, which in turn can be used to derive the most probable parameters as well as their uncertainties.Our deep learning-based approaches are based on a variational Bayesian inference framework, which is implemented using two different deep neural networks based on conditional variational auto-encoder (CVAE), CVAE-dual-encoder and CVAE-dual-decoder. The conventional CVAE framework, i.e., CVAE-vanilla, can be regarded as a simplified case of these two neural networks. We applied these approaches to a simulation study of dynamic brain PET imaging using a reference region-based kinetic model.In the simulation study, we estimated posterior distributions of PET kinetic parameters given a measurement of time-activity curve. Our proposed CVAE-dual-encoder and CVAE-dual-decoder yield results that are in good agreement with the asymptotically unbiased posterior distributions sampled by Markov Chain Monte Carlo (MCMC). The CVAE-vanilla can also be used for estimating posterior distributions, although it has an inferior performance to both CVAE-dual-encoder and CVAE-dual-decoder.We have evaluated the performance of our deep learning approaches for estimating posterior distributions in dynamic brain PET. Our deep learning approaches yield posterior distributions, which are in good agreement with unbiased distributions estimated by MCMC. All these neural networks have different characteristics and can be chosen by the user for specific applications. The proposed methods are general and can be adapted to other problems. I.1, in which images are treated as deterministic. To assess the uncertainty, frequentist inference requires repeated measurements, which is impractical for medical imaging. Without uncertainty information, assessment of research results and clinical images can be challenging and, under certain circumstances, lead to incorrect conclusions and clinical decisions. However, we usually have prior knowledge of the image to be estimated before the measurement is made. Such prior knowledge can be combined with the measurement to obtain an estimation of the posterior distribution, which can then be used to assess the uncertainty of the image. This falls into Bayesian inference (BI)1, which is a coherent solution to the problem of uncertainty estimation. The posterior distribution is a full distribution on the parameter. It is possible to make all sorts of probabilistic statements about the parameter. For example, we can make a statement of credible interval  if a posterior distribution is known.Uncertainty quantification of medical imaging data is fundamentally important for clinical diagnosis and clinical trials. However, medical images presented in both research and clinical settings are usually non-statistical in the sense that they do not contain information about uncertainty. From the point of view of statistical inference, this belongs to the frequentist methodx in a parameter space given an observable measurement y. In the framework of BI, we define the problem as: given y and a prior, p(x), which represents our knowledge on x before the measurement, what is the posterior distribution, p(x|y)? The conventional method to tackle this problem is to use Markov Chain Monte Carlo (MCMC)2, which is known to produce an asymptotically unbiased estimation of the posterior distribution. MCMC does not require a full analytic posterior description as long as the ratios of probability density functions at pairs of locations  can be calculated3. Although this requirement is met for many medical imaging problems, MCMC has been rarely used in the past. One reason is that recomputing likelihood p(y|x) becomes too expensive for most problems without even accounting for the fact that a large number of burn-in steps are needed for MCMC. Using a dynamic positron emission tomography (PET) study performed on a GE Discovery MI-5 scanner as an example, a time series of sinogram set, y, has a dimension of 54\u00d71981\u00d7415\u00d7272 , while the corresponding time series of image volumes, x, has a dimension of 54\u00d7256\u00d7256\u00d7256 . Approximate Bayesian Computing (ABC) is another well-known method for estimating posterior distributions for a given measurement4. In ABC, model parameters sampled from the prior are used to generate artificial measurement datasets. If the resulting datasets are very close to the given measurement according to a predefined discrepancy function, the corresponding parameters are then accepted as the part of the posterior. Unlike MCMC, ABC is an approximation. Also, it does not offer much advantage over MCMC in terms of computational time. Another reason is that the prior is subjective in BI. A poor prior certainly leads to a poor posterior estimation.Most medical imaging problems can be generalized as the estimation of As a large amount of training data becomes available in medical imaging, BI combined with deep learning (DL) has the potential to play an important role in posterior estimation in the future. We first define a very general problem, which is not limited to medical imaging, as:D samples, y, and a testing observable measurement, y*, what is the posterior distribution, p(x|y*)?Given a training dataset of p(x), is no longer subjective but implicitly defined by the training dataset itself. To solve the above problem using MCMC is challenging because only training data rather than the underlying analytic forward and noise models are available. This makes it difficult to compute the ratios of probability density functions at pairs of locations as required by MCMC. For such a problem, it is also difficult to use ABC from the training data without knowing the underlying model. We intend to sample the posterior distribution, p(x|y*), using a conditional variational auto-encoder (CVAE), in which the generation process is conditioned on y*. In addition, we introduce a latent multivariate random variable z to account for the information loss in the forward process from x to y5. The CVAE is trained with the paired dataset p(x|y*), which represents a complete picture of the parameter space, using a predefined distribution of the latent variable, p(z). Based on this strategy, we have derived different DL-based approaches for estimating posterior distributions using the CVAE framework 9. However, INNs require special coupling layers to achieve the normalizing flow, which can be insufficiently expressive and computationally expensive10. In addition, a CVAE can be used as as baseline for INN5. This approach, which is denoted by CVAE-vanilla is an oversimplication since y and z are assumed to be independent, and therefore cannot guarantee accurate estimation of the posterior distribution.In the past, there have been various types of DL-based approaches proposed for BI. One is to directly train a deterministic inverse mapping from p(x|y*), a ground truth is necessary, but it is not available if the only available data is the training dataset, y*. We, therefore, used a simple simulation study for dynamic brain PET imaging, in which we can not only generate a training dataset for our DL-based approaches, but also perform MCMC to produce asymptotically unbiased posterior distributions to be used as the gold standard  in a target region based on a simplified reference tissue model (SRTM12) and Gaussian noise model. For a given testing TAC, the posterior distributions of kinetic parameters using our generative DL-based approaches were compared to the unbiased distributions sampled by MCMC.In order to validate our DL-based approaches for estimating II.In this section, we first propose our DL-based methods for posterior estimation. We then describe how we performed the simulation for dynamic brain PET using SRTM and Gaussian noise model. Afterward, we explain in detail how we performed MCMC and our DL-based approaches to obtain the posterior distributions of the kinetic parameters for a given dynamic PET measurement, i.e., a TAC. Finally, we describe how we evaluated the performance of our DL-based approaches using the unbiased posterior distributions sampled by MCMC as the gold standards.II.A.14.In this work, we propose to use a CVAE framework for efficiently sampling the posterior distributions given an observed measurement. We propose different deep neural networks (DNN) for estimating posterior distributions based on the evidence lower bounds (ELBOs)p(x|y) for a given observable measurement y, we define a random multidimensional latent variable z to capture the information loss in the forward process from x to y. We intend to train a neural network (known as decoder), \u03b8, which performs z is sampled from distribution p, i.e., z ~ p. To make such training possible, we introduce another neural network (known as encoder), \u03d5, which maps x and y to z. The two neural networks, i.e., \u03b8 and \u03d5, must be decoupleable after the training, which can be achieved by minimizing the following Kullback-Leibler (KL) divergence:\u03b5A and \u03b5B are two equivalent ELBOs, since logp(y) is independent to the value of z. Specifically, we have:p, p(z|y), and p(y|z) with p\u03b8, p\u03d5\u2032(z|y), and p\u03b8\u2032(y|z), respectively . In addition, if we assume that z is independent of y, i.e., p(z|y) = p(z), we have: \u03b5B \u2248 \u03b5C + logp(y).To estimate the posterior distribution \u03b5A, \u03b5B, and \u03b5C, respectively.We therefore propose three different DNNs: CVAE-dual-encoder, CVAE-dual-decoder, and CVAE-vanilla See , which aII.A.1.\u03b5A, which consists of an encoder \u03d5 , a decoder KL||p\u03d5\u2032(z|y)) in \u03b5A, we use the reparameterization trick13 in both the encoder neural networks, i.e., \u03d5 and \u03d5\u2032, with two K-dimensional multivariable normal distributions defined by \ud835\udca9) and \ud835\udca9) representing p\u03d5 and p\u03d5\u2032(z|y), respectively. As a result, we introduce another loss function given a pair of training sample:K is the dimension of the latent code z or \u03bck and k-th node. In practice, the output layer of each of the two encoders has two branches (each branch consists of K nodes), which represent mean and variance, respectively. We then sample z and z = \u03bc + \u03c3 \u2299 \u03f5 and \u03f5 is a standard multivariable normal distribution, i.e., \u03f5 ~ . We then we define the overall loss function as:\u03b2A is a hyperparameter to weight \u2112A2, defined in Maximizing y*, we use \u03d5\u2032 to predict \u03c3\u2032 and \u03bc\u2032, followed by sampling y* to the decoder \u03b8 to generate the corresponding For inference, given the observation II.A.2.\u03b5B, which consists of an encoder \u03d5 , a decoder B1, which is used to maximize the first term in \u03b5B, is the same as \u2112A1. Similar to CVAE-dual-encoder, we use the same reparameterization trick to handle the KL term in \u2112B1 with the only difference being the use of  to represent p(z). The second loss function becomes\u03b5B:\u03b2B and \u03bb are the hyperparameters to weight \u2112B2 and \u2112B3, respectively. Notably, \u2112B2 is different from \u2112A2.Obviously, the first loss function \u2112z ~ , and concatenate z and y to the decoder to generate the corresponding For inference, we use II.A.3.\u03b5C, which consists of an encoder \u03d5  and a decoder C1, which is the same as both \u2112A1 and \u2112B1, and \u2112C2, which is the same as \u2112B2. An overall loss function is defined as:\u03b2C is the hyperparameter to weight \u2112C2. For inference, we use z ~  and concatenate z and y to the decoder to generate the corresponding II.B.x, when a measurement of TAC, y, is given in a target region. In this study, we used SRTM for tracer kinetics in a brain region, which can be formulated as:CT (t) and CR(t) are the activity concentrations in the target region and a pre-defined reference region respectively at time t, DV R is the distribution volume ratio between the target and reference region, k2 is the rate constant from free to plasma compartment, and R1 is the ratio of rate constants for transform from plasma to free compartment. The analytic solution of TAC in the target region is:x {DVR, k2, R1}, to tn = tn \u2013 tn\u22121, and \u03c3 is the standard deviation. We assumed that \u03c3 follows a gamma distribution, i.e., \u03c3 ~ 10\u22124Gamma. For this simulation study, we chose the temporal lobe and cerebellum grey as the target and reference region, respectively. We also set the number of time frames to N = 54. We used the following sequence of time frame durations: 6 \u00d7 10s, 8 \u00d7 15s, 6 \u00d7 30s, 8 \u00d7 60s, 8 \u00d7 120s, and 18 \u00d7 300s. In the simulation, kinetic parameters were randomly sampled from predefined priors , based on our knowledge before the measurement, the posterior distribution is determined as p(x|y) \u221d p(y|x)p(x). In this work, we chose to use the widely used random walk Metropolis-Hastings MCMC (MH-MCMC) to sample the posterior distributions of kinetic parameters. A symmetric proposal distribution that represents a Markov Chain transition from step l \u2212 1 to step l, J(x(l)|xl\u22121) = N(xl)(|xl\u22121), was used. The diagonal covariance matrix \u2211 was used to control the acceptance rate of MCMC.The conventional approach for sampling posterior distribution is to follow a rejection sampling scheme with MCMC15. To provide a more reliable assessment of convergence, we calculated the mean of the first 10% and last 50% steps counted after burn-in steps to check if the difference between these two means is approaching zero16.In the implementation of the MCMC, an important step is the judgment of convergence, which usually indicates whether the algorithm is drawing the sample from the true distribution and achieves balance. Trace plots of the  log-likelihood are often used as visual and subjective tool to give a hintII.D.p(x) as DV R ~ N, k2 ~ N, and R1 ~ N, based on a previous [18F]MK-6240 study across 35 subjects11. To demonstrate the effectiveness on multiple simulated kinetic parameter sets, we further increased the mean, variance, and both mean and variance of the prior by 20%, and denoted as setting 2, 3, and 4, respectively. For the purpose of quantitative evaluation of our approaches, we kept sampling x = {DV R, k2, R1} from the prior distributions until we collected a total of 200 testing x\u2019s that satisfy i = 1, 2, 3, where \u03b1 = 0.26 was chosen based on the variance of measured DV R across all subjects in the previous study11. The corresponding testing measurement of TAC, y, for each testing x was then generated using the SRTM and the Gaussian noise model (See II.B).In this study, we first (setting 1) defined the prior For each testing measurement, we first used MCMC to sample its corresponding asymptotically unbiased posterior distributions using the defined prior distributions as well as the forward and noise models as described in \u03b2 = 1 and \u03bb = 1 13. We used the same network structure in encoder \u03d5 and decoder \u03b8. Specifically, in the encoder, we used four fully connected layers, which contain 128, 100, 50, and 20 nodes. The output layer of the encoder has ten nodes for mean values and ten nodes for variance values, which are in turn used to define the distribution of z, whose dimension is K = 10. In the decoder, we also used four fully connected layers, which contain 128, 100, 50, and 3 nodes. The output layer of the decoder is a three-dimensional vector, i.e., . In both the encoder and decoder, ReLU is used as an activation function. For the CVAE-dual-encoder, we have an additional encoder \u03d5\u2032, which has the same structure as encoder \u03d5, though parameters in these two encoders are not shared. For the CVAE-dual-decoder, we had an additional decoder \u03b8\u2032, which has four fully connected layers containing 16, 16, 32, and 54 nodes.For all our DL-based approaches, we set x using the defined priors. Each sampled x was then used to generate its corresponding y using the SRTM and the Gaussian noise model. The resulting training data pairs were used to train the neural network in each one of our DL-based approaches. We used the same learning rate, i.e., 10\u22124, and stochastic gradient descent (SGD) optimizer with a momentum of 0.9 for all the neural networks. For each approach, the trained neural network was used to generate 45,000 samples to obtain posterior distributions for each testing y afterward.To construct the training set for our DL-based approaches, we generated 10,000 samples of M = 200 testing samples for each kinetic parameter using:m-th sample using a Gaussian function. We also computed the average KL divergence, m-th observable testing sample.To evaluate the performance of each DL-based approach using MCMC as the reference, we first computed the average relative difference of normalized mean and standard deviation, i.e., We used the PyTorch toolbox for the implementation of our DL-based approaches. We performed all the computation on a server with an NVIDIA V100 GPU (32GB graphics RAM version) and an Intel Xeon 8-core CPU alongside 24GB of RAM.III.DV R, k2, and R1 obtained from MCMC and DL-based methods for a single noisy TAC measurement y* generated using DV R = 1.0, k2 = 0.0006 min\u22121, and R1 = 0.74. All DL-based approaches agree reasonably well with asymptotically unbiased MCMC, while both CVAE-dual-encoder and CVAE-dual-decoder yield better agreement than the CVAE-vanilla.\u03b2A, \u03b2B and \u03bb in CVAE-dual-encoder and CVAE-dual-decoder. We note that all of the standard deviations for \u03b2A, \u03b2B and \u03bb) for the same range of . Therefore, we simply use \u03b2A = 1, \u03b2B = 1 and \u03bb = 1 for all of our DL-based approaches.17, a python based MCMC implementation. All the neural networks in our DL-based approaches were trained with 200 epochs, which took ~2, 2, and 2.5 hours for CVAE-vanilla, CVAE-dual-decoder, and CVAE-dual-encoder, respectively. It took less than 15 seconds for each trained CVAE neural network to infer posterior distributions for all three parameters  for a given y*. For estimating posterior distributions for a problem where MCMC is feasible, our DL-based approaches can be, therefore, much more efficient than MCMC. In this study, we focused on a single-region dynamic brain PET, which allows us to perform both MCMC and our DL-based approaches for estimating posterior distributions. For a problem with high-dimensional data, MCMC can be computationally intractable, while a trained neural network is still feasible.It took ~10 minutes to sample 45,000 samples using PyMCIn the following subsections, we provide some detailed discussions on a few topics related to MCMC and DL-based methods for estimating posterior distributions.16. DV R values sampled by MCMC. After 15,000 burn-in steps, the sampled values become stable. For all three parameters , with 15,000 burn-in steps, the difference between the mean values from the first 10% and from the last 50% steps are less than 0.001, which indicates a good convergence16.A critical question in MCMC is to determine if the sampling has converged to a stationary distribution. Though several convergence criteria have been proposed in the past, in practice, the convergence is often determined empirically, e.g., using Geweke\u2019s test based on the trace of temporal seriesDV R value used to generate the measurement, y*, is low based on the prior distribution of DV R used to generate the training data. DV R*, which is the DV R value used to generate y* measurements. We can see that DV R* if DV R* < 3.35, i.e., the sum of mean  and full width at half maximum (FWHM) of N . The increase of DV R* becomes much faster if DV R* > 3.35. As a result, when we apply our DL-based methods to the problem as defined in p(x), which is implicitly defined by the training data, should cover the value of x corresponding to measurement y*.For all the DL-based methods, data shift represents a mismatch between the distributions of the training and testing data, which can degrade the performance. For this simulation study, we expect that the performance, measured using As shown in Compared to CVAE-dual-encoder, CVAE-dual-decoder requires more training time because it has one more loss term. However, CVAE-dual-decoder is faster in inference because it has a simpler inference structure than CVAE-dual-encoder  that can be described by SRTM. In such a problem, we can not only generate the data for the training of deep neural networks but also perform MCMC. As a result, we are able to evaluate the performance of our deep learning approaches using MCMC posterior distributions as reference. For this particular problem, both MCMC and one of our deep learning approaches can be used to estimate posterior distributions for a given measurement  on a subject (a definition of prior of kinetic parameters is needed for both approaches). It is also worth noting that source and target domains should be the same for our deep-learning based approaches to avoid inference bias18. For example, unless some domain adaption techniques are used, it is not appropriate to apply a neural network trained for one tracer to obtain posterior distributions for a different tracer because priors, for example, can be very different for different tracers even the same kinetic model is used.We would like to point out that our goal is to use deep learning to solve the general problem as stated in y*, in dynamic brain PET. We can, for example, extend our work so that y represents dynamic sinogram data rather than a TAC. As stated in In this work, we estimated the posterior distributions of kinetic parameters given a measurement of TAC, i.e., IV.We have proposed DL-based approaches for estimating posterior distributions. Our approaches, which are based on a deep variational inference framework, are implemented using two different deep neural networks, CVAE-dual-encoder and CVAE-dual-decoder. The conventional CVAE framework, i.e., CVAE-vanilla, can be regarded as a simplified case of these two neural networks. All these neural networks have different characteristics and can be chosen by the user for specific applications. We have applied these approaches to a simulation study of dynamic brain PET and evaluated their performance using asymptotically unbiased MCMC as the reference. Both CVAE-dual-encoder and CVAE-dual-decoder yield good agreement with MCMC for estimating posterior distributions of kinetic parameters given a measurement of TAC. For our simulation study, we have also found that CVAE-vanilla can also be used for estimating posterior distributions, although it has an inferior performance to both CVAE-dual-encoder and CVAE-dual-decoder."}
+{"text": "Depending on the particular order, the core matrix has additional properties. Our results are graph-theoretic/algebraic in nature. As a first application, we further clarify the binomial structure of (weakly reversible) mass-action systems, arising from chemical reaction networks. Second, we extend a classical result by Horn and Jackson on the asymptotic stability of special steady states . Here, the new decomposition of the graph Laplacian allows us to consider regions in the positive orthant with given monomial evaluation orders . As it turns out, all dynamical systems are asymptotically stable that can be embedded in certain binomial differential inclusions. In particular, this holds for complex-balanced mass-action systems, and hence, we also obtain a polyhedral-geometry proof of the classical result.We provide a new decomposition of the Laplacian matrix (for labeled directed graphs with strongly connected components), involving an invertible  It can be seen as a discrete version of the Laplace operator defined on graphs. On the one hand, the Laplacian matrix of an ng\u00a0Mohar . On the V of a simple digraph E represent transitions. Moreover, edge labels k represent transition rate constants. The dynamical system for a state variable A for the graph Laplacian and indicate its dependence on the edge labels k by a subscript.) The linear system can be called \u201cLaplacian dynamics\u201d, it is equivalent to the stochastic master equation, and it is studied in applications ranging from biochemistry to systems biology\u00a0, and edge labels k. In particular, every edge Y collects the complexes y(i) for Y (by stoichiometry) as well as by the Laplacian matrix\u00a0Now, we can introduce a mass-action system as a simple digraph entclass1pt{minimacomplex-balanced equilibrium (CBE), also known as vertex-balanced steady state. Indeed, at a CBE, the sum of all \u201cflows\u201d from vertex i/complex y(i) equals the sum of all to the latter. As shown by Horn . Moreover, the polynomial dynamical system is a sum of binomials. (Just note that every reversible reaction x). We show that this also holds for weakly reversible networks. To this end, we provide a new decomposition of the graph Laplacian, involving an invertible core matrix, based on an order on the vertices. Further, we extend the classical result by Horn and Jackson on the asymptotic stability of complex-balanced equilibria. In addition to a Lyapunov function , we consider regions in the positive orthant with given monomial evaluation orders . As it turns out, all dynamical systems are asymptotically stable that can be embedded in certain binomial differential inclusions. In particular, this holds for complex-balanced mass-action systems, and hence, we also obtain a polyhedral-geometry proof of the classical result.For symmetric digraphs (\u201creversible\u201d networks), core matrix, based on an order on the vertices. Depending on the particular order, the core matrix has additional properties.In Sect.\u00a0monomial evaluation orders and corresponding geometric objects . In Sect.\u00a0binomial differential inclusions and show that all equilibria of the latter are asymptotically stable, and in Sect.\u00a0In Sect.\u00a0In \u201cAppendix\u00a0A\u201d, we provide explicit formulas for the vector of tree constants and the Laplacian matrix, using cycle decomposition. In \u201cAppendix\u00a0B\u201d, we state auxiliary results used in the new decomposition of the graph Laplacian. In \u201cAppendix\u00a0C\u201d, we give another proof of the asymptotic stability of complex-balanced equilibria (and the non-existence of other steady states) without using differential inclusions.Notation We denote the positive real numbers by I, we write y(j) is the column of Y with index For vectors In the following, we assume that the components of a digraph are strongly connected. For the simplicity of the presentation, we first consider one strongly connected component separately.k is the vector of transition rate constants in the continuous-time, linear process We consider a strongly connected, simple, directed graph G is connected, G is strongly connected,tree constants) can be given explicitly in terms of k,G rooted at vertex Since f of Eq.\u00a0,\u00a0Lemma\u00a01Clearly, the matrixk. For a derivation of this formula and a discussion of the Birkhoff/von Neumann Theorem\u00a0 or of the form star graph with root For an auxiliary digraph Let V  In the labeled digraph chain graphs. For example, for E), we findE), we findLet Explicitly, let V, That is,  plus the common entry of row i and column j. That is,A, it has positive diagonal entries and nonpositive off-diagonal entries and is (row and column) diagonally dominant.  Let mentclass2pt{minimExample (continued) In the labeled digraph star graphs. For example, for E), we findE), we findRemark In applications to mass-action systems in Sect.\u00a0In general, we consider a labeled, simple digraph Propositions\u00a0core matrix of the graph Laplacian, such thatLet Explicitly,We apply the graph-theoretic/algebraic results from the previous section to mass-action systems. We start with a brief summary of fundamental concepts and results.chemical reaction network  is given by a simple directed graph (reactions)complexG is \u201cembedded\u201d in G (the linkage classes) are strongly connected, then the network is called weakly reversible.A mass-action systemG,\u00a0y) where every edge rate constantA concentrations of n molecular species) is given bystoichiometric subspace is given by stoichiometric (compatibility) class.The resulting dynamical system for complex-balanced equilibrium (CBE), also known as vertex-balanced steady state.If an equilibrium Remark In the linear setting, the Laplacian matrix captures state transitions on a graph. Let x is a CBE. If x is a general equilibrium.the mass-action system is weakly reversible\u00a0 equilibrium in every stoichiometric class\u00a0 Let G be weakly reversible and Remark (result 2) In Sect.\u00a0In \u201cAppendix\u00a0C\u201d, we give another proof for the asymptotic stability of complex-balanced equilibria (and the non-existence of other steady states) without using differential inclusions.Remark (result 3) Technically, result 3 states that y Fulton , where iy Fulton , where iy Fulton . For geny Fulton , M\u00fcller y Fulton , M\u00fcller y Fulton , Craciuny Fulton  and Gopay Fulton .G are strongly connected), our main graph-theoretic/algebraic result, Theorem\u00a0Given that the network is weakly reversible , but truly is a binomial dynamical system.In particular, for a complex-balanced equilibrium, not just the right-hand side of  is zero,y (the matrix Y).Let total orderpartial orderG and hence, on the values of the monomials.For fixed In the following, we will consider monomials with coefficients:Let monomial evaluation order  has a different meaning in algebra). We represent the order by a chain graph We call an order on the entries of Analogously, the maximal entries of Conversely, fix an auxiliary graph If there exists a positive CBE k.  The lineality space of In the following study of complex-balanced mass-action systems , we use chain graphs stratum, cf. Siegel and Johnston  and  The positive orthant is a union of strata corresponding to monomial evaluation orders. In particular, consider the stratum given by the order G have two strongly connected components y(1), y(2), y(3) as above, and Finally, let In general, Finally, we extend a classical result by Horn and Jackson from 1972. is a strict Lyapunov function, and All proofs are based on the entropy-like Lyapunov function Previous proofs further use inequalities for the exponential function or the logarithm and cycle decomposition of the graph, cf. Horn and Jackson , Sontag In the following, we extend the stability result and provide a maximally transparent, polyhedral-geometry proof. First, we relate the dynamics in a given stratum to the corresponding polyhedral cone.C, where In Proposition\u00a0Let Let l system\u00a0 and Theo in Eqs.\u00a0 and 10)\\documentBy Theorem\u00a0binomial differential inclusion asNow, let l system\u00a0. ProposiLet l system\u00a0. Then, tmentclasspt{minimaFinally, we extend Theorem\u00a0Let mentclasspt{minimaL(x) is a strict Lyapunov function. Let recession cone of a set C.Even if a weakly reversible mass-action system cf.\u00a0Eqs.\u00a0. That isbinomial differential inclusions (BDIs), introduced in this work. Every positive equilibrium of a BDI is asymptotically stable, see Theorem\u00a0As Horn and Jackson in 1972\u00a0 with graph E) and on some positive equilibrium\u00a0Given a reaction network  have been used in a proposed proof\u00a0, In previous work, we have studied"}
+{"text": "Nature 10.1038/s41586-023-06551-1 Published online 24 August 2023Correction to: In the version of the article initially published, there was an error in the tenth paragraph, where in the sentence now reading \u201c\u2026 where CO flux dominates  and, conversely, where H2 emission prevails \u201d, the colours \u201clight yellow-white\u201d and \u201cdark orange-red\u201d were inadvertently swapped. This has been corrected in the HTML and PDF versions of the article."}
+{"text": "The factorial structure and the reliability of the Observer Report of HEXACO-MSI-E were confirmed. Convergent and divergent validity were successfully established with a version of the inventory filled out by parents. Convergent and divergent validity were also established with BFQ-C notwithstanding some only apparent anomalies. Criterion validity was established with respect to four specific groups of criteria collected in both self-report and observer form. HEXACO-MSI-E traits were more predictive with respect to self-report than to observer criteria and the majority were common. Together with the positive results of this study, implications and issues for future studies are discussed.In this cross-sectional study we aimed at: 1) validating the observer (Obs) version of HEXACO Medium School Inventory Extended (MSI-E); 2) establishing convergent and divergent construct validity of the HEXACO-MSI-E; 3) establishing criterion validity of HEXACO-MSI-E. We administered the HEXACO-MSI-E, the Big Five Questionnaire-Children (BFQ-C), the Internalizing and Externalizing scales of Youth Self Report (YSR), some items of the 2019 Middle School Youth Risk Behavior Survey (YRB) and some items about adolescents\u2019 values, beliefs, behaviors, and desired features of a possible future job to 1175 adolescents (M During the past two decades, there emerged a near-consensus that human personality variation can be summarized by five broad dimensions that are collectively known as the Big Five \u20133. TheseResearch suggests that the HEXACO model has practical and theoretical advantages over the Big Five for predicting individually, organizationally, and academically relevant outcomes , 24. ForIn conclusion, this brief review of the predictive capacity of the HEXACO with respect to many criteria together with many other systematic review on the topic \u201341 showsth, 8th and 9th grade), construct validity with respect to an observer report and to BFQ-C and, finally, criterion validity with respect to school grades. Indeed, three factors, Conscientiousness, Honesty-Humility, and eXtraversion proved good predictors of school grades. Despite several merits, this preliminary version of the inventory had some weaknesses regarding the extent of content validity and the balance among reversed and not reversed items. To solve these problems, Gnisci and colleagues set up two studies ; CFI = .929, DWLSAs shown in Table A in All dimensions of Obs HEXACO-MSI-E had at least excellent levels of internal consistency, as shown by alpha indexes reported in the Skewness and kurtosis provide evidence of normality for each factor . Note, hThe multitrait\u2013multimethod matrix of self-report HEXACO-MSI-E (N = 1175), Obs HEXACO-MSI-E (N = 343) and the BFQ-C (N = 400), reporting observed  and latent traits (below) correlations is shown in As regard self-report and Obs HEXACO-MSI-E, first, correlations between the same self-report and observer traits of HEXACO-MSI-E showed a very good convergent validity: homotrait-heteromethod correlations ranged from .529 to .705. Second, correlations between different self-report and observer traits\u2013that is, heterotrait-heteromethod coefficients\u2013were, in general, low (max r = |.372|) and always lower than homotrait-heteromethod coefficients. Therefore, convergent and divergent construct validity of HEXACO-MSI-E with respect to the observer form of HEXACO-MSI was established.As regards the correlation coefficients between the HEXACO-MSI-E self-report traits and their BFQ-C counterparts, three of them were strong , one was adequate (O-Openness), one negligeable (between E and Neuroticism). Taking aside this last correlation (and the extra-trait H), 17 out of 20 correlations between different traits assessed by different methods were lower than the above-described correlations. The three higher correlations were due to A correlating strongly and negatively with Neuroticism and moderately and positively with Conscientiousness as well as C correlating moderately with Openness. In general, out of the 20 correlations between different traits assessed by different methods, in absolute value, two are negligible (.00-.09), 12 weak (.10-.39), 5 moderate (.40-.69) and one strong (.70-.89). As mentioned, E does not correlate with Neuroticism and has null or weak correlations with the other BFQ-C factors. As far as the H trait is concerned, it shows weak but consistent co-variation with Neuroticism, Agreeableness and Conscientiousness.Finally, as expected, correlations between observed and latent dimensions are very strong within each method (min .953), indicating that factor scores are representative of the estimated constructs.In this section, we will present data on criterion validity of the self-report HEXACO-MSI-E traits with respect to a particular group of criteria connected to: 1) relevant dimensions connected to internalizing and externalizing problems of adolescents (YSR and YOR); 2) risk factors in adolescence (YRB); 3) personal passions, values, beliefs and behaviors (PVB&B); 4) desired features of a possible future job (FFJ). Each group of criteria has been measured in two different forms, self-report and observer , and we have verified how the six traits predict indicators of each group considered in both versions. For each group, zero-order correlations between the criterion indices and the six HEXACO traits of adolescents were preliminarily calculated and are shown in Correlations between the same items but in self-report (YSR) and observer (YOR) form for specific and general internalizing and externalizing problems ranged between .24 and .47  as target were performed for both self-report and observer criteria : H negatively predicted all the YSR criteria  apart from one; E positively all the YSR criteria but three, delinquent behavior is the only one that correlates negatively (4); X negatively predicted all the YSR criteria (7); A negatively predicted only two YSR scores (2); C negatively all the YSR criteria (6) but one; finally, O positively predicted three YSR criteria (3).The following factors significantly predicted the following YOR criteria (N = 373): H negatively predicted three criteria ; E negatively one (1); X negatively four (4); A negatively two and one positively (3); C negatively two (2); finally, O negatively one criterion (1).Significant observer traits predictions (YOR) were few with respect to the self-report analogous (YSR); however, in 11 cases out of 14 they shared the sign.MIN = 80, NMAX = 124; refer to Table Q in Correlations between the same items of Youth Risk Behavior (YRB) in self-report and observer form ranged between .17 and .63  as target. All the models were significant  and observer N = 373) PVB&B criteria. All the models were significant  and three negatively . E predicted seven criteria, five positively  and two negatively (being engaged and playing sports). Out of the nine criteria predicted by X, seven were positive  and two negative . A predicted four criteria in all, three positively  and one negatively (listening to music). C predicted six behaviors, four positively  and two negatively (being engaged and sleeping late). Finally, O predicted five behaviors, three positively  and two negatively .The six HEXACO traits predicted 27 observed criteria. H predicted four criteria, two positively (respecting older people and using polite words) and two negatively . E predicted five criteria, three positively  and two negatively . X predicted only two behaviours positively (attending religious services and feeling good). A predicted three criteria, one positively (preferring science to art) and two negatively (writing a diary and joking). Out of the nine criteria predicted by C, seven were positive  and two negative . Finally, O predicted four criteria, three positive  and one negative .Traits predicted more self-report (38) than observed (27) PVB&B criteria. Out of the 27 observed predictions, 17 were shared with self-report ones.Correlations between the same items of the features of a possible future job of the participant (FFJ) in self-report and observer form ranged between .18 and .36  and by the parent/legal guardian . All the models were significant  than observer (8) features of a future job. Out of the eight predicted observed, six were shared with the self-report ones.In the next sections, we will briefly discuss the most important outcomes of this contribution with respect to the declared aims and delineate possible implications of the results of the research as well as its limitations and future developments.One important outcome is having provided a validation of an Observer Report of the HEXACO-MSI-E that we make public and available to interested researchers. This result can be considered as a relevant contribution especially for the fields of child and adolescent psychology, where reports from significant others are particularly important. Indeed, the factorial structure and the reliability of the Observer Report of the HEXACO-MSI-E was confirmed. Therefore, it is possible to affirm that the observer version of the HEXACO-MSI-E provides the same valid and reliable measure of the adolescent HEXACO traits as the self-report version . HoweverAnother important result of the research is having reported strong evidence of construct validity, contrasting the self-report HEXACO-MSI-E inventory, first, with the analogous Observer Report and then, with BFQ-C, meant to measure personality in children from the perspective of FFM.While construct convergent and divergent validity of the HEXACO-MSI-E with respect to its observer counterpart was excellent and straightforward, correlations between BFQ-C needs more elaboration. Indeed, all the dimensions converged with their BFQ-C homologue apart from E, and, in general, the dimensions with convergent validity also showed a divergent validity almost satisfying with some interesting \u2018anomalies\u2019. We want to discuss now these \u2018anomalies\u2019 taking into consideration some important references: the theoretical difference between the two models (the HEXACO and the FFM), the correlations found in adult literature between the two instruments, in particular, the recent meta-analysis by Thielmann et al. , on 152 As stated in the results, apart from the correlation between A and BFQ-C Neuroticism, the highest discriminant correlations were found between A and BFQ-C Conscientiousness, C and BFQ-C Openness and Neuroticism, and, finally, O and BFQ-C Conscientiousness. We are going to provide a rationale for the associations found.In the 30-item BFQ-C we have utilized in this research, Openness is better defined as Intellect because it expresses the capability of succeeding in a school setting  while most of the HEXACO-MSI-E items partaking to C refer to effectively organizing and successful doing and monitoring schoolwork and assignments. Therefore, given the emphasis on similar contents applied to school setting, it is no surprise if they share variance, as our results show, and also that they share more variance than the one shared in the adult versions of the two instruments (r = .16) . AnalogoAs far as regard the extra factor H, as stated in the results, it correlated negatively with BFQ-C Neuroticism, positively with BFQ-C Agreeableness and Conscientiousness. We should underline that the sign of the three correlations is the same found in adults while the intensity is superimposable for H and Agreeableness (.40 and .47), close for H and Conscientiousness (.37 and .24), and farther for H and Neuroticism (-.41 and -.13). Indeed, H shares variance with FFM\u2019s Conscientiousness but also with FFM\u2019s Agreeableness \u201363. PartAll in all, if we consider the correlations higher than .30 between cousin traits of HEXACO-MSI-E and BFQ-C found in the present research, nine out of 14 showed the same sign and similar intensity with respect to the ones we found in 2020 . This isThe third important outcome of this research is having established criterion validity too in the four areas investigated.As far as the YSR, the most predictive HEXACO factors of many emotional and behavioral youth problems were X, H and C. They all predicted the behavioral problems in a negative way: the more a person was honest and humble, extroverted and conscientious, the less they reported such kind of problems. Therefore, these factors, in the direction of their polarity, seem broad-spectrum protective factors in adolescence. The E dimension was found as a predictive factor as well but, predictably, mainly for internalizing problems: lower E was linked to less anxiety and somatic problems. These results partially confirm what Barbaranelli and colleagues\u2019 study  found: EAs regards the risk factors in the teenage years (self-report YRB), data showed that the stronger predictors were C, H and X. These adolescents\u2019 personality traits were related to their participation in risky behaviors in a fairly intuitive pattern. Unconscientious, dishonest, not humble, and introverted adolescents were more likely to participate in health-compromising behaviors than their conscientious, honest, humble, and extroverted peers. In other words, adolescents who were irresponsible, not planning , unfair, pretentious , shy and unsociable  were most susceptible to engage in healthy risky behaviors. These results are consistent with Weller and Tikir  findingsThe traits more predictive of self-report PVB&B in adolescence were X, H and E. Moderately less predictively resulted C, O and A. Many significant predictions show coherence between the predictive trait and the passions, values, beliefs or behaviors. For example, adolescents high in O preferred science and music and used to write art or diary; adolescents high in C, H and E adopted respectful behaviors. Of course, we also found few predictions that can be regarded as neutral, that is, neither favorable nor contrary to the semantic of the traits significantly associated .Most HEXACO traits made coherent predictions with respect to the questions asked to the adolescents participating in the research on their possible future job (self-report FFJ): for example, H predicted positively an honest job and negatively a good income, O predicted job allowing to be in contact with nature and art, X people wanted to collaborate with other people, C people wanted an organized and planned job. Some of the arisen patterns were not coherent .In their self-report form, the most predictive factors with respect to all the four categories of criteria, were H, X and C, particularly for the YSR and YRB. For the other criteria (PVB&B and FFJ) also E emerged as predictive. All in all, many of the previsions of the criteria were coherent with the trait involved.In general, values of the correlations between traits and criteria can depend on same factors that we want to highlight. For example, due to the content of some of the chosen criteria , we expected that many respondents scored to the extreme endpoints of the measurement scale and this is what happened for some items within the criteria .Correlations between self-report and observer criteria showed, for some items, a good level of covariance; however, many other items showed little covariance. Therefore, parents/legal guardians\u2019 ratings not necessarily reflect self-report ratings by their children, highlighting the need for external evaluations in adolescence. In any case, we should consider this result with caution because, for methodological reasons connected to the way we formed the samples of adolescents and parents/guardians, sample sizes for these analyses were relatively small. Future studies should confirm these results.In general, and within each of the four categories of criteria utilized, the self-report criteria significantly associated with traits in adolescents  were always more than the analogous observer criteria . What is more, almost two thirds of the significant ones with observer criteria coincide with the self-report ones (about 67%). This could be due, of course, to a similarity of methods  but also indicates that traits often predict criterion from an inside and outside perspective.The HEXACO traits provided specific predictions of the YOR criteria (observed), differently by the wide-spectrum predictions of many of the YSR criteria (self-report): indeed, X predicted mainly observerd internalizing problems whereas H, A and C predicted mainly externalizing problems, a pattern just found by Mottola et al.  when criHEXACO traits predicted few observed risk behaviors (YRB), the most predictive were C (5 predictions), X and O (both 3) while A did not predict any YRB. Also, for these results, similarities have been found in the same study . Indeed,This paper adds significantly to the one on content and dimensional validity, invariance across males and females and across the three classes of middle school, and reliability as internal consistency and 1-year stability , providiThis study, as any, has also limitations that indicate future prospects of research. For example, given that the inventory was validated only in Italy, we consider it important to adapt the inventory to different languages and replicate the study to verify the psychometric properties of the inventory in different countries and cultures. Moreover, given that we were from the beginning very concerned about the representativeness of the facets and the dimensions of the inventory, we settled on an extended version of the inventory that would guarantee that representativeness. However, this could, in some conditions, be impractical for its length. Therefore, we think it important to develop a validated short form of the HEXACO-MSI-E that might come in handy under certain testing conditions and practical constraints. Finally, as suggested by one of the reviewers of this paper, for some items in the Social Self-Esteem scale of Extraversion factor, within the observer report from, i.e., \u201cOthers enjoy spending time with her/him\u201c, \u201cNobody likes talking to her/him\u201d and \u201cPeople like her/him\u201d, it would be more appropriate to express them in this way: \"S/he believes others enjoy spending time with her/him\u201c, \u201cS/he believes nobody likes talking to her/him\u201d, and \u201cS/he believes people like her/him\u201d. This is because they aim at measuring levels of a person\u2019s perception of popularity or attractiveness and not measuring objective levels of it. Therefore, we hope that, in future studies, this inventory may be used in view of these suggestions.S1 File(DOCX)Click here for additional data file. 9 Aug 2023 <div> PONE-D-23-19901 </div>  <div> Construct and criterion validity of the HEXACO Medium School Inventory Extended (MSI-E) </div>  <div> PLOS ONEDear Dr. Gnisci,Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE\u2019s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process .As an absolute minimum, column 17 must be added. And just to avoid any mistake, could you go back to your data and check that neuroticism (BFQ-C) was correctly calculated?plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.Please submit your revised manuscript by Sep 23 2023 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at\u00a0 </div> A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.An unmarked version of your revised paper without tracked changes. 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For instructions see: We look forward to receiving your revised manuscript.Kind regards,Frantisek SudzinaAcademic EditorPLOS ONEJournal Requirements:When submitting your revision, we need you to address these additional requirements.1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at\u00a0https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and\u00a0https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf2. We note that you have stated that you will provide repository information for your data at acceptance. Should your manuscript be accepted for publication, we will hold it until you provide the relevant accession numbers or DOIs necessary to access your data. If you wish to make changes to your Data Availability statement, please describe these changes in your cover letter and we will update your Data Availability statement to reflect the information you provide.3. We note you have included a table to which you do not refer in the text of your manuscript. Please ensure that you refer to Table 7 in your text; if accepted, production will need this reference to link the reader to the Table.Additional Editor Comments:Reviewers noticed several issues that could be improved, and one column that must be added.Just to avoid any mistake, could you go back to your data and check that neuroticism (BFQ-C) was correctly calculated?Personally, I would not omit information that were already provided in the original submission.[Note: HTML markup is below. Please do not edit.]Reviewers' comments:Reviewer's Responses to Questions <font color=\"black\"> Comments to the Author1. Is the manuscript technically sound, and do the data support the conclusions? </font> The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 2. Has the statistical analysis been performed appropriately and rigorously?  </font> Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data\u2014e.g. participant privacy or use of data from a third party\u2014those must be specified. </font> The Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 4. Is the manuscript presented in an intelligible fashion and written in standard English? </font> PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 5. Review Comments to the Author </font> Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1:\u00a0Review of PONE-D-23-19901, \u201cConstruct and criterion validity of the HEXACO Medium School Inventory Extended (MSI-E)\u201dAs its title suggests, this manuscript reports on the validity of a questionnaire for assessing the HEXACO personality characteristics in middle-school students. The research is based on a fairly large sample of adolescents (average age about 12.0 years) for whom self-reports (and in most cases parent reports) were obtained; a variety of outcome variables were also assessed in self-report or (for some of the sample) parent reports.The results generally showed good psychometric properties for the instrument. For example, the expected factor structure of the instrument was largely recovered, self/parent convergent correlations were generally strong , correlations with a measure of the Big Five were largely consistent with expectations, and correlations with a variety of outcome variables .I think that this manuscript provides a great deal of useful information about this rather new instrument, which should be of much value for researchers who study personality in children of middle-school age. I believe it is suitable for publication, but I have several recommendations for revision, all of which I think should be easy to incorporate.1. It would be useful to report frequency distributions for the items of the various criterion outcomes. In many cases it seems likely that most respondents will report a zero level. If this information won\u2019t fit into the existing tables, it could be given in additional tables, perhaps as a supplement.2. Also, some mention of these frequency distributions will be warranted in cases where the distribution is highly skewed and/or has a large fraction of responses at the highest or lowest possible value. In general, this will attenuate correlations with the personality scale scores, which presumably will be roughly normally distributed.3. One difference between the HEXACO-MSI-E and the HEXACO-PI-R is that the HEXACO-MSI-E shows much higher correlations between the scales assessing the C and O dimensions. The authors discuss on page 26 the fact that O correlates with Big Five C in this study, noting the prominence of school-related content in the items of these scales. But the authors could also note the high correlation between C and O within the HEXACO-MSI-E itself, presumably for the same reason.4. The Discussion section seems to be a very detailed recapitulation of the Results; I think it could be greatly shortened.5. This is not really a recommendation for revision, but I did notice that the authors emphasize those correlations that reached the threshold of statistical significance, in some cases counting those correlations. There is nothing wrong with this, but it should be kept in mind that this threshold depends on the sample size as well as the effect size. Some statistically significant correlations are rather small, and some correlations that do not reach statistical significance in a medium-size sample might have population values that are non-trivial in size. I wanted to mention this only because the authors appeared to emphasize the statistical significance threshold; again, though, there is not necessarily any revision needed on this point.6. Points about Information in Tables:The descriptive statistics for the HEXACO-MSI-E scales (self and observer) should be reported somewhere.In correlation and regression tables, perhaps the F-statistic results could be deleted, because the F values don\u2019t tell the reader directly about the size of the effect.For all of the outcome variables for which self-reports and observer reports are available, it would be useful to report the self/observer correlations.Regarding Table 2, the correlations given are based on different samples or subsamples. It would be useful to show (either in the main text or as a supplement) a version of this table based on only those respondents for whom all of these variables were assessed.Also for Table 2, I didn\u2019t understand why the correlations between HEXACO-MSI-E scales in self-report were not reported. I might have misunderstood something, but otherwise these should be added.In Table 2, alpha reliabilities should be reported for the scale scores. Also in relation to Table 2, the column for BFQ-C Openness is missing; it would be number 17.In the title of Table 3, could specify \u201cSelf-Report HEXACO-MSI-E\u201d7. Various Minor CorrectionsThe abbreviation \u201cObs\u201d can be useful when referring to the name of the instrument, but when writing a full sentence it\u2019s better to say \u201cObserver Report\u201d. This point applies in several places throughout the manuscript; one example is on page 2, line 438.In several places the authors use the word \u201ctutor\u201d where I think they mean \u201cguardian\u201d In several places \u201cConsciousness\u201d is used where \u201cConscientiousness\u201d is intended; this could be fixed with a \u201cfind-and-replace\u201dp. 3, line 65: \u201chas showed\u201d should be \u201chas shown\u201dpp. 4-5, line 92-93: \u201cLongitudinal studies showed\u201d should be \u201cLongitudinal studies have shown\u201dp. 5: \u201cscale\u201d is sometimes used in referring to the entire instrument, but \u201cinstrument\u201d or \u201cinventory\u201d or \u201cquestionnaire\u201d would be betterp. 5, line 117: \u201cprovided\u201d should be \u201cprovide\u201d p. 6, line 122: \u201cfilled up\u201d should be \u201cfilled out\u201d (one fills up a cup or bowl but fills out a questionnaire)p. 6, line 127: \u201cBFF\u201d has not yet been declared; it could be given as \u201cBig Five\u201d insteadp. 6, line 143: \u201cinternalization and externalization problems\u201d are usually stated as \u201cinternalizing and externalizing problems\u201dp. 10, line 233: could specify \u201clow C\u201d for the secondary loading of Dependence on Cp. 14, line 289: could specify as \u201csix self-report HEXACO scales\u201dp. 14, line 294: \u201cthe unique\u201d should be \u201cthe only one\u201dp. 25, line 455: \u201chomologous\u201d should be \u201ccounterpart\u201dp. 25, line 451: \u201cTielman\u201d should be \u201cThielmann\u201dp. 27, line 506: \u201chomo- and hetero-trait\u201d should be \u201cmono- and hetero-trait\u201d p. 28, line 516: \u201cmore emotional stability\u201d would probably be better as \u201clower E\u201d or \u201cless emotionality\u201d, because E is not exactly opposite to emotional stability p. 28, line 521: \u201cin teenage age\u201d would sound better as \u201cin the teenage years\u201dp. 29, lines 548-549: should \u201cYOS\u201d and \u201cYRS\u201d be \u201cYOR\u201d and \u201cYSR\u201d, respectively?p. 29, line 560: \u201cwe have proved evidence\u201d should be \u201cwe have provided evidence\u201dp. 29, line 562: \u201creconducted\u201d should be \u201cattributed\u201d (I think)Reviewer #2:\u00a0The present research reports on psychometric properties of the observer report form of HEXACO-MSI-E as well as on further evidence for construct validity of self-report form of the inventory. The HEXACI-MSI-E was shown to have favorable psychometric properties in terms of factor structure, internal consistency reliability, and criterion-related validity. Given the importance of parents/caretakers\u2019 reports in adolescent psychology, developing and validating the observer report form of the HEXACO-MSI-E seems to make an important contribution to the literature.Below, I provide some suggestions that the authors may consider in revising the current manuscript.1. On p. 12, the relationships between the BFQ-C and HEXACO-MSI-E variables are described using the MTMM terms . As the authors mentioned in the discussion section, the FFM variables should not be considered the same as the HEXACO variables. In this sense, it may be incorrect to call some of the correlations involving the BFQ-C variables to be homotrait-heteromethod coefficientst; as such, I would remove BFQ-C variables from the MTMM matrix (Table 2). Relationships between the HEXACO-MSI-E and BFQ-C can be described in another table . This way, the authors might be able to streamline the results presentation on page 12 and the associated discussions on pages 25\u201427.2. In Table 2, I wasn\u2019t sure why the values above the diagonal for self-reports HEXACO-MSI-E variables are all blank.3. In Table 2, column 17 is missing.4. It would be helpful to mention somewhere in the text  that self-reports of the HEXACO-MSI-E were used in these analyses (as opposed to observer reports). 5. I have some suggestions for Tables 3, 4, 5, 6, and 7, which the authors may or may not accept: (1) I would omit F values and dfs from the tables for the sake of simplicity. (2) I am wondering if it is more straightforward to conduct standard multiple regression analyses instead of stepwise multiple regression analyses. (3) it might be informative to provide zero-order correlations in addition to (or instead of) beta coefficients.6. The discussions involving criterion-related validity (from p. 27) seem to be a bit repetitive to what was stated in the results section, and it might be helpful if the authors could streamline it by discussing some implications of the results.7. I have one suggestions for some items in the Social Self-Esteem scale within the observer report from; e.g., \u201cOthers enjoy spending time with her\u201c, \u201cNobody likes talking to her\u201d and \u201cPeople like her\u201d. These items are not intended to measure objective levels of the target person\u2019s popularity or attractiveness, but to measure target person\u2019s perception of it. As such, it might be more appropriate to add \u201cS/he believes\u201d or \u201cS/he thinks\u201d to those items.8. The manuscript may benefit from a more thorough proofreading. The followings are what I spotted while reading the manuscript, and they are not meant to be a thorough list of typos. &#x0f0e0;  \u201cshown\u201dLine 65, \u201cshowed\u201d\ufffdLine 66, \u201cto a lesser extent\u201d may sound better than \u201cto little extent\u201dLine 127, \u201cBFF\u201d may need to be spelled out. &#x0f0e0;  \u201cnever had access\u201d?Line 160, \u201chad never access\u201d \ufffd &#x0f0e0;  In the literature it is known as\u201d?Line 187, \u201cin literature is known as\u201d \ufffdThroughout, \u201cAs regard\u201d should be \u201cAs regards\u201d &#x0f0e0;  \u201cThielmann\u201dLine 461, \u201cTielman\u201d \ufffd &#x0f0e0;  \u201cwe have provided evidence\u201d?Line 560, \u201cwe have proved evidence\u201d \ufffd********** <font color=\"black\"> 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose \u201cno\u201d, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. </font> Reviewer #1:\u00a0NoReviewer #2:\u00a0No**********https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at\u00a0figures@plos.org. Please note that Supporting Information files do not need this step.While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool,\u00a0 20 Sep 2023Reviewer #1: Review of PONE-D-23-19901, \u201cConstruct and criterion validity of the HEXACO Medium School Inventory Extended (MSI-E)\u201dAs its title suggests, this manuscript reports on the validity of a questionnaire for assessing the HEXACO personality characteristics in middle-school students. The research is based on a fairly large sample of adolescents (average age about 12.0 years) for whom self-reports (and in most cases parent reports) were obtained; a variety of outcome variables were also assessed in self-report or (for some of the sample) parent reports.The results generally showed good psychometric properties for the instrument. For example, the expected factor structure of the instrument was largely recovered, self/parent convergent correlations were generally strong , correlations with a measure of the Big Five were largely consistent with expectations, and correlations with a variety of outcome variables .I think that this manuscript provides a great deal of useful information about this rather new instrument, which should be of much value for researchers who study personality in children of middle-school age. I believe it is suitable for publication, but I have several recommendations for revision, all of which I think should be easy to incorporate.A: We thank R1 for his/her words and for the provided suggestions that improved the paper very much. As detailed below, we have followed almost all the suggestions by R1.1. It would be useful to report frequency distributions for the items of the various criterion outcomes. In many cases it seems likely that most respondents will report a zero level. If this information won\u2019t fit into the existing tables, it could be given in additional tables, perhaps as a supplement.A: We thank R1 for this suggestion. We have reported frequency distributions for the items of the various criterion outcomes in additional tables .2. Also, some mention of these frequency distributions will be warranted in cases where the distribution is highly skewed and/or has a large fraction of responses at the highest or lowest possible value. In general, this will attenuate correlations with the personality scale scores, which presumably will be roughly normally distributed.A: We thank R1 for this good point. We have mentioned this aspect in the conclusions of our paper (lines 1120-1123).3. One difference between the HEXACO-MSI-E and the HEXACO-PI-R is that the HEXACO-MSI-E shows much higher correlations between the scales assessing the C and O dimensions. The authors discuss on page 26 the fact that O correlates with Big Five C in this study, noting the prominence of school-related content in the items of these scales. But the authors could also note the high correlation between C and O within the HEXACO-MSI-E itself, presumably for the same reason.A: As we reported in the paper, the BFQ-C Openness is better defined as Intellect because it expresses the capability of succeeding in a school setting . In the HEXACO-MSI-E, Openness to Experience is better defined as the attraction toward beauty of art and nature, inquisitiveness about various domains of knowledge and about ideas that may seem radical or unconventional, while most of the HEXACO-MSI-E items partaking to C refer to effectively organizing and successful doing and monitoring schoolwork and assignments. For this reason, we think that it is difficult to explain the high correlation between C and O within the HEXACO-MSI-E in the same way as we explained the high correlation between C and BFQ-C Openness.4. The Discussion section seems to be a very detailed recapitulation of the Results; I think it could be greatly shortened.A: We thank R1 for this suggestion. We have streamlined the Discussion, avoiding repetitions, and provided more keys to understanding results and their implications, also based on the few existing literature. 5. This is not really a recommendation for revision, but I did notice that the authors emphasize those correlations that reached the threshold of statistical significance, in some cases counting those correlations. There is nothing wrong with this, but it should be kept in mind that this threshold depends on the sample size as well as the effect size. Some statistically significant correlations are rather small, and some correlations that do not reach statistical significance in a medium-size sample might have population values that are non-trivial in size. I wanted to mention this only because the authors appeared to emphasize the statistical significance threshold; again, though, there is not necessarily any revision needed on this point.A: We thank R1 for this observation. In the revised conclusions of our paper (lines 1128-1129) we have highlighted that despite the use of a conservative procedure such as False Discovery Rate correction, the statistical significance threshold may have been affected by the sample size. 6. Points about Information in Tables:The descriptive statistics for the HEXACO-MSI-E scales (self and observer) should be reported somewhere.A: As correctly noted by R1, we did not report descriptive statistics in the first version of the paper. Now, in the Table 1, we have added descriptive statistics for the Obs HEXACO-MSI-E. The descriptive statistics for the self HEXACO-MSI-E are reported in the Table 7 of the already published work of Gnisci et al. (2023).In correlation and regression tables, perhaps the F-statistic results could be deleted, because the F values don\u2019t tell the reader directly about the size of the effect.A: We thank you for this suggestion. We have moved the F-statistic results from regression tables in the manuscript to the tables of frequency distribution in the Supplementary Materials. For all of the outcome variables for which self-reports and observer reports are available, it would be useful to report the self/observer correlations.A: This is a very important information to be provided. Unfortunately, for methodological reasons due to the way we sampled the adolescents and the parents/legal guardians (see Method), we have relatively few participants who had self-report and observer ratings. Normally, they were 124-125 but, in some cases, even 80. Therefore, we decided to provide in the text, for each of the four groups of criteria, the minimum and maximum value of the correlations (and N), providing the detailed tables of correlations in the Supplementary Materials. Regarding Table 2, the correlations given are based on different samples or subsamples. It would be useful to show (either in the main text or as a supplement) a version of this table based on only those respondents for whom all of these variables were assessed.A: We thank R1 for this suggestion. We prefer not to apply it because we have too few respondents, which would make the results unreliable. However, we have realized that we did not clearly report subsample sizes on which we computed correlations. We have added this information in a note of Table 2.Also for Table 2, I didn\u2019t understand why the correlations between HEXACO-MSI-E scales in self-report were not reported. I might have misunderstood something, but otherwise these should be added.A: In the first version of the paper, we decided to not report the correlations between HEXACO-MSI-E scales in self-report because these had already been reported and published in a previous work . However, as also suggested by the Editor and by R2, as well as by R1, in this new version of the paper, we have added these data and specified that they are already published in a previous work (see note 2 of Table 2). In Table 2, alpha reliabilities should be reported for the scale scores. A: We thank R1 for this observation. The alpha coefficients for self HEXACO-MSI-E were just published in Gnisci et al. (2023) while the ones for Obs HEXACO-MSI-E are in the Table 1 of the present paper. As far BFQ-C is concerned, in the paragraph \"Big Five Questionnaire-Children\" of Measures section, we have now added information on the factorial structure of the BFQ-C and the alphas for each of the BFQ-C factors.Also in relation to Table 2, the column for BFQ-C Openness is missing; it would be number 17.A: We thank R1 for noting this, we have added the column for BFQ-C Openness (column 17) in the Table 2 and the related correlations.In the title of Table 3, could specify \u201cSelf-Report HEXACO-MSI-E\u201dA: Done. Thanks.7. Various Minor CorrectionsThe abbreviation \u201cObs\u201d can be useful when referring to the name of the instrument, but when writing a full sentence it\u2019s better to say \u201cObserver Report\u201d. This point applies in several places throughout the manuscript; one example is on page 2, line 438.A: We thank R1 for this consideration that we have applied in all pertinent places throughout the manuscript.In several places the authors use the word \u201ctutor\u201d where I think they mean \u201cguardian\u201d A: We thank R1 for this specification, we replaced the word \u201ctutor\u201d with \u201cguardian\u201d or \u201clegal guardian\u201d, depending on the case, in all the manuscript.In several places \u201cConsciousness\u201d is used where \u201cConscientiousness\u201d is intended; this could be fixed with a \u201cfind-and-replace\u201dA: Done. Thanks. p. 3, line 65: \u201chas showed\u201d should be \u201chas shown\u201dA: Done.pp. 4-5, line 92-93: \u201cLongitudinal studies showed\u201d should be \u201cLongitudinal studies have shown\u201dA: Done.p. 5: \u201cscale\u201d is sometimes used in referring to the entire instrument, but \u201cinstrument\u201d or \u201cinventory\u201d or \u201cquestionnaire\u201d would be betterA: We thank R1 for this suggestion. In all the manuscript, we have replaced the term \u201cscale\u201d with \u201cinventory\u201d when referring to entire instrument. p. 5, line 117: \u201cprovided\u201d should be \u201cprovide\u201d A: Done. Thanks. p. 6, line 122: \u201cfilled up\u201d should be \u201cfilled out\u201d (one fills up a cup or bowl but fills out a questionnaire)A: Done. p. 6, line 127: \u201cBFF\u201d has not yet been declared; it could be given as \u201cBig Five\u201d insteadA: We have removed and replaced it with \u201cBig Five\u201d. Thanks for this observation. p. 6, line 143: \u201cinternalization and externalization problems\u201d are usually stated as \u201cinternalizing and externalizing problems\u201dA: We have replaced \u201cinternalization and externalization problems\u201d with \u201cinternalizing and externalizing problems\u201d in all the manuscript. Thanks. p. 10, line 233: could specify \u201clow C\u201d for the secondary loading of Dependence on CA: Done.p. 14, line 289: could specify as \u201csix self-report HEXACO scales\u201dA: Done.p. 14, line 294: \u201cthe unique\u201d should be \u201cthe only one\u201dA: Done.p. 25, line 455: \u201chomologous\u201d should be \u201ccounterpart\u201dA: Done. p. 25, line 451: \u201cTielman\u201d should be \u201cThielmann\u201dA: Done. p. 27, line 506: \u201chomo- and hetero-trait\u201d should be \u201cmono- and hetero-trait\u201d A: Done.p. 28, line 516: \u201cmore emotional stability\u201d would probably be better as \u201clower E\u201d or \u201cless emotionality\u201d, because E is not exactly opposite to emotional stability A: We thank R1 for this suggestion. We have replaced \u201cmore emotional stability\u201d with \u201clower E\u201d. p. 28, line 521: \u201cin teenage age\u201d would sound better as \u201cin the teenage years\u201dA: Done.p. 29, lines 548-549: should \u201cYOS\u201d and \u201cYRS\u201d be \u201cYOR\u201d and \u201cYSR\u201d, respectively?A: We thank R1 for noticing this error. We have replaced \u201cYOS\u201d and \u201cYRS\u201d with \u201cYOR\u201d and \u201cYSR\u201d respectively. p. 29, line 560: \u201cwe have proved evidence\u201d should be \u201cwe have provided evidence\u201dA: Done. Thanks.p. 29, line 562: \u201creconducted\u201d should be \u201cattributed\u201d (I think)A: We thank R1 for this suggestion. We have replaced \u201creconducted\u201d with \u201cattributed\u201d.Reviewer #2: The present research reports on psychometric properties of the observer report form of HEXACO-MSI-E as well as on further evidence for construct validity of self-report form of the inventory. The HEXACI-MSI-E was shown to have favorable psychometric properties in terms of factor structure, internal consistency reliability, and criterion-related validity. Given the importance of parents/caretakers\u2019 reports in adolescent psychology, developing and validating the observer report form of the HEXACO-MSI-E seems to make an important contribution to the literature.Below, I provide some suggestions that the authors may consider in revising the current manuscript.A: We thank R2 for his/her words and for the provided suggestions that improved the paper very much. Based on his/her positive consideration, we have emphasized the importance of having a validated observer report form, especially in child and adolescent psychology, in the definition of aims (lines 139-141) and in the discussions of our paper (lines 956-957). As detailed below, we have followed almost all the suggestions by R2.1. On p. 12, the relationships between the BFQ-C and HEXACO-MSI-E variables are described using the MTMM terms . As the authors mentioned in the discussion section, the FFM variables should not be considered the same as the HEXACO variables. In this sense, it may be incorrect to call some of the correlations involving the BFQ-C variables to be homotrait-heteromethod coefficientst; as such, I would remove BFQ-C variables from the MTMM matrix (Table 2). Relationships between the HEXACO-MSI-E and BFQ-C can be described in another table . This way, the authors might be able to streamline the results presentation on page 12 and the associated discussions on pages 25\u201427.A: We thank R2 for this point. At the beginning of this study, we were not yet aware of the systematic differences between the BFQ-C and the HEXACO-MSI-E, indeed they emerged later just in the present study. Therefore, we still consider it appropriate to talk about convergent and divergent validity with respect to the BFQ-C but, when describing these results, we abandoned the terminology associated with the MTMM matrix, as R2 suggests. In particular, we specified this aspect in the research questions  and \"heterotrait-heteromethod\" with the periphrasis \"between different traits assessed by different methods\" (Lines 354 and 357). Having adopted these solutions, we think Table 2 can remain in the manuscript as it is because it is very informative.2. In Table 2, I wasn\u2019t sure why the values above the diagonal for self-reports HEXACO-MSI-E variables are all blank.A: It is because these data are already reported and published in a previous work. Despite this, in the revised version of paper, following the Editor and R1\u2019s suggestions, we have decided to report the results on correlations of observed score within the self-reports HEXACO-MSI-E specifying in the note 2 of Table 2 that those data have already been published in a previous work and also indicating the reference of the latter.3. In Table 2, column 17 is missing.A: We thank R2 for rising up this point. Also following the Editor and R1\u2019s suggestions, we have added, in the Table 2, the column 17 for BFQ-C Openness.4. It would be helpful to mention somewhere in the text  that self-reports of the HEXACO-MSI-E were used in these analyses (as opposed to observer reports). A: We thank R2 for noticing this missing information. First of all, we confirm that R2 is right; in these analyses, we used the self-reports of the HEXACO-MSI-E. Therefore, following his/her suggestion, we have better specified in different places of the manuscript and also in the captions of Tables 3, 4, 5, 6, 7, and 8 that we used the self-reports of the HEXACO-MSI-E. Specifically, in the text, we specified this aspect in the following paragraphs:- \"Data analysis\" ;- \"Criterion Validity with respect to Self-Report and Observer Criteria\" ;- \u201cCriterion Validity with respect to Dimensions Connected to Internalizing and Externalizing Problems of Adolescents in Self-report and Observer Form\u201d;- \"Criterion Validity with respect to Features of a Future Job in Self-report and Observer form\" .5. I have some suggestions for Tables 3, 4, 5, 6, and 7, which the authors may or may not accept: (1) I would omit F values and dfs from the tables for the sake of simplicity. (2) I am wondering if it is more straightforward to conduct standard multiple regression analyses instead of stepwise multiple regression analyses. (3) it might be informative to provide zero-order correlations in addition to (or instead of) beta coefficients.A: We thank R2 for all the suggestions. We answer below for each point.1) Following R1\u2019s suggestion, we have removed F values and dfs from regression tables and we have reported them in frequency distribution tables of Supplementary Materials (Tables F to O).2) Results are not much different. We ran a standard regression (with beta not corrected for multiple testing) on each of the 92 criteria, as R2 suggests, and out of 166 significant correlations that emerged with stepwise in our study, 145 were confirmed and 11 new emerged. Given these similar patterns, we confirmed the stepwise given that it makes possible comparisons with other studies in literature which used also stepwise method.3) For the sake of simplicity, we have reported the zero-order correlations in Supplementary Materials .6. The discussions involving criterion-related validity (from p. 27) seem to be a bit repetitive to what was stated in the results section, and it might be helpful if the authors could streamline it by discussing some implications of the results.A: We thank R2 for this suggestion. We have streamlined the discussions involving criterion-related validity and, in general, the whole discussions section, avoiding repetitions. We added more interpretations of the results based on the small existing literature and some theoretical and practical implications of the results.7. I have one suggestions for some items in the Social Self-Esteem scale within the observer report from; e.g., \u201cOthers enjoy spending time with her\u201c, \u201cNobody likes talking to her\u201d and \u201cPeople like her\u201d. These items are not intended to measure objective levels of the target person\u2019s popularity or attractiveness, but to measure target person\u2019s perception of it. As such, it might be more appropriate to add \u201cS/he believes\u201d or \u201cS/he thinks\u201d to those items.A: We thank R2 for this interesting suggestion. In the revised version of this paper, we have included this aspect as a limitation (lines 1165-1171) of our study suggesting the use of this inventory, in future studies, in the light of these tips. To this end, we have also uploaded on our webpage a revised version of Obs HEXACO-MSI-E with a note specifying that, after the validation of the inventory, we realized that three items of the Social Self-Esteem scale would be better expressed in the format that includes \"S/he believes\".8. The manuscript may benefit from a more thorough proofreading. The followings are what I spotted while reading the manuscript, and they are not meant to be a thorough list of typos. &#x0f0e0;  \u201cshown\u201dLine 65, \u201cshowed\u201d\ufffdA: Done.Line 66, \u201cto a lesser extent\u201d may sound better than \u201cto little extent\u201dA: Done. Line 127, \u201cBFF\u201d may need to be spelled out.A: We thank R2 for noticing this. Also following R1\u2019s suggestion, we have removed \u201cBFF\u201d and replaced it with \u201cBig Five\u201d. &#x0f0e0;  \u201cnever had access\u201d?Line 160, \u201chad never access\u201d \ufffdA: Done. &#x0f0e0;  In the literature it is known as\u201d?Line 187, \u201cin literature is known as\u201d \ufffdThroughout, \u201cAs regard\u201d should be \u201cAs regards\u201dA: Done. &#x0f0e0;  \u201cThielmann\u201dLine 461, \u201cTielman\u201d \ufffdA: Done. Thanks. &#x0f0e0;  \u201cwe have provided evidence\u201d?Line 560, \u201cwe have proved evidence\u201d \ufffdA: Done.________________________________________6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose \u201cno\u201d, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.Reviewer #1: NoReviewer #2: No________________________________________https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, AttachmentResponsesToEditor&Reviewers_R1_DEF.docxSubmitted filename: Click here for additional data file. 28 Sep 2023Construct and criterion validity of the HEXACO Medium School Inventory Extended (MSI-E)PONE-D-23-19901R1Dear Dr. Gnisci,We\u2019re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you\u2019ll receive an e-mail detailing the required amendments. When these have been addressed, you\u2019ll receive a formal acceptance letter and your manuscript will be scheduled for publication.http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at onepress@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they\u2019ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. 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+{"text": "Scientific Reportshttps://doi.org/10.1038/s41598-023-30574-3, published online 02 March 2023Correction to: The original version of this Article contained errors in Equations 7 and 8.In the original version of this article, the value \u201c55.5\u201d was incorrectly placed as a denominator, wherenow reads:The original Article has been corrected.Additionally, the original PDF version of this Article contained errors\u00a0in Equation\u00a08, where the minus sign is missing:now reads:This error has now been corrected in the PDF version of the Article; the HTML version was correct from the time of publication."}
+{"text": "More precisely, given a multifurcated (non-binary) gene tree with leaves labeled 0 or 1 depending on whether the corresponding genes belong to the mitochondrial or nuclear genome of the corresponding species, we investigate the problem of inferring a most parsimonious Duplication, Loss and EGT (DLE) Reconciliation of any binary refinement of the tree. We present a general two-steps method: ignoring the 0\u20131 labeling of leaves, output a binary resolution minimizing the Duplication and Loss (DL) Reconciliation and then, for such resolution, assign a known number of 0s and 1s to the leaves in a way minimizing EGT events. While the first step corresponds to the well studied non-binary DL-Reconciliation problem, the complexity of the label assignment problem corresponding to the second step is unknown. We show that this problem is NP-complete, even when the tree is restricted to a single polytomy, and even if transfers can occur in only one direction. We present a general algorithm solving each polytomy separately, which is shown optimal for a unitary cost of operation, and a polynomial-time algorithm for solving a polytomy in the special case where genes are specific to a single genome  in all but one species. This work represents the first algorithmic study for reconciliation with endosymbiotic gene transfers in the case of a multifurcated gene tree.Reconciling a non-binary gene tree with a binary species tree can be done efficiently in the absence of horizontal gene transfers, but becomes NP-hard in the presence of gene transfers. Here, we focus on the special case of  Reconciliation is the process of embedding a gene family tree into a species tree (i.e. reconstructing a mapping between the gene tree and the species tree) to explain how the gene family evolved inside the species tree according to the gene tree model, through evolutionary events modifying gene contents in genomes, such as losses, duplications or horizontal gene transfers (HGTs). This allows deciphering the orthology (divergence through speciation), paralogy (divergence through duplication) or xenology (divergence through HGT) relation between genes, which has important implications on understanding functional specificity of gene copies. For this purpose, the most critical part is the construction of a \u201cgood\u201d gene tree, i.e. a gene tree reflecting the true evolution of the nucleotide or amino acid sequences of genes. In fact, as shown in many studies , the resUnfortunately, for many reasons related to sequence alignment, limitations of the considered phylogenetic method or issues with the sequence dataset , gene trees are almost never inferred with absolute certainty. As phylogenetic reconstruction methods are usually accompanied with statistical evaluations on branches, a solution for removing ambiguities in a tree is collapsing its weakly supported branches, leading to a non-binary tree . The problem then becomes one of simultaneously finding a binary refinement and optimal reconciliation of the multifurcated tree, more precisely, inferring an optimal evolutionary scenario leading to a binary refinement of the tree. This strategy has been applied, for example, to infer the evolution of the gene families responsible for alkaloid accumulation in plants .Reconciling a non-binary gene tree with a binary species tree can be done efficiently in the absence of HGTs (a review can be found in ). As farIn this paper, we focus on the particular case of DTL non-binary gene tree reconciliation, where transfers can only move genes between the mitochondrial and nuclear genome of the same species \u2013 called endosymbiotic gene transfers. In fact, it is well known that episodes of such gene transfers, mainly from the mitochondria to the nucleus, have marked the eukaryote evolution since an initial endosymbiotic event integrating an From a computational point of view, EndoRex  is the fHere, we explore the case of a non-binary gene tree. More precisely, given a multifurcated gene tree for a gene family with 0\u20131 labeled genes (leaflabels of the gene tree), the problem consists in inferring a most parsimonious duplication, loss and EGT scenario leading to a binary refinement of the tree. Our method is in two steps: ignoring the 0\u20131 labeling of the gene tree leaves, output all resolutions minimizing the DL-Reconciliation cost and then, for each resolution (i.e. binary tree), assign a known number of 0s and 1s to the leaves in a way minimizing EGT events. Step one can be done efficiently as recalled above. Therefore, we focus on the second step which consists in assigning a 0\u20131 labeling to the nodes of a binary tree, in a way minimizing the considered evolutionary distance. We show in \"b-labeling problem in the special case where, in each polytomy, genes are specific to a single genome  in all but one species. We first begin, in the next section, by formally defining our problems.Except for species conserving the traces of an ancestral eukaryotic origin, few genes are expected to reflect an intermediate endosymbiotic integration of the mitochondrial gene content to the nucleus, with gene copies in both the nuclear and mitochondrial genome. This is the case of the eukaryotes with complete mitochondrial genomes explored in   its root, by V(T) its set of nodes and by size of T. A node x is a descendant of y if x is on the path from y to a leaf of T and an ancestor of y if x is on the path from r(T) to y; x is a strict descendant (respect. strict ancestor) of x is the parent of p(y), if it directly precedes y on this path. In this latter case, y is a child of x. We denote by E(T) the set of edges of T, where an edge is represented by its two terminal nodes , with x being the parent of y. More generally, if x is an ancestor of y,  denotes the path between x and y. The subtree of T rooted at x  is denoted T[x]. The lowest common ancestor (LCA) in T of a subset L(T), denoted All trees are considered rooted. Given a tree unary if it has a single child, binary if it has two children, and a polytomy if it has at least two children. Moreover, a star-tree is a tree with a single internal node. We will denote by the sibling of An internal node (a node which is not a leaf) is said to be R is an extension of a tree T if it is obtained from T by grafting unary or binary nodes in T, where grafting a unary node x on an edge  consists in creating a new node x, removing the edge  and creating two edges  and , and in the case of grafting a binary node, also creating a new leaf y and an edge . In the latter case, we say that y is a grafted leaf. Moreover, given a function f defined from U to V, an extensionf is a function defined from A tree species tree for a set S with a bijection between L(S) and S for a given set of species S in Fig.\u00a0gene family is a set G is a gene tree for a gene family G is meant to be fully identified by its species labeling, i.e. the species A mentclass2pt{minimmentclass2pt{minimb-labeling for a gene x: x belongs to the mitochondrial genome of x belongs to the nuclear genome of G is fully identified by these two labels (e.g. trees (2) and (4) in Fig.\u00a0G, G are identified. Later, we will need to define labeling for internal nodes of G.In this paper, we will consider an additional mentclass2pt{minimbinary tree is a tree with all internal nodes being binary. If internal nodes have one or two children, then the tree is said partially binary. A multifurcated tree is a tree containing at least one polytomy. For example, in Fig.\u00a0A binary refinement of (binary refinement) Let b-labeling.As for a multifurcated tree In Fig.\u00a0count matrixCount(X) for X is a We need a final notation. Let Speciation (Spe) when the species to which they belong do, but also Duplication (Dup) i.e. the creation of a new gene copy, Loss of a gene copy, and transfer when a gene is transmitted from a source to a target genome. In this paper, we only consider endosymbiotic gene transfers, denoted EGT, i.e. the special case of transfers only allowing the transmission of genes from the mitochondrial genome to the nuclear genome of the same species, or vice-versa. If the transmission of a gene from a genome A to a genome B is accompanied by the loss of the gene in A, we refer to the event as an EGTL for  is a quadruplet R is a partially binary extension of G, s is an extension of V(R) to V(S), b is an extension of V(R) to e is an event labeling of the internal nodes of R, such that: x with a single child y is such that x is an EGTL event with source genome s(y)).Each unary node x of R with two children s(x) in S and y be the element of e(x) is an EGT with source genome For each binary node Grafted leaves in the extension R correspond to gene losses.(DLE-Reconciliation) Let R is as an extension of G, each node in G has a corresponding node in R. In particular, the s, b and e labeling on R induce an s, b and e labeling on the nodes of G. The difference between G and R are additional binary nodes with a child being a grafted leaf (a loss), and unary nodes corresponding to EGTL events.As DL-reconciliation of b-labeling, i.e. it is a tuple R is an extension of G. For example, in Fig.\u00a0A entclass1pt{minimaOptimal reconciliation: Let c be a function attributing a cost to each event in R plus the sum of costs of the losses, i.e. optimal reconciliation. We denote by DLE ) the cost of an optimal DLE-Reconciliation (respec. DL-Reconciliation).Given a DLE-Reconciliation unitary when From now on, we denote by The following lemma makes the link between an optimal DLE-Reconciliation and the optimal DL-Reconciliation.Any optimal DLE-Reconciliation x be a duplication of x is either a duplication or an EGT node in x is a duplication in x is the root then its other child becomes the new root) would result in a DLE-Reconciliation If x is an EGT in If Therefore, G. Let G with S. Note that G, it has also a corresponding node in x in x in x would be a speciation. Similarly to the previous case, x is either a duplication or an EGT in x transformed into a speciation, and thus Let\u2019s consider, by contradiction, an optimal DLE-Reconciliation iliation . As eachx of G, x of G, C.Recall that the optimal DL-Reconciliation is unique and -mapping , i.e. fomentclass2pt{minimGiven a DLE-Reconciliation compressed DLE-Reconciliation of e restricted to the nodes of G and G indicating the presence or absence of an EGTL node on that edge, i.e. obtained as follows: Let R by removing grafted leaves and their parental nodes (i.e. ignoring losses). For each edge  of G, let G only by unary nodes). Then:(Compressed reconciliation) A compressed DL-Reconciliation of b and the A mentclass2pt{minimP, i.e. the number of EGTL events, and define the cost of For a compressed DLE-Reconciliation compressed DLE-ReconciliationFrom a Let G with S. We construct a DLE-Reconciliation p(x),\u00a0x)   in Let b-labeling of M(x) for each I is the subset of M,\u00a0I) is called the b-constraint of G  for G, a labeling consistent with  if, for any Given a binary tree s labeling of an optimal DLE-Reconciliation should be the LCA-Mapping. We denote it Moreover, recall from Lemma\u00a0DLE-BinL problem and (2) is its output.The main problem Step\u00a02) can thus be defined as follows. See an example in Fig.\u00a0 can thusDLE-BinL Problem:Input: A binary tree M,\u00a0I) and a species tree S;Output: An optimal DLE-Reconciliation S, where b-labeling consistent with .Notice that, from Lemma\u00a0DLE-BinL1 the DLE-BinL problem where I is restricted to the root of G .We call DLE-BinL problem in its decision version is defined bellow; the decision version of DLE-BinL1 is defined similarly.In this section, the considered cost is unitary; the complexity results are then naturally extendable to a general cost. The DLE-BinL decision version:Input: A binary tree M,\u00a0I), a species tree S and an integer Cost;Question: Is there a DLE-Reconciliation S where b-labeling consistent with  for which DLE-BinL decision problem is in NP. In fact, given a DLE-Reconciliation Cost) and verify if the b-labeling M,\u00a0I) in polynomial time by traversing the tree G.First observe that the DLE-BinL problem is NP-complete event with this requirement, in all but one very constrained version of the problem.According to the considered Resolution method presented in \"S. The DL-DLE-BinL (respec. DL-DLE-BinL1) decision problem is defined as the DLE-BinL (respec. DLE-BinL1) decision problem with the additional restriction that the binary tree given as input is in For a multifurcated tree Weighted Monotone 1-in-3-SAT Problem), that the DL-DLE-BinL1 decision problem is NP-complete. We can then deduce that DL-DLE-BinL is also NP-complete, as well as the more general DLE-BinL problem.We first show, by reduction from Weighted Monotone one-in-three-satisfiability problem .As the Weighted Monotone 1-in-3-SAT:Instance: A set of clauses n  is defined as follows:For each species n of the m leaves mapped to For each species Finally, Cost is set to DL.The b-constraint  of G.Let j, TA, we set x of the subtree TA . If x on the path from the parent of y on the path from the parent of r(G). Else (when x on the path from the parent of r(G).For all b-label. Notice that all nodes on the the path from the parent of r(G) are duplication nodes in TA, we set TA, we set There are no EGTL events in the subtrees In both case, it is easy to see that this mapping is valid and that no EGTL events are required in DL and thus As there are no EGTL events in x of G, we set n variables are set to true in TA and as one variable per clause is set to True in TA, we know, by construction, that for each species n of the m leaves mapped to b-labeling b we constructed is thus consistent with .For each leaf b-labeling consistent with  for which DL-DLE-BinL1 decision problem admits a DLE-Reconciliation of cost lower than or equal to Cost. We then obtain a DLE-Reconciliation Weighted Monotone 1-in-3-SAT problem. Then its corresponding instance DL-DLE-BinL1 decision problem does not admit a DLE-Reconciliation of cost equal or lower than Cost.Let Weighted Monotone 1-in-3-SAT problem, its corresponding instance DL-DLE-BinL1 decision problem does admit an optimal DLE-Reconciliation Cost. In that case, By contradiction, let us suppose that for an unsatisfiable instance mentclass2pt{minimS, we know from Lemma\u00a0b-label.As there are no duplication nodes in the DL-Reconciliation of the subtrees mentclass2pt{minimTA as follows: for all b-label of the nodes in We now define a truth assignment G. Therefore the truth assignment TA satisfies TA. We know that exactly n variables are set to True in TA, as exactly n subtrees M,\u00a0I) requiring exactly n of the m leaves mapped to For each species Weighted Monotone 1-in-3-SAT problem, then its corresponding instance DL-DLE-BinL1 decision problem does not admit a DLE-Reconciliation of cost equal or lower than Cost. Weighted Monotone 1-in-3-SAT is NP-complete, Lemmas\u00a0Since DL-DLE-BinL1 decision problem is NP-complete.The DL-DLE-BinL and DLE-BinL decision problems are NP-complete.The multiplicitymultiplicity factorGiven S, and the multiplicity factor DL-DLE-BinL1 Problem is fixed parameter tractable with respect to the multiplicity factor The two following lemmas make the link between the maximum number of non-loss nodes in an optimal DL-Reconciliation S.Let We consider for this proof non-compressed reconciliations.V(S), there are more than k speciation nodes of R that are mapped to separated, i.e. for any node v of R, v belongs to at most one of these subtrees.Let Consider Algorithm\u00a01 above. We show that it transforms R in a position respecting definition 2 . By Lemma\u00a0p(x) is at most x is at most From Lemma\u00a0S and b-labeling for the non-loss nodes of R. The optimal DLE-Reconciliation O(n) time where Let EGTcopy holds for an EGT event and EGTcut holds for an EGTL event. We can do so by using Algorithm\u00a01 in . Note thS. For the proof of the next Theorem, given a node S, we denote by b-labeling for all non-loss nodes of R mapped to k such nodes, then the number of possible S, we define R which roots are mapped to S.Let DL-DLE-BinL1 decision problem is fixed-parameter tractable with respect to the multiplicity factor The Here, we consider non-compressed reconciliations.DL-DLE-BinL1 decision problem using Algorithm\u00a03.We can solve the S and all possible b-labelings We show by induction that Algorithm\u00a03 computes the correct cost S, then Algorithm\u00a03 computes the correct If the node b-labelings for the two children S. Let show that Algorithm\u00a03 is correct for R, the two children of a non-loss and non-leaf node mapped to the node We may suppose now by the induction hypothesis that Algorithm\u00a03 computes the correct cost for all possible costOp computed in line 24 of Algorithm\u00a03 is the cost of an optimal DLE-Reconciliation of S.Note that, S. The number of possible b-labelings for the nodes mapped to S, then all nodes of the subtrees in b-labeling As for the complexity of the algorithm, from Lemma\u00a0CurrentCost in line 13 can be computed in time Now for internal nodes, in line 13, The problem can thus be solved in time DL-DLE-BinL1 and DL-DLE-BinL, the general problems DLE-BinL1 and DLE-BinL remain NP-complete even if the multiplicity factor of Finally, the next theorem states that, in contrast to DLE-BinL1 decision problem is NP-complete, even for The The proof, given in DLE-BinL decision problem is NP-complete, even for The b-labels can only switch from 0 to 1, or only from 1 to 0. In the following definition, with no loss of generality, we assume transitions from 0 to 1.As endosymbiotic transfer events often move genes from the mitochondrial to the nuclear genome, and rarely in the opposite direction, we address the specific case where transfers are only allowed in one direction, i.e. when One-direction DLE-Reconciliation for x,\u00a0y) of G, if (One-direction DLE-Reconciliation) Let One-DLE-BinL Problem:Input: A binary tree M,\u00a0I) and a species tree S;Output: An optimal One-direction DLE-Reconciliation S where b-labeling consistent with .One-DLE-BinL1 problem where I is restricted to the root of G, and the corresponding decision problems. We next show that even this very restricted version of our initial problem is intractable. Moreover, the One-DL-DLE-BinL (respec.One-DL-DLE-BinL1) problem is defined as the One-DLE-BinL (respec. One-DLE-BinL1) problem with the additional restriction that the binary tree given as input is in We also define, in a similar way as before, the One-DL-DLE-BinL1 and One-DL-DLE-BinL are NP-hard but fixed parameter tractable with the multiplicity factor, while One-DLE-BinL1 and One-DLE-BinL are NP-hard even with a multiplicity factor of two.We show that One-DL-DLE-BinL decision problem is NP-complete.The One-DL-DLE-BinL1 is the same as that of Theorem\u00a0One-DL-DLE-BinL follows. The proof for NP-completeness of One-DL-DLE-BinL1 is fixed parameter tractable with respect to the multiplicity factor The One-DL-DLE-BinL1 Problem using the algorithm in the proof of Theorem\u00a0Note that the proof of Lemma\u00a0One-DLE-BinL is NP-complete. However, as for DLE-BinL1 and DLE-BinL, One-DLE-BinL1 and One-DLE-BinL remain NP-complete even if the multiplicity factor of It follows from Theorem\u00a0One-DLE-BinL1 and One-DLE-BinL decision problems are NP-complete, even for The DLE-BinL problem for G is a binary resolution of an initial multifurcated tree with initial polytomies reflected by a b-Constraint , would be to solve each polytomy, i.e. each subtree rooted at a node x of I, individually, in a post-order traversal of the tree. In fact, this strategy leads to an exact algorithm for the DL Non-binary Reconciliation Problem  and replaces it by a single leaf, with an appropriate b-label.Algorithm\u00a04 traverses the tree G has been completely traversed, the subtrees are put back in the tree. Notice that on line 13, the algorithm adds a new intermediate species to b-label. Such nodes are technically ignored for the rest of the traversal of G and just used to re-graft the corresponding subtrees at the end (line 27).Once the tree DLE-BinL1 Problem such that DLE-BinL1 Problem is also NP-complete. In the next section, we will present DLEBinL1OneSpecies which can be substituted to DLEBinL1 in Algorithm\u00a04 for a restriction of the problem, where, for each polytomy, genes belonging to the same species have the same b-label for all but one species.Algorithm\u00a04 calls a function M,\u00a0I) be a b-Constraint for S be a species tree. Then, with the input b-labeling consistent with .Let The proof is by induction on the number of node b is a b-labeling consistent with  by construction.Notice that the DLE-Reconciliation x is the root of G by definition. The algorithm then returns an optimal solution, as we assume that we can solve If there is only one node G is in I by definition. By induction, we may assume that for each node G[x] computed by the algorithm is exact. For each of those subtrees G[x], we then know the possible b-label(s) at the root leading to an optimal reconciliation of G[x] and the corresponding optimal reconciliation of G[x]. We now give the index 1 to G and replace it by a new leaf without a b-label. It solves G by the solved G is solved). b-label of the parent of G we can obtain an optimal reconciliation of b-label as its parent .G and replace it by a new leaf with b-label by Then, Algorithm\u00a04 solves If there is more than one node Let\u2019s show that this solution is optimal. By contradiction, suppose that there is Thus, Algorithm\u00a04 returns an optimal solution for the input We conclude, by induction, that the solution returned by Algorithm\u00a04 is optimal. DLE-BinL1 Problem where genes are specific to a single genome  in all but one species. We call it the DLE-BinL1-OneSpecies problem. In its simplest version where a single species is present, the problem reduces to assigning a multiset of two labels (a given number of 0\u00a0s and a given number of 1\u00a0s) to the leaves of a tree-shape (i.e. a tree with no leaf labels), in a way minimizing 0\u20131 transitions in the tree. Similar problems on assigning leaves to tree-shapes or to multilabeled trees (MUL-trees) have been considered in the context of other tree distances , most of them being NP-complete  with S. The proof is by induction.The key point is therefore showing that the arrays computed by Algorithm\u00a06 are exact, i.e., for each node x is a leaf (either free or fixed), it is easy to see that x.array is correct.If x is an internal node, we may assume that i,\u00a0j) such that j free leaves labeled by 0 under x, the sum of the numbers of free leaves labeled by 0 under j. If the genome labels of the children of x are not the same as i, x is converted as an EGT event if x is a duplication node in the DL-Reconciliation (and possibly an EGTL event is added) and if x is not a duplication node then some EGTL events may be added on the edges between x and its children. As the algorithm considers all possibilities of genome labels for j free leaves under x labeled to 0  needed from x to its children), the particular possibility leading to i,\u00a0j) and x.array is exact.Now, if We conclude, by induction, that the arrays computed by Algorithm\u00a06 are exact. DLE-BinL1-OneSpecies problem in Algorithm\u00a05 computes the solution of the G, the associated array is computed in time O(k). For each internal node of G, the associated array is computed in time For each leaves of G in time O(n)Once all the arrays are computed, the algorithm finds the optimal assignation of the internal nodes with a preorder traversal of We conclude that the time complexity of Algorithm\u00a05 is b-labeling  to the nodes of the tree in a way minimizing a total DLE  cost.In this paper, we present the first method for DLE-Reconciliation, that is a reconciliation accounting for duplications, losses, but also EGTs, for a multifurcated gene tree. It is a natural extension of the DL-Reconciliation of a multifurcated tree, where we first consider a solution for this problem, i.e. an optimal DL-Reconciliation, and then appropriately assign the binary b-labeling assignment step is NP-complete even if the gene tree in input is a binary refinement of a star-tree, and even when genes are present in only two copies in each species. Moreover, the problem remains NP-complete when the transfers are allowed in a single direction (e.g. only from 0 to 1) and even if the gene tree in input is an optimal resolution for the DL-Reconciliation. In this latter case, the problem is shown fixed-parameter tractable with respect to the gene tree\u2019s multiplicity factor. We then present a greedy heuristic for the general version of the problem solving each polytomy independently in a bottom-up traversal of the tree. This heuristic is shown to be exact for a unitary cost of operations. Moreover, we give a polynomial-time algorithm for the resolution of a single polytomy in the case where genes are specific to a single genome in all but one species. We did not explore the case where genes are specific to a single genome in all but a fixed number of species, but we believe Algorithm\u00a05 can be extended to solve this problem in polynomial time.We show that the optimal From a biological point of view, the next step will be to apply our method to the orthologous mitochondrial protein-coding genes (MitoCOGs) dataset , 10.DLE-BinL and DLE-BinL1 problems in the general case, a more fundamental question is whether an exact one-step method, considering all the events at once, can be developed. In fact, the complexity results obtained here do not allow to conclude on the complexity of the DLE Non-binary Reconciliation problem. It is indeed not excluded that the polynomial-time PolytomySolver algorithm [b-labeling of leaves, at least in special cases. In the near future, we will first explore the extension of PolytomySolver to the one species restriction of the model, before considering generalization to an arbitrary number of species.From a theoretical and algorithmic point of view, many open questions remain. Apart from the fact that a heuristic combining accuracy and time-efficiency should be developed for both the lgorithm  can be e"}
+{"text": "Nature Communications 10.1038/s41467-023-35836-2, published online 14 January 2023Correction to: The original version of this Article contained errors in Fig. 4d and Supplementary Fig. 4e, which showed plots of erroneous cumulative distance values, which arose from an erroneous handling of NaN values in the underlying code for distance calculations.The correct version of Fig. 4d is:which replaces the previous incorrect version:This has been corrected in both the PDF and HTML versions of the Article.The correct version of Supplementary Fig. 4e is:which replaces the previous incorrect version:The HTML has been updated to include a corrected version of the\u00a0The Is to increase along the rostral-caudal axis  as IS values decrease across the forebrain regions \u201d incorrectly referred to Fig. 5b, g\u2013i, instead of Fig. 5c, g\u2013i. These errors have been corrected in both the PDF and the HTML versions of the Article.In addition, in the results section \u201cIntegrated microfluidics-light sheet fluorescence microscopy system for imaging neuronal activities and behavior\u201d the sentence \u201cSimultaneously, the tail flipping behaviors were monitored using high-speed IR camera imaging at 200 fps \u201d incorrectly referred to Fig. 3b, instead of Fig. 3c, and in the results section \u201cRevealing brainwide representation of cadaverine sensing using the integrated optofluidic system\u201d the sentence \u201cInterestingly, apart from observing a supralinear gain of information for the majority of neurons , there is a trend for FUpdated Supplementary InformationUpdated Source Data"}
+{"text": "Scientific Reportshttps://doi.org/10.1038/s41598-023-38966-1, published online 24 July 2023Correction to: The original version of this Article contained a formatting error in Equation 1. As a result, the subsequent paragraph,\u201cYit is the logit binomial plague occurrence at site i in year t. Parameter a is the overall intercept, f is the thin-plate spline function, and \u03b5 is the uncorrelated random error term. 1 is the smooth function of marmot density at site i in year t,\u201dnow reads:\u201cYi,t is the logit binomial plague occurrence at site i in year t. Parameter a is the overall intercept, f is the thin-plate spline function, and \u03b5 is the uncorrelated random error term. 1 is the smooth function of marmot density at site i in year t,\u201dThe original Article has been corrected."}
+{"text": "In the published article, there was a mistake in the keyword \u201craw sugarcane vinegar\u201d.The correct keyword is \u201csugarcane original vinegar\u201d.In the published article \u201cChen et al. 2015b\u201d was cited in the Introduction, first-paragraph, line 5 as \u201cIt is an advanced type of vinegar product \u201d.The correct citation is \u201cIt is an advanced type of vinegar product . Research on the production technology of sugarcane vinegar and fruit vinegar beverages. The correct reference is: \u201cChen, G.-L., Zheng, F.-J., Lin, B., Wang, T.-S., and Li, Y.-R. (2013). Preparation and characteristics of sugarcane low alcoholic drink by submerged alcoholic fermentation. Sugar Tech. 15, 412\u2013416. doi: 10.1007/s12355-013-0248-3\u201d.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated."}
+{"text": "Empirical studies have demonstrated that self-relevant information affects temporal order perception. Therefore, the question arises of whether personal values\u2014which are the core components of the self\u2014influence temporal order perception. To explore this problem, we chose harmony, one of the most common values in Chinese culture, as the starting point. First, the harmony scale was used to measure the harmony values of the participants, and the participants were divided into high- and low-harmony groups. The validity of the grouping was then verified using an implicit-association test. Furthermore, two temporal order judgment (TOJ) tasks were used to explore the impact of harmony values on temporal order perception. The results revealed that in both TOJ tasks, participants in the high-harmony group tended to perceive harmonious stimuli before non-harmonious stimuli, while the effect was not found in the low-harmony group. We conclude that harmony values affect temporal order perception, and only if the values are important to the individual. Personal values are broadly desirable goals that motivate people\u2019s actions and serve as guiding principles in their lives. Values affect people\u2019s perception, cognition, and behavior over time and across situations . So, do Values are closely linked to the self. Verplanken (2002)  affirmedGallagher (2000)  collatedA few studies based on the SoA found that in the TOJ task, participants reported that the stimuli caused by them appeared earlier than the stimuli caused by others. For example, in the study of Haering and Kiesel (2012) , red andChinese people hold a deep-rooted desire to pursue \u201charmony\u201d when cultivating one\u2019s self, handling interpersonal matters, and confronting the universe and nature. In China, many proverbs show Chinese people\u2019s emphasis on harmony values. For example, \u201c\u5bb6\u548c\u4e07\u4e8b\u5174\u201d (harmony in a family makes everything successful), \u201c\u548c\u6c14\u751f\u8d22\u201d , and so on. A few empirical studies have demonstrated that harmony values rank highly in the Chinese personal values system ,17. The The stimuli presented to the participants in the TOJ tasks were usually simple graphics. In Chinese, the writing of harmony- and disharmony-related words is quite complicated, so we believed that it might not be appropriate to use Chinese characters as stimuli for order perception. The perceptual matching task can help to solve this problem. In the perceptual matching task used in a previous study, participants were asked to associate an abstract graph with a certain label, and then use the graph as a stimulus for subsequent research . TherefoM = 21.80 years). All participants were right-handed. Participants had normal or corrected-to-normal vision.This study was approved by the Ethics Committee of Southwest University. A group of 53 undergraduates were initially recruited to participate in the experiment. Four participants performed unsatisfactorily in the TOJ tasks and were excluded, and 49 valid participants were retained , \u201c\u548c\u7766\u201d (concord), \u201c\u878d\u6d3d\u201d (in tune), \u201c\u534f\u8c03\u201d (coordinate), \u201c\u53cb\u597d\u201d (friendly), and \u201c\u7965\u548c\u201d (auspicious and harmonious). Words related to non-harmony were: \u201c\u51b2\u7a81\u201d (conflict), \u201c\u77db\u76fe\u201d (contradiction), \u201c\u5bf9\u7acb\u201d (oppose), \u201c\u6469\u64e6\u201d (friction), \u201c\u4e89\u6267\u201d (dispute), and \u201c\u5bf9\u6297\u201d (confrontation). The attribute words included six agreement-related words, and six disagreement-related words. The agreement-related words were: \u201c\u8d5e\u540c\u201d (agree), \u201c\u540c\u610f\u201d (consent), \u201c\u8d5e\u6210\u201d (approve), \u201c\u6ee1\u610f\u201d (satisfaction), \u201c\u63a5\u53d7\u201d (accept), and \u201c\u652f\u6301\u201d (support), while the disagreement-related words included \u201c\u53cd\u5bf9\u201d (oppose), \u201c\u62d2\u7edd\u201d (reject), \u201c\u6392\u65a5\u201d (repulsion), \u201c\u4e0d\u60a6\u201d (dissatisfaction), \u201c\u5426\u8ba4\u201d (deny), and \u201c\u6297\u62d2\u201d (resist).Materials for TOJ tasks. In the shape-matching TOJ task, the targets were a black cir-cle and a black triangle of 1.5\u00b0 in width and 1.5\u00b0 high, presented randomly at two different positions, at a 4.8\u00b0 visual angle from the fixation on a white background. The fixation point consisted of a centrally presented black fixation cross . In the color-matching TOJ task, the targets were a red circle and a green circle of 1.5\u00b0 in width and 1.5\u00b0 high.The experiment was divided into two parts. Part A involved the measurement of harmony values, and included explicit questionnaire measurement and IAT procedure measurement. Half of the participants performed explicit measurements first, and implicit measurements later, while the other half did the opposite. Part B included TOJ tasks, including the shape-matching TOJ task and the color-matching TOJ task. Half of the participants completed the shape-matching TOJ first, and then the color-matching TOJ, while the other half did the opposite. Some participants completed Part A first and then Part B, while others did the opposite. The E-Prime 1.0 software was used for programming and timing the experimental operations.Procedure of implicit harmony value measures. The participants were instructed to classify a series of stimulus words into the target category, and two attributive categories. The IAT procedure consisted of seven stages. In the first stage, the F key was pressed when the agreement-related word appeared, and the J key was pressed when the disagreement-related word appeared . In the second stage, the participants pressed the F key when they saw the harmonious stimulus, but pressed the J key when they saw the non-harmonious stimulus . In the third stage, the F key was pressed when the harmony words or agreement-related words appeared, while the J key was pressed when the non-harmony words or disagreement-related words appeared . The first three stages were practice stages, and the fourth stage was the formal test of the third stage . The fifth stage was the practice stage, in which the participants were asked to press the F key when the non-harmony words appeared, and press the J key when the harmony words appeared. The sixth stage was also the practice stage. At this stage, the F key was pressed when the non-harmony words or agreement-related words appeared, while the J key was pressed when the harmony words or disagreement-related words appeared . The seventh stage was the formal test of the sixth stage . Each incorrect response was signaled by a red X centered below the stimulus word for 150 ms, while a correct response was signaled by a green O centered below the stimulus word for 150 ms.Procedure of TOJs. Before the TOJ task, the participants were asked to complete the perceptual-matching task. Taking the shape-matching task as an example, the participants were first told that the circle represented the harmonious stimulus, while the triangle represented the non-harmonious stimulus, and then the participants carried out the shape-matching task. In each trial, a fixation point of 500\u20131000 ms was first presented on the screen. Subsequently, a pairing of a shape and label (harmony or non-harmony) was presented for 2000 ms. Two geometric shapes  were presented above the fixation at the center of the screen. The word of harmony or non-harmony (3.1\u00b0/3.6\u00b0 \u00d7 1.6\u00b0) was displayed below the fixation. The angular distance between the center of the shape or the word, and the fixation cross, was 3.5\u00b0. All stimuli were shown on a white background. Participants judged whether the pairings of shape and label matched. Feedback (correct or incorrect) was given on the screen for 500 ms at the end of each trial. Each participant performed 120 trials. The color-matching task was the same procedure, except that in the color-matching task, the green circle represented the harmonious stimulus, while the red circle represented the non-harmonious stimulus.In each trial of the TOJ tasks, a fixation point was presented at the center of the screen for 500\u20131000 ms, and then a stimulus appeared on one side of the fixation point (left or right). After a variable interval, the second stimulus appeared on the other side of the fixation point. Once the second stimulus had appeared, the image remained rendered for 1000 ms, before disappearing. A question mark then appeared at the center of the screen, asking the participants to judge which stimulus appeared first. In the shape-matching TOJ, participants were asked to judge which shape stimulus appeared first, while in the color-matching TOJ, they were asked to judge which color stimulus appeared first. Stimulus-onset asynchrony (SOA) had nine levels at \u00b1120 ms, \u00b190 ms, \u00b160 ms, \u00b130 ms, and 0 ms. The SOA was positive for the first circle (or green circle), and negative for the first triangle (or red circle). The SOA was 0 when the stimulus appeared simultaneously on both sides. Half of the participants attempted the shape-matching TOJ, followed by color-matching TOJ. Meanwhile, the other half of the participants attempted the TOJ in reverse order. The response key was balanced between the different participants. Half of the participants pressed \u201cD\u201d when the circle (or green circle) side stimulus appeared earlier, and pressed \u201cK\u201d when the triangle (or red circle) side stimulus appeared earlier. Each condition was repeated 15 times. The total number of trials was 270. Participants had some practice before the official experiment. The TOJ task process is depicted in t-test was conducted for the score , and the median value 3. The results revealed a significant difference between the score and the median value (t(48) = 13.00, p < 0.001, d = 1.86), indicating that participants regarded harmony as an important value. Each participant\u2019s level of harmonious values was then assessed by comparing the difference between the harmony scores of the participants and the median value 3. It was found that 33 participants had scores significantly higher than 3, and these participants were classified in the high-harmony group . The other 14 participants whose scores were not significantly different from 3 were placed in the low-harmony group . An independent samples t-test was conducted on the harmony values scores of the two groups, and the results revealed a significant difference in the scores of the two groups (t(47) = 6.72, p < 0.001, d = 2.13). This indicated that participants in the high-harmony group hold harmony values in higher esteem than those in the low-harmony group do.The harmony values questionnaire was analyzed, and the one-sample t-test was performed on this value  of all participants, and the results showed significant difference from 0 (t(48) = 30.60, p < 0.001, d = 4.37), which indicated that participants had implicit harmony values. A one-sample t-test was conducted on the implicit effects of the high-harmony group  and the low-harmony group . The results demonstrated that both the high-harmony group (t(34) = 37.20, p < 0.001, d = 0.28) and the low-harmony group (t(13) = 11.60, p < 0.001, d = 3.11) were significantly different from 0. An independent samples t-test was conducted on the d-prime of the implicit effect of the two groups. The results showed that the implicit effect size of the participants in the high-harmony group was significantly larger than that of the low-harmony group (t(47) = 3.88, p < 0.001, d = 1.23), which indicated that the classification of high- and low-harmony groups was effective.In accordance with the recommendations of Greenwald et al. (1998) , first, t-test was conducted on the accuracy of participants in the high- and low-harmony groups. The results revealed that there was no significant difference between the performance of the two groups in either the shape-matching task (t(47) = \u22121.45, p = 0.16, d = \u22120.46) or the color-matching task (t(47) = \u22120.48, p = 0.63, d = \u22120.15).The participants\u2019 accuracy reached 0.95 in both perceptual-matching tasks, which indicated that the participants indeed combined the shape with the value words. An in-dependent samples R2 value was less than 0.75 [For the shape-matching TOJ task-data analysis, first, E-prime was used to calculate the correct responses under each SOA. Then, MATLAB software was used to calculate the point of subjective simultaneity (PSS). The psychometric function was obtained by calculating the percentages of \u201charmony first\u201d (circle first) responses as a function of SOA , and a chan 0.75 , the datt-test on the participants\u2019 PSS against a test value of 0 to determine the PSS shift between stimuli [M = \u22123.13, SD = 7.77) were significantly different from 0 ms (t(48) = \u22122.82, p < 0.01, d = \u22120.40, BF10 = 5.19 (moderate evidence for H1)). We then explored the relationship between participants\u2019 harmony scores and the PSS; the correlation between the D score and PSS was significant (r (49) = \u22120.41, p < 0.01), and the correlation between the Harmony Scale score and PSS was marginally significant (r (49) = \u22120.27, p = 0.06). The PSS of participants in the high-harmony and low-harmony groups were then analyzed separately. The results showed that the PSS of the high-harmony group  was significantly different from 0 ms (t(34) = \u22123.87, p < 0.001, d = \u22120.66, BF10 = 63.00 (very strong evidence for H1)), while the PSS of the low-harmony group  was not significantly different from 0 ms (t(13) = 1.24, p = 0.24, d = 0.33, BF10 = 0.52 ).We conducted a one-sample  stimuli ,26. The The color-matching TOJ task-data analysis method was consistent with the shape-matching TOJ task. The psychometric function was obtained by calculating the percentages of \u201cgreen first\u201d responses as a function of SOA , and thet-test was performed on the PSS. The results showed that the PSS of all the participants  were significantly different from 0 ms (t(48) = \u22122.77, p < 0.01, d = \u22120.40, BF10 = 4.59 (moderate evidence for H1)). We then explored the relationship between participants\u2019 harmony scores and the PSS; the correlation between d-prime and PSS was significant (r (49) = \u22120.51, p < 0.001), and the correlation between the Harmony Scale score and the PSS was significant (r (49) = \u22120.32, p < 0.05). The PSS of participants in the high-harmony and low-harmony groups were then analyzed separately. The results revealed that the PSS of the participants with high-harmony values  was significantly different from 0 ms (t(34) = \u22123.79, p <0.001, d = \u22120.64, BF10 = 50.56 (very strong evidence for H1)), while the PSS of the participants with low-harmony values  had no significant difference from 0 ms (t(13) = 1.04, p = 0.32, d = 0.28, BF10 = 0.43 ).A single-sample F = 0.03, p = 0.86, F = 13.42, p < 0.001,F = 0.06, p = 0.81,We conducted a mixed-factor ANOVA with the perceptual-matching type (shape-matching or color-matching) as a within-subject factor and the harmony group (high-harmony group or low-harmony group) as a between-subject factor. The results revealed that the main effect of the matching type was not significant   found thThis study has a few shortcomings, which can be improved on in the follow-up research. For example, in the perceptual-matching task, we only associated green with harmonious information and red with disharmonious information. A more rigorous operation should consider the opposite condition. In addition, only harmony, a common value in Chinese culture, was selected in this study, and several more values should be selected in subsequent studies, to further verify the influence of values on temporal order perception.This study used two TOJ tasks to explore the effect of harmony values on temporal order perception; the result revealed that values do affect temporal order perception, and only if the values are important to the individual."}
+{"text": "An additional detail regarding the computation of the weighted average 2.1 Performance metric design\u201d, paragraph 7. This sentence previously stated:A correction has been made to Section 2. Materials and methods, subsection \u201c\u201cThe intra-class dispersion is computed using:2 \u2208  is a constant, \u03d5k\u22121, c is the intra-class dispersion for the class c trials of the (k-1)th block, and \u03d5k, c is the intra-class dispersion of class c trials computed only during the current (kth) block.\u201dwhere \u03b1The corrected sentences appear below:classDistinct and classStability metrics, we made the following modification to the calculation of the intra-class dispersion. We split the set of trials, T, into Ns subsets of Nt trials, Tj, such that\u201cFor the weighted average Nt trials performed during a block would be grouped into subset T1. Using these subsets, we computed a modified intra-class dispersion as:Subsets were formed by splitting trials according to the chronological order in which they were performed; for example, the first Ns is the number of trial subsets, Nt is the number of trials in each subset, jth subset of trials, \u0393Tj, i is the covariance matrix of the ith trial within subset Tj, and \u03b4R denotes the Riemannian distance. The motivation behind this modification was to reduce the impact of signal non-stationarities that may artificially increase the intra-class dispersion when considering a large number of trials. For our analysis, we set Nt = 5. Trial subsets were disjoint save for when computing within-block post-trial intra-class dispersion values. If the number of trials completed within the block was not divisible by Nt, subset TNs was formed using the most recently completed Nt trials; consequently, this subset could share up to Nt\u22121 trials with subset TNs \u2212 1.where The post-trial intra-class dispersion was computed using this modified intra-class dispersion:2 \u2208  is a constant, c trials of the (k\u22121)th block, and c trials completed only during the current (kth) block.\u201dwhere \u03b1The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated."}
+{"text": "Subject clustering  is a problem of significant interest. In recent years, many approaches have been proposed, among which unsupervised deep learning (UDL) has received much attention. Two interesting questions are 1) how to combine the strengths of UDL and other approaches and 2) how these approaches compare to each other. We combine the variational auto-encoder (VAE), a popular UDL approach, with the recent idea of influential feature-principal component analysis (IF-PCA) and propose IF-VAE as a new method for subject clustering. We study IF-VAE and compare it with several other methods  on 10 gene microarray data sets and eight single-cell RNA-seq data sets. We find that IF-VAE shows significant improvement over VAE, but still underperforms compared to IF-PCA. We also find that IF-PCA is quite competitive, slightly outperforming Seurat and SC3 over the eight single-cell data sets. IF-PCA is conceptually simple and permits delicate analysis. We demonstrate that IF-PCA is capable of achieving phase transition in a rare/weak model. Comparatively, Seurat and SC3 are more complex and theoretically difficult to analyze . Suppose we have a group of n subjects  measured on the same set of p features . The subjects come from K different classes or groups , but unfortunately, the class labels are unknown. In such a case, we say the data are unlabeled. For 1 \u2264 i \u2264 n, we denote the class label of subject i by Yi and denote the p-dimensional measured feature vector of subject i by Xi. It is important to note that Yi takes values from {1, 2, \u2026, K}. The class labels are unknown, and the goal is to predict them using the measured features X1, X2, \u2026, Xn.We are interested in the problem of big data era: although the volume of available scientific data increases rapidly, a significant fraction of them are unlabeled. In some cases, it is simply hard to label each individual sample , where k. We assumeA reasonable model is as follows. We encode the class label Let In addition, it is reasonable to assume that out of many measured features, only a small fraction of them are useful in the clustering decision. Therefore, letting n \u00d7 p signal matrix K.It follows that the W is the normalized data matrix. Similar to W as the sum of a signal matrix and a noise matrix. However, due to the normalization, the rank of the signal matrix is reduced to (K \u2212 1).We recall that \u03c0i. For this reason, we may view Models In Models f  belongs to a class of non-linear functions. For example, we may assume f  belongs to the class of functions :A1, A2, \u2026 , AL are matrices of certain sizes and s1, s2, \u2026 , sL are some nonlinear functions. Similar to Models The recent idea of neural network modeling provides a wide class of non-linear models, which may be useful for our setting. As an alternative to Models X and number of clusters K. Output: predicted class label vector n \u00d7 K matrix kth left singular vector of X .\u2022 We obtain the n rows of K groups by applying the classical k-means assuming there are i. Output \u2022 We cluster the PCA is a classical spectral clustering approach, which is especially appropriate for linear models like those in W. As explained before, we can similarly write W as the sum of a \u201csignal\u201d matrix and a \u201cnoise\u201d matrix as in K to (K \u2212 1). In such a case, we replace the n \u00d7 K matrix n \u00d7 (K \u2212 1) matrixkth left singular vector of W.From time to time, we choose to apply the PCA clustering approach to the normalized data matrix X (or W) directly, Spectral-Gem constructs an n \u00d7 n symmetric matrix M, where M can be viewed as a similarity metric between subject i and subject j. The remaining part of the algorithm has many small steps, but the essence is to apply the PCA clustering approach to the Laplacian normalized graph induced by M.The PCA clustering approach has many modern variants, including, but not limited to, Spectral-Gem  and SCOR\u2022 The signal matrix p \u226a n) or how the sparsity can be exploited is unclear.\u2022 It is hard to exploit sparsity in the data: either the data are non-sparse , the essence of the PCA spectral clustering approach is to obtain a rank-d approximation of X to use singular value decomposition (SVD),\u03c3k is the kth smallest singular value of X, and uk and vk are the corresponding left and right singular vectors of X, respectively. The VAE can be viewed as an extension of SVD, which obtains a rank-d approximation of X from training a neural network. The classical SVD is a linear method, but the neural network approach can be highly non-linear.Given an X into a matrix d \u226a p), and the decoder maps d approximation of X. Different from classical SVD, X and The VAE was first introduced by K, and dimension of the latent space d . Output: predicted class label vector n \u00d7 d matrix \u2022 (Dimension reduction by the VAE). We train the VAE and use the trained encoder to obtain an n subjects into K classes by applying k-means to the rows of \u2022 (Clustering). We cluster all A popular way to use the VAE for subject clustering is as follows . Input: W or the unnormalized data matrix X. We call them VAE(W) and VAE(X), respectively. In the context of using these notations, it is unnecessary to use (W) and (X) at the same time, so we write VAE(W) as VAE for short  as VAE(X)).Except for using a non-linear approach to dimension reduction, the VAE is similar to the PCA approach in clustering. We can apply the VAE either to the normalized data matrix Q have a large \u21132-norm; the \u21132-norm of other columns is small or 0). In such a setting, it is appropriate to conduct feature selection, which removes a substantial amount of noise while keeping most non-zero columns of Q.For many genomic and genetic data, Models Such observations motivate the (orthodox) IF-PCA. The IF-PCA was first proposed in n (univariate) samples z1, z2, \u2026 , zn from a cumulative distribution function (CDF) denoted by F. We introduce the empirical CDF byThe first component of the IF step is the use of the Kolmogorov\u2013Smirnov (KS) test for feature selection. Suppose we have z = . The KS testing score is thenLet F to be the theoretical CDF of i \u2264 n; and z1, z2, \u2026 , zn, respectively.In the IF-PCA given as follows, we take p marginal p-values, one for a feature, and outputs a threshold for feature selection. Suppose we have p-values \u03c01, \u03c02, \u2026 , \u03c0p. We sort them in the ascending order:The second component of the IF step is the higher criticism threshold (HCT). Higher criticism (HC) was initially introduced by We define the feature-wise HC score by K. Output: predicted class label vector j \u2264 p, we compute a KS score for feature j by applying z = wj. We denote the KS scores by \u03d5n (w1), \u2026, \u03d5n (wp) and let \u03bc* and \u03c3* be their empirical mean and standard deviation, respectively. Let p-values by F is the same CDF used in \u03c01, \u03c02, \u2026 , \u03c0p. We retain feature j if \u2022 (IF step). For each 1 \u2264 WIF be the n \u00d7 m sub-matrix of W consisting of columns of W corresponding to the retained features only [m is the number of retained features in (a)]. For any 1 \u2264 k \u2264 min{m, n}, let WIF corresponding to the kth largest singular value of WIF. Let n subjects by applying the k-means to the n rows of K clusters. Let \u2022 (Clustering step). Let IF-PCA runs as follows. Input: normalized feature vectors In the IF step, the normalization of rrection , a simplrrection . We remaW. Seemingly, for the IF step, applying the algorithm to W instead of the un-normalized data matrix X is preferred. However, for the clustering step, whether we should apply the algorithm to W or X remains unclear. We propose a small variant of IF-PCA by applying the IF step and the clustering step to W and X, respectively.W as in the (orthodox) IF-PCA previously mentioned.\u2022 (IF step). We apply exactly the same IF step to XIF be the n \u00d7 m sub-matrix of X consisting of columns of X corresponding to the retained features in the IF step only. For any 1 \u2264 k \u2264 min{m, n}, let XIF corresponding to the kth largest singular value of XIF. Let n subjects by applying the k-means to the n rows of K clusters. Let \u2022 (Clustering step). Let In the (orthodox) IF-PCA, we apply both the IF step and the clustering step to the normalized data matrix To differentiate from the (orthodox) IF-PCA , we call the aforementioned variant IF-PCA(X). See Near the end of K, and dimension of the latent space in the VAE (denoted by d). Output: predicted class label vector IF step). We run the same IF step as in m is the number of retained features).\u2022 (Clustering step). We apply the VAE with n \u00d7 d matrix WIF. We cluster the n samples into K clusters by applying the classical k-means to K classes. Let \u2022 . See In the clustering step, we apply the VAE to the normalized data matrix We now introduce Seurat and SC3, two recent algorithms that are especially popular for subject clustering with single-cell RNA-seq data. We discuss them separately.m, N, k0, \u03b4, where m is the number of selected features in the feature selection step, and N, k0, \u03b4 are the clustering step, corresponding to the PCA part, the k-nearest neighborhood algorithm part, and the modularity optimization part, respectively.Seurat was proposed in n \u00d7 p data matrix X, number of clusters K, and tuning parameters m, N, k0, \u03b4. Output: predicted class label vectors m features that are mostly variable. We obtain the n \u00d7 m post-selection data matrix.\u2022 (IF step). We select the N left singular vectors. For each pair of subjects, we compute how many neighbors  they share with each other and use the results to construct a shared nearest neighborhood (SNN) graph. We cluster the class labels by applying a modularity optimization algorithm to the SNN graph, where we need a resolution parameter \u03b4.\u2022 (Clustering step). We normalize the post-selection data matrix and obtain the first A high-level sketch for Seurat is mentioned as follows  = , but it remains unclear how to select .An apparent limitation of Seurat is that it needs four tuning parameters. Following the recommendations by K groups by applying the classical hierarchical clustering method to the consensus matrix. SC3 uses one tuning parameter x0 in the gene-filtering step and two tuning parameters, d0 and k0, in the clustering step, corresponding to the PCA part and the hierarchical clustering part, respectively.SC3 was first presented by n \u00d7 p data matrix X, true number of clusters K, and tuning parameters x0, d0, k0. Output: predicted class label vectors x0% of cells or expressed  in at least (100 \u2212 x0)% of cells. This step may reduce a significant fraction of features, and we consider it to be more like a feature selection step than a preprocessing step.\u2022 (Gene-filtering step). Removes genes/transcripts that are either expressed  in less than n \u00d7 n matrix M, where M is some kind of distance  between subject i and j. Second, let kth singular vector of M . Third, for d = 1, 2, \u2026 , d0, we cluster all n subjects to K classes by applying the k-means to the rows of the n \u00d7 d sub-matrix of d columns and use the results to build a consensus matrix using the Cluster-based Similarity Partitioning Algorithm (CSPA) (k0 levels of hierarchy.\u2022 (Clustering step). First, we take a log-transformation of the post-filtering data matrix and construct an m (CSPA) . FinallyA high-level sketch for SC3 is given as follows  =  and take k0 to be the true number of clusters K. Such a tuning parameter choice may work effectively in some cases, but for more general cases, we may , IF-VAE, and IF-VAE(X)) have never never proposed before. Among these methods, the VAE is a popular UDL approach, Seurat and SC3 are especially popular in clustering with single-cell data, and IF-PCA is a conceptually simple method that has been shown to be effective in clustering with gene microarray data. It is important to note that some of the methods are conceptually similar to each other, with some small differences . For example, many of these methods are two-stage methods, containing an IF step and a clustering step. In the IF step, we usually use the normalized data matrix https://github.com/ZhengTracyKe/IFPCA. The 10 microarray data sets can be downloaded at https://data.mendeley.com/datasets/cdsz2ddv3t, and the eight single-cell RNA-seq data sets can be downloaded at https://data.mendeley.com/drafts/nv2x6kf5rd.Our study consists of two parts. In X or the normalized data matrix W. The version of IF-PCA associated with X is called IF-PCA(X), and the version associated with W is still called IF-PCA; similar rules apply to the VAE and IF-VAE. A total of eight different algorithms were obtained.First, we compare the IF-VAE approach introduced in K clusters) of these methods. The results of SpecGem and IF-PCA are copied from d = 25 and use a traditional architecture in which both the encoder and decoder have one hidden layer; the encoder uses the ReLU activation, and the decoder uses the sigmoid activation; when training the encoder and decoder, we use a mini-batch stochastic gradient descent with 50 batches, 100 epochs, and a learning rate of 0.0005. The same neural network architecture and tuning parameters are applied to the VAE. We note that the outputs of these methods may have randomness due to the initialization in the k-means step or in the VAE step. For the VAE, IF-VAE, and IF-VAE(X), we repeat the algorithm 10 times and report the average clustering error. For k-means, we repeat it five times (because the results are more stable); for IF-PCA(X), we repeat it 20 times. We use the clustering errors to rank all eight methods for each data set; in the presence of ties, we assign ranks in a way such that the total rank sum is 36 . The average rank of a method is a metric of its overall performance across multiple data sets. In addition to ranks, we also compute regrets: for each data set, the regret of a method is defined to be r = (e \u2212 emin)/(emax \u2212 emin), where e is the clustering error of this method and emax and emin are the maximum and minimum clustering error, respectively, among all the methods. The average regret also measures the overall performance of a method .W or on X), which combines k-means with non-linear dimension reduction, significantly improves k-means on some \u201cdifficult\u201d data sets, such as BreastCancer, ColonCancer, and SuCancer. However, for those \u201ceasy\u201d datasets, such as Leukemia and Lymphoma, the VAE significantly underperforms compared to k-means. It suggests that the non-linear dimension reduction is useful mainly on \u201cdifficult\u201d datasets. Third, the IF-VAE (either on W or on X) improves the VAE in the majority of data sets. In some datasets, such as LungCancer (1), the error rate of the IF-VAE is much lower than that of the VAE. This observation confirms that the IF step plays a key role in reducing the clustering errors. There are several notable observations. First, somewhat surprisingly, the simple and tuning-free method, IF-PCA, has the best overall performance. It has the lowest average rank among all eight methods and achieves the smallest number of clustering errors in four out of 10 data sets. We recall that the key idea of IF-PCA is to add a tuning-free feature selection step prior to dimension reduction. The results in m, we select the m top-ranked features, perform VAE on the unnormalized data matrix X restricted to these m features, and report the average number of clustering errors over five repetitions of the VAE. m. An interesting observation is that as m increases, the clustering error first decreases and then increases . A possible explanation is as follows: when m is too small, some influential features are missed, resulting in weak signals in the VAE step; when m is too large, too many non-influential features are selected, resulting in large noise in the VAE step. There is a sweet spot between 200 and 400, and the tuning-free procedure in the IF step selects m = 251. Next, we study IF-VAE(X) more carefully with the LungCancer (1) data set. We recall that the IF step ranks all the features using KS statistics and selects the number of features by a tuning-free procedure. We use the same feature ranking but manually change the number of retained features. For each Remark 1 (comparison with other clustering methods for microarray): https://hemberg-lab.github.io/scRNA.seq.datasets). It contains scRNA-seq datasets from Human and Mouse. Among them, we selected eight datasets that have a sample size between 100 and 2,000 and can be successfully downloaded and pre-processed using the code provided by the Hemberg Group under the column \u2018Scripts\u2019. The datasets Camp1, Camp2, Darmanis, Li, and Patel come from Human, and the data sets Deng, Goolam, and Grun come from Mouse. Each data matrix contains the log-counts of the RNA-seq reads of different genes (features) in different cells (samples). The cell types are used as the true cluster labels to evaluate the performances of clustering methods. We first pre-processed all the data using the code provided by the Hemberg Group, then features (genes) with fractions of nonzero entries m is the number of selected features, N is the number of principal components in use, k0 is the number of clusters in k-nearest neighbors, and \u03b4 is a \u2018resolution\u2019 parameter. We fix  =  for all datasets  are the default ones; the default value of m is 2,000, but we found that m = 1,000 gives the same results with the eight data sets and is faster to compute). We choose a separate value of \u03b4 for each dataset in a way such that the resulting number of clusters from a modularity optimization is exactly K . We fix  fails in this case, where the error rate is approximately the same as that of random guess. The proof of Next, we study the performance of classical PCA and IF-PCA. However, before we perform that, we present a lemma on classical PCA in Suppose we have a data matrix \u03be is the first singular vector of X. By basic algebra, it is the first eigenvector of the N \u00d7 N matrix XX\u2032, or equivalently, the first eigenvector of XX\u2032 \u2212 mIN. We write\u03bc\u20162YY\u2032 should be much larger than that of (ZZ\u2032 \u2212 mIN). It is important to note that \u2016\u03bc\u20162YY\u2032 is a rank-1 matrix, where the spectral norm is N\u2016\u03bc\u20162. In addition, by random matrix theory (ZZ\u2032 \u2212 mIN) concentrates at In such a setting, we investigate when the PCA approach in x theory , the speWe have the following lemma.Lemma 4.1\u03bc\u20162 \u226b log(N + m). Let \u03be be the first left singular vector of X. When min{N, m} \u2192 \u221e, with probability 1 \u2212 o(m\u22123),Here, we consider Model r with \u2016r\u2016\u221e = o (1) such thatBy Therefore, if we let This says that the PCA approach can fully recover the true class labels.We now come back to Models \u03c72-test is feasible. As mentioned before, let\u03c72-testing scores and recall that approximately,We first discuss when feature selection by \u03c72-test for a useful feature. We have two cases.\u03b2 < 1/2). In this case, the number of useful features sp is much larger than \u03c8j for a useful feature j may be much smaller than 1, even though \u03c72-test is not useful. Consequently, except for a negligible probability, the IF step of IF-PCA selects all features, so IF-PCA reduces to PCA.\u2022 (Less sparse case of \u03b2 > 1/2). In this case, the number of useful features sp is much smaller than \u03c8j \u2192 \u221e if j is a useful feature. In such a case, feature selection maybe successful and IF-PCA is significantly different from PCA.\u2022  =  and noting that in this setting,Consider the first case and suppose we apply the PCA approach in Comparing this with the definition of We have the following theorem.Theorem 4.2Region for PCA). We fix  \u2208 2 and consider the clustering problem for Models p \u2192 \u221e, if.(Possibility \u03b2 < 1)Consider the second case, where we may have successful feature selection, so it is desirable to use IF-PCA. We assumeS(\u03bc) is the true support of \u03bc andWe recall that j, the SNR isBy , for any useful feature By elementary statistics, we have that approximately,\u03bcS is the sub-vector of \u03bc with all entries restricted to S, and XS and ZS are the sub-matrices of X and Z respectively, with columns restricted to S. Therefore, in the clustering step of IF-PCA, we are, in effect, applying the PCA approach of XS, where we recall |S|/sp \u2248 1. Applying N, m) =  and noting thatTherefore, except for a negligible probability,Combining this with Comparing this with the definition of Theorem 4.3Region for IF-PCA). We fix  \u2208 2 and consider the clustering problem for Models p \u2192 \u221e, if partitions the region {: 0 < \u03b2 < 1, \u03b1 > 0} into two regions.Impossibility {: \u03b1 > \u03b1*, 0 < \u03b2 < 1}. In this region, the Hamming clustering error rate of any method with polynomial computation time is bounded away from 0.\u2022 Region of Possibility {: \u03b1 < \u03b1*, 0 < \u03b2 < 1}. The region further partitions into two parts: \u03b2 < 1/2 (left) and \u03b2 > 1/2 (right).\u2022 Region of less sparse case where the number of useful features \u03b1, \u03b2) in this region, the Hamming error rate of PCA is o(1), so PCA achieves the optimal phase transition. In addition, in this case, the signals are too weak individually and feature selection is infeasible. Therefore, in the IF step, the best we can do is to select all features, so IF-PCA reduces to PCA.\u2022 The left is the \u03b1, \u03b2) in this region, the Hamming error rate of IF-PCA is o(1), so IF-PCA achieves the optimal phase transition. In addition, in this case, the signals are strong enough individually and feature selection is desirable. Therefore, IF-PCA and PCA are significantly different.\u2022 The right is the more sparse case, where the number of useful features \u03b2 < 1, (1 \u2212 \u03b8 \u2212 2\u03b2) < \u03b1 < (1 \u2212 \u03b2)/2} (shaded green region of o (1), but that of PCA is bounded away from 0. Therefore, PCA is non-optimal in this particular region.\u2022 In particular, for any fixed parameters in the region {1/2 < We fix 0 < See IF-PCA is a simple and tuning-free approach to unsupervised clustering of high-dimensional data. The main idea of IF-PCA is a proper combination of feature selection and dimension reduction by PCA. In this study, we make several contributions. First, we extend IF-PCA to IF-VAE, by replacing PCA with the VAE, a popular UDL algorithm. Second, we study the theoretical properties of IF-PCA in a simple clustering model and derive the phase transitions. Our results reveal how the feature sparsity and the feature strength affect the performance of IF-PCA and explain why IF-PCA can significantly improve the classical PCA. Third, we investigate the performances of IF-PCA and IF-VAE on two applications, the subject clustering with gene microarray data and the cell clustering with single-cell RNA-seq data, and compare them with those of some other popular methods.X instead of the normalized data matrix W. On the eight single-cell RNA-seq data sets considered in this paper, IF-PCA(X) has the second-best accuracy in almost all the data sets, showing a stable performance across multiple data sets. We think IF-PCA has significant potential for single-cell clustering, as the method is simple, transparent, and tuning-free. Although the current IF-PCA(X) still underperforms compared to the state-of-the-art methods  in some data sets, it is hopeful that a variant of IF-PCA  can outWe also find that UDL algorithms do not immediately yield improvements over classical methods with the microarray data and the single-cell data. The IF-VAE underperforms compared to IF-PCA in most data sets; there are only a few data sets in which the IF-VAE slightly outperforms IF-PCA. The reason can be either that non-linear dimension reduction has no significant advantage over linear dimension reduction in these data sets or IF-VAE is not optimally tuned. How to tune the deep learning algorithms in unsupervised settings is an interesting future research direction. Moreover, the theory on the VAE remains largely unknown . A theorThe framework of IF-PCA only assumes feature sparsity but no other particular structures on the features. It is possible that the features are grouped  or have K, is given. When K is unknown, how to estimate K is a problem of independent interest. One approach is to use the scree plot. For example, K. Another approach is based on global testing. Given a candidate K, we may first apply a clustering method with this given K and then apply the global testing methods in K such that the global null hypothesis is accepted in all estimated clusters. In general, estimating K is an independent problem from clustering. It is interesting to investigate which estimators of K work best for gene microarray data and single-cell RNA-seq data, which we leave to future work.In the real data analysis, we assume that the number of clusters,"}
+{"text": "G be a finite group, let H be a core-free subgroup and let b denote the base size for the action of G on G/H. Let H of G with G is a strongly base-two group if G has base size 2. In this paper, we study the strongly base-two finite groups with trivial Frattini subgroup.Let  H. A subset B of base for G if the pointwise stabilizer of B in G is trivial. We write b for the base size of G, which is the minimal size of a base for G. Here H is a core-free subgroup of G and b is the smallest positive integer b with the property thatG is a base-two permutation group if Let The base size of a finite permutation group is a classical invariant that has been studied for many decades, finding a wide range of applications and connections to a diverse range of problems in group theory and related areas  such that G on G/H. We call G a strongly base-two group if Let H is a proper subgroup, then  for an unspecified solvable group of order n. We adopt the standard notation for simple groups of Lie type from . As in the above analysis of case (II), we may assume that L. Since H,\u00a0W], say Let G in Theorem 6.4 with A, with the Sylow 2-subgroup of L acting faithfully on L acting as scalars on G is isomorphic to Let us consider the groups Suppose L is abelian and every subgroup of F(G) is normal in G. Now apply Corollary 3.11.Since By combining Theorems 6.1, 6.2, 6.4 and 6.6, we obtain the following corollary.G is solvable and either Suppose G is a finite group with In this section, we prove Corollaries 5 and 6. As usual, we assume :L as in .Corollary 5\u00a0\u00a0Let G be a finite nonsolvable group. If G has the form given in part (i) of the corollary (note that the possibilities for T are recorded in Theorem 2).c(G) and r(G) as before. Since G is nonsolvable, it follows that L and S is an abelian 2-group. In particular, G is solvable and so we may assume G is nonsolvable.Now assume Now let us turn to Corollary 6. We first establish a more general result on regular orbits.L has no regular orbit on F(G). Then P and trivially on Q. In particular, Suppose F(G) contains an involution and so L does not have a regular orbit on F(G). For the remainder, let us assume L has no regular orbit on F(G).Clearly if p be an odd prime and set R has a regular orbit on R is abelian, so let us assume R is nonabelian. This implies that R as a subgroup of O(R) is cyclic and the Sylow 2-subgroup of R is abelian. Since we are assuming R| is indivisible by p. This implies that either R acts imprimitively on R acts primitively and is contained in the normalizer of a nonsplit maximal torus.First assume (a) holds and write R-invariant and we claim that R has a regular orbit on the remaining y acts trivially on a unique line. It follows that R has no regular orbit on R contains all such involutions. However, the group generated by these involutions has a nonabelian Sylow 2-subgroup, a contradiction.Let N that act trivially on a line are involutions in R has no regular orbit, then all such involutions must be in R and once again we reach a contradiction since the Sylow 2-subgroup of the group generated by these involutions is nonabelian. This justifies the claim.A very similar argument applies in case (b). Here L acting trivially on Q. By the previous claim, p, so there exists K acts faithfully on K does not have a regular orbit. Since K is normal in L, and since K is its own automorphism group, we deduce that Now write L has no regular orbit on F(G). Then A is an abelian group of odd order.Suppose L does not have a regular orbit on F(G), it follows that G has the prescribed form, then it is easy to see that L is the only core-free subgroup H of G (up to conjugacy) with Since L has a subgroup H and L are conjugate and thus A is a complement to F(G). Therefore, A is abelian and we note that A| is even, so the hypothesis A| is odd.To complete the proof, suppose p.We will also need the following proposition, which handles a family of groups with a primitive permutation representation of degree (i)If (ii)L is abelian. Then Suppose (iii)L is nonabelian and acts imprimitively on F(G). Then r is an odd prime divisor of Suppose (iv)L is nonabelian and acts primitively on F(G). Then Suppose Let p is odd and H is a nontrivial core-free subgroup of G. If L has a regular orbit on F(G) by Proposition 7.1. In particular, if p.The result is clear if L| is indivisible by p. In particular, F(G) in G are conjugate. Let L.Since L is abelian and let D be a subgroup of order p. Then Z has composite order. On the other hand, if Z has prime order, so L/Z acts regularly on the set of order p subgroups of F(G), in which case L fixes a line, this implies that L is cyclic of order Z is the stabilizer of any line, this forces First assume L is nonabelian. We divide the analysis according to whether or not L acts imprimitively (as a linear group) on F(G).For the remainder we may assume L acts imprimitively on F(G). Then L has a normal abelian subgroup L, then clearly F(G) fixed by L. This observation, together with the fact that r and we deduce that (iii) holds. Here it is straightforward to see that the only core-free subgroups H of G with First assume L is nonabelian and primitive on F(G). Since L is contained in the normalizer of a nonsplit torus in L has an abelian subgroup Now let us assume L is a dihedral group and |L| divides L has order at most 2. Since the involutions in L are self-centralizing, we deduce that the stabilizer of a pair of conjugate lines is trivial and thus H of G. In particular, we conclude that If Z has prime order and L/Z acts regularly on the set of lines of F(G), so D\u00a0:\u00a0Z is a maximal core-free subgroup of G for any subgroup D of order p, so Z must be the stabilizer of every line in F(G). Since L has even order, this implies that L must be in Z and no element in L of order 4 fixes a line. Therefore, the Sylow 2-subgroup of L is cyclic of order 4 and thus Now assume Corollary 6\u00a0\u00a0\u00a0\u00a0Let G be a finite group with socle N and a core-free maximal subgroup. Then S and positive integer d. If S is nonabelian, then Theorem 3 implies that F(G) is the unique minimal normal subgroup of G.If Finally, let us assume r(G) denotes the maximal rank of a minimal normal subgroup of G. Since G has rank 1 or 2. As usual, write In this final section, we consider the strongly base-two groups with :L as in .H of F(G) with H, which means that Recall that if We have already handled several special cases in this setting. For instance, the nonsolvable strongly base-two groups were determined in Corollary 5, while the examples with a core-free maximal subgroup are recorded in Corollary 6. The latter result shows that we can find groups with O(L) be the largest odd order normal subgroup of L. Then O(L) is abelian and S. Note that the condition G has a minimal normal subgroup G acts as a nonabelian group, then For the remainder, let us assume L has a regular orbit on F(G). As a consequence, it is straightforward to show that there are no core-free subgroups H of G such that In view of Corollary 7.2, we may assume that L has odd order.The following result gives necessary and sufficient conditions for (i)L has a regular orbit on F(G).(ii)H is a core-free subgroup of F(G), then If (iii)L does not contain a subgroup G-module.Each y acts as a nontrivial scalar on each G-module and y acts nontrivially on G.(iv)L does not contain a subgroup G-module, and J acts faithfully on U.Suppose H of G contained in F(G).The necessity of (i) is clear . Set Y be the normal closure of L. Note that each nontrivial element of Y either acts as a scalar on each G and acts trivially on Y normalizes U and we deduce that VY is the normal closure of G. Since Let us assume there exists an element J as in (iv). Let G and set VJ is the normal closure of H. Then Now suppose that there exists a subgroup H be a maximal core-free subgroup of G with X is a nontrivial proper subgroup of H by conditions (i) and (ii). Let V be the normal closure of X and write H.We have now shown that if L on L of order H acts completely reducibly on Suppose L-module) is either reducible, or irreducible and primitive, then the intersection of the stabilizers of distinct L-conjugate lines in L on L-invariant just consists of scalars). On the other hand, if L-orbit, or the intersection of the stabilizers consists of scalars. By (ii), we can choose i, which implies that h acts as a scalar on L-module and h stabilizes each of the two lines permuted by L. If we now write W is a normal subgroup of G, then there are two cases to consider.Next observe that if W, which means that W and acts as a scalar on each First assume that W. By Proposition 7.1, this implies that U . Then by arguing as in the previous paragraph, we see that V. This contradicts (iv) and completes the proof.Now suppose that J is normal in L. This is clear in case (iv) and indeed we note that y acts as a scalar on each y is central in L and thus y is not central in L. Then G-module. Let Y be the normal closure of L. If Y and so L acts on Y as an elementary abelian 2-group. In particular, Y is a completely reducible L-module with 1-dimensional summands and therefore we can choose L.Let us note that we may modify conditions (iii) and (iv) in Theorem 8.2 so that the subgroup By inspecting the proof of Theorem 8.2, together with the relevant proofs in Sections\u00a0G be a finite group with H of G with N is the normal closure of H in G.Let H of G contained in F(G).The next result shows that F(G) contains a core-free subgroup H of G with Suppose H is a maximal core-free subgroup of G. In particular, K is a proper subgroup of H, then Seeking a contradiction, let us assume H in G and write L on Let L acts imprimitively on L-orbit of i, it follows that H and U are L-conjugate and so there is some element i. But this gives First assume that y acts trivially on y stabilizes y centralizes Finally, suppose i, it follows that x must normalize Let To conclude, let us briefly explain how one can use Theorem 8.2 and Proposition 8.5 to analyze the groups with H represents the unique conjugacy class of core-free subgroups of G with H must intersect F(G) nontrivially, but it cannot be contained in F(G). Furthermore, there exists a normal subgroup J of L, as described in parts (iii) or (iv) of Theorem 8.2 (see Remark 8.3). Then First observe that if C of G ].Now F(G) has a subgroup L-module, then G. Therefore, in case (iii) we may assume that y acts as a scalar on each G has no imprimitive minimal normal subgroups. We leave the task of describing the precise structure of the groups with For example, if"}
+{"text": "Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen\u2013Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods\u2014whose complexity does not scale up with the dimension\u2014for generating such non-Kochen\u2013Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure. Quantum contextuality, which precludes assignments of predetermined values to dense sets of states, has found applications in quantum communication ,2,3, quaThere are three classes of contextual sets elaborated on in the literature which are not of the more common kind of Kochen\u2013Specker (KS) sets ,33,34 anThe first class consists of the operator-based state-independent contextual (SIC) sets put forward by Klyachko et al. , Yu and n vectors, where n is the dimension of space in which a hypergraph resides [The second class consists of hypergraphs built by multiples of mutually orthogonal vectors where at least one of the multiples contains less than  resides ,34,41.The third class consists of the so-called true-implies-false and true-implies-true sets ,43.All sets from these three classes as well as their hypergraph generalization that we elaborate on are contextual, and therefore, we call them non-KS contextual\u00a0sets.We provide a general method for arbitrarily generating many non-KS hypergraphs in spaces of up to 16-dim. In\u00a0order to achieve these goals, we make use of non-binary non-KS McKay\u2013Megill\u2013Pavi\u010di\u0107 hypergraphs (MMPHs) and their language. By\u00a0means of our algorithms and programs, we arbitrarily obtain many MMPHs, which can be used for various applications, e.g.,\u00a0to generate new entropic tests of contextuality or new operator-based contextual\u00a0sets.The paper is organized as\u00a0follows.n-dim space correspond to vectors and their orthogonalities, i.e.,\u00a0m-tuples  lines passing through them.Definition\u00a02.An n-dim non-binary MMPH (NBMMPH),  [is an MMPH 1 s and 0 s in such a way\u00a0thatfor which each hyperedge contains m vertices, 1.\u00a0No two vertices within any of its edges are both assigned a value of 1;2.\u00a0In any of its edges, not all of the vertices are assigned a value of 0.H), n\u22653,  is an MMDefinition\u00a03.An NBMMPH in which  KS MMPH.For  theorem ,34,45,46Definition\u00a04.An NBMMPH in which  non-KS MMPH.In this paper, we consider only those non-KS MMPHs for which Definition\u00a05.An n-dim binary MMPH (BMMPH),  MMPH for which each hyperedge contains m vertices, 1.\u00a0No two vertices within any of its edges are both assigned a value of 1;2.\u00a0In any of its edges, not all of the vertices are assigned a value of 0.Definition\u00a06.A non-KS NBMMPH to which vertices are added so as to make the number of vertices equal to n in every hyperedge is called a filled MMPH.Filled MMPHs are mostly\u00a0BMMPHs.Definition\u00a07.A critical NBMMPH is an NBMMPH that is minimal in the sense that removing any of its hyperedges turns it into a BMMPH.Definition\u00a08.Vertex multiplicity is the number of hyperedge vertexes \u201ci\u201d belongs to; we denote it by Definition\u00a09.A master is a non-critical MMPH that contains smaller critical and non-critical sub-MMPHs. A\u00a0collection of sub-MMPHs of an MMPH master forms its class.parity proof ofthe contextuality of a k-l NBMMPH with odd l and where each vertex shares an even number of edges stems from its inherent contradiction: because each vertex shares an even number of hyperedges, there should be an even number of hyperedges with 1 s. At\u00a0the same time, each edge can contain only one 1 by definition, and\u00a0since there are an odd number of hyperedges in the MMPH, there should also be an odd number of edges with 1 s.A Definition\u00a010.A coordinatization of a non-KS NBMMPH is a set of vectors assigned to its vertices that is a subset of n-dim vectors in  MMPH or its smallest master (they need not coincide) or any of its masters.n-tuple of orthogonal vectors, while a \u201ccoordinatization\u201d of each hyperedge of the original non-KS NBMMPH is represented by a vector m-tuple  or any its masters. In our present approach, a\u00a0coordinatization is automatically assigned to each hypergraph by the very procedure of its generation from master MMPHs, as we show\u00a0below.In other words, a\u00a0\u201ccoordinatization\u201d of each hyperedge of a filled MMPH or a smallest master MMPH is represented by an k vertices and l edges is denoted as a k-l MMPH. ASCII string representation is used for computer processing. MMPH strings are handled by means of algorithms embedded in the programs SHORTD, MMPSTRIP, MMPSUBGRAPH, VECFIND, STATES01, and others [An MMPH is encoded with the help of printable ASCII characters, with the exception of \u201cspace\u201d, \u201c0\u201d, \u201c+\u201d, \u201c,\u201d and \u201c.\u201d, organized in single strings; its hyperedges are separated by commas, and each string ends with a period. When all ASCII characters are exhausted, one reuses them prefixed by \u201c+\u201d, and then again by \u201c++\u201d, and\u00a0so forth. An\u00a0MMPH with d others ,49,50,51To generate non-KS NBMMPHs, we make use of the following\u00a0methods.M1 consists of dropping vertices contained in single hyperedges (multiplicity ity m=1)  of eitheM2 consists of a random addition of hyperedges to MMPHs so as to obtain bigger ones, which then serve us to generate smaller non-KS NBMMPHs by stripping hyperedges randomly again;M3 consists of the random deletion of vertices in either NBMMPHs or a BMMPHs until a non-KS NBMMPH is reached.We combine all three methods to obtain an arbitrary number of non-KS NBMMPHs in an arbitrary dimension. The methods rely on the property of MMPHs where, by stripping an MMPH or\u00a0NBMMPH  or\u00a0BMMPH of its hyperedges, we can arrive at smaller non-KS NBMMPHs in contrast to a critical KS NBMMPH whose stripping of hyperedges can never yield another  NBMMPH.k-l MMPHs refer to hypergraphs with k vertices and l hyperedges (Definition 1), while the corresponding graphs have more than l edges. For example, in\u00a0ALK corresponds to a graph clique with three edges: AL, LK, and\u00a0KA.In M1. The\u00a013-16 MMPH is not critical, and it contains four critical sub-MMPHs, the smallest of which is 10-9 [Yu-Oh\u2019s three-dim non-KS NBMMPH, shown in  is 10-9 .Howard, Wallman, Veitech, and\u00a0Emerson\u2019s four-dim 30-108 non-KS NBMMPH, shown in Cabello, Portillo, Sol\u00eds, and\u00a0Svozil\u2019s five-dim 10-9 non-KS NBMMPH, shown in Our methods can generate NBMMPHs that are critical as well as those that are not. Therefore, although\u00a0none of the aforementioned examples are critical, we focus on critical ones, because they offer the simplest implementation and presentation. The\u00a0rationale for adopting such an approach is that only minimal contextual sets, i.e.,\u00a0critical NBMMPHs, are relevant for experimental implementations, since their supersets just contain additional orthogonalities that do not change the contextuality property of their smallest critical set. Hence, while designing MMPHs for particular implementations, we should attempt to find the ones that are critical and are provided via automated generations of\u00a0MMPHs.M1 and M2. Therefore, below,\u00a0we give distributions and samples of just four- and five-dim critical non-KS NBMMPHs presented in n vertices (n being the dimension of the considered MMPH), none of which has the multiplicity In , we giveM1, we first generate the supermasters from the vector components. In\u00a0the four-dim space, we obtain the 24-24 supermaster from the To obtain non-KS NBMMPHs via n-dim critical non-KS MMPHs under the requirement that at least one of their hyperedges must contain n vertices, of which none have a multiplicity of 1 , because We generate Cabello, Portillo, Sol\u00eds, and\u00a0Svozil also give a number of minimal six-dim TIFS non-KS NBMMPHs in . In\u00a0dimensions greater than nine, such vertices do not appear, although even here we can avoid their generation by applying M3 to KS NBMMPHs, as shown in In the seven-dim space, masters obtained from simple vector components, such as M1. However, the\u00a0MMPHs with M3, as shown in M3.The eight-dim MMPH master is big (2768-1346016), but the stripping technique can still provide us with non-KS NBMMPHs via riticals  so as toM1 applicable. Thus, after\u00a0the random stripping of 12,068,200 hyperedges, we obtained submasters with 505 hyperedges. By requiring that at least one of the hyperedges contains n vertices and that some of them can have the multiplicity 4ac7efhK2 contains nine vertices.  The filled 13-16, i.e., 44-6, also shown in M2 inapplicable.The nine-dim NBMMPH master obtained from n-vertex requirement in full If we wanted to keep our pscaling ,56, as fM3. The\u00a0procedure consists of removing vertices and/or hyperedges in such a way that an NBMMPH stops being critical, which enables us to generate smaller critical non-KS NBMMPHs from it via\u00a0STATES01.A 10-dim or any higher-dimensional masters are too big to be generated from vector components. Therefore, to obtain the non-KS MMPH in those dimensions, we rely on minimal KS NBMMPHs obtained via dimensional upscaling  while apIn In M3.In the following sections, we stay with this approach while applying n vertices, none of which has the multiplicity It has been proven that the minimal complexity  of the dimensional upscaling of KS MMPHs does not scale up with dimension . In\u00a0 5656, we giIn this paper, we first generated non-KS contextual NBMMPHs (non-binary MMP hypergraphs) with the help of master sets generated from simple vector components whose complexity exponentially scales with dimension\u2014for dimensions four to eight\u2014and then by means of methods whose complexity does not scale with dimension. The\u00a0need for developing such methods and obtaining MMPHs in higher dimensions has emerged from recent elaborations of classes of contextual sets that are not of the KS kind, all of which have an MMP hypergraph representation. Examples of such elaborations in the literature and their correspondence with MMPHs are given in In Therefore, to ensure arbitrarily exhaustive generation of MMPHs in ever higher dimensions, we need a method whose complexity does not grow with the dimensions. For\u00a0comparatively small KS MMPHs, such a method\u2014dimensional upscaling\u2014was recently developed in  based onhttp://puh.srce.hr/s/Qegixzz2BdjYwFL (accessed on 22 July 2023). MMPHs can be visualized via hypergraph figures consisting of dots and lines and represented as a string of ASCII characters. The\u00a0latter representation enables the processing of billions of MMPHs simultaneously via supercomputers and clusters. For\u00a0the latter elaboration, we developed other dynamical programs specifically to handle and parallelize jobs with arbitrary numbers of MMP hypergraph vertices and\u00a0edges.The methods used to handle quantum contextual sets rely on algorithms and programs within the MMP language: VECFIND, STATES01, MMPSTRIP, MMPSHUFFLE, SUBGRAPH, LOOP, and\u00a0SHORTD developed in ,51,57,58To summarize, based on elaborations of non-KS sets that recently appeared in the literature and of which we provided several examples in"}
+{"text": "Correction: Mol Cancer 18, 82 (2019)https://doi.org/10.1186/s12943-019-1016-0https://doi.org/10.18632/oncotarget.18204) are indeed the same and this image belongs to the \u2018si-NC of NOZ/Dox\u2019. During that time, we were working on several projects simultaneously and the error should be occurred in the data storage. And we had contacted the editorial office of Oncotarget to explain and correct this error.After receiving the comment, we have carefully re-checked the raw data and confirmed the error in Fig.\u00a04A. The two images of \u2018si-NC of NOZ/Dox\u2019 in Fig.\u00a04A in this article and the \u2018si-NC of NOZ\u2019 in Fig.\u00a06C in our other article in Oncotarget (Besides, in order to make sure no further problems will be pointed out after the correction of this time, we have self-examined all the raw data of all the projects conducted simultaneously during that time for article . And we"}
+{"text": "Retraction Note: BMC Cancer 19, 224 (2019)10.1186/s12885-019-5419-5The Editors have retracted this article because of significant concerns with a number of figures, specifically:Figure\u00a07d, CD133 panel, appears to be the same as Fig.\u00a02D, Oct 4 panel, in [Figure\u00a04b, FAP-a panel, appears to be the same as Fig.\u00a03D, p53 panel, in Figure\u00a03a, b-actin panel, appears to be the same as Fig.\u00a03K, b-actin panel, in [The authors were contacted and asked for an explanation but did not provide one. The Editors therefore no longer have confidence in the integrity of the data in this article.Kai-qun Ren agrees with the retraction. None of the other authors have responded to any correspondence from the Editors about this retraction."}
+{"text": "In the published article, there was an error in the article title. Instead of \u201cSARS-CoV-2 antibody response after mRNA vaccination in healthcare workers with and without previous COVID-19, a follow-up study from a university hospital in Poland during 6 months 2021\u201d, it should be \u201cSARS-CoV-2 antibody response after mRNA vaccination in healthcare workers with and without previous COVID-19, a follow-up study from the University Hospital in Krakow, Poland\u201d.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated."}
+{"text": "Nature Communications 10.1038/s41467-023-36884-4, published online 01 March 2023Correction to: The original version of this Article contained an error in Fig. 1, in which panel b was missing, and panels c\u2013e were incorrectly labelled as b\u2013d respectively. The correct version of Fig. 1 is:which replaces the previous incorrect version:This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Nature Ecology& Evolution 10.1038/s41559-023-02058-0. Published online 18 May 2023.Correction to: x-axis label order: \u201cPhloem\u201d and \u201cBlood,\u201d in the second and third positions, respectively, were accidentally reversed. The labels have been corrected in the HTML and PDF versions of the article.In the version of this article originally published, there was an error in the Fig. 1c"}
+{"text": "The developed method has been motivated by laboratory tracer experiments. To investigate the kinetic properties and behavior of a substance of interest, we computationally label this species in order to track it throughout its life cycle. The corresponding mathematical model is extended by an additional set of reactions for the labeled species, avoiding any double-counting within closed circuits, correcting for the influences of upstream fluxes, and taking into account combinatorial multiplicity for complexes or reactions with several reactants or products. A profile likelihood approach is used to estimate confidence intervals on the label half-life and transit-time.Mathematical models of dynamical systems facilitate the computation of characteristic properties that are not accessible experimentally. In cell biology, two main properties of interest are (1) the time-period a protein is accessible to other molecules in a certain state - its half-life - and (2) the time it spends when passing through a subsystem - its transit-time. We discuss two approaches to quantify the half-life, present the novel method of Application to the JAK-STAT signaling pathway in Epo-stimulated BaF3-EpoR cells enabled the calculation of the time-dependent label half-life and transit-time of STAT species. The results were robust against parameter uncertainties.http://www.potterswheel.de).Our approach renders possible the estimation of species and label half-lives and transit-times. It is applicable to large non-linear systems and an implementation is provided within the PottersWheel modeling framework ( The second one, the label transit-time, is the time-period it takes for a fraction of labeled entities to pass through a subsystem of the network. Both quantities are calculated using a novel approach called in silico labeling, which is also introduced in the present work.An increasing number of biological phenomena are described by mathematical models, specifically on the basis of biochemical reaction networks ,2. The din silico labeling approach, where an additional set of reactions is added to an existing mathematical model describing the kinetic behavior of a tracer, called the label. In contrast to real tracer experiments, the in silico method offers the opportunity to define dead-ends, avoid double-counting of cycling label, and to restrict the label to a sub-network of reactions. This allows asking specific questions about the original system, like how long it takes for 50% of the molecules of a substance to travel along a certain path, while in reality an alternative path may exist. In addition, predominant paths can be identified in deterministic models as has been done previously for stochastic systems  \u2250 ix. The time-profile of each species can then be calculated for given initial values ku(t). The flux j vof reaction j may be a non-linear function of one or more species concentrations i xand externally defined ku. To improve readability, we omit explicitly denoting the time-dependency, i.e. ix(t) is rather written as ix.Here, i xof interest is determined by extending the differential equation network (4) by one equation for an artificial quantity y depending only on the outfluxes of ix,The half-life of a species i xis given by T1/2 for whichwith initial value t0. In a numerical integration, it is important to limit the maximum integrator step size for an accurate approximation of the y0/2 threshold crossing.Note that a half-life characterizes the decay of a quantity, independent of any production rates. Therefore, all influx contributions are neglected in equation (5). In general, only linear processes possess a constant half-life. Otherwise, the half-life depends on the initial concentration i xis only partially related to the time it takes for 50% of an experimental tracer to leave the source pool. The two values coincide if i xhas either no influx or when the outflux from i xis described by a linear process, which will be proved in the next two subsections. Therefore, we suggest the in silico labeling half-life as a means to determine a time-characteristic which is motivated by laboratory tracer experiment with the additional property to avoid tracer-double counting in kinetic cycles.The half-life of a species x \u2208 {x1, . . . , mx} is consumed only in one reaction. In in silico labeling, the flux of the corresponding label z depends on the outflux of x byFor simplicity, we assume that the species of interest in silico labeling half-life of x is defined as the time when z drops to z0/2. We will show that this time equals the species half-life of x if its influx in vis zero. This property is independent from the amount of initially labeled entities, i.e. it holds for any z0/x0 \u2208 \u211d+:The Proof:x be determined by the processing with an unknown, potentially non-linear outflux out vand no influx in v= 0, i.e. v = outv,Let z(t) is given byThen, the kinetics of the label species It can be shown that the factor t = 0, the proportionality constant is given by Since this relation holds also true for x(t) and z(t) share the same half-life T1/2, sinceBoth processes in v\u2260 0, because the fraction z/x becomes time-dependent as the labeling gets diluted, except for linear outfluxes as shown in the next section.This relation does not hold for processes with x which is produced by an unknown, potentially non-linear influx in vand is consumed by a linear process.In this section, we prove that the label half-life coincides with the half-life of a species Proof:in vand a linear outflux, kx,Let x can be determined viaThen, the analytical half-life of z it holds thatFor the labeled system i xbelong to the group of tracked, i.e. potentially labeled entities. Let us assume that they are given by x1, . . . , \u03b1 xand untracked ones by x\u03b1+1, . . . , mx. Further, it can be assumed without loss of generality that (1) x1, . . . , x\u03b3 \u2264 \u03b1 are not complexes consisting of two or more tracked single entities, and (2) that the tracked single entities within each complex x\u03b3+1, . . . , \u03b1 xbelong to the set x1, . . . , \u03b3x. In the JAK-STAT example, S, pR_S, and pS belong to x1, . . . , \u03b1 xand pS_pS to x\u03b1+1,. . . , m xas it contains two labeled single entities pS.Some entities xLF is created based on the original x, by applying the following rules:A new set of labeled or free entities xLF = {}\u2022 Start with an empty set, i x\u2208{x1, . . . , \u03b3x}, xLF is enlarged by a labeled \u2022 Single entities: For each i x\u2208 {x\u03b3+1, . . . , x\u03b1} is decomposed into \u2022 Complex entities: Each complex ix, and are added to xLF. The complex pS_pS for instance leads to the four new complexes F_pSF, pSL_pSF, pSF_pSLpS, and L_pSLpS.possible combinations using labeled rLF , the combinatorial multiplicity has to be applied not only to complexes but also to the ordered lists of reactants and products. Suppose an ordered list I of entities from the set {ix}i\u2264\u03b1 1 \u2264 with possible repetition, as for example the reactants of the reaction A + A + pA_pA \u2192 A_A_pA_pA corresponding to I = . Summing up all single reactants and elements of the complexes leads to p single entities, in this case p = 4. Taking into account all combinations of labeled and free entities, 2p different lists can be derived, in the exampleIn order to create a new set of reactions \u03b4 reactions of the original system are assumed to affect a tracked entity. In these reactions, at least one reactant or product is a tracked entity. Then, a new set of reactions rLF can be established. Starting with the empty set rLF = {}, for each reaction i r\u2208 {r1, . . . , \u03b4r} with one or more reactants of tracked entities,Without loss of generality, only the first 1. all reactants and products not belonging to the group of tracked entities are removed,I of the remaining reactants leading to 2. the combinatorial multiplicity approach is applied to the ordered list p reactions are added to rLF with reactants 3. 24. the fluxes Note that again the same symbol has been used for the entity name and its concentration. The sum over all weighting factors is 1.i r\u2208 {r1, . . . , \u03b4r}without reactants produce only free entities, which simplifies the conversion of i rbefore adding to rLF: All untracked entities are removed, all i xare replaced by Reactions When calculating the label half-life, products that coincide with the initially labeled entity are replaced by the corresponding free entity. This corresponds to removing the label and is necessary to avoid double-counting and to exclude upstream fluxes.rLF by their free counterparts. At the same time, a new product is added to those reactions where the target entity is a product to accumulate the returned label, RL.In order to calculate the label transit-time, entities entering the target pool must be released from their labeling, again, to avoid double-counting. Therefore, all labeled target entities are replaced in the reaction network injected at time-point 0, but the procedure is repeated for a series of time-points t (let i xbe the source species):Since the label half-life and transit-time characteristics are time-dependent, the label is not only 1. Set all initial values for labeled entities and RL, if available, to 0. Set the initial value of free entities to the value of their counterpart in the original network.r, rLF} from 0 to t.2. Numerically integrate the ordinary differential equations corresponding to the extended reaction network {injection.3. Apply a complete labeling of the source species: Set 4. Continue the numerical integration.t\" of the time-profiles t' > t) with t\"-t, respectively. The threshold crossing is determined by linear interpolation of the discrete samples given by the numerical integration.Threshold crossing at We recently suggested a profile likelihood-based approach to determine simultaneous and separate confidence intervals for calibrated unknown model parameters . In ordeT/21(t) of simple and isolated biochemical reactions can be calculated analytically. Except for first-order processes, it usually depends on the concentration x0 = x(t0) at the time-point of interest t0 and is therefore time-dependent:The half-life n >1 with The half-life calculation for a process of order x(t) with known x0 at t = t0:In order to calculate the half-life for Michaelis-Menten kinetics, rived in , for x:pR(t) triggering the phosphorylation of STAT (S \u2192 pS). After dimerization (pS + pS \u2192 -pSpS), the complexes enter the nucleus (pS_pS \u2192 npS_npS). Then they dissociate and are dephosphorylated (npS_npS \u2192 nS + nS). Finally, single STAT molecules leave the nucleus again (nS \u2192 S). Model parameters were estimated using a Levenberg-Marquardt approach and the PottersWheel modeling software. The pools of total and phosphorylated cytoplasmic STAT have been used as observation functions. The kinetic parameters were estimated as k1 = 1.37, k2 = 0.22, k3 = 0.63, k4 = 0.59, and k5 = 0.59. The initial value of S was calibrated to 0.96 and the scaling factors for the observables to 1.45 for -obs pSand 0.98 for -obsS.A smoothing spline approximation of the phosphorylated receptor served as the input function S is both, the initially labeled entity and the target pool. The flux of the label is illustrated in Figure in silico labeling approach allowed for discrimination between these two dynamics. In order to determine the transit-time for t >0, the label is injected at a series of time-points, which is visualized in Figure In order to determine the label half-life and transit-time of STAT, LS. It reaches a minimum of 0.6 \u00b1 0.1 minutes after ten minutes compared to a half-life of approximately 3 to 4 minutes at the starting point of the time-course analysis. For later time-points, the stimulus decreases (not shown) and STAT is no longer phosphorylated, resulting in an increased label half-life of STAT molecules. The minimum label transit-time for a complete cycle of STAT molecules was estimated as 12 \u00b1 2 minutes.Figure k1), dimerization (k2), nuclear import (k3) and export (k5) were systematically varied consecutively within four orders of magnitude between 0.01fit kand 100fitk, with fit kbeing the parameter value for the best fit. For each variation, the other free parameters were calibrated resulting in a profile likelihood estimation (see Fig. S2 in additional file X2-threshold of the separate 95% confidence interval are used to recalculate the label half-life and transit-time. Figure t = 0 and t = 20 minutes. The label transit-time has a wider confidence interval reflecting the larger number of reactions involved in a complete cycle of shuttling STAT.In order to investigate how uncertainties in calibrated model parameter values propagate to the estimated time-characteristics, we applied the profile likelihood approach on an identifiable version of the model. The kinetic parameters involved in phosphorylation k, dimerizin silico labeling method, which relies on an extended reaction network taking into account constraints concerning double-counting, upstream fluxes and combinatorial multiplicity. Our model-based in silico approach allows for insights into reaction networks that cannot be determined experimentally.In this paper, the half-life of a species has been compared conceptually, analytically, and numerically to the half-life of a label in a hypothetical tracer experiment. Two time-characteristics, the label half-life and label transit time have been introduced, which capture the kinetics of a dynamical system on a higher level than e.g. single rate constants. Calculation of the time-characteristics and their profile likelihood-based confidence intervals for an identifiable pathway model showed that the approach is robust against parameter uncertainties. The quantities are calculated based on the novel The proposed method provides important information for a wide spectrum of biological applications ranging from cell biology and pharmacokinetics to population dynamics. We applied it to a non-linear model of the cellular JAK-STAT signaling pathway, which allowed for calculating the time-dependent label half-life and transit-time of cytoplasmic STAT.In summary our approach enables to calculate the amount of time a molecule spends in a certain state or compartment and therefore provides novel insights into the temporal scale of networks. This knowledge will have profound impact on drug design, as it offers the possibility to predict the life-time of a specific molecule and provides a basis to improve drug targeting.TM and JB: Definition of the biological question, initiation, development, and implementation of the proposed method, writing of the manuscript. AR: Development of the proposed method, writing of the manuscript. SH, MS, SS, VB, UK, JT: Definition of the biological question, initiation of the method, critical discussion and contribution to manuscript. All authors read and approved the final manuscript.Application within PottersWheel. This additional file contains MATLAB scripts to run various tasks related to the in silico labeling approach. http://www.biomedcentral.com/imedia/4654854926777309/supp1.pdf..Click here for file"}
+{"text": "Networks are ubiquitous in modern cell biology and physiology. A large literature exists for inferring/proposing biological pathways/networks using statistical or machine learning algorithms. Despite these advances a formal testing procedure for analyzing network-level observations is in need of further development. Comparing the behaviour of a pharmacologically altered pathway to its canonical form is an example of a salient one-sample comparison. Locating which pathways differentiate disease from no-disease phenotype may be recast as a two-sample network inference problem.We outline an inferential method for performing one- and two-sample hypothesis tests where the sampling unit is a network and the hypotheses are stated via network model(s). We propose a dissimilarity measure that incorporates nearby neighbour information to contrast one or more networks in a statistical test. We demonstrate and explore the utility of our approach with both simulated and microarray data; random graphs and weighted  correlation networks are used to form network models. Using both a well-known diabetes dataset and an ovarian cancer dataset, the methods outlined here could better elucidate co-regulation changes for one or more pathways between two clinically relevant phenotypes.Formal hypothesis tests for gene- or protein-based networks are a logical progression from existing gene-based and gene-set tests for differential expression. Commensurate with the growing appreciation and development of systems biology, the dissimilarity-based testing methods presented here may allow us to improve our understanding of pathways and other complex regulatory systems. The benefit of our method was illustrated under select scenarios. Networks, a construct emphasizing the interrelations between objects, have application in studying human behaviour, mathematics, physics, econometrics, etc. With the introduction of microarrays and other high-throughput systems, networks increasingly provide a means to organize and study the interdependencies of genes, proteins, metabolites, etc. Gene transcription/regulatory networks, metabolic pathways, protein-protein interaction systems (PPIs), signal transduction pathways, and phylogenetic trees are established tools in biology. Prone-to-noise experiments are routinely coupled with computational algorithms to infer relationships. Given the empirical reliance on uncertain data it seems natural to ask, \u201cDo these networks differ from one another?\u201d This paper outlines and demonstrates an inferential process for performing one- and two-sample hypothesis tests when the sample data are biological networks.et al.[et al. [et al. [et al. [Numerous books are devoted to networks. Bornholdt et al. and Junk.[et al.  provide  [et al.  is a col [et al.  appears  [et al.  provide p, play an important conceptual role in our understanding of graphs [et al. [p* models in social network analysis, offer a theoretical model for stochastic networks and have been used in biological applications [et al. [C. elegans protein interaction growth model. Cardelli [et al. [Testing graphs is not trivial; comparing two static graphs is conceptually different from comparing a sample of stochastic graphs under one or more treatments. Defining a suitable null probability model for a network is a difficult consideration . Erd\u0151s-Rf graphs . The usef graphs . Chung e [et al.  explore  [et al. , in discications . ERGM paications . Motif fications . Wiuf et [et al.  outline Cardelli  suggests [et al.  argue anet al. [p* models and correspondence analysis to compare networks. Banks et al. [et al. [et al. [et al. [et al. [Approaches for both two- and one-sample comparisons occur in the literature. Faust et al.  use a cos et al. , using a [et al.  extend [ [et al.  to netwo [et al. , in a re [et al.  propose  [et al.  use an aet al. [et al. [et al. [et al. [While our focus here is on forming statistical comparisons of network model parameters, computer scientists can divide the graph comparison problem into two areas \u2013 exact graph matching and graph similarity . Graph set al.  propose  [et al.  combine  [et al.  extend a [et al.  capture et al. [et al. [The use and analysis of weighted (correlation-based) networks is increasingly relevant in biological applications. Zhang et al. , in a cl [et al. , as part [et al.  contains [et al.  uses a det al. [et al.[Resampling methods are common in network analysis, e.g., see , and wilet al.  use bootet al.  combines. [et al. use a pe0 state of a signal transduction network. Algorithms that derive networks using in silico or in vitro/vivo data could be tested for the comparability of their network model estimates in either a one- or two-sample context. For obvious reasons, two-sample comparisons have a broad application range. Two-sample tests are conducted by drug developers to compare pathways between an investigative compound at various doses or to a competitor\u2019s compound. We conduct one- and two-sample tests using both simulated and microarray-based network data. To evaluate both Type I error control and the power of our procedure, we examine both null and non-null cases under a small set of network models. We assume that each sampling unit is an independent realization of a network. Our testing approach follows the traditional hypothesis testing route: define the null and alternate hypotheses  and the risk associated with a decision; define a \u2018nearby neighbour\u2019 dissimilarity-based test statistic for testing the hypothesis; compute the test statistic; compute the distribution of the test statistic under the null hypothesis; and, make a decision using the sampling distribution and the calculated test statistic. Our approach applies to edge/no-edge graphs, weighted graphs, and can be extended to directional networks. In the one-sample hypothesis testing context a null network model is assumed or based on resamples from an a priori null sample to generate the sampling distribution of our test statistic under the null hypothesis. To implement a two-sample comparison we rely on the permutation testing principle as the formal basis of our inferential approach [Hypothesis tests for networks have a variety of obvious applications. A one-sample comparison can occur when comparing a network estimate to a known \u2018gold standard\u2019 model. The standard could reside in an online ontology, be defined via a data processing algorithm , or reflect the starting tapproach .xi, i = 1, \u2026, n} of independent observations is therefore a set of networks. In contrast to social networks, where the sampling unit is often the node, we assume that the biological network is inherent to each sample observation. We propose a dissimilarity measure as a test statistic to capture the separation between two networks. We assume that we can align the nodes across the networks to be compared. Since each node in the network represents a gene or other molecular entity, the ability to align nodes across a set of networks implies that we know a unique identifier for each node to allow for a molecule-by-molecule comparison across a set of networks. We determine the sampling distribution of the test statistic under the null hypothesis via resampling techniques.We consider an observed network as a realization of a stochastic process. A sample {G is an ordered pair of disjoint sets  where both V and E are finite sets. V = V(G) is the set of vertices and E = E(G) is the set of edges. An edge {x,y} is said to join, or tie, the vertices x and y and is denoted xy. If xy \u2208 E(G) then x and y are adjacent, or neighbouring, vertices of G and the vertices x and y are incident with the edge xy. Two edges are adjacent if they have exactly one common endvertex. G\u2019 =  is a subgraph of G =  if V\u2019 \u2282 V and E\u2019 \u2282 E. If x is a vertex of G we write x \u2208 G in place of x \u2208 V(G). The order of G is the number of vertices in G; the size of G is the number of edges of G. G denotes an arbitrary graph of order n and size m. A graph of order n and size n-graph. A covariance matrix of nonzero elements with dimension n, \u03a3n, is a complete n-graph. The set of vertices adjacent to x \u2208 G, the neighbourhood of x, is \u0393(x). For adjacent vertices x and y we have x \u2208 \u0413(y) and y \u2208 \u0413(x). The degree of x is |\u0393(x)|. A vertex of degree 0 is an isolated vertex (or isolate). A path is a graph P where V(P) = {x0, x1, \u2026, xl} and E(P) = {x0x1, x1x2, \u2026, xl-1xl}. The length of P is the size of P. A graph without any cycles, a path with length greater than or equal to three and comprised of distinct vertices, is an acylic graph. Unlike trees, we allow for cyclic graphs with isolates. Paths have an obvious tie to motifs and other regulatory functions. By definition, a loop (xx \u2208 E(G)) is not allowed; multiple edges joining the same two vertices are not allowed. A graph G can contain a subgraph G\u2019 that is not connected to the remainder of G. Isolated nodes and subgraphs occur in biological networks. Accommodating isolates is necessary to align nodes between two graphs.First, we begin with some definitions. Our definitions are consistent with Bollob\u00e1s . A graphG in matrix form. The adjacency matrix A = A(G) = (aij) of a graph G is the nxn matrix given by wij, where wij is the strength, covariance, etc., between vertices vi and vj. Given nxn network matrices G = (gij) and H = (hij) we define G-H in the standard algebraic sense, i.e., gij-hij. We do not require a matrix be square; some directed network forms are nxm matrices. But, our use of element-wise subtraction is key; we are not suggesting a definition based on subspaces/subgraphs or set complements. We need to map an nxn network onto the real line in order to define a measure of separation. Under this definition of matrix subtraction, G-H = 0, where 0 is an appropriately dimensioned matrix of zeros, implies no separation between two networks.It is common to represent a graph drs between r and s satisfies the following: drs\u2265 0 for every r, s, drr= 0 for every r, and drs= dsr for every r, s. Refer to Gan et al. [x and y are generally based on a simple matching distance, The concept of dissimilarity (or similarity) is standard fare, especially in cluster analysis and pattern recognition. The dissimilarity measure n et al.  for an edistance  is a symWO= (wijO) be a (weighted) adjacency (or directed incidence) matrix for the observed network estimate and WT= (wijT) the target network. In a one-sample comparison WT represents the true network model. For a two-sample comparison the distinction between the two labels is arbitrary. Both WO and WT represent graphs of order n; the nodes are labeled, common to, and aligned between both graphs. For node i define the dissimilarity at that node to be a combination of that node\u2019s dissimilarity, i\u2019s neighbours, j \u2260 i, j \u2208 \u0413(i). For the overall network, the dissimilarity D is defined asLet I is defined as the standard mathematical indicator function. For a graph of order n a set/neighbourhood is formed at each node wii, i = 1,\u2026,n. We measure the dissimilarity between a node and its adjacent neighbours between the two graphs. To account for the intrinsic network structure the neighbourhood is then extended to those neighbouring nodes that are incident to nodes in \u0393(wii) for both the target and observed networks. I.e., we now measure the dissimilarity for the two subgraphs induced by \u0393(wjj), where i \u2260 j and wjj is an element of \u0393(wii). This \u2018extended\u2019 neighbourhood dissimilarity is added to the dissimilarity measured at wii. The contribution of the second nearest neighbours is weighted by cij in the definition of D. In a weighted network, e.g., a correlation network, this weight is easily motivated. In an unweighted network cij is set by the researcher. Assuming a weight of cij= 0 for an unweighted 0\u20131 graph reduces D to an unscaled version of the familiar Hamming distance and is comparable to the edit distance approach listed in [isted in .D using separate edge and weight L1-norms. We elaborate on this choice later. The need to align the two graphs is critical to calculating D. Our approach does result in additional computational overhead since edge xy will be counted for nodes x and y. But, the counting is consistent and avoids the need for complex single-count network partitioning schemes. Only those nodes with a path length of 2 or less from wii are included; D can easily be extended to include path lengths greater than 2.We form n, G, the obvious parameter to test is p. Apart from ERGMs and  correlation networks, explicit network parametric models may not be readily apparent. The basic form of a one-sample network hypothesis test here is H0: \u03b7 = \u03b70 versus H1: \u03b7 \u2260 \u03b70, where \u03b7 is anticipated to be a vector-valued parameter for most realistic (weighted) biological networks. For a G graph we have \u03b7 = p and one could test H0:G = G versus H1:G \u2260 G. We intentionally provide no explicit guidance for how to determine p. And, we make explicit the probability model for the graph rather than state the hypothesis in a more compact manner, i.e., H0:p = p0. For a network defined using a correlation matrix \u03a9 we construct hypotheses of the form H0:\u03a9 = \u03a90 versus H1:\u03a9 \u2260 \u03a90. One needs to make explicit the procedure used to establish the edges in the network and the probability model for the observation data. In an example we test H0:G = G versus H1:G > G. Here, one needs to recognize that the amount of randomness/entropy for a G graph is less when p is close to 0 or 1 relative to p close to 0.5 to successfully perform a one-sided test. Primarily, we are interested in the question, \u201cDoes this differ from the target?\u201dDefining an appropriate hypothesis in the context of networks can be nontrivial. For an Erd\u0151s-R\u00e9nyi graph of order D may be suitable in its stock form or require customization for the problem at hand. Third, compute the test statistic. Fourth, determine the distribution of the test statistic under the null hypothesis via a suitable resampling procedure. Finally, make a decision using the sampling distribution of the test statistics as a guide.We employ a resampling approach to perform one- and two-sample network hypothesis tests. Following the five-step procedure outlined in Good  we firstD in the one-sample case we assume a parametric model or explicit generative algorithm is available in order to draw samples from the null network model. In most customary testing situations a test statistic is an estimate for a parameter of interest. However, in some cases the sample itself is the statistic \u2013 concise reductions of the data may be limited or not obvious/possible. Biological networks, where each edge or weight may be associated with transcription activity or a regulatory cascade, are inherently high-dimensional objects and may therefore lack parsimonious model parameterizations. In many applications a network algorithm F is required to produce an observed network. In these instances we may need to resample from F(x) instead of resampling from the observed data {xi}. In other cases, e.g., the Erd\u0151s-R\u00e9nyi G graph, the role of the xi may be suppressed or not apparent since we observe F(x). For networks based on explicit probability models, e.g.,  correlation networks, parametric bootstraps or Monte Carlo procedures may be possible under suitable assumptions [To generate a null distribution for umptions .H0: \u03b71= \u03b72 versus H1: \u03b71\u2260 \u03b72 two-sample problem allows one to draw upon established parametric and nonparametric comparisons. A null hypothesis of network equality versus an alternate hypothesis of network inequality is expected to be commonplace. Alternate hypotheses such as H1: \u03b71> \u03b72 are possible but not explored here. We make the standard assumption of two independent and identically distributed samples {x1, \u2026, xn} and {y1, \u2026, ym}, where xi and yj are network-valued. Following the notation of [P be a family of distributions for {X1, \u2026, Xn} that are symmetric in the sense that for a permutation \u03c0 of the subscripts {1, \u2026, n} we have P{ \u2208 B} = P{( X\u03c0(1), \u2026, X\u03c0(n)) \u2208 B} for all Borel sets B. The random variables Xi are said to be exchangeable \u2013 a condition established under the assumption of independent and identically distributed samples or via the principle of randomization/random allocation in experimental design. As noted in Good, permutation tests rely on the assumption of exchangeability under the null hypothesis.Although a one-sample comparison has application for biomedical researchers, relative comparisons are of broad practical relevance. Research clinicians and pharmacologists are interested in exploring standard-of-care and new treatment comparisons for therapeutics. Transitioning to the ation of , let P bn<p\u2019 wide data and the lack of closed-form sampling distributions for various test statistics proposed. Pesarin [Permutation testing, a procedure which relies on samples drawn from the combined pool of experimental units and the random assignment of a treatment label to each unit, is common in the bioinformatics literature due to the prevalence of \u2018 Pesarin  lists a  Pesarin , to the D using an Erd\u0151s-R\u00e9nyi G graph. We test H0:G = G versus H1:G > G. The order of G is 25 and p0 is 0.20. We simulate four cases with 100 hypothesis tests (or experiments) in each case. For the null case we assume that the observed network is a p = p0 = 0.20 model. For the remaining two cases we assume that p = 0.25. We set cij = 0 for both a null and an alternate case and cij = exp(\u22122) for the remaining two cases. These four cases illustrate the Type I and II error rates of our procedure both with and without the inclusion of the neighbouring information in calculating D. 1,000 resamples were used to estimate the null distribution for D. The execution time for the set of 100 experiments using 1,000 resamples was approximately 1 hour on a standard personal computer. The R package Statnet [G graphs. All of our computations were conducted using R (http://www.r-project.org/). For testing large networks or large numbers of networks a more computationally efficient language such as Fortran or C++ is recommended. The representation diversity and size of networks, combined with a need or interest to tailor D for a particular application, poses a challenge for software developers.We first demonstrate  Statnet  was usedD for a correlation-based network model we assume that the p-dimensional observations follow a multivariate normal distribution, Np, with mean vector \u03bc and positive definite covariance matrix \u03a3. Transforming \u03a3 into correlation form \u03a9 allows us to form a partial correlation matrix. Applying a threshold to each \u03c1 estimate or a testing procedure to the entries of \u03a9 can be used to define a correlation network. Given \u03a9-1= (\u03c9ij) we compute the partial correlation matrix \u03a0 = (\u03c0ij) via (\u03c0ij) = \u2212\u03c9ij/\u221a(\u03c9ii\u03c9jj). Under multivariate normality two variables are conditionally independent given the remaining variables if and only if the partial correlation vanishes. The zeros in \u03a9-1 determine the conditional independence graph. As before, a threshold or testing procedure is used to define the partial correlation network. We evaluate both the Type I error rate and the power of D under an alternate hypothesis.To evaluate xi~ N. To mimic a sparse biological network \u03a9 consists of 6 nonzero 5x5 blocks along the diagonal. A sample rejection scheme guaranteed that the magnitude of each block entry exceeded a predefined threshold. The number of nodes (30) and the threshold (\u03c1 = 0.2) was common to all simulations. The same threshold \u03c1 was used to define the data generation model and to estimate the observed correlation network in the one-sample case. For both comparisons we evaluated D using sample sizes of n1= n2 = 200. For the one-sample comparison the target correlation network \u03a90 is estimated from the sample data and the resamples are drawn from the observed samples to determine the null distribution for D. Admittedly, this approach violates the true spirit of a one-sample test under an assumed null model. But, if historical sample observations are available for analysis and reflect the null hypothesis then these samples might provide the most scientifically defensible null distribution for \u03a90. The same approach is used for the derived microarray-based correlation network comparison; a case where the true null model is unknown. To simulate the alternate hypothesis of network inequality at least 10% of the 5\u2009\u00d7\u20095 blocks for a 30\u2009\u00d7\u200930 correlation matrix, with a minimum of one block per experiment, were varied using a random number generator. A total of 100 experiments were performed and 1,000 resamples used in calculating each p-value. For both the correlation and partial correlation networks we calculate D using only the weight portion of the index since the existence of an edge was defined via the  correlation estimate. The execution time for the 100 experiments using 1,000 resamples was approximately 1\u20132 hours on a standard personal computer for the one-sample comparison. The two-sample setting execution time was on the order of 4\u20136 hours. For select simulation data the algorithm used to estimate the partial correlation network, see below, would abruptly terminate. All of the resample p-values shown here were obtained upon a successful completion of the estimation process. The computation time for the actual biological data was negligible. This is likely due to the small networks involved; network comparisons involving a large number of nodes and/or edges present a non-trivial computational burden. Refer to Additional file Apart from the Erd\u0151s-R\u00e9nyi example, the one- and two-sample simulation comparisons assume that the observations are in their correlation form, i.e., et al. [et al. [et al. [et al. [http://cran.r-project.org). The algorithm broadly consists of 3 steps. First, the correlation (or covariance) matrix \u03a9 is converted to a partial correlation matrix \u03a0; pseudoinverses may be involved. The second step tests for the presence of \u2018significant\u2019 edges. The final step extracts the significant edges based on a user-defined criterion. We used the magnitude of the estimated (shrunken) partial coefficient to establish this cut-off \u2013 the cutoff.ggm parameter for \u03c0ij was set to 0.5. Default settings were used for the remainder of the GeneNet settings. We do not claim that GGMs are superior for modeling gene/protein networks. [We selected partial correlation networks as presented in   is a serious metabolic disorder affecting a large number of people worldwide. Mootha et al. , using m website .\u03c1. To facilitate a one-sample comparison the normal tissue samples are used to define a target network. The resampling procedure was outlined in the previous section. Rather than analyze severely ill-conditioned correlation matrices (numerous gene sets contained over 100 genes), we formed correlation networks only for those gene sets with fewer than 18 probes in the pathway. A significant one-sample finding for one or more gene sets may suggest differences in co-regulation network behaviour of a person with DM2 relative to a normal subject.The original study examined average expression levels across the two groups. Here, we explore the differences in covariance or correlation structures between the two phenotypes as expressed in a correlation network formed via a threshold for et al. [et al. [E2F/Rb pathway in SBTs and SCAs. Chien et al. [p53 and E2F pathways in serous carcinomas and reinforced the role of E2Fs listed in [Ovarian cancer is the foremost lethal neoplasm of the female genital tract. We examine here the gene expression signatures of ovarian serous carcinomas (SCAs) relative to serous borderline tumors (SBTs) based on three recent studies. Sieben et al.  confirme [et al.  investign et al.  demonstristed in . These tet al. [E2F target genes with the studies of Bracken et al. [et al. [BRCA2), 1 development gene, 5 DNA damage and repair genes, and 13 DNA synthesis/replication genes. A table of the specific genes included is in Additional file The microarray data analyzed here was obtained from the NCBI GEO database  via acceet al.  screenedn et al.  and Bied [et al. . 43 of t [et al. : 5 for tG random graph comparison refer to Figure\u00a0cij = 0 and cij = exp(\u22122) cases the p-values are approximately uniformly distributed under the null hypothesis. In panels (a) and (c) we see that the nominal Type I \u03b1 level is approximately 0.05. Comparing panel (b) to (d) we see the improvement in the power of D when p = 0.25 and cij = exp(\u22122). When the neighbouring information was not used in calculating D 34% of the resample p-values were below a nominal \u03b1 level of 0.05. When the neighbouring information was included in D and scaled by cij = exp(\u22122) 55% of the p-values were below the nominal 0.05 level. The likelihood of D detecting the true alternative hypothesis increased from 34% to 55% just by including the neighbouring information here.For the Erd\u0151s-R\u00e9nyi D to reject H0: \u03a9 = \u03a90 versus H1: \u03a9 \u2260 \u03a90. The tests were performed using cij = 0, i.e., excluding the neighbouring information, and cij= rij, the thresholded correlation estimate. Under the assumed null model the distribution of p-values, for both cij = 0 and cij= rij, had less mass at the extremes of the p-value range. Additional simulation work, see [n1= n2 = 100 the Type I error rate was conservative, produced an inflated error rate when n1= n2 = 2,000, and the test achieved a proper size when the a priori sample size was a factor of 10 larger than the observed network based on a sample of n = 200. These results suggest caution when trying to determine the null distribution for D using a finite set of a priori samples. Figure\u00a0D via cij= rij penalized our ability to reject the null hypothesis when compared to the use of cij = 0.For the one-sample correlation network comparison we examined both the Type I error rate and the power of ork, see , suggestH0: \u03a01= \u03a02. In Figure\u00a0D  suggests that the edge portion of D is redundant to the weight component and panels (b-c) suggest that including the neighbouring information detracts from the power of D. Table\u00a0\u03c1 = 0.35 and \u03c1 = 0.5  in Table\u00a0For the two-sample comparisons we examined a limited ordered comparison of the SBT, SCA1, and SCA3 phenotypes for the 5 biological processes. Our subjective rationale was that a comparison of the SBT and SCA1 phenotypes might suggest a biomarker candidate; comparing the SCA1 and SCA3 phenotypes might better characterize disease progression or provide insight regarding resistance to chemotherapy agents. Table\u00a0et al. . Apart fD was inspired by the question, \u201cHow long is the coast of Britain?\u201d This question motivates the definition of fractal dimension, a concept suited for complex objects. Cutler\u2019s [et al. [D to internodal path lengths strictly less than three since this is the minimum distance necessary to capture a feedforward/feedback loop, it limits the range of topological comparisons, and D is prevented from revisiting the \u2018centre\u2019 of a neighbourhood in a cyclic graph. D can be extended to include a larger neighbourhood. Apart from obvious computational implications, defining a second set of cij\u2019s is necessary and the efficiency of D may deteriorate as D integrates a larger set of imprecise or variable estimates. In contrast to fractals, viewing a network as an inhomogeneous mixture of subgraphs suggests that a local distance may be preferable to large distances that span a large set of nodes.The definition of Cutler\u2019s  definiti [et al.  suggest D is or will be optimal under a broad range of network models. Apart from the literature related to ERGMs, weighted biological network models with well-developed inferential theory analogous to maximum likelihood, uniformly minimum-variance unbiased, or minimax estimators is largely unavailable. The ability to apply D to a broad range of edge/no-edge and weighted/unweighted networks is sure to involve tradeoffs. Banks et al. [1-based edit distance for unweighted binary networks using protein signaling logic. While not constituting a definitive argument, we speculate that the value of including the neighbouring information in the G simulation example is due to the uniformity of p across the set of nodes. The loss in performance using the neighbouring information for a pairwise correlation network model is likely due to D unnecessarily integrating across a larger set of imprecise estimates. For the two-sample partial correlation network comparison, the gain in performance via the use of neighbours may be influenced by the fact that each edge is formed using a plurality of variables. For researchers interested in alternate network models, e.g., preferential attachment or small-world models, evaluating D (or comparing it to a competing procedure) under various scenarios is recommended.We do not claim that s et al.  illustras et al.  state ths et al.  modify aD on a more general form of a Hamming distance parallels efforts in the area of global network alignment scoring. Others have proposed alignment-based operations for use with biological networks, e.g., [D incorporate neighbouring information might be obvious to a systems biologist; see [D and may interact with network estimation procedures, data collection requirements, etc.Basing s, e.g.,  for comps, e.g., ,21,56. Hist; see  for an eist; see  for a paist; see , using pist; see  use leveist; see  outline ist; see  present D\u2019s simplicity and potential for use across a broad set of network models, the importance (and weighting) of D\u2019s components should receive serious consideration by the investigator. Gower [D to gage or improve its performance for a specific network model is advised. The selection of the weight constant cij for weighted graphs was motivated by the idea of conditional probabilities. If A and B represent two adjacent edges and information flows through their common vertex then it is reasonable to assume that some form regarding the state of B is meaningful to A. It is plausible to assume that the force two objects exert on one another is proportional to their proximity. Preferential attachment networks assume that new edges are formed at a node conditional on the number of existing edges at that node. Wei et al. [et al. [D is complicated. Gao et al. [et al. [D and the total sums of squares in regression modeling we allow for nodes with a high degree  to contribute more to the calculation of D. If one chooses to normalize portions of D at each node by some topological property then one has to justify the scaling factor. Does one scale by the node\u2019s (weighted) degree, a clustering coefficient, in- or out-degree for a directed network, etc.? If a network model has an efficient estimator whose sampling distribution is well characterized, the use of D may be contraindicated. At present, we do not expect this to be the case for experiment-based weighted biological networks. As a conservative measure, D could be reduced to its Hamming-like form and only the inferential procedures outlined here applied. Evaluating D using an in silico model under plausible scientific scenarios of interest to the investigator could also reduce concerns about aspects of the definition of D.Despite r. Gower  concedesr. Gower . For boti et al.  employ g [et al.  found quo et al.  allow hu [et al.  normalizD was limited. Computational expediency, an ability to explore and contrast common parametric models and their associated weighted network forms, and the use of a canonical structure  graphs) motivated our network model selection. Both Marbach et al. [et al. [et al. [et al. [D may be restrictive in the one-sample case; but, the complexities surrounding network probability models and the intractability of network-based test statistics does not suggest easy alternatives. Large (weighted) networks are likely to be costly in terms of the data needed to estimate a family of network parameters. The literature on the analysis of large networks, with its emphasis on select topological comparisons, typically imposes a vast reduction in network complexity. Thorne et al. [Our choice of network architectures to evaluate with h et al.  and Alta [et al.  discuss  [et al.  found th [et al.  suggest e et al. , in propD for observation studies raises the topic of partial exchangeability. It is unreasonable to assume that either of the biological datasets presented here met the assumption of exchangeability. However, unconditional procedures also struggle when confronted with observational data and/or missing or hidden covariates. Our one- and two-sample comparison approaches require or assume a hypothesized network model for the purpose of sampling; we do not employ fixed-network random rewiring schemes or variations that seek to align a set of topological measures across a set of stochastic networks.General criticisms leveled against the use of resampling methods are applicable here; see Berger . The praD is a sum of node-based dissimilarities, a test for dissimilarity between two aligned nodes or subgraphs can be formed using the portion of D attributable to that node or subgraph. Such an approach may help isolate molecular targets or subnetworks for closer study. Determining the sampling distribution for the modified test statistic is identical to the procedure developed here. See Yates [A significant one- or two-sample finding naturally suggests the question, \u201cWhere do the networks differ?\u201d Similar to individual effect tests in regression, the answer to this question will involve one or more nodes or subgraphs. Answering targeted questions routinely appear in the literature, see ,72. Dongee Yates  for moreIn this paper we have demonstrated an inferential framework for performing one- and two-sample hypothesis tests for biological networks. We proposed a suitable test statistic and evaluated it with both simulated and microarray data under a variety of situations. The dissimilarity test statistic proposed is a logical extension of existing measures used in sequence alignment/nominal data comparisons. In generating the null distribution of the test statistic we used an assumed parametric model, resamples from a collection of null samples, and made use of permutation testing principles. Resampling methods suggest that counterintuitive behaviours may occur when dealing with a  network model. While not explicitly demonstrated here, our procedure easily facilitates node-level or subgraph post hoc tests.The authors declare that they have no competing interests.This work is based on the PhD dissertation of PDY. NDM suggested the problem and supervised the research. All authors read and approved the final manuscript.R code.Click here for fileOvarian cancer genes analyzed. Subset of analyzed genes as categorized by Bracken et al. [n et al. .Click here for fileTwo-sample comparison for partial correlation networks under H0. A uniform qq-plot of the 100 resample p-values for a test of H0 \u03a01= \u03a02 versus H1 \u03a01\u2260 \u03a02 under the null hypothesis. The y-axis is the observed p-value; the x-axis the expected p-value.Click here for file"}
+{"text": "A/GABAB receptors. All metabotropic neurotransmitter receptors are GPCRs. There are, however, a large number of non-GPCRs that also fulfill the original definition for a metabotropic receptor, namely \u201cthat the transmitter acts indirectly, by triggering a chemical reaction or a series of reactions\u201d  in the postsynaptic cell from other glutamate receptors that pass an ion current (ionotropic) -spanning proteins as typical for GPCRs but do not couple to a heterotrimeric G-protein. With the given 7-TM topology it was as yet not clear how the channelrhodopsin proteins have to arrange to form an ion channel. Recently, the non-selective cation channel, channelrhodopsin-2 from"}
+{"text": "Reading habits are thought to play an important role in the emergence of cultural differences in visuo-spatial and numerical tasks. Left-to-right readers show a slight visuo-spatial bias to the left side of space, and automatically associate small numbers to the left and larger numbers to the right side of space, respectively. A paradigm that demonstrated an automatic spatial-numerical association involved the generation of random numbers while participants performed lateral head turns. That is, Westerners have been shown to produce more small numbers when the head was turned to the left compared to the right side. We here employed the head turning/random number generation (RNG) paradigm and a line bisection (LB) task with a group of 34 Iranians in their home country. In the participants\u2019 native language (Farsi) text is read from right-to-left, but numbers are read from left-to-right. If the reading direction for text determines the layout of spatial-numerical mappings we expected to find more small numbers after right than left head turns. Yet, the generation of small or large numbers was not modulated by lateral head turns and the Iranians showed therefore no association of numbers with space. There was, however, a significant rightward shift in the LB task. Thus, while the current results are congruent with the idea that text reading habits play an important role in the cultural differences observed in visuo-spatial tasks, our data also imply that these habits on their own are not strong enough to induce significant horizontal spatial-numerical associations. In agreement with previous suggestions, we assume that for the emergence of horizontal numerical mappings a congruency between reading habits for words and numbers is required. Our thoughts, perception and actions are shaped by the culture in which we live. Our way of thinking, for example, depends on the social systems we grew up with. That is, East Asians tend to reason in a holistic way, while Westerners exhibit a more analytical thinking style . Based on the previous literature we here expected to find a slight bias to the right of the line\u2019s true center  participated in this study. The 25 right and 9 left-handed participants  as a within-subjects factor and Handedness  as a between-subjects factor. The analysis revealed neither a main effect for Condition  = 0.17, p = 0.85) nor for Handedness  = 0.32, p = 0.57). The interaction between Condition and Handedness was not significant either  = 0.73, p = 0.49). Due to its theoretical importance for the current study we also directly compared the number of generated \u201csmall\u201d numbers during left and right head turns. Paired t-tests revealed no significant differences in the number of \u201csmall\u201d numbers between lateral head turns  = 0.65, p = 0.52; only right-handers: t(24) = 0.91, p = 0.37; only left-handers: t(8) = \u22120.21, p = 0.84).The number of \u201csmall\u201d numbers was submitted to a repeated-measure ANOVA with t-tests were conducted to investigate whether there was a bias for naming too many \u201csmall\u201d numbers in any of the three conditions. As there was no handedness effect in the ANOVA, data were collapsed across this factor for this analysis. The number of \u201csmall\u201d numbers generated did not differ from the expected value of 20.0 in any of the three conditions (t(33) < 1.61, p > 0.11, see Figure t(33) = 1.21, p = 0.23).One sample t-test comparing the participants\u2019 mean deviation to 0 indicated that there was a significant rightward bias (t(33) = 2.67, p < 0.02) for the 34 participants. The performance in the LB task differed between left  and right-handers  = 2.08, p < 0.05). One sample t-tests showed that right-handers deviated significantly to the right of the true center (t(24) = 3.02, p < 0.01) and that there was no LB bias for left-handers (t(8) = \u22121.79, p > 0.11).The subjective midpoint in the LB task was shifted 0.93 mm (SEM = 0.35) to the right side of the lines\u2019 true center. A one sample r = 0.21, p = 0.23).The bias in the LB task was not related to the average magnitude of generated \u201csmall\u201d numbers across all three conditions . A paradigm that revealed an automatic mapping of small and large numbers to left and right head turns respectively in Westerners  and numbers (left-to-right) differ in Farsi. Our working hypothesis is that these opposite reading habits lead to the disappearance of any preferred lateral association of numbers along the horizontal mental number line. Hebrew readers also use opposite reading directions for words and numbers, and these readers also lacked reliable spatial-numerical associations in a SNARC paradigm  exhibit a radial spatial-numerical mapping when response buttons in a SNARC paradigm were placed in a radial instead of the conventional horizontal arrangement (Shaki and Fischer, Participants\u2019 handedness only affected performance in the visuo-motor LB task, but not in the RNG task. This finding is consistent with previous research. Differences between left and right-handers in LB tasks are commonly observed (Sampaio and Chokron, The observed rightward shift in the LB task is analogous to that described in previous studies assessing visuo-spatial biases in right-to-left reading cultures (Chokron and Imbert, The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Finally, a polynomial-time approximation algorithm for the problem of sorting unsigned genomes by double-cut-and-join operations is devised, which achieves the approximation ratio In this paper we study the problem of sorting unsigned genomes by double-cut-and-join operations, where genomes allow a mix of linear and circular chromosomes to be present. First, we formulate an equivalent optimization problem, called maximum cycle/path decomposition, which is aimed at finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths in a breakpoint graph. Then, we show that the problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than  A fundamental problem in the study of genome rearrangements is to compute the genomic distance between two genomes based on their gene orders, where the genomic distance is generally defined as the minimum number of evolutionary operations necessary to transform one genome to another. This problem has been extensively studied in the last two decades -4.double-cut-and-join (DCJ). It basically cuts a genome in two places and then joins the resulting four ends in a new way. Noticeably, computing the genomic distance based on DCJ operations can be applied between two genomes that allow a mix of linear and circular chromosomes to be present.The choices of genome evolutionary operations include reversals , translocations, fissions, fusions, transpositions and block-interchanges. To unify all these classical operations, Yancopoulos et al  introducsigned genomes in [unsigned genomes in [The complexity of computing the genomic distance between two genomes seems to largely depend on the availability of gene strand information rather than on the choice of evolutionary operations. For instance, the problem of sorting by reversals is tractable when gene strand information is available ,6, but bnomes in ,8, wherenomes in ,10; in tuni-chromosome genomes, Chen presented in [linear genomes, Jiang et al [To tackle an NP-hard optimization problem, it is of highly practical interest to develop a polynomial-time approximation algorithm with provable performance guarantee. For the problem of sorting by double-cut-and-join operations, in the case of unsigned ented in  an approng et al  recentlylinear and circular chromosomes to be present. The main goal is to devise a polynomial-time approximation algorithm for this NP-hard problem. To this end, we first formulate a new and equivalent combinatorial optimization problem, called maximum cycle/path decomposition, which is aimed at finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths in the breakpoint graph constructed from two input genomes. Then, we show that the problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than l in the breakpoint graph can be reduced to the well-known degree-bounded k-set packing problem, where k = 2l. Finally, we present a polynomial-time approximation algorithm for the problem of sorting unsigned genomes by DCJ operations and then obtain its approximation ratio In this paper we study the problem of sorting unsigned genomes by double-cut-and-join operations in the more general case where genomes allow a mix of gene is a stretch of DNA with two ends: the 3\u2032 end and the 5\u2032 end. Both are called the extremities of a gene. A chromosome is a single double-stranded DNA molecule that contains a sequence of genes. It can be either a linear molecule or a circular molecule. For a linear chromosome, there is a telomere marker located at each of its two ends. A genome is the whole collection of chromosomes in a cell. For example, the following gives a genome containing two linear chromosomes and one circular chromosome.A a, c, d, o), , }Genome A = {, then the corresponding genome is called signed. For a signed genome, Bergeron et al [adjacencies between extremities from different genes or between telomeres and extremities. For example, we may represent a signed genomeHere we use the symbol \u2018o\u2019 to represent a telomere marker, further indicating that the corresponding chromosome is linear. An on et al  introducasha and ta represents the 5\u2032 end and 3\u2032 ends of gene a, respectively.where double-cut-and-join (DCJ) is an operation that cuts a genome in two places and joins the resulting four ends in a new way. Specifically, the cuts are applied between two adjacent extremities from different genes, between a telomere and its adjacent gene extremity, or between the two extremities of a null chromosome if necessary. The DCJ operation was first introduced by Yancopoulos et al [The os et al  and lateos et al  to unifyA and B on the same set of genes, the problem of sorting unsigned genomes by DCJ operations (UDCJ) is defined to find a shortest sequence of DCJ operations that transform one genome into the other. The length of such a sequence is called the double-cut-and-join distance between two genomes A and B, and denoted by DdCJ.Given two unsigned genomes Example 1. Let two unsigned genomes beGenome A has two linear chromosomes and one circular chromosome, while genome B has two linear chromosomes and two circular chromosomes. Sorting A into B can, for example, be done in the following four DCJ operations, where the places to be cut are underlined:We will see later that at least four DCJ operations are needed to transform one genome into the other. Therefore, DCJthe DCJ distance between A and B is d = 4.S and a collection S of subsets of S, the set packing problem asks for the maximum number of pairwise disjoint subsets in S. The k-set packing problem is a restricted variant of the set packing problem where every subset in S has size at most k. If in addition the number of occurrences in S of any element is upper bounded by a constant \u0394, then it reduces to the degree-bounded k-set packing problem. The following theorem states the best-to-date approximability and its detailed proof can be found in [Given a base set found in .Theorem 2  and will be used in our approximation for computing the DCJ distance between two unsigned genomes. Its running time complexity is This algorithm is denoted by APPROX-SP =  as follows. Each vertex in |V| corresponds to a distinct gene or a telomere, so |V| = n + 2Al + 2Bl. Every adjacency in A forms a black edge belonging to bE and every adjacency in B forms a gray edge belonging to g.E It is easy to see that |bE| = n + Al, g||E = n + BI, and |E| = 2n + Al + B.l Moreover, every telomere of genome A (resp. genome B) has degree one and is incident to a black (resp. gray) edge, whereas every gene has degree four and is incident to two black and two gray edges. For short, a telomere of genome A is referred to as an A-telomere, and a telomere of genome B as a B-telomere. Note that the number of A-telomeres is not necessarily equal to the number of B-telomeres in a breakpoint graph.The breakpoint graph  is first introduced in  and wideExample 3. Consider the two unsigned genomes A and B given in Example 1, Awhere l = 2 Band l = 2. The breakpoint graph G =  is depicted in Figurein which |V| = 15, |bE| = 9, g||E = 9, and |E| = 18.G is called alternating if its edges are alternatively black and gray. From now on, whenever we mention cycles/paths in a breakpoint graph, they are alternating and edge-disjoint. A path is called an AA-path (resp. BB-path) if it connects two A-telomeres (resp. two B-telomeres) or an AB-path if it connects an A-telomere and a B-telomere. The length of a cycle/path is referred to as the number of black edges that it contains.A cycle/path in the breakpoint graph cycle/path decomposition of G into edge-disjoint cycles, AA-paths, AB-paths and BB-paths. A maximum cycle/path decomposition refers to a cycle/path decomposition that contains the maximum number of edge-disjoint cycles, AA-paths and AB-paths. Note that this maximum number does not take into account any BB-paths. The maximum cycle/path decomposition problem is hence defined as the problem of finding such a maximum cycle/path decomposition of a breakpoint graph. See Figure Since every telomere vertex has degree one and every gene vertex has two incident black edges and two incident gray edges, there always exists a Before proceeding to study the problem of sorting unsigned genomes by DCJ operations, we take a first look at the case of signed genomes. Note that the above concept of breakpoint graph extends naturally to two signed genomes , et al.  further Given a breakpoint graph for two signed genomes Theorem 4 .Lemma 5. For every cycle/path decomposition of G, there exists a signed versionandof genomes A and B such thatwhere b is the number of black edges in the breakpoint graph G and c (AA and IABresp. I) is the number of cycles (resp. AA-paths and AB-paths) in the given cycle/path decomposition of G.Proof. Note that every gene vertex would be visited twice if we traverse all the cycles/paths in a fixed cycle/path decomposition of G. When a gene vertex  is visited for the first time, we may assume that we are visiting the 5\u2032 end of the gene (denoted as ha). When it is visited for the second time, we may assume that we are visiting the 3\u2032 end of the gene (denoted as ta). To obtain a signed genome A and B, respectively.G\u2014that is, there are still b black edges, AAI AA-paths, ABI AB-paths and BBI BB-paths. After closing paths into cycles, the breakpoint graph Moreover, the breakpoint graph Lemma 6. For every signed versionandof genomes A and B, there exists a cycle/path decomposition of G such thatwhere b is the number of black edges in the breakpoint graph G and c (AA and IABresp. I) is the number of cycles (resp. AA-paths and AB-paths) in this cycle/path decomposition of G.Proof. Observe that we would obtain the breakpoint graph G if we combine two extremity vertices of a same gene into a single vertex in the breakpoint graph G which preserves the same numbers of black edges/cycles/AA-paths/AB-paths/BB-paths . After closing paths into cycles, the breakpoint graph Therefore, the trivial cycle/path decomposition of Theorem 7. Let A and B be two unsigned genomes defined on the same set of genes. Then, we haveDCJd = b \u2013 (c + AAI + ABI)where b is the number of black edges in G and c  is the number of cycles  in a maximum cycle/path decomposition of G.Proof. Let us consider a maximum cycle/path decomposition of G. By Lemma 5, we would obtain a signed version A and B such that A into genome B. It hence follows that DCJd DCJ operations can be applied to transform genome A into genome B. Let A in which all genes are positive. We then apply the same sequence of DCJd DCJ operations to the signed genome B if we disregard all the gene signs; in other words, B. Thus, G such that DCJd \u2265 b \u2013 (c + AAI + ABI).Assume now that a sequence of Note that, for a given pair of genomes, the number of black edges is fixed without regard to any cycle/path decomposition. Theorem 7 hence suggests a way to approximate the DCJ distance between two unsigned genomes via maximizing the number of cycles/AA-paths/AB-paths in a cycle/decomposition of the breakpoint graph. To do so, our proposed approximation algorithm performs three subroutines to find edge-disjoint cycles/paths of length one, of length two, and of length no more than three, respectively.Lemma 8. There exists a maximum cycle/path decomposition of G which contains a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length one.Proof. Let C be a maximum cycle/path decomposition of G and C1 a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length one in G. If C3 is a cycle/AA-path/AB-path contained in C1 but not in C . In this case, we would modify the maximum cycle/path decomposition C as follows: take one gene vertex of the only black edge of C3 and re-connect its incident black edges and gray edges in a new way. Consequently, C1 and C2 would be replaced by the two distinct cycles/paths C3 and C4 in C. Suppose by contradiction that the above modification decreases the number of cycles/AA-paths/AB-paths so that the new C is no longer a maximum cycle/path decomposition. Note first that this would happen only when C1 and C2 are two distinct cycles/AA-paths/AB-paths but C4 is a BB-path. Since no AA-path in G could be of length one, C3 is either a cycle or an AB-path. Hence, C3 and C4 together use at least two B-telomeres and at most one A-telomere, and so do C1 and C2 together. Since neither C1 nor C2 is a BB-path, they together shall use A-telomeres no less than B-telomeres, contrasting the previously established fact that they together use at least two B-telomeres and at most one A-telomere. Continue this process with the remaining cycles/AA-paths/AB-paths that are contained in C1 but not in C. It would necessarily end up with a maximum cycle/path decomposition that contains a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length one.G which could contain all the cycles/AA-paths/AB-paths of length one.It is worth noticing that there might be no maximum cycle/path decomposition of Lemma 9. The problem of finding a largest collection of edge-disjoint cycles, AA-paths and AB-paths of length one in the breakpoint graph G is solvable in polynomial time.Proof. We can transform a problem instance of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length one into an instance of the 2-set packing problem, where the base set S contains all the edges of G and each subset of the collection S is comprised of edges of a cycle/AA-path/AB-path of length one in G. The 2-set packing problem can be reduced to the maximal matching problem which is well-known to be solvable in polynomial time by a simple greedy algorithm [lgorithm .G.Following Lemma 9, we assume from now on that there does not exist any cycle/AA-path/AB-path of length one in the breakpoint graph l that traverse a common edge. Although this upper bound is no way the tight one, it is already enough for our purpose to devise an approximation algorithm.The following lemma gives an upper bound on the number of distinct cycles/paths of length less than or equal to Lemma 10. Every edge in the breakpoint graph G belongs to at most (22l+1 \u00d7 2l) distinct cycles/AA-paths/AB-paths of length less than or equal to l.Proof. Let us consider a breadth-first traversal of edges in the breakpoint graph G that starts at a given edge e, and then count all the cycles/AA-paths/AB-paths of length less than or equal to l that use the edge e. Note that every vertex is incident to at most two black edges and at most two gray edges and also that every edge is at distance at most (2l \u2013 1) from another edge of the same cyle/path of length less than or equal to l. The traversal of every such cycle/path will end at two edges at distance i and j from the root edge e, respectively, such that i ,j \u2265 0 and i + j \u2264 2l \u2013 1. If we fix values for i and j, there are at most 2i \u00d7 2j = 2i+j \u2264 22l\u20131 cycles/paths whose traversals end at two edges in distance i and j from the root edge e, respectively. For all the combinations of values i and j such that i \u2264 2l \u2013 1 and j \u2264 2l \u2013 1, there are at most 2l \u00d7 2l \u00d7 22l\u20131 = 22l+1 \u00d7 l2 cycles/paths to be reached; in other words, there are at most 22l+1 \u00d7 l2 cycles/paths of length less than or equal to l that use the edge e.l, we may construct a collection S of subsets of the base set S, where S is comprised of all the edges in G and each subset of S is comprised of edges of a distinct cycle/AA-path/AB-path of length no more than l in G. Then, we obtain an instance  of the k-set packing problem where k = 2l. Further by the above lemma, we obtain the following observations.To find a largest collection of edge-disjoint cycles/paths of length no more than Corollary 11. Finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length two can he transformed into an instance of the degree-bounded 4-set packing problem.Corollary 12. Finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than three can he transformed into an instance of the degree-bounded 6-set packing problem.It is worth noting that, if, as previously done in  on the bLemma 13. The problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length two in the breakpoint graph G can be approximated with ratioin polynomial time, for any positive \u03b5.Lemma 14. The problem of finding a largest collection of edge-disjoint cycles/AA-paths/AB-paths of length no more than three in the breakpoint graph G can be approximated with ratioin polynomial time, for any positive \u03b5.A and B be two unsigned genomes defined on the same set of genes. Given a breakpoint graph G, our proposed algorithm for the cycle/path decomposition is summarized below:Let C1 of cycles/AA-paths/AB-paths of length one by a greedy algorithm;1. Find a largest collection C1;2. Remove from the breakpoint graph all the edges used by the cycles/AA-paths/AB-paths of C2 of cycles/AA-paths/AB-paths of length two by Algorithm APPROX-SP;3. Find a collection C3 of cycles/AA-paths/AB-paths of length no more than three by Algorithm APPROX-SP;4. Find a collection C4 of cycles/AA-paths/AB-paths/BB-paths;5. Decompose the remaining edges arbitrarily into a collection C1 \u222a C2 \u222a C4 or C1 \u222a C3 \u222a C4, depending on which one has the larger size.6. Output either r2 denote the number of cycles/AA-paths/AB-paths of length two, r3 the number of cycles/AA-paths/AB-paths of length three, and r\u2032 the total number of cycles/AA-paths/AB-paths. Let r be the total number of cycles/AA-paths/AB-paths in the cycle/path decomposition returned by our proposed algorithm. The cycles/AA-paths/AB-paths of length one are all excluded from the above counts since it would not affect the worst-case algorithmic performance. We find the worst-case approximation ratio of our algorithm by solving the following optimization problem:For a maximum cycle/path decomposition, let fractional linear programming problem  can be approximated with ratioin polynomial time, for any positive \u03b5.emma 16 . Let A In view of this lemma, the third constraint in the above fractional linear programming problem can be replaced by the inequality Theorem 17. The problem of sorting unsigned permutations by DCJ operations can be approximated within ratioin polynomial time, for any positive \u03b5.Since the introduction of the NP-hard problem of sorting unsigned genomes by double-cut-and-join operations in , the polsitive \u03b5 . The secsitive \u03b5 . In thisdegree-bounded k-set packing problem . In this paper we established this reduction, which then leads to the improved approximation ratios.Conceptually, our proposed algorithm operates in the same spirit as many previous algorithms for approximating the genomic distance via genome rearrangement operations ,10,14,15The authors declare that they have no competing interests.XC conceived the study. All authors contributed to the algorithm analysis, read and approved the final manuscript."}
+{"text": "Flux coupling analysis (FCA) is a useful method for finding dependencies between fluxes of a metabolic network at steady-state. FCA classifies reactions into subsets  in which activity of one reaction implies activity of another reaction. Several approaches for FCA have been proposed in the literature.We introduce a new FCA algorithm, FFCA , which is based on checking the feasibility of a system of linear inequalities. We show on a set of benchmarks that for genome-scale networks FFCA is faster than other existing FCA methods.http://www.bioinformatics.org/ffca/.We present FFCA as a new method for flux coupling analysis and prove it to be faster than existing approaches. A corresponding software tool is freely available for non-commercial use at  Constraint-based analysis of metabolic networks has become increasingly important for describing and predicting the behavior of living organisms ,2. WhileFlux coupling analysis (FCA)  is a useIn the rest of this section, we first recall some basic definitions. Then we briefly review the previously proposed FCA methods.m  metabolites and n reactions, the stoichiometric matrix S is an m \u00d7 n matrix, where element ij Sis the stoichiometric coefficient of metabolite i in reaction j. We denote by R = {1, ..., n} the set of reactions and by M = {1, ..., m} the set of metabolites.For a metabolic network with Irr is the set of irreversible reactions which are assumed to always have non-negative flux values. Rev is the set of reversible reactions which are allowed to have positive, negative or zero flux values. If a reversible reaction has a positive (resp. negative) flux, we say that it is working in forward (resp. backward) direction. Splitting a reversible reaction i means making reaction i irreversible and adding one more irreversible reaction i + n to the network, which works in the backward direction. Without loss of generality, we assume that in the numbering of reactions, the first |Rev| reactions are the reversible ones.There are two types of reactions in a metabolic network. v is the vector of metabolic fluxes through all the reactions, the steady-state condition holds for v if S \u00b7 v = 0. The steady-state flux cone is defined as C = {v \u2208 \u211dn | S \u00b7 v = 0, i \u2265v0, for all i \u2208 Irr}. The lineality space of C is given by lin.space(C) = {v \u2208 \u211dn | S \u00b7 v = 0, i v= 0, for all i \u2208 Irr}.If r \u2208 R, r v= 0 for all v \u2208 C, then r is called blocked, otherwise r is unblocked. The set of blocked reactions will be denoted by Blk. The set of unblocked reactions can be further partitioned based on the reversibility type of reactions [Irev as the set of all reactions that can work only in one direction, i.e., those reactions that take only non-negative or only non-positive flux values at steady-state. If i \u2208 Irev and i v\u2264 0 for all v \u2208 C, one can multiply by -1 the i-th column of the stoichiometric matrix, such that in the modified network, we have i v\u2265 0 for all v \u2208 C. Without loss of generality, we assume that all reactions in Irev are operating in the forward direction.If for some reaction eactions . We defia) Prev, the set of pseudo-irreversible reactions, and (b) Frev, the set of fully reversible reactions. A reaction i is in Prev if it can work in both directions, and additionally, for all flux vectors v in the lineality space of the flux cone, we have i v= 0. Accordingly, we define Frev as the set of those reactions, which can work in both directions, and additionally, can have a non-zero flux value if fluxes through all irreversible reactions are set to zero.The set of reactions that can work in both directions at steady-state is further partitioned into two subsets:  = {i \u2208 R | i v\u2260 0} of reactions active in v is called the support of v. Suppose v \u2208 C is a flux vector and A \u2286 R is a subnetwork. The flux pattern of v for A is defined as A \u2229 supp(v), which is the set of those reactions in A which have non-zero values in v[elementary flux pattern (EFP) if it cannot be written as the union of other flux patterns. For studying EFPs, Kaleta et al. [The set lues in v. A flux a et al.  assume tIn this subsection, we briefly recall existing approaches to flux coupling analysis. For additional information and the technical details on the implementation of these algorithms, we refer to Additional file i and j, two LPs are solved. Depending on the optimal values obtained, the coupling relation between i and j is determined. There is a post-processing step in FCF. Since the reversible reactions have been split, flux coupling relations for these reactions have to be obtained from the coupling relations of the corresponding irreversible forward and backward reactions.The most widely used method for FCA is the Flux Coupling Finder (FCF) algorithm . This apThe FCF algorithm has been successfully used for finding coupling relations in a number of metabolic networks -13,16. HLarhlimi and Bockmayr ,17 have i and j. If each of these reactions can have a non-zero flux independently of the other  that i is directionally coupled to j, then the EFPs of this subnetwork are {i, j} and {j}. Finally, if the reactions are partially coupled, we will have only one EFP, which is {i, j}. With this method, it is not possible to distinguish between partial and full coupling, since flux patterns only contain the information about the activity or inactivity of the fluxes, but not the flux values.Recently, Kaleta et al.  introducIn FCF, and some other FCA approaches, every reversible reaction is split into a forward and a backward reaction. This splitting procedure results in an increase in the number of LPs and also in the size of each LP to be solved. Moreover, a complicated postprocessing step is required to infer the flux coupling relations of the original reversible reactions. For all these reasons, it might be better to perform flux coupling analysis without splitting the reversible reactions. An implementation of FCF without splitting is presented in Additional file i and j can be coupled only if one of the following 4 cases holds  would be possible):Additionally, Larhlimi and Bockmayr  show thai, j \u2208 Irev: In this case, i and j can be directionally, partially or fully coupled.1. i \u2208 Irev and j \u2208 Prev: The only possibility is j \u2192 i.2. i, j \u2208 Prev: In this case, we can only have i \u21d4 j.3. i, j \u2208 Frev: In this case, we can only have i \u21d4 j.4. i and j, and then check if the corresponding coupling relation holds. This will be referred to as \"Reversibility-Type prunings\" . RT-prunings were originally used in MMB-FCA as presented in [Therefore, it is enough to determine the reversibility types of ented in .S, the columns corresponding to the blocked reactions have been removed. According to Proposition 6.13 in [i and j such that i, j \u2208 Prev or i, j \u2208 Frev, the following two statements are equivalent:After RT-prunings, a further improvement can be applied to LP-based FCA methods. Assume that in the stoichiomtric matrix  6.13 in , for two\u2022 i \u21d4 j\u2022 For all v such that Sv = 0, i v= 0 implies j v= 0.This means that it is sufficient to solve only one LP:i and j will be fully coupled if and only if in the above LP Prev/Frev-based improvement .The two reactions An improved version of FCF, which takes into account all of the above-mentioned improvements, has been suggested in . Here weFCA is a promising tool for metabolic network analysis. However, to perform FCA most authors seem to use their personal implementation of the FCF algorithm ,13. Onlymaximize(T x c| Ax \u2264 b) can be solved by enumerating a sequence of feasible solutions, i.e., solutions of the system of linear inequalities Ax \u2264 b such that at each solution x the objective function value T x cimproves. Accordingly, finding one feasible solution could be faster than computing an optimal solution . If (P1) and (P2) are both infeasible, then i and j are partially (and maybe fully) coupled. To check whether they are fully coupled, one has to use other methods, e.g. computing enzyme subsets [If (P1) and (P2) are both feasible, then  subsets  or solvi subsets .i \u2208 Irev and j \u2208 Prev: The only possible coupling relation is j \u2192 i (but not i \u2192 j). Hence, (P1) will always be feasible, because feasibility of (P1) means that i \u2192 j does not hold. However, we need to check the feasibility of (P2). Additionally, since j can take negative values, one more system should be checked for feasibility:2. j \u2192 i. Otherwise, i and j are uncoupled.It can be easily shown that if (P2) and (P3) are both infeasible, then i, j \u2208 Prev or i, j \u2208 Frev: In this case, the following system of linear inequalities should be checked for feasibility:3. i \u21d4 j (because feasibility of (P4) implies j \u2192 i, which in turn implies i \u21d4 j based on Proposition 2 in [i and j are uncoupled.If (P4) is infeasible, then ion 2 in ). If , one can solve the following LP:i vis constant, the optimal value exists if and only if this problem is feasible. Similar LPs can be solved to check the feasibility of (P2) and (P3).Since In Table H. pylori network and especially for the large networks of S. cerevisiae and E. coli, FFCA proves to be faster than MMB-FCA. The computation time required for MMB-FCA rapidly grows when the number of reactions increases. This is due to the possibly exponential size of the set of generating vectors which has to be computed before finding the coupled reactions . EFP-FCBoth the FCF algorithm and the current implementation of FFCA solve LPs for flux coupling analysis. One might ask why FFCA is faster than the classical FCF method. There are at least five major differences between FCF and FFCA:\u2022 When an LP is solved in FFCA, finding the first feasible solution is sufficient, while the LPs should be solved to optimality in case of the FCF algorithm.\u2022 In the FCF method, in contrast to FFCA, every reversible reaction is split into two (forward and backward) irreversible reactions. This step slows down the procedure and increases the size of the LPs to be solved.\u2022 For computing the flux coupling relation between any pair of reactions, we always need two LPs in FFCA, while in FCF sometimes more LPs have to be solved. For example, for computing the coupling relation between an irreversible and a reversible reaction (after splitting), four LPs are solved  FCF was re-implemented without splitting reactions (W-FCF); (ii) FCF was re-implemented without splitting reactions and with the RT-prunings (WR-FCF); and (iii) FCF was re-implemented without splitting reactions and with the RT-prunings and the PF-improvement (WRP-FCF), as suggested in [One can think of implementing FCF without splitting reversible reactions and/or with the RT-prunings and/or PF-improvement. In order to assess the importance of these issues, three improved versions of FCF were implemented  FCA hasE. coli [E. coli [Since FFCA includes the RT-prunings and PF-improvement, it might be interesting to see how the number of coupling relations  depends on the number of reversible reactions in a network. This problem is studied in Additional file E. coli , for the[E. coli   genome-scale metabolic network [E. coli (iJR904) [E. coli (iAF1260) [Nine metabolic networks were used in this study: (i) ork from ; (ii) RBood cell ; (iii) E E. coli ; (iv) H. network ; (v) yea network ; (vi) th(iJR904) ; (vii) tiAF1260) ; (viii) iAF1260) ; and (ixiAF1260) .For FCA, all uptake reactions were assumed to be able to carry non-zero fluxes.Unless indicated otherwise, all tools were implemented in Matlab v7.4. Details about the implementation of the different FCA approaches, together with the corresponding pseudo-codes are presented in Additional file All computations were performed on a 64-bit Debian Linux system with Intel Xeon 3.0 GHz processor. The running times include the CPU time for preprocessing, computation of flux coupling relations, and post-processing (where necessary).Prev/Frev-based improvement.FCA: Flux Coupling Analysis; FFCA: Feasibility-based Flux Coupling Analysis; FCF: Flux Coupling Finder; MMB-FCA: Flux Coupling Analysis based on Minimal Metabolic Behaviors; EFP-FCA: Flux Coupling Analysis based on Elementary Flux Patterns; LP: Linear Program; MILP: Mixed-Integer Linear Program; RT-prunings: Reversibility-Type prunings; PF-improvement: The authors declare that they have no competing interests.SAM, LD and AB presented the original idea of the work and designed the study. AL and LD introduced the improved versions of FCF. BM and LD implemented the tools and carried out the experiments. The manuscript was first drafted by SAM. The final manuscript was approved by all authors.Different approaches to flux coupling analysis and implementation details. In this file, pseudocodes and implementation details of different FCA methods are presented.Click here for fileDependence of flux coupling analysis on the number of reversible reactions. In this file, we show how flux coupling relations depend on the number of reversible reactions in the E. coli metabolic network.Click here for file"}
+{"text": "In the sensing applications of optical fiber grating, it is necessary to reduce the transmission-type polarization dependence to isolate the sensing parameter. It is experimentally shown that the polarization-dependent spectrum of acousto-optic long-period fiber grating sensors can be suppressed in the transmission port of a \u03c0-shifted Sagnac loop interferometer. General expressions for the transmittance and reflectance are derived for transmission-type, reflection-type, and partially reflecting/transmitting-type polarization-dependent optical devices. The compensation of polarization dependence through the counter propagation in the Sagnac loop interferometer is quantitatively measured for a commercial in-line polarizer and an acousto-optic long-period fiber grating sensor. In adIn this work, three types of polarization-dependent devices, a transmission-type, reflection-type, and mixed (both transmitting and reflecting)-type, are analyzed by use of Jones matrix method. It is shown that the polarization-dependent spectra of transmission-type optical devices can be suppressed in the transmission port of \u03c0-shifted Sagnac loop interferometer ,6, and tWe also characterize experimentally PDL suppression using Sagnac loop interferometer for various devices exhibiting various degrees of PDL such as an in-line polarizer (ILP) and an acousto-optic LPFG sensor. The cancellation of polarization dependence through the counter propagation in the Sagnac loop interferometer is quantitatively measured using a commericial PDL measurement control system. This simple PDL suppression method can be used to minimize the various PDL effect.2.deviceT, between the input and transmitted field and the reflection, deviceR, between the input field and reflected field are described by the Jones matrices in \u03b1, \u03b2, \u03b4, and \u03b5 are all real numbers and birefringence of the device is considered to be negligible. These transmission and reflection relations hold for bi-directional propagation.A schematic diagram of the Sagnac loop interferometer with a polarization-dependent device, similar to the one demonstrated in , is showSagnacT, and reflectance, SagnacR, of a Sagnac interferometer can be solved analytically using Jones matrix analysis. In the waveplate in \u03b8, with respect to the laboratory coordinates.  The two cases when \u03b8 = 0, \u0393 = 0 and \u03b8 = \u03c0/4, \u0393 = \u03c0 are expressed in \u03b8 = 0, \u0393 = 0 (no waveplate), the Sagnac loop interferometer works as mirror; that is, it exhibits maximum reflection and minimum transmission. Contrarily, for a waveplate with \u03b8 = \u03c0/4, \u0393 = \u03c0 (\u03c0-shifted waveplate at angle \u03c0/4), maximum transmission and minimum reflection can be achieved in Ports 2 and 1, respectively. We consider Port 1 as the reflection port and Port 2 as the transmission port of a Sagnac interferometer with a nested optical device. With 1l set equal to the length between Ports 3 and 5 and 2l set equal to the arm length between between Ports 4 and 6, \u0394l is defined as 1l \u2212 2l. When \u0394l = 0 or 1l = 2l, as the Sagnac interferometer is referred to as a length-symmetric Sagnac loop interferometer. The longitudinal phase constant for a traveling wave in the fiber is represented as k.Using a procedure similar to the one shown in , the traSagnacR, contains polarization-dependent terms in each of the three types of devices. The transmittance, SagnacT, also includes polarization-dependent terms, except for the case of a transmission-type device, in which the intensity is null at the transmission port. In comparison, the \u03c0-shifted Sagnac loop interferometer shows us an interesting theoretical result. Both the reflectance, SagnacR, and the transmittance, SagnacT, do not have polarization-dependent terms in both transmission-type and reflection-type devices. The case of In this research, more general cases are considered. For a length-symmetric Sagnac loop interferometer, the expression for the reflectance in 3.As a representative polarization-dependent device having the highest polarization dependence to the input polarization state, a commercial in-line polarizer (ILP-155-09-09-1) is selected in this experiment  because Without a Sagnac loop, the average PDL of the ILP is measured to be \u223c55 dB in each transmission direction. However, the average PDL value is dramatically reduced to less than 0.45 dB when it is placed within a Sagnac loop. The polarization dependence, quantified as PDL, can be measured from a control system consisting of a tunable laser , polarizer, and polarimeter . The intrinsic polarization dependence of the transmission-type polarization-dependent optical device can be measured by placing it between polarizer and polarimeter in any direction when the device has similar transmission characteristics in both transmission directions. Thus, the measured PDL values are similarly measured in both directions. As shown in These can in principle be minimized by optimizing all components used to construct the Sagnac loop. A large number of the packaged optical devices have been treated as failure products at their final test stage just due to the high PDL value only. It is expected that the intrinsic and fabrication-induced PDL of these products can be easily compensated with the incorporation of a Sagnac loop in the packaging process.4.01, TM01, and HE21 modes is clearly observed for an acousto-optic LPFG sensor with an interaction region consisting of a 28-cm-long dispersion compensating fiber (OFS EHS100), [The polarization dependent transmission and reflection of an acousto-optic LPFG sensor are also experimentally examined by placing it inside the Sagnac loop interferometer with waveplate and are compared with expressions in EHS100), . The out\u03b8 = 0). The spectral reflectance is easily changed by tuning the input polarization as shown in \u03b8 = \u03c0/4 by maximizing the intensity in the transmission Port 2 as shown in For the case of 4.We have generally analyzed and measured the polarization dependence cancellation of optical fiber grating sensor using a \u03c0-shifted Sagnac loop interferometer. For the feasible intrinsic PDL-free integrated optical devices, a commercial-grade in-line polarizer device was tested to verify the proposed PDL compensating method. A representative type of polarization-dependent device, an acousto-optic LPFG sensor, is also experimentally proved for the polarization-dependence suppression. It is expected that the use of the Sagnac loop can save many optical sensor products, such as FBG sensors and micro-bending LPFG sensors which have been limited in their applications solely due to their high PDL."}
+{"text": "Recent studies have revealed the importance of considering the entire distribution of possible secondary structures in RNA secondary structure predictions; therefore, a new type of estimator is proposed including the maximum expected accuracy (MEA) estimator. The MEA-based estimators have been designed to maximize the expected accuracy of the base-pairs and have achieved the highest level of accuracy. Those methods, however, do not give the single best prediction of the structure, but employ parameters to control the trade-off between the sensitivity and the positive predictive value (PPV). It is unclear what parameter value we should use, and even the well-trained default parameter value does not, in general, give the best result in popular accuracy measures to each RNA sequence.pseudo-expected accuracy, which can easily be computed from base-pairing probabilities, is introduced. It is shown that the pseudo-expected accuracy is a good approximation in terms of sensitivity, PPV, MCC, or F-score. The pseudo-expected accuracy can be approximately maximized for each RNA sequence by stochastic sampling. It is also shown that well-balanced secondary structures between sensitivity and PPV can be predicted with a small computational overhead by combining the pseudo-expected accuracy of MCC or F-score with the \u03b3-centroid estimator.Instead of using the expected values of the popular accuracy measures for RNA secondary structure prediction, which is difficult to be calculated, the This study gives not only a method for predicting the secondary structure that balances between sensitivity and PPV, but also a general method for approximately maximizing the (pseudo-)expected accuracy with respect to various evaluation measures including MCC and F-score. To predict the secondary structure of an RNA sequence is a classic problem of sequence analysis in bioinformatics. The importance of accurate predictions of secondary structures has increased due to the recent finding of functional non-coding RNAs whose functions are closely related to their secondary structures -3. SeconThere are many tools and algorithms for secondary structure prediction -11. The et al. [et al. [Therefore, another approach that considers the entire distribution of possible secondary structures of a given sequence has been introduced. Ding et al.  proposed [et al.  proposed [et al. ,10,19-22 [et al. -25 and o [et al. -28.not employ the accuracy measures that are used in actual evaluation of RNA secondary structure, namely, sensitivity (SEN), positive predictive value (PPV), Matthews correlation coefficient (MCC) and F-score, with respect to predicted base-pairs. From a view- point of MEA, it is useful to consider the estimators that maximize expectation of those accuracy measures. Because the computation of those estimators generally demands huge computational time, the previous studies could not use those accuracy measures directly.For RNA secondary structure predictions, two MEA-based estimators have been proposed: (i) the estimator proposed by  and (ii)Moreover, the previous MEA-based estimators contain a parameter that controls the balance between SEN and PPV of base-pairs in a predicted secondary structure. It is, however, unclear how to select the parameter in order to obtain one reasonable secondary structure , although there are situations that only one predicted secondary structure is required. There is also a possibility that the optimal parameter might depend on the length of sequence and/or the type of RNA family, although the \u03b3-centroid estimator (and the estimator proposed by ) employspseudo-expected accuracy of a secondary structure with respect to a given accuracy measure, which is a function of the number of true positive base-pairs (TP), true-negative base- pairs (TN), false-positive base-pairs (FP) and false- negative base-pairs (FN). The pseudo-expected accuracy is then defined by using expected TP, TN, FP and FN. As the accuracy measures, we utilize SEN, PPV, MCC and F-score with respect to base-pairs, which are commonly used in the evaluations of RNA secondary structure predictions, because the base- pairs are essential for forming secondary/tertiary structures, which are known to be biologically important.In this study, to address the drawbacks of the current MEA-based methods described above, We introduce the The pseudo-expected accuracy is easily calculated using the base-pairing probability matrix, and can be computed much more efficiently than the expected accuracy. Although the pseudo-expected accuracy is not equal to the expected accuracy of a predicted secondary structure, we found that the pseudo-expected accuracy gives a good approximation of the expected accuracy in our situation. Accordingly, we also introduce the approximated estimators that maximize the expected accuracy of a given accuracy measure. Moreover, by combining the pseudo-expected MCC/F-score with the \u03b3- centroid estimator, it is possible to predict the balanced secondary structure between SEN and PPV (which seems to be a reasonable secondary structure in many situations when only one predicted secondary structure is required), although there is a small computational overhead.The techniques described in this paper will be extended to design the maximum expected accuracy estimator for various evaluation measures (cf. ).x as a triangular binary matrix:\u03b8 = {\u03b8ij}i < j where \u03b8ij = 1 means that i-th base xi and j-th base xj form a base-pair, and \u03b8ij = 0 means that i-th base xi and j-th base xj do not form a base-pair. In this study, pseudo-knotted base-pairs are not allowed in a secondary structure. For an RNA sequence x, where |x| is the length of x. A probability distribution on S(x) (denoted by p(\u00b7|x)) is given by the McCaskill [x, {pi,j}i <j, has entries I(\u00b7) is the indicator function that returns 1 if the condition is true and 0 otherwise. The base-pairing probability matrix of a given RNA sequence x can be computed using the McCaskill (Inside-Outside) algorithm, whose complexities are O(|x|3) and O(|x|2) for time and space, respectively .\u03b8 = {\u03b8ij}i < j \u2208 S(x) and \u03c3 = {\u03c3ij}i < j \u2208 S(x) of an RNA sequence x, we defineFor two secondary structures \u03b8 is a reference (correct) secondary structure and is a predicted secondary structure of x, Eqs. (1), (2), (3), (4), (5), (6), (7), and (8) are the number of true positive base-pairs, the number of true negative base-pairs, the number of false positive base-pairs, the number of false negative base-pairs, the SEN, the PPV, the MCC and the F-score, respectively. Because the base-pairs in a secondary structure are biologically important, accuracy measures based on base-pairs are useful and SEN, PPV, MCC and F-score are widely-used accuracy measures for secondary structure predictions. Note that MCC and F-score are balanced measures between SEN and PPV.  In the following, Acc means one of the SEN, PPV, MCC and F-score.When p(\u03b8|x) on S(x), we calculate the expected values of Eq. (1) to Eq. (4).Given a probability distribution pij} indicates the base-pairing probability matrix. Moreover, we calculate the expected accuracy of an accuracy measure Acc  of \u03c3 as follows:Where {Acc for a given secondary structure \u03c3  has been reported. The number of candidate secondary structures increases exponentially with the length of the RNA sequence , so to compute the expected Acc is an intractable problem. Therefore, we approximate it using stochastic sampling: For N secondary structures In order to compute the expected sampling ,31 of seN is sufficiently large by the properties of stochastic sampling. It should be noted that the sample size N grows exponentially with the sequence length to Acc of \u03c3.for Acc is generally written as a function of TP, TN, FP and FN:In our situation, Acc = fpseudo-expected Acc of is defined byThen, for a secondary structure \u03c3, the For example, the pseudo-expected MCC is given byx, the pseudo-expected Acc of \u03c3 can be easily computed by using Eqs. (9), (10), (11) and (12) without employing sampling/enumerating algorithms. Although the pseudo-expected Acc is not equal to the expected Acc, we shall see later that the pseudo-expected Acc is a good approximation of the expected Acc when Acc is equal to SEN, PPV, MCC or F-score.If we have the base-pairing probability matrix of The \u03b3-centroid estimator  for RNA >0 controls SEN and PPV of a predicted secondary structure. This estimator is suitable when we would like to predict more TP and TN and fewer FP and FN because Eq. (17) is equivalent towhere \u03b3 1 + \u03b14)/(\u03b12 + \u03b13) and \u03b1k \u2265 0. Hamada et al. [with \u03b3 =  indicates that the \u03b3-centroid estimator is not optimized for the actual evaluation measures . It is useful to introduce the estimator that maximizes expected SEN, PPV, MCC or F-score directly:Acc efficiently for given \u03c3 and p(\u03b8|x). Because Acc contains products or divisions of TP, TN, FP and FN, no efficient method to compute the estimator Eq. (19) has been found, in contrast to the \u03b3-centroid estimator of Eq. (17). Instead, we consider estimators that maximize pseudo-expected Acc as follows.It is, however, difficult to compute the expected The pseudo-expected SEN and PPV of a secondary structure \u03c3 can be computed byTherefore, the secondary structure given by maximizing pseudo-expected SEN (Eq. (20) with SEN)) is equivalent to the secondary structure that maximizes the sum of base-paring probabilities of the predicted base-pairs. The secondary structure is, therefore, equivalent to the one given by the \u03b3-centroid estimator with a sufficiently large \u03b3 . On the S(x). The number of secondary structures of a given RNA sequence, however, is so large that it is not practical to enumerate all of them. Therefore, we again employ the stochastic sampling of secondary structures and approximate the estimator of Eq. (20) byBecause of the computational difficulty of computing \"argmax\" in Eq. (20) with MCC and F-score (see \"Discussion\" section for more details), we need to evaluate all the secondary structures in S is a set of secondary structures given by stochastic sampling. Note that the computational cost of this estimator is much smaller than that of predictions based on maximizing the expected MCC/F-score. If the pseudo-expected MCC/F-score gives a good approximation of the expected MCC/F-score and we use a sufficiently large sample size, then the estimator in Eq. (23) should be a reliable approximation to the estimator in Eq. (19) that maximizes the expected MCC/F-score.where In the \u03b3-centroid estimator  of Eq.  [g Sthat has the best pseudo-expected MCC/F-score:Eq. (18), which is equivalent in form to the \u03b3- centroid estimator, indicates that the \u03b3-centroid estimator can Acc is equal to MCC or F-score. The pseudo-expected MCC/F-score of each secondary structure \u03c3 \u2208 g Sis easily computed because the base-pairing probability matrix has already been computed.where bias to MCC and F-score  of the secondary structures of RNA sequence x, we used the CONTRAfold model (version 2.02) [\u03b8 is a reference structure.For the dataset, we utilized the S-151Rfam dataset  that conon 2.02)  and the on 2.02)  (in the on 2.02) ). For evAcc (Eq. (15)) with the expected Acc (Eq. (13)) where Acc is SEN, PPV, MCC or F-score. First, we obtained a set of secondary structures from the S-151Rfam dataset in the following way. For each RNA sequence in the S-151Rfam dataset, we predicted the secondary structures using the \u03b3-centroid estimator [k: -5 \u2264 k \u2264 10} \u222a {6} and two models (the McCaskill [Acc (Eq. (13)) of a given secondary structure, because the number of possible secondary structures is immense. Therefore, we plotted Acc of; Eq. (15)) and Acc of \u03c3 approximated by 1 M  samples; Eq. (14)) for each secondary structure \u03c3 in the set of secondary structures.In this experiment, we compared the pseudo-expected stimator  (implemecCaskill  and CONTcCaskill  models).The result is shown in Figure We conducted the experiments on RNA secondary structure prediction by maximizing the pseudo-expected MCC/F-score of the predicted secondary structure with stochastic sampling (the estimator in Eq. (23)). Note that the results in the previous section suggest that the estimator of Eq. (23) with a sufficiently large sample size is a good approximation to the estimator of Eq. (19) that maximizes the expected MCC/F-score.The results are shown in Figure It should be noted that the performance of the estimator that maximizes the pseudo-expected SEN (PPV) corresponds to the leftmost (rightmost) point in the SEN-PPV curve of the \u03b3-centroid estimators.Figure It is also much better than the performance of RNAfold, Sfold and Simfold, all of which return a single prediction. Note that Method M2 with a fixed probabilistic model  generally achieves performance that differs from that of the \u03b3-centroid estimator with the same model for any \u03b3 value. This is because Method M2 automatically selects the secondary structure with the best pseudo-expected MCC/F-score from a set of secondary structures given by the \u03b3-centroid estimator for 17 \u03b3 values, while each point in a SEN-PPV curve of the \u03b3- centroid estimator comes from a fixed \u03b3-value.Table The comparison between the 2nd and 3rd rows in Table In summary, by combining the pseudo-expected accuracy with the \u03b3-centroid estimator, we successfully predict the well-balanced secondary structure between SEN and PPV  and the performance (with CONTRAfold model) is better than that of RNAfold, Simfold, Sfold and CentroidFold.pseudo-expected accuracy,  of a given RNA secondary structure under a probability distribution of possible secondary structures. The pseudo-expected accuracy can be computed much more easily than the expected accuracy, because it is computed using the base-pairing probability matrix of the RNA sequence. Although the pseudo-expected accuracy of a given secondary structure is not equal to the expected accuracy of the structure, our computational experiments have indicated that the pseudo-expected accuracy of a given secondary structure is a good approximation of the expected accuracy of the structure when SEN, PPV, MCC and F-score were used as the accuracy mea-sure. This finding is one of the contributions of this study, which has not been reported in previous research.In this study, we introduced the expected accuracy, it is still unacceptably slow. Therefore, we then proposed the combination of the pseudo-expected MCC/F-score and the \u03b3-centroid estimator, which produces one well-balanced secondary structure with small computational overhead. The computational experiments indicate that this approach achieved the best accuracy among state-of-the-art tools. To employ the \u03b3-centroid estimator in Method M2 is suitable because the \u03b3-centroid estimator is able to represent a secondary structures with an arbitrary balance between the expected TP, TN, FP and FN by adjusting the parameter \u03b3 (see Eq. (18)). This, however, does not prove that there always exists a \u03b3 such that the \u03b3-centroid estimator achieves the best pseudo-expected MCC or F-score. Note that the combination of the pseudo-expected MCC/F-score with the MEA-based estimator proposed by [bias to MCC and F-score, compared to the \u03b3-centroid estimator [Based on this finding, we introduced the approximate estimator that maximizes the pseudo-expected accuracy of a prediction by stochastic sampling, which achieved favorable accuracy in our computational experiments. Although the computational cost of this estimator is much smaller than the estimator that maximizes the posed by  is not sstimator .Although the trade-ff between SEN and PPV is inherent, and MCC or F-score is not always the best choice of quality measure for predicted secondary structures, the proposed method (Method M2) can be applicable when only a single structure is required. The pseudo-expected MCC/F-score is also employed as a ranking measure of several predicted secondary structures.Y that contains all the possible candidate solutions of the target problem, a function Acc for \u03b8 \u2208 Y and y \u2208 Y , and a probability distribution p(\u03b8|D) on Y given data D, then the estimatorAs we described in the Introduction section, the term \"maximum (maximizing) expected accuracy\" (MEA) has been used in a number of previous studies ,7,10,26 Acc is equal to an accuracy measure (or is designed according to an accuracy measure) for a reference \u03b8 and a prediction y. This also implies that p(\u03b8|D) is considered to be a probability distribution of references, which is misleading because p(\u03b8|D) does not usually represent the distribution. In RNA secondary structure prediction, for example, The McCaskill model provides not a probability distribution of reference secondary structures but rather a full ensemble of possible secondary structures [is introduced. When this estimator is called a \"maximum expected accuracy\" (MEA) estimator, ructures .Acc according to accuracy measures for a target problem and a probability distribution p(\u03b8|D) of solutions empirically achieves better performance than other estimators such as the maximum likelihood estimator and the centroid estimator  in RNA secondary structure predictions [The estimator of Eq. 25) with a well-designed function dictions ,10 and i with a wEq. (20) with MCC and F-score can be rewritten asapproximation of Eq. (20) with MCC since TN  is much larger than the others in RNA secondary structure predictions.respectively. Note that Eq. (26) is an The denominators in both equations prevent division of this optimization problem into sub-problems, which is required to design a dynamic programming algorithm, and hence no efficient algorithms to compute Eqs. (26) and (27) have yet been devised. Note that the \"argmax\" operation for only the numerator can be efficiently solved by dynamic programming . .et al. [Recently, Lu et al.  proposedet al. ) with vaet al. ).global alignment problems, the balance between SEN and PPV with respect to aligned bases is important in local alignment problems.The method presented in this paper can be applied to local alignments for biological sequences be-cause the \u03b3-centroid estimator was also introduced in the problem . In contMH and KA conceived the study. MH developed the algorithms, performed the experiments and wrote the manuscript. KS implemented the algorithm in the CentroidFold software. All authors have read and approved the final manuscript.Supplementary Information for the main text. This file includes supplementary information for the main text.Click here for file"}
+{"text": "According the Taqqu's law, 1/f noise has the properties of long-range dependence and heavy-tailed probability density function (PDF). The contribution of this paper is to exhibit that the prediction error of a biomedical signal of 1/f noise type is long-range dependent (LRD). Thus, it is heavy-tailed and of 1/f noise. Consequently, the variance of the prediction error is usually large or may not exist, making predicting biomedical signals of 1/f noise type difficult.A fractal signal  Theoretically speaking, in general, we cannot assume that Var[x(t)] always exists [\u03b1-stable distributions [x(t)] may be infinite. That Var[x(t)] does not exist is particularly true for signals in biomedical engineering and physiology, see Bassingthwaighte et al.  should be minimized. Thus, the premise that Var[e(m)] can be minimized is that it exists.Let e(m)] may be large if p(e) is heavy tailed. In a certain cases, Var[e(m)] may not exist. To explain the latter, we assume that e(m) follows a type of heavy-tailed distribution called the Pareto distribution.It is obviously seen that Var does not exist if a = 1 or a = 2 and if e(m) follows the Pareto distribution.Denote by on. Then , it is ie(m)] does not exist may not occur if e(m) is light-tailed. Therefore, the question in this regard is whether e(m) is heavy-tailed if a biomedical signal x(n) is of 1/f noise. The answer to that question is affirmative. We explain it below.Note that the situation that Var may in general be large. In some cases [e(m)] may not exist, making the prediction of biomedical signals of 1/f noise type difficult with the way of minimizing Var[e(m)].We have explained that the prediction error me cases , Var[e(m"}
+{"text": "Do humans prefer the self even over their favorite other person? This question has pervaded philosophy and social-behavioral sciences. Psychology\u2019s distinction between explicit and implicit preferences calls for a two-tiered solution. Our evolutionarily-based Dissociative Self-Preference Model offers two hypotheses. Other-preferences prevail at an explicit level, because they convey caring for others, which strengthens interpersonal bonds\u2013a major evolutionary advantage. Self-preferences, however, prevail at an implicit level, because they facilitate self-serving automatic behavior, which favors the self in life-or-die situations\u2013also a major evolutionary advantage. We examined the data of 1,519 participants, who completed an explicit measure and one of five implicit measures of preferences for self versus favorite other. The results were consistent with the Dissociative Self-Preference Model. Explicitly, participants preferred their favorite other over the self. Implicitly, however, they preferred the self over their favorite other . Results are discussed in relation to evolutionary theorizing on self-deception. Is the self the most cherished entity that humans possess, preferred even over their most valued other person ? Alternatively, as cultural animals explicit level? Second, are preferences for self more or less prevalent than preferences for favorite other at an implicit level? Our answers to these two questions are guided by an evolutionary model that we outline next.Recent psychological advances call for a two-tiered solution to this age-old dilemma. Preferences, like self-oriented versus other-oriented ones, can be held at an explicit level; as such, they are conscious, reflective, and reasoning-based Explicitly, preferences for favorite other should prevail over preferences for self. Explicit other-preferences are evolutionarily adaptive, because they convey caring for others Implicitly, however, preferences for self should prevail over preferences for favorite other. Implicit self-preferences are also evolutionarily adaptive, because they facilitate self-favoring automatic behavior in live-or-die situations To address the above two pivotal questions, we propose the Dissociative Self-Preference Model. Its evolutionary backbone generates divergent hypotheses for explicit and implicit preferences. explicit level. However, preferences for self will predominate over preferences for favorite other at the implicit level. We test these hypotheses on a large and divergent sample, using five established implicit measures for generalizability purposes.We report a study in which we examine the two hypotheses derived from the Dissociative Self-Preference Model. Preferences for favorite other will predominate over preferences for self at the www.dfg.de) to the second author (grant identifier: GO 1107/4-1). The DFG's board of ethics passed the research proposal that underlies the present study. DFG-funded projects do not require additional approval by other ethics committees . Irrespective, we informed participants at the outset that the study concerns the psychological representation of their favorite person and that they therefore will be asked to complete corresponding self-report measures and sorting tasks. Participants were also informed that participation is anonymous, consented to participate in this study by clicking on a button, and were shown a debriefing screen at the conclusion of the study session.The study was run as part of a research grant awarded by the German Research Foundation . Following that, we wondered whether participants had chosen themselves as their favorite other. 42 participants (3%) had done so, and we excluded their data from our analyses. Next, participants reported their own name. Subsequently, participants completed one of five implicit self-other preference measures and one explicit self-other preference measure. For each participant, we determined randomly which implicit measure (s)he had to complete. Also, for each participant, we determined randomly whether (s)he received the implicit or the explicit measure first.We used a diverse internet sample in terms of age, occupation, and family status comprising 1,519 German volunteers  \u201c\u2026more positive feelings?\u201d, (2) \u201c\u2026more negative feelings?\u201d (reverse-scored), and \u201cWho is more\u2026\u201d (3) \u201c\u2026 worthy to you?\u201d, (4) \u201c\u2026pleasant to you?\u201d, (5) \u201c\u2026likable to you?\u201d, (6) \u201c\u2026worthless to you?\u201d (reverse-scored), (7) \u201c\u2026unpleasant to you?\u201d (reverse-scored), and (8) \u201c\u2026unlikable to you\u201d (reverse-scored) (\u03b1 \u200a=\u200a.89).Participants responded to the following eight items on rating scales ranging from 1\u200a=\u200a \u201c[Different implicit measures may assess somewhat distinct facets of self-preference own full name]\u201d and \u201c[favorite person\u2019s full name].\u201d Attitude-stimuli of the stimuli-based measures  were idiosyncratically generated by each participant. Specifically, participants were instructed to provide \u201cthree words that clearly and spontaneously signify [favorite person\u2019s full name], and three different words that clearly and spontaneously signify yourself.\u201d The instructions set two additional constraints. First, the chosen words for self and favorite other had to be equivalent . Second, each word had to signify distinctively one attitude-category and not the other . Instructions also included examples suggesting the use of first names, last names, nicknames, or initials.Attitude-categories of the category-based measures  were \u201c[Valence-categories of the category-based measures  were \u201cPositive\u201d and \u201cNegative.\u201d Valence-stimuli of the stimuli-based measures  were \u201cworthy,\u201d \u201cpleasant,\u201d and \u201clikable\u201d for the \u201cPositive\u201d category and \u201cworthless,\u201d \u201cunpleasant,\u201d and \u201cunlikable\u201d for the \u201cNegative\u201d category . These valence-stimuli were chosen to match the items of the explicit measure.In the IAT, the two halves of critical trials are administered in separate blocks, one after the other. The SBIAT is a variant of the IAT that administers all its critical trials randomly within a single block. This can address several alternative explanations of IAT effects In the APP, participants are instructed to indicate\u2013as fast as possible\u2013whether valence items are positive or negative. Shortly before a valence item is presented, however, an attitude item (here: from the categories \u201cself\u201d or \u201cfavorite other\u201d) is presented. Presentations of valence items and attitude items are randomized, so that four types of trials emerge: self-positive trials, self-negative trials, favorite other-positive trials, and favorite other-negative trials. Comparison of the reaction times between self-positive and favorite other-negative trials with favorite other-positive and self-negative trials constitutes an implicit index of self-other preference. Specifically, the degree to which a person is faster at self-positive and favorite other-negative trials, compared to favorite other-positive and self-negative trials, is an indicator of self-preference over other-preference In the NLT, participants indicate, for all letters of the alphabet, how positive or negative they perceive them to be. The degree to which participants rate their initials more positive than the initials of their favorite other is an indicator of self-preference over other-preference r \u2264.29, all ps <.05  as comparison value, t \u200a=\u200a -23.70, p<.001 . Implicitly, however, participants preferred self over their favorite other, as indicated by one-sample t-tests with the implicit measures' scale-midpoints  as comparison values, t \u200a=\u200a4.95, p \u200a=\u200a.001 , t \u200a=\u200a3.04, p \u200a=\u200a.003 , t \u200a=\u200a2.29, p \u200a=\u200a.02 , t \u200a=\u200a2.59, p \u200a=\u200a.01 , t \u200a=\u200a5.78, p \u200a=\u200a.001 .Next, we tested the two hypotheses derived from the Dissociative Self-Preference Model. Results were fully in line with these hypotheses . ExpliciF \u200a=\u200a2.03, p \u200a=\u200a.09, justifying their aggregation. In line with our results for each implicit measure, the aggregate implicit index revealed a clear preference for self over favorite other as indicated by a one-sample t-test with the implicit index's midpoint  as comparison value, t \u200a=\u200a8.48, p<.001 .Further, we wondered whether it is justified to treat the five implicit measures interchangeably in our subsequent analyses. Therefore, we conducted an ANOVA with type of implicit measure as the Independent Variable (IV) and standardized implicit self-preference as the Dependent Variable (DM) . Despite sufficiently large samples to detect reliably even small effects, this analysis revealed that the standardized effects did not differ significantly across implicit measures, t-test revealed a significant difference between standardized explicit preferences for favorite other  and standardized implicit preferences for self , t \u200a=\u200a25.53, p<.001. This result buttresses the substantial difference between explicit other-preferences and implicit self-preferences. Additionally, comparison of absolute means and effect sizes  and standardized implicit self-preference as the DV. Despite sufficiently large samples to detect reliably even small effects, this analysis revealed that the standardized effects did not differ significantly across type of favorite other, F \u200a=\u200a.12, p \u200a=\u200a.88. In contrast, an ANOVA with the three major types of favorite other as the IV and explicit other-preference as the DV was significant, F \u200a=\u200a22.05, p \u200a=\u200a.001. Post-hoc analyses revealed significant differences between all three types of favorite other at ps <.003 (Scheff\u00e9-tests). Specifically, other-preferences were strongest for child as favorite other , weaker for spouse/partner as favorite other , and weakest for best friend as favorite other   .People share more genes with their child than with their partner/spouse or best friend. Thus, from an evolutionary standpoint, it is conceivable that implicit preferences for self should be diminished when favorite other is one's child, rather than one's spouse/partner or best friend. Such pattern may be expected because it may maximize the survival-chances of one's genes. However, implicit self-preferences did not vary as a function of type of favorite other and a closer examination of the prehistoric parent-child relationship may provide an evolutionary explanation for our results. Specifically, in prehistoric humans both, the fertility rate as well as the child death rate were high F \u200a=\u200a1.28, p \u200a=\u200a.26, as well as for implicit preferences, F \u200a=\u200a1.08, p \u200a=\u200a.30.We tested for sex differences in explicit and implicit preferences, using a MANOVA with sex as the IV and explicit and implicit preferences as simultaneous DVs. Despite sufficiently large samples to reliably detect even small differences, we found no sex differences for explicit preferences, r \u200a=\u200a -.03, p \u200a=\u200a.23, as well as with implicit preferences, r \u200a=\u200a.01, p \u200a=\u200a.66.We also tested whether explicit and implicit preferences varied as a function of participant age. Despite sufficiently large samples to reliably detect even small effects, age was uncorrelated with explicit preferences, N1\u200a=\u200a520, N2\u200a=\u200a793) completed two prior studies, each including a different, well-validated measure of self-presentation (datasets were linked via anonymous key-strings). Comparison of correlation coefficients using Fisher z transformation revealed that the influence of self-presentation on implicit and explicit preferences did not differ significantly with regard to the first index, z \u200a=\u200a.74, p \u200a=\u200a.46 . Together, conscious self-presentational efforts to deceive others are unlikely to account substantially for other-preferences (Do explicit other-preferences reflect genuine beliefs or conscious self-presentational efforts to deceive others? Additional analyses suggest the former. First, internet studies minimize self-presentation ferences .Explicitly, humans prefer their favorite other over the self. Implicitly, however, they prefer the self over their favorite other\u2013be it their spouse/partner, best friend, or child. We consistently documented these results across five subsamples using five divergent implicit measures. The uncovered dissociative preferences may reflect ancestral traces and confer, in distinct ways, evolutionary advantages to the individual: Explicit preferences establish and cement interpersonal ties Von Hippel and Trivers distal evolution-based predictions\u2013namely, the general human tendency to hold explicit other-preferences, but implicit self-preferences. Future research could examine the proximate mechanisms underlying the reported findings. For example, humans seek self-awareness in positive situations, but avoid self-awareness in negative situations The present hypotheses tested In conclusion, the findings are pertinent to a long-standing controversy in philosophy and the social-behavioral sciences: the dilemma of self-love versus other-love. Offering a middle-ground solution, the findings favor the arguments by Rousseau, Mencius, and Botero at the explicit level, while favoring the arguments of Hume, Xunzi, and Machiavelli at the implicit level. In Aristotle\u2019s"}
+{"text": "By the practical success of the COSMO-RS fluid phase thermodynamics model ,2 in manSince the same intermolecular interaction modes, which govern fluid phase thermodynamics, are also responsible for binding of ligands to receptors, it is most plausible that a \u03c3-based description of of ligand-ligand similarity or of ligand-receptor interactions should be very promising. Yet, since in COSMO-RS theory the 3D- distribution of the polarization charge density \u03c3 on the molecular surface is reduced to a histogram, the \u03c3-profile, the initial approaches in this direction [The same technique can be used to consistently align a set of ligand molecules based on their local \u03c3-profiles. After such alignment, the local \u03c3-profiles or the set of local \u03c3-moments, which is a compressed representation of the \u03c3-profiles, are available as a grid-based local descriptor set, which can be used for subsequent molecular field analysis (MFA). COSMO-RS theory even provides a rationale that the binding free energy, including desolvation, must be a linear function of this set of descriptors. First validation studies have proven that the COSMOsim3D based MFA yields very promising results."}
+{"text": "In this article, we present a graph-based method using a cubic template for volumetric segmentation of vertebrae in magnetic resonance imaging (MRI) acquisitions. The user can define the degree of deviation from a regular cube via a smoothness value \u0394. The Cube-Cut algorithm generates a directed graph with two terminal nodes (s-t-network), where the nodes of the graph correspond to a cubic-shaped subset of the image\u2019s voxels. The weightings of the graph\u2019s terminal edges, which connect every node with a virtual source s or a virtual sink t, represent the affinity of a voxel to the vertebra (source) and to the background (sink). Furthermore, a set of infinite weighted and non-terminal edges implements the smoothness term. After graph construction, a minimal s-t-cut is calculated within polynomial computation time, which splits the nodes into two disjoint units. Subsequently, the segmentation result is determined out of the source-set. A quantitative evaluation of a C++ implementation of the algorithm resulted in an average Dice Similarity Coefficient (DSC) of 81.33% and a running time of less than a minute. Lumbar stenosis (LS), a narrowing of any part of the lumbar spinal canal with encroachment on the neural structures by surrounding bone and soft tissue Sometimes, degenerative spondylolisthesis, an asymptomatic slipping forward of one lumbar vertebra on another one with an intact neural arch, can be linked to LS Several features of the spinal anatomy can be distinguished by their different grey values in an MR image. In most T1- and T2-weighted image slices, normal adult vertebral body bone marrow can be differentiated from the outer boundaries of the vertebral body by a homogeneously lighter grey value This, however, does not apply to slices that depict the pedicles. Several approaches for vertebra segmentation have been proposed in the literature Klinder et al. gold standard CT data and they regard their algorithm as robust. Furthermore, they point out that different threshold levels, within visually acceptable intervals, had very little effect on the registration results. The authors conclude that in general, the accuracy of the registration relies on the similarity between actual and automatically generated surfaces as well as the precision of the digitized points used for the registration.Hoad and Martel \u0160tern et al. Aslan et al. Weese et al. Yao et al. Ghebreab and Smeulders Zuki\u0107 et al. Kelm et al. Square-CutOur approach to solve the problem of three-dimensional vertebral body segmentation is a non-trivial enhancement of the previously introduced two-dimensional graph-based segmentation strategy Section 2 presents the methods behind the introduced algorithm, Section 3 presents the results of our experiments and Section 4 concludes the paper and outlines areas for future work.The rest of this contribution is organized as follows: Cube-Cut. Cube-Cut extends a two-dimensional approach, previously introduced by Egger et al. Cube-Cut have been presented on a workshop The new vertebral body segmentation algorithm presented here will be referred to as P, Cube-Cut first selects a subset P\u2019P of the image's voxels and in a last step it tags each voxel pP\u2019 with either one of the labels sL or tLGiven a volumetric MR image pP\u2019 involves two penalties The labeling of a voxel p(t(p))\u22650 is the penalty for assigning the label t(p) to p andDp,p\u2019(t(p),t(p\u2019))\u22650 is the penalty for assigning t(p) to p when t(p\u2019) is the label of the voxel p\u2019VD describes a voxel's affinities to the labels sL and tL. For example, the higher p(t(p)\u200a=\u200aLt)D, the more p is affiliated with sL. V on the other hand reflects a voxel's affiliation to another voxel. In practice, p,p\u2019(t(p), t(p\u2019))V is greater than zero only if t(p)\u2260t(p\u2019). Thus, V indirectly describes p's affiliation with p\u2019 by awarding a penalty for tagging the two voxels with different labels: The higher p,p\u2019V, the more p is affiliated with p\u2019. Nevertheless, note that p,p\u2019(t(p), t(p\u2019))\u200a=\u200a0 for t(p)\u2260t(p\u2019)V does not necessarily mean that the two voxels p and p\u2019 can be tagged differently without penalty costs. If, for instance, p,p\u2019\u2019(t(p), t(p\u201d))>0V, for t(p)\u2260t(p\u2019\u2019) and p\u2019\u2019P\u2019 and if p\u2019\u2019,p\u2019(t(p\u2019\u2019), t(p\u2019)) >0V for t(p\u2019\u2019)\u2260t(p\u2019), then the penalty cost for assigning different labels to p and p\u2019 is at least p,p\u2019\u2019, Vp\u2019\u2019,p\u2019}min{V.L which minimizes.L\u200a=\u200a{t(p)|pP\u2019} is a labeling of the subset P\u2019Cube-Cut tags the voxels in a way such that the overall penalty cost is minimized. The overall cost is described by (2). Cube-Cut thus returns the argument P\u2019 and implements D and V (on the basis of the predetermined subset P\u2019) in a way such that the returned labeling is to be interpreted in the following manner (Cube-Cut selects g manner :pP\u2019 for which st(p)\u200a=\u200aL inside the vertebral body andCube-Cut assumes all voxels pP\u2019 for which tt(p)\u200a=\u200aL can be assumed outside the vertebral body.all voxels Hence, in a first step Cube-Cut selects a subset of voxels, and on the basis of this subset, implements two penalty functions which then determine a clustering of the subset into two disjoint units of voxels. One unit describes the vertebral body while the other describes the background (which may include other vertebrae). The following paragraphs will describe the implementation of the algorithm.pn rays that expand from a user-defined seed point in the MR image. Each ray consists of k equidistantly spread voxels, where for all rays, the first voxel is always the user-defined seed point, so that |P\u2019|\u200a=\u200an * (k - 1) +1. As the seed point, the number and the length of the rays as well as the number of voxels per ray can be determined by the user. It is assumed that each ray exceeds the vertebral body. In the following, let P\u2019 denotes a voxel on ray r, where 1\u2264 r \u2264 n and where the voxel 1p or r might be omitted. Furthermore, from now on, k will always denote the number of voxels per ray and n the number of rays).The voxels i\u200a=\u200aj \u2260 1 and m \u2260 n, then the voxels k voxels on each ray, there are k-1 different sized cubes for which 1p is the center , E(G))), c, s, t), where G is a directed, two-terminal graph and |V (G)|\u200a=\u200a|P\u2019| +2. Each vertex vV(G)\\{s,t} corresponds to exactly one voxel pP\u2019 and no two vertices correspond to the same voxel. In the following, pv will denote a mapping of the vertex vV(G)\\{s,t} onto its corresponding voxel pP\u2019 and vp will describe the reverse mapping. The source s and the sink t have no counterparts in P\u2019 and thus they are referred to as virtual nodes. In E(G), there exist two types of edges Cube-Cut generates a network i-links (inter-links) connect vertices vV(G)\\{s,t} with each other. The i-links are further subdivided into z-edges and xy-edges, where z-edges connect vertices corresponding to neighboring voxels of the same ray (e.g. (xy-edges connect vertices corresponding to voxels of different rays (e.g. (o-links (outward-links) connect all vertices vV(G)\\{s,t} with the source s (s-links) and the sink t (t-links). Hence, there are two o-links for each vertex.i- and o-links reflect the penalty functions D and V in the following manner (The capacities of the g manner :(3)c\u200a=\u200a0 is assumed, if / E (G). After the graph has been set up, Cube-Cut determines a minimal s-t-cut  by deploying the Boykov-Kolmogorov algorithm http://vision.csd.uwo.ca/code/, accessed: March 2014) and then it labels P\u2019 as follows:Note that the skew symmetry constraint does not have an effect since by convention Since by definition, the capacity of a minimal s-t-cut is minimal among all possible s-t-cuts, the labeling above minimizes (2).z-edges is introduced that ensures that each ray is exactly cut one time by a minimal s-t-cut n is the user-defined number of rays and k the total number of voxels per ray, again . The set of z-edges connects each vertex iv with its predecessor (i-1)v on the same ray , a minimal s-t-cut  has to cut each ray at least once. Yet, it does not cut any ray more than once because that would cost at least 2\u00b7By making sure that the seed point is in , ) around the user-defined seed point (inside the vertebra) and determines its interval of grey values I\u200a=\u200a, where.thi element of a tuple. Furthermore, Cube-Cut also iterates over the cube to determine an average grey value avgg byA voxel o-links, the interval I and the average grey value avgg are used as frames of reference.o-links (note: Each ray r consists of k voxels):The following Pseudo-Code depicts the fundamental principle of how Cube-Cut assigns capacities to the 0 1 2 3 4 5 6 7 8 9 10 11 12 sL. The premise on which this is based is that the user defines the seed point within the vertebral body (in the center).The tL, the t-links  is consequently initialized to zero (line 4 - 6)Furthermore, it is assumed that the last voxel on each ray . This is in order to \"mark\" the outer boundaries.The capacities of all of the other, intermediate Introduction). Thus, on each ray, the difference in value between the last voxel in the vertebral body and the first voxel on the outer boundaries can be assumed high.As already mentioned above, the rays expand from the user-defined seed point in the center of the vertebral body and they eventually intersect with the outer boundaries. Ignoring occasional outliers and homogeneous object/background transition regions for now, the inner vertebral body is characterized by a homogeneous set of voxel grey values, which are all higher or lower than the grey values that make up the outer boundaries . Note that this makes a cut right in front of the corresponding vertices very probable. The next sections explain how peculiarities and anomalies in vertebral MRI data sometimes prevent a cut from happening right in front of the outer boundaries and how Cube-Cut addresses these adverse effects.Taking the condition in line 7 into account, the outer boundaries therefore implement high A cut right in front of the outer boundaries is a cut that separates the last vertex that corresponds to a voxel which is still located inside the vertebral body from the subsequent ones on the same ray. If, for each ray, the cut takes place right in front of the outer boundaries of the vertebral body, then Cube-Cut returns a satisfactory segmentation result.r that corresponds to a voxel on the outer boundaries/background. If a minimal s-t-cut  cuts the ray right in front of S and T, then.s-weights since behind the outer boundaries, the rays mostly penetrate homogeneous areas dissimilar from the vertebral body (compare lines 7 & 8 of the pseudo code). Let Nevertheless, there are exceptions. w, which loads the s-weights according to their distance from the seed point (see next section). Line 8 of the pseudo code is extended to:As a consequence, the condition in line 7 of the pseudo code holds true for a sufficient number of background voxels on each of the affected rays, which is why condition (8) is not satisfied. Thus, the overrun occurs. Observe that the same applies to homogeneous object/background transition regions. Among others, Cube-Cut tackles this problem by introducing a coefficient Another phenomenon that negatively affects the segmentation result is outliers. Outliers share all relevant properties  that distinguish the vertebra's boundaries except that they are part of the inner vertebral body.s-capacities and then the smoothness constraint will be discussed.To be specific, an outlier causes the violation of w(\u00b7) loads an s-capacity according to the corresponding voxel's \u200a=\u200ami+b, where kib\u200a=\u200a1-m.The coefficient  the ray . For a rw\u200a=\u200a1 for the seed point i\u200a=\u200a1), w\u200a=\u200a0.5\u200a=\u200a0 for the last voxel on each ray. A voxel far away from the seed point is more likely to be outside the vertebral body.Observe that since the voxels are distributed uniformly on each ray, on a ray  and w: The smoothness constraint, which also addresses a violation of condition (9), will be the subject matter in the next section.I\u200a=\u200a, where X, Y, Z0N, can be characterized by a bijection S : XYZ, where XYXY is a cohesive area. Li et al. refer to a surface as feasible if two smoothness constraints are satisfied:S and S as well as S and S are neighboring x- and y-positions. Thus, two neighbors on a feasible surface cannot be arbitrarily distant from each other. Hereby, the smoothness constraints assure what Li et al. refer to as \"surface connectivity\". Observe that for a plane The smoothness constraint is based on the optimal surface segmentation algorithm developed by Li et al. z-axis. The voxels that make up a ray do not necessarily have to lie on neighboring positions in the image. Furthermore, for convenience, assume that I is a binary image with only two possible values for each voxel: \u201ccolored\u201d xor \u201cwhite\u201d. In addition, let all rays intersect with a colored surface S(XY) in I, which means that each ray extends from XY and shares exactly one colored voxel with the surface.Now consider a number of equidistant rays that consist of the same number of uniformly spread voxels and which all extend parallel to the x-direction , which extend parallel to the z-axis, as described above. Here, a smoothness parameter In this context, in which only a subset of the image's voxels is observed, the smoothness constraint has to be defined via the neighborhood relations of the rays. Cube-Cut allows the user to impose a smoothness constraint on the segmentation result. It interprets each of the six sides of a vertebral body's outer boundaries  as a feasible surface. Furthermore, it takes into account that the six surfaces are anatomically connected, which is why the neighborhood relations overlap at the \"edges\" of the boundaries.xy-edgesCube-Cut implements the smoothness constraint 4N denotes a 4-neighborhood and as already mentioned above, the neighborhood relations overlap at the \"edges\" of the cubic voxel subset that the algorithm observes.xy-edges ensures that a minimal s-t-cut cuts the rays in a way such that the vertebra is segmented within the boundaries of the user-defined smoothness constraint The infinity-weighting of the straint  . Note thxy-edges for a For a smoothness constraint www.mevislab.de). We used two T2-weighted, volumetric, pathological MR-images (512\u00d7512\u00d716 and 512\u00d7512\u00d710), both of which had an anisotropic voxel spacing in x- and y-directions of 0.63 millimeters and 4.4 millimeters along the z-axis. We obtained isotropic voxel sizing  by resampling the two images, using the MeVisLab Resample3D-module, which resulted in resolutions of 159\u00d7159\u00d735 and 159\u00d7159\u00d722 respectively. The first image contained a stenosis and a spondylolisthesis; the second image showed a slipped disc.A C++ implementation of Cube-Cut was tested within the medical image processing platform MeVisLab 2.2.1 . For initialization of the GrowCut algorithm, strokes have been drawn inside and outside the vertebral body on a two-dimensional, sagittal image, a two-dimensional axial image and a two-dimensional coronal image  operating system, version 6.1.7601, the most expensive parameter settings took Cube-Cut less than a minute  to terminate. The settings that resulted in a maximum DSC of over 86% only took 19 seconds to execute. Overall, we achieved a mean DSC-value of 81.33%.A novel approach towards the volumetric segmentation of vertebral bodies was presented. Cube-Cut is a non-trivial, three-dimensional extension of the previously introduced two-dimensional segmentation strategy Square-Cut development of a specific graph-based algorithm for vertebral body segmentation;algorithm bases on a cubic template which is a novelty in the segmentation domain;scale-invariant segmentation by an optimal mincut through cubic-shaped divergences;physicians performed slice-by-slice segmentations to obtain ground truth boundaries;segmentation quality of the algorithm has been evaluated via the Dice Coefficient.The proposed method only requires a single user seed, while other approaches In addition, contrary to most of the alternative approaches Furthermore, whereas other approaches 2e(G) |Cmin|)O(v(G), where v(G) is the number of vertices, e(G) the number of edges and min||C the capacity of a minimal cut, the algorithm is most effective for networks of low complexity, like the one Cube-Cut generates. In addition, we want to point out here that Boykov's graph cut model can support high dimensional data in its own settings.To summarize, Cube-Cut generates a two-terminal s-t-network where the vertices correspond to a cubic shaped subset of the image's voxels. By only observing a subset of the image\u2019s voxels, the algorithm improves the theoretical runtime in comparison to other graph-based approaches that consult the whole voxel set. The capacities of the terminal edges reflect a voxel's affiliation with the object  and the background, while the topology of non-terminal \u221e-weighted edges implements the smoothness-constraint. After network construction, a minimal s-t-cut, computed in polynomial time, determines the segmentation result. For the mincut computation, the Boykov-Kolmogorov algorithm is applied, since it was demonstrated For evaluation, Cube-Cut 3D-masks were compared to manual vertebral body segmentation results, obtained in a time-costly slice-by-slice manner, performed by trained physicians, achieving a promising mean DSC of 81.33%, which is on par with the state of the art (comparable to Moreover, we also used a spherical template instead of the cubic shaped one, to set up a graph and applied it to vertebra segmentation. As shown in Furthermore, we also compared the Cube-Cut masks with GrowCut results and found that Cube-Cut clearly outperformed GrowCut in this setup, regardless of the similar DSC values. Besides others, GrowCut regularly did not recognize the vertebral body\u2019s outer boundaries in the pedicle-regions, which led to false boundary detections as shown in Nevertheless, visual evaluations of Cube-Cut's segmentation results indicate that the algorithm frequently segments the same specific areas of a vertebral body inaccurately. Recognizing the rectangle shape of a vertebral body, on sagittal slices, these areas could be referred to as the vertebral body's \"vertices\" . AlthougRegarding the robustness of Cube-Cut in general, we can report that the method only performs satisfactory if the cube\u2019s volume is larger than the vertebral body\u2019s , left siFurthermore, as already mentioned above, the seed has to be placed roughly around the center region of the vertebral body in order to obtain satisfactory segmentation results. Nevertheless, the algorithm proved itself relatively stable against small deviations and moreover, the replacement of the seed only takes a second which is one of the distinguishing advantages of Cube-Cut."}
+{"text": "This paper is a comment on \u201cIntra- and interday reliability of spine rasterstereography\u201d . We thinIn research, validity is the extent to which a conclusion corresponds accurately to the reality. Differently, reliability is the overall consistency of a measure . ValiditIn conclusion, \u201cTherefore, this study validated aspects of the rasterstereographic measuring system that potentially could replace X-rays in follow-up of spinal deformities helping to reduce X-rays irradiation\u201d . DiscussWe should verify the data from this study with caution before suggesting such a clear indication , 9. Atte"}
+{"text": "A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more leaves share a label, e.g., a species name. A MUL-tree can imply multiple conflicting phylogenetic relationships for the same set of taxa, but can also contain conflict-free information that is of interest and yet is not obvious.T as the set of all conflict-free quartet topologies implied by T, and define the maximal reduced form of T as the smallest tree that can be obtained from T by pruning leaves and contracting edges while retaining the same information content. We show that any two MUL-trees with the same information content exhibit the same reduced form. This introduces an equivalence relation among MUL-trees with potential applications to comparing MUL-trees. We present an efficient algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its performance on empirical datasets in terms of both quality of the reduced tree and the degree of data reduction achieved.We define the information content of a MUL-tree Our measure of conflict-free information content based on quartets is simple and topologically appealing. In the experiments, the maximally reduced form is often much smaller than the original tree, yet retains most of the taxa. The reduction algorithm is quadratic in the number of leaves and its complexity is unaffected by the multiplicity of leaf labels or the degree of the nodes. Multi-labeled trees, also known as MUL-trees, are phylogenetic trees that can have more than one leaf with the same label-5 Figur. MUL-treMUL-trees, unlike singly-labeled trees, can contain conflicting species-level phylogenetic information due to biological processes such as whole genome duplications or incomHere we provide a way to extract this information; specifically, we have the following results. MUL-Trees and information content on page 3).\u2022\u2009We introduce a new quartet-based measure of the information content of a MUL-tree, defined as the set of conflict-free quartets that the tree displays , and show that any two MUL-trees with the same information content have the same MRF (Theorem 3).\u2022\u2009We introduce the concept of the maximally-reduced form (MRF) of a MUL-tree The reduction algorithm on page 7). Its running time is quadratic in the number of leaves and does not depend on the multiplicity of the leaf labels or the degrees of the internal nodes.\u2022\u2009We present a simple algorithm to construct the MRF of a MUL-tree (see Results and discussion on page 8). In our test data, the MRF is often significantly smaller than the original tree, while retaining most of the taxa.\u2022\u2009We present computational experience with an implementation of our MRF algorithm  of the leaf set, where each part is the set of leaves on one of the two sides of e. From , we derive a collection of bipartitions ab|cd of quartets, such that {a,b}\u2009\u2286\u2009A and {c,d}\u2009\u2286\u2009B. Clearly, if one edge in a singly-labeled tree implies some bipartition q\u2009=\u2009ab|cd of {a,b,c,d}, then there can be no other edge that implies a bipartition, such as ac|bd, that is in conflict with q. Indeed, the quartet topologies implied by a singly-labeled tree uniquely identify it[We now give the intuition behind our notion of information content, deferring the formal definitions of this and other concepts to the next section. Quartets  are a natural starting point, since they are the smallest subsets from which we can draw meaningful topological information. A singly-labeled tree implies exactly one topology on any quartet. More precisely, each edge ntify it.b and c \u2014 b(1) and b(2), and, c(1) and c(2) \u2014 leads to two conflicting topologies on the quartet {b,c,d,e}. Edge  implies the bipartition bc|de, corresponding to the labels {b(1),c(1),d,e}, while edge  implies bd|ce corresponding to the leaves {b(2),c(2),d,e}. On the other hand, the quartet topology af|bc, implied by edge , has no conflict with any other topology that the tree exhibits on {a,b,c,f}. We show that the set of all such conflict-free quartet topologies is compatible (Theorem 1). That is, for every MUL-tree T there exists at least one singly-labeled tree that displays all the conflict-free quartets of T \u2014 and possibly some other quartets as well. Motivated by this, we only view conflict-free quartet topologies as informative, and define the information content of a MUL-tree as the set of all conflict-free quartet topologies it implies.The situation for MUL-trees is more complicated, as illustrated in FigureWe should note that conflicting quartets may well provide valuable information, whether about paralogy, deep coalescence, or mistaken annotations. In some cases, species-level phylogenetic information can be recovered from conflicted quartets through application of, e.g., gene-tree species-tree reconciliation . Howevev,w) implies is either in conflict with some other topology  or is already implied by some other edge ). Thus,  can be contracted without altering the information content. In fact, the information content remains unchanged if we also contract  and remove the leaves labeled b(1) and c(1). We define the MRF of a MUL-tree T as the tree that results from applying information-preserving edge contraction and leaf pruning operations repeatedly to T, until it is no longer possible to do so. The MRF of the tree in FigureAn example on page 8). If the MRF is itself a MUL-tree, it is not possible to reduce the original to a singly-labeled tree without either adding at least one quartet that did not exist conflict-free in T or by losing one or more conflict-free quartets.A MUL-tree may have leaves that can be pruned and edges that can be contracted without altering the tree\u2019s information content, i.e., without adding or removing conflict-free quartets. For example, in Figurelabeled b and c(1)Since any two MUL-trees with the same information content have the same MRF, rather than comparing MUL-trees directly, we can instead compare their MRFs. This is appealing mathematically, because it focuses on conflict-free information content, and also computationally, since an MRF can be much smaller than the original MUL-tree. Indeed, on our test data, the MRF was frequently singly-labeled. This reduction in input size is especially significant if the MUL-tree is an input to an algorithm whose running time is exponential in the label multiplicity, such as Ganapathy et al.\u2019s algorithm to compute the contract-and-refine distance between two area cladograms or HuberFor our experiments, we also implemented a post-processing step, which converts the MRF to a singly-labeled tree, rendering it available for analyses that require singly-labeled trees, including supermatrix,15 and sPrevious work on MUL-trees has concentrated on finding ways to reduce MUL-trees to singly-labeled trees , and to MUL-tree is a triple , where (i) T is an unrooted treea with leaf setM is a set of labels, and (iii)T a label from M.  For brevity we often refer to a MUL-tree by its underlying tree T. In what follows, unless stated otherwise, by a tree we mean a MUL-tree.A u,v) in T is internal if neither u nor v belong topendant otherwise. A pendant node is an internal node that has a leaf as its neighbor.An edge  be an edge in T and T\u2032 be the result of deleting  from T. ThenT\u2032 that contains u (v).Cuv is the set of labels common to bothCuv partition M. For example, in FigureCuv\u2009=\u2009{b,c}.Let  in T withu,v)\u2009resolves\u2009ab|cd. For example, in Figuret,u) resolves af|bc.A (resolved) information content of an edge  of a MUL-tree T, denoted \u0394, is the set of quartets resolved by . An edge  in tree T is informative if |\u0394|\u2009>\u20090;  is maximally informative if there is no other edge  in T with \u0394\u2009\u2282\u2009\u0394. The information content of T, denotedE denotes the set of edges in T.The The next result shows that the quartets inFor every MUL-tree T, there is a singly labeled tree T\u2032such thatT has no multiply-occurring labels. Pick any multiply-occurring label \u2113 in T, select an arbitrary leaf labeled by \u2113, and relabel every other leaf labeled by \u2113, by a new, unique, label. The resulting tree T\u2032 is singly labeled, and all labels of T are also present in T\u2032. Consider a quartet ab|cd in T, that is resolved by edge . Assume thata. Clearly, this also holds for the only occurrence of a in T\u2032. Similar statements can be made about labels b, c, and d. Thus, the quartet ab|cd is resolved by edge  in T\u2032, and, hence, T\u2032 displays all quartets of T. \u25a1Repeat the following step until Note that there are examples where the containment indicated by the above result is proper.The reduction algorithm, beginning on page 7). In the next lemmas,  and  denote two edges in tree T that lie on the pathTo conclude this section, we give some results that are useful for the MUL-tree reduction algorithm \u2009\u2286\u2009\u0394 if and only if\u0394((Only if) Suppose \u0394\u2009\u2286\u2009\u0394; therefore,(If) Supposeu,v)\u2009\u2286\u2009\u0394. \u25a1Suppose \u0394\u2009\u2286\u2009\u0394. Then, for any edge  onPu,xsuch thatvis closer toythan toz, \u0394\u2009\u2286\u2009\u0394\u2009\u2286\u2009\u0394.u,v)\u2009\u2286\u2009\u0394, we havey,z) on Pu,x. By definitionu,v)\u2009\u2286\u2009\u0394\u2009\u2286\u2009\u0394. \u25a1By Lemma 2, since \u0394: Delete leaf v from T. If, as a result, v\u2019s neighbor u becomes a degree-two node, connect the former two neighbors of u by an edge and delete u. Contract (e): Delete an internal edge e and identify its endpoints.Our goal is to provide a way to reduce a MUL-tree v in T is prunable if the tree that results from pruning v has the same information content as T. An internal edge e in T is contractible if the tree that results from contracting e has the same information content as T. T is maximally reduced if it has no prunable leaf and no contractible internal edge.A leaf Every internal edge in a maximally reduced tree T resolves a quartet that is resolved by no other edge.We rely on two facts. First, every internal node in the tree has degree at least three. Second, every internal edge in the tree resolves a quartet; otherwise, the edge would be contractible and the tree would not be maximally reduced.u,v) in the tree. To prove that  resolves a quartet not resolved by any other edge, we need to show that there exists a quartet ab|cd of the form shown in Figurea and b. Consider the following cases: Consider any edge  resolves. Without such a leaf,  would resolve the same set of quartets as , so one of these two edges would be contractible, contradicting the assumption that the tree is maximally reduced. We select this leaf as b and we select any2. u, except v, are leaves. Then, at least two of its neighbors must participate in a quartet, because  must resolve a quartet. We select the two neighbors as a and b.3. All neighbors of a and b. By a similar argument, we can also select the desired c and d. This proves the existence of the desired quartet ab|cd. Therefore, each internal edge of T uniquely resolve a quartet. \u25a1In every case, we can select the desired leaves The next result shows that the set of quartets resolved by a maximally reduced tree uniquely identifies the tree.Let T and T\u2032be two maximally reduced trees such thatThen, T and T\u2032are isomorphic.maximally reduced form (MRF) of a MUL-tree T is the tree that results from repeatedly pruning prunable leaves and contracting contractible edges from T until this is no longer possible. Theorem 3 shows that we can indeed talk about \u201cthe\u201d MRF of T. Before proving Theorem 3, we mention some of its consequences.The Every MUL-tree has a unique MRF.Any two MUL-trees with the same information content have the same MRF.If a maximally reduced MUL-treeTis not singly-labeled, there does not exist a singly-labeled treeT\u2032such thatf. However, doing so will also introduce quartets that are not resolved by the maximally reduced MUL-tree.Note that Corollary 3 does not contradict Theorem 1. If the MUL-tree in Theorem 1 is maximally reduced and not singly-labeled, the containment is proper; i.e.,The relation \u201csharing a common MRF\u201d is an equivalence relation on the set of MUL-trees.The last result implies that MUL-trees can be partitioned into equivalence classes, where each class consists of the set of all trees with the same information content. Thus, instead of comparing MUL-trees directly, we can compare their maximally reduced forms.We now proceed to the proof of Theorem 3. We need two lemmas.There is a bijection\u03d5between the respective sets of internal edges of T and T\u2032with the following property. Let  be an internal edge in T and let \u2009=\u2009\u03d5. Then,andTherefore, \u0394\u2009=\u2009\u0394.u,v) in T. By Theorem 2,  must resolve a quartet ab|cd not resolved by any other edge as shown in Figureu\u2032,v\u2032) in T\u2032. Suppose not. Using arguments similar to those in the proof of Lemma 3, we can show that all edges that resolve ab|cd in T\u2032 form a path , where possibly x\u2032\u2009=\u2009w\u2032, as shown in FigureConsider an edge  resolves a quartet not resolved by any other edge, by Theorem 2 there exists a label \u2113 as shown, whereab|\u2113d is a quartet in T\u2032 andT. Clearly, T does not resolve the quartet on {a,\u2113,d,c} in the same way, a\u2113|cd, as T\u2032. This contradicts the assumption thatu\u2032,v\u2032) must be an edge. Moreover, only one such edge exists in T\u2032 as it uniquely resolves the quartet ab|cd.Since \u2009=\u2009\u0394.Now consider any label\u03d5 from edges in T to edges of T\u2032 such that \u0394(e)\u2009=\u2009\u0394(\u03d5(e)). To complete the proof, we show that \u03d5 is onto. Suppose that for some edge e\u2032 in T\u2032 there is no edge e in T such that \u03d5(e)\u2009=\u2009e\u2032. But then e\u2032 must resolve a quartet not resolved by any other edge in T\u2032. This quartet cannot be inWe have shown that there is a one-to-one mapping \u03d5 be the bijection between the edge sets of T and T\u2032 from the preceding lemma.Let Let  and  be any two neighboring internal edges inT, and let \u2009=\u2009\u03d5 and \u2009=\u2009\u03d5 be the corresponding edges in T\u2032such thatandThen,  and  are neighbors in T\u2032with q\u2009=\u2009r.u,v) and  are neighbors, and each resolves a quartet that is not resolved by the other,p,q) and  can exist in T\u2032 is as part of the pathq\u2009\u2260\u2009r, then consider the edge  on Pps such that p is closer to t than to r. Then, the following must hold:Since \u2009=\u2009\u03d5\u22121 be the edge in T corresponding to . Irrespective of the position of  in T, (1) and (2) cannot be simultaneously true with respect to edges ,  and  in T. Therefore, q\u2009=\u2009r, which proves the desired result. \u25a1Let  in T such that v is a pendant node andu\u2032,v\u2032)\u2009=\u2009\u03d5 be the corresponding edge in T\u2032 such thatT nor T\u2032 have prunable leaves. Thus, the same set of leaves must be attached at v and v\u2032 respectively. In subsequent steps, we select an internal edge  in T such that v is a pendant node and all the other pendant nodes inu\u2032,v\u2032)\u2009=\u2009\u03d5 such thatv and v\u2032 respectively. Proceeding this way, each pendant node in T can be paired with the corresponding pendant node in T\u2032, and be shown to have the same set of leaves attached to them. This shows that T and T\u2032 are isomorphic, as claimed. \u25a1Lemmas 4 and 5 show that In preparation for the MUL-tree reduction algorithm of the next section, we give some results that help to identify contractible edges and prunable leaves.u,v) and  are two edges in tree T that lie on the pathbranches out from the path Pu,x if y\u2009\u2208\u2009Pu,x\u2212{u,x}, and z\u2009\u2209\u2009Pu,x.The setting for the next result is the same as for Lemmas 2 and 3: \u2009\u2286\u2009\u0394 thenevery internal edge on a subtree branching out from Pu,xis contractible, and1. if \u0394\u2009=\u2009\u0394, every leaf on a subtree branching out from Pu,xis prunable. Thus, the entire subtree can be deleted without changing the information content of the tree.2. Refer to FigureA,B) in a subtree branching out of Pu,x, as shown. We claim thatM appear inA,B) is uninformative.1. Consider any edge \u2009\u2286\u2009\u0394, we haveTo prove the claim, observe first that, by definition,M. SinceNow,u,v)\u2009=\u2009\u0394. By an argument similar to the one used in the proof of Lemma 3, we can show that any edge  on the path Pv,w\u2009=\u2009(v\u2026w)  still resolves the same quartet in S because(a)\u2009c adds a quartet toS must be resolved by an edge  in\u2113\u2009\u2208\u2009Cjk, but now has\u2113\u2009\u2208\u2009Cjk and the edge still cannot resolve the quartet, a contradiction.(b)\u2009c is prunable. \u25a1Hence, Suppose that T is a MUL-tree where no pendant node is adjacent to two or more leaves with the same label. Let \u2113 be any multiply-occurring label in T and let T\u2032be the minimal subtree of T that spans all the leaves labeled by \u2113. Then, any leaf in T labeled \u2113 attached to a pendant node of degree at least three in T\u2032is prunable.v of degree at least three in T\u2032 attached to a leaf labeled \u2113. Clearly deleting the leaf does not change the information content of any edge in Tu or Ty. Now consider an edge  in T\u2032 as shown. Note that \u2113\u2009\u2208\u2009Cwx, so \u2113 does not contribute to \u0394. After deleting the leaf, we still have \u2113\u2009\u2208\u2009Cwx, so \u0394 remains unchanged. Therefore, the leaf is prunable. \u25a1Refer to FigureO(n2) algorithm to compute the MRF of an n-leaf MUL-tree T. In the previous section, the MRF was defined as the tree obtained by applying information-preserving pruning and contraction operations to T, in any order, until it is no longer possible. For efficiency, however, the sequence in which these steps are performed is important. Our algorithm has three distinct phases: a preprocessing step, redundant edge contraction, and pruning of redundant leaves. We describe these next and then give an example.We now describe a u,v) in T, we computeO(n2) time as follows. First, traverse subtreesu,v) whereFor every edge  and  such that \u0394\u2009\u2286\u2009\u0394 or vice-versa, and contract the less informative of the two. By Lemmas 1 and 2, we can compare \u0394 and \u0394 in constant time using the precomputed values ofv or in the subtrees branching out of v. Further, by Lemma 6 (2), if \u0394\u2009=\u2009\u0394, we can in fact delete these subtrees entirely, since their leaves are prunable. Lemma 3 implies that all such edges must lie on a path, and hence can be identified in linear time. The total time for all these operations is linear, since at worst we traverse every edge twice.Next, we repeatedly find pairs of adjacent edges ,O(n2) time and O(n) space.The tree that is left at this point has no contractible edges; however, it can still have prunable leaves. We first prune any leaf with a label \u2113 that share a common neighboring pendant node. Such leaves can be found in linear time. For each such set, we delete all but one element. Let T be the tree that results from removing such leaves. Now, the only prunable leaves with a given label \u2113 that might remain are leaves attached to different pendant nodes. By Lemma 7, we can identify and prune such leaves by performing the following steps. Next, we consider sets of leaves with the same label \u2113, consider the subgraph on the leaves labeled by \u2113.1. For each label 2. In this subgraph, delete any leaf not attached to a degree 2 pendant node as it is a redundant leaf.O(n) time per label and O(n2) time total. The space used is O(n). Hence, the overall time and space complexities are O(n2) time and O(n), respectively.This takes The resulting tree has no contractible edges nor prunable leaves. Therefore, it is the MRF of the orginal MUL-tree.We illustrate the reduction of the unrooted MUL-tree shown in Figuret,u),  and  are uninformative. They are therefore contracted, resulting in the tree shown in Figure1. In the preprocessing step, we find thatu,v)\u2009\u2282\u2009\u0394, contract . The result is shown in Figure2. Since \u0394\u2009=\u2009\u0394, delete the subtree branching out at w from the path from v to y and contract . The result is shown in Figure3. Since \u0394, which included a broad range of label-set sizes, from 4 to 1500 taxa.We implemented our MUL-tree reduction algorithm, as well as a second step that restricts the MRF to the set of labels that appear only once, which yields a singlylabeled tree. We tested our two-step program on a set of 110,842 MUL-trees obtained from the PhyLoTA database  were of this kind. Trees in set B were reduced to singly-labeled trees in the second step; 36,392 trees (32.8%) were of this kind. Reducing a tree to its MRF (step 1), led to an average taxon loss of 0.83% of the taxa in the input MUL-tree. The total taxon loss after the second step (reducing the MRFs in set B to singly-labeled trees), averaged 12.81%. This taxon loss is not trivial, but it is far less than the 41.27% average loss from the alternative, na\u00efve, approach in which all MUL-taxa (taxa that label more than one leaf) are removed at the outset. Note that, by the definition of MRFs, taxa removed in the first step do not contribute to the information content, since all non-conflicting quartets are preserved. On the other hand, taxa removed in the second step do alter the information content, because each such taxon participated in some non-conflicting quartet. Information content, in this case, will be lost but new information is never introduced, so the algorithm can be considered conservative.There were 8,741 trees (7.8%) with essentially no information content; these lost all resolution either when reduced to their MRFs, or in the second step. The remaining trees fell into two categories. Trees in set Taxon loss is sensitive to the number of total taxa and, especially, MUL-taxa, as demonstrated in FigureIn addition to the issue of taxon loss, we investigated the effect of our reduction on edge loss, i.e., the level of resolution within the resulting singly-labeled tree. Input MUL-trees were binary and therefore had more nodes than twice the number of taxa , a phylogenetic tree search engine that takes a user-provided list of species names and finds matches with a precomputed collection of phylogenetic trees, more than half of which are MUL-trees, assembled from GenBank sequence data. The trees returned are ranked by a tree quality criterion that takes into account overlap with the query set, support values for the branches, and degree of resolution. We have added functionality to provide reduced singly-labeled trees as well as the MUL-trees based on the full leaf set and the label sets from the reduced singly-labeled trees are used in downstream supermatrix construction.We have integrated our reduction algorithm into STBase , result in relatively large MRF trees. Comparing the MRF to the original MUL-tree may well provide a method for efficiently assessing and segregating data sets with respect to the causes of multiple labels.It would be interesting to compare our results with some of the other approaches for reducing MUL-trees to singly-labeled trees  or, indaThe results presented here can be extended to rooted trees, using triplets instead of quartets, exploiting the well-known bijection between rooted and unrooted trees .The authors declare that they have no competing interests.MMM and DFB conceived the problem. AD, DFB and MMM designed the experiments and drafted the manuscript. AD designed and implemented the algorithms, and implemented the experiments. DFB coordinated the project. All authors read and approved the final manuscript."}
+{"text": "This work presents a data-centric strategy to meet deadlines in soft real-time applications in wireless sensor networks. This strategy considers three main aspects: (i) The design of real-time application to obtain the minimum deadlines; (ii) An analytic model to estimate the ideal sample size used by data-reduction algorithms; and (iii) Two data-centric stream-based sampling algorithms to perform data reduction whenever necessary. Simulation results show that our data-centric strategies meet deadlines without loosing data representativeness. Examples of these applications include: surveillance systems, biometric sensing, and intrusion detection. These applications have soft real-time characteristics, i.e., environment is not controllable, applications usually use probabilistic models to process data, and communication does not have acknowledgment.Despite their potential application, wireless sensor networks (WSNs) -3 have set al.  and we have 10 equals histogram classes. To obtain such a sample, we choose the central elements of each histogram class, respecting the sample size | V\u2032| and the class frequencies of the histogram. Thus, the resulting sample will be represented by the same histogram. Meanwhile, considering the sensor-stream reduction algorithm presented by Aquino et al  >V [fst]+wid or k = |V|- 1 then\u2003\u20039coln' \u2190 \u2308n'col | V\u2032|/|V| \u2309{number of elements per columns in V\u2032}\u2003\u2003\u200310index \u2190f st+\u2308(col-n'coln)/2\u2309\u2003\u2003\u200311forl\u21900 colto n'do\u2003\u2003\u200312V\u2032[w] \u2190V[index]\u2003\u2003\u2003\u200313w \u2190 w + 1\u2003\u2003\u2003\u200314index \u2190 nextIndex\u2003\u2003\u2003\u200315end\u2003\u2003\u200316col \u2190n 0\u2003\u2003\u200317fst \u2190 k\u2003\u2003\u200318end\u2003\u200319col \u2190 ncoln + 1\u2003\u200320end\u200321Sort(V\u2032) {according to the original order}\u200322end6.(http://nsnam.isi.edu/nsnam/index.php/Main_Page). Each simulated scenario was executed with 33 random topologies. At the end, for each scenario we plot mean values with 95% (symmetric asymptotic) confidence intervals.This section presents the simulation study of our data-centric strategy in specific scenarios. We perform our evaluation by using the NS-2 (Network Simulator 2), version 2.33 V|). The evaluated parameters are the delay and error in data quality, specified by two statistical tests. The default parameters used in simulations are presented in To identify assess the network behavior, we variate the number of nodes and the stream size (| mmd) for each number of nodes and |V| being considered. To do this, we consider different network sizes , the |V| = {256, 512,1024, 2048{, and only one data source generating V. In our case, the mindvalues is determined by measuring the time between the first data packet sent by the source and the last packet received by the sink, i.e., the time for V to be entirely received by the sink. mindvalues for all scenarios being considered.To evaluate the delay in real-time scenarios, it is important to determine the minimum deadline  concurrent traffic; minimum deadlines with delay caused by relay nodes in each packet transmitted with(out) concurrent traffic. These study are discussed in the next subsections. For all scenarios, we evaluate the simplified and complex formulations, both using mulation  consider6.1.a = dmin/2d) without concurrent traffic in this case, the application cannot send V and meet ad. In this case, V is reduced by using our data-centric strategy. In Monte Carlo simulation, we change the number of nodes  and |V| . V| = 2048.The first scenario considers half of minimum deadlines per a/d10000 or 0.01% of the ad. In this scenario, the application cannot send V, because the relay nodes eventually can be executing another task, consequently, the deadline ad cannot be met. We change the number of nodes  and |V| . The objective of this scenarios is to identify the appropriate strategy when relay nodes have other high priority tasks.The second scenario, considers V| = 2048. In contrast to prior scenario, ad is always met. The complex formulation, in a more realistic scenario, presents a better time usage, i.e., the delay is closer to deadline values. This occurs because the \u03a8-reduction estimation in sample case [a, i.e.d, if a > dmind reduction cannot be efficient, when we consider other delay aspects like concurrent traffic. Another important observation is that more data is received in the complex formulation strategy. When the number of nodes is 1024, nearly 20% of data are deliver, in the complex formulation, against 18%, in the simplified one. This fact indicates that, considering only the deadline achievement, the complex formulation is more appropriate to more realistic scenarios.ple case  is relat\u03a8random, in both formulation, has a smaller \u03d2-error, because the random choice improves data dispersion. However, the simplified formulation has a smaller \u03d2-error. In \u03a6 \u2248 5%. Again, \u03a8central, in both formulation, has a smaller \u03a6-error ecause the central elements choice improves the average test. Although, the simplified formulation has a smaller \u03a6-error with 128, 256 and 512 nodes, the complex formulation presents a better performance for 1024 nodes.\u03a8random is preferable when the dstR has higher priority compared to the valR, otherwise, \u03a8central should be chosen. However, the complex formulation is more appropriate when we have large scale networks. The partial conclusion, considering more realistic real-time scenarios, is that the complex formulation is more appropriate, because the deadlines are met in all cases and the data representativeness is kept.Error evaluations suggest that the simplified formulation is more appropriate for small networks and the complex formulation is more scalable. In general, 6.3.ad = min/d2) with concurrent traffic. We use a 128-node network (we do not consider more nodes due to NS limitations), and vary the percentage of nodes generating data traffic  and |V| . The objective of this scenario is to identify the best strategy in critical applications when the network traffic gradually increases.This scenario considers 50% of minimum deadlines . The reason is that the complex formulation executes fewer consecutive \u03a8-reductions. \u03a6 \u2248 20%, note the increase in terror, compared to previous scenarios (\u03a6 \u2248 5%). The reason is that in both formulations there more consecutive \u03a8-reductions affecting data quality. Therefore, considering the confidence interval, both \u03a8-reductions have the same behavior. Again, when the percentage of nodes generating data is high, the simplified formulation has a smaller \u03a6-error.\u03a8-reduction strategies.The data error evaluation suggests that the simplified formulation is slightly better than the complex one. However, the partial conclusion, considering this critical and realistic real-time scenario, is that the complex formulation is more appropriate, because deadlines are met and data representativeness is kept. Considering the sampling algorithms, the behavior is kept in both 6.4.ad = mind, concurrent traffic, and all relay nodes delay the stream fragments at 0.01% of the ad. Again, we use a 128-node network and vary the percentage of nodes generating traffic  and |V| . TheThe last scenario considers objective of this scenario is to identify the best strategy when the relay nodes have extra tasks with high priority and the network has a traffic that gradually increases.ad is met in most cases. The complex formulation presents a more scalable behavior considering the percentage of nodes generating data. This occurs because the \u03a8-reduction estimation [ad, i.e., if a \u2265 dmind the \u03a8-reduction cannot be efficient, when we consider other delay aspects, like concurrent traffic.timation  is relatV| = 256. Simplified and complex formulation are presented by using \u03a8central and \u03a8random. \u2264 40%. The \u03a8*central, in complex formulation, has a smaller \u03d2-error. The reason is that the complex formulation performs the maximum \u03a8-reduction sooner . This result shows that because fewer successive *-reductions are performed, more representativeness is kept in the reduced data, i.e., data degradation is mitigated.\u03a6 \u2264 30%. The complex formulation with \u03a8central presents \u03a6 \u2248 5%. The reason is that the \u03a8central has a smaller \u03a6-error because the central elements choice improves the average test and the complex formulation performs the maximum \u03a8-reduction early.\u03a8central strategy. The partial conclusion, considering this scenario, is that the complex formulation is actually more appropriate, because the deadlines are met in all cases while keeping data representativeness. Considering the sampling algorithm, the \u03a8central strategy with complex formulation is always indicated.The errors evaluation suggest that the complex formulation is more appropriate with the 7.In real-time applications of wireless sensor networks, the time used to deliver sensor-streams from source to sink nodes is a major concern. The amount of data in transit through these constrained networks has a great impact on the delay. In this work, we presented a data-centric strategy to meet deadlines in soft real-time applications for wireless sensor networks. This work represents shows how to deal with time constraints at lower network levels in a data-centric way.With our data-centric strategy we met application deadlines in several scenarios. In additional, we showed how to design real-time sensor-stream reduction applications and a analytical model used to found the ideal sample size. Results showed the efficiency of the strategy by reducing the delay without losing data representativeness. If the application is not strongly dependent on data accuracy, or the network operates in exception situation , then data reduction algorithms are powerful tool for real-time applications for resource-constrained networks.O(n), by considering some rank selection algorithms.As future work, we intend to match the proposed application-level solution with lower-level ones, for example, by considering some real-time-enabled signal processing method. In this case, not only data from a source is reduced, but similar data from different sources is also reduced, resulting in a more efficient solution. Another future work is to use feedback information to enable the source nodes to perform the reduction sooner. However, we intend to improve the central sampling algorithm complexity to"}
+{"text": "Sex determination networks evolve rapidly and have been studied intensely across many species, particularly in insects, thus presenting good models to study the evolutionary plasticity of gene networks.We study the evolution of an unlinked gene capable of regulating an existing diploid sex determination system. Differential gene expression determines phenotypic sex and fitness, dramatically reducing the number of assumptions of previous models. It allows us to make a quantitative evaluation of the full range of evolutionary outcomes of the system and an assessment of the likely contribution of sexual conflict to change in sex determination systems. Our results show under what conditions network mutations causing differential regulation can lead to the reshaping of sex determination networks.The analysis demonstrates the complex relationship between mutation and outcome: the same mutation can produce many different evolved populations, while the same evolved population can be produced by many different mutations. Existing network structure alters the constraints and frequency of evolutionary changes, which include the recruitment of new regulators, changes in heterogamety, protected polymorphisms, and transitions to a new locus that controls sex determination. In rentiation ,7, or brentation . In contentation ,10 and wentation . Althougentation ,13, wormentation , fishes entation  and mammentation . Sex detSex-lethal (Sxl), an upstream regulator of sex determination first found in D. melanogaster [doublesex (dsx) is conserved across insects, worms [en) appear highly conserved and where the degree of conservation becomes progressively reduced for genes both upstream and downstream [transformer (tra) autoregulates in the Mediterranean fruit fly Ceratitis capitata [Sxl was recruited as an upstream regulator in Drosophila. Likewise, high regulatory variability is seen in the phylogenetically common dsx locus, which is regulated via alternative splicing of RNA by tra in many Diptera [tra-1 in worms [Comparative study shows that sex determination networks evolve by recruitment of novel regulators higher up the pathway . For exanogaster , does nonogaster ,19,20. Is, worms ,22 and ms, worms . A similwnstream ,25. In scapitata  but lost Diptera , but viain worms .D. melanogaster in a step-by-step fashion [D. melanogaster, particular evolutionary outcomes were addressed to account for the peculiarities of the genes involved in the network, for example multiple promoter sites, alternative splicing, and premature stop codons [Previous theoretical study showed how regulatory changes causing alterations in signal strength, could account for the evolution of the sex determination regulatory cascade of  fashion . In seekp codons . This dep codons -30. Thisp codons  and sexuHere we present a model that combines gene network evolution with population genetics, allowing us to study the effect of differential gene expression with general applicability and minimal assumptions. Standard approaches to gene network evolution have used haploid models to simplify the dynamics -38. Thisi may be regulated by an allele j at another locus (e.g. via cis-regulatory elements or RNA splicing sites), indicated by a parameter i, j I\u2208 {-1, 0, 1} which is 1 for up-regulation, -1 for down-regulation and 0 for no regulation. Second, an allele i may code for a regulatory domain (e.g. transcription factor or RNA recognition motif), indicated by a parameter i Z\u2208 {0, 1} which is 1 when the allele is regulatory and 0 otherwise. Third, each allele i has a constitutive output level defined by a parameter iT, which is either low (i T= -1) or high (i T= 1). These features determine the (time-dependent) expression level i Sof each allele i via the dynamical systemWe extend a general model of gene regulation ,39, usinj, and we assume thatThe summation is over all alleles h (see Table iS(0) = \u03c3(ikT) which are equilibrium expression levels if there is no regulation. The parameter k > 0 is a global constant that defines the relative contribution of the constitutive output to total gene expression. Note that the steady state output i is the solution ofis a sigmoid function. Most gene regulatory interactions can be approximated using this class of function -42 whichi in the summation term of Eq(1)).attained from these initial conditions. Note that this model can also incorporate autoregulation by allowing alleles at the same locus to regulate their own expression  simplifies toTm = -1) and high (Tf = + 1) output levels respectively. We consider an XY male heterogametic system consisting of m/f males and f/f females  expression determines somatic sex in Drosophila, where high expression of the female form of the dsx protein is required for a female phenotype [\u03b8 = \u03c3 (k)+1/2. Thus, larger values of k mean a larger difference in gene expression around the threshold value \u03b8 between the two sexes.The D locus controls sex determination. Specifically, if the sum of outputs of the two D locus alleles, d1 and d2, exceeds a threshold henotype . In our Za = 0. Consider a mutant allele A at the R locus that has a regulatory domain able to interact with the D locus, ZA = 1. In order for a regulatory interaction to evolve, the R locus allele A must be present together with a variant m or f allele at the D locus that is capable of being regulated by A. The m and f variant alleles are labeled according to whether the interaction causes up-regulation of expression  to calculate the expression level of the alleles at the R locus, and then use Eq(3) to calculate the regulated expression of the alleles at the D locus.We study the evolution of regulation controlled by a second locus R. We start from a situation in which the R locus is fixed for an allele a that does not regulate the D locus, + allele (D locus) which contains a novel input binding domain. This creates a positive regulatory connection from the R locus to the D locus. We denote this example a\u2192A/f\u2192f+ (background/mutant). If we reverse the order to f\u2192f+/a\u2192A, then the allele f+ already exists in the background state and the connection is completed by the mutation of the a allele to the A allele which contains a novel output regulatory domain.As the evolution of regulation by the R locus of the D locus requires change at both loci, we consider that one part of the connection exists in the background state, with the remaining part being completed by a subsequent mutation at the other locus. For example, if the allele A (R locus) is already present in the background state, it can complete a connection through the mutation of the f allele to the f-, (2) a\u2192A/f\u2192f+, (3) a\u2192A/m\u2192m-, (4) a\u2192A/m\u2192m+, (5) f\u2192f-/a\u2192A, (6) f\u2192f+/a\u2192A, (7) m\u2192m-/a\u2192A, (8) m\u2192m+/a\u2192A . In cases (5) to (8), either f-, f+, m- or m+ already are present in the background state (having replaced f or m), and we follow the mutant A allele introduced at the R locus. Note that the first four cases involve a cis mutation at the D locus occurring after a trans mutation at the R locus, and vice versa for the second four cases.There are eight possible combinations of background state and mutant that give rise to a novel regulatory connection: (1) a\u2192A/f\u2192f-,  a\u2192A/f\u2192f+W) of each genotype. In the background state, male (WM) and female (WF) fitness are set to 1. The fitness of mutant genotypes is measured relative to the background state genotypes: +/f and expression in males TA = 1 - see Methods). If the ancestral male was a/a; m+/f then the ancestral expression is wM and wF define the direction and magnitude of selection in males and females respectively. Within the simulations (see Methods), we use random numbers in the range  for both WF and WM to avoid negative fitness values for WF and WM . For each run, we recorded whether the mutation spread and caused a -/a\u2192A . The mutant A is then introduced at low frequency. The A mutant down-regulates f-, so the expression of - males than in ancestral males. The A mutant also reduces -/f- genotype. If -/f- males and homozygous a/a;f-/f- females. There is no change in the female genotype, but the dominant masculinizing m allele at the D locus is replaced by the dominant masculinizing A allele at the R locus. This occurs in Region I of Figure To illustrate our approach, we consider the mutation pair f\u2192fA Figure . In this-/f- is female  produces two new genotypes that are AA homozygous: A/A;m/f- and A/A;f-/f-. The genotype A/A;m/f- is male because its -/f- can be male or female. If 2\u03c3(-2(k)+k)-(\u03c3(k)+1/2) < 0 then it is male, which can lead to a population composed of A/A;f-/f- males and a/A;f-/f- females , and has a minor effect on the evolutionary outcome . In addition, the outcome depends on the fitness of each genotype, which we consider in a separate section below.The outcomes depend on the values of e Figure . When k  \u03c3 of Eq , and has-/a\u2192A and m\u2192m+/a\u2192A -(3)) and the A allele causes a large change in gene expression at the D locus. When this is sufficient for \u03b8 threshold, it causes a change in genotypic sex . It can then lead to fixation of the regulated allele at the D locus (either f- or m+), with transition of the control of sex determination to genetic variation at the R locus  following mutation at the D locus. Under these conditions we again observed sex determination locus transitions with the f- and m+ mutation pairs, but not with f+ and m- . However, as the A allele up-regulates f+, the output + homozygous genotype impossible. Similarly, for the m\u2192m-/a\u2192A mutation pair, the A allele down-regulates m- and makes a female m- homozygous genotype impossible. In these cases, transition of sex determination to the R locus cannot occur and build-up of the sex determination cascade is impossible [A second constraint governs the absence of transitions for f\u2192fpossible , a condipossible ).-/a\u2192A and m\u2192m+/a\u2192A , whereas in the a\u2192A/f\u2192f- mutation pair, the new allele is a recessive masculinizer . The pattern is more complex with a\u2192A/m\u2192m+ mutation pairs. In this case the up-regulation of m+ caused by the A alleles is sufficient to cause \u03b8 and so result in sex change. There are three possibilities. Two of these cause a change in heterogamety: a dominant m+ feminizer leading to A/A;m/m+ females, or an m+ allele which only feminizes in conjunction with the f allele leading to A/A;m+/f females. Alternatively the m+ allele is a recessive feminizer leading to A/A;m+/m+ females, which remain the homogametic sex. In contrast, changes in heterogamety never occur with the m- mutation (either a\u2192A/m\u2192m- or m\u2192m-/a\u2192A), as the m- allele is a dominant masculinizer and so can never be expressed in a female.With lower values of s Figure . For exa\u03b8) to result in a change in genotypic sex.Changes in heterogamety thus require the new regulatory connection to cause sufficient change in gene expression . The condition for selection to favor spread is WM > 1. As there is no mutant female genotype, WF = 1. For example, in the mutation pair a\u2192A/m\u2192m- . Male-only mutants  were found in all mutational classes, except for f\u2192f+/a\u2192A and a\u2192A/f\u2192f+. In these two cases, there are no conditions under which the f+ mutation is ever restricted to males. There are no cases of female-only mutants . Under conditions of ancestral female heterogamety this pattern is reversed with female-only mutants but no male-only mutants . However, there are many examples of sexual conflict in which the new regulatory connection is favored in one sex but deleterious in the other . Consider the mutation pair a\u2192A/f\u2192f- when k is large  is male and the other two (f-/f and f-/f-) are female . The new male genotype m/f- has lower expression at the D locus (-/f and f-/f-) also have lower wM < 0, wF < 0), the new genotypes raise fitness in both sexes . However when lower expression is only favored in one sex  there is sexual conflict . Under this condition, recruitment occurs as long as the combined fitness across the sexes is raised, (WM - 1)+(WF - 1) > 0 , polymorphism occurs at the D locus, while for X/a\u2192A mutation pairs , polymorphism occurs at both the A and D loci. Protected polymorphisms are restricted to those sub-regions  is not sufficient to eliminate the new f- allele that is favored in f-/f- males alone.As an example, consider Region II of mutation pair a\u2192A/f\u2192f- Table . Here, t- Table . Protects Figure . Protect0 Figure , where s-/f in this example) cannot be the most favored genotype as its expression lies between the new and ancestral homozygotes. So when selection favors lower expression in males and females , the new f- allele is favored and goes to fixation. The same pattern is seen for f+, m- and m+ mutation pairs.Protected polymorphisms are abundant in some regions Figure . With a\u2192With X/a\u2192A mutation pairs, protected polymorphisms require retention of multiple alleles across both the A and D loci. They are abundant in regions Figure  in whichcis and trans mutations contribute to evolutionary change in sex determination. Previous population genetic models [+s). Instead we let sex determination and fitness arise through the expression dynamics of the network. We then study evolution following a cis mutation in an existing sex determining allele  followed by a trans gain-of-function mutation at a locus not previously involved in sex determination (R locus) or vice versa.In this paper, we develop a diploid gene network model that explicitly considers how c models -30,44 haGenerally, we observe a many-to-many relationship as the same mutation can produce many outcomes and the same outcome can arise through many mutations Figure , Table 3-/a\u2192A and m\u2192m+/a\u2192A, in which the f- and m+ alleles exist prior to the mutation of a to A). In these cases, a single allele at the ancestral sex determination locus (D) is driven to fixation, with the A allele at the regulatory locus (R) becoming the new determiner of sex. For f\u2192f-/a\u2192A, the f- allele goes to fixation. When the f- homozygote is down-regulated by A it produces a male, but in the absence of A (or a lower dose of A) it is female  of A. Such switching is not possible for mutations involving f+ and m- alleles. The up-regulation of f+ and down-regulation of m- homozygotes caused by the A regulator merely strengthens existing female and male signals respectively. Hence for these mutants, the ability to determine both male and female sexes requires retention of polymorphism at the ancestral D locus , and sex determination cannot pass to the new R locus.Some constraints are identifiable. Of the eight possible mutation pairs  has retained the ancestral, non-sexual, regulatory functions as its expression pattern is similar to the non-duplicated version of Sxl found in the related fly Megaselia scalaris [+/a\u2192A sequence of mutations, in which the novel Sxl allele  was capable of up-regulating an ancestral m+ allele of tra (D locus). In this reconstruction we assume that the ancestral sex determination system was based on tra locus polymorphism [There is a further constraint as transitions to a new upstream regulator are only possible when mutation to fr Figure . This cor Figure . However network . In the scalaris . In termmorphism .WF, WM > 1), or are favored in one sex but do not segregate in the other , spread with surprising frequency as well (Table WM - 1)+(WF - 1) > 0. That is, given the sex ratio is constrained to be 1:1, there must be an overall fitness gain summed across the mutant male and female genotypes, as has been pointed out in other contexts [As well as these network features, recruitment of mutants is most likely when they are favored in both sexes . Alternatively, the new regulatory arrangement causes a change in genotypic sex accompanied by a switch from male to female heterogamety . The latter occurs when the effect of the upstream regulator A is relatively strong and causes a change in the sex of some genotypes. In either eventuality, A is fixed in the derived population. There are many potential examples of fixed regulators of sex determination genes. For example, the splicing activity of the SXL protein in Drosophila is dependent on interactions with a number of other proteins like SNF and PPS [Sxl in sex determination.Many mutations establish a new regulatory connection with the recruitment of new alleles but without change to a new sex determination locus Table . Many of and PPS -50. WhatMusca domestica [Xiphophorus maculates [The conditions that give rise to changes in heterogamety can also result in protected polymorphisms in which more than one male or female genotype occurs at equilibrium Figure . Protectomestica  and the aculates . These maculates ,52 or coaculates , that reaculates ,51.+/a\u2192A and m\u2192m-/a\u2192A mutation pairs , but is dependent on ancestral heterogamety.We have extensively studied evolutionary change when the ancestral condition is male heterogamety. Symmetrical constraints apply when the ancestral condition is female heterogamety. Here, transitions to a new sex determination locus only occur with the f\u2192fk  are relatively weak and thus major re-organisation of the sex determination systems does not occur. In effect this stabilizes the established sex determination mechanism. A high value of k might therefore explain the rareness of heterogamety changes in birds [k is small, regulation is relatively strong, opening up the possibility of changes in genotypic sex, transitions of the sex determination system and changes in heterogamety. The latter are common in frogs [The importance of the model parameters in birds  and mammin birds . In contin frogs , medaka in frogs  and insein frogs ,59. Diffin frogs ,47 and sin frogs  are likeDrosophila melanogaster and related species [cis and trans mutations, for predicting transitions to a new upstream sex determination locus as well as the recruitment of other regulators which establish new regulatory interactions at sex determining loci. Our network approach allows sex and fitness to emerge directly from the regulatory interactions rather than being imposed by assumptions made about \"modifiers\". This approach demonstrates that the same mutation can produce many different evolutionary outcomes, while the same evolved state can be produced by many different mutations.The work in this paper was motivated by the complexities of the sex determination mechanism of  species ,13. We hWM, WF) of each genotype. Random mating amongst adults assuming unlinked loci was used to define the zygote frequencies in the following generation. This procedure was repeated until the population reached equilibrium. We measured the maximum difference  between successive timesteps, e(t) = maxG|p(t) - p(t - 1)|, where p(t) is the frequency of a genotype at generation t. The system is considered stable when e(t) < 10-12 . We imposed a maximum of 1011 timesteps, however, in every simulation the criterion was reached before this maximum number of steps. A mutant allele was classified as non-invasive if it was driven out, with the final population being the same as the ancestral population. Invasive mutants resulting in recruitments or transitions caused the loss of one of the ancestral alleles. To distinguish invasive mutants resulting in protected polymorphism from neutral or very weakly selected mutants, we first removed genotypes at \u22641% frequency . If more than one female or male genotype was observed (i.e. protected polymorphism), a second genotype threshold of 0.1% was used to ensure inclusion of all relevant genotypes. Simulations were performed using a custom-built C++ program capable of generating novel genotypes in real time and assigning sex and fitness dynamically. Examples of genotype frequency dynamics for simulations leading to both recruitment and protected polymorphism are shown in Additional file We use a standard population genetics simulation to study the evolutionary fate of each mutation. The model assumes an infinite diploid population with non-overlapping generations, with a 1:1  sex ratio. Each mutant allele was introduced at low frequency (0.5%) in the heterogametic sex . At each generation the following steps were taken. First, gene expression h, k, wM, and wF) which remain fixed for the entire duration of each simulation. A uniform distribution is assumed for all parameters. For h, we assume the biologically realistic range  observed for a wide range of behavior in vitro in the lac operon , since no interesting behavior is observed for higher values  to avoid negative fitness values [the range for \u03b8 is calculated once h and k are known and remains fixed throughout the simulation. Separate experiments were performed for different strengths of the regulatory allele A (i.e. TA = -1 or +1). In the main text we only report the case TA = +1 (i.e. high constitutive expression) as the other case is qualitatively equivalent; see Additional file TA= -1).For each of the eight network mutations, 10,000 independent evolutionary simulations were performed, with a set of random parameter values .Click here for fileGenotype ordering with respect to Click here for fileSimulation examples. Per generation change in genotype frequency is shown for two cases, one leading to recruitment, the other to protected polymorphism.Click here for fileA = -1Simulation results with T. In the text we consider the case of high constitutive expression of the A allele (i.e. TA = +1). We demonstrate qualitatively similar results with low constitutive expression of the A allele (i.e. TA = -1).Click here for file"}
+{"text": "Intergroup conflict is often driven by an individual's motivation to protect oneself and fellow group members against the threat of out-group aggression, including the tendency to pre-empt out-group threat through a competitive approach. Here we link such defense-motivated competition to oxytocin, a hypothalamic neuropeptide involved in reproduction and social bonding. An intergroup conflict game was developed to disentangle whether oxytocin motivates competitive approach to protect (i) immediate self-interest, (ii) vulnerable in-group members, or (iii) both. Males self-administered oxytocin or placebo (double-blind placebo-controlled) and made decisions with financial consequences to themselves, their fellow in-group members, and a competing out-group. Game payoffs were manipulated between-subjects so that non-cooperation by the out-group had high vs. low impact on personal payoff , and high vs. low impact on payoff to fellow in-group members (in-group vulnerability). When personal vulnerability was high, non-cooperation was unaffected by treatment and in-group vulnerability. When personal vulnerability was low, however, in-group vulnerability motivated non-cooperation but only when males received oxytocin. Oxytocin fuels a defense-motivated competitive approach to protect vulnerable group members, even when personal fate is not at stake. Intergroup relations are often marked by non-cooperation and competitive behavior, creating levels of aggression and violence that bring about severe societal costs Competitive approach of, and defense-motivated non-cooperation towards rivaling out-groups serves the individual's personal interests, as it signals the individual's loyalty and commitment to fellow group members, encouraging inclusion rather than exclusion from profitable within-group exchange and cooperation Because of its functionality to individual and group survival, the human brain may have evolved neurobiological mechanisms that support and sustain defense-motivated non-cooperation towards rivaling out-groups Three lines of evidence suggest that oxytocin not only promotes cooperation, but is involved also in defense-motivated non-cooperation towards rivaling out-groups. In free-living meerkats, infusion of oxytocin versus placebo motivated an array of cooperative behaviors including longer time-on-guard Disentangling these different possibilities would advance our understanding of the role of oxytocin in the evolution of group life. If, in intergroup conflict, oxytocin-motivated competitive approach varies as a function of the extent to which self-interest is at stake, we have to re-interpret previous work as showing that oxytocin up-regulates what Adam Smith called \u201cenlightened self-interest.\u201d But if oxytocin-motivated competitive approach varies  as a function of the extent to which the interests of fellow in-group members is at stake, we may be in a position to infer that oxytocin shifts the individual's focus away from immediate self-interest and towards in-group interests, and that oxytocin's functions include a tendency to tend-and-defend the in-group.To disentangle these possibilities, we developed a behavioral game in which participants acted as the representative of a group of three that competed with a protagonist representing a three-person out-group. Cardinal payoffs in the game were manipulated so that non-cooperation by the out-group had strong versus weak impact on the participant's personal outcome  and, independently, the outcomes for the two other in-group members that were represented by the participant (in-group vulnerability). We expected to replicate earlier work In keeping with past work The game was modeled after the Prisoner's Dilemma PD;  so that In Following instructions using the games in F\u200a=\u200a7.86, p\u200a=\u200a0.006, partial \u03b72\u200a=\u200a0.076, a trend towards an interaction between In-Group Vulnerability and Treatment, F\u200a=\u200a3.19, p\u200a=\u200a0.077, and a significant three-way interaction, F\u200a=\u200a5.97, p\u200a=\u200a0.016, partial \u03b72\u200a=\u200a0.06. Fs<1. When Personal Vulnerability was low, however, non-cooperation was higher when In-Group Vulnerability was high rather than low, but only among individuals given oxytocin rather than placebo \u00d72 \u00d72 (In-Group Vulnerability: High/Low) between-subjects ANOVAs. For non-cooperation there was a main effect for Personal Vulnerablity, M\u200a=\u200a3.828 vs. M\u200a=\u200a3.002, F\u200a=\u200a7.23, p\u200a=\u200a0.008, partial \u03b72\u200a=\u200a0.071  In-group defending was measured in 72 participants \u200a=\u200a7.18, p<0.010, partial \u03b72\u200a=\u200a0.093. F\u200a=\u200a6.18, p<0.015 rather than placebo, F\u200a=\u200a1.89, p<0.178. Further supporting hypothesis (ii), in-group defending positively related to non-cooperation, r(72)\u200a=\u200a0.428, p<0.001.Oxytocin-induced non-cooperation appears motivated by the desire to protect vulnerable in-group members, as predicted in hypothesis (iii). Indeed, as predicted in hypothesis (i), in-group tending was higher when participants received oxytocin rather than placebo, icipants , and wasF<1.41, ps>0.238, partial \u03b72<0.015; Moverall\u200a=\u200a2.873, SD\u200a=\u200a1.978): Oxytocin's effects on participants' non-cooperation cannot be attributed to altered expectations of out-group behavior.The game structure was symmetrical see , and parM\u200a=\u200a0.715) rather than low (M\u200a=\u200a\u22120.095), F\u200a=\u200a5.59, p\u200a=\u200a0.020, partial \u03b72\u200a=\u200a0.056. Second, we observed a Treatment by In-Group Vulnerability interaction, F\u200a=\u200a4.14, p<0.045, partial \u03b72\u200a=\u200a0.042  (see M\u200a=\u200a0.115) or low (M\u200a=\u200a0.522), F\u200a=\u200a0.65, p\u200a=\u200a0.424. When given oxytocin, however, participants' level of non-cooperation was higher when in-group vulnerability was high (M\u200a=\u200a0.778) rather than low (M\u200a=\u200a\u22120.192), F\u200a=\u200a4.01, p\u200a=\u200a0.048. In fact, and as shown in t[27]\u200a=\u200a2.294, p<0.030; all other t<|1.199|, ps>.243). Thus, males engaged in excessive non-cooperation when in-group vulnerability was high and they received oxytocin rather than placebo.To explore whether in-group protection creates excessive non-cooperation, we analyzed the difference between participant non-cooperation and expected out-group non-cooperation. This revealed, first, more excessive non-cooperation when personal vulnerability was high (.22) see . When giThe neuropeptide oxytocin not only motivates cooperation towards familiar others, and those belonging to one's in-group Because groups were ad hoc and formed on the basis of a trivial criterion the (vulnerable) individuals protected here were relative strangers and not genetically related to the participant, findings are at odds with kin-selection theory of altruism that predicts altruism to be close to absent for genetically unrelated others There is no evidence that oxytocin motivates greed and spiteful tendencies towards rivaling out-groups Whether self-interest and the interest of fellow in-group members can be truly separated may be debatable. For example, human and non-human cooperation may be explained as serving the individual's long-term personal interests in survival and (re)productive success, and defense-motivated non-cooperation towards an out-group accrues quality signals to the individual that provide long-term benefits Participants engaged in decision making without feedback. In as much as cooperation tends to elicit cooperation, non-cooperation often begets non-cooperative responses N\u200a=\u200a105; Mean age\u200a=\u200a21.13 years, SD\u200a=\u200a1.29) were recruited via an on-line system and offered \u20ac10 (approx. USD 13) for participating in a study on medication and decision-making. Exclusion criteria were significant medical or psychiatric illness, prescription-based medication, smoking more than five cigarettes per day, and drug or alcohol abuse. Data of three participants were discarded because they erred on all six questions verifying their understanding of the experimental game. The experiment was approved by the Psychology Ethics Committee of the University of Amsterdam, and adhered to the guidelines set forth in the Declaration of Helsinki. Participants provided informed consent prior to the experiment.Males (Participants were instructed to refrain from smoking or drinking (except water) for 2 hours before the experiment and randomly assigned to the oxytocin or placebo group . Participants self-administered a single intranasal dose of 24 IU oxytocin  or placebo. The placebo contained all the active ingredients except for the neuropeptide, was prepared according to Good Manufacturing Practice (GMP) and Good Clinical Practice (GCP), and delivered in the same bottles as Syntocinon.N\u200a=\u200a75), and in Spring 2012 (N\u200a=\u200a30). Analyses revealed no interaction effects involving data collection wave on any of the dependent variables and this factor is further ignored. Participants were seated in individual cubicles preventing them from seeing others and communicating, signed an informed consent, and self-administered the medication under experimenter supervision. The experimenter left and participants completed a series of unrelated questionnaires and tests that were presented on their computer screen, using the keyboard to answer questions.Participants came to the laboratory and learned that pay was equivalent to their show-up fee and their earnings during the decision task (range \u20ac1\u2014\u20ac8). Data were collected in Spring 2011 (Because effects of oxytocin plateau after approximately 35 min Participants then read that their income to \u201cTriangle\u201d (their in-group) and to \u201cCircle\u201d (the out-group) depended on the participant's own decisions, and those of a representative of Circle's whom they would be paired with through the computer network. A table showed the payoffs to Triangle (in-group) and Circle (out-group) as a function of the four possible combinations of choices . We altered the cardinal payoffs to create variation in Personal and In-Group Vulnerability while at the same time maintaining the ordinal structure of the game as well as Greed and Cooperator's Gain (see main text). This resulted in four different games , were assured that decisions would remain confidential, and asked five times to make a choice between 1 (cooperation) and 2 (non-cooperation) (no feedback was given). To motivate serious decision making, participants were reminded prior to each choice that this choice might be randomly selected for pay-out to all members of Triangle and Circle. As participants interacted through the computer network they could not see each other. Following decision making, we assessed in-group tending (\u201cduring decision making I tried to serve the interests of my group\u201d and \u201cduring decision making I tried to help my team\u201d)  and in-group protection . Due to a programming error, data on in-group protection were recorded only for the Spring 2011 wave. The main experimental task  took 14\u201417 min. Upon finishing the questionnaire, participants were thanked and dismissed. They returned four to six weeks later to pick up a sealed envelope containing their credits, additional earnings, and a full debriefing. We used a time-lag between experimental session and debriefing to prevent that any insight on methods and materials became known before the entire experiment was completed. All participants agreed to this procedure."}
+{"text": "Each window generates its own measurements using a random sensing matrix. The more significant elements are contained by more windows, so they are captured by more measurements. This design makes the EW-CS scheme have more convenient implementation and better overall recovery quality for non-uniform compressible signals than ordinary CS schemes. These advantages are theoretically analyzed and experimentally confirmed. Moreover, the EW-CS scheme is applied to the compressed acquisition of image signals and networked data where it also has superior performance than ordinary CS and the existing unequal protection CS schemes.Many practical compressible signals like image signals or the networked data in wireless sensor networks have non-uniform support distribution in their sparse representation domain. Utilizing this prior information, a novel compressed sensing (CS) scheme with unequal protection capability is proposed in this paper by introducing a windowing strategy called expanding window compressed sensing (EW-CS). According to the importance of different parts of the signal, the signal is divided into several nested subsets,  In the CS methodology, the signal which is sparse or compressible on a certain orthonormal basis can be successfully recovered from a highly incomplete set of samples, called measurements. Moreover, the measurements can be obtained by multiplying the signal by a randomly generated sensing matrix that is incoherent with most of the orthonormal basis. Thus, CS greatly improves the efficiency and decreases the complexity of signal compression.Compressed sensing (CS) ,2 is an The compressible signal can be indicated by the index of the sparse non-zero components and the value of the non-zero components, where the index of the sparse non-zero components is called sparse support. The ordinary CS algorithms are designed without any constraint on the distribution of the support of the sparse signal. Actually, many natural signals do have special support structures. For example, the image signal is compressible in the discrete cosine transform (DCT) basis or discrete wavelet transform (DWT) basis. The transform coefficients constitute a non-uniform compressible signal where the significant coefficients mostly appear at lower frequency, as shown in Considering these largely existing non-uniform compressible signals, if we can utilize the prior-knowledge of the support distribution to provide unequal protection for different parts of the signal, we can instinctively achieve better performance. In this paper, such a CS algorithm is proposed to improve the sensing and recovery efficiency for the non-uniform compressible signals, called the expanding window compressed sensing (EW-CS). The windowing method is inspired by the expanding window fountain codes ,6, whereThe proposed EW-CS scheme treats the different parts of the compressible signal discriminately to pursue the improved overall performance. The more attention on the more important parts is at the expense of the less important parts. Nevertheless, it is worthwhile to do this, because most of the energy or the useful information is contained in the more important parts. The overall performance improvement also has its prerequisite that is the prior knowledge of the rough non-uniform distribution of the significant elements. This prior information is not difficult to get in most cases. For image signals, the significant transform coefficients mostly appear at lower frequency. For networked data, the significant data is surrounding the emerging event. The above statements about the EW-CS are presented and proved from theoretical and numerical perspectives in our paper. Moreover, the EW-CS is applied to image signals and networked data, and shown to provide better performance than the ordinary CS and the existing unequal protection CS schemes.The rest of this paper is organized as follows: in Section 2, the key issues of CS are briefly reviewed, and the related existing CS algorithms considering non-uniform compressible signals are presented and compared with our EW-CS algorithm. The details of the EW-CS scheme are introduced in Section 3. Section 4 is devoted to analyze the recovery error upper bounds of the proposed EW-CS to compare with the ordinary CS. In Section 5, the variation of basic EW-CS algorithm is discussed. The experimental results are shown and analyzed in Section 6. Section 7 concludes this paper and gives some directions for future work.2.2.1.X \u2208 \u211dN is said to be sparse, if the transform coefficient vector \u0398 = { i\u03b8, i = 1,2, \u2026, N}, of X in an orthogonal basis \u03a8N\u00d7N are mostly zero. The sparse support of \u0398 (or X) is defined as S = {ii: \u03b8 \u2260 0, i = 1,2,\u2026, N}, and the length of S is the sparsity K = |S|, K \u226a N, so signal X is called as K-sparse signal. We consider a linear sparse case that K = \u03b1N, 0 < \u03b1 \u226a 1 is a constant. If the most coefficients are not exactly zero but with small magnitude, signal X is called compressible signal. The elements with larger absolute value are regarded as significant. CS theory l1-norm mCompared with the unequal protection methods like the hidden Markov tree model in . which u3.The proposed EW-CS scheme is detailed in this section. First, the non-uniform compressible signal is formularized. Then, the general EW-CS encoding and decoding algorithms are presented. Finally, we simplify the EW-CS to a two-window case which is quite important for applications and analysis.3.1.X = {ix | i = 1,2,\u2026N}T is compressible in the canonical basis, i.e., the orthogonal basis \u03a8N\u00d7N = I. The scheme can be directly applied to other basis. A more tractable definition of the compressible signal X is using the power law that the k-th largest entry of the signal obeys |(k)x| \u2264 pC\u00b7k\u22121/p, where pC > 0 and 0 <p <1. pC represents the energy of the signal which is a constant depending on p, and p is the speed of decay. The sparsity is defined as K when there are K significant elements containing the most energy of the compressible signal, i.e., the first K largest elements |(k)x|, k = 1,\u2026K.In the proposed EW-CS scheme, for clearer explanation, we assume that the signal X is divided into W non-overlapped importance classes. The size of the w-th class is defined by ws so that w = 1, 2, \u2026, W, 0 \u2264 ws \u2264 N. We further assume that the importance of a class decreases with the class's index, i.e., the w-th class is more important than the (w + 1)-th class. The division can be described using a generating polynomial (GP) k = (k/Ns) \u03f5  is the ratio of the elements in the importance class w to all the N elements. The sparsity distribution is given as w \u2264 1 is the proportional factor representing the number of significant elements placed in the w-th class.The non-uniform compressible signal means that the distribution of the significant elements in the sparse support is non-uniform, that is, the support distribution has some structured characteristics. We use importance classes to describe this distribution. From the sparsity perspective, the importance of a class is corresponding to how many significant elements it contains. The compressible signal 3.2.3.2.1.w-th window consists of all the first w classes, so the size of the window is, w = 1, 2, \u2026, W; thus, the last window contains all the signal's elements with wn = N. The structure of the EW-CS is shown in The importance class determines a sequence of strictly increasing subsets of the signal's elements, which we call windows. The N . Given the overall sensing rate R, the number of the random projections is M = RN. The measurements allocated for each window can also be given by a measuring polynomial (MP) w \u2264 1 denotes the ratio of measurements assigned for the w-th window to all the measurements. It means that we generate wm = \u03a9wM random projections X is the vector of the elements in w-th window, and (w)X = X.In the classical CS algorithm, one method to generate the random sensing matrix is by picking the entries from Gaussian distribution w-th importance class belongs to the w-th window and all its subsequent windows, so the elements of w-th importance class are sampled by the w-th and all the subsequent classes of measurements. For example, the first importance class  is sampled in all M measurements, and the last importance class is sampled only in \u03a9wM measurements. Therefore, the elements in importance class with smaller index corresponding to more measurements obtain more protection.It can be noticed from w is the probability that the w-th window is chosen. Encoding with the window selection distribution may bring uncertain sensing rate, but it can be roughly regarded that wm = \u0393wM. As in a CS system each measurement is actually the inner product of the corresponding row of the sensing matrix and the signal vector, it can be calculated separately. For instance, if one measurement k = 1, 2, \u2026, wm, j = 1, 2, \u2026, M is the k-th measurement assigned to the w-th window, we get kn and k-th row of the sensing matrix Although the classes of measurements are described to be generated sequentially in 3.2.2.X simultaneously through CS reconstruction method. If we use the sequential generation method, the joint sensing matrix \u0424M\u00d7N can be written as a combination of all the window sensing matrix \u0424w, as shown in The encoding strategy of the EW-CS is presented class by class. This is sometimes necessary for constrained encoder or distributed coding scenarios, but it is usually more efficient to use joint decoder, which combines the measurements together, and recovers the original M\u00d7N, i.e., Y = \u0424M\u00d7NX. Thus, the signal X can be recovered using ordinary CS recovery algorithms mentioned in Section 2.Thus, the joint decoding can be implemented using this joint sensing matrix. At the decoder side, all the received random projections compose a measurement vector 3.3.In the previous subsection, we described the proposed EW-CS scheme in general format. Nevertheless, the most common situation is that the significant elements of a natural compressible signal are concentrated at a certain part of the signal. Therefore, two importance classes are enough for the usual non-uniform compressible signal. The first importance class consists of more large elements than the second importance class. The first importance class is also the first window, and the entire signal is the second window. The two-window EW-CS has wider application prospects; thus, this special case of the EW-CS is discussed in detail below.x) = \u03a01x + (1 \u2212 \u03a01)x2 which is determined by only one coefficient \u03a01 \u2208 . Similarly, the sparsity distribution can be written as \u039b(x) = \u039b1x + (1 \u2212 \u039b1) x2. If the first class really has more significant elements, 0.5 < \u039b1 \u2264 1; otherwise 0 < \u039b1 \u2264 0.5. For clarification, we adopt the sequential generation as shown in x) = \u03a91x + (1\u2212\u03a91)x2. By increasing \u03a91, we progressively increase the protection of the first importance class. The extreme cases of \u03a01 = M1 = 0 and \u03a01 = M1 = 0 are the ordinary CS problems.In the two-window EW-CS, the GP is \u03a0(1 for short form), and2 =  for short form). Then the encoding procedure can be given as:Y1 and Y2 denote the measurement vectors for the two windows respectively. The encoding can also be written in joint coding format that:Based on above definitions, the joint sensing matrix is given as:X1 and X2 denote the signal elements of the two importance classes not the two windows, which are defined as different from X(1) and X(2). The joint coding format is necessary for facilitating the performance analysis of the EW-CS and contrast with the ordinary CS in the next section.It must be noted that 4.In this section, the reconstruction error upper bounds of the EW-CS is analyzed and contrasted with the ordinary CS scheme (using CS for short). The simple two-window EW-CS is firstly discussed, and then the results are further extended to the general EW-CS.4.1.l2-norm recovery error defined as \u2016X \u2212 X\u0302\u2016l2 is adopted to judge the recovery performance. The performance analysis is presented by contrasting between the CS and the EW-CS. According to the joint coding format of the EW-CS in Subsection 3.3, the CS problem is also formulated by correspondingly divided the signal vector X, the measurement vector Y and the sensing matrix \u0424 into different parts. It is given as:The 1,2 with all zero matrix of the same size, and then the CS problem becomes the EW-CS as shown in The most direct relationship between the CS and the EW-CS can be obtained by replacing the sub-matrix \u0424i.e., Y1CS and Y1EW. However, the joint recovery algorithms for the CS and the EW-CS use both of the two classes of measurements, so we need a joint coding representation to reveal the difference shown in X can be written as N dimensional vector X for the first n1 elements, and the remaining (n2 \u2212 n1) elements of X for the last (n2 \u2212 n1) elements, and the remaining elements of It can be found that the only difference between the CS and the EW-CS is the different generation of the first class of measurements, X1 and X2 separately. This is equal to consideringFor analyzing the discriminational protection of different importance classes, we should consider The first terms on the right hand of l2-norm recovery error from inaccurate measurements have the upper bound as:sf denotes the truncated vector corresponding to the S largest values of compressible signal f . S is chosen such that \u03b43S + 3\u03b44S < 2, and f's sparsity K \u2264 S. \u03b5 is the maximum l2-norm of the noise e, i.e., \u2225e\u2225\u21132 \u2264 \u03b5. The constants C1,S and C2,S depend on the reasonable value of \u03b44S. The second term on the right hand side of This result can also be proved with the aid of mathematical formulae. From the Theorem 2 in , the l2-For the X2 is all zero vector. Based on \u03b51EW \u2264 \u03b51CS. It means that the upper bound of the EW-CS for X, i.e., the subset of elements in Note that the second terms on the right side of 1) percentage of all the measurements, so they may not guarantee the best recovery. Oher looser bounds for approximation error are introduced here for analyzing Comparing with l1-norm obeys the following result with overwhelming probability:M \u2265 logN is the number of measurements, and N is the length of signal f. pC, the fixed decay speed p and \u03b1. The parameter \u03b1 is a sufficiently small positive number to ensure f\u2225\u21131R and p = 1 when For compressible signals obeying the power law, there is an earlier result in  and 2]  2] whichM2 is the number of effectual measurements for i.e., 1 is defined in previous section as the ratio of number of measurements assigned to the first window . Obviously, p2. It is easy to find that when 0 < p2 < 2, the CS's bound is lower than the EW-CS's; when p2 = 2, they are equal; when p2 > 2, the EW-CS's bound is lower than CS's in return. However, the error bound is behaved for compressible signal usually with 0 < p2 < 1 or with 0 < p2 < 2 [This is a looser one than X is discussed. The square error of signal X is given as:Now, the comparison between the CS and the EW-CS for the entire signal X using the CS and the EW-CS can be derived by substituting Thus, the overall recovery error upper bounds for \u03b51 and M2 which are determined by sparsity distribution and MP, i.e., the parameters \u039b1 and \u03a91. However, if there are really more significant elements placed in i.e., 0.5 < \u039b1 \u2264 1, the first term will dominate the overall error upper bounds; otherwise, the second term will do so. Thus, the EW-CS is superior to the CS for a non-uniform compressible signal with proper importance classes assignment.We assume that 4.2.W \u2265 3 windows case. The encoding of the W-window EW-CS is written as:Based on the ana1ysis of the two-window EW-CS, the results are easily extended to EW is a lower triangular matrix. We only consider one importance class Note that the EW-CS's sensing matrix \u03a6w is, the w-th importance class has better recovery quality. Finally, the overall error upper bound for the EW-CS is given as:Comparing with the conventional CS, only for the first importance class vector 5.i.e., 0.5 < \u039b1 \u2264 1 in the two-window case. Thus, the extension of the EW-CS is necessary for this case. The two basic variations are shown in During the introduction of the EW-CS scheme in Section 3, there may be a question that what happens if the importance of classes doesn't decrease with the class index as we assumed. From the analysis in last section, we know that the performance of the EW-CS degraded badly when the more important class doesn't contain more significant elements, It doesn't mean that the EW-CS can only be used in the simple cases where the significant elements concentrate in the front, in the middle or at the back of the signal. It has an even more complicated variation in a certain case. Recall that we have designed a window selection distribution such that each measurement can select the window it belongs to. Similarly, the signal element can also choose the window that it belongs to. It looks a little abnormal in our usual practice, for the signal element may not know its own importance or even do the selection. However, it can be realized in certain case, the wireless sensor network scenarios.N sensors' data is regarded as a compressible signal X = {ix | i = 1, 2, \u2026, N}, where ix is the data of the i-th sensor. Using ordinary CS, each sensor send ijy = jixi\u03c6 to the sink node, and then the sink can collect all the received data to generate one measurement X. This mechanism assumes that all the sensors' data are equal importance, but it is a common situation in wireless sensor networks that a warning line is set a priori for the temperature, pressure or gas strength detection systems. In this case, the EW-CS scheme can be used to simplify this collection process. Each sensor can decide its sensed data is important or not according to the warning line, and then choose the window it belongs to. With one warning line, the two-window EW-CS is applied. If the sensor's data is beyond the warning line, it is in the first window and sends its jiy for M times. If its data is within the security region, it is in the second window and sends its jiy for only m2 < M times. This leads to the better recovery quality for the warning sensor's data, and resaves the transmission energy for the safe sensors.Let us consider the CWS  problem.6.6.1.l2-norm of the recovery error, i.e., \u2225 X \u2212 X\u0302 \u2225\u21132, is used to evaluate the performance of the proposed EW-CS algorithm. A compressible signal X \u2208 \u211dN is generated obeying the power law with the parameters pC = 10 and p = 1 The length of the signal is N = 512, and the sparsity is set as K = 50. The two-window EW-CS is used to compare with the ordinary CS. For constructing the signal in a non-uniform format, the randomly selected \u039b1K elements from the first K K largest elements are placed in the first importance class, and the rest (1\u2212\u039b1)K elements are placed in the second importance class. Other (N\u2212K) smaller elements are distributed randomly. The parameters defining the size of the first importance class and its corresponding number of measurements are fixed as \u03a01 = 0.3 and \u03a91 = 0.5.In our simulation, the R, and the total number of measurements is M. The sensing matrix \u0424EW is constructed by first creating a M \u00d7 N matrix, i.e., the sensing matrix \u0424CS, with i.i.d. draws of a Gaussian distribution N, then the right upper \u03a91M \u00d7 (1\u2212\u03a01)N sub-matrix is replaced by all zero matrix with the same size. The recovery algorithm we used is the l1 based method which is implemented by using a package for specifying and solving convex programs [The overall sensing rate is programs ,24.1 = 0.8 and R = 0.4. The original signal and its recovered version are plotted in l2-norm error for the component signals l2-norm error for the signal X is 1.1808. Note that the significant elements of the signal are almost well recovered and the elements in the first importance class have better recovery quality than that in the second class.In the first example, we consider a compressible signal with \u039b1, the l2-norm error of the signal X and the component signals R = 0.2 and R = 0.4. The results indicate that the performance of the EW-CS varies with the ratio \u039b1, while the ordinary CS is not impacted by \u039b1. With the increase of \u039b1, the recovery error of the EW-CS decreases. Roughly speaking, when 0 \u2264 \u039b1 \u2264 0.5, the CS outperforms the EW-CS. This because that the first importance class is not the really most important one. It means that using the EW-CS with wrong matched window settings will introduce more errors.For various choices of \u039b1 \u2264 1, the EW-CS begins to outperform the CS. In this case, the window settings match the signal's features, so the superiority of the EW-CS is demonstrated. It can also be noticed that the performance for the component signal Nevertheless, when 0.5 \u2264 \u039b6.2.i.e., \u201cLena\u201d, \u201cBoat\u201d, \u201cPeppers\u201d and \u201cAerial\u201d, are used for simulation. The images are divided into 32 \u00d7 32 blocks for computational facility.For testing the practical performance of the proposed EW-CS, instead of using artificially generated signals, we used real-world non-uniform compressible signals. The image signals' DCT or DWT coefficients constitute non-uniform compressible signals. With this prior knowledge, the random sensing with the EW-CS can be accomplished. The 512 \u00d7 512 test gray images with different features, l1 based method to recover the wavelet coefficients, and did the inverse wavelet transform to recover the original image. In our simulation, the three level DWT is used in M-CS with the measurement allocation rule in [The M-CS scheme in  is simul rule in . The levAlthough the importance class design in the EW-CS can also directly use the sub-bands of 2-D DWT coefficients, the additional transform process is not willing to do. Thus, we choose 1-D DCT as the sparse representation basis which will be used only at the decoder so that the low-complexity encoder is guaranteed. The ordinary CS is also simulated with the 1-D DCT.1 = 0.3 and \u03a91 = 0.5. The visual quality comparison for \u201cLena\u201d is given in Firstly, we use the two-window EW-CS with the parameters \u03a0In M-CS, the significant coefficients are only sampled by the measurements allocated to the sub-band they belong, not all the measurements, so its performance is worse than the EW-CS at most sensing rates. At low sensing rate, the number of measurements for the most significant coefficients in the M-CS is fixed to guarantee successful recovery, and these measurements are noiseless. However, the EW-CS cannot recover the elements in the first importance class from the noisy measurements even though they are more. When the sensing rate increases, this problem will not exist.R = 0.4. In order to compare the PSNR performance of the original CS method and the EW-CS method, we fix the signal power, and compensate the power of the all zero matrix \u03a61,2 to the \u03a61,1 to enlarge the signal power of the most significant class. The PSNR performances with different signal-to-noise ratio (SNR) for the four images are shown in In the second simulation, we reconstruct the images from the noisy measurements which are transmitted through an AWGN channel. The sensing rate is fixed as We can observe that the EW-CS is worse than the CS at lower SNR, but outperforms the CS when the SNR increases. The M-CS's PSNR is lowest at the same SNR, but its decay speed is similar to the CS and is slower than the EW-CS. When the channel noise energy gets greater, the advantage of recovery the first importance class of the EW-CS is weaken, and the recovery quality of the second importance class degrades further. Thus, the EW-CS algorithm is more applicable to the mild transmission environments.1 is given in 1 for different measurement allocation parameters \u03a91 will be different. That's why the x axis for each curve in 1, there is a optimal first window size, but the general trend is the first window should not be too large.Then, we investigate the impact of changing window size on the recovery quality of the two-window EW-CS. The PSNR performance of \u201cLena\u201d with different \u03a01 when \u03a01 = 0.2, \u03a01 = 0.3 and \u03a01 = 0.4. The available ranges of \u03a91 for different \u03a01 are different according to the design rule of the joint sensing matrix. The simulation results are plotted in 1 = 0.2 and \u03a01 = 0.3, there is an optimal number of measurements that should be assigned to it. For \u03a01 = 0.4, however, the more measurements, the better.We also evaluate the PSNR performance of the EW-CS with different \u03a9x) = 0.3x + 0.2x2 + 0.5x3 and MP \u03a9(x) = 0.5x + 0.2x2 + 0.3x. The four-window EW-CS is designed with\u03a0(x) = 0.1x + 0.2x2 + 0.3x3 + 0.4x4 and \u03a9(x) = 0.1x + 0.2x2 + 0.3x3 + 0.4x4. The five-window EW-CS is designed with \u03a0(x) = 0.1x + 0.1x2 + 0.1x3 + 0.2x4 + 0.5x5 and \u03a9(x) = 0.1x + 0.1x2 + 0.3x3 + 0.2x4 + 0.3x5. The PSNR performance for different window designs for image \u201cLena\u201d is shown in Finally, we design the EW-CS with more than two windows. The rank law should also be obeyed. So the three-window EW-CS is designed with the GP \u03a0(6.3.N = 256 sensors are randomly distributed within this area to monitor the events of interest. When E events happen, the sensor's data is affected by all the events, and the relationship between them is assumed to be a distance decaying model, which is determined by the distance i,jd from the sensor i to the event j, where i = 1, 2, \u2026, N and j = 1, 2, \u2026, E, and the attenuation factor. If the j-th event's magnitude is jC, the i-th sensor's data is calculated as \u03b1 is the propagation loss factor. Here we assume that E = 3, and all jC are equal to 100, \u03b1 = 3.8.The variation of the EW-CS applied in wireless sensor networks is implemented here. We define a 500 m \u00d7 500 m sensing area. 1 = 0.3. The first window size is determined by the threshold given to each sensor from the collection centre (not shown in 1 = 0.5. The l2-norm recovery error of this example is 0.2401. More simulation results with different transmission rates are plotted in l2-norm recovery error with different SNR is given in For the two-window EW-CS, 1 = 0.5 and the transmission channel is noiseless. The EW-CS in CWS case has the feature that the \u03a01N elements in the first window are expected to be the first \u03a01N largest ones. With the same ratio \u03a91, the smaller the first window is, the more measurements are assigned to the most largest or significant elements, so the overall performance is inversely proportional to the size of the first window as shown in Finally, the performance of the EW-CS with changing first window size is shown in 7.i.e., image signals and networked data, to verify its superior performance. However, its noise-resilient performance is not very good, which is the problem we decided to solve in future work. The adaptive version of the proposed scheme that can optimize the parameters of designed windows is also an interesting direction to be investigated.A novel compressed sensing scheme called expanding window compressed sensing is proposed in this paper to provide unequal protection for non-uniform compressible signals. The efficiency of the proposed scheme is analyzed from the recovery error upper bounds perspective by comparing with ordinary compressed sensing. Different from weighted methods, the windowing technology is adopted to make the scheme more flexible and efficient. Comparing with the blocked sensing method, the nested window design gets more benefit from the joint recovery algorithm for the nested window. The scheme is further applied to practical non-uniform compressible signals,"}
+{"text": "One of the most fundamental and challenging tasks in bio-informatics is to identify related sequences and their hidden biological significance. The most popular and proven best practice method to accomplish this task is aligning multiple sequences together. However, multiple sequence alignment is a computing extensive task. In addition, the advancement in DNA/RNA and Protein sequencing techniques has created a vast amount of sequences to be analyzed that exceeding the capability of traditional computing models. Therefore, an effective parallel multiple sequence alignment model capable of resolving these issues is in a great demand.O(1) run-time solutions for both local and global dynamic programming pair-wise alignment algorithms on reconfigurable mesh computing model. To align m sequences with max length n, we combining the parallel pair-wise dynamic programming solutions with newly designed parallel components. We successfully reduce the progressive multiple sequence alignment algorithm's run-time complexity from O(m \u00d7 n4) to O(m) using O(m \u00d7 n3) processing units for scoring schemes that use three distinct values for match/mismatch/gap-extension. The general solution to multiple sequence alignment algorithm takes O(m \u00d7 n4) processing units and completes in O(m) time.We design O(m) run-time. We also provide a new parallel algorithm for the Longest Common Subsequence (LCS) with O(1) run-time using O(n3) processing units. This is a big improvement over the current best constant-time algorithm that uses O(n4) processing units.To our knowledge, this is the first time the progressive multiple sequence alignment algorithm is completely parallelized with  The advancement of DNA/RNA and protein sequencing and sequence identification has created numerous databases of sequences. One of the most fundamental and challenging tasks in bio-informatics is to identify related sequences and their hidden biological significance. Aligning multiple sequences together provides researchers with one of the best solutions to this task. In general, multiple sequence alignment can be defined as:Definition 1Given: m sequences, , over an alphabet \u2211, where each sequence contains up to n symbols from \u2211; a scoring function h: and a gap cost function. Multiple sequence alignment is a technique to transform  to where is si \u222a '-' [gap insertions], that optimizes the matching scores between the residues across all sequence columns  as in  and 29]29]. In , the indO(m2n2) to O(n) and step (iii) from O(mn4) to O(m3n) \u2248 O(n4), [or O(m4) if n <m]. The overall run-time complexity of the original progressive multiple sequence alignment algorithm is still dominated by step (iii) with an order of O(m3n) regardless of how many processing units are used. The bottle-neck is the pair-wise group alignments must be done in order dictated by the dendrogram (O(m)), and each alignment requires all the column pair-wise scores be calculated (O(m2)). To address these issues, we design our parallel progressive multiple sequence alignment on a reconfigurable mesh (r-mesh) computing model similar to the ones used in , the unary 1UN presentation of x in n-bit is: x = , where bi = 1 for all i \u2264 x and bi = 0 for all i > x  can be found in O(c) time on an n \u00d7 n r-mesh . As a result, a DP r-mesh can be built with 1-bit input components to handle all pair-wise alignments using constant scoring schemes that can be converted to  range. For instance, the scoring scheme for the longest common subsequence rewards 1 for a match and zero for mismatch and gap extension.ci, j loads or computes its symbol matching score for the symbol pair at row i column j, initially. The next step is to configure all the adder/subtractor units based on the loaded values and the gap cost g. Finally, a signal is broadcasted from c0,0 to its neighboring cells c0,1, c1,0, and c1,1 to activate the DP algorithm on the r-mesh. The values coming from cells ci-1, j and ci, j-1 are subtracted with the gap costs. The value coming from ci-1, j-1 is added with the initial symbol matching score in ci, j. These values will flow through the DP r-mesh in one broadcasting step, and cell cn, n will receive the correct value of the alignment.To align two sequences, O(1). Each cell uses 10n processing units (4n for the 1-bit max switch and 2n for each of the three adder/subtrator units). These processing units are bounded by O(n). Therefore, the n \u00d7 n dynamic programming r-mesh uses O(n3) processing units.In term of time complexity, this dynamic programming r-mesh takes a constant time to initialize the DP r-mesh and one broadcasting time to compute the alignment. Thus, its run-time complexity is k \u00d7 n adder/subtractor r-meshes and n \u00d7 n max switches must be used. In addition, to avoid overflow (or underflow) all pre-defined pair-wise symbol matching scores may have to be scaled up (or down) so that the possible smallest (or largest) number can fit in the 1UN representation. With this configuration, the dynamic programming r-mesh takes O(n4) processing units.To handle all other scoring schemes, g = 0).The complication of signed numbers does not exist in the longest common subsequence problem. The arithmetic operation in LCS is a simple addition of 1 if there is a match. The same dynamic programming r-mesh as seen in Figure x and y, each max switch in the DP r-mesh is configured as in Figure ci-1, j-1 is fed into the North-West processing unit, and the other values are fed into the North-East unit. Then, ci, j loads in its symbols and fuses the South-East processing unit (in bold) as NS,E,W if the symbols at row i and column j are different; otherwise, it loads 1 into the adder unit and fuses N,E,SW. These configurations allow either the value from cell ci-1, j-1 or the max value of cells ci-1, j and ci, j-1 to pass through. These are the only changes for the DP r-mesh to solve the LCS problems.To find the longest common subsequence between two sequences O(n3) processing units. However, this is an order of reduction comparing the current best constant parallel DP algorithm that uses an r-mesh of size O(n2) \u00d7 O(n2)  of the progressive MSA algorithm is following the dendrogram, built in the earlier step, to perform pair-wise dynamic programming alignment on two pre-aligned groups of sequences. The dynamic programming alignment algorithm in this step is exactly the same as the one in step (i); however, quantifying a match between two columns of residues are no longer a simple constant look-up, unless the hierarchical expected probability (HEP) matching scoring scheme is used . The mosf is a column from one pre-aligned group of sequences and g is a column from the other pre-aligned group of sequences. fi and gj are residue symbols from columns f and g, respectively, and s is the matching score between these two symbols fi and gj. For example, to calculate the sum-of-pair of the following two columns f and g:where anda to residue b is the same as the matching between residue b to residue a, these pairs become , 3, , 3, , 3, 3. These redundancies occur since the set of symbols representing the residues is small (1 for gap plus 20 for protein [or 4 for DNA/RNA]). Thus, if we combine the two column symbols with their number of occurrences, the sum-of-pair method can be transformed into a counting problem and can be defined as:we will have to score 15 residue pairs:, , , , , , , , , , , , , , . Since the matching between residue f, g are the two columns, T is the number of different residue symbols (T = 4 for DNA/RNA and T = 20 for proteins), s is the pair-wise matching score, or substitution score, between two residue symbols i and j, and ni and nj are the total count of symbols/types i and j (i.e. the occurrences of residue symbols/types i and j), respectively. Since residues from both column f and g are merged, there is no distinction in which column the residue are from. Since T is constant, the summations in Equation remain constant, regardless how many sequences are involved.where Thus, the sum-of-pair score of the two columns given above will be:m processing units as follows. First, map each residue symbol into a numeric value from 1 to T. Next, m residues from any two aligning columns are assigned to m processing units. Any processing unit holding a residue sends a 1 to processing unit pk, where k is the number represents the residue symbol it is holding. pk sums the 1's it receives. The sum-of-pair score can be computed between the pairs of processing units containing a sum larger than 0 calculated from previous steps. All of these steps are carried out in constant time. There are n2 possible pair-wise column arrangements of two pre-aligned groups of sequences of max length n. Thus, the sum-of-pair column pair-wise matching scores for two pre-aligned groups of sequences can be done in O(1) using m \u00d7 n2 processing units.This scoring function can be implemented on an array of O(1) using O(m) time using O(m) r-meshes. The latter is preferred since the dendrogram [step (ii)] and the progressive alignment [step (iii)] each takes O(m) time to complete. Then, a dendrogram is built, using the parallel neighbor-joining clustering algorithm described earlier, from all the pair-wise DP alignment scores from step (i). Lastly, [step (iii)], for each pair of pre-aligned groups of sequences along the dendrogram, the sum-of-pair column matching scores are pre-calculated for the DP r-mesh initialization before proceeding with the dynamic programming alignment. There are m - 1 branches in the dendrogram leading to m - 1 pair-wise group alignments to be performed. In terms of complexity, the progressive multiple sequence alignment takes O(m) time using O(n) DP r-meshes to complete all the pair-wise sequence alignments [step (i)] - (or O(1) time using O(m) time using O(m3) processing units. Finally, the progressive step, [step (iii)], takes O(m) time using a DP r-mesh. Therefore, the overall run-time complexity of this parallel progressive multiple sequence alignment is O(m). The number of processing units utilized in this parallel algorithm is bounded by the number of DP r-meshes used and their sizes. The general DP r-mesh uses O(n4) processing units to handle all scoring schemes with affine gap cost. And step (i) needs m of such DP r-meshes resulting in O(mn4) \u2248 O(n5) processing units used.Progressive multiple sequence alignment algorithm is a heuristic alignment technique that builds up a final multiple sequence alignment by combining pair-wise alignments starting with the most similar pair and progressing to the most distant pair. The distance between the sequences can be calculated by dynamic programming algorithms such as Smith-Waterman's or Needle-Wunsch's algorithms (step i). The order in which the sequences should be aligned are represented as a guiding and can be calculated via hierarchical clustering algorithms similar to the one described in Section (step ii). After the guiding tree is completed, the input sequences can be pair-wise aligned following the order specified in the tree (step iii). In the previous Sections, we have described and designed several r-meshes to handle individual operations in the progressive multiple alignment algorithm. Finally, a progressive multiple sequence alignment r-mesh configuration can be constructed. First, the input sequences are pair-wise aligned using the dynamic programming r-mesh described previously in Section. These O(mn3) \u2248 O(n4) processing units to complete in O(m) time.For alignment problems that use constant scoring schemes without affine gap cost, this parallel progressive multiple sequence alignment algorithm only needs Table m sequences with max length n, we are able to reduce the algorithm run-time complexity from O(m \u00d7 n4) to O(m) using O(m \u00d7 n4) processing units. For a scoring scheme that rewards 1 for a match, 0 for a mismatch, and -1 for a gap insertion/deletion, our algorithm uses only O(m \u00d7 n3) processing units. Moreover, to our knowledge, we are the first to propose an O(1) run-time dynamic programming pair-wise alignment algorithm using only O(n3) processing units.In this study, we have designed various r-mesh components that can run in one broadcasting step, which enabling us to effectively parallelize the progressive multiple sequence alignment paradigm. to align The authors declare that they have no competing interests.KN designed parallel models used in this study. YP and GN participated in designing and criticizing the parallel models and their analysis. All authors read and approved the final manuscript."}
+{"text": "Darwinian selection should preclude cooperation from evolving; yet cooperation is widespread among organisms. We show how kin selection and reciprocal altruism can promote cooperation in diverse 2\u00d72 matrix games . We visualize kin selection as non-random interactions with like-strategies interacting more than by chance. Reciprocal altruism emerges from iterated games where players have some likelihood of knowing the identity of other players. This perspective allows us to combine kin selection and reciprocal altruism into a general matrix game model. Both mechanisms operating together should influence the evolution of cooperation. In the absence of kin selection, reciprocal altruism may be an evolutionarily stable strategy but is unable to invade a population of non-co-operators. Similarly, it may take a high degree of relatedness to permit cooperation to supplant non-cooperation. Together, a little bit of reciprocal altruism can, however, greatly reduce the threshold at which kin selection promotes cooperation, and vice-versa. To properly frame applications and tests of cooperation, empiricists should consider kin selection and reciprocal altruism together rather than as alternatives, and they should be applied to a broader class of social dilemmas than just the prisoner\u2019s dilemma. Darwinian selection precludes any action that increases the competitive ability of others at the expense of one\u2019s self c), a benefit to the recipient (b), and their genetic relatedness (r), Hamilton r>c/b. The concept is based on \u2018inclusive fitness\u2019: the sum of an individual\u2019s reproductive success plus the effects the individual has on the reproductive success of its relatives. For example, sterile worker ants can accrue reproductive benefits by helping their relative, the queen. In so doing, their shared genes survive and get passed on to the next generation.The three standard motives for the evolution of cooperation include kin selection, reciprocity, and group selection Parallel to kin selection, Trivers Kin selection and reciprocal altruism are often viewed and tested as alternatives. Furthermore, theories of kin selection rely on population genetic models while models for reciprocal altruism focus on the specifics of repeated interactions and the capacity to shape conditional strategies. The two have never melded easily The germs of kin selection and reciprocal altruism can be traced back to Darwin r, the probability that like-individuals interact with like) and repeated interactions ; and 2) develop a general model for the evolution of cooperation that satisfies the requirements of all three games. While simple and straightforward, this combined treatment of kin selection and reciprocal altruism across a variety of social dilemmas is necessary for empiricists to properly frame applications and tests of cooperative behaviours.Here we formally combine kin selection and reciprocal altruism and show how they are mutually inclusive properties of games. We apply a game theoretic approach We describe three games \u2013 prisoner\u2019s dilemma, snowdrift, and hawk-dove game \u2013 separately, to illustrate why individuals should act selfishly and under what conditions they should cooperate. We incorporate elements of both kin selection and reciprocal altruism, and combine all three games into a single general model.The prisoner\u2019s dilemma provides the archetype for games pitting community interests against those of the individual. Two prisoners being questioned each have the choice to either defend the other\u2019s innocence or betray their guilt. It is better for both players to defend rather than betray each other. The highest payoff of all, however, accrues to one who betrays while being defended by the other. The worst outcome accrues to a player that defends a betraying opponent.b) to its opponent at cost (c) to itself. A defector incurs no costs and bestows no benefits. We assume that b>c insuring that two co-operators enjoy a higher payoff than two defectors. While cooperation maximizes group payoffs, a defector will always enjoy higher payoffs than a co-operator when played against the same opponent. For this game, D is the non-invadable evolutionarily stable strategy (ESS), also known as the Nash equilibrium in conventional games As a 2\u00d72 matrix game, the prisoner\u2019s dilemma  has straDefection is an ESS so long as interactions occur at random with respect to strategy, and if the game is played but once. We relax these assumptions by considering non-random interactions and an iterative game by which individuals can gain information about others\u2019 predispositions.r be the probability of non-random interactions where like-individuals interact with like, independent of the frequencies of co-operators and defectors in the population r occurs with like-individuals while the portion 1-r occurs with randomly selected individuals  and reciprocal altruism (w>c/b) into a single model by simultaneously considering non-random interactions (represented by r) in an iterative game (represented by w). These adjustments to the prisoner\u2019s dilemma yield a new payoff matrix  game, opponents have the opportunity to play Hawk and fight , or play Dove and give way . Payoffs are maximized when both players give way and play Dove (cooperate). Unfortunately, in a world of doves, it pays to defect and play Hawk (defect). This game\u2019s payoffs can be couched in terms of costs and benefits and modified to consider the joint consequences of kin selection and reciprocal altruism .a>d in b+c)/2; and 4) C played against C yields less payoff than D played against C (c>a). In a social dilemma, the always-cooperate (All-C) strategy, that is, individuals cooperating in all situations, provides the best collective outcome, but there is an incentive to cheat and play the strategy of defect (D) in a world of co-operators. Always-cooperate strategy is not an ESS. These games have a mixed strategy ESS when b>d, and always-defect strategy (All-D) is the global ESS when d>b.Any game with a social dilemma can be considered in terms of kin selection and reciprocal altruism, with the following elements: 1) Games with social dilemmas must be non-zero sum; 2) The strategy of cooperation (C) played against cooperation must produce a higher payoff than the strategy of defect (D) played against D a>d in ; 3) The r >0) with no prior knowledge of one\u2019s opponent (w\u200a=\u200a0) (We make this a model of kin selection by permitting non-random interactions ( (w\u200a=\u200a0) .We combine kin selection and reciprocal altruism into a single model, by simultaneously considering non-random and repeated interactions .r occurs with like-individuals while the portion 1-r occurs with randomly selected individuals, with the following outcomes +(1\u2212r)(b\u2212c)>r(0)+(1\u2212r)(b)r<c/b).Always-defect (All-D) strategy is the ESS when the condition is reversed  we obtain a different payoff matrix  is the ESS when:w(b\u2212c)+(1\u2212w)(b\u2212c)>w(0)+(1\u2212w)(b)\u2212 (1\u2212w)c.Note that the always-defect strategy is an ESS for this matrix since 0> w, exceeds the cost-to-benefit ratio Reciprocal altruism only leads to the evolution of cooperation if the probability of recognizing others, r>c/b) and reciprocal altruism (w>c/b) combine to yield a new payoff matrix when we simultaneously permit non-random interactions (represented by r) and an iterative game (represented by w) (The matrix models for kin selection (ed by w) .We can examine when always-cooperate, tit-for-tat, and always-defect strategies are possible ESSs :All-C is an ESS when All-C played against All-C yields higher rewards than All-D played against All-C:r(b\u2212c)+(1\u2212r)(b\u2212c)>r(0)+(1\u2212r)(b)TFT is an ESS so long as TFT played against TFT serves better than All-D played against TFT :r(b\u2212c)+(1\u2212r)(b\u2212c)>r(0)+(1\u2212r)(1\u2212w)(b)r\u200a=\u200a0), tit-for-tat strategy can still be an ESS so long as the probability of recognizing others is greater than the cost-to-benefit ratio: w>c/bIt is easier for tit-for-tat strategy to be an ESS than it is for the always-cooperate strategy. Individuals using tit-for-tat strategy can benefit both from non-random interactions, and from having an iterative game that provides knowledge of others. If there are no non-random interactions (All-D is an ESS so long as All-D played against All-D serves better than TFT played against All-D:r(b\u2212c)+(1\u2212r)(1\u2212w)( \u2212c)0> w or r increases the likelihood of always-defect being an ESS. When there are no non-random interactions (r\u200a=\u200a0), defection is always an ESS .Decreasing either sensuw as a function of r, thus providing the isoleg in the state space of familiarity, w, versus non-random interactions, r. Outside of the C-ESS (or TFT-ESS) isoleg, always-cooperate (or tit-for-tat) strategy is an ESS . Inside these isolegs, always-cooperate (or tit-for-tat) is not an ESS. Inside of the D-ESS isoleg, always-defect is an ESS, and outside of this isoleg it is not.We can consider all of the combinations of non-random interactions and foreknowledge of others that permit cooperation to evolve . The thrr) and familiarity (w) increases the range over which cooperation can evolve, and reduces the likelihood that All-D will be an ESS. Rather than alternative hypotheses for the evolution of cooperation, kin selection and reciprocal altruism can be considered jointly  and iterative games  extends to other games of social dilemmas, such as the snowdrift and hawk-dove games.b/2\u2013 c >0, always-defect (All-D) is not an ESS either. Thus, the ESS is a mixture of cooperators (C) and defectors (D) (mixed strategy). When b-c >0> b/2\u2013 c, always-defect is an ESS even though always-cooperate would provide each player with higher payoffs. Regardless of whether the snowdrift game has a mixed ESS or an ESS of All-D, it represents a social dilemma.The results in snowdrift game are interesting  in that r>c/b), and for repeated interactions remains w>c/b.As in the prisoner\u2019s dilemma, kin selection or reciprocal altruism can allow for All-C to be an ESS. The conditions for cooperation to be the ESS under non-random interactions remains Hamilton\u2019s Rule All-C is the ESS when b/2\u2212c/2> b/2(1\u2212r)(1\u2212w)TFT is the ESS when b/2+cr/2\u2212bw+brw\u2212c+cw\u2212crwAll-D is the ESS when 0> b/2\u2013 c >0), there are All-C and All-TFT isolegs , the TFT-ESS isoleg intersects the D-ESS isoleg producing four outcomes for the ESS , always-defect is the global ESS \u2013 there is no cooperation. With high costs (b/2\u2212c>0), a mixed strategy of cooperation and defect is the global ESS. High costs and a mixed-strategy ESS are the typical form of the hawk-dove game. Both kin selection and reciprocal altruism permit additional outcomes to the game favouring the evolution of cooperation.Like snowdrift, the hawk-dove game has a low and high cost form. Regardless of cost, always-cooperate is never an ESS. With low costs (w\u200a=\u200a0), always-cooperate can be the ESS when r>b/(b+2c). Under strict reciprocal altruism (r\u200a=\u200a0), tit-for-tat can be an ESS when w>b/(b+2c). When we modify the hawk-dove game to include both non-random interactions and iterative plays of the game, we get the following matrix +(1\u2212r)w(b/2\u2212c)+(1\u2212r)(1\u2212w)bTFT is the ESS when b/2\u2212c>r(b/2)+(1\u2212r)(w)(b/2\u2212c)All-D is the ESS when r and w. At higher w and low r, always-defect or tit-for-tat is the local ESS resulting in alternate stable states. A mixed strategy ESS results at high r but low w. With alternate stable states, a small increase in non-random interactions can make tit-for-tat the global ESS. Similarly, with a mixed strategy ESS, a small increase in the knowledge of one\u2019s opponent can make tit-for-tat the global ESS.The low cost hawk-dove game generates the same configuration of ESSs as the high cost snowdrift game . Always-r and w), tit-for-tat as the global ESS, or always-cooperate as an ESS once the level of non-random interactions is sufficiently high +(1\u2212r)a>r(d)+(1\u2212r)cFor All-C to be ESS, r(d)+(1\u2212r)d>r(a)+(1\u2212r)bFor All-D to be ESS, Both All-C and All-D may be local ESSs  when w >0 and r\u200a=\u200a0, All-D is always an ESS +(1\u2212w)a>w (d)+(1\u2212w)c w>(d\u2212a)/(c\u2212d).For All-TFT to be an ESS, When we combine kin selection and reciprocal altruism into a single model, by simultaneously considering non-random and repeated interactions , we get 1For All-TFT to be ESS:a>r(d)+(1\u2212r)(1\u2212w)c+(1\u2212r)wdr\u200a=\u200a0, then w>(c\u2212a)/(c\u2212d), and w must be positive for any cooperation to evolve.When 2For All-D to be ESS,d>r(a)+(1\u2212r)(1\u2212w)b+(1\u2212r)(wd)Prisoner\u2019s dilemma, snowdrift, and hawk-dove games pose a dilemma for Pareto efficiency. The natural inclination of an individual player is to defect, even though both players would benefit from cooperation. Our model shows various \u201cdoses\u201d of reciprocity and kin selection together can generate cooperation as the sole ESS, both cooperation and defection as local ESSs, cooperation and defection as mixed strategy ESS, and defection as the sole ESS.r), or the probability of knowing the identity of one\u2019s opponent (w). We suggest that non-random and iterative interactions occurring together ease the evolution of cooperation: non-random interactions (kin selection) reduce the threshold of w necessary for cooperation, and iterative interactions that increase the probability of knowing one\u2019s opponent reduces the threshold of r necessary for cooperation. A similar finding on the importance of joint effect of assortment (kin selection) and reciprocity for understanding cooperation has recently been made Research on kin selection and reciprocal altruism have followed independent paths r) may have obscured the connections between reciprocal altruism and kin selection. This may obscure the ecological factors promoting assortative interactions and iterated games. For instance, in many vertebrate species, the direct benefits of helping may be sufficient to maintain cooperative societies Modellers\u2019 preoccupation with genetic relatedness (r). Such game theoretical models show a transition from models that consider well-mixed populations to spatial grids and complex networks Although we explicitly integrated kin selection and reciprocal altruism, with matrix model, we note that other mechanisms besides the synergistic conditions generated by kin selection and reciprocal altruism may influence the evolution of cooperation"}
+{"text": "In this paper a new framework, called Compressive Kernelized Reinforcement Learning (CKRL), for computing near-optimal policies in sequential decision making with uncertainty is proposed via incorporating the non-adaptive data-independent Random Projections and nonparametric Kernelized Least-squares Policy Iteration (KLSPI). Random Projections are a fast, non-adaptive dimensionality reduction framework in which high-dimensionality data is projected onto a random lower-dimension subspace via spherically random rotation and coordination sampling. KLSPI introduce kernel trick into the LSPI framework for Reinforcement Learning, often achieving faster convergence and providing automatic feature selection via various kernel sparsification approaches. In this approach, policies are computed in a low-dimensional subspace generated by projecting the high-dimensional features onto a set of random basis. We first show how Random Projections constitute an efficient sparsification technique and how our method often converges faster than regular LSPI, while at lower computational costs. Theoretical foundation underlying this approach is a fast approximation of Singular Value Decomposition (SVD). Finally, simulation results are exhibited on benchmark MDP domains, which confirm gains both in computation time and in performance in large feature spaces. A Random Projections is a simple but elegant technique that has both a strong theoretical foundation and a wide range of applications including signal processing, medical image reconstruction, machine learning and data mining. Its theoretical foundation rests on the Johnson\u2013Lindenstrauss lemma [S in a high-dimensional feature space nR, if we construct an orthogonal projection of those sample points onto a random d-dimensional subspace, then if P > 1/2) up to a small distortion factor of 1 \u00b1 \u025b. Intuitively, this process can be thought of as applying a random rotation to a high-dimensional manifold and then reading off the first d coordinates. Compared with other linear dimension reduction methods, like Principal Component Analysis (PCA), Factor Analysis (FA), etc., Random Projections are data-independent, which significantly reduces the computational cost. In [This paper explores a technique called ss lemma : given a=Olog|S|\u025b, the procost. In  is analycost. In , Random L2 regularization is also intensively studied in these Gaussian process driving approaches and also in [Kernelized reinforcement learning, as it is named, aims at bring the benefits of non-parametric kernel approaches to reinforcement learning algorithms family. A kernelized least-squares policy iteration (KLSPI) is proposed in  by repla also in . In KLSP also in . KLSPI rIn this paper, a new framework, called Compressive Kernelized Reinforcement Learning (CKRL), for computing near-optimal policies in sequential decision making with uncertainty is proposed via incorporating the non-adaptive data-independent Random Projections and nonparametric Kernelized Least-squares Policy Iteration (KLSPI). One of the central ideas is that Random Projections are able to constitute an efficient sparsification technique and this brings about both faster convergence rate and lower computational costs than regular LSPI. Theoretical foundation underlying this approach is a fast approximation of Singular Value Decomposition (SVD). Experimental results also demonstrate that this approach enjoys the benefit of nonparametric approaches as well as alleviating the computation cost induced by non-adaptive random projections.Here is a brief roadmap to the rest of the paper. In Section 2, background knowledge of the three major perspectives comprising this paper is introduced on compressed sensing and random projections, kernel regression and sparsification and approximate Markov Decision Processes algorithms. In Section 3, unified framework and overview of state-of-art kernelized reinforcement learning algorithm is given, with extensive analysis on both kernel sparsification and error decomposition analysis. In Sections 4 and 5, the algorithms of Compressive Kernelized Reinforcement Learning algorithm are proposed with intensive theoretical analysis in Section 5. Finally, experimental results are conducted in the context of various experimental settings on different benchmark domains to validate the effectiveness of the proposed approach in Section 6.2.2.1.Let us first have a brief review of some important concepts and theorems that will be used in this paper.Lemma 1: (Restricted Isometry Property) A m \u00d7 n compression matrix C \u2208 Rm\u00d7n satisfies the Restricted Isometry Property (RIP), -RIP, if it acts as a near-isometry with distortion factor \u03b5 over all k-sparse vectors, that is, for any k-sparse vector x \u2208 nR, the following near-isometry property holdsC whose columns have unit lengths. Each entry of C matrix ijc is draw from zero mean, unit variance distributions, which looks as if using random noise basis at the first glance, and exert a pairwise distance preserving projection that satisfies Johnson\u2013Linderstrauss Lemma. Geometrically, RP is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while approximately preserving pairwise distances with high probability P > 1/2 (w.h.p). If \u025b. From the sampling perspective, RP is performing coordinate sampling after a spherically random rotation to nR [d coordinates. RP is computationally efficient because of its data-independence nature, yet sufficiently accurate for dimensionality reduction of high-dimensional data sets.on to Rn . Intuiti2.2.K is a symmetric matrix with each entry ijK = k . If the kernel matrix K is not only symmetric but also positive semi-definite, Mercer\u2019s theorem states that the kernel function can be interpreted as an inner product of nonlinear function \u03d5  between every pair of instances without explicitly knowing the nonlinear function\u2019s form. Kernel trick is application of Mercer\u2019s theorem to enrich the expressiveness of the feature space without manually adding more features. Geometrically, kernelization is a way of obtaining linearity by practising a high-dimensional embedding through a nonlinear mapping: First, an inner product is introduced by defining the \u201cnonlinear\u201d kernel, then the whole space is embedded into the high-dimensional kernel space with inner-product preserving, and finally linearity is obtained in this high-dimensional kernel space.Now we give a brief introduction of kernel, kernel matrix, kernel trick and kernel regression. A kernel is a symmetric function representing the similarity between two samples,t = \u03a6w + \u03b5, the sum-of-squares error function without L2 regularization term is given by w = \u03a6Ta, and Gram matrix K = \u03a6\u03a6T, we have t represents the target values of the sample points, and k(x) is a column vector where ik (x) = k . The problem with this method is that there is no guarantee that the kernel matrix is invertible. The most common remedy for this problem is to introduce ridge regression/L2 regularization into this kernelized version, adding regularization term \u03bbI to the diagonal so that K will be invertible. Thus (3) would becomeK while preserve its rank so that it is more likely to be nonsingular as its dimension decreases. ALD method can be considered as a tentative approach in this category. Another approach is to try to practise the pairwise-distance preserving compression, e.g., using Random Projections for matrix compression. We hereby give a brief review of Compressed Linear Regression by [C = m,nC. Firstly we introduce compression matrix d,nC to linear model, so there isL2 regularization term is given byKernel regression , also cassion by . SupposeTCKC is nonsingular whenever rank(K) \u2265 d.We now give proof that the compressed kernel matrix Theorem 1: If the kernel matrix K satisfies rank(K) \u2265 d, the compressed kernel TCKC will be nonsingular, i.e., rank(TCKC) = d, where C is the randomly generated compression matrix.Proof:rank(K) \u2265 d, there exists a sequence {ir1, ir2, \u22ef, rdi} and {ic1, ic2, \u22ef, cdi} such that the sub-matrix subK which are drawn from K with rows of index {ir1, ir2, \u22ef, rdi}, and columns of index {ic1, ic2, \u22ef, cdi} such that rank (subK) = d Next draw arbitrary d rows and columns from C, which form square matrix subC such thatC is approximately orthogonal, so is subC. Also since the rank of a matrix is invariant by left-multiplying a full column-rank matrix or right-multiplying a full row-rank matrix, we have rank (TCKC) = d. This explains why the compressed kernel matrix TCKC is more prone to be nonsingular compared with the original kernel matrix K, which provides an alternative way besides ridge regression to handle K if it is ill-conditioned.If 2.3.Markov Decision Process (MDP) [S, A, R, \u03b3), comprised of a set of states S, a set of (possibly state-dependent) actions A (sA), a dynamical system model comprised of the transition probabilities s\u2032 from state s under action a, and a reward model R. A policy \u03c0: S \u2192 A is a deterministic mapping from states to actions. Associated with each policy \u03c0 is a value function \u03c0\u03c5, which is a fixed point of the Bellman equation:\u03b3 < 1 is a discount factor. In what follows, we often drop the dependence of \u03c0\u03c5 on \u03c0, for notational simplicity. When the set of states S is large, it is often necessary to approximate the value function v using a set of basis functions . In linear value function approximation, a value function is assumed to lie in the linear span of a basis function matrix \u03a6 of dimension S \u00d7 k, where we assume that k \u226a |S|. Hence, \u03c5 \u2248 \u03c5\u0302 = \u03a6w. The vector space of all value functions is a normed inner product space, where the \u201clength\u201d of any value function f can be measured with respect to a weighted norm \u03be as\u03be. It is often the case that \u03be is selected to be the invariant distribution of the Markov chain induced by a policy \u03c0, where the distribution is assumed to be ergodic. For example, one approach to approximately solving the Bellman equation is the fixed point (FP) solution, often referred to as the TD approach, which is defined as finding a set of weights FPw such that\u03a6 is the orthogonal projection onto the column space of \u03a6, given bycombined projected back-up operator \u03a0\u03a6T. Bellman residual methods, in contrast, find a set of weights BRw under which the difference between the approximated value function and the back-up approximated value function T(\u03a6w) is minimized. That is,L1-based feature selection method, i.e., LARS, LASSO, etc. Compressed Sensing and Random Projections provide another path to tackle this problem as an alternative to L1-regularization, e.g., the work presented in [L1-regularization methods.A ss (MDP)  is definented in , which pi.e., samples are not used only once (as in Q-learning), but for multiple times instead. Since samples would be scarce in the large feature space, data reusage is of critical importance.In Reinforcement Learning, it is indeed a huge computational challenge for LSPI to work with large amount of features. Besides heavy computation costs, another concern is learning performance, since a lot of training data is needed for large feature spaces. The third concern is data efficiency. Often the key to data-efficiency is sample reusage, L1 based method into LSPI, which is called LARS-TD [L1 regularization and feature selection. Another way is to do feature compression with Random Projections as an alternative of feature selection, as proposed in [Corresponding to the methods mentioned above, introducing  LARS-TD , provideposed in , which iposed in , a kerneposed in  on kerne3.3.1.Nonparametric approximators have been combined with a number of algorithms for approximate policy evaluation. For instance, kernel-based approximators are combined with LSTD and LSTD-Q by ,11, and i.e., the number of samples that contribute to the solution ..i.e., thKernel-based LSPI introduces the kernel trick into least-square temporal difference learning to derive a kernelized version of LSTD. In KLSPI, kernels are used as basis in LSPI framework for efficient policy evaluation. A generalized kernelized model-based LSTD framework is presented in , where kK\u2032 = PK, whereK, K\u2032 is not symmetric. K\u2032 can be thought of kernelized model of transition matrix P. The kernel regression of the reward model isis, ia, ir, s\u2032i, \u03c0 (s\u2032i)) are drawn from an identical trajectory, we haveG is a nil-potent upper shift matrixLet us define 3.2.L2-regularized kernelized LSTD, which can be roughly divided into three categories to the best of our knowledge. The first is adding regularization term to the kernel regression model of (12) and (13), respectively, i.e.,R and \u03a3P are L2-based regularization terms of reward model and transition model, respectively. Further discussions regarding the corresponding value function formulation and relations between the two regularization term \u03a3R, \u03a3P is in [How to successfully implement kernelized reinforcement learning algorithm involves various sparsification and regularization method. There are two main questions concerning the regularization. The first question is \u201cHow to regularize?\u201d. To answer this question, there are several frameworks of \u03a3P is in . Gaussian is constructed, where n is the number of samples, which uses kernel values between pairs of next state. The authors have shown that the algorithm can be used efficiently when the value function approximation lie in a reproducing kernel Hilbert space (RKHS). They also developed finite sample error bound for the regularized algorithm.Another category of regularized kernelized LSTD is in , in whicLemma 2 [Lemma 2 : The KLSProof: We give a sketch proof here which extends mainly three steps. In a same trajectory, s\u2032i = is+1, so we have K\u2032 = GK. Secondly using K\u2032 = GK we can haveThe third sparsification technique is aiming at reducing sample complexity in streaming data, which renders it applicable in real applications. A sparsification procedure based on approximate linear dependency (ALD) can be performed, which is an online, fast approximate version of PCA . ALD reapreprocessing and postprocessing. Preprocessing is to directly compress the feature space by feature selection. It then learns a basis of the sample  from the compressed feature space, and then use it in LSPI. In this case, it is equivalent to compressing the feature set in advance, and the same feature vector is used at every iteration for a new sample. The ALD sparsification is a typical method of this approach. In this method, each sample in the compressed dictionary spans a feature, and ALD is aiming at compressing this dictionary so that the number of elements in the dictionary is much smaller compared with the number of the whole sample set. In the ALD approach, a subset of samples x\u03031, ..., dx\u0303 is constructed in order to avoid redundant information. The dictionary is used such that \u03d5(x\u03031), ..., \u03d5(dx\u0303) spans approximately \u03d5(x1), ..., \u03d5(nx), while being of minimal size. So the sparsification is actually in the feature space and can be counted as doing feature selection via abandoning redundant samples in forming the dictionary. KLSPI is an adaptation of this idea into LSTD framework. In [Except the first question on how to implement to regularization, another question, both palpable and profound, is when to implement regularization. Generally there are two possible sparsification schemes which differ in when to practise sparsification: work. In , ALD is indirectly adapt sparsification to LSTD, which is to learn a high-dimensional basis k\u0303 (is) of the sample ) first, then use some technique for sparsification, and use the sparsified basis k (is) in policy iteration to generate the new policy. In this case, one needs to recompute a basis at each iteration of LSPI since different feature vectors are used at each iteration, as \u03c0 (s\u2032) depends on the current policy. The A, b matrix is computed as follows:The postprocessing scheme is to 3.3.R and the transition matrix P, respectively. The geometric illustration can be seen in Let us move to introduce the Bellman error of the kernelized value function, which is the one-step temporal difference error,rding to , the Bel4.The General Framework of KLSPI with sparsification is described in 5.C to stand for compressed version, K for kernelized version, CK for kernelized LSTD-RP, and KC for compressed KLSTD. In the following, n stands for the number of samples, D stands for the dimension of full dimensional space, and d stands for the dimension of compressed dimensional space. In kernel regression, we have D = n.We use subtitle Here is using ALD as an optional pre-processing sparsification step and LSTD-RP as a post-processing sparsification step.5.1.C is generally not orthogonal . A linear mapping can cause significant distortions in the data set if C is not orthogonal. Orthogonalizing C is, however, usually very computationally expensive and thus does not justify its cost. Instead, we can rely on a result in [almost orthogonal than orthogonal directions. Thus vectors having random directions might be sufficiently close to orthogonal, and equivalently T CC \u2248 I, where I is the identity matrix, and according to experimental experience [T CC and an identity matrix was about We have to be careful to extend any conclusion of linear projection to Random Projections since there is no guarantee that the Random Projections matrix is a projection operator, because esult in , that isperience , the mealemma in  can be uTheorem 2 Suppose that A is a real m \u00d7 n matrix. Select a target rank k \u2265 2 and an oversampling parameter p \u2265 2, where k + p \u2264 min {m, n}. Execute the proto-algorithm with a standard Gaussian test matrix to obtain an m \u00d7 (k + p) matrix Q with orthonormal columns. Then the expectation of approximation error is boundedProposition 1: For compression matrix C, the following holds:C is approximately orthogonal.Each column of TCC formulates an approximately identity matrix, i.e., T CC \u2248 I.etc. Principal Component Analysis, as a unsupervised dimensionality reduction method, is the optimal solution when the target cost function is the sum of the mean square reconstruction error. The general idea of PCA, kernel PCA and ALD is to project the entire ambient feature space onto a lower dimensional manifold spanned by the topmost eigenvectors of the sample covariance matrix in feature space corresponding to the leading eigenvalues.Low rank matrix approximation is important in a wide variety of scientific applications including statistics, signal processing, machine learning, X to minimize the approximation error of ||A \u2212 X||. If we limit the minimizer to the form of X = T ACC, the problem formulation of this family would be divided into fixed-precision approximation problem and fixed-rank approximation problem [The problem formulation is trying to find a low rank matrix  problem .fixed-precision approximation problem, suppose we are given a m \u00d7 n matrix A and a positive error tolerance \u03b5. The task is to find a compression d \u00d7 m matrix C with minimal d = d (\u03b5) orthonormal column such thatL2 norm. The range of C is a d\u2013dimensional subspace that captures most of the actions of A, and d is desired to be as small as possible.For the fixed-rank approximation problem, given a matrix A, a predefined compression rank d, the problem is to find matrix C with orthonormal columns such that the approximation error \u03b5 = \u03b5 (d) is minimized.fixed-precision problem, i.e., given a matrix A, a target compression rank d, the problem is to findC and the topmost d dominant left singular vectors of A, specifically, X = TUSV, where dU is of size n \u00d7 d and contains these d singular vectors, namely,A in the compressed d-dimensional subspace.For 5.2.A, b is defined in [CV\u0302 (s) is represented asFirst let us have a brief review of LSTD-RP. In LSPI-RP, there isfined in ,(25)A=\u03a65.3.i.e., if we perform Compressed Linear Regression to the sample set, and practise Kernel-based LSTD based on the compressed kernel matrix, this would be identical to the performance of the kernelized version of LSTD-RP for feature compression.Next we will prove the equivalence of the compressed Kernel-based LSTD with kernelized LSTD-RP, Theorem 3: The solution of the kernelized LSTD-RP is the approximate solution of the compressed kernel-based least-square temporal difference learning algorithm, namely,Proof:(1): For kernelized LSTD-RP, we just replace the basis set \u03a6n,D with n,nK in n = D. Thus we getCKV\u0302 is,(2):Next we develop the compressed version of kernelized value function approximation. As in [KV\u0302 can be represented asn. As in , the ker(3): Based on the above analysis, we haveKCV\u0302 isNote that if we insert 6.6.1.C; it is thus reasonable that the variance will be higher than in the ALD-based methods. Also we restrict the problems with finite sample set and large amount of features.We now present several comparison studies to show the effectiveness of our method. It is noteworthy to mention that the benefit of introducing Random Projections for feature compression lies mainly in reduction of computational cost. The overall performance, however, highly depends on the quality of the randomly generated compression matrix L1 regularization, LSPI-RP does not assume that the representation w.r.t the original basis is sparse. To implement L1-regularized method, we need the target function to be sparse in the selected representation. Mathematically, the sparsity appears in the bound instead of the dimension. So, if the signal is not sparse, its sparsity will be equal to the dimension, and thus, the large dimension appears in the bound. In LSPI-RP, however, instead of the requirement on sparsity of the original basis, a requirement is imposed on the features such that they are supposed to be of specific form in order to perform better than LSPI in high-dimensional space. So in LSPI-RP it would be of critical importance of the basis [F, which would often lead to overfitting for regular LSPI. The setting is preferable for LSPI-RP where the number of samples is smaller than or at the same order of the number of features.Unlike he basis . The sec6.2.d: the compression dimensionn: the number of samples, which is also the full dimension in kernelized LSPI\u03b8: the compression ratio of d/D.\u025b: the threshold parameter for ALD dictionary.First we define parameters used in the experiment:The pendulum domain is a typical under-actuated system which is highly unstable. Here we give some illustrative example of compressed kernelized LSPI in pendulum domain. Here we collect 2, 000 samples, and the compression ratio is 0.2. Here we take 20 runs on average, and the average runs to converge of compressed KLSPI, ALD-based KLSPI and regular LSPI are 7.4, 7.8, 8.6 runs. From here we can see that compressed KLSPI has the advantage of faster convergence. This merit will be more explicit as we will show in \u03b81 and \u03b82, and the angular velocities, \u03b8\u03071 and \u03b8\u03072. There are three actions corresponding to positive (a = 1), negative (a = \u22121), and zero (a = 0) torque. The time step was set to 0.05 and actions were selected after every fourth update to the state variables according to the equations of motion. The goal for this domain is to raise the tip of the second link above a certain height in minimum time . The reward function is therefore \u22121 for each time step until the goal is achieved and the discount factor is \u03b3 = 0.99. Episodes begin with the all state variables at value 0 which corresponds to the two links hanging straight down and motionless. The Acrobot is an under-actuated double pendulum which is a typical working benchmark for its nonlinear dynamics. It consists of two arms where torque can only be applied at the second joint. The system is described by four continuous variables: the two joint angles, d with different number of samples. Up to our best knowledge, there is no tighter bound on how to choose d in compressed LSPI yet. In [d is given with an empirical extension to a rule of thumb that In this experiment, we shall seek the optimal compressing dimension  yet. In , a cover\u03b5. Likewise, the compressed sensing technique also depends on one parameter: the compressed ratio \u03b8 = d/D. To be fair, we will give identical compression dimension d, which means that the compressed dimension is equal to the size of the ALD dictionary. The problem setting in Experiment 2 is like this: given large amounts of data, the ALD dictionary is still considerably large. How to compress this dictionary further is an interesting topic worth attention. One heuristic idea, of course, is to make the accuracy threshold of ALD dictionary \u03c5 larger so that the accuracy tolerance becomes larger, and correspondingly the dictionary size becomes smaller. However, based on the compressive reinforcement learning framework, here is another attractive method, first we build the ALD dictionary with a very strict accuracy threshold \u03c5 and build an ALD dictionary with large size. Then we use the Random Projections to compress the basis generated by this \u201clarge\u201d dictionary. Comparison studies are carried out and experimental results in In this experiment, several comparison studies are carried out to compare the two kernel sparsification technique: ALD and Compressed Sensing. Briefly, both two methods are highly adaptable and only depends on one parameter. The ALD method depends mainly on one parameter: the dictionary threshold 6.3.In this experiment, we will show the approximated value function of Compressed Kernelized LSPI on pendulum domain. From 6.4.In here we give a new kernel function, namely, Geodesic Gaussian Kernel (GGK). Compared with RBF kernel, GGK can capture the topology on the manifold where the samples lies on instead of the Euclidean distance used in RBF kernel. Moreover, since GGKs are local by nature, the ill effects of local noise are constrained locally.Geodesic Gaussian Kernels on Graphs:SP  denotes the shortest path from state s to state s\u2032. Since the shortest path on the graph can be interpreted as a discrete approximation to the geodesic distance on a nonlinear manifold, geodesic Gaussian kernel (GGK) includes rich information of the manifold formed by the data. Shortest paths on graphs can be efficiently computed using the Dijkstra algorithm. The result for two-room domain using GGK is show in A natural definition of the distance would be the shortest path. So we define Gaussian kernels on graphs based on the shortest path:7.L1 regularization into this framework is a promising topic to explore. Another promising future direction is to introduce this compressive reinforcement learning framework to policy gradient approaches with regular MDP [In this paper a new nonparametric reinforcement learning framework called Compressive Kernelized Reinforcement Learning (CKRL) is proposed based on Gaussian process, compressed Sensing and random projections. We compare compressed kernelized LSPI, kernelized LSPI, and regular LSPI along with different kernels based on Euclidean distance and Graph-based Geodesic distance, respectively. Preliminary theoretical proof and experimental results are also given. There are various interesting future directions along this research venue. For instance, how to integrate ular MDP  and POMDular MDP ."}
+{"text": "In this paper, the potential sensitivity in Kelvin probe force microscopy (KPFM) was investigated in frequency modulation (FM) and heterodyne amplitude modulation (AM) modes. We showed theoretically that the minimum detectable contact potential difference (CPD) in FM-KPFM is higher than in heterodyne AM-KPFM. We experimentally confirmed that the signal-to-noise ratio in FM-KPFM is lower than that in heterodyne AM-KPFM, which is due to the higher minimum detectable CPD dependence in FM-KPFM. We also compared the corrugations in the local contact potential difference on the surface of Ge (001), which shows atomic resolution in heterodyne AM-KPFM. In contrast, atomic resolution cannot be obtained in FM-KPFM under the same experimental conditions. The higher potential resolution in heterodyne AM-KPFM was attributed to the lower crosstalk and higher potential sensitivity between topographic and potential measurements. Kelvin probe force microscopy (KPFM)  combinedz2. AM-KPFM, proposed by Kikukawa et al. [z, and a serious stray capacitance effect [On the other hand, there are mainly three kinds of KPFM modes: frequency modulation (FM), amplitude modulation (AM) , and heta et al. , has dema et al. ; howevere effect ,15. As ae effect  and Ma ee effect , has beeConsequently, to elucidate the origin of atomic resolutions of potential measurements in FM, AM, and HAM-KPFMs, it is necessary to clarify the performance of topographic and potential measurements using the three modes. Here, since the serious stray capacitance effect on LCPD images in AM-KPFM has been illustrated in the past , we simpIn this study, for the first time, we investigated HAM-KPFM as a method of enabling quantitative surface potential measurements with high sensitivity by showing the contrast between FM- and HAM-KPFMs. The principle and experimental setup of FM- and HAM-KPFMs are presented. The high sensitivity of HAM-KPFM compared to FM-KPFM is experimentally demonstrated. Finally, we gave atomic resolution images of surface potential measurements on a Ge (001) surface using a W-coated cantilever in HAM-KPFM.f) in cantilever vibration and the energy dissipation results in an amplitude variation (\u2206A) of the cantilever's oscillation; these parameters are given by \u25b3f\u2009=\u2009- f0Fc/(2kA), \u25b3A\u2009=\u2009QFd/k[f0, k, Q, and A are the resonance frequency, the spring constant, the quality factor, and the amplitude of the cantilever, respectively. Fc and Fd are the tip-sample conservative and dissipative interactions, respectively.Firstly, we theoretically compared the performance of potential sensitivities in FM- and HAM-KPFMs. In NC-AFM, the frequency shift  between the tip and the sample, \u03b50 and R are the dielectric constant in vacuum and the tip radius, respectively. zt0 and A are the average tip position and the oscillation amplitude of the cantilever, respectively.here, Direct current (DC) component of the frequency shift induced by alternating current (AC) bias voltage is given by:From the equation ribed by \u03b4VCPD-FM is approximately 15.11\u00a0mV with a VAC of 1\u00a0V. That means that if we want to obtain a potential resolution higher than 15\u00a0mV, VAC has to be higher than 1\u00a0V.Note that the minimum detectable CPD in FM-KPFM is independent of the quality factor of the cantilever. Under the typical conditions in Table\u00a0VBias\u2009=\u2009VDC\u2009+\u2009VACcos (\u03c92\u2009-\u2009\u03c91) t is applied; the electrostatic force at frequency \u03c92 is given byIn HAM-KPFM, a bias voltage \u03c92 are described byamplitude variation induced by the electrostatic forces at frequency A\u2009=\u2009QFd/k, the minimum detectable CPD is given byfrom the equation \u25b3VCPD-HAM is approximately 5.52\u00a0mV with a VAC of 1\u00a0V. This value is around three times smaller than that of \u03b4VCPD-FM. In other words, to achieve an equivalent potential resolution, the VAC in HAM-KPFM is smaller than that in FM-KPFM.Note that minimum detectable CPD in HAM-KPFM is inversely proportional to the quality factor of the cantilever. Increasing the quality factor of the cantilever decreases the minimum detectable CPD, which means that the potential sensitivity in HAM-KPFM is enhanced. Under the typical conditions in Table\u00a0These results show that the potential and force sensitivity detected by HAM-KPFM is higher than in FM-KPFM especially with the higher quality factor of the cantilever in vacuum condition.Next, we experimentally confirmed that the potential sensitivity of HAM-KPFM is higher than that of FM-KPFM. All experiments were performed with homemade optical interference detection UHV-AFM equipment operating at room temperature. FM-AFM was performed to provide topographic and dissipation information. The frequency shift was fed into the SPM controller  as feedback to keep it constant; data acquisition and distance spectroscopy were performed by the Nanonis system.\u03c9m component of the frequency shift for FM, and \u03c92 component of the cantilever deflection for HAM-KPFM, respectively, which was generated by the lock-in amplifier into the SPM controller. The FM- and HAM-KPFM setup diagrams are shown in Figure\u00a0ACcos (\u03c9mt) which was generated by the commercial phase-locked-loop detector was applied between the tip and the sample, the \u03c9m component of the frequency shift \u0394fm is measured with the PLL circuit and the lock-in amplifier. In HAM-KPFM, an AC bias voltage of VACcos (\u03c92\u2009-\u2009\u03c91) t was applied between the tip and the sample, the \u03c92 component of the cantilever deflection is measured with a lock-in amplifier . The details of the experimental setup have been given in references [Simultaneous measurements of the potential information (LCPD) were measured by FM- and HAM-KPFM, respectively. The DC bias voltage was tuned to minimize the electrostatic interaction with the bias feedback by feeding the ferences ,12.k, resonant frequency f1st, and quality factor Q of about 40\u00a0N/m, 165\u00a0kHz, and 20,000, respectively, and where f2nd is approximately 6.3 times higher than f1st (f2nd\u2009\u2248\u20091.05\u00a0MHz). The modulation frequencies in FM- and HAM-KPFM were fmod-FM\u2009=\u2009500\u00a0Hz, fmod-HAM\u2009=\u2009f2nd\u2009=\u20091.05\u00a0MHz. The cantilever was initially treated with an Ar+ ion bombardment  to remove the native oxidized layer and maintain tip sharpness. The tip was then coated by a tungsten layer with a thickness of several nanometers by sputtering the tungsten mask plate for 10\u00a0h  to ensure sufficient tip conductivity [+ ion sputtering at 1\u00a0keV followed by annealing to 973 to 1,073\u00a0K.A commercial silicon cantilever (Nanosensors: NCLR-W) which was detected by an optical fiber interferometer was used as the force sensor, with a spring constant uctivity . A Ge  and (8), one can find that the minimum detectable CPD in HAM-KPFM is 1/3 that obtained in FM-KPFM in theory, in contrast, the SNR in HAM-KPFM is just 1.5 times higher than that in FM-KPFM. A possible explanation for this difference comes from the fact that quality factor of the cantilever we used was less than the simulation one. The SNR of FM-KPFM results at VAC\u2009=\u2009500\u00a0mV is consistent with the measurement result in literature [We compared the signal-to-noise ratios (SNRs) of detected signals at different bias modulation amplitudes to investigate their sensitivities to short-range electrostatic force in FM- and HAM-KPFMs. Figure\u00a0terature .VAC\u2009=\u2009150\u00a0mV, \u2206f\u2009=\u2009-68.5Hz, and modulation frequencies in FM- and HAM-KPFMs are identical to the previous SNR measurements, respectively. The scanning area was 4\u00a0nm\u2009\u00d7\u20094\u00a0nm.We have taken potential distribution measurements on a Ge (001) surface by FM- and HAM-KPFMs using the system mentioned above. The cleaned Ge (001) surface showed a buckled dimer structure with a low, missing-dimer defect distribution. There are two main buckled dimer structures: the symmetric dimer phase p (2\u2009\u00d7\u20091) configuration and the c (4\u2009\u00d7\u20092) configuration ,19. ThisVDC approximately at 1\u00a0V) and this voltage easily makes the dimer atoms on the surface adsorbing to the tip apex to form double covalent bonding with the surface atoms. Besides, the influence of the topographic measurement seriously affects the potential images with high AC bias voltage. In contrast, for HAM-KPFM, this phenomenon can be ignored (the results are not shown here).These results demonstrated that the HAM-KPFM has a higher potential resolution and lower crosstalk than FM-KPFM.Figure\u00a0VAC than that of FM-KPFM. The higher potential sensitivity of HAM-KPFM was explained as follows: the oscillation of the frequency shift at \u03c91 in FM-KPFM and the oscillation of the amplitude at \u03c92 in HAM-KPFM are both proportional to the gradient of the electrostatic force, whereas the quality factor in UHV for the AFM system is approximately several tens of thousands greater, and finally, that the minimum detectable electrostatic force in HAM-KPFM is smaller than in FM-KPFM according to Equations (1) and (2). Hence, the potential sensitivity in HAM-KPFM is higher than that in FM-KPFM. Further, lower crosstalk between topography and potential images in HAM-KPFM compared to that in FM-KPFM is due to the first and second resonance signals being separated from each other using low- and high-pass filters in HAM-KPFM; on the other hand, the potential and topography signals are difficult to separate because the first resonance of the cantilever was oscillated in both measurements.Quantitatively, the potential line profile contrast is shown in Figure\u00a0VAC effect was apparently removed because small AC bias voltages were applied and the VCPD which compensated the CPD between tip and sample is 20 to 100\u00a0mV [VAC influence to the potential measurement [In HAM-KPFM measurements, the high o 100\u00a0mV ,12, and o 100\u00a0mV . In somesurement .In summary, the potential sensitivity and crosstalk were compared in FM- and HAM-KPFM experimentally and theoretically. We demonstrated that the potential sensitivity in HAM-KPFM is higher than that in FM-KPFM theoretically. Then, we experimentally confirmed that SNRs of electrostatic force measurements, which determined the potential sensitivity in HAM-KPFM, are higher than that of FM-KPFM. Further, we applied the FM- and HAM-KPFM measurements to a Ge (001) surface under the same conditions, and atomic resolution in potential and topography images were obtained in HAM-KPFM, whereas the atomic resolution was not visible in FM-KPFM. We attribute this to the higher sensitivity and lower crosstalk in HAM-KPFM compared to the FM-KPFM. Consequently, the HAM method proposed here is a useful tool for detecting the actual potential distribution on the surface.The authors declare that they have no competing interests.ZM, JM, JT, HX, and HZ carried out the calculations, performed the experiments, and drafted the manuscript with the help of CX and JL. YL participated in the design of the study and helped to draft the manuscript. All authors read and approved the final manuscript."}
+{"text": "According to ideomotor theories, intended effects caused by a certain action are anticipated before action execution. In the present study, we examined the question of whether action effects play a role in cued task-switching. In our study, the participants practiced task-response-effect mappings in an acquisition phase, in which action effects occur after a response in a certain task context. In the ensuing transfer phase, the previously practiced mappings were changed in a random, unpredictable task-response-effect mapping. When changed into unpredictable action-effects, RT as well as switch-costs increased, but this occurred mainly in trials with short preparation time and not with long preparation time. Moreover, switch costs were generally smaller with predictable action-effects than with unpredictable action-effects. This suggests that anticipated task-specific action effects help to activate the relevant task-set before task execution when the task is not yet already prepared based on the cue. The question of how human actions are mentally controlled is one that has been investigated since the early beginnings of cognitive psychological research in the nineteenth century , to shift attention to the new, currently relevant task-set, and to activate the new task-set  and error rate] is worse after a task switch than after a task repetition. These Action effects, that is, effects that happen as a consequence of the specific task execution, might help to reduce the conflict of ambiguous task-sets. When referring to action effects, we are referring to effects or events that take place after the response, as explicit consequence of the response. Examples for action effects are the tone that is heard after pressing a piano\u2019s keyboard or the light that is turned on after pressing the light switch.anticipation of the effect, which happens temporally before response execution, as assumed in the ideomotor principle. For example, when playing a piano, the pianist anticipates already the tone he/she wants to produce before pressing the key  effect anticipation.Kiesel and Hoffmann  reportedand vertically aligned. A cue indicated if the position of the horizontal or the vertical target should be determined. The task-related action effect was a red light-up of the target in the position which indicated the correct response. This means, if the correct response was \u201cright,\u201d the target on the right side appeared red as consequence of the response, whereas the vertical target stayed colorless; and if the correct response was \u201cup,\u201d the target turned red on the up-position, whereas the horizontal target stayed colorless. The action effects were thus semantically associated with the correct response. The task-unspecific effect was just a feedback with the information whether the task was executed correctly or not. The authors found a significant two-way interaction of task transition and type of effect for trials with a long cue-target interval . In the task-specific effect condition, residual switch costs were reduced compared to the unspecific effect condition. That is, anticipating task-specific action effects might help to discriminate the task sets of the upcoming trial and select the appropriate one. However, in this study, only trials with a long CTI were analyzed so that no statement can be made about how action effects influence task performance in trials with a short CTI.In another study, Ruge et al.  providedbefore response execution , we assume that they play a stronger role primarily when the task is not yet fully prepared .If the influence of anticipated action-effects needs time to build up, we would assume an influence of task preparation time. To examine the influence of preparation time on the impact of action effects in task-switching, we manipulated the cue-target interval. If the task-response-effect association becomes stronger with more time to activate the task set, then we would expect a more pronounced increase in RT and switch costs for long preparation intervals compared to short preparation intervals. However, with the presentation of the cue, the cue-task association is as well retrieved, entailing a sustained bias to the relevant task components Meiran, , so thatTwenty-four students of the RWTH Aachen university  took part in the experiment. They received partial course credit or 8\u20ac. The participants were equally and randomly assigned to the experimental vs. the control group. Informed consent was obtained from all subjects, and the experiment was performed according to the ethical standards of the Declaration of Helsinki.The experiment was programmed with the experimental runtime system ERTS . Participants sat in front of a screen with a viewing distance of approximately 60\u2009cm. The stimuli consisted of digits ranging from one till nine, without the five. They appeared in white on a black background at the center of the screen with a height of 1.4\u2009cm .The two tasks were two numerical judgment tasks. In one task, the participants had to decide if a presented number was greater or less than five . In the other task, the participants had to decide if the presented number was odd or even . The tasks switched randomly and were indicated by a cue. Each number was framed by either a diamond or a rectangle. If the number was framed by a diamond, the magnitude task was required; if the number was framed by a rectangle, the parity task was required. The diamond was 3\u2009cm high and 3\u2009cm wide . The rectangle was 3.6\u2009cm high and 3.5\u2009cm wide . Responses were to be made by manually pressing one of two response keys  with the left or right index finger. Participants were instructed to press left for a smaller or an odd number and to press right for a greater or an even number. If the response given by the participants was correct, an action-effect occurred. The effects were assigned to the task and the response in the experimental group in the first eight \u201cacquisition blocks.\u201d For example, for the magnitude task, visual action-effects and for the parity task, auditory action-effects occurred. If the response was \u201cless\u201d (left key-press), the background of the screen turned yellow and if the response was \u201cgreater\u201d (right key-press), the background of the screen turned green. For the parity task, a honking tone was presented after the correct response for \u201codd\u201d (left key-press) and a ringing tone after the correct response for \u201ceven\u201d was presented (right key-press). The mapping between task, response, and action-effect was counterbalanced across participants in the experimental group. For the control group, the action effects were completely random, that is, participants could not establish an association between task, response, and action-effect and thus could not anticipate the action effect. If the response was wrong, nothing happened, the background just turned black in both groups. Participants were instructed to react as fast and as correct as possible. They were informed in both groups that the effects happening after the key-press should be used as feedback whether the task was performed correctly.Each trial started with a cue, which appeared in half of the trials 100\u2009ms prior to the target stimulus (CTI of 100\u2009ms) and in the other half of the trials 900\u2009ms prior to the target stimulus. The CTI duration varied randomly. Cues and stimuli stayed on the screen until a response was given. For both CTI levels, an action effect was presented for 200\u2009ms immediately after a correct response. That is, the response-cue interval (RCI) was held constant at 400\u2009ms and the response-stimulus interval (RSI) was 500\u2009ms for trials with a short CTI and 1300\u2009ms for trials with a long CTI.Before the experiment started, the participants performed a practice block with 16 trials. The experiment consisted of eight acquisition blocks and one transfer block. The acquisition blocks as well as the transfer block comprised 96 trials each plus four warm-up trials that were not recorded. Altogether, one session lasted about 45\u2009min.In the experimental group, the task-response-effect associations were predictable so that a mental task-response-effect association could be established by the participants. In the transfer block, the learned associations were changed into random action-effects as in the control group. There was no difference between the acquisition blocks and the transfer block in the control group. To analyze the influence of the change in the action-effect assignment, performance in the last acquisition block (Block 8) was compared with that in the transfer block (Block 9).Task transition (switch vs. repetition), block (Block 8 vs. Block 9), and CTI (short vs. long) were used as independent within-participants variables; group  was used as independent between-participants variable. RT and error rate were measured as dependent variables. Significance was tested at \u03b1\u2009=\u20090.05.In addition to the four non-registered warm-up trials, the first recorded trial of each block was excluded from analysis because it could not be categorized as a switch or repetition trial. All trials with RT less than 200\u2009ms or exceeding 3 SD of each participant\u2019s mean were discarded as RT outliers . Furthermore, all incorrect trials and that following an incorrect trial were not included in the analysis. Errors occurred in 4.8% of the trials.F\u2009=\u20095.49, p\u2009=\u20090.029, \u03b72\u2009=\u20090.2 \u2009=\u20094.98, p\u2009=\u20090.036, \u03b72\u2009=\u20090.185. Only in the experimental group, RT increased in Block 9 (from 817 to 882\u2009ms), but not in the control group (776 vs. 775\u2009ms). This interaction is also reflected in the split ANOVA, as described below.The data were submitted to a four-way mixed analysis of variance (ANOVA) with the independent variables task transition, block, CTI, and group. To forestall the most important result: the four-way interaction of task transition, block, CTI, and group was significant, F, 22\u2009=\u20095.experimental group, the three-way interaction of task transition, block, and CTI was significant, F\u2009=\u200912.34, p\u2009=\u20090.005, \u03b72\u2009=\u20090.529. Switch-costs increased significantly from Block 8 (75\u2009ms) to Block 9 (226\u2009ms) in short CTI trials, whereas they even somewhat decreased numerically from Block 8 (61\u2009ms) to Block 9 (49\u2009ms) in long CTI trials. Further, the two-way interaction of task transition and CTI was significant, F\u2009=\u20096.7, p\u2009=\u20090.025, \u03b72\u2009=\u20090.378, showing that switch-costs decreased from 150\u2009ms for short CTIs to 56\u2009ms for long CTIs. The main effects of task transition, F\u2009=\u200930.03, p\u2009<\u20090.001, \u03b72\u2009=\u20090.732, block, F\u2009=\u200910.3, p\u2009=\u20090.008, \u03b72\u2009=\u20090.484, and CTI, F\u2009=\u200911.05, p\u2009=\u20090.007, \u03b72\u2009=\u20090.501 were significant, too. RT was shorter for repetition trials (798\u2009ms) than for switch trials (901\u2009ms), for Block 8 (817\u2009ms) than for Block 9 (882\u2009ms) and for long CTIs (807\u2009ms) than for short CTIs (893\u2009ms). To go more into detail, and understand better the three-way interaction, we further split the analysis in two two-way ANOVAs for short and long CTI trials.For the F\u2009=\u20096.75, p\u2009=\u20090.025, \u03b72\u2009=\u20090.380, indicating that switch-costs increased in the transfer block. Further, the main effect of task transition was significant, F\u2009=\u200935.38, p\u2009<\u20090.001, \u03b72\u2009=\u20090.763 whereas the main effect of block was just not significant, F\u2009=\u20094.13, p\u2009=\u20090.067, \u03b72\u2009=\u20090.273. For the trials with a long CTI, the two-way interaction of task transition and block was not significant, F\u2009<\u20091. The main effect of task transition failed to reach significance, F\u2009=\u20094.07, p\u2009=\u20090.069, \u03b72\u2009=\u20090.270, but the main effect of block was significant, F\u2009=\u200911.26, p\u2009=\u20090.006, \u03b72\u2009=\u20090.506. RT was increased from Block 8 (770\u2009ms) to Block 9 (843\u2009ms).The trials with a short CTI showed a significant two-way interaction of task transition and block, control group, the three-way interaction of task transition, block, and CTI was not significant, F\u2009<\u20091. The well-known two-way interaction of task transition and CTI was significant, F\u2009=\u200911.03, p\u2009=\u20090.007, \u03b72\u2009=\u20090.501. It reflects a reduction of switch costs with a long preparation interval . The main effects of task transition, F\u2009=\u200920.74, p\u2009=\u20090.001, \u03b72\u2009=\u20090.653, and CTI, F\u2009\u2009=\u200947.69, p\u2009<\u20090.001, \u03b72\u2009=\u20090.813 were significant. RTs were faster in repetition trials (707\u2009ms) than in switch trials (844\u2009ms) and faster with a long preparation interval (709\u2009ms) than with a short preparation interval (841\u2009ms). There was neither a main effect of block, nor an interaction including this variable (Fs\u2009<\u20091).In contrast to the experimental group, in the F\u2009=\u200920.02, p\u2009<\u20090.001, \u03b72\u2009=\u20090.476. Switch costs were higher in the control group (190\u2009ms) than in the experimental group (50\u2009ms). Also, the three-way interaction of transition, CTI, and group was significant, F\u2009=\u20094.51, p\u2009=\u20090.045, \u03b72\u2009=\u20090.17. Switch costs were especially high in the control group in short CTI trials (250\u2009ms), but could be reduced with a long CTI (130\u2009m), which is a reduction of 48%. However, in the experimental group, switch costs were even more reduced with a long CTI (from 75 to 24\u2009ms), which is a reduction of 68%. In addition, also the expected interaction of transition and CTI was significant, F\u2009=\u200928.29, p\u2009<\u20090.001, \u03b72\u2009=\u20090.563. Switch costs were higher in trials with a short CTI (162\u2009ms) than with in trials with a long CTI (77\u2009ms). As expected, the main effect of transition, F\u2009=\u200958.41, p\u2009<\u20090.001, \u03b72\u2009=\u20090.726, and of CTI were significant, too, F\u2009=\u2009105.26, p\u2009<\u20090.001, \u03b72\u2009=\u20090.827. Neither the main effect of group was significant, F\u2009=\u20091.3, nor the interaction of CTI and group, F\u2009=\u20092.29.In the analysis of trials with a long preparation interval in the experimental group, we found small and non-significant switch-costs, like in the study of Ruge et al. . Hence, F\u2009=\u20091.2. Already in the first two blocks, the switch costs were smaller in the experimental group  than in the control group . The interaction of transition and group in the first two blocks was accordingly significant, F\u2009=\u200920.02, p\u2009<\u20090.001, \u03b72\u2009=\u20090.476.To check at which point of time the switch-costs decreased for the experimental group, we additionally took a look at the switch costs in the first eight blocks for the experimental and the control group. The main effect of group was not significant, F\u2009=\u20097.86, p\u2009=\u20090.01, \u03b72\u2009=\u20090.263. No other main effect or interaction was significant, Fs\u2009<\u20091.9.For the error rate, the four-way ANOVA for Block 8 and 9 was conducted. It revealed only a main effect of task transition with fewer errors in repetition trials than in switch trials (3.9 vs. 5.97%), F\u2009<\u20091, nor an interaction with switch costs.Also in the first eight blocks, no difference between group was shown, The aim of the present study was to investigate the role of action effects in task-switching. In order to examine this question, we designed a task-switching paradigm in which task-irrelevant, but predictable action-effects occurred. The task-response-effect mappings were practiced in eight acquisition blocks, so that action effects could be reliably anticipated. In a ninth (transfer) block, the action effects were random, so that the effects could no longer be anticipated in a task- and response-specific way. Additionally, the CTI was manipulated to examine effects of task preparation. The results showed that going from predictable  to unpredictable action-effects increased both RT and switch costs. However, this influence of anticipated action-effects was found only in trials with a short CTI.anticipated because otherwise an influence of stimuli that occur after response execution would be quite inexplicable. Hence, this influence of action effects is consistent with the already existing literature on effect anticipation . Although intended action-effects may be weighted more in the action code (Hommel, Our results also showed a difference in the switch costs between groups already in the acquisition phase. The experimental group with the predictable action-effects revealed smaller switch costs than the control group with the random action-effects, corroborating the results of the study of Ruge et al. . However Hommel, , having  Hommel, , 2011.This association seems to occur very fast, as the switch costs were already smaller in the first two blocks for the experimental group compared to the control group, although participants had only little opportunity to experience the predictable task-response-effect mapping. There is also evidence in the study of Kiesel and Hoffmann  that theTaken together, our data support the hypothesis that action effects play an important role in task implementation. Further, we can conclude that the learned associations are task-specific, that means task-response-effect associations instead of stimulus-response-effect associations, because the switch costs are affected. In this regard, one might ask if action effects do not only influence task-set activation but are even a part of the task set as a distinct task-set component. With respect to our study, this assumption is not yet necessary, but this may be a theoretical option that should be investigated in future studies. Either way, one should not forget that in our daily life, performing tasks has mostly external effects. Hence, to really understand how humans are dealing with multiple tasks in their daily life, action effects should be considered as an important influence in task performance in future studies.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography. This sub-wavelength interference pattern has been obtained using entangled light56\u03bb/2. In our study, we find that using the appropriate scanning method, even super sub-wavelength interference patterns can be achieved. This surprising result encourages us to consider the physics behind this phenomenon and to determine whether we can achieve an interference pattern with arbitrarily high resolution. We address these questions in this manuscript and suggest how to obtain a full understanding of the second-order intensity correlation.Quantum lithography was first proposed by Boto E(\u2212) and E(+) are operators for the negative and positive frequencies of the light field, \u03c1 is the density matrix operator for the light source, and r is a transverse coordinate vector on the detection plane. The measured first-order correlation in Eq. (1) directly represents the distribution of light intensity on the detection plane.In interference and diffraction experiments with light, the observed quantity is the first-order correlation function of the light on a detection plane in the far-field region, In addition to the first-order correlation, light can have a second-order correlation, which is defined ash. If the source is thermal light, the second-order correlation function on the detection plane can be written as16In T(r\u2032), the impulse response function can be expressed ask = 2\u03c0/\u03bb is the wave number. If the light source is fully incoherent, as it is for thermal light, the first-order correlation function of light just emitted from the source \u03b4(r) is the Dirac delta function, and n is the mean photon number. Here, we have assumed that the intensity distribution of the incoherent light on the source plane is uniformT2(r). This result shows that a well-defined Fourier-transform image of the transmittance of an object can be extracted from the second-order correlation function.Under the paraxial approximation and the assumption that the source is covered by an object with a transmission function x1, y1) and  of the detection plane. Simply but without loss of generality, a one-dimensional object such as a double-slit is usually employed to force the correlation function to become a two-variable function. For a one-dimensional symmetric double-slit placed along the y-axis, the correlation function is independent of the coordinates y1 and y2. In this way, the second-order correlation function in Eq. (5) can be further simplified to the formEq. (5) clearly shows that the second-order correlation function is a four-variable function of the transverse coordinates (\u03bb = 457\u2005nm and a rotating ground glass disk (GGD). The angular velocity of the GGD is maintained at \u03c9 = \u03c0 rad/s. A double-slit is placed immediately after the GGD. The width of each slit is a = 0.038\u2005mm, and the distance between centres of the two slits is d = 0.12\u2005mm. The diffracted light is split into two parts after the double-slit using a beam splitter (BS) and is then recorded by two charge-coupled devices (CCDs). Both of the CCDs are located at z = 23\u2005cm behind the double-slit; therefore the CCDs are placed in the Fraunhofer diffraction region with respect to the double-slit.The experimental setup is shown in 1 and CCD2. Here, we extract the relevant row data from the two CCDs, and construct the second-order correlation function. The result is shown in x1 and x2 are the horizontal coordinates on CCD1 and CCD2, respectively. Here, we use colour to represent the value of the second-order correlation function. This second-order correlation function is the two-dimensional second-order interference pattern of the double-slit.As shown above, the second-order correlation function Eq. (6) describes the correlation between two arbitrary points on CCD2 plane is fixed and another point detector on the CCD1 plane is moved along the x1 direction. The curve obtained along this line, is identical to the traditional Young's interference pattern, as shown in A cross-sectional curve with arbitrary spatial resolution can be obtained by choosing the correct line on the two-dimensional figure. Line (a) in x1 = x, and x2 = \u22122x, we obtain a narrower interference pattern than the sub-wavelength pattern, as shown in \u03bb/3. If we set x1 = x, and x2 = x/2, as represented by line (d) in \u03bb  in \u03bb . The expet al.et al.et al. found that the two-photon double-slit interference pattern is 2-fold narrower than the traditional pattern obtained using coherent light. If one assumes that the entangled photon pairs are generated simultaneously at either the upper or lower-slit and propagate to the detection plane independently, the coincidence count at the detection plane can be approximately expressed in the form262728The above conclusion can be applied to sub-wavelength interference from an entangled light source. In this case, Angelo et al.For simplicity, the single-slit diffraction function has been ignored. As shown in Eq. (7), the second-order correlation function is a two-dimensional function of the detection plane coordinates. In x1 = x, x2 = 2x) and , respectively. In \u03bb/3 and 3\u03bb, respectively. As described in Ref. As in the analysis for thermal light, line (a) in Based on the above results for both thermal and entangled light, it is clear that a cross-sectional curve can be constructed with arbitrary spatial resolution by choosing the scanning method for the detectors in the detection plane. However, cross-sectional curves represent only part of the information obtained from the second-order interference. To obtain all of the information, we should consider all possible combinations of arguments for the second-order correlation function. For example, when including all possible variations of the two arguments, the full picture of the second-order interference of a double-slit is a two-dimensional pattern.N-photon absorption) materials, although proof-of-principle experiments that display certain aspects of quantum lithography have been performed. In these proof-of-principle experiments, N photons should appear at same point on the N detectors simultaneously because the N-photon absorber is simulated by N-fold coincidence. From this perspective, we can see that if N detectors scan with different paces and in different directions, it is impossible to take advantage of the resulting super sub-wavelength patterns to achieve quantum lithography. In other words, for thermal light, the second-order interference pattern becomes flat when two detectors scan in the same directions (x1 = x2), and this method clearly can-not be used for writing sub-Rayleigh structures. However, for entangled light, a sub-wavelength interference pattern is obtained when two detectors are scanned with x1 = x2 , represent the positions of two detectors. Thus, all the information available from the second-order correlation function can be obtained only by considering all possible combinations of x1 and x2 in the detection plane. In previous sub-wavelength interference experiments using a thermal light source5\u03bb/2 spatial resolution cross-sectional curves were obtained when two point detectors were scanned in opposite directions . However, there are no mathematical or physical reasons to limit the scanning methods for two detectors to the coordinates x1 and x2 in Eq. (6). For example, if the two point detectors move in the detection plane along x1 = x, x2 = x/2, one can obtain the cross-sectional curve with spatial resolution 2\u03bb. In contrast, if the two point detectors move in the detection plane along x1 = x, x2 = \u22122x, one can obtain cross-sectional curve with spatial resolution \u03bb/3. In general, the cross-sectional curve with spatial resolution N\u03bb or N > 0) can be obtained when the two point detectors scan in the detection plane along x1 = x, x1 = x, x2 = (1 \u2212 N)x, respectively. Therefore a cross-sectional curve with arbitrary spatial resolution can be obtained merely by choosing an appropriate scanning method. The result that the physical quantity G(2) is not independent of the scanning method appears surprising. However, noting the second-order correlation function Eq. (6), we can find the reason for this effect\u2014the second-order correlation pattern is a two-dimensional surface rather than a one-dimensional curve. To further clarify our argument, we perform a second-order interference experiment using pseudo-thermal light with a setup similar to that employed in Ref. The two variables d in Eq. , represed in Eq. , represeR.L. constructed and operated the experiment, and collected the data. P.Z. and F.L. devised and designed the experiment. Y.Z. and H.G. performed the theoretical calculations. All authors contributed to the manuscript."}
+{"text": "Estimating \u03c01 is usually done through P-values, but computing P-values can be viewed as a nuisance and potentially problematic step. We evaluated methods for estimating \u03c01 directly from test statistics, circumventing the need to compute P-values. We adapted existing methodology for estimating \u03c01 from t- and z-statistics so that \u03c01 could be estimated from other statistics. We compared the quality of these estimates to estimates generated by two established methods for estimating \u03c01 from P-values. Overall, methods varied widely in bias and variability. The least biased and least variable estimates of \u03c01, the proportion of differentially expressed genes, were produced by applying the \u201cconvest\u201d mixture model method to P-values computed from a pooled permutation null distribution. Estimates computed directly from test statistics rather than P-values did not reliably perform well.The goal of many microarray studies is to identify genes that are differentially expressed between two classes or populations. Many data analysts choose to estimate the false discovery rate (FDR) associated with the list of genes declared differentially expressed. Estimating an FDR largely reduces to estimating  Gene expression microarrays are a standard tool for large-scale measurement of gene expression. Microarrays are widely used to detect genes that are differentially expressed (DE) across different groups. Methodology for detecting DE genes has matured over the past decade. Methods have evolved from simple fold-change rules, to the use of classical statistical methods, to the use of test statistics developed specifically for the microarray context . The search for DE genes is usually done in the framework of statistical hypothesis testing. A hypothesis test is performed for each gene. Since microarray studies usually involve tens of thousands of genes, detecting DE genes automatically involves multiple testing issues. Rather than controlling false positives through the traditional family-wise error rate (FWER), most researchers prefer to consider the false discovery rate (FDR). The false discovery rate is an alternative to FWER that was originally proposed by Benjamini and Hochberg . The FDRP-value for every gene. (3) For some threshold \u03b1 close to 0 , call all genes with P-values less than \u03b1 significant. (4) Estimate the FDR associated with the list of significant genes. In reality steps (3) and (4) might be done iteratively, with the P-value threshold adjusted depending on the estimated FDR resulting from step (4). Next, we review methodology for these 4 steps, which will introduce the question this paper will address.Controlling the FWER is too conservative in the microarray setting, because usually investigators are willing to get a small proportion of false positives in exchange for a sizeable list of potentially DE genes for further study. There is a near-consensus that FDR-estimation procedures are the preferred method for addressing multiple testing in the microarray context , 3. A tyXjk be the (possibly log-transformed) level of expression of a given gene in sample j of population k. Let nk be the number of samples drawn from population k. Define k. Also define k. Typically expression levels are compared across two populations or groups . To identify DE genes, one could use the classical two-sample t-statistic:t-statistic relies on estimates of the expression variances. With the sample sizes typical of most microarray studies (only a few samples per group), these estimates are very unstable. Given the large number of genes in microarray studies, some genes will exhibit a low variance by chance. In real data one often finds that the genes with the largest t-statistics are those with the smallest denominators, not necessarily those that are DE between groups. Step (1) involves the choice of test statistic. The earliest approaches to identifying DE genes were simple fold-change rules. An example of a fold-change rule is to declare a gene DE if its average expression level varies by more than a factor of two between the comparison groups. However, such rules are generally considered unsatisfactory because they do not incorporate the variability of the data, and there is no associated level of confidence in the conclusion of declaring a gene DE . It was s-statistic,s-statistic is identical to the t-statistic with the addition of a constant, \u03b4, to the denominator. The constant \u03b4 has the effect of stabilizing the denominator of the t-statistic. We will refer to \u03b4 as the stabilizing constant.Tusher et al.  proposed\u03b4. Tusher et al. [\u03b4 to ensure that the variance of the s-statistic \u201cis independent of gene expression.\u201d Broberg [t-statistic denominators as \u03b4, and Xie et al. [\u03b4: 0; 5th, 50th, and 90th percentiles, and the limit as it approached infinity and found the 90th percentile worked best. There is no consensus on the best way to choose r et al.  state th Broberg  used thee et al.  used thee et al.  comparedt-statistic for detecting DE genes. In each of the papers mentioned above , sim, simt-stn et al.  assessed and Cao  employedP-value computed for each gene to test the null hypothesis that the gene is not DE. MMMs consider these P-values as a mixture of P-values for genes for which the null hypothesis is true and P-values for which the null hypothesis is false. Estimators of the FDR have the form\u03b1 is the P-value threshold, \u03c00 is the proportion of non-DE genes, \u03c01 = (1 \u2212 \u03c00) is the proportion of DE genes, and Fp(\u00b7) is the cumulative distribution function of all P-values. Most MMMs use the observed number of P-values less than \u03b1 to estimate Fp(\u03b1). Therefore, most MMMs differ only in their estimates of \u03c01. Step (4) involves estimating the FDR associated with a list of genes declared significant. Many different \u201cMixture Model Methods\u201d (MMMs)  have beeP-value\u2014step (2)\u2014one needs to know the distribution of the test statistic under the null hypothesis. Obtaining an empirical null distribution by permutation is a very popular choice in the microarray context. However, Kerr [P-values resulting from permutation tests and MMMs may be incompatible since permutation-test P-values may not satisfy all of the assumptions implicit in MMM methodology. Therefore, estimating the FDR directly from test statistics\u2014skipping step (2) altogether\u2014could be advantageous. In order to compute a er, Kerr  showed tThere are few tools available to estimate the FDR directly from test statistics. One such tool, \u201clocfdr\u201d , operateP-value together with a MMM for P-values. In this approach, a single null distribution of the test statistic is estimated by pooling all the permutation null test statistics across genes. Kerr [P-values\u201d are different from permutation test P-values. However, \u201cpooled null P-values\u201d have the attractive feature that they have a monotone relationship with the test statistic. For our second class of methods for estimating \u03c01, we computed pooled null permutation P-values and then estimated the FDR with an MMM. We used two MMMs that we have seen to work well: \u201cqvalue\u201d [There are many different Specialized Test Statistics to choose from; we use the SAM-statistic in our investigation due to its simplicity and popularity. We compare results to a procedure in current common practice, which is to use a variant of a permutation-test es. Kerr  showed t\u201cqvalue\u201d  and \u201ccon\u201cqvalue\u201d .s-statistics or any other Specialized Test Statistics as input. Since \u201cfdrtool\u201d accepts t-statistics, and s-statistics are similar to t-statistics, we investigated whether we could apply \u201cfdrtool\u201d to s-statistics and get accurate results. Our idea was to compute both s-statistics and t-statistics on the same data, and then rescale the s-statistics to have the same spread as the corresponding t-statistics. We considered two measures of variability: standard deviation and interquartile range. In addition, we considered four different s-statistics, each using a different stabilizing constant term in the denominator. We designed simulations to investigate the accuracy of using \u201cfdrtool\u201d to estimate FDR's from s-statistics in this way. Our simulated data were based on real microarray data.The methodology of \u201cfdrtool\u201d is not designed to take t-statistic and an s-statistic for each gene. Due to the addition of the stabilizing constant in the denominator of the s-statistic, the 100\u2009s-statistic values will be closer to zero than the 100 t-statistic values. In other words, the addition of \u03b4 to the denominator pulls the s-statistic values toward zero, so that the variance of the s-statistics across genes is smaller than the variance of the t-statistics. As a simple example, suppose that we have 100 genes with measured expression levels on two samples from two groups we wish to compare. We compute a s-statistics. We examined two measures of variability: the standard deviation (SD) and the interquartile range (IQR). We took the ratio of the variability of the t-statistic to the variability of the s-statistic as our rescaling factor. For the SD, we transformed the s-statistics by multiplying them by the factor (SDT/SDS), where SDT and SDS are the standard deviations across genes of t-statistics and s-statistics, respectively. The rescaling factor for the IQR was similarly defined, with IQR in the place of SD. Note that rescaling the s-statistics maintains their rank order, which retains the s-statistic's advantages for accurately detecting DE genes.Accordingly, we used a measure of the difference in variability of the statistics across genes as the rescaling factor to rescale the s-statistics one must choose the value of the stabilizing constant \u03b4 in the s-statistic denominator. We considered four choices for \u03b4, and so defined four different s-statistics: the s30, s50, s70, and s90. The s30-statistic uses the 30th percentile of all t-statistic denominators as \u03b4, the s50-statistic uses the 50th percentile of all t-statistic denominators as \u03b4, and so forth. In summary, for each simulated data set, we computed the t-statistic and the four s-statistics. We transformed the s-statistics by two different rescaling factors (SD and IQR). When loading the rescaled s-statistics into \u201cfdrtool,\u201d we evaluated two different specifications to the software. We could specify that the input was t-statistics or z-statistics. We evaluated the performance of these five statistics using the four different combinations of rescaling factors and two different input options.In computing The design of the simulation study is that same as Kerr (2009) , and we For each gene, we calculated the sample mean and sample standard deviation of that gene in each population group (CEU and CHB). We rounded the sample mean values to the nearest tenth digit, so that means could be unambiguously declared equal or unequal between groups. We simulated CEU and CHB sample data  from independent normal distributions with parameters based on the values from the actual data. We simulated datasets of 10,000 transcripts.\u03c01) were differentially expressed in the mean. For the simulated DE genes, the difference in means for the simulated CEU and CHB samples was taken from the observed sample means in the real data. The variances of the simulated CEU and CHB samples differed between the three simulation types.We ran three types of simulations: EV, UV1, and UV2. In each simulation, a proportion of genes  simulations, the standard deviation of both the simulated CEU sample and the simulated CHB sample came from the observed standard deviation from the CEU data. This was not the case in the UV  simulations. In the UV1 simulations, the standard deviation of the simulated CEU sample came from the observed standard deviation from the CEU data, and the standard deviation of the simulated CHB sample came from the observed standard deviation from the CHB data. In the UV2 simulations, this was reversed: the standard deviation of the simulated CEU sample came from the observed standard deviation from the CHB data, and the standard deviation of the simulated CHB sample came from the observed standard deviation from the CEU data.\u03c01: 0.01, 0.05, 0.10, and 0.25, and three different sample sizes: large, intermediate, and small. Letting nCEU and nCHB denote the sample sizes for CEU and CHB, respectively, our sample sizes were as follows: large  = , intermediate  = , and small  = . Note that all of the sample sizes maintain the 4\u2009:\u20093 ratio of the original data. With three sample sizes, four values of \u2009\u03c01, three simulation types, two rescaling factors (SD and IQR), and two input specification options , there were a total of 144 different simulation scenarios. After examining the results, we performed additional EV simulations for \u03c01 = 0.005, 0.02, 0.03, and 0.04 for the three sample sizes, two rescaling factors, and two input specification options, adding an additional 48 simulation scenarios, for a total of 192 simulation scenarios. We repeated each scenario 20 times. We initially simulated data for four different values of s-statistics outperformed the t-statistic in identifying DE genes. s-statistics outperform the t-statistic across all sample sizes and values of \u03c01. This difference in performance is more marked for the smaller sample sizes than the larger sample sizes, across all values of \u03c01. The four s-statistics are generally close in performance. The s30-, s50-, and s70-statistics perform comparably. The s90-statistic (purple curve) stands slightly apart from the other three, giving less sensitivity at low false positive rates and better sensitivity at higher false positive rates. The difference in the ROC curves for the s90-statistic and the other s-statistics is more pronounced in the smaller sample sizes. However, the difference between the s90-statistic and the other s-statistics is not as large as the difference between the t-statistic and the four s-statistics.First, we verified that the s-statistics when \u201cfdrtool\u201d treated them as either t-statistics or z-statistics. Specifying in \u201cfdrtool\u201d that the inputted s-statistics were t-statistics . In the first row of \u03c01 have a modest conservative bias for the s30- and s50-statistics in the two smaller sample sizes. However, for higher proportions of DE genes , the \u201cfdrtool\u201d estimates of \u03c01 are poor, with excessive conservative bias. This result held regardless of whether statistics were rescaled with IQR , but showed anticonservative bias for low percentages of DE genes (\u03c01 = 0.01). Bias and variability is mostly improved over \u03c01 = 0.01. All results presented here are for the EV simulations; results for the UV1 and UV2 simulations were similar (see supplementary File 1).In contrast to the results for the atistics  worked bP-value. In this approach, a single null distribution of the test statistic is estimated by pooling all the permutation null test statistics across genes. \u201cPooled null P-values\u201d can be computed from a single empirical null distribution. We also obtained estimates of \u03c01 using pooled null P-values and then estimating the FDR with an MMM. We obtained estimates of \u03c01 using two MMMs that we have seen to work well: \u201cqvalue\u201d [A popular approach in practice is to compute a variant of a permutation-test \u201cqvalue\u201d  and \u201ccon\u201cqvalue\u201d .qvalue\u201d results for the EV simulations. For a low percentage of DE genes , the \u201cqvalue\u201d results , the story is similar, with \u201cqvalue\u201d estimates generally showing less bias than \u201cfdrtool\u201d estimates, but greater variability. However, the higher variability in the \u201cqvalue\u201d results seems more clearly acceptable when \u03c01 = 0.10, 0.25, given the dramatic reduction in bias. Interestingly, \u201cqvalue\u201d does not appear to perform worse for the t-statistic than it does for the s-statistics, whereas \u201cfdrtool\u201d almost always performs better for s-statistics. The comparison of the \u201cfdrtool\u201d results to the \u201cqvalue\u201d results was similar for the UV1 and UV2 simulations .\u03c01 for the EV simulations. Overall, the \u201cconvest\u201d estimates show less bias and comparable or less variability than the \u201cfdrtool\u201d or \u201cqvalue\u201d results. Thus, although it relies on P-values that could be considered invalid as permutation test P-values [\u03c01 (and hence FDR) in terms of bias and variability. Similar to the \u201cqvalue\u201d results, \u201cconvest\u201d performs comparably for t-statistics as for s-statistics.P-values , \u201cconvesP-values and was not prohibitive. The more important difference is that \u201cconvest\u201d requires P-values, which we computed via permutation, whereas the \u201cfdrtool\u201d is applied directly to test statistics and does not require any data permutations.The \u201cconvest\u201d method took longer to compute than the \u201cfdrtool\u201d approach (approximately 20 times as long). However, computation time was on the order of 6.5 seconds for 1 set of 10,000 An important limitation of this study is that all simulations were based on one dataset. We also did not explore different correlation structures for the simulated gene expression.\u03c01, the proportion of differentially expressed genes, from microarray data. The approaches were in two classes: (1) adapting the methodology of \u201cfdrtool\u201d to Specialized Test Statistics and (2) applying mixture model methods (MMMs) to P-values computed from a pooled permutation null distribution. The best-performing method was in the second class, using the MMM \u201cconvest\u201d to P-values computed from a pooled permutation null distribution. Overall, estimates of \u03c01 exhibited the least bias and variability, and bias tended to be conservative rather than anti-conservative.We compared approaches for estimating \u03c01 adapted existing methodology of \u201cfdrtool\u201d to s-statistics. Interestingly, \u201cfdrtool\u201d generally performed better for s-statistics than it did for t-statistics, even though the empirical modeling is designed for t-statistics. The performance of the \u201cfdrtool\u201d-based approach varied substantially on the proportion of differentially expressed gene. However, the \u201cconvest\u201d-based approach outperformed the fdrtool approach in almost all scenarios.The first class of approaches for estimating The Supplementary Material File contains the complete set of results for all simulation scenarios examined in the research.Click here for additional data file."}
+{"text": "It has been proposed that, contrary to the \u201cclassical\u201d view in which cortical action potentials are encoded as purely digital, all-or-none events, action potential (AP) shape may be used by the brain for representing and processing information -4. Corti"}
+{"text": "Identifying reliable domain-domain interactions will increase our ability to predict novel protein-protein interactions, to unravel interactions in protein complexes, and thus gain more information about the function and behavior of genes. One of the challenges of identifying reliable domain-domain interactions is domain promiscuity. Promiscuous domains are domains that can occur in many domain architectures and are therefore found in many proteins. This becomes a problem for a method where the score of a domain-pair is the ratio between observed and expected frequencies because the protein-protein interaction network is sparse. As such, many protein-pairs will be non-interacting and domain-pairs with promiscuous domains will be penalized. This domain promiscuity challenge to the problem of inferring reliable domain-domain interactions from protein-protein interactions has been recognized, and a number of work-arounds have been proposed. This paper reports on an application of Formal Concept Analysis to this problem. It is found that the relationship between formal concepts provides a natural way for rare domains to elevate the rank of promiscuous domain-pairs and enrich highly ranked domain-pairs with reliable domain-domain interactions. This piggybacking of promiscuous domain-pairs onto less promiscuous domain-pairs is possible only with concept lattices whose attribute-labels are not reduced and is enhanced by the presence of proteins that comprise both promiscuous and rare domains. Proteins comprise domains which are evolutionary conserved sequence segments with the ability to fold and be functional. An important class of domains mediates protein-protein interactions (PPIs); although not all interactions between proteins can be attributed to interactions between domains, and not all domains in multi-domain proteins play a direct role in protein interaction. Nonetheless, many computational methods which seek to predict PPIs with high accuracy rely on computationally inferred domain-domain interactions (DDIs), e.g. Ideally, the inferred DDIs used to support the predicted PPIs are highly reliable themselves, that is there is a large overlap between the set of inferred DDIs and the set of DDIs confirmed to interact by 3D crystal structures of proteins. This latter set is referred to in this paper as the gold standard domain-domain interactions (GDDIs). This ideal is desirable not only to tease out specific interactions in a protein complex, but also to give predictive power to protein-protein interaction prediction methods (more on this point later in this section).promiscuous domains. Promiscuous domains can occur in many domain architectures However, using GDDIs to predict PPIs generates a large number of false positives (non-interacting protein-pairs predicted as interacting) and thus reduces the accuracy of the prediction method. The large number of false positives stem from the fact that GDDIs are enriched with It is parsimonious to re-use domain-pairs that can interact to facilitate PPIs. Indeed, many DDIs are conserved across organisms by evolution not GDDIs. Promiscuous domains are observed to be heavily involved in PPI mediation promiscuity prevents GDDIs from being highly ranked in computational methods to infer DDIs. Recognizing this domain promiscuity problem, additional measures have been taken to counteract its effects when inferring DDIs from PPIs, e.g. The \u2018drift towards rare domain-pairs\u2019 phenomenon in PPI prediction methods has been noted piggy-backing potential of promiscuous domain-pairs. Piggy-backing occurs when a domain-pair improves its score because either one or both of its domain partners happen to occupy the same attribute-label set as one or more rarer domains. Piggy-backing potential is possible only in concept lattices that are not attribute-reduced, and is enhanced by the presence of many mixed architecture proteins. One of the challenges of doing bioinformatics research is the volatility and variety of bioinformatics datasets which exerts a high validation cost for any new method. Therefore, it is useful to understand why a bioinformatics method works and under what conditions. Identifying such conditions also automatically suggests the limits of a method. Towards this end, effort is made to investigate conditions favourable to the proposed concept-based domain-pair ranking method.In this paper, I propose that Formal Concept Analysis (FCA) P be the set of proteins and D the set of domains. Every protein in P comprises one or more domains in D. D(x) denotes the finite set of domains for protein x. If | D(x) |\u200a=\u200a1, x is a single-domain protein; if | D(x) | > 1, x is a multi-domain protein. The set of proteins which contains domain a is P(a)\u200a=\u200a{ x \u2208 P | a \u2208 D(x) }. The frequency of domain a in P is N(a)\u200a=\u200a| P(a) |. x\u200a=\u200aD(x)\u200a=\u200a{a, b, c} where x \u2208 P and {a, b, c} \u2282 D denotes protein x is its set of domains D(x) which in turn comprises domains a, b and c.Let P. This relation is symmetric, i.e. if  is an interacting protein-pair, then so is . It is possible for proteins to self-interact. Let 1 denote  \u2208 the set of PPIs. 1 implies proteins x and y come from the same organism, i.e.: O(x)\u200a=\u200aO(y). The set of non-PPIs is also a symmetric relation on 3, and a non-interacting protein-pair 0 also implies O(x)\u200a=\u200aO(y). O(x)\u200a=\u200aO(y) implies either 1 or 0. There may be pairs in P \u00d7 P which are neither interacting nor non-interacting because they do not satisfy the same organism condition.The set of PPIs is a relation on D, and domain self-interaction is possible. A protein-pair  generates domain-pairs, each of which may or may not be reliable, through the cross-product of their domains, i.e. D(x) \u00d7 D(y). A domain-pair  generates a set of protein-pairs, each of which may or may not be interacting, through the cross-product of their respective protein sets, i.e. P(a) \u00d7 P(b). For a domain-pair  to be a DDI, it must generate at least one interacting protein-pair.The set of DDIs is a symmetric relation on The Riley dataset x and y implies interactions between the domains of x and the domains of y. The Riley set of proteins, domains and PPIs generate 177,233 putative domain-domain interactions (DDIs). Amongst these possible DDIs are 783 gold standard domain-domain interactions (GDDIs). These GDDIs were obtained from iPfam The proteins are associated with 12,455 Pfam-A and Pfam-B domains. Amongst the set of proteins are 26,032 protein-protein interactions (PPIs). Interactions and non-interactions between protein-pairs are restricted to proteins from the same organism In the following sub-sections, the Riley dataset is examined to support assertions made in this paper. Specifically, the data characteristics of interest are:Highly reliable domain-domain interactions (GDDIs) are enriched with promiscuous domains.GDDIs generate significantly more true positive PPIs and also more false positive PPIs than non-GDDIS. More true positive PPIs agrees with the parsimony or the re-use principle for GDDIs, and more false positive PPIs accords with the promiscuity of gold domains.Protein domain architectures are mostly a mix of rare and promiscuous domains.gold domain is a domain that participates in at least one gold standard domain-domain interaction (GDDI). There are 642 gold domains in the Riley dataset. A domain is more promiscuous if it occurs more frequently in a given set of proteins, i.e. given P and {a, b} \u2282 D, N(a)>N(b) implies a is more promiscuous than b.All domains that participate in at least one GDDI were pooled and their frequencies were compared against the frequency of occurrence of all 12,455 domains. In agreement with previous observation in y for a domain occurrence value of x means y fraction of all domains that occurs x times are gold domains. The tendency is for Gold/All to equal 1 as domain occurrence increases. This supports the notion that GDDIs are significantly enriched with promiscuous domains. This conclusion is not surprising given that the GDDIs are sourced from the iPfam database The bar chart in S. pombe.Because the dataset comprises multi-organisms, there is a possibility that the heavy imbalance between rare and promiscuous domains in the set of all domains may be due to the many organisms with only a handful of proteins  in the da, b) as [N(a)+N(b)]/2. The promiscuity of GDDIs is then compared against the promiscuity of all non-GDDIs. R\u2019s Wilcox.test confirms that GDDIs have significantly larger promiscuity scores than non-GDDIs.The previous test examined the promiscuity of single domains. In the following test, the promiscuity of domain-pairs are examined by quantifying the promiscuity of a domain pair  generates a set of protein-pairs, each of which may or may not be interacting, through the cross-product of their protein sets, i.e. P(a) \u00d7 P(b). A DDI is either a GDDI or a non-GDDI. The set of DDIs comprise 783 GDDIs and 176,450 non-GDDIs. A PPI prediction for a protein-pair  predicts that protein x interacts with protein y. This prediction is a true positive if 1 can be found in the given set of PPIs and a false positive otherwise.The set of all interacting protein-pairs (PPIs) and the set of all non-interacting protein-pairs (non-PPIs) were generated for each of the 177,233 putative domain-domain interactions (DDIs). A domain-pair (R\u2019s t.test (non-homogeneous variance) and Wilcox.test were used to compare the sizes of the PPI sets generated by GDDIs and by non-GDDIs, and the sizes of the non-PPIs sets produced by GDDIs and by non-GDDIs. The statistical tests confirm that GDDIs generate significantly larger sets of PPIs than non-GDDIs and that GDDIs generate significantly larger sets of non-PPIs than non-GDDIs. Thus, GDDIs generate significantly more true positive and more false positive PPIs than non-GDDIs. More true positive PPIs agrees with the parsimony or the re-use principle for GDDIs, and more false positive PPIs accords with the promiscuity of gold domains.rare domain threshold x, domains which occur \u2264 x times in the protein set are classified as rare. While a rare domain may occur in only a handful of proteins, collectively the set of rare domains occur in many proteins. When the rare domain threshold is 2, 54.8% of the proteins in the Riley dataset have at least one rare domain.Promiscuous domains are those which occur frequently in proteins. Rare domains are those which occur infrequently in proteins. The ratio of promiscuous to rare domains varies with the rare domain threshold . At rareonly-rare proteins, i.e. proteins comprising only rare domains, increases, while the proportion of only-promiscuous proteins, i.e. proteins comprising only promiscuous domains, decreases. Both only-rare and only-promiscuous proteins may be single- or multi-domain proteins. Mixed architecture proteins comprise both rare and promiscuous domains and are thus necessarily multi-domain proteins. The proportion of mixed architecture proteins is influenced by the proportions of rare and promiscuous domains. When the rare domain threshold is between 2 and 16, mixed architecture proteins make up the largest proportion (at least a third) of the protein population in the Riley dataset. The peak occurs at rare domain threshold 4 where 37.8% of the proteins have mixed architecture.The concept-based scoring method proposed in this paper does not require or depend on the specification of a rare domain threshold. However, since mixed architecture proteins are the workhorse proteins of the proposed method (Results section), it is reassuring to know that mixed architecture proteins are not rare phenomena in the Riley dataset and that there exists a range of rare domain threshold values where at least a third of the proteins have mixed domain architecture. However for the concept-based scoring method to be feasible at least in principle, the mixed architecture proteins also need to cover gold domains.Up to and including rare domain threshold 11, proteins with mixed architecture provide the largest coverage of all domains  top. HowG by their common attributes and dually a (finite) set of attributes M by their common objects into a (finite) set of partially ordered pairs of sets called  concepts. Implicit is a binary relation I \u2286 G x M which associates objects with attributes.  \u2208 I or equivalently g I m denotes object g has attribute m. The triplet  forms the  context within which a FCA is carried out. For small finite examples, a context can be specified completely with a cross-table. The resulting set of concepts, denoted B, forms a concept lattice.Formal Concept Analysis (FCA) G\u200a=\u200aP, the set of attributes is the set of domains, i.e. M\u200a=\u200aD, and g I m denotes protein g has domain m, i.e. m \u2208 D(g) and dually g \u2208 P(m). S. pombe in the Riley dataset. The (fully-labeled) concept lattice depicting this context is given in For the application in this paper, the set of objects is the set of proteins, i.e. This section describes FCA for those unfamiliar with the theory and in enough detail to support the discussion in this paper. The more mathematically inclined are referred to c \u2208 B is an ordered pair of sets  such that O \u2286 G, A \u2286 M and the set of all attributes common to all objects in O under relation I is A and the set of all objects with attributes in A under relation I is O. More formally, the last two conditions are A\u200a=\u200aO\u2032\u200a=\u200a{m \u2208 M | (\u00b5g \u2208 O) g I m} and O\u200a=\u200aA\u2032\u200a=\u200a{g \u2208 G | (\u00b5m \u2208 A) g I m} respectively. If this seems a bit chicken-and-egg, these last two conditions can be satisfied by working from the power-set of objects or alternatively from the power-set of attributes; but there exist more efficient FCA algorithms such as Lindig\u2019s C implementation called Colibri-conceptsA concept O is called the extent of concept c, and the set of attributes A is known as the intent of concept c. A concept\u2019s extent is denoted O(c) and its intent as A(c). The prime symbol \u2032 denotes the mapping from an extent to its intent and vice versa, i.e. let a concept c\u200a=\u200a, then O\u2032\u200a=\u200aA, A\u2032\u200a=\u200aO, O\u200a=\u200aO\u2033, A\u200a=\u200aO\u2033\u2032, and so on. This pair of maps between the set of extents and the set of intents forms a Galois connection between the two partially ordered sets. The statements O\u200a=\u200aO\u2033 and A\u200a=\u200aO\u2033\u2032 are true due to the maximal condition for extents and intents. This implies that if a set of objects (attributes) forms the extent (intent) of a concept, then the set of objects (attributes) uniquely identifies the concept, and conversely a concept unambiguously identifies its extent and its intent.The set of objects B; \u2264\u232a. For two distinct concepts in B ,  \u2264  implies O1 \u2282 O2 and dually A1 \u2283 A2. The join (least upper bound) and meet (greatest lower bound) are defined for every pair of non-comparable concepts in \u2329B; \u2264\u232a. \u2329B; \u2264\u232a forms a concept lattice. Intuitively, a concept lattice is a two-in-one lattice with a right-side up lattice for the set of extents and an upside down lattice for the set of intents. More formally, a concept lattice is a complete lattice with a top element  and a bottom element . A complete lattice defined on a subset of a power-set is closed under arbitrary joins (in the form of unions) and meets (in the form of intersections) c1 \u2228 c2\u200a=\u200a ((O(c1) \u222a O(c2))\u2033, A(c1) \u2229 A(c2) ), and the meet (infimum) of two arbitrary concepts c1 \u2227 c2\u200a=\u200a ((O(c1) \u2229 O(c2), (A(c1) \u222a A(c2))\u2033 ). c1 \u2228 c2 is a concept since A(c1) \u2229 A(c2)\u200a=\u200a (O(c1) \u222a O(c2))\u2032 and  is always a concept. Similarly, c1 \u2227 c2 is a concept since O(c1) \u2229 O(c2)\u200a=\u200a(A(c1) \u222a A(c2))\u2032 and  is always a concept. The intersection of any number of extents (intents) always results in an extent (intent). The same is not generally true for unions of extents (intents) c1) \u222a O(c2)) \u2286 (O(c1) \u222a O(c2))\u2033 and (A(c1) \u222a A(c2)) \u2286 (A(c1) \u222a A(c2))\u2033 hold.The set of concepts is ordered by set inclusion \u2329c represented as \u2193{c}\u200a=\u200a{x \u2208 \u2329B; \u2264\u232a | x \u2264 c}. The up-set of c represented as \u2191{c}\u200a=\u200a{x \u2208 \u2329B; \u2264\u232a | c \u2264 x}. The extent of a concept c is the union of the extent of each concept \u2208 \u2193{c}. The intent of a concept c is the union of the intent of each concept \u2208 \u2191{c}. This relationship between concepts makes it possible to reduce the labeling of concepts to objects and attributes specific to a concept (reduced concept lattice.The down-set of  concept . ChanginOA); (ii) with reduced object labels and reduced attribute labels (oa); (iii) with complete object labels and reduced attribute labels (Oa); and (iv) with reduced object labels and complete attribute labels (oA). The oa and oA combinations produce object-reduced concept lattices. The oa and Oa combinations produce attribute-reduced concept lattices. In an object-reduced concept lattice, object labels appear exactly once and the set of object labels (proteins) is finite. Similarly in an attribute-reduced concept lattice, attribute labels appear exactly once and the set of attribute labels (domains) is finite. Each combination is explored in this paper for the proteins and their domains in the Riley dataset. It is possible for two different combinations to produce two different outcomes because the labels of objects and attributes are used instead of the objects and attributes themselves. OL(c) refers to the set of object-labels for O(c), and similarly AL(c) refers to the set of attribute-labels for A(c).There are then four possible ways to label a concept lattice: (i) with complete object labels and complete attribute labels  >1 are Pkinase (5), SAM_2 (2) and Cyclin_N(2)  means a larger extent, and as one goes up in a concept lattice extents increase in size, culminating in the top element whose extent is the entire object set. For lin_N(2)  and theylin_N(2) . In contS. pombe have promiscuous domains (N(d) >1), and these single-domain proteins  reside in concepts one step away from the top element in The position of a protein in an object-reduced concept lattice depends on the promiscuity of its domain(s). Three of the four single-domain proteins for L(c)\u200a=\u200a\u2205 is more likely towards the top of an object-reduced concept lattice. Concepts with multi-domain protein(s) in their extents will tend to have empty attribute-label sets in an attribute-reduced concept lattice unless the multi-domain protein(s) introduces \u201cnew\u201d domains. E.g. concept 7 in L(c)\u200a=\u200a\u2205 is more likely towards the bottom of an attribute-reduced concept lattice. The presence of empty object-label sets and empty attribute-label sets influences the number of concept-pairs available to evaluate domain-pairs, and the diversity of CB and PG values produced by the concept-based scoring method.In a reduced concept lattice, there will be concepts with an empty object-label set or an empty attribute-label set. At the very least the object-label sets and attribute-label sets of the top and bottom elements will be, by definition, empty. The more numerous rare domains will \u201cconsume\u201d proteins and leave fewer proteins available to fill the object-label sets of concepts with promiscuous domains. Thus an empty object-label set OOne of the earliest methods for detecting over-represented \u2018correlated sequence-signatures\u2019 e.g. domain-pairs, in a database of protein-protein interactions used the log-odds of the ratio between observed and expected frequencies to score pairs of sequence-signatures a, b) with the Association method is AM\u200a=\u200a log2 [M/(N(a) \u00d7 N(b))]. M\u200a=\u200a| {1 | a \u2208 D(x) and b \u2208 D(y)} | is the number of interacting protein-pairs in the database such that a is a domain of protein x and b is a domain of protein y. N(d) is the number of proteins in the database that has domain d in its domain architecture. The scores are negative in value with a maximum of log2(1)\u200a=\u200a0 which is the score for domain-pairs that occur only between interacting protein-pairs, and an undefined minimum of log2(0) which is the score for domain-pairs that occur only between non-interacting protein-pairs. Domain-pairs with larger scores are ranked more highly.Specifically, the score of a domain-pair \u200a=\u200alog2 [M/+Z)]. M is defined previously. Z\u200a=\u200a| {0 | a \u2208 D(x) and b \u2208 D(y)} | is the number of non-interacting protein-pairs in the database such that a is a domain of protein x and b is a domain of protein y.The Riley dataset comprises proteins from multiple organisms, and both interacting and non-interacting proteins are restricted to those from the same organism. To handle this situation, AM described before, but the scoring is done using pairs of concepts. The concepts used exclude the top and the bottom concepts, and any other concepts with an empty object-label set or an empty attribute-label set. Protein-pairs generated by the object-label sets of a concept-pair, i.e. OL(c1) \u00d7 OL(c2), are used to compute the log-odds ratio which is then used to evaluate the domain-pairs generated by the attribute-label sets of said concept-pair, i.e. AL(c1) \u00d7 AL(c2). Essentially, each concept-pair  provides a different context (in the form of protein-pairs) to evaluate a domain-pair. The set of concept pairs {} used to evaluate a domain-pair  is determined by the attribute-label sets, and comprises all distinct concept-pairs where a \u2208 AL(ci) and b \u2208 AL(cj). Concept-based scoring and ranking is demonstrated in Figures S6, S7, S8 and S9, and Table S2 in The is paper  also useoA and OA), a domain-pair can have more than one score. CB is the largest score found for domain-pair , while PG is the number of unique scores for  which are strictly smaller than CB. Domain-pairs with larger CB scores are ranked more highly. The PG scores help to break ties between domain-pairs with identical CB scores. Given identical CB scores, domain-pairs with larger PG scores are ranked more highly.With concept lattices that are not attribute-reduced (oa concept lattice when many concepts are excluded because of empty object-label or empty attribute label sets), or if its evaluation results in an undefined score, i.e. log2(0). Scoreless domain-pairs are given a negative PG value, and are placed in random order below domain-pairs with CB scores. The Oa scores are identical to those obtained with the Associative method since every domain appears exactly once in an Oa concept lattice and all proteins containing a domain appears in the object-label set of a concept whose attribute-label set has the domain.A domain-pair may be left scoreless if it was not evaluated at all , domains that are more promiscuous have more opportunity to appear in different attribute-label sets. The question then becomes is it better for a promiscuous domain to appear with other promiscuous domains or with rare domains. The results suggest that a promiscuous domain-pair is more likely to improve its score if either one or both of its partner domains appear with rare domains. This is because rare domains tend to produce fewer non-interacting protein-pairs. The Thus, several conditions favourable to the concept-based scoring method arise:The domain-pairs that need to be ranked highly are promiscuous. The GDDIs are promiscuous.not attribute-reduced, i.e. OA and oA. Strictly speaking then, neither oa nor Oa can produce concept-based scores since their PG values are always \u2264 0. The Oa scores are identical to those of the Association method.It must be possible to evaluate a domain-pair with different protein-pairs. This is possible only with concept lattices that are To improve the score of promiscuous domain-pairs through piggy-backing, it must be possible for promiscuous domains to reside with rare domains in one or more attribute-label sets. This is made possible by multi-domain proteins, in particular those which have a mix of promiscuous and rare domains in their architecture, i.e. mixed architecture proteins. Within a sensible range of rare domain thresholds, a substantial proportion of proteins in the Riley dataset are proteins with mixed architecture  and thesThe concept-based scoring method is applied to the Riley dataset using all four types of concept lattices. The algorithm in A, 0.60% in B, 0.21% in C and 0.11% in D. Median promiscuity of GDDIs to DDIs is 7.0\u22365.0 in A, 8.5\u22365.5 in B, 9.5\u22365.5 in C and 15.0\u22364.0 in D. With a smaller GDDI to DDI percentage and a much larger GDDI to DDI promiscuity ratio, scenario D is the most difficult of all. The resultant number of PPIs, DDIs, GDDIs and GPPIs for each scenario is summarized in Table S3 in The concept-based scoring method is evaluated under the following four circumstances, all of which are related to input data characteristics. In all scenarios, R\u2019s Wilcox.test confirms that the set of GDDIs is still significantly more promiscuous than the set of non-GDDIs. More promiscuous GDDIs are more likely to survive the changes. GDDIs make up 0.44% of DDIs in Under the default or original circumstance, the complete Riley dataset is used without modification. Since all PPIs in the given input data are used, the probability of including a PPI, Pe is 1.0.PPI data obtained via high-throughput methods are error-prone. To account for the inaccuracies in PPI data, the robustness of computational methods when dealing with PPIs is commonly tested by using Pe <1.0. Ref. The log-odds ratio depends on the set of protein-pairs used and also on the PPI network. To test the robustness of the results against changes in PPIs, the nodes of each organism\u2019s PPI network were shuffled amongst themselves. Node shuffling generates a new set of PPIs, but the number of PPIs per organism and the original PPI network structure  remains unchanged. The new set of DDIs overlaps but is no longer a subset of the original DDIs.Finally, to test the influence of domain architecture on the results, the domains of proteins are shuffled. For this scenario domain repetition within a protein is allowed and a protein becomes a multi-set of domains. The shuffle changes the frequency of domains in a small but still statistically significant way. The new set of DDIs overlaps but is no longer a subset of the original DDIs. Domain shuffling was accomplished with the following steps:Place every instance of a domain in the input data into a sequence, sorted by frequency of occurrence. Domain instances with identical frequency are shuffled amongst themselves.Sort the proteins by their size, i.e. number of domains they contain.Starting from the largest to the smallest protein, assign domains to proteins starting from the least to the most frequently occurring domains. The reason for this is to reduce domain repetition within a protein.The impact of shuffling on domain architecture is shown in a, b)\u200a=\u200a[N(a)+N(b)]/2 where N(d) is the number of times domain d occurs in a protein set. The GDDI rankings were extracted from the rankings of all DDIs (ranking domain-pairs is described in step 6 of OA and oA ones exhibit a negative correlation between GDDI promiscuity and rank. A negative correlation implies that higher ranking GDDIs tend to be more promiscuous. The relationship is strongly positive (Spearman\u2019s rank correlation rho\u200a=\u200a0.88) when the Oa rankings are used. Oa results are identical to the Associative method which is known to penalize promiscuous domain-pairs.Of the four plots in oa to rank promiscuous GDDIs less highly (Spearman\u2019s rank correlation rho\u200a=\u200a0.49), but this positive relationship is not as strong as Oa\u2019s because scoreless GDDIs are included in the plot . When the oa concept lattice is used, only 350 of the 783 GDDIs have CB scores. The remaining 55.3% of GDDIs which are scoreless are ranked in random order below the GDDIs with CB scores. But R\u2019s Wilcox.test confirms that the domain-pairs (including non-GDDIs) with CB scores are significantly less promiscuous than the scoreless domain-pairs. Hence, the oa concept lattice tends to ranks more promiscuous domain-pairs less highly.There is also a tendency for oa) concept lattice is the reason many domain-pairs are scoreless. Concepts with an empty object-label set or an empty attribute-label set are ignored when computing scores for domain-pairs (oa concept lattice. The many scoreless domain-pairs means the oa results are unsuitable or too weak for identifying strong interactions in protein complexes. oa performs poorly in the Nye test (Results section). Although oA has empty object-label sets and Oa has empty attribute-label sets, they do not produce any scoreless domain-pairs for the Riley dataset. The number of concepts used by each type of concept lattice for the Riley dataset is given in Table S4 in The increased presence of empty object-label sets and empty attribute-label sets in a reduced , both OA and oA GDDI rankings become positively related with promiscuity, i.e. less promiscuous GDDIs are ranked more highly  and domain frequency (the number of times a domain appears in a protein in a set of input proteins) (oA and OA produce similar results to Oa in Domain shuffling in scenario proteins  and chanroteins) . InsteadD, only 1.69% of the domain-pairs evaluated with oA have PG >0  to evaluate promiscuous domain-pairs, and a decrease in piggy-backing opportunities. ve PG >0  bottom. e highly .GDDI recovery is concerned with finding as many GDDIs as possible while making as few mistakes as possible. The GDDIs are sourced from the iPfam database reliable DDIs, it is preferable to keep the FPR low. Even at FPR\u200a=\u200a0.2, there are already 35,290 false positives to eliminate either experimentally or through literature search in scenario A. Further, errors in predicting DDIs can be propagated to other areas that rely on DDI data, such as prediction of protein-protein interactions and identification of protein binding surfaces. Hence, the argument for low FPR or high Specificity. A cost-efficient high-throughput method to eliminate non-interacting domain-pairs with high confidence would render computational efforts to predict reliable DDIs obsolete.For the problem of identifying D, when FPR \u2264 0.2, rankings produced by the non-attribute-reduced concept lattices (OA and oA) have larger TPR or higher Sensitivity than the attribute-reduced concept lattices (Oa and oa). This outcome supports the hypothesis that using concept lattices that are not attribute-reduced is necessary to create a favourable condition for the concept-based scoring method to identify GDDIs. This outcome is robust to changes in the PPI data as evidenced by the results from scenarios B and C. The oa rankings become slightly more competitive when FPR \u22650.25, but the rankings quickly become random as oa is unable to score many domain-pairs due to empty object-label and empty attribute-label sets in the oa concept lattice. For instance, 72.14% of the possible domain-pairs and 55.3% of GDDIs are left scoreless by oa in scenario A. The Oa rankings or Associative method gave the worst GDDI recovery performance.The TPR vs. FPR or ROC graphs are shown in D, up to an FPR as large as 0.5, oA\u2019s GDDI recovery dominates that of OA. A closer look at the top 100 domain-pairs . However, high ranking non-GDDIs do at times interfere with OA\u2019s Nye test results (Results section).Except for the concocted scenario in-pairs  reveals oA domain-pair rankings dominates that of OA is given in oA\u2019s TPR dominates the other three rankings. Of the four rankings , oA contains the most number of GDDIs, DOMINE domain-pairs and 3did domain-pairs in the top 100 domain-pairs  which is not a GDDI and whose interaction is neither recorded in DOMINE nor predicted by 3did. However, a possible 3D structure for the obesity-related protein adipose (adp) involves interaction between TPR and WD40 domains Further evidence that the in-pairs . AmongstoA producing better GDDI recovery results than OA. However, oA is more vulnerable to changes in protein domain architecture than OA. When the domains are shuffled to reduce the number of mixed architecture proteins (scenario D), oA\u2019s TPR which previously has been above 0.2 when FPR \u2264 0.2 drops to less than 0.2. This decline in oA\u2019s GDDI recovery performance supports the notion that mixed architecture proteins play an important role in the success of concept-based scoring.The discussion so far all point to OA\u2019s prioritization of promiscuous domain-pairs, but the effect on GDDI recovery is dampened by OA\u2019s ability to provide many more contexts to evaluate domain-pairs. In scenario D, the oA rankings are produced with only 53.71% of the concepts. In contrast, oA uses 82.38% of the concepts in the other three scenarios . While domain shuffling reduces the range of PG values for OA, the proportion of domain-pairs still able to piggy-back in OA remains above 62%. In contrast, only 1.69% of the domain-pairs evaluated with oA have PG >0  are left scoreless by the highest ranking DDI for a GPPI is a GDDI. It was first performed by Nye et al. This test is concerned with whether OA and oA) produce much higher pass rates than the attribute-reduced concept lattices (Oa and oa). OA\u2019s higher pass rate is attributed to its greater piggy-backing potential  become less able to pass the Nye test. None of the GPPIs that generate more than 50 DDIs pass the Nye test when oa\u2019s ranking is used. For the Oa concept lattice (the Associative method), the cut-off point is even earlier, at 16 DDIs. In contrast, several GPPIs with more than 50 DDIs could still pass the Nye test when ranking is based on concept-based scores computed with the non-attributed-reduced concept lattices (OA and oA).The Nye test results for scenario A is broken down by difficulty in OA ranking than with the oA ranking . This GPPI is supported by only one GDDI, , which has a promiscuity of 100. oA ranks  as the highest domain-pair for GPPI  and so the Nye test is passed. OA ranks  as the second highest, below  which has a promiscuity of 189.5 but is not a GDDI, and so the Nye test is failed. The Nye test is also passed by oa since  is the only domain-pair with a score for GPPI . However, oa\u2019s Nye test performance on a GPPI with this high level of difficulty is more the exception than the norm.With a few exceptions, regardless of difficulty, more GPPIs pass the Nye test with the  ranking . This isy-backed . HoweverOA. These promiscuous Pfam-B domains also suppress GDDI recovery for OA. All domain-pairs in OA\u2019s top 100 that do not involve a Pfam-B domain is either a GDDI, or identified in DOMINE or 3did (Oa). Therefore, there is a need to evaluate the effectiveness of the concept-based scoring method in the absence of Pfam-B domains and on a more current dataset for single organisms. The organisms tested here are yeast (NCBI taxid 559292) and human (NCBI taxid 9606), and the data come from Biogrid (version 3.2.107) A conditions.The previous case with GPPI  illustrates how the presence of promiscuous Pfam-B domains can cloud the Nye test results for  or 3did . HoweverOa is no longer below the y\u200a=\u200ax line as it was in OA and oA) still dominate that of the attribute-reduced concept lattices (Oa and oa) although now it is no longer as clear as it was in oA\u2019s TPR dominates OA\u2019s TPR , but between attribute-reduced where piggy-backs are impossible and non-attribute-reduced where piggy-backs are possible. The results in OA and oA can still outperform both Oa and oa. The Nye test for yeast and for human is also more successfully passed by both OA and oA than either Oa or oa Click here for additional data file.File S2(XLS)Click here for additional data file."}
+{"text": "The mean field model formulated by Liley et al.  describeIn this study, we fix the model parameters to values that have previously been shown to lead to physiologically interesting \u03b3-range activity . We locaAlthough for small system size, spatially homogeneous periodic solutions appear, for system sizes of a few square centimeters we observe centimeter-scale, oscillating patterns, which appear in subcritical Hopf bifurcations and have a strong \u03b3-band component in their power spectrum. An example is shown in Fig. We have implemented a time-stepper in the open-source PETSc environment . It uses"}
+{"text": "The secondary structure of RNA molecules is intimately related to their function and often more conserved than the sequence. Hence, the important task of searching databases for RNAs requires to match sequence-structure patterns. Unfortunately, current tools for this task have, in the best case, a running time that is only linear in the size of sequence databases. Furthermore, established index data structures for fast sequence matching, like suffix trees or arrays, cannot benefit from the complementarity constraints introduced by the secondary structure of RNAs.We present a novel method and readily applicable software for time efficient matching of RNA sequence-structure patterns in sequence databases. Our approach is based on affix arrays, a recently introduced index data structure, preprocessed from the target database. Affix arrays support bidirectional pattern search, which is required for efficiently handling the structural constraints of the pattern. Structural patterns like stem-loops can be matched inside out, such that the loop region is matched first and then the pairing bases on the boundaries are matched consecutively. This allows to exploit base pairing information for search space reduction and leads to an expected running time that is sublinear in the size of the sequence database. The incorporation of a new chaining approach in the search of RNA sequence-structure patterns enables the description of molecules folding into complex secondary structures with multiple ordered patterns. The chaining approach removes spurious matches from the set of intermediate results, in particular of patterns with little specificity. In benchmark experiments on the Rfam database, our method runs up to two orders of magnitude faster than previous methods.Structator a complete and robust open-source software solution for index-based search of RNA sequence-structure patterns. The Structator software is available at http://www.zbh.uni-hamburg.de/Structator.The presented method's sublinear expected running time makes it well suited for RNA sequence-structure pattern matching in large sequence databases. RNA molecules containing several stem-loop substructures can be described by multiple sequence-structure patterns and their matches are efficiently handled by a novel chaining method. Beyond our algorithmic contributions, we provide with  The discovery of new roles of non-coding RNAs (ncRNAs) has made them of central research interest in molecular biology ,2. Like RNAforrester , 0 \u2264 i < n denotes the character of S at position i. Let \u03b5 denote the empty sequence, the only sequence of length 0. By n \u2265 0 over \u03b5 is denoted by A S = S[0]S[1] ... S[n - 1] and 0 \u2264 i \u2264 j < n, S[i..j] denotes the substring S[i]S[i + 1] ... S[j] of S. We denote the reverse sequence of S with S-1 = S[n - 1]S[n - 2] ... S[0]. For S = uv, u and u is a prefix of S, and v is a suffix of S. The k-th suffix of S starts at position k, while the k-th prefix of S ends at k. Note that the 0-th suffix of S is S itself and that S[0] is the 0-th prefix of S. The k-th reverse prefix of S is the k-th suffix of S-1. For 0 \u2264 k <n, k Sdenotes the k-th suffix of S, and k-th reverse prefix of S.For a sequence RNA alphabet {A, C, G, U}. Its characters code for the nucleotides adenine (A), cytosine (C), guanine (G), and uracil (U). In the following we fix a sequence S over the RNA alphabet S|< 232, such that sequence positions and lengths can be stored in 4 bytes.Let complementary and can form a base pair if and only if non-crossing RNA structure R of length m is a set of base pairs , 0 \u2264 i < j < m, stating that the base at position i pairs with the base at position j, such that for all ,  \u2208 R: i < i' <j' <j or i' <i < j < j' or i < j < i' <j' or i' <j' <i < j. For the algorithms and methods presented in this paper we only consider this class of structures. For an example of such an RNA secondary structure see Figure stem-loop structure. We call R a stem-loop RNA structure if and only if for all ,  \u2208 R : i < i' <j' <j or i' <i < j < j'. Note that due to our definition a stem-loop can contain bulges and interior loops } with an equal number of characters (and ). There is a bijection between the set of (non-crossing) RNA structures R and the set of structure strings H, both of length m, such that for each base pair  \u2208 R, H[i] = (and H[j] = ), and H[r] = . for positions r, 0 \u2264 r < m, that do not occur in any base pair of R, i.e. r \u2260 i \u2227 r \u2260 j for all  \u2208 R. Due to this equivalence we identify both representations.A sequence pattern is a sequence m denote its length |P|. An occurrence of P in a sequence S is a position i, 0 \u2264 i < n, such that P[k] = S[i + k] with S[i + k] \u2208 \u03c6(P[k]) for all 0 \u2264 k < m. An RNA sequence-structure pattern (RSSP) m is a pair of a sequence pattern P and a structure string R, both of length m. A match or occurrence of m in an RNA sequence S is an occurrence i of P in S, such that for all base pairs  \u2208 R: S[i + l] and S[i + r] are complementary. Furthermore, define Let \u03a6 = {R, Y, M, K, W, S, B, D, H, V, N} be a set of characters. The IUPAC nucleotide base code introduces the characters in \u03a6 to code nucleotide ambiguity and assigns a specific character class In this paper, structures described by RSSPs are non-branching.affix array is described. This index structure supports efficient unidirectional as well as bidirectional searches and is more space efficient than the affix tree  = 0, and lcpX [i] is the length of the longest common prefix between i \u2264 n. Each of the tables lcpF and lcpR requires n bytes and store entries with value up to 255, whereas occasional larger entries are stored in an exception table using 8 bytes per entry [F and lcpR can be accomplished in F and sufR [X . Two important concepts of affix arrays are suffix-intervals and lcp-intervals. An interval [i..j] representing the set of suffixes i \u2264 j \u2264 n, of width j - i + 1, is a suffix-interval in sufX with depth (prefix length) \u2113 \u2208 {0,..., n}, or \u2113-suffix-interval, denoted \u2113 - [i..j], if and only if the following three conditions hold:For notational convenience, we define nd space . In pracnd space ,33 conster entry . More sper entry ). The coand sufR . In contand sufR  where afX [i] <\u2113;1. lcpX [j + 1] <\u2113; and2. lcpX [k] \u2265 \u2113 for all k \u2208 {i + 1,..., j}.3. lcp\u2113 - [i..j] in sufX lcp-interval in sufX with lcp-value \u2113 \u2208 {0,..., n}, or \u2113-interval, if and only if i < j and lcpX [k] = \u2113 for at least one k \u2208 {i + 1,..., j}.We call a suffix-interval \u2113 - [i..j] in sufX , we denote the common prefix of length \u2113 of its suffixes X\u03b4(\u2113 - [i..j]) = XS[sufX [i]..sufX [i] + \u2113 - 1]. In case of an lcp-interval \u2113 - [i..j] in sufX , X \u03b4(\u2113 - [i..j]) is the longest common prefix of all suffixes in this interval.For a suffix-interval \u2113 - [i..j] in sufX describes simultaneously:In summary, a suffix-interval X by interval borders i and j and depth \u2113. For an example, see the yellow marked region in Figure F.\u2022 A location in the index structure sufF in Figure \u2022 A  sequence of suffixes SX of length \u2113, namely X\u03b4(\u2113 - [i..j]). That is, for the suffix-interval 4 - [4..6] in sufF in Figure \u03b4F(4 - [4..6]) = CUGC.\u2022 A substring of XS, namely at positions sufX [i],..., sufX [j]. To give an example, consider Figure F[4] = 10, sufF[5] = 7, and sufF[6] = 4 in SF = AUAGCUGCUGCUGCA.\u2022 The occurrences of this substring in S it is sufficient to process lcp-intervals only in sufF. For bidirectional pattern search using affix arrays, described in detail in the next section, we employ information from table sufF as well as sufR. Therefore, we need to associate information of one table to the other. This is done by linking intervals via tables aflkF and aflkR. We observe that there exists a mapping between lcp-intervals in sufF and sufR. This is stated by the following proven lemma [For unidirectional left-to-right search of some pattern in en lemma .Lemma 1 For every lcp-interval q = \u2113 - [i..j] in table sufX there is exactly one lcp-interval q-1 = \u2113' - [i'..j'] in table  called reverse lcp-interval of q, such that \u2113' \u2265 \u2113 and the \u2113 - 1-th prefix of  equals (\u03b4X(q))-1. The number of suffixes (prefixes) represented by q and q-1 are the same, i.e., j - i = j' - i'.q = (q-1)-1 is not necessarily true. This is stated by the next lemma.We note that the equivalence Lemma 2 If the lcp-interval q-1 with depth \u2113' in  is the reverse of the lcp-interval q with depth \u2113 in sufX and \u2113 = \u2113', then q = (q-1)-1. Otherwise, if \u2113' > \u2113, then q \u2260 (q-1)-1.SF and SR is encoded in tables aflkF and aflkR as follows. Tables aflkF and aflkR store, for each lcp-interval in sufF and sufR respectively, a pointer to the reverse interval in the reverse tables X , defined asThe mapping between intervals in \u2113 - [i..j] is an lcp-interval in sufX . Hence, the home position is one of two boundary positions. Strothmann [X ([i..j]) \u2260 homeX ([i'..j']) for different lcp-intervals \u2113 - [i..j] and \u2113' - [i'..j'].where rothmann  shows thX of string XS$ with total length n + 1 can now be defined as a table in the range 0 to n such that aflkX [homeX (q)] = i', where q is an lcp-interval in sufX and i' is the left border of the reverse interval q-1 = [i'..j'] in X as affix links. Tables aflkF and aflkR occupy 4n bytes each. They can be computed by traversing the lcp-intervals in sufX while simultaneously looking for the corresponding reverse lcp-intervals in et al. , \u2113 >0, -m < k < \u2113, describes a substring X\u03c9(v) of X Sof length \u2113 - k, defined as the k-th suffix of X\u03b4(q), i.e. X\u03c9(v) = XS[sufX [i] + k..sufX [i] + \u2113 - 1]. At the same time v identifies all occurrences of X\u03c9(v) in XS, namely the positions sufX [i] + k,..., sufX [j] + k.An affix-interval v  = \u2329k, q, X\u232a, we therefore also use the notation X = F and X = R. As an example, consider the affix-interval v = \u23291, 4 - [4..6], F\u232a in sufF of the affix array shown in Figure k = 1, q = 4 - [4..6], and X = F. v identifies all occurrences of substring SF at positions sufF[4] + 1 = 11, sufF[5] + 1 = 8, and sufF[6] + 1 = 5. Observe that \u03b4F(q) = CUGC due to context k = 1.For Pattern matching using affix arrays means the sequential processing of characters in the pattern guiding the traversal of the data structure. This can be performed in either a traditional left-to-right order resulting in a unidirectional search or in a bidirectional way where character comparison is started at any position of the pattern extending the already matched substring of the pattern to the left or to the right. We will see that bidirectional search using alternating series of left and right extensions is very well suited for fast database search with RNA sequence-structure patterns (RSSPs) containing both paired and unpaired bases. In the following we will explain the two different traversal strategies underlying unidirectional and bidirectional search using affix arrays.S in a unidirectional left-to-right way using information from table sufF only. To search for P , we call the procedure unidir-search of Figure unidir-search. Therefore, in step 0 we start searching for the characters in \u03c6(P[0]) in the suffix-interval q0 = 0 - [0..n] in sufF, which represents all suffixes of S$. In each step k, k \u2265 0, we locate the k + 1-suffix-intervals k qof maximal width, such that P [0..k - 1]d matches \u03b4F(kq). For each d \u2208 \u03c6(P [k]), this step is performed by a binary search in the suffix-interval qk-1 = \u2113 - [i..j] for k q= (\u2113 + 1) - [i'..j'], i \u2264 i' \u2264 j' \u2264 j, j' - i' maximal, and S[sufF[i'] + k] = d.Let m steps, if all k qcould be located, \u03b4F(mq), m q= m - [r..s], matches the pattern P and the occurrences sufF[r], sufF[r + 1],..., sufF[s] of \u03b4F(mq) are reported as occurrences of P in S. Note that in this approach the matched substring of S is extended only to the right and at each step k the occurrences of the already matched prefix are represented by a suffix-interval.After P character by character to the text, where we can freely switch between extending to the left or to the right. Note that as in the case of unidirectional search, ambiguous nucleotides x in the pattern can be handled by enumerating all characters c in the corresponding character class \u03c6(x). We can focus on the situation in the search, whereFor the bidirectional search, we start at some position in r..r' (0 \u2264 r \u2264 r' <m) of the pattern P is already compared,\u2022 a range S matching P[r..r'] are represented by an affix-interval v = \u2329k, \u2113 - [i..j], X\u232a in sufX , and\u2022 the occurrences of a substring P[r - 1] or P[r' + 1]). This will result in a new, extended affix-interval xv.\u2022 we want to extend X = F and to the right for X = R. However, there are \"corresponding\" affix-intervals representing the same substring of S but allowing extension to the opposite direction.Like its suffix-interval, an affix-interval directly supports extension of the represented substring in only one direction, namely searching to the left for v, this switch of the search direction requires determining the corresponding affix-interval v' in i = j or v has non-empty context k \u2260 0. There are these two exceptions, since first if i = j, independently of the value of k, X\u03c9(v) is already a unique substring of XS. Second, for a non-empty context k \u2260 0, all occurrences of substring X\u03c9(v) in SX are followed (if k > 0) or preceded (if k < 0) by the same substring If the new search direction differs from the supported search direction of k = 0 and i < j. The affix-interval reverse affix-interval of v = \u2329k, \u2113 - [i..j], X\u232a if and only if j' - i' = j - i, \u2113' \u2265 \u2113, and i' and j' of v' are determined via a lookup in table aflkX . We set i' = aflkX [homeX ([i..j])] and j' = i' + (j - i). Observe that \u2113 is not necessarily the length of the longest common prefix of all suffixes in [i..j]. For this reason we define \u2113lcp = min{lcpX [k] | i < k \u2264 j} \u2265 \u2113 and compute the context of v' as k' = \u2113lcp - \u2113. Further, we set \u2113' = \u2113lcp. Hence the reverse affix-interval v' is the required corresponding interval of v.Let u of S matching P[r..r'].In our situation, right (left) extension of v by a character c-extension of v, is an operation that computes the affix-interval x vrepresenting all occurrences of a substring uc (cu). It fails, if there is no such substring. We elaborate the cases for right extension. The cases for left extension are symmetric and therefore omitted. For right c-extension of v = \u2329k, \u2113 - [i..j], X\u232a, we determine the interval x v= \u2329xk, x \u2113- [xi..xj], xX\u232a with The X = F and i = j. u is a unique substring S. If S[sufF[i] + \u2113] = c, then x v= \u2329k, (\u2113 + 1) - [i..j], F\u232a.\u2022 Case X = F and i < j. We determine the minimal x i\u2265 i and maximal x j\u2264 j in sufF such that S[sufF[xi] + \u2113] = c and S[sufF[xj] + \u2113] = c by binary search in the suffix-interval \u2113 - [i..j]. If x iand x jexist, we set x v= \u2329k, (\u2113 + 1) - [xi..xj], F\u232a.\u2022 Case The following cases require switching the search direction.X = R, i = j. We evaluate SR[sufR[i] + k - 1]. If SR[sufR[i] + k - 1] = c, set x v= \u2329k - 1, \u2113 - [i..j], R\u232a.\u2022 Case X = R, i < j, and k = 0. We first determine the reverse affix-interval v' = \u2329k', \u2113' - [i'..j'], F\u232a of v via a switch of the search direction as described above. Then we compute the minimal x i\u2265 i' and maximal x j\u2264 j' via binary search, such that S[sufF[xi] + \u2113'] = c and S[sufF[xj] + \u2113'] = c. If x iand x jexist, we set x v= \u2329k', (\u2113' + 1) - [xi..xj], F\u232a.\u2022 Case X = R, i < j, and k >0. We evaluate the (k - 1)-th character of \u03b4R(\u2113 - [i..j]). That is, if \u03b4R(\u2113 - [i..j])[k - 1] = c, then we consume the context k by setting x v= \u2329k - 1, \u2113 - [i..j], R\u232a.\u2022 Case x vcannot be determined.The operation fails if S with an RNA sequence-structure pattern (RSSP) P in S under the complementarity constraints imposed by the structure string R (cf. our definition of RSSP-occurrence). We introduce a search algorithm that checks for complementarity constraints as early as possible in bidirectional search to maximally reduce the search time due to this restriction.Searching a sequence S, each RSSP describes a set of pattern instances, i.e. the set of potential subsequences matching the pattern. Often, there are several patterns that describe the same set of instances. For example, the pattern  ) ) ) describes the same set of instances as  ) )  since the additional base pair  in ( ( ( . . . . ) ) ) does not make the pattern more specific. We will define a pattern to be structure minimal if there is no, in this sense, equivalent pattern containing a true subset of the base pairs. An RSSP structure minimal if and only if for all base pairs  \u2208 R it holds thatFor further considerations, we will assume a special 'canonical' form for RSSPs, which we define in the following. Independently of a sequence inconsistent if it does not have any instance. Formally, a pattern is consistent if and only if for each base pair  it holds that P = UAUACACGAN and R = ( ( . . . . . . ) ).R but the bases P[1] = A and P[8] = A are not complementary. An example of a structure minimal and consistent RSSP is  ) ). Note that a pattern can be transformed into an equivalent structure minimal pattern and checked for consistency in Furthermore, a general pattern is called P, R), the non-branching structure R suggests a search strategy, i.e. an order of left and right extensions, which requires switching the search direction at every base pair but makes optimal use of the complementarity constraints due to the base pairs.In this case, one can restrict the search space by comparing the two positions of each base pair immediately after each other. Due to this, the enumeration of characters matching the pattern symbols at each base pair can be restricted to the smaller number of complementary ones. In the search for a sequence-structure pattern this can reduce the number of enumerated combinations of matching characters exponentially. Thus, for structure minimal patterns , where \u23290, 0 - [0..n], F\u232a is an affix-interval and r0 is any position in the loop region of the RSSP or any position of a completely unpaired pattern. Then, the procedure traverses the affix-intervals by performing right and left extensions, while at the same time checking base complementarity of paired positions. This verification takes constant time by using a binary table of size To match r0 (or any position if R is empty) for starting our bidirectional search algorithm. However, in order to reduce the combinatorial explosion of the search space due to ambiguous IUPAC characters, it is preferable to match non-ambiguous pattern characters first. To keep the selection simple, we set r0 to the position of the first character c in the possible range such that |\u03c6(c)| is minimal. That is, we start the search with the most specific (least ambiguous) character.In principle, we are free to choose any loop position bidir-search can be extended to support variable-length RSSPs. Such an extended version of bidir-search is provided in Additional file A detailed example of bidirectional RSSP search along with the underlying affix array traversal is provided in Additional file S of length n for an RSSP m < n, where the index structures for S are already computed.We analyze the complexity for searching in a sequence F and sufR, lcpF and lcpR, and aflkF and aflkR. Under our assumption that n <232, each of the four tables sufX and aflkX consumes 4n bytes, and the two tables lcpX are each stored in n bytes . This amounts to a space consumption of 18n bytes for the index structures. The algorithm performs a depth first search, where the depth is limited by m, and therefore requires The bidirectional search algorithm requires tables sufWe assume that F using binary search for locating intervals in z is the number of occurrences of P in S. We remark that this time bound can be lowered at the price of higher memory consumption to Algorithm 1 accomplishes the search for a non-ambiguous pattern ption to  or even tion to , X\u232a. Consider the following two cases.First, we analyze the time required for performing a single switch of the search direction. Therefore we assume that the current affix-interval is i = j or k \u2260 0. If i = j, S, or, if k \u2260 0, all occurrences of  substring S are followed (if k >0) or preceded (if k <0) by the same substring of length |k| (known as context). Switching the search direction does not require locating the reverse interval of v, because the algorithm can perform the c-extension in the new search direction by consuming context. Therefore, this case requires constant time.(1) Case i < j and k = 0. The algorithm needs to locate the reverse affix-interval v. Interval boundaries i' = aflkX [homeX ([i..j])] and j' = i' + (j - i) of v' are computed in constant time.(2) Case v requires knowing \u2113lcp. Then, \u2113' = \u2113lcp and k' = \u2113' - \u2113. Without child-tables, we determine \u2113lcp by computing the length of the longest common prefix between \u2113lcp - \u2113 + 1 = k' + 1 character comparisons only, since both suffixes \u2113. With the help of child-tables, \u2113lcp is determined in constant time , X\u232a, with k = 0, i < j, and X = F (X = R), be the current affix-interval. We assume without loss of generality that we perform a left (right) c-extension of v and thus locate the reverse interval t k\u2265 0, t \u2113= \u2113 + tk, and t j- t i= j - i (see Lemma 1). Observe that t k= 0 implies kt > 0 implies that substring tk, namely To show t vis only located if k = 0, otherwise the context k has to be consumed. Hence there is no reverse interval s \u2264 C, s \u2260 t, and ks > 0, such that the (s k- 1)-th prefix of t kcan be determined by performing exactly t k+ 1 character comparisons, this implies w in S that matches Note that Therefore, when searching for S, the sequence S must have a certain minimal length. In the case of p = 0, the possible matches are the words in de Bruijn sequence of order m . The order \u226a of the RSSPs in i land i rwe denote the start and end positions of i Ain the multiple alignment, respectively. In practice, An SSD ike Rfam ,4. A matS of length n. A match is represented by a pair p in S. With each collinear, written as chain Consider an RNA SSD i, 1 \u2264 i \u2264 k - 1.all from global chain score for chain There are two modes to score chains, depending on the nature of the search problem. If the multiple sequence-structure alignment our SSD is derived from and the searched sequences have comparable length, we want the chain to cover as much as possible of the sequence and we define the g and thus the local chain score is defined byThen, the global chaining problem is to find a chain whereO(q log q) time where q is the size of To solve the local chaining problem we use our own implementation of a fast local chaining algorithm described in  with modTo solve the global chaining problem we have developed a new efficient chaining algorithm described next.S1,..., k Sas it occurs when searching a large sequence database. I.e. in case of databases like Rfam k can be in the range of millions. To handle these, we concatenate the single sequences with separator symbols and construct the affix array for the concatenation. For a given SSD i \u2264 L, are matched one after the other using fast bidirectional search on the affix array. This results in match sets L is typically in the range of tens while the number of RSSP matches for a particular sequence j Sis in the order of hundreds to thousands if j Sis an mRNA or complete genome sequence. For each match f the following information is recorded:So far our description was based on a single sequence. However, the results described below are based on a large set of sequences i of the RSSP f. This is denoted by f.rssp.\u2022 The ordinal number f. This is denoted by f.length.\u2022 The length of the RSSP involved in j of the sequence Sj f occurs in. This is denoted by f.seqnum.\u2022 The number f in jS. This is denoted by f.pos.\u2022 The starting position of f. The weight of f is denoted by f.weight.\u2022 The weight i \u2264 L, is sorted in ascending order of f.seqnum. Matches with identical sequence numbers are sorted in ascending order of the ordinal number of the RSSP, i.e., by f.rssp. Suppose that b* is the size of b* sequences with at least one RSSP match, the sorting according to the sequence numbers can be done in k* is the number of sequences with at least one RSSP match. As k* \u2264 b*, the sorting requires j \u2264 k, where jS. As f.rssp = i. In a second sorting step, each j, i bis the size of In an initial sorting step the union lgorithm . Here, kS1, S2,..., k Sone now solves independent chaining problems for sets j \u2264 k, of matches sorted according to the ordinal number of the RSSP and the starting position of the matches in jS. Let j be fixed, but arbitrary. For each match f.weight is positive. Hence, an optimal chain ends with a match f such that there is no match f' satisfying f \u226a f'. Similarly, an optimal chain begins with a match f' such that there is no match f satisfying f \u226a f'.For all f'.score of all chains ending with f'. In addition, it computes the predecessor f'.prec of f' in a chain with maximum score ending with f'. To obtain f'.score, one has to maximize over all matches f such that f.rssp < f'.rssp and f.pos + f.length - 1 <f'.pos. This is a two dimensional search problem. As the matches in b is the number of matches in L, and a match for RSSP i. Moreover, matches at position i in the first sequence can be treated as being of equal length because they are matches to the same RSSP i, 1 \u2264 i \u2264 L, the matches in jS. All these properties allow us to simplify and improve the algorithm of [The chaining problem is solved by a dynamic programming algorithm which tabulates for all matches erved in , and ledrithm of  was deverithm of  in the f\u2022 While the algorithm of  requiresj, i bsatisfy \u2022 While the algorithm of  requiresL is considered to be a constant, the running time becomes linear in b, where \u2022 While the algorithm of  solves ti, 1 \u2264 i \u2264 L be arbitrary but fixed and assume that all match sets b containing references to the matches. The separation into two loops allows us to get rid of this extra array.To explain our algorithm, let rithm of  where thjS. Let f' be the current element. At this point, all matches f such that f.rssp < f'.rssp have been processed already. In particular, the score f.score and the previous match (if any) in an optimal chain ending with f has been determined. Among the processed matches we only have to consider those matches f satisfying f.pos + f.length - 1 <f'.pos. If there is such a match, one takes the one with maximal score, say f. Then, the optimal chain ending with f' contains the previous match f, and the score is f'.score = f'.weight + f.score. If there is no such match, then the optimal chain ending with f' only consists of f' and f'.score = f'.weight.Now consider the first loop over all elements in f' be the current element to be inserted. As explained in the previous case, one has to make sure that, among the processed matches, one can efficiently determine the match f with the maximum score such that f.pos + f.length - 1 is smaller than some value depending on f'. The processed matches are stored in a linear list which is sorted in ascending order of the position of the matches in jS. Let \u227apos denote this order, that is f \u227apos f\" if and only if f.pos + f.length < f\".pos + f\".length for any matches f and f\". If for two processed matches f and f\" one has f.pos < f\".pos and f.score > f\".score, then an optimal chain does not include f\". Each chain that uses f\" can also use f and increase the chain score. As a consequence, one has to take care that f\" is not inserted into the linear list or it is deleted if it was inserted earlier. In this way, f \u227apos f\" always implies f.score \u2264 f\".score for two matches f and f\" in the linear list. As the elements to be scored in the first loop and to be inserted in the second loop are ordered in the same way as the elements in the linear list, one can perform the scoring and the insertion loop  by merging two lists of length l1 and l2 in l1 is the number of matches to be scored and inserted and l2 is the length of the linear list involved. Let l1 + l2 \u2264 b, one obtains a running time of L such sets, the running time is Now consider the second loop over all elements in BIDsearch), (3) an online variant operating on the plain sequence  for validation of BIDsearch and reference benchmarking, and (4) the efficient global and local chaining algorithms. Algorithm ONLsearch shifts a window of length m = |RSSP| along the sequence of length n to be searched and compares the substring inside the window with the RSSP from left to right until a mismatch occurs. Hence, it runs in BIDsearch and ONLsearch were implemented in the program afsearch. The afconstruct program makes use of routines from the libdivsufsort2 library (see http://code.google.com/p/libdivsufsort/) for computing the sufF and sufR tables in F and lcpR tables we employ our own implementation of the linear time algorithm of [F and aflkR are constructed in F and skpR [We implemented (1) the algorithms necessary for affix array construction, (2) the fast bidirectional search of RSSPs using affix arrays as sketched in Algorithm 2  ) ) ) ) ) ). Allowed base pairs were , , , and . We measured the time needed by BIDsearch and ONLsearch to search for these patterns in the RFAM10 dataset. Results are given in Figure BIDsearch performed very well and was faster than ONLsearch for all parameter combinations. We also investigated the influence of different stem length (data not shown here) and found that the impact on the total running time is negligible. We observe that the advantage of BIDsearch over ONLsearch decreases with increasing loop length l for fixed q. We explain this behavior with the increasing number of affix-intervals that have to be processed for finding all different substrings of the sequences that match the RSSP. However, even for an RSSP with loop length l = 20 containing only structural constraints (q = 0), BIDsearch is still faster than ONLsearch. We further notice that the number of non-ambiguous characters in the loop region has a strong influence on the running time of BIDsearch. That is, by specifying only a few conserved nucleotides in the RSSP's loop region, the running time of BIDsearch is reduced dramatically. For an example of this effect, see the running times of BIDsearch in Figure l = 15 and q \u2208 {2, 3, 4}. This renders BIDsearch in particular useful for searching with RSSPs with moderate loop length or existing sequence conservation in the loop region. The speedup factors measured in this experiment were in the range from 1.001 to 78.1 for q = 0 and from 9.28 to 11 \u00d7 103 for q = 4. Table BIDsearch over ONLsearch for all investigated combinations of q and l.In a second experiment we investigated the influence of the loop length and the number of non-ambiguous characters in the loop of an RSSP on the running time of BIDsearch for non-artificial real-world RSSPs, we manually compiled a set of 397 RSSPs describing 42 highly structured RNA families taken from the RFAM10 database. These were all families with a consensus secondary structure containing at least 5 stem-loop substructures. We measured the running time needed by BIDsearch, ONLsearch, and the widely used tools RNAMotif [RNABOB [BIDsearch less than 50 seconds to search for the 397 patterns as shown in Table RNABOB and RNAMotif needed more than 2.5 and 3.2 hours respectively to complete the same task. This made for a speedup factor of 196.5 (254.7) for BIDsearch over RNABOB (RNAMotif). Even if we include the time needed for affix array construction, BIDsearch is still faster than RNABOB and RNAMotif.To measure the performance of RNAMotif  and RNAB [RNABOB  to searcBIDsearch when searching for the 397 RSSPs. We observed that BIDsearch is more than 50,000 times faster than RNABOB and RNAMotif for the majority of the patterns and that the total search time required by BIDsearch is dominated by only a small number of patterns. These patterns describe large unconserved loop regions. See Figure S3 in Additional file We also investigated the distribution of speedup factors obtained by BIDsearch and ONLsearch for an increasing size of sequences to be searched. For this, we searched with different RSSPs on random subsets of RFAM10 of different sizes and measured the running time for both algorithms. The results are given in Figure In a further experiment we investigated the scaling behavior of BIDsearch clearly showed a sublinear scaling behavior, whereas ONLsearch scaled only linearly. It took BIDsearch only 566.8 (pattern1), 133.8 (pattern2), and 37.1 (pattern3) milliseconds to search the whole RFAM10 dataset. The obtained speedups of BIDsearch over ONLsearch were in the range from 4.63 (1 MB subset) to 104.79 (full RFAM10) for pattern1, from 12.23 (1 MB subset) to 223.18 (full RFAM10) for pattern2, and from 35.0 (1 MB subset) to 618.37 (full RFAM10) for pattern3. We observe again that the specification of only one or two nucleotides in an RSSP's loop region considerably reduces the running time of the BIDsearch algorithm.In this experiment E. coli [Structator syntax, see Figure Structator delivers 8,619 matches for RSSP1, 1,699 matches for RSSP2, and 142,219 matches for RSSP3. Instead of reporting these matches, Structator computes high-scoring global chains for each sequence containing matches to all three RSSPs. The chains and the sequences they occur in are reported in descending order of the chain score. This procedure resulted in 61 sequences, all belonging to the OxyS family which contains 115 members in total. Hence, by considering only high-scoring chains all the spurious RSSP matches were eliminated. We also described the same three stem-loops in a format compatible with RNAMotif  mode with subsequent global chaining of RSSP matches needed only 3.9 (122.5) seconds to identify all family members, whereas RNAMotif needed 84.7 seconds. The search times for Structator include 0.05 seconds required for the chaining.To demonstrate the effect of global chaining of RSSP matches, we searched with an SSD built for the Rfam family of OxyS RNAs (Acc.: RF00035). OxyS is a small 109-nucleotide long non-coding RNA which is included in response to oxidative stress in E. coli . MembersStructator operating in BIDsearch (ONLsearch) mode and global chaining of RSSP matches it took only 1.3 (138.7) seconds to search RFAM10 with this SSD, where 0.06 seconds were required for the chaining. The computed global chains with a minimum length of 5, computed from the 184,199 single RSSP matches, were ranked according to their global chain score. We observe that the sequences containing the 37 highest scoring chains are exactly all 37 members of the family.We also employed global chaining to detect members of the structurally more complex family of Citrus tristeza virus replication signal (Rfam Acc.: RF00193). Therefore we built an SSD comprising 8 RSSPs, describing 8 of 10 stem-loops the molecule is predicted to fold into. For more information on the molecule's secondary structure and the used descriptor, see Additional file Structator using global chaining for RNA family classification with manually compiled SSDs for 42 Rfam families. For the results of this experiment see Additional file In addition we measured the performance of \u03b1(RSSPi) = 10, for 1 \u2264 i \u2264 3. Affix array construction for all human chromosomes was accomplished in 12.6 hours by afconstruct. We searched with Structator for the three RSSPs and found 15,090, 1,578, and 14,491 matches for RSSP1, RSSP2, and RSSP3, respectively. For these RSSP matches we computed local high-scoring chains  this task needed 3.1 (633.4) seconds only, including 0.02 seconds for the chaining. RNAMotif also found a single match corresponding to the correct location of the gene, but needed 274.7 seconds. See Figure S5 in Additional file RNAMotif descriptor.As an example of searching a complete genome or whole chromosomes for non-coding RNAs, we searched for the RNA gene Human accelerated region 1F (HAR1F) on both strands of the human genome sequence. HAR1F is one of 49 regions in the human genome that differ significantly from highly conserved regions of the chimpanzee . The conStructator's running time using using BIDsearch with the time needed by a recently published bidirectional pattern search implementation for the same task. The implementation of [BWI, uses a compressed data structure called bidirectional wavelet index. We remark that BWI can only search with a small set of hard-coded patterns, i.e., the user cannot use it to search with his/her own patterns. Moreover, unlike Structator, which provides a full command line interface with many configurable options (see section about the software package), BWI reports neither matching substrings nor matching positions . It onlructures . Neverthurements . BecauseStructator is an open-source software package for fast database search with RNA structural patterns implementing the algorithms and ideas presented in this work. It consists of the command line programs afconstruct and afsearch.afconstruct implements all algorithms necessary for affix array construction, namely a lightweight suffix sorting algorithm for construction of the suffix arrays sufF and sufR, the algorithm for construction of tables lcpF and lcpR [F and aflkR. The program constructs all or if necessary only some of the tables of the affix array for a target database provided in FASTA format and stores them on disk. Therefore the program can also be used to compute only the tables needed for a traditional enhanced suffix array [afconstruct can handle RNA as well as DNA sequences. Moreover, it supports the transformation of input sequences according to user-defined (reduced) alphabets and allows the index construction for transformed sequences. Such personalized alphabets are easily specified in a text file.and lcpR , and theix array . afconstafsearch is the program for performing structural pattern matching. That is, it searches (ribo)nucleic acid sequence databases for entries that can adopt a particular secondary structure. For an overview of the supported RNA sequence-structure patterns (RSSPs), see Figure afsearch, e.g. N standing for nucleotides A, C, G, and U (and T) and R standing for A and G. Besides fixed-length RSSPs with or without ambiguous characters  and maxrightloopextent (mrlex) a variable number of allowed extensions to the left  . This is done by simply specifying a series of RSSPs in the pattern file describing the stem-loop substructures the RNA molecule is composed of in the order of their occurrence in 5' to 3' direction. To incorporate different levels of importance or significance of an RSSP into SSD models and subsequently in the computation of chain scores, RSSP specific weights can be defined in the pattern file. This is particularly useful in the context of RNA family classification where the used SSD may be derived from a multiple sequence-structure alignment or a consensus structure-annotated multiple sequence alignment. Here, it permits the assignment of higher weights to RSSPs describing highly conserved functionally important structural elements occurring in a family of RNAs, and lower weights to RSSPs describing less conserved substructures that occur only in certain members of the family.RSSP matches can be reported directly by afsearch contains all available information of a match or chain of matches, either in a human-readable, or a tab-delimited format. Moreover, afsearch can also report matches in BED format. This allows a direct visualization of the results in e.g. the UCSC genome browser.The output format of Structator software. As part of the software, we give the first publicly available implementation of bidirectional pattern search using the affix array data structure. For the majority of biologically relevant RSSPs, our implementation of BIDsearch shows superior performance over previous programs. In a benchmark experiment on the Rfam database, BIDsearch was faster than RNAMotif and RNABOB by up to two orders of magnitude. Furthermore, in a comparison between BIDsearch and the program of [BIDsearch was faster by up to 2 times. We observed that for RSSPs with long unconserved loop regions, the advantage of BIDsearch over ONLsearch decreases. For such cases, Structator can also employ ONLsearch on the plain sequence data. As a further contribution, we presented for the first time a detailed complexity analysis of bidirectional search using affix arrays. While bidirectional search does not does not improve the worst-case time complexity compared to online search, in practice it runs much faster than online search algorithms and the running time scales sublinearly with the length n of the searched sequences.We have presented a method for fast index-based search of RNA sequence-structure patterns (RSSPs), implemented in the ogram of , which wn bytes of space. This is a significant space reduction compared to the ~ 45n bytes needed for the affix tree. With the program afconstruct we present for the first time a command line tool for the efficient construction and persistent storage of affix arrays that can also be used as a stand-alone program for index construction.Our implementation of the affix array data structure requires only 18Structator, we also introduce a powerful technique to describe RNAs with complex secondary structures. This even allows to effectively describe RNA families containing branching substructures like multi-loops, by decomposition into sequences of non-branching substructures that can be described with RSSPs. Compared to programs like RNAMotif , Structator's pattern description language for RSSP formulation is simple but powerful, in particular in combination with the SSD concept. Beyond the algorithmic contributions, we provide with the Structator software distribution a robust, well-documented, and easy-to-use software package implementing the ideas and algorithms presented in this manuscript.With the new concept of RNA secondary structure descriptors (SSDs) combined with fast global and local chaining algorithms, all integrated into Structator software package including documentation is available in binary format for different operating systems and architectures and as source code under the GNU General Public License Version 3. See http://www.zbh.uni-hamburg.de/Structator for details.The Structator manual. SK developed and implemented the RSSP chaining algorithms and contributed to the manuscript. SW provided supervision and wrote parts of the manuscript. MB initiated the project, provided supervision and guidance, designed/performed the experiments and wrote large parts of the manuscript. RB contributed to the introduction. All authors read and approved the final manuscript.FM implemented the presented algorithms and wrote parts of the manuscript and the Supplemental material. Additional file Click here for file"}
+{"text": "An error was introduced in the preparation of this article for publication. In the Methods section, there is an error in the fourth equation of the \"Statistical Analyses\" section. There is a \"/\" missing between (b-c) and b. The correct equation is N=(b-c)/b x 100."}
+{"text": "In a \u201cblock-copying paradigm\u201d, subjects were required to copy a configuration of colored blocks from a model area to a distant work area, using additional blocks provided at an equally distant resource area. Experimental conditions varied between the inter-area separation  and the complexity of the block patterns to be copied. Two major behavioral strategies were identified: in the memory-intensive strategy, subjects memorize large parts of the pattern and rebuild them without intermediate visits at the model area. In the acquisition-intensive strategy, subjects memorize one block at a time and return to the model after having placed this block. Results show that the frequency of the memory-intensive strategy is increased for larger inter-area separations  and for simpler block patterns. This strategy-shift can be interpreted as the result of an optimization process or trade-off, minimizing combined, condition-dependent costs of the two strategies. Combined costs correlate with overall response time. We present evidence that for the memory-intensive strategy, costs correlate with model visit duration, while for the acquisition-intensive strategy, costs correlate with inter-area transition  times. Getting around in a constantly changing world relies on contributions from multiple behavioral or cognitive processes competing for common resources such as metabolic energy, information processing capacity, or processing time. The allocation of such resources to the individual processes requires some sort of \u201cdecision making\u201d or \u201cexecutive function\u201d For memorization and processing of visual information, the visual working memory (WM) is an essential resource. WM can be defined as a system for maintaining and processing a certain amount of information temporarily \u2018Just-in-time\u2019 acquisition of visual information by repeated looking as opposed to keeping more information in memory Trade-offs between gaze movements and WM use have been studied in a number of tasks which involve looking back and forth between two or more experimental areas In the above studies of the acquisition vs. memory trade-offs, acquisition behavior amounted to gaze shifts carried out by movements of the eyes and/or the head. Clearly, this kind of motor behavior is executed within small spatial scales and within very short periods of time. For example, a saccade is usually performed in less than 100 ms In the present study we approach this question by replacing the gaze-shift component of the block-copying task The goal of the present study was to assess and quantify strategy trade-offs in a walking paradigm including manipulations in acquisition and memorization costs. With overall higher costs for locomotion compared to saccadic motor behavior, we expect a general shift of the task solving strategies towards a greater reliance on memory. Furthermore, we hypothesize that both types of cost manipulations are capable of modulating walking strategies. This modulation can be modeled as a linear optimization of combined costs.48 na\u00efve subjects volunteered to participate in this study . Participants were under- and postgraduate students from the University of T\u00fcbingen and their ages ranged from 19 to 36 years (mean 24.6 years). Participants were paid for their participation and gave informed written consent. This research was performed in accordance with the 1964 Declaration of Helsinki and was approved by the ethical committee of the University Hospital of T\u00fcbingen.Each block pattern was composed of six quadratic LEGO\u00ae duplo\u00ae blocks of six different colors, forming a connected pattern. Blocks were placed on a grid where every block covered two by two grid cells. To control memorization demands, we varied the neighborhood rules between adjacent blocks. In \u201csimple patterns\u201d, adjacent blocks shared a complete edge ; in \u201ccomThree separate areas arranged in the shape of an equilateral triangle were defined for model (M), resource (R), and workspace (W) operations cf. . SubjectTo record the walking trajectories produced by subjects while operating between the three areas  an infrared light-based tracker system  with 6 degrees of freedom was used. This device tracked a rigid target object  that was fixed on a special helmet participants had to wear. The temporal tracking frequency of the system was 60 Hz. From the trajectories, area visits were detected using a criterion of 0.5 m. For analysis of the areas subsequently visited during a trial, subjects' body-in-space positions were evaluated cf. .In a 2\u00d72 factorial, between subject design, the 48 subjects were randomly assigned to one of four different experimental groups . Across these groups, we varied pattern complexity and locomotion distance in order to quantify the trade-off between memorization and acquisition intensive strategies. Thus, the four experimental groups include the combinations: simple/near, simple/far, complex/near, and complex/far.Subjects were familiarized with the particular task operations in a pre-test where one four-block pattern had to be copied. Afterwards, each subject had to complete ten experimental trials consecutively, each with a different block pattern. Subjects started and finished each trial by standing still for about ten seconds at the central point of the triangular configuration cf. . After eSubjects could visit each of the three areas in any sequence as often as necessary for replicating the current block pattern. They were instructed to do so as quickly and reliably as possible. No feedback was given to subjects during the experiment, neither about their copying performance nor about the walking strategies.In all conditions subjects had to follow three rules throughout the copying task: i) it was forbidden to carry more than one block while walking between the areas ii) once a block was placed at the workspace area no repositioning was allowed, and iii) after placing the last block at the workspace area subjects had to go back immediately to the central point of the area configuration denoting the end of the trial.We analyzed the errors made during copying the block patterns for each of the four experimental groups. Errors were analyzed as pattern errors and block errors. Pattern errors denote the proportion of incorrectly copied patterns. Block errors denote the amount of single blocks copied at a false position or with the false color and were calculated as the proportion of the total number of blocks in the 10 patterns (n\u200a=\u200a6 blocks\u00d710 patterns\u200a=\u200a60) averaged over subjects. A pattern was considered erroneous if at least one block error occurred.The focus of the present study was to identify and characterize the trade-off between WM load and re-acquisition via locomotion. For that purpose a method was needed that assessed the extent of memory usage quantitatively. Following Ballard et al. A sub-strategy is a section of the walking sequence between two subsequent visits of the workspace area; it usually (except for the \u2018control\u2019 sub-strategy W-M-W) corresponds to the placement of one block. As an example, the sequence of visited areas \u2026-W-R-W-M-R-W-R-M-W-\u2026 was divided into the sub-strategies W-R-W, W-M-R-W, and W-R-M-W. The W-R-W  sub-strategy is the strategy with the highest memory involvement. Here, all required information concerning (at least) the next block  is retrieved from memory and no additional visit of the model is needed. In contrast, the sequence W-M-R-M-W  denotes the sub-strategy with the lowest memory involvement, where subjects walk to the model area to look for the color of the next block. After picking a suitable block from the resource area, they come back to the model area once again, presumably because they did not remember the position of that block. Thus, color is remembered during the M-R step and position during the M-W step of the sequence. In contrast to the \u2018high-memory\u2019 sub-strategy, the associated walking distance is doubled when using the \u2018just-in-time\u2019 strategy. The \u2018low-memory\u2019 sub-strategy (W-M-R-W) uses an intermediate amount of memory and path length; color has to be remembered during the M-R step, while position has to be remembered during both the M-R and R-W steps. An overview of the different sub-strategies (together with the name that is used throughout the manuscript) and the demands on memory is provided in Starting at the central point, the initial sub-strategy of all subjects for all trials was M-R-W. Since this sequence was a simple consequence of the task design, it was not significant for later analysis of walking strategies and thus excluded. In addition to the analysis of walking trajectories, the time subjects needed for walking and the time spent at each area was recorded. The duration for an area visit was measured from entering until leaving a catchment area defined by a radius of 0.5 meters around each operating area. The time subjects spent at the model area was separated into time for the first and subsequent visits in the course of the analysis of memorization processes.2\u200a=\u200a1.4, p\u200a=\u200a.71) nor on block errors .Task performance was quantified by the number of pattern errors and block errors. In all conditions participants showed a high level of performance, i.e., on average 9 out of 10 patterns were copied correctly . Furtherp2\u200a=\u200a.44) and the distance condition \u200a=\u200a56.81, MSE\u200a=\u200a173.54, p<.001, \u03b7p2\u200a=\u200a.56). We found no interaction between these two factors \u200a=\u200a1.17, MSE\u200a=\u200a173.54, p\u200a=\u200a.28). Independent of pattern complexity, subjects needed significantly more time to reproduce the patterns in the far as compared to the near distance condition  sub-strategies were \u2018high-memory\u2019 (WRW) and \u2018low-memory\u2019  and distance \u200a=\u200a4.9, MSE\u200a=\u200a187.42, p<.05, \u03b7p2\u200a=\u200a.1). Thus, with an increase in distance and a decrease of pattern complexity the trade-off between acquisition and memory is shifted towards the memory-intensive sub-strategy \u2018high-memory\u2019. This shift of the trade-off is also reflected in the other main sub-strategy \u2018low-memory\u2019. Here, the influence of both factors was inverted \u200a=\u200a15.38, MSE\u200a=\u200a160.16, p<.001, \u03b7p2\u200a=\u200a.26; distance: F\u200a=\u200a7.33, MSE\u200a=\u200a160.16, p<.01, \u03b7p2\u200a=\u200a.14). A decrease in distance and an increase in pattern complexity induced a shift of the trade-off between acquisition and memory towards the \u2018low-memory\u2019 sub-strategy. For both main sub-strategies no significant interaction between the two factors (distance and complexity) was found \u200a=\u200a.75, MSE\u200a=\u200a187.42, p\u200a=\u200a.39; \u2018low-memory\u2019: F\u200a=\u200a.44, MSE\u200a=\u200a160.16, p\u200a=\u200a.51). However, based on the estimated parameters of the linear model of the ANOVA on the proportion of \u2018high-memory\u2019 (goodness of fit\u200a=\u200aRadj2\u200a=\u200a.35) a difference in distance condition depending on model complexity was apparent, indicating an ordinal interaction.Statistical analysis reveals an influence of both, distance and pattern complexity on the frequency of occurrence of the two main sub-strategies. By calculating a two-factorial ANOVA for the proportion of \u2018high-memory\u2019, we identified main effects of pattern complexity \u200a=\u200a22.15, MSE\u200a=\u200a187.42, p<.001, \u03b7In order to assess the degree to which the model is used in the various conditions, we analysed the duration and number of model visits and the number of blocks processed after the initial model visit of each trial.p2\u200a=\u200a.31; distance: F\u200a=\u200a.9, MSE\u200a=\u200a39.92, p\u200a=\u200a.35). Within each experimental condition, subjects spent significantly more time for the first model visit compared to subsequent model visits (p2\u200a=\u200a.23). No significant influence of the distance \u200a=\u200a.012, MSE\u200a=\u200a1.297, p\u200a=\u200a.91) was found.The total time for all visits subjects spent at the model  dependedl visits . Similarl visits . HoweverTo estimate the amount of memory subjects allocated in the different experimental conditions we analyzed the number of model visits per trial and the number of consecutive \u2018high-memory\u2019 cycles after the initial model visit . Initialp2\u200a=\u200a.24; distance: F\u200a=\u200a2.14, MSE\u200a=\u200a.55, p\u200a=\u200a.15). Subjects visited the model for memory refresh more often in the complex conditions (means: 2.77 for the far and 3.19 for near distance) than for simple patterns (means: 2.08 for the far and 2.28 for near distance).The number of model visits per trial was dependent only by pattern complexity but not by the distance \u200a=\u200a13.86, MSE\u200a=\u200a.55, p<.001, \u03b7p2\u200a=\u200a.24) and distance condition \u200a=\u200a5.33, MSE\u200a=\u200a.89, p<.05, \u03b7p2\u200a=\u200a.11). No significant interaction between these two factors was found.We found an overall higher number of consecutive \u2018high-memory\u2019 cycles in the simple pattern conditions (means: 3.2 for the far and 2.57 for near distance) than in the complex pattern conditions (means: 2.18 for the far and 1.54 for near distance). Within pattern complexity, also an increase of memorization was found with an increase of the distance. The two-factorial ANOVA with pattern complexity (complex vs. simple) and distance condition (far vs. near) as factors showed significant main effects of pattern complexity \u200a=\u200a14.03, MSE\u200a=\u200a.89, p<.001, \u03b7In a trial by trial analysis of blocks processed after the initial model visit, we found moderate correlations between the duration of the initial model visit and the number of consecutive \u2018high-memory\u2019 cycles. Correlations reached significance for all conditions .The influence of trial order on the occurrence of used sub-strategies was analyzed by comparing the frequencies of sub-strategies per trial within each experimental group. No influence of the trial order on any of the walking sub-strategies could be found. Working memory (WM) supports many higher cognitive functions by maintaining representations of a limited number of items, and by selecting and attending to those representations which are most relevant for the current task. Memory items include multiple types of information, such as verbal or visuospatial, as well as task rules and are represented in WM through sustained patterns of neural activity The main objective of the present study was to investigate if such a trade-off, already described for the balancing of WM and gaze movements The main result of this paper is that alternative behavioral strategies, which can be used to achieve the same goal, are used to various extents if task parameters are varied. In our block-copying task, the main behavioral strategies are i) initial acquisition of large amounts of information and subsequent operation from memory (\u201cmemory-intensive strategy\u201d), and ii) the repeated acquisition or re-acquisition of smaller pieces of data and subsequent processing of these individual packages (\u201cacquisition-intensive strategy\u201d). The memory-intensive strategy is realized by long initial model visits and high proportions of the \u2018high-memory\u2019 sub-strategy. The acquisition-intensive strategy, in contrast, uses relatively short initial model visits and a high proportion of the \u2018low-memory\u2019 sub-strategy.For more complex patterns, the use of the memory-intensive strategy is reduced, while more re-acquisition steps are performed. A similar but weaker effect was found for walking distance: if walking of larger distances is required, the frequency of the memory-intensive strategy increases.The observed pattern of the dependence of sub-strategy usage  on condiAs compared to the findings of Ballard et al. As measures of memory involvement in a given strategy we analyzed the duration and number of model visits (i.e. the time spent with the encoding of information) and the number of blocks processed , see These findings support the idea that longer and more frequent model visits lead to the build-up of extended memory which in turn is available for the processing of blocks. This idea can be tested directly by calculating within each condition trial-by-trial correlations between the duration of the first model visit and the number of blocks processed consecutively. Here we did indeed find moderate but significant correlations.The first model visit was significantly longer than the second or any later visit, indicating that it plays a special role. Conceivably, the subject could use this first visit to built up a memory of some global features of the pattern which is not necessarily used for immediate block positioning but may be useful for later information intake. Examples of such features are chunks or templates known to reduce working memory load 5\u200a=\u200a210, corresponding to an information content of 10 bits per pattern. A similar calculation for the complex pattern, where 16 positions of the second block are possible, yields 165\u200a=\u200a220 possible patterns corresponding to an information content of 20 bits per pattern. If we assume that the same total memory capacity is used for both cases, we should expect that the number of blocks processed per model visit in the simple conditions is about twice the number processed in the complex conditions. As can be seen from Simple and complex patterns require different amounts of storage capacity. A simple estimate of this capacity can be derived from the following consideration: Suppose the first block of a simple pattern is placed. For the next block, there are four possible positions observing the neighborhood rules described in the The trade-off idea states that behavioral strategies are selected so as to minimize certain task and condition dependent costs. Generally two types of costs are considered: i) processing time and ii) energy consumption or other, non-temporal measures of cognitive effort. The soft constraints hypothesis Gray et al. As revealed by the overall response times , harder a\u2013d in the figure. The model is in good general agreement with the data shown in In this analysis, the individual cost functions are assumed to be stable and known by the trade-off controller. This is in line with the trade-off stability reported in In summary, the analysis presented in"}
+{"text": "Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis.Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches.Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the \"true\" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a \"pan-viral\" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data. X \u2208 \u211dp\u00d7n, where each column corresponds to one of n samples, quantifying the associated gene-expression values for all p genes under investigation. We typically must address the \"large p, small n\" problem , o, oA reprtudent-t ) priors.tudent-t  and the tudent-t .i.e., to infer r). The non-Bayesian approaches are often sequential, and one may infer r by monitoring the error ||F E||as a function of iteration number  to  to 9] toss (IBP) , 20]. I. Ir (in ss (IBP) , 22]..r , computational efficiency is of major practical importance. In previous use of nonparametric Bayesian methods to this problem, a Gibbs sampler has typically been employed .In practice ak from the Beta-Bernoulli construction above defines the kth column of the factor-loading matrix A. The factor-score matrix S utilizes the binary vectors zj = T defined in (5), for j \u2208 {1, . . . , n}. Specifically, we define the jth column of S as S are sparse.To complete the model specifications, note that S, as above, they may alternatively be used to define A, with factor scores designed as in traditional factor models. This approach was considered in [p draws from the IBP to construct A, and typically p is very large for the gene-expression problems of interest. When presenting results in Section II-B, we discuss our experience with this model on small-scale problems, although this approach was found computationally intractable for the motivating virus studies considered in Section II-D.In the above discussion the Beta-Bernoulli and IBP processes were presented for a specific construction of the factor-analysis model, with the goal of making the connection to the model explicit and hence clearer. However, there are alternative ways of utilizing the IBP for design of factor models. Specifically, rather than using the binary vectors to construct dered in , using ar is closely related to the non-Bayesian sparse-PCA [ak}k = 1,K as before, using a sparseness-promoting prior like that discussed in Section IV-A. Further, the factor scores \u03bek for factor loading k is drawn \u03bek ~ In), for kth row of S, and we consider K such rows, for large K (relative to the anticipated r). Finally, the vector of pseudo singular values \u03bb =  is generatedThe final Bayesian construction considered for inferring arse-PCA  and penaarse-PCA  models. \u03bb select the columns of A used across all columns of X. As discussed in Section IV, the number of non-zero components of \u03bb is drawn Binomial)), and the posterior on the number of such components provides desired information on the number of factors r. Note that this construction is like the Beta-Bernoulli process discussed above, in that it utilizes k \u03c0~ Beta) and the Bernoulli distribution; however, it only draws the binary vector z once, and therefore there is not the idea of multiple \"customers\", as in the two IBP-related formulations discussed above.The matrix product AS in (1) is now constituted as r. Running on a typical modern PC, the computation times are summarized in Table The MCMC results presented here correspond to using 5000 collection samples, after a burn-in of 2000 iterations. However, with 2000 burn-in iterations and 500 collection samples, the average results of the factor scores and factor loadings are almost identical to those found with 5000. For all MCMC results, we employed a singular value decomposition (SVD) of the data matrix to initialize the factor loading and factor score matrix in the FA model, as well as the right-and left-singular matrix in the matrix decomposition model. For each iteration of the Gibbs sampler a particular number of factors r are employed, and based upon all collection samples one may infer an approximate posterior distribution for \u03b1 = 1, \u03b2 = 1, c = 1, and d = g = h = e = f = 10\u22126. These parameters were not optimized, and were set in the same manner for all experiments. Although the PMD model is a non-Bayesian method, it also has parameter settings that must be addressed carefully; two hyper-parameters need adjusting: the sparseness threshold and the stop condition [To be explicit, we provide detailed hyper-parameter settings for the model in (7)-(14); the other models are set similarly. Specifically, ondition . In all All calculations were performed on PCs with Intel Pentium Dual E2200 processors and 2.00 GB memory, and all software was written in Matlab. For the large-scale analysis performed on the real data discussed above, MCMC required approximately 4 hours of CPU, while VB required 3 hours .The following authors performed the statistical analysis: BC, MC, JP, AH, JL, DD and LC. The following authors executed the three viral challenge studies, and performed all biological interpretation of the ressults: AZ, CW and GSG. All authors read and contributed to writing this paper.We here provide a concise summary of the inference methods applied to one of the Bayesian FA models discussed above, with this representative of the analysis applied to the rest. Specifically, we consider the model discussed in Section IV-B, in which the BP is applied within the factor-score matrix. The complete model may be expressed asi = 1, . . . , n, j = 1, . . . , p and k = 1, . . . , K.where The full likelihood of the model isThe sequential update equations of the Gibbs sampler are as follows.kiz. The probability of ki z= 1 is expressed as\u2022 Sample each entry of the binary matrix, k \u03c0from kp(\u03c0|-) = Beta where \u2022 Sample jk Afrom jkp(A|\u2212) = jkA; jk\u03bc, \u03a3jk) where \u2022 Sample each entry of factor loading matrix, si, from sip(|\u2212) = is; \u03bei, \u039bi) where K-dimensional vector,iz, repeated p times, 1 \u2264 i \u2264 n.\u2022 Sample each column of factor score matrix, j \u03c8from \u2022 Sample jk from p(\u03b3jk|-) = Gamma  where c' = c+1/2 and \u2022 Sample \u03b3\u03b4 from p(\u03b4|-) = Gamma  where e' = e + nK/2 and jk|p(\u03b3\u2212) represent the probability of jk \u03b3conditioned on all other parameters.\u2022 Sample X), where in \u0398 \u2261{A,S,Z,\u03b1,\u03c0,\u03c8,\u03b3,\u03b4} Our objective is to optimize the parameters \u0393 in the approximation Q. Toward that end, consider the variational expressionWe seek a distribution Q to approximate the exact posterior p(\u0398|p(X) is a constant with respect to \u0393, and therefore KL||p(\u0398|X)) is minimized. However, we cannot explicitly compute the KL divergence, since p(\u0398|X) is unknown. However, the denominator term in p(X)p(\u0398|X) = p(X|\u0398)p(\u0398), and the prior p(\u0398) and likelihood function p(X|\u0398) are available. To make computation of Q(\u0398|\u0393) has a factorized form Q = \u03a0iQi. With appropriate choice of iQ, the variational expression Note that the term ki zwe have ki z= 1. We consider the following two conditions:\u2022 For discussion below, the symbol < \u2022 > represents the expectation of the argument.k \u03c0we have \u2022 For jk Awe have \u2022 For , where i swe have K-dimensional vector of all zi repeated p times. In order to exactly calculate the expectation, \u2022 For B are k \u2264 K, 1 \u2264 j \u2264 p and 1 \u2264 i \u2264 n., we have to consider it as two parts. Specifically, the off-diagonal elements of j \u03c8we have \u2022 For jk \u03b3we have \u2022 For \u03b4 we have Q(\u03b4) Gamma , where e' = e + Kn/2 and \u2022 For The research reported here was supported under the DARPA PHD program. The research and results presented here are the contributions of the authors, and the results were not influenced in any way by the sponsor."}
+{"text": "The abnormal event detection problem is an important subject in real-time video surveillance. In this paper, we propose a novel online one-class classification algorithm, online least squares one-class support vector machine (online LS-OC-SVM), combined with its sparsified version (sparse online LS-OC-SVM). LS-OC-SVM extracts a hyperplane as an optimal description of training objects in a regularized least squares sense. The online LS-OC-SVM learns a training set with a limited number of samples to provide a basic normal model, then updates the model through remaining data. In the sparse online scheme, the model complexity is controlled by the coherence criterion. The online LS-OC-SVM is adopted to handle the abnormal event detection problem. Each frame of the video is characterized by the covariance matrix descriptor encoding the moving information, then is classified into a normal or an abnormal frame. Experiments are conducted, on a two-dimensional synthetic distribution dataset and a benchmark video surveillance dataset, to demonstrate the promising results of the proposed online LS-OC-SVM method. After recording events by a visual sensor, such as a camera, obtaining detailed information of individual or crowd behavior is a challenging object in this area; automatic abnormal event detection is required to provide convenience, safety and an efficient lifestyle for humanity . An abnoIn \u20134, abnorOn the other hand, low-level motion features were employed. In , the autTrajectory information is also adopted to detect abnormal events. In ,11, the We consider the model-free approach, which does not require an explicit statistical model. To be accurate, the support vector machine (SVM) classification method is relied on in this paper. Inspired by the satisfactory performance of a covariance feature descriptor representing object in a tracking problem, a covariance descriptor characterizes the moving information of a global frame. In a tracking problem, the covariance descriptor is constructed of the blob intensity or color for template matching. In this paper, covariance encodes the optical flow of the global frame.The rest of the paper is organized as follows. In Section 2, related works are briefly reviewed. In Section 3, the online least squares one-class support vector machine (online LS-OC-SVM) classification method is originally derived. In Section 4, a covariance matrix descriptor is described to provide feature vectors for the classification algorithm. In Section 5, we propose abnormal detection methods based on the online LS-OC-SVM. In Section 6, we present the results on synthetic data and real-world video scenes. Finally, Section 7 concludes the paper.2.i.e., all training data are given a priori and are learned together. If additional training data arrive afterward, the SVM must be retrained from scratch T at the time step, n, could be calculated as:A, B, C and D with suitable sizes T becomes:Instead of i.e.,After providing these relations with the dictionary, we now discuss the dictionary construction. The coherence criterion is adopted to characterize a dictionary in sparse approximation problems. It provides an elegant model reduction criterion with a less computationally-demanding procedure ,40,41. Txjw is the element in the dictionary, x. Presetting a threshold, \u03bc0, the new arrival sample, xt, at the time step, t, is tested with the coherence criterion to judge whether the dictionary remains unchanged or is incremented by including the new element. For n training samples, the subset, which includes m (1 \u2264 m \u226a n) samples, is considered the initial dictionary. Then, each remaining sample is tested with t\u03f5 \u2264 \u03bc0, it will be included into the dictionary. Concretely, the algorithm is performed with two cases described herein below.In the online case, the coherence between a new datum and the current dictionary is calculated by:First case:t\u03f5 > \u03bc0n + 1, the new data, xn+1, is not included into the dictionary. The Gram matrix, K, with the entries, \u03ba, i, j \u2208 {1, 2, \u2026, D}, is unchanged. When a new sample, x, arrives, we need to compute:n + 1, \u03ba is the column vector with entries \u03ba, j \u2208 {1, 2, \u2026, D}. K (x) is the matrix with the -th entry \u03ba, i \u2208 {1, 2, \u2026, n}, j \u2208 {1, 2, \u2026, D}.In this case, at time step Second case:\u03f5t \u2264 \u03bc0nx+1, is added into the dictionary, x. Then, the Gram matrix should be changed by:In this case, the new data, where K\u0305 is the Gram matrix of the dictionary, including the new arrival dictionary sample, xn+1, and K is the Gram matrix of the dictionary at the last time step, n. Let x = {xw1, xw2, \u2026, xDw } denote the dictionary at time step n; d is the column vector with entries j= \u03bad, j \u2208 {1, 2, \u2026, D}, and d = \u03ba. By adopting the matrix inverse identity K(x) and also S denote the updatedn + 1; we have:n + 1, q is the column vector with entries iq = \u03ba, i \u2208 {1, 2, \u2026, n}, and xD+1 is the new arrival datum xn+1, which is included into the dictionary. The matrix inverse in A, U, C and V, such that U and V should be chosen as two vectors, and A should be chosen as a scaler. Thus, the inverse, (C\u22121 + V A\u22121U), is a scaler; K(x)bq\u22a4), we regard two vectors, (K(x)b) and q\u22a4, as vector U and V, respectively, while C in with proper choices of matrices S, using \u03ba with entries \u03ba, j \u2208 {1, 2, \u2026,D, D + 1}, xjw is an element of the dictionary.Once knowing 4.I is the intensity of the image, xI, yI and tI are the derivatives of the image intensity value along the x, y and time t dimension, u and \u03c5 are the components of the optical flow in horizontal and vertical direction and \u03b3 represents the weight of the regularization term.The optical flow is chosen as the basic low-level feature to represent the movement direction and amplitude. We apply the Horn-Schunck (HS) method to compute optical flow in this paper. The optical flow can provide important information about the spatial arrangement of the object and the change rate of this arrangement . The optI is the image , hue-saturation-value (HSV), hue-lightness-saturation (HLS), etc), i\u03d5 is a mapping relating the image with the i \u2013 th feature, F is the W \u00d7 H \u00d7 d dimension feature, W is the image width, H is the image height and d is the number of the chosen features. For each frame, the feature, F, can be represented as the d \u00d7 d covariance matrix:n is the number of the pixels sampled in the frame, \u03bc is the mean of n feature vectors of the selected points and zk is the feature vector of the k \u2013 th point. C is the covariance matrix of the feature vector, F. The covariance matrix descriptor proposes a way to merge multiple features. Different choices of feature vectors are shown in u and \u03c5 are horizontal and vertical components of optical flow, xu and x\u03c5 are the first derivatives of horizontal and vertical optical flow in the x direction, respectively, yu and y\u03c5 are the first derivatives of the corresponding feature in the y direction, xxu and xx\u03c5 are the second derivatives in x direction and yyu and yy\u03c5 are the second derivatives in y direction. The flowchart of covariance matrix descriptor computation is shown in The covariance feature descriptor was originally proposed by Tuzel  for pattXi and Xj are matrices in Lie group G; the parameter \u03c3 determines the scale at which the data is probed.If proper parameters are given, classical kernels, such as Gaussian, polynomial and sigmoidal kernels, have similar performances . In our fined as ,46:(45)5.I1, I2,\u2026, nI} (the positive class), describing the normal behavior is obtained. The abnormal detection strategies relative to the online algorithms proposed in Section 3.3 and Section 3.4 are introduced below.In an abnormal event detection problem, it is assumed that a set of training frames, {5.1.The general architecture of the abnormal event detection method via online least squares one-class SVM (online LS-OC-SVM) proposed in Section 3.3 is summarized in Algorithm 1; the flowchart is shown in Algorithm 1: Visual abnormal event detection via online least squares one-class support vector machine (LS-OC-SVM) and sparse online LS-OC-SVM.Requiren training frames {Ii}i=1nand the corresponding optical flow {OPi}i=1n.(a)Online strategy: Applying LS-OC-SVM on the small subset of training samples to calculate the coefficient matrix.(b)Sparse online strategy: Applying LS-OC-SVM to train the initial dictionary, C, offline.(a)Online strategy: Applying online LS-OC-SVM on the remaining samples to calculate the coefficient matrix.(b)Sparse online strategy: Applying sparse online LS-OC-SVM on the remaining samples to calculate the coefficient matrix and to update the dictionary.Each frame Cn+l is classified via LS-OC-SVM.Compute the covariance matrix of each frame.Step 1: The first step consists of calculating the covariance matrix descriptor of the training frames. The features could be chosen as any form shown in OP1,OP2,\u2026, nOP} are the image optical flows of the 1st to n \u2013 th frames; {C1,C2,\u2026, Cn} are the covariance matrix descriptors.where {Step 2: The second step is applying LS-OC-SVM on a small subset of the training samples to calculate the coefficient parameters, \u03b1 and \u03c1, in m \u226a n of data selected from the training set m frames are chosen. These m samples are trained offline. This step can be described in the following equation:K ] and [\u03b1 \u2212 \u03c1 ]T are defined in Step 3: After learning the first m samples, the coefficient matrices, K and [\u03b1 \u2212 \u03c1 ]T, are obtained. The online LS-OC-SVM method (Section 3.3) is applied to learn the remaining n \u2013 m samples {Cm+1,Cm+2n\u2026C}. This step can be expressed as:Step 4: Based on the coefficient matrix, [\u03b1 \u2212 \u03c1 ]T, the distance of the training samples Cn+l, with respect to the decision plane is computed. By comparing the distances of the samples, an abnormal event is detected:Cn+l is the covariance matrix descriptor of the (n + l) \u2013 th frame needed to be classified, and iC is the sample of the training data. \u201c1\u201d corresponds to an abnormal frame; \u201c \u2212 1\u201d corresponds to a normal frame. disT is the threshold of the distance, it is the maximum distance of the training samples to the hyperplane.where 5.2.C, making a sparse representation of the training data. The initial dictionary, C, is learned offline. Each remaining training sample is learned one-by-one online. Meanwhile, it is checked to be included, or not, into the dictionary. The test datum is classified based on the dictionary. The feature extraction step (Step 1) and the detection step (Step 4) are the same as the ones presented in Section 5.1. Owing to the dictionary, the training steps are different.The abnormal event detection via sparse online least squares one-class SVM (sparse online LS-OC-SVM) is introduced below. A subset of the samples is chosen to form the dictionary, Step 2-sparse: The second step is applying LS-OC-SVM to train the initial dictionary offline. The first m samples are the initial dictionary denoted as C. This step can be generalized as:Step 3-sparse: After learning the initial dictionary, C, including the first m(1 \u2264 m \u226an) samples, the remaining training samples, {Cm+1, Cm+2, \u2026, Cn}, are learned via sparse online LS-OC-SVM described in Section 3.4. This step can be described in the following equations:C is the dictionary and Ck is a new incoming remaining sample in the training dataset. According to the coherence criterion introduced in Section 3.4, if the new sample, Ck, satisfies the dictionary updated condition, it will be included into the dictionary, C.6.This section presents the results of experiments conducted to illustrate the performance of the two proposed classification algorithms, online least square one-class SVM (online LS-OC-SVM) and sparse online least square one-class SVM (sparse online LS-OC-SVM). The two-dimensional synthetic distribution dataset and the University of Minnesota (UMN)  dataset 6.1.Two synthetic data, \u201csquare\u201d and \u201cring-line-square\u201d , are useThe first sample is used for initializing the online LS-OC-SVM proposed in Section 3.3; the 399 remaining samples in \u201csquare\u201d and 849 remaining samples in \u201cring-ling-square\u201d are learned in the online manner.Via the sparse online LS-OC-SVM method proposed in Section 3.4, the first sample is trained offline, and this sample is considered the initial dictionary. Then, each arrival sample in 399 remaining samples in \u201csquare\u201d and 849 remaining samples in \u201cring-ling-square\u201d are checked by the coherence criterion to determine whether the dictionary should be retained or updated by including the new element.\u03c3 = 0.065. The preset threshold of the coherence criterion is \u03bc0 = 0.08. The detection results obtained by these two online training algorithms are the same as the ones when training data were learned in a batch model.The distances are shown in contours illustrating the boundary. The contours of \u201csquare\u201d and \u201cring-line-square\u201d are shown in 6.2.\u03c3, in the Gaussian function and the penalty factor, C, are chosen to form the receiver operating characteristic (ROC) curve. In the indoor scene, time lags of the frame labels lead to the lower area under the ROC curve (AUC) value. In the last few frames, labeled as abnormal of abnormal sequences, there are no people, while, in the training samples, there are no people in the upper half of the image. The covariance of the training frame is similar to the covariance of the abnormal frame without people. Our covariance feature descriptor-based classification method cannot distinguish between these two situations. However, this issue can be resolved by utilizing the foreground information. For example, if there are no moving objects in the frame, this frame is immediately classified as abnormal. The results of these three scenes show that the covariance descriptor can distinguish between normal and abnormal events. The performance of online LS-OC-SVM is almost the same as that of the offline method.UMN dataset detection results via online LS-OC-SVM proposed in Section 3.3 are shown below. The UMN dataset consists of eleven sequences of crowded panic escape events, which are recorded in a lawn, an indoor and a plaza scene. A frame where the people are walking in different directions is considered as a normal sample for training or for normal testing. A scene where the people are running is taken as an abnormal sample for testing. The detection results of the lawn scene, the indoor scene and the plaza scene are shown in 6.3.UMN dataset abnormal event detection results via sparse online LS-OC-SVM proposed in Section 3.4 are presented. Taking the lawn scene as an example, the first normal covariance matrix descriptor from the training samples is included into the dictionary firstly; then, the remaining training covariance descriptors are learned online by the sparse online LS-OC-SVM method. The ROC curve of the detection results of the lawn scene, the indoor scene and the plaza scene are shown in The resulting performances when all training samples are learned offline via one-class SVM (OC-SVM), learned via least squares one-class SVM (LS-OC-SVM), learned via online least squares one-class SVM (online LS-OC-SVM) and learned via sparse online least squares one-class SVM (sparse LS-OC-SVM), are shown in The resulting performances of the covariance matrix descriptor-based online least squares one-class SVM method, and of state-of-the-art methods, are shown in 7.In this paper, we proposed a method to detect abnormal events via online least squares one-class SVM (online LS-OC-SVM) and sparse online least squares one-class SVM (sparse online LS-OC-SVM). Online LS-OC-SVM learns training samples sequentially; sparse online LS-OC-SVM incorporates the coherence criterion to form the dictionary for a sparse representation of the detector. The covariance matrix descriptor encodes the movement feature of the frame to distinguish between normal and abnormal events. The proposed detection algorithms have been tested on a synthetic dataset and a real-world video dataset yielding successful results in detecting abnormal events."}
+{"text": "To evaluate if white matter lesions (WML) on MRI can be a potential marker for onabotulinum toxin A (Botox\u00ae) treatment success in migraine, given the limited response rate and high costs per treatment.Retrospective data base and MRI analysis of 529 migraineurs who received Botox\u00ae between 2002 and 2009. Responders were defined as patients who underwent three or more treatments, whereas non-responders had only one or two treatments. MRIs were analysed on axial T2 and coronar FLAIR (fluid attenuated inversion recovery) sequences for the presence of WML. Statistical analysis was done with the Chi-Square-Test and the Mann\u2013Whitney-U-Test.Of 529 Botox\u00ae treated migraineurs, 111 patients had a MRI. Of these 111 patients, 47 were responders, 64 non-responders to Botox\u00ae. Response rate to Botox\u00ae in migraineurs with WML was 55.3%, in migraineurs without WML 44.7%. In the investigated items \u201cage\u201d, \u201cage at onset\u201d, \u201cgender\u201d, \u201cattack duration\u201d, \u201cfrequency\u201d, \u201caura\u201d, \u201cWML\u201d, \u201csize of WML\u201d, we found no statistical significant difference between the two groups. 55% of the responders and 50% of the non-responders showed WML. All WML were located supratentorially, anteriorly, mostly of small size (3\u20135\u00a0mm).WML on MRIs cannot serve as a marker to predict a positive response to Botox\u00ae. Migraine is a primary headache disorder. According to the WHO, the lifetime prevalence of migraine in Europe and North America is 6% in men and 15-18% in women for one year  mediates its postulated mechanism of action in migraine by inhibiting the release of nociceptive agents, such as glutamate, substance P, calcitonin gene-related peptide and acetylcholine , medium (6\u20139\u00a0mm) or large (>10\u00a0mm). Total number of lesions was recorded. The distribution was classified in supratentorial or infratentorial. If supratentorial, in anterior or posterior, with cut at the middle of corpus callosum.Each WML analysis was performed independently by two neurologists, each blinded to the history of the patient. In case of disagreement between the two readers, a consensus was achieved by discussion.Statistical analysis followed the statistical program SPSS (Superior Performing Software System). The Chi-Square-Test was applied for the items gender, duration, frequency (episodic vs. chronic), aura and non-parametric values such as age, age at onset, WML, were analyzed by the Mann\u2013Whitney-U-Test.In the current group of 111 Botox\u00ae treated patients, 47 have been responders and 64 non-responders. We found in none of the investigated parameters a statistical significance to characterize or distinct responders from non-responders, details are shown in Table\u00a0The analyzed WML in the MRIs followed no pattern to permit a conclusion for a positive response to a Botox\u00ae treatment. WML were absent in 45% of the responders, present in 55%. In the non-responders, WML were absent in 50%, present in 50%. Mean lesion load of small-size- WML in responders was 2.3 per person, in non-responders 2.9 per person. Mean lesion load of medium-size- WML was 0.2 in both groups per person and of large-size- WML was 0.02 per person in responders and 0.03 per person in non-responders. Figure\u00a0The aim of our study was to find a marker of response to Botox\u00ae, in order to optimize treatment of migraine patients in clinical practice.The response rate to Botox\u00ae in the treatment of migraine is generally in a range of 30% to 50%  was demonstrated in a study over three years  could be \u201ccured\u201d of migraine for a certain time. Second, patients with a very long treatment interval were included in the study, ending in 2009. Third, patients, corresponding to a treatment, but unable to pay for further treatments. Some false results in the responder group (\u2265 three treatments) could arise, first, from non-responders, having tried several times Botox\u00ae. However, more than three treatments without any sort of response are very unlikely. Second, an initial responder becomes a non-responder.Improvements could be obtained by carrying on the study in a prospective design and by realizing more MRIs in our clinic.WML on MRI scans cannot serve as a marker to predict a positive response to Botox\u00ae. The meaning of the WML in the migraine population remains unclear, being probably not of clinical importance. But they are often a sign for migraine chronification and longer lifetime history of migraine. They can be seen as well in other clinical conditions like cerebrovascular diseases, different types of dementia, inflammatory diseases and bipolar depression, which can be important comorbidities to migraine. They have to be considered while having a look at white matter lesions in the context of migraine."}
+{"text": "Photoplethysmography is one of the optical techniques has been developed for experimental use in vasculardisease. It has several advantages over other traditional experimental approaches. Because of its non-invasive, safe, costeffectiveand easy-to-use properties, it is considered as a useful diagnostic tool. The further developments in the Photoplethysmographmay replace it among other tools used in the assessment of vascular diseases such as blood test and ultrasound.This overview discusses the different terminologies used for the photoplethysmograph and reveals the researchdiscontinuity among different disciplines. Moreover, it suggests standard terminologies as a resolution for a confusionpersisted for more than 50 years. It is an optical measurement technique uses an invisible infrared light send in the tissue and the amount of the backscattered light corresponds with the variation of the blood volume [Photoplethysmography reflects the blood movement in the vessel, which goes from the heart to the fingertips through the blood vessels in a wave-like motion , as showd volume .The photoplethysmography (PPG), introduced by Hertzman in 1938 [1b). Therefore, the second derivative of the photoplethysmogram was developed as a method allowing more accurate recognition of the inflection points and easier interpretation of the original plethysmogram wave.In 1978, Ozawa reported (in Japanese)  that the1a). The second derivative of the original photoplethysmogram waveform includes four systolic waves and one diastolic wave, namely a-wave (early systolic positive wave), b-wave (early systolic negative wave), c-wave (late systolic reincreasing wave), d-wave (late systolic redecreasing wave) and e-wave (early diastolic positive wave), as shown Fig. (1b). The original photoplethysmogram wave form consists of two waves: systolic and diastolic waves, as shown Fig. , as well as the values of sanguineous pressure, whereas abPWV = Lab / \u0394T , and Lab measured distance between ankle-brachial location. In 2006, Padilla et al.  used the et al. [In 2007, Alty et al.  used theet al. [In 1999, Mishima et al. [In 2005, Yashima et al.  used theet al. [In 2007, Kageyama et al.  used theet al. [In 2008, Abe et al.  used theet al. [In 2008, Cox et al.  used theet al. [In 2009, Gil et al.  used theSome of the literature review to explain the different usage of different terminologies for the second derivative plethysmogram:et al. [b/a ratio reflects increased arterial stiffness, hence the b/a ratio increases with age. Moreover, they found the (b-c-d-e)/a ratio may be useful for evaluation of vascular aging and for screening of arteriosclerotic disease. The waves a, b, c, d, and e are demonstrated in Fig. (1b).In 1998, Takazawa et al.  used theet al. [b/a of the APG is related to the distensibility of the peripheral artery, and suggest that magnitude of b/a is a useful non-invasive index of atherosclerosis and altered arterial distensibility.In 1998, Imanaga et al.  used theet al. [b/a ratio and the aging index (SDPTG-AI) increased with age, and the c/a, d/a, and e/a ratios decreased with age. The informal aging index (b-e)/a has been suggested as a replacement for the known formula (b-c-d-e)/a.In 2007, Baek et al.  used theet al. [In 2007, Kimura et al.  used theet al. [In 1994, Katsuki et al.  used theet al. [In 1996, Takada In 2000, Bortolotto [et al. [(b - c - d)/a upon Sho treatment, which includes Kamishoyosan. Sho is one of the main concepts of Kampo medicine, and corresponds to the holistic tailored treatment suitable for the individual patient\u2019s symptoms. In 2005,Ushiroyama et al.  used the et al. [ et al. [ et al. [In 2006, Nousou et al.  used the[ et al.  used the[ et al.  used the et al. in 2003 [To date, two papers have been found using the SDDVP. The first by Millasseau in 2003  when the et al. in 2007, [The second paper by Rivas-Vilchisin 2007,  when the et al. [In 2007, Taniguchi et al.  used theStandardization of Photoplethysmogram terminologies is highly desirable.Each terminology system should be as simple as possible and has been used the most in literature.The symbols should indicate the nature of the Photoplethysmogram signal type.A symbol representing a given charge should not be easily confused with any of those representing the other biomedical signals types. Several general preferences regarding standard terminologies for Photoplethysmogram signals have been introduced as following:Photoplethysmograph, Photoplethysmogram,and Digital Pulse Volume are the same terminologies with different a symbol PTG, PPG, and DVP.Second Derivative Photoplethysmograph, Acceleration Photoplethysmograph are the same terminologies with different symbols SDPTG, and APG.Various sets of symbols were proposed and problems associated with each set were noted as following:The data collected from PubMed database has been used for English literature and ScienceLinksJapan for Japanese literature. The reason behind choosing the PubMed database, it comprises more than 19 million citations for biomedical articles from MEDLINE and life science journals back to 1948.PubMed includes links to full-text articles which may be found in other databases such as PubMed Central or at publisher web sites.The total number of references for \u201cPhotoplethysmography\u201d terminology was 1024, \u201cPhotoplethysmogram\u201d was 91, \u201cPPG\u201dwas 232, \u201cPTG\u201dwas 13, \u201cDVP\u201d was 10, \u201cAPG\u201d was 4, and \u201cSDPTG\u201d was 15 in PUBMED database. On the other hand, the total number of references for \u201cPhotoplethysmography\u201d terminology was 23, \u201cPhotoplethysmogram\u201d was 24, \u201cPPG\u201dwas 2, \u201cPTG\u201dwas 4, \u201cDVP\u201d was 8, \u201cAPG\u201d was 28, and \u201cSDPTG\u201d was 8 in SCIENCELINKS Japanese database.2a); the number of publications for \u201cPPG\u201d is increasing with years more than \u201cPTG\u201d and \u201cDVP\u201d. In Fig. (2b), the cumulative sum of PPG clearly shows an exponential increase through years.As shown in Fig. (3a); the number of publications for\u201cAPG\u201d is increasing with years more than \u201cSDPTG\u201d. In Fig.(3b), the cumulative sum of APG clearly shows an exponentialincrease through years.As shown in Fig. (4a) that the usage of \u201cPPG \u201c,\u201dPTG\u201d, and \u201cDVP\u201d terminologies is more in Engineering than science \u201cSDPTG\u201d. In Fig. (4b), the usage of \u201cAPG\u201d and \u201cSDPTG\u201d vanishes in Engineering compared to Science.By categorizing the number of publication by its discipline, it is interesting to notice in Fig. (5) shows that all Photoplethysmography terminologies are coherent between PubMed and ScienceLinksJapan in all terminologies except APG. APG has been used by Japanese scientist more than western scientist. Therefore, the recommended as standard naming for the discussed terminologies is: The significant result in Fig.  and APG (for the second derivative photoplethysmogram) terminologies in oral presentations and written publications. The usage of different terminologies for the same signal can lead to a disconnect between different groups of engineers and scientists. These standard terminologies will save the researcher\u2019s efforts and overcome generating redundant results. It will also speed up the scientific progress in this multidisciplinary field. This paper is an attempt to resolve the difficulties and confusion regarding plethysmography terminologies which have persisted for more than 50 years."}
+{"text": "Gamma (30\u201380 Hz) rhythms in hippocampus and neocortex resulting from the interaction of excitatory and inhibitory cells (E- and I-cells), called Pyramidal-Interneuronal Network Gamma (PING), require that the I-cells respond to the E-cells, but don't fire on their own. In idealized models, there is a sharp boundary between a parameter regime where the I-cells have weak-enough drive for PING, and one where they have so much drive that they fire without being prompted by the E-cells. In the latter regime, they often de-synchronize and suppress the E-cells; the boundary was therefore called the \u201csuppression boundary\u201d by B\u00f6rgers and Kopell . The mod Gamma-frequency (30\u201380 Hz) oscillations in hippocampus and neocortex are known to result, in many instances, from the interaction of excitatory pyramidal cells (E-cells) and fast-spiking inhibitory interneurons (I-cells)  relation is said to be of type 1 if it has no discontinuity, i.e., if arbitrarily slow spiking is possible for drives sufficiently close to (but above) threshold, and of type 2 if it has a discontinuity at spike onset. , and mav = \u221220 and dv/dt < 0. If the firing period is T > 0, the frequency is f = 1000/T. The factor of 1000 arises because we measure time in ms, but frequencies not in reciprocal ms, but in reciprocal s, namely, in Hz.We define the \u201cfiring times\u201d of the neurons as times at which f - I) relation of the Erisir model neuron as follows. We begin with a simulation for I = 6, starting at  = . The computed trajectory converges to a fixed point which appears to be globally attracting. We then raise I, in steps of 0.05, from 6.0 to 7.5, starting each new simulation at the point in phase space at which the previous simulation ended. As soon as I rises above 7.0 (approximately), periodic spiking begins, at an onset frequency of approximately 60 Hz. The dots in Figure f as a function of I. We then lower I, in steps of 0.05, from 7.5 to 6, again starting each new simulation at the point in phase space at which the previous simulation ended. Periodic spiking continues as I falls below 7, and ceases only when I falls below 6.5. The circles in Figure f as a function of I, as I is gradually lowered. For I approximately between 6.5 and 7, there is bi-stability: both rest and periodic spiking are possible and stable in this range.We compute the frequency-current . Denote the firing period by T. Suppose that  =  is the uniquely determined point on the limit cycle with v = \u221220 and dv/dt < 0. At time t = 0, we start a simulation at this point. At time \u03c6T, with 0 < \u03c6 < 1, we abruptly increase v by 1 mV; this corresponds to an instantaneous charge injection at time \u03c6T. Denote by v = \u221220, dv/dt < 0. The phase advance produced by the input isWe also compute a phase response curve for the Erisir interneuron, defined as follows. Assume that g, for I = 7.2. It is of type 2: Excitatory input received early in the cycle delays the next spike instead of advancing it. Since in our network simulations, the I-cells inhibit each other, we also compute the phase response curve for the Erisir interneuron with an inhibitory autapse, modeled as described in Section 2.4, with maximal conductance equal to 0.2. The self-inhibition makes the type 2 character of the phase response more pronounced; see Figure Figure I \u2264 7.4. For I = 6.2, there is a single stable fixed point. Figure I rises.I, with blue indicating stability, and red instability. At a value of I near 6.5, a stable limit cycle arises; Figure I very slightly above 7.Figure I in Figure To confirm that the fixed point loses its stability in a Hopf bifurcation, we plot, in Figure f - I relation and the phase response curve, without self-inhibition (panel B) and with self-inhibition (panel C). The f - I relation now indicates no region of bi-stability, and is of type 1, with a square-root-like appearance. The phase response is of type 1 as well, positive throughout.We compare networks in which the I-cells are the Erisir neurons presented in the previous section with networks in which they are Wang\u2013Buzs\u00e1ki (WB) neurons  = (1 + tanh(v/4))/2, v denotes the presynaptic membrane potential, and \u03c4R and \u03c4D are the rise and decay time constants, respectively. To model the synaptic input from neuron i to neuron j, we add to the right-hand side of the equation governing the membrane potential vj of neuron j a term of the form gijsi(t) (vrev \u2212 vj) where gij denotes the maximal conductance associated with the synapse, si denotes the gating variable associated with neuron i, and vrev denotes the synaptic reversal potential. For excitatory, AMPA-receptor-mediated synapses, we use \u03c4R = 0.1, \u03c4D = 3, and vrev = 0; for inhibitory, GABAA-receptor-mediated synapses, \u03c4R = 0.3, \u03c4D = 9, and vrev = \u221280.where \u03c1 denotes a smoothed Heaviside function, \u03c1 of neurons i and j. For instance, we denote by gEI the value of gij when the i-th neuron is an E-cell, and the j-th neuron is an I-cell. Parameters gIE, gII, and gEE are defined similarly. We scale these parameters with network size: gEI = \u011dEI/NE, gIE = \u011dIE/NI, gII = \u011dII/NI, gEE = \u011dEE/NE. We choose parameters similar to those in B\u00f6rgers and Kopell (EI is so strong that a population spike volley of the E-cells promptly triggers one of the I-cells (but not much stronger), and \u011dIE is significantly stronger: \u011dEI = 0.2, \u011dIE = 0.8, \u011dII = 0.2, \u011dEE = 0. The value of \u011dIE is varied in Figure Connectivity is all-to-all in our networks.  The value of d Kopell : \u011dEI is i-th and j-th I-cells are gap-junctionally connected with probability 1/5. If vi and vj are the membrane potentials of the two cells, we add to the right-hand side of the equation for vi the term ggap(vj \u2212 vi), and to the right-hand side of the equation for vj the term ggap(vi \u2212 vj), with ggap = 0.8; this ensures that the I-cells remain synchronous when there are gap junctions.In some of our networks, the I-cells are also gap-junctionally coupled. The Each figure in this paper was generated by a stand-alone Matlab code, available from the first author upon request.II, increases linearly with time. The drive to the I-cells is heterogeneous, here and in all of our large network simulations; actual drive to the j-th I-cell isFigure II varies from 0 to 2 for WB neurons, and from 6 to 8 for Erisir neurons. The horizontal axis shows II. Panel (A) of the figure illustrates the \u201csuppression boundary\u201d as described in B\u00f6rgers and Kopell  through (D) of Figure B and C). When both changes are made at the same time, however, one returns to an abrupt suppression transition (panel D). In the presence of gap junctions  through (C) of Figure (D) of Figure II. We discuss these two points in greater detail in sections 3.2 and 3.3.Panels Our main goal in this section is to explain why the suppression transition is gradual in Figure II, to the I-cell for which the E-cells skip every second cycle; see Figure If one couples an RTM neuron with a WB neuron, there is typically a fairly broad range of drives, II = 7.27 shown in the figure, there is no cycle-skipping, and the network settles into an oscillation with a period of approximately 26 ms. If II is raised from 7.27 to 7.28 (not shown in the figure), the E-cell is suppressed altogether, and the period of the I-cell falls to approximately 23 ms. Because the I-cell is of type 2, the input from the E-cell, by lasting for a few milliseconds beyond the spike of the I-cell, does not advance the next I-cell spike; it delays it. Thus if the I-cell is unable to suppress the E-cell on a given cycle, it will be delayed on the next cycle, and is therefore even less able to suppress the E-cell on the next cycle. As a result, the E-cell is either suppressed on all cycles, or on none.Figures fE, of E-cell spikes in 1000 ms  as a function of II, with gIE = 0.5 (blue), 0.8 (black), and 1.1 (red). The figure confirms that there is an abrupt suppression transition when the I-cell is an Erisir neuron (panel B), but not when it is a WB neuron (panel A).In Figure II typically causes either an abrupt drop in fE, or a slight increase. The reason for the increase in fE with increasing II is that the enhanced drive to the I-cells makes them fire earlier on each cycle, thereby allowing the E-cell to fire earlier on the next cycle, unless there is a change in entrainment pattern, and the E-cell is suppressed on more cycles than before. When there is a change in entrainment pattern as a result of an increase in II, the frequency fE drops abruptly.In Figure II, to the I-cells in the transition regime. For illustration, Figure (C) of Figure There are seemingly irregular sequences of strong and weak E-cell spike volleys in Figure sk the number of E-cells that fire on the k-th gamma cycle in Figure sk, sk + 1) for the simulation of Figure sk < 160, then sk + 1 can be deduced from sk, approximately at least:g has exactly one fixed point s*, which is unstable: g\u2032(x*) < \u22121. If sk = 160, then sk + 1 is not determined by sk. Instead, sk + 1 then depends on the precise placement of the inhibitory spike volley in the k-th cycle, relatively to the excitatory one. If the inhibitory spike volley comes early, then the following I-cell spike volley comes so early that it largely or completely suppresses the E-cell spike volley; see Figure To understand this irregularity, we reduce the network dynamics to a one-dimensional map, examining how the strength of a given E-cell spike volley depends on the strength of the previous volley. We denote by sk, sk + 1). However, we describe now a method for constructing an idealized version of Figure To construct a figure analogous to Figure t = 0, in a point, X0, in phase space chosen so that a full population spike volley of the E-cells is imminent within a few milliseconds. Exactly how X0 is defined is largely irrelevant. We obtain it from the simulation of Figure t = t0 > 0, we re-set the phase space variables associated with the I-cell population to a point Y0 to force an immediate population spike volley of the I-cells. Again, it is largely irrelevant exactly how Y0 is defined. We obtain it from the simulation of Figure We start the simulation of the network, at time t0, the first E-cell spike volley may be suppressed partially or completely. The number, s1, of E-cells firing soon after time t = 0, 0 \u2264 s1 \u2264 160, is a function of t0 \u2265 0; see Figure s2, of E-cells firing in the second E-cell spike volley, and plot it as a function of t0 , where g = g(s) is a smooth function defined for 0 \u2264 s \u2264 160 with 0 \u2264 g(s) \u2264 160, may not have a stable fixed point when g is decreasing, but it does have at least one stable fixed point when g is increasing. So the mapping from s1 to s2 has an attracting fixed point when the interneurons are of type 2, but not necessarily, and in particular not in the example shown in Figure An iteration of the form II denotes the mean drive to the I-cells. With increasing II, increasingly many I-cells have enough drive to fire without being prompted by the E-cells. Once enough I-cells are in this group, the E-cells are suppressed altogether. In a network of cells coupled by inhibitory chemical synapses, but not by gap junctions, heterogeneity of drives typically prevents synchronization (White et al., Simulations similar to that of Figure II passes through it rapidly.This discussion suggests that even in Figure f - I relations of WB and Erisir neurons.Figure broader suppression transition than with WB interneurons. This is opposite to what is seen in the presence of gap junctions. We have no explanation of this effect. In particular, our arguments based on the phase response of the I-cells do not apply when the I-cells are not kept synchronous by gap junctions: once the I-cells de-synchronize, they receive excitatory input from the E-cells at all phases, not just at the early phases at which type 2 I-cells are delayed by such inputs.Figures The fast-spiking inhibitory basket cells believed to be central in the formation of gamma rhythms are in fact gap-junctionally connected (Beierlein et al., In this paper, we have discussed the loss of gamma rhythms due to too much excitation of the I-cells. By contrast, a recent paper of B\u00f6rgers et al.  investigAll numerical experiments in this paper have been for \u201cstrong PING,\u201d that is, for PING oscillations in which participating E-cells fire at or near gamma frequency. By contrast, \u201cweak PING\u201d oscillations are noise-driven, and individual participating E-cells fire on a small, randomly selected fraction of cycles only. In B\u00f6rgers et al. , it was Our discussion suggests that the competition among E-cells associated with PING oscillations [see for instance (Olufsen et al., In summary, we have found that in the presence of gap junctions, when the I-cells are of type 2, the suppression transition tends to be both narrower and more orderly than when the I-cells are of type 1. It is tempting to speculate that fast-spiking inhibitory basket cells might have evolved to have type 2 phase response curves precisely because that leads to clean suppression transitions, reducing the amount of modulation of local recurrent inhibition needed to turn gamma frequency cell assemblies off or on, an operation that seems likely to be crucial in brain function.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Analogously, the consciousness makes the mental phenomenon fundamental to any voluntary motor operation as seen from the psychological perspective.The graphical presentation of Bernstein five-level movements' construction system has been presented in Figure A-level\u2014intrinsic stimuli,B-level\u2014extrinsic contact stimuli,C-level\u2014extrinsic remote stimuli,D-level\u2014verbal code,E-level\u2014symbolic code  A, B and C levels are \u201cdriven\u201d by physical stimuli, whereas the D and E levels are \u201cpowered\u201d by purely mental representations of environment, where any connection with reality is possible, indeed, but not necessary. The \u201ccommon denominator\u201d of Bernstein's model and ML is the same, systemic structure. The final product of the information processing system is a movement, even if merely that of jaws and tongue.Symptomatically enough, also Rochat (who did not refer to Bernstein) developed a five-level model of self-awareness Rochat, . Though Such differentiation of information processing modalities assigned to particular levels remains in keeping with the scales' conformity premise by Morawski , p. 162.In physics one of the especially important laws is the \u201ccorrespondence rule\u201d formulated by Jammer . It stat"}
+{"text": "In this paper, we explore a new resource called multi-target diversity to optimize the performance of multiple input multiple output (MIMO) radar with widely separated antennas for detecting multiple targets. In particular, we allocate antennas of the MIMO radar to probe different targets simultaneously in a flexible manner based on the performance metric of relative entropy. Two antenna allocation schemes are proposed. In the first scheme, each antenna is allocated to illuminate a proper target over the entire illumination time, so that the detection performance of each target is guaranteed. The problem is formulated as a minimum makespan scheduling problem in the combinatorial optimization framework. Antenna allocation is implemented through a branch-and-bound algorithm and an enhanced factor 2 algorithm. In the second scheme, called antenna-time allocation, each antenna is allocated to illuminate different targets with different illumination time. Both antenna allocation and time allocation are optimized based on illumination probabilities. Over a large range of transmitted power, target fluctuations and target numbers, both of the proposed antenna allocation schemes outperform the scheme without antenna allocation. Moreover, the antenna-time allocation scheme achieves a more robust detection performance than branch-and-bound algorithm and the enhanced factor 2 algorithm when the target number changes. Unlike a standard phased-array radar, where different antennas transmit the scaled and phase-shifted version of the same waveform, MIMO radar can transmit different waveforms at different antennas . In geneThere are many resource optimization problems we could consider to improve the performance of MIMO radar. Waveform design is one of the most interesting resource optimization problems \u201317. Optii.e., relative entropy, was used to study the detection performance. It originated from Stein's lemma , where the subscript k1 \u2208 k denotes the first transmit antenna in k steered towards target k. The transmitted waveform is assumed to be narrowband. Therefore, the waveform that arrives at the n-th receiver can be modeled as T is a kM \u00d7 1 vector, which denotes the k-th target scattering coefficients for receiver n, and each element mh,k,n in hk,n denotes the scattering coefficient from the m-th transmitter to the n-th receiver for the k-th target. Let Rk denote the matrix that collects rk,n at different receivers  as its columns: Rk = . Thus, Rk can be written as:Hk =  is the kM \u00d7 N target scattering matrix. The total received signal at all receivers is the superposition of signals from the K target cell, which can be written as follows:W =  is the noise matrix, and wn is the noise vector at the n-th receiver.Assume that the entire search area of the space is divided into = sk1, sk, \u22ef, skMkdeled as :(1)rkHk can be ignored T. Based on Assumptions 2 and 3, the autocorrelation matrix of the waveform transmitted by the k-th antenna subset and the autocorrelation matrix of the k-th target scattering coefficients are both diagonal matrices, which can be written as Assuming that the transmit waveform i.e., the next allocation is determined while the MIMO radar system is in operation and in view of the results obtained from prior radar measurements in prior epochs 30], the -complete in the strong sense [The minimum makespan scheduling problems are classified as ng sense . We use 3.2.1.This is a classical algorithm for finding optimal solutions of various optimization problems, which was first proposed by Land and Doig in . If compThe branch and bound algorithm also consists of an enumeration of all candidate antenna allocation solutions. The search process for all antenna combinations is a tree structure, whose nodes are the antenna subsets of all combinations. The step that splits an antenna set into two or more smaller antenna sets is called branching. The step that computes upper and lower bounds for the relative entropy value within a given antenna set is called bounding. A tree node will be discarded, if its upper bound is less than some other node's lower bound. This step is called pruning -36. Usin edit 1 To apply the branch-and-bound algorithm in our problem, the problem  can be wTherefore, a branch-and-bound algorithm can be used for this integer programming problem. We need to be aware that branch-and-bound algorithm has exponential worst case complexity, but luckily, it can work with much less effort in some cases. We obtain the optimal antenna allocation result through the branch-and-bound algorithm as a performance bound and compare it with the performance of the proposed enhanced factor 2 algorithm in the experiments.3.2.2.i.e., the antenna that can contribute more to the detection performance must have priority. The heuristic scheme is summarized as Algorithm 1.The enhanced factor 2 algorithm is proposed based on the factor 2 algorithm in . The prok = 0, k \u2208 . For each kQ,m corresponding to target k and transmit antenna m, calculate m to target k. Out of k \u2208  and m \u2208 , select a pair  with the maximal kr,m, and \u211ak\u2032 = \u211ak\u2032 + kQ\u2032,m\u2032. Meanwhile, the antenna is discarded from the remaining antenna set,  = \\m\u2032. Next, we consider the targets, except k\u2032, and thus, we set kr\u2032,m = \u2212 1(\u2200m \u2208 ). Repeat this step till all targets have been selected once. After that, out of k \u2208 , select the one with the minimal \u211ak. For this cell k\u2033, select a transmit antenna m\u2033 from the remaining antenna set with the maximal kQ\u2033,m, and \u211ak\u2033 = \u211ak\u2033 + kQ\u2033,m\u2033. Next, transmit antenna m\u2033 is also discarded. Repeat this step till all transmit antennas have been selected, and max min kD (p0 \u2016 p1) = min \u211ak.The relative entropy of each target cell is initialized \u211aDk(p0 \u2016 p1) is achieved, there can be some antenna m\u0303 illuminating the target k\u0303 that is not assigned the least relative entropy. Thus, we could reduce the power of these antennas, i.e., kD (p0\u2016p1), but it is useful in realistic applications.Though an exhaustive search algorithm can always achieve a solution if it exists, it is implemented with exponential complexity. The branch-and-bound algorithm has exponential worst case complexity. However, the proposed heuristic enhanced factor 2 algorithm offers significantly reduced complexity, and the performance can be seen in the experiments. Here, we need to note that after max min Algorithm 1 Enhanced factor 2 algorithm.1k = 0, k \u2208 .Initialize \u211a2k \u2208 , m \u2208 .Calculate 3fori = 1 : Kk\u2032 \u2208  and m\u2032\u2208  s.t. max kr,m;\u2003\u2003select k\u2032 = \u211ak\u2032 + kQ\u2032,m\u2032;\u2003\u2003\u211akr\u2032,m = \u22121 (\u2200m \u2208 ),  =  \\ m\u2032;\u2003\u2003end.4while \u2260 nullk\u2033, s.t. min \u211ak;\u2003\u2003select m\u2033 \u2208 , s.t. max kQ\u2033,m;\u2003\u2003select k\u2033 = \u211ak\u2033 + kQ\u2033,m\u2033,  = \\ m\u2033;\u2003\u2003\u211aend.5kD (p0\u2016p1) = min \u211ak.max min 3.3.Other valid approximation algorithms with high precision for the minimum makespan scheduling problem can be exploited, but we do not focus on these in this paper. We consider that if each target has an opportunity to be illuminated by all transmit antennas, a new appropriate antenna allocation result can be explored. Therefore, we propose an antenna-time allocation scheme to solve the problem from another perspective. Using the antenna-time allocation scheme, antennas are allocated to illuminate different targets with different illumination times.In order to achieve a proper antenna-time allocation, we propose a method to partition the illumination time based on the illumination probabilities. In particular, the optimal illumination probabilities are obtained first; next, the illumination probabilities can be converted to the illumination time. identical units of time. Denote the illumination from antenna m to target k at the l-th unit time by:l = 1,2,\u2026, . Over each unit time, each transmit antenna selects one of all target cells to illuminate at random with a certain probability. Next, our objective is to obtain the optimal probabilities. We introduce a variable kp,m(l), which denotes the probability of kI,m(l) = 1. For any unit time l, it is obvious that Assume that the total illumination time is divided into kp,m(l) can be obtained by solving the following linear optimization problem: edit 1 The optimal solution of kp,m(l). Observing the problem kp,m(l) remains constant for l = 1, 2,\u2026, , since kQ,m is a constant for given k and m. In fact, we assume the target features remain the same over the entire illumination time. Therefore, kp,m(l) can be written as:l = 1, 2,\u2026, . So far, transmit antenna m has been arranged to illuminate target k at random with a probability kp,m per unit time. Next, we consider the entire illumination process from antenna m to target k, which consists of a sequence of illumination units: kI,m(l), kI,m(2), \u2026, kI,m(L). This illumination process can be regarded as a stochastic process, which is denoted by kI,m(l). According to l = 1, 2,\u2026, . Next, in order to convert the illumination probabilities to the illumination time, we introduce a lemma.Through linear programming, we can easily obtain the optimal numerical solution of m to target k is a stochastic process with ergodicity:The entire illumination process from antenna kI,m(l) is the same as the ensemble average. Denote the illumination time from antenna m to target k by kt,m. According to Lemma 1, kt,m can be obtained:unitt and totalt are the unit of illumination time and the total illumination time, respectively. Here, we need to be aware that kQ,m in kQ,m does not increase linearly with the unit time, the unit time should not be too short. Though this method is based on approximation analysis, it is not a relaxed solution to the previous -hard allocation problem. In fact, it is an implementable scheme for antenna-time allocation, and the effectiveness of this method can be demonstrated in the experiments.Therefore, when the number of unit time is sufficiently large, the time average of the sequence Next, in order to show an intuitive explanation of the antenna-time allocation scheme, we compare the antenna-time allocation scheme with the antenna-only allocation scheme proposed before. Uniform allocation and time allocation are also used for comparison, both of which employ all antennas to sequentially detect targets one by one. Time allocation optimizes the division of the entire time, while uniform allocation divides the entire time into equal parts for all targets without any optimization.4.M > K. However, the number of targets can be very large in the entire surveillance region. Therefore, we have to detect several times to cover the entire region. For each detection, the number of targets to be illuminated simultaneously should not exceed the number of transmitters, i.e., M > K.In this section, we set scenarios to investigate the detection performance via four different illumination schemes, including a uniform allocation scheme, a time allocation scheme, an antenna-only allocation scheme and an antenna-time allocation scheme. Moreover, the antenna-only allocation scheme contains the branch-and-bound algorithm and the enhanced factor 2 algorithm. Therefore, we use five methods in total to make a comparative analysis. Before simulations, we need to note that in order to allocate transmit antennas for each target cell, we need 4.1.M = 4, N = 4 and target number K = 2. Consider a typical scenario in which RH,1 = diag, RH,2 = diag, which means some antennas are more suitable to illuminate a certain target than the others. Particularly, Target 1 is more sensitive to the illumination from Antennas 1 and 4, while Target 2 is more sensitive to the illumination from Antennas 2 and 3. On the whole, the target scattering intensity of Target 1 is higher than that of Target 2. The different sensitivities can be caused by different path losses, angular views, wave lengths and polarizations. versus 0\u201325 dB transmitted power via different schemes. It can be observed that the relative entropy of the schemes that we propose outperforms that of uniform allocation and time allocation. It is obvious that uniform allocation is the worst, since it does not use any optimization. When the transmitted power grows, the relative entropy of the antenna-time allocation scheme gradually outperforms that of the antenna-only allocation scheme, i.e., branch-and-bound algorithm and enhanced factor 2 algorithm. In addition, we can find that branch-and-bound algorithm and enhanced factor 2 algorithm have the same relative entropy value for each transmitted power.We set In fact, the branch-and-bound algorithm and enhanced factor 2 algorithm lead to the same antenna allocation result for each point on the curves in versus transmitted power via different schemes. The parameters used for simulation in fP = 0.0001. The transmitted power per antenna ranges from 0 dB to 25 dB. In order to observe the detection performance, 104 Monte Carlo trials are executed to achieve the detection probability of each point on the curves. We can find that the branch-and-bound algorithm, the enhanced factor 2 algorithm and the antenna-time allocation scheme almost have the same detection probability for each transmitted power point. All of them can improve detection performance significantly compared with time allocation and uniform allocation.versus -12-12 dB radar cross-section (RCS) fluctuations of targets. The statistics of RCS fluctuations can be given by the log-normal distribution model. The variance is from -12 dB to 12 dB. In 6 Monte Carlo trials are executed to achieve the detection probability for each RCS fluctuation variance. It can be observed that two antenna-only allocation algorithms, i.e., the branch-and-bound algorithm and the enhanced factor 2 algorithm, outperform the time allocation scheme.In order to investigate the influence of different targets on the proposed schemes, we use all illumination schemes to detect different targets in different scenarios. Over a large range of RCS fluctuations, the antenna-time allocation scheme is the best, while the uniform allocation is the worst.M = 9, N = 9. The target number varies from two to nine. versus target number via different schemes. It can be observed that the proposed antenna-only allocation scheme and antenna-time allocation scheme still have advantages over time allocation and uniform allocation with different target numbers. Moreover, the antenna-time allocation scheme achieves the most robust detection performance when the number of targets is larger.Next, we investigate the influence of the target number on the proposed schemes. We set more antennas: 4.2.In the experiments above, we have found that the idea of antenna allocation has advantages over the idea without antenna allocation for multi-target detection. In this part, we will show some theoretical analysis.i.e., SNR. Let kL is the pulse number for the k-th target. To obtain an intuitive explanation of the relative k\u03c1,m's for different k and m are equal, which means all targets are the same isotropic scatterers, and all antennas are the same transmitters with the same path losses, angular views, wave lengths, polarizations, etc. Therefore, we drop the subscript of k\u03c1,m and obtain:In the relative entropy kD (p0\u2016p1) increases linearly with the number of receive antennas N. Therefore, when the other parameters are fixed, the number of receivers should be as large as possible to increase kD (p0 \u2016 p1).Observing N to study the influence of kM and kL. Applying the Taylor expansion of log(\u00b7) in the small \u03c1 region, \u03c1 region, Next, we fix K denotes the target number. In the scheme without antenna allocation, i.e., time allocation or uniform allocation, we employ all antennas to illuminate targets sequentially Thus, kM = M and kL = L/K, where M and L are the total number of transmit antennas and the total number of signal pulses, respectively Therefore, we have:For multi-target detection, K targets simultaneously Thus, the average value of kM is M/K, and kL = L. We still obtain C is a constant for a given K. Substituting kL in the small \u03c1 region. kD (p0\u2016p1) in \u03c1 region, we should select a scheme with larger pulse number kL, i.e., longer illumination time for a given pulse repetition frequency. Considering kM \u00d7 kL is a constant, we should increase kL and decrease kM. Thus, for multi-target detection, we will adopt antenna allocation to illuminate multiple targets simultaneously to lengthen illumination time in low SNR region.In antenna allocation scheme, we partition all antennas to illuminate kD (p0\u2016p1) in kM \u00d7 kL is a constant, we can conclude that we should decrease kL and increase kM when \u03c1 is relatively large. In Substituting 5.In this paper, a multi-target detection problem for MIMO radar with widely separated antennas is investigated based on relative entropy. In order to explore multi-target diversity, we propose the antenna-only allocation scheme and the antenna-time allocation scheme to implement multi-target detection simultaneously. In the antenna-only allocation scheme, we use a branch-and-bound algorithm and an enhanced factor 2 algorithm, respectively. In contrast to sequential illumination without antenna allocation, simultaneous illumination via antenna allocation can increase illumination time at the expense of decreasing the number of illumination antennas for each target. It is shown that proper antenna allocation outperforms time allocation and uniform allocation over a large range of transmitted power, RCS fluctuations and target numbers. Moreover, the antenna-time allocation scheme can achieve a more robust performance than branch-and-bound algorithm and enhanced factor 2 algorithm for more targets."}
+{"text": "E = b + skN, where E: expended energy, b: baseline rate, k: cost per spike, and sN: the number of spikes fired. Figure s(t) as a spike-train. Given an energy constraint E, the goal is to obtain the best possible reconstruction r(t) of s(t), with a simple low-pass filter h(t) = A exp(-t/\u03c4) (mimicking a post-synaptic cell membrane) such that average squared reconstruction error e(t) = s(t) - r(t)  and firing level \u03b3. Here, we show that this encoder can be interpreted as an instantaneous rate encoder with rate i(t) = (s(t)/\u03c4 + s'(t))/A. The function closely approximates the PSTH. We tested the instantaneous rate coder by predicting: i) spike-times . For signals with little variability, this predicts a rate-code of signal intensity. For signals with high variability, the spike-rate is driven by the changes in the signal . We conclude that optimal encoder can optimally time spikes while maintaining high coding fidelity, which can be interpreted as an instantaneous rate code.An action potential (spike) is metabolically expensive to generate, and it is likely that selective pressure has been exerted on the nervous system to generate energy-efficient neural codes . An addi) Figure  is minims Figure ee rasters Figure op panel,s Figure  for sing"}
+{"text": "The zero field equation of state (EOS) is hard sphere without any re-scaling of particle size, and the hydrodynamic corrections to the long-time self-diffusion coefficient are quantitatively consistent with the expected value for hard spheres. Care is taken to ensure that both the dimensionless gravitational energy, which is equivalent to a Peclet number Peg, and dipolar strength \u039b are of order unity. In the presence of an external electric field, anisotropic chain-chain clusters form; this cluster formation manifests itself with the appearance of a plateau in the diffusion coefficient when the dimensionless dipolar strength \u039b\u2009~\u20091. The structure and dynamics of this chain-chain cluster state is examined for a monodisperse system for two particle sizes.In this work, we use structure and dynamics in sedimentation equilibrium, in the presence of gravity, to examine,  Electric-field-induced dipolar colloids are a simple two-component system where both cluster formation and network formation123453710kBT).Computer simulations of colloidal hard spheres with an imposed pair-wise electric polarization interaction that neglect contributions of higher order than the point-dipolar term seem to capture the essence of the behaviours261251415Peg scales as a4, and colloids of the size and particle-solvent density mismatch that is typical in many microscopy experiments have Peg ~ O(1), and thus gravity can often not be neglected.One can minimize the effects of gravity by density matching, by ensuring that the gravitational length, defined by equilibrium colloidal systems with competing interactions on different lengthscales4Other forms of aggregation have been studied extensively in colloidal systemsa\u2009=\u20090.8 and 1.0\u2009\u03bcm-diameter in a nearly density-matched solvent mixture, our system, with Peg ~ O(1) is as strongly Brownian as possible while still allowing the particles to be just large enough for microscopy. In our experiments, there is a 20% difference in the two particle sizes used, which is significant given the a4 dependence of the Peclet number, and much larger than the (less than) 5% polydispersity in particle size. Sedimentation in the presence of gravity has been used to good effect in many colloidal systems to extract information about equations of state; an early example is from Hachisu and TakanoIn this work, we employ a colloidal system to study dipolar clusters. Our system is easily index matched and density matched for confocal microscopy experiments, and we show it to be an excellent candidate for true hard-sphere-plus-dipolar interactions. With colloidal spheres of diameter 2\u03bcm-diameter spheres, as well as a bidisperse system, at several values of a uniaxial AC electric field (see Methods). Snapshots of colloidal sediments at zero field and some selected field strengths are shown in z, i.e. parallel and anti-parallel to the direction of gravity (which points to the left). \u03bcm diameter PMMA colloids in 70:30 decalin/TCE. As the field increases from zero to 1667\u2009V/mm, the sediment goes from fluid-like to fully-formed chains. The middle panel in \u03bcm diameter PMMA colloids in 60:40 decalin/TCE. The field strengths chosen are ones for comparable values of the dipolar strengthExperiments were carried out for two monodisperse colloidal systems with 0.8 and 1\u2009\u03b5p and \u03b5f are the particle and fluid dielectric constant respectively, a is the particle radius, and E0 is the amplitude of the sinusoidal AC electric field; see E0 and \u039b). For comparison, \u03bcm and 1.0\u2009\u03bcm diameter particles  in 50:50 ratio by volume fraction. The particle columns in the bidisperse system are always thicker: this is even clearly the case when only half the particles (by volume fraction) are visible.where z, for all fields for the 0.8\u2009\u03bcm-diameter colloids (mean volume fraction \u03a6\u2009=\u20090.017), obtained from the 3-dimensional image stacks. We see in z) in thin slices dz at height z, parallel to and above the bottom substrate and the local osmotic pressure \u03bcm PMMA particles shows excellent agreement with what is expected for a hard-sphere EOS from the Carnahan-Starling relation, and is in agreement with careful experiments in true bulk (non-microscopy) systems24even at low concentrations. For example, in the work of Li et al.apparent osmotic pressure \u03a0. It is nevertheless a useful quantity because the intra-chain structure is the result of both gravitational force and free thermal exchange of particles when \u039b is O(1). At non-zero fields (i.e. with increasing \u039b), the key observation is that \u03a0 at any given packing fraction \u03a6 is larger than the hard-sphere value, and increases with the field. This is in contrast with experiments , the probability of unassociated two-particle clusters is not zero. On the other hand, as the field is increased, the probability of size 2, 3, and larger chain clusters increases systematically above the zero-field value; this represents real in-plane clustering  of chains .D  as a function of distance z from the substrate. At zero field, the diffusion coefficient D saturates to the bulk value D0\u2009~\u20090.44\u2009\u03bcm2/s when z is greater than 50\u2009\u03bcm. We can utilize the diffusion profiles in D\u2009=\u2009D0(1+KL\u03a6) with KL\u2009=\u2009\u22122.80\u2009\u00b1\u20090.05. This is comparable to the range \u22122.8 to \u22122.9 obtained in experiments by Blees et al.et al.28Evidence of clustering can also be obtained from \u201csedimentation-diffusion\u201d profiles where we measure the lateral (in-plane) self-diffusion coefficient z\u2009=\u200930\u2009\u03bcm in D\u2009=\u20090.42\u2009\u03bcm2/s to 0.27\u03bcm2/s as the field increases from zero to E\u2009=\u20091667\u2009V/mm. At high fields, there is a plateau for z\u2009=\u200928\u2009\u03bcm (position B) where sharp clusters are seen at the highest fields, and in time averages of the movies (bottom panel), where the particle dynamics smear the intensities at lowest fields, but the clusters are still visible at highest fields, suggesting particles stay confined to their respective clusters. At intermediate fields, the time average  is more diffuse than the snapshot , but the clusters are still visible, indicating that the dynamics is also intermediate between free \u201cparticle\u201d and cluster \u201cparticle\u201d  occurs at a dipolar strength \u039b that is close to 1 for both particle sizes . This again suggests that a pure-dielectric dipolar interaction is a dominant contributor to the interactions.Finally, we can assess the magnitude of the dipolar strength at the transition from single particles to clusters. For the chain-cluster (or \u201cstring fluid\u201d) structure, the hard-sphere-plus-dipolar model\u03bcm-scale colloids in a solvent mixture of decahydronapthalene and tetrachloroethylene are hard-sphere-like, density- and refractive-index-matchable, and yet have a strong enough dipolar inter-particle interaction in the presence of an external field.In this work, we have examined Brownian colloidal systems where the equation of state is shown to be in quantitative agreement with the hard-sphere equation of state, even in a thin sediment, and with no use of \u201ceffective\u201d particle sizes. In addition, we find that First, we used sedimentation-diffusion profiles, in zero field, to obtain self-diffusion coefficients as a function of volume fraction \u03a6. The colloidal systems exhibited a decrease in self-diffusion coefficient with increasing \u03a6 that was consistent with bulk experiments for hard-sphere colloids.apparent osmotic pressure at any given volume fraction \u03a6 is found to be greater than the hard-sphere value. It should be noted that, in the presence of clustering, the true local volume fraction is larger than the mean value at a particular height, so the EOS must be taken with a pinch of salt; however, we reiterate the observation in the raw sedimentation profiles that the profiles are more extended with higher fields.Next, we applied external electric fields. The \u201chard-sphere-plus-dipolar\u201d equation of state (EOS) is obtained: the We characterized the onset of field-induced interactions by sedimentation-diffusion profiles. The deviation from zero field profiles occurs at \u039b\u2009~\u20091 see . Stable \u03bcm-diameter particles than for 0.8\u2009\u03bcm-diameter particles, as can be seen even by a visual inspection of The lateral extent of chain-chain clusters increases with the dipolar strength. This is unsurprising, but the nature of the clusters is interesting: the clusters are thicker for 1\u2009For context, two close-to-Brownian colloidal systems used in optical microscopy in which dipolar colloidal interactions have been previously employed are either at Peclet numbers of order 10, or not true hard-sphere systems. In the first system, silica microspheres in aqueous suspensions610Finally, an interesting aspect of the cluster state might have relevance to the low-density networking forming \u201cvoid\u201d phase, which are seen in experiments51415a\u2009=\u200910 and 0.8\u2009\u03bcm), the solvent mixture was adjusted to volume ratios of 60:40 and 70:30 of decalin to TCE respectively /tetrachloroethylene (TCE) solvent mixture; in this case the gravitational length, lg was significantly larger than the sample thickness. The 2a\u2009=\u200910 and 0.8\u2009\u03bcm particles are dyed with 4-methylaminoethylmethacrylate-7-nitrobenzo-2-oxa-1,3-diazol (NBD) and 1,1-dioctadecyl-3,3,3,3-tetramethylindocarbocyanine perchlorate (DiIC18) respectively, and excited by 490\u2009nm (blue) and 561\u2009nm (green) laser lines. In the binary mixture, while the emission from the green excitation comes purely from the 0.8\u2009\u03bcm particles, the emission from the blue excitation also has a small contribution from the 1.0 and 0.8\u2009\u03bcm particles. Shown in The system used is a colloidal suspension of PMMA colloids in a cis-trans-decahydronaphthalene  and tetrachloroethylene (TCE) solvent. Two particle diameters were used in the experiments. For both particle diameters  at 29 frames per second (fps) using a Visitech VT Eye confocal scanner. Slices in z are acquired in 0.15\u2009\u03bcm z-increments. Standard particle-tracking and counting methodsa being identified as connected.For all the electric-field cells, the top and bottom plates were 22\u2009mm square cover slips coated with a transparent conducting layer of indium tin oxide (ITO). These cover slides were glued together  with two sets of 50\u2009fps or 56\u2009fps. From these time series mean-squared displacements versus time are obtained, and fitted to obtain diffusion coefficients. The time of seconds, in colloids with reasonably high local densities, is in the long-time limit.Time series are obtained at several depths How to cite this article: Newman, H. D. and Yethiraj, A. Clusters in sedimentation equilibrium for an experimental hard-sphere-plus-dipolar Brownian colloidal system. Sci. Rep.5, 13572; doi: 10.1038/srep13572 (2015)."}
+{"text": "Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90\u00b0 out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs\u2014a type of system where out-of-unison resonance has not previously been identified\u2014is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems. A large class of resonant interactions may be described as a vibration-in-unison, meaning that the physical displacement coordinates of the system reach their extrema and pass through zero simultaneously. The vibration-in-unison concept was famously used by Rosenberg to give the first definition of a nonlinear normal mode for a conservative system \u20134. In moHere we define out-of-unison resonance as a resonant interaction between two displacement coordinates of a conservative system, where one coordinate reaches an extrema as the other passes through zero, such that they are 90\u00b0 out-of-phase. The best-known physical example of this behaviour is whirling which can occur, for example, in a taut cable . As we sPrevious authors have applied approximate analytical techniques to problems involving weakly nonlinear oscillators e.g. \u201315). The. The15])In this paper, the second-order normal form technique  is used A method for the application of the second-order normal form technique is introduced in \u00a72. Then, in \u00a73, we consider whirling motion in a taut, horizontal, undamped cable, which is a well-known physical example of out-of-unison resonance. In \u00a74, we consider an in-line, conservative, two degree-of-freedom (2-d.f.) oscillator to demonstrate how out-of-unison motion may exist in other nonlinear systems. Furthermore, we demonstrate how, from the analytical descriptions developed, we may determine the values of the physical parameters that yield out-of-unison resonance. Finally, we demonstrate how the out-of-unison motion, seen in the conservative systems, translates to a similar behaviour when the in-line system is forced and damped (and so is non-conservative).2.In this paper, we use the second-order normal form technique to transform the equations of motion of weakly nonlinear systems into sets of time-invariant equations, describing the approximate dynamics. The technique uses the assumption that the nonlinear terms are small; therefore, as the amplitude decreases the results converge to the true solution, but they diverge at higher amplitudes. Here, we consider responses in amplitude and frequency ranges where the nonlinear terms are small, and it is confirmed that the resulting errors are negligible via comparison with results found using numerical continuation. Methods for directly estimating the validity of the normal form results may also be used (e.g. ). The deN d.f. may be writtenM, C and K are the {N\u00d7N} mass, damping and stiffness matrices respectively, Nx and Px are {N\u00d71} vectors of nonlinear terms and forcing amplitudes, respectively, and \u03a9f is the forcing frequency. To find the backbone curves of this system, we consider the unforced and undamped equivalent of equation , where u describes the fundamental response, and h  contains the harmonic contents of q. From this, we can write the transformed equation of motion asun  to be sinusoidal, such that it may be writtenUn, \u03c9rn and \u03d5n are the amplitude, response frequency and the phase of un, respectively. Note that \u03c9rn and \u03c9nn are distinct and represent the fundamental response frequency and linear natural frequency of qn, respectively. The subscripts p and m denote the positive and negative (plus and minus) signs of the complex exponents, respectively.Next we apply the nonlinear near-identity transform Nq is small in relation to other terms\u2014denoted as order \u025b1, where \u025b is a bookkeeping parameter denoting smallness. Furthermore, as the harmonics are small we may also state that h is of order \u025b1. Therefore, we may write \u025bNq(u+\u025bh)\u2248\u025bNq(u) whilst maintaining order \u025b1 accuracy. Substituting equation (Nq(u) allows us to write Nq(u)=[nq]u* where [nq] is an {N\u00d7L} matrix of coefficients and u* is an {L\u00d71} vector of all the unique combinations of unp and unm that exist in Nq(u). The \u2113th element of u* can be written as follows:skp\u2113 and skm\u2113 are the exponents of ukp and ukm in As we are assuming the system to be weakly nonlinear, we assume that equation  into Nq by defi\u2113=0 , the cable exhibits a small sag, breaking the rotational symmetry about x. This leads to a difference in the dynamic behaviour of the corresponding linear modes in the y-direction and in the z-direction\u2014most notably, a difference in the linear natural frequencies  (see equations\u00a0(2.10)), and hence Nu, using Nu=[nu]u*. We may then calculate \u03a9=\u03c9r1=\u03c9r2. The real parts of equations\u00a0(3.4) then lead top=\u00b11 where p=+1 corresponds to responses where u1 and u2 are in-phase or anti-phase, and p=\u22121 corresponds to u1 and u2 being \u00b190\u00b0 out-of-phase.From equations , we may equation ) as3.3aquations  and  can be found by setting U1\u22600 and U2=0, and U1=0 and U2\u22600. These correspond to sets of responses of the system, denoted S1 and S2, which are defined byU1\u22600 and U2\u22600, equations\u00a0(3.5) can be written as follows:\u03c9n2\u2260\u03c9n1 (due to the influence of gravity), p=+1 cannot be a valid solution.Besides the trivial solution where p=\u22121 two additional sets of responses, denoted S3+ and S3\u2212 (or S3\u00b1 when referring to both), are produced. S3\u00b1 have the phase differences (\u03d51\u2212\u03d52)=\u00b1\u03c0/2. Substituting p=\u22121 into equation  at a bifurcation, the point on S3\u00b1 where U2=0 is the point at which the bifurcation occurs. From equations\u00a0(3.10), this point is described byS1, which can be seen from equation \u22123, a Young's Modulus of 2\u00d71011\u2009Pa and a static tension of 200\u2009N. The equations derived by Warnitchai et al. =. All other system parameters are those used in \u00a74c. Owing to the antisymmetric shape of the forcing, only the second underlying linear mode, q2, experiences direct modal forcing. We therefore expect the forced responses to only follow backbone curves with a q2 component (i.e.\u00a0the responses will not follow S1). \u03a9 , against the maximum displacement amplitude of the first physical coordinate, X1. Light-blue lines represent S1, S2 and S3\u00b1 whilst dark-blue lines represent S4\u00b1 . Thin-black and dashed-red lines show the stable and unstable forced responses, respectively. The forced responses that are of interest here (following S4\u00b1) are highlighted with a thick-black line. Other responses in We now compare the backbone curves to the forced and damped responses of this system. The damping and forcing parameters used here are S2. This branch of the forced response . Reducing the forcing and damping would result in the secondary branches collapsing onto S4\u2212 and a decrease in the distortion of the responses.Four sets of points\u2014labelled Ab shows that, aside from the distortion, the linear modal coordinates are out-of-unison for responses on the secondary branches, i.e.\u00a0as one coordinate reaches an extrema the other passes through zero. Figure\u00a09d shows that, in responses B1,2 and D1,2, the physical coordinates are neither in-unison nor out-of-unison, i.e.\u00a0as one coordinate reaches an extrema or zero the other does not. In response C1,2, however, the physical coordinates are out-of-unison (aside from the distortion). As discussed in \u00a74c, this corresponds to the point on the backbone curves where the amplitudes of q1 and q2 are equal (neglecting harmonics). The similarity between the corresponding responses in the forced system and in the backbone curves shows that, for lightly damped systems, the forced response is governed by the backbone curves.Figure\u00a095.In this paper, we have investigated the phenomenon of out-of-unison resonance for systems of weakly nonlinear, coupled oscillators. This phenomenon has physical manifestations, such as whirling in a taut cable, and we have shown how this phenomenon can be modelled in order to describe the dynamic behaviour of the system. A cable was modelled using two sets of modes, one in the vertical and the other in the transverse direction, where the natural frequencies of the corresponding modes are close. The proximity of these natural frequencies allows for resonant interactions between the modes at a 1\u2009:\u20091 ratio and leading to out-of-unison resonance. We then investigated an in-line nonlinear oscillator, with two close linear natural frequencies. Using a backbone curve analysis, we demonstrated that there were specific parameters for this system that led to out-of-unison resonance. In addition to this, we considered the case where the system was forced and lightly damped using continuation methods to track the steady-state periodic motion. As would be expected for a lightly damped system, the forced responses were shown to be governed by the backbone curves defined for the underlying conservative system. Therefore, for this particular system, we were able to show examples of resonances in the forced responses that have similar features to those obtained from studying the underlying conservative system."}
+{"text": "Biomedical researchers often encounter the large-p-small-n situations\u2014a great number of variables are measured/recorded for only a few subjects. The authors propose a fuzzy permutation method to address the multiple testing problem for small sample size studies. The method introduces fuzziness into standard permutation analysis to produce randomized p-values, which are then converted into q-values for false discovery rate controls. Simple algebra shows that the fuzzy permutation method is at least as powerful as the standard permutation method under any alternative. Monte-Carlo simulations show that the proposed method has desirable statistical properties whether the study variables are normally or non-normally distributed. A real dataset is analyzed to illustrate its use. The proposed fuzzy permutation method is recommended for use in the large-p-small-n settings. Biomedical studies nowadays often involve a large number of variables for the study subjects, such as gene expression data analyses and genome-wide association studies, etc.123Benjamini and Hochbergn\u2009<\u2009107n\u2009<\u200910 again, are repeatedly tested in different batchesIn this paper, we are concerned with situations where only very few subjects say, <10) are recruited but a great number of variables  are measured/recorded for each person\u2014the \u2018large-p-small-n\u2019 situations.  are measured for each and every subject in the study. The algorithm of the fuzzy permutation procedure is described below:pj, for j\u2009=\u20091, \u2026, m.Perform a two-sample test, such as Student t test or Wilcoxon rank sum test, and calculate the p-value, j\u2009=\u20091, \u2026 m, where U is a uniform  distribution, and \u03b5 is a very \u2018small\u2019 number (explained later).Add a fuzzy term to the p-value: j\u2009=\u20091, \u2026 m, based on the permuted data.Permute case and control status, and calculate the p-value j\u2009=\u20091, \u2026 m.Add a fuzzy term to the p-value: k times.Repeat Steps 3 and 4 for a total of k permutations, for j\u2009=\u20091, \u2026 m.Calculate a permutation-based p-value, Convert the permutation-based p-values in Step 6 to q-values.Assume that a case-control study recruits a total of \u03b5\u2009\u2192\u20090, so that they will have absolutely no effects on the ranking of the p values when they are not tied. But \u03b5 should not be exactly zero, otherwise ties will not be resolved. In practice, we can let \u03b5 to be slightly larger than the precision of a computer as allowed by a programming language. The limit of resolution for the widely used R code is 10\u221216. Thus one can safely use \u03b5\u2009=\u200910\u221212, which shall be small enough for all data size. S1 Exhibit presents an alternative but equivalent algorithm based on fractional counting.Note that the fuzzy terms to be added are very small numbers. Ideally one should let Theoretical comparisons of fuzzy and standardA function (fuzz.perm) written in R codep1\u2009=\u20090.744222017 (using two-sample Student t test). After adding a fuzzy term  to the p-value p1, we obtain p1\u2009=\u20090.744222017\u2009=\u2009We perform Monte-Carlo simulations to study the performances of the fuzzy permutation procedure. We assume the study variables to follow respectively, the normal distribution, the gamma distribution, the truncated normal distribution and the beta distribution. The total number of variables is set at 100000. For each of the four types of distributions, we consider four scenarios: HS, HW, LS and LW, respectively . The parameters for all these scenarios are detailed in S4 Exhibit. We assume a total sample size of 10 (5 cases and 5 controls).Using the algorithm described above, we calculate the permutation-based p-values using the fuzzy permutation method with Student t test and with Wilcoxon rank sum test, respectively. A total of 5000 permutations were performed for each of the HS, HW, LS and LW alternative hypotheses. [We also simulate the null hypothesis when all the variables are noises and find that the fuzzy permutation p-values are indeed distributed according to a uniform  distribution under the null (results not shown).] For comparison, we also calculate the p-values, using the Student t test (without permutation), the Wilcoxon rank sum test (without permutation), as well as the standard permutation methodWe use Package fdrtool in RThe results when the variables are normally distributed are shown in We reduced the total number of variables to 20000, and the results (S5\u2013S8 Exhibits) are essentially the same as the above The gene expression data of Biswas and PoidingerWe use the six methods in the previous section to analyze this example. A total of 10000 permutations were performed. With FDR controlled at a higher value of 0.09, the fuzzy permutation method with Student t test can now detect a total of 245 significant genes. When FDR controlled at 0.10, the fuzzy permutation method with Student t test and with Wilcoxon rank sum test can even detect more significant genes than the Student t test without permutation.For this example, the three discrete tests are extremely conservative in making significant calls. Not until FDR control value being raised to 0.20 that the standard permutation method with Student t test is beginning to detect 2 significant genes. When the FDR control value is raised to 0.40, the standard permutation method with Student t test can detect 18 significant genes, the Wilcoxon rank sum test without permutation, a total of 10523 significant genes, and the standard permutation method with Wilcoxon rank sum test, still zero significant gene. By contrast, with the same high FDR control value of 0.40, the fuzzy permutation method with Student t test can detect a total of 22745 significant genes, and the fuzzy permutation method with Wilcoxon rank sum test, a total of 22135 significant genes.A study with a very small sample size (such as this example) should best be viewed as a screening study. Any statistically significant gene found in the study is to be subject to further confirmatory testing in studies with larger sample sizes. In consideration of this, many researchers may not opt for more significant genes in the initial screening study; due to limited budget they may work with only a fixed number of genes in subsequent follow-up large sample sized studies. Under this constraint, the fuzzy permutation method is still a better choice; the FDR control value can be set more stringent than other methods to obtain the same requested number of genes. For example, if one wishes to select for further study around 10000 genes from among the total 47322 genes in this example, the FDR control value for Wilcoxon rank sum test without permutation has to be set at 0.40, producing <10000\u2009\u00d7\u20090.4\u2009=\u20094000 false positives (this test was found to be conservative in the simulation study). But for the two fuzzy permutation methods, the FDR control value can be at 0.10, producing ~10000\u2009\u00d7\u20090.1\u2009=\u20091000 false positives (these two tests were found to be well controlled in the simulation study). If one wishes to select no more than 300 genes, the FDR control value for the standard permutation with Student t test will need to be set higher than 0.40 , but for the fuzzy permutation with Student t test, it can be at 0.09 .Previously, Kulinskaya and Lewin also used randomized p-values for FDR controlThe standard permutation methodIn summary, the proposed method introduces fuzziness into standard permutation analysis to produce randomized p-values, which are then converted into q-values for FDR controls. It is a distribution-free method and is recommended for use in the large-p-small-n settings.How to cite this article: Yang, Y.-H. et al. A Fuzzy Permutation Method for False Discovery Rate Control. Sci. Rep.6, 28507; doi: 10.1038/srep28507 (2016)."}
+{"text": "Controlling laser-beam patterns is indispensable in modern technology, where lasers are typically combined with phase-modulating elements such as diffractive optical elements or spatial light modulators. However, the combination of separate elements is not only a challenge for on-chip miniaturisation but also hinders their integration permitting the switchable control of individual modules. Here, we demonstrate the operation of phase-modulating lasers that emit arbitrarily configurable beam patterns without requiring any optical elements or scanning devices. We introduce a phase-modulating resonator in a semiconductor laser, which allows the concurrent realisation of lasing and phase modulation. The fabricated devices are on-chip-sized, making them suitable for integration. We believe this work will provide a breakthrough in various laser applications such as switchable illumination patterns for bio-medical applications, structured illuminations, and even real three-dimensional or highly realistic displays, which cannot be realised with simple combinations of conventional devices or elements. Several recent laser applications, such as maskless lithography11121314The PCSEL is a surface-emitting semiconductor laser that utilises a two-dimensional periodic structure , namely a photonic crystal111213161920222322162222We here introduce an internal holographic modulation of the lattice arrangement in a PCSEL to obtain freely configurable two-dimensional beam patterns. We employ a phase-modulating resonator in which the in-plane position of air holes is slightly shifted from a square lattice in a holographic manner. The arrangement is thus no longer periodic and the modulation must be imposed carefully so as not to compromise lasing. This novel on-chip-sized device, realising both lasing and phase modulation, is henceforth named an \u201cintegrable phase-modulating (iPM) laser\u201d. We demonstrate that the iPM laser, which is small enough for integration, can emit characters, line drawings, multi-spot beams, and even grayscale images.a\u2009=\u2009282\u2009nm (see Methods - \u201cDevice structure\u201d). There is no air hole at the lattice point of the square lattice (point O). Instead, the centre (point C) of each air hole is on the perimeter of a circle of radius d\u2009=\u20090.06a or 0.10a (see Methods - \u201cDevice structure\u201d) centred on O. The rotation angle \u03d5 is chosen according to the designed phase distribution, described in Methods - \u201cPhase distribution of phase-modulating resonator\u201d. This type of modulation is similar to the \u201cdetour-phase\u201d methodWe now focus on the main results. d and rotation angle \u03d5. Therefore, the diffracted light wave propagating in the surface-normal direction has a phase that deviates locally at each point, eventually forming a phase distribution. As a result, a finely modulated wave front is emitted and arbitrary beam patterns can be obtained. As the resonance mechanism is similar to that of PCSELs, the operating wavelength of iPM lasers can be scaleda and by choosing an appropriate active medium, the emission wavelength can be controlled. Furthermore, devices for different wavelengths can be integrated into a single module.As demonstrated above, iPM lasers can successfully emit arbitrarily configured light patterns, implying that phase modulation is fully achieved in our devices. We now turn to the lasing mechanism. 29In conclusion, we have proposed a class of new devices referred to as \u201ciPM lasers\u201d, which comprise a phase-modulating light source, suitable for on-chip integration. These devices involve a structure with concurrent phase-modulation and lasing functionality. We demonstrated the operation of semiconductor iPM lasers that emit characters, line drawings, multi-spot beams, and even grayscale images. These results suggest that iPM lasers can emit arbitrary beam patterns. We also discussed the working mechanism of the devices. We believe that iPM lasers will open a new field of applications which ranging from the small scale integration such as switchable illumination patterns for wearable modulated imaginga was 282\u2009nm for the devices used in d. The smaller d, the lower the threshold current. On the other hand, large values of d diminish the zero-order light  and a beam profiler . Each image was acquired by averaging 8 times. The measurements were carried out under pulsed operation to suppress thermal effects at room temperature (25\u2009\u00b0C). We used a pulsed current source  and a current probe . The pulse width and frequency were 50\u2009ns and 10\u2009kHz, respectively. The driving current was 4\u2009A. To enhance visibility, the central zero-order spot was saturated.The output power was measured using a photodiode  and measuring software  with no ND filter. Starlab parameter settings for the wavelength, range, and averaging interval were 930\u2009nm, \u201cauto\u201d, and 1\u2009s, respectively. The measurements were carried out under pulsed operation at room temperature (25\u2009\u00b0C). We used a pulsed current source  and a current probe . The pulse width and frequency were 50\u2009ns and 10\u2009kHz, respectively. The distance between the device and the photodiode was approximately 3\u2009mm for \u201cTotal\u201d and 150\u2009mm for \u201cZero-order\u201d, respectively. The output power of \u201cPattern (each)\u201d was calculated astotal and Pzero are the measured output powers for \u201cTotal\u201d and \u201cZero-order\u201d, respectively. We calculated Ppattern because the size of the beam pattern at a distance of 150\u2009mm exceeds the measurement area of the photodiode and cannot be measured directly.where PThe lasing spectra were measured using an optical spectrum analyser  through a single-mode fibre. The resolution, sensitivity, and averaging time were 0.02\u2009nm, \u201cHigh 2\u201d, and 1, respectively. The measurements were carried out under pulsed operation at room temperature (25\u2009\u00b0C). We used a pulsed current source  and a current probe . The pulse width and frequency were 50\u2009ns and 10\u2009kHz, respectively. The driving current was 4\u2009A.\u03b8tilt and the azimuthal angle \u03b8rot were transformed into the normalised wavevector  in reciprocal space as follows:The measurement setup consisted of a multi-channel spectrometer , multi-mode optical fibre, lens, and rotating arm see . Emissiokx and ky are the wavevectors parallel to the \u0393-X and \u0393-Y directions, a is the lattice constant, and \u03bb is the wavelength in air. In kx and the vertical axis corresponds to ky. In kx in the \u0393-X direction and where kx, ky, \u03bb). Then, a horizontal cross section through this array at a desired wavelength yields the angular dependence of the device. The colour scale indicates the light intensity.To obtain the angular dependence of the device at the lasing wavelength , the meaWe refer to the method of computer-generated hologramsHow to cite this article: Kurosaka, Y. et al. Phase-modulating lasers toward on-chip integration. Sci. Rep.6, 30138; doi: 10.1038/srep30138 (2016)."}
+{"text": "In other models, the resultant out-degree distribution decays as a poisson or an exponential distribution. However, it has been found that in real complex networks, the out-degree distribution decays as a power-law. In order to obtain out-degree distribution with power-law behavior some models have been proposed. This work introduces a new model that allows to obtain out-degree distributions that decay as a power-law with an exponent in the range from 0 to 1.Many growth models have been published to model the behavior of real complex networks. These models are able to reproduce several of the topological properties of such networks. However, in most of these growth models, the number of outgoing links ( CN) that reproduce some topological properties of real systemsi.e., their out-degree is a constant), as in the model proposed by Barab\u00e1si-Albertet.alCN. For example, in metabolic networksWWWet.al.et.al.i.e. where the average out-degree of nodes is infinite when N \u2192 \u221e.In the literature, there are many growth models for complex networks , we solve s = 1, s = 2, and so on as follows:where Q1(N), we need to consider the initial condition\u2022\u2003\u2003for n0 with no outgoing links, that is N = 1. For this case the quantity Q1(1) of nodes with out-degree s = 1 is zero (Q1(1) = 0). When the node n1 is added (N = 2), the probability for node n1 to have out-degree s = 1 is Q2(N), we need to consider the initial condition\u2022\u2003\u2003for n2, only nodes n0 and n1 are in the network (N = 2) and any of them has s \u2265 2, therefore Q2(2) = 0. When node n2 is added (N = 3), the probability that node n2 has out-degree s = 2 is From the previous results in Normalizing out\u03b3 of the out-degree distribution obtained with the proposed model is only determined by the probability p. That is, the out-degree distribution obtained decays as a power-lawout\u03b3 = p.with exponent p (second rule of the proposed model), the average out-degree of the nodes grows with the network size. To validate this hypothesis, we analytically calculate the average out-degree On the other hand, we can deduce that as a consequence of the random out-degree selection by new nodes with probability 1 \u2212 N of nodes in the network. On the right-hand side of N by a new node. Thus, the term that describes the increment of the average out-degree Solving N \u226b 1), we can approximate As the total number of nodes in the network increases (N \u2192 \u221e.From p = 0.1, p = 0.3, p = 0.6, and p = 0.9. In each simulation, we considered the growth of a directed network from 1 to 104 nodes. N for any value of 0 < p < 1 as stated by N \u2192 \u221e. This contrasts with some large networks that are sparse where the number of edges is much smaller than the maximum possible and the average out-degree increases slowly as the network growsIn order to validate the analytical solutions for the out-degree distribution  and averCN seems to be the result of a set of local processes. We consider that the proposed model in this work can contribute to develop new growth models for directed CN which consider local processes that shape the out-degree of the nodes and, therefore, produce better predictions of the behavior of real CN and thus increases the understanding of these systems.The topological properties of real J.E.G., E.S.N., U.P.N. and J.A.E. designed, performed the research and wrote the manuscript."}
+{"text": "However, such structures are rarely known; moreover, predicting them computationally is no rescue, since single sequence structure prediction is highly unreliable.Identifying sequence-structure motifs common to two RNAs can speed up the comparison of structural RNAs substantially. The core algorithm of the existent approach ExpaRNA solves this problem for The novel algorithm ExpaRNA-P computes exactly matching sequence-structure motifs in entire Boltzmann-distributed structure ensembles of two RNAs; thereby we match and fold RNAs simultaneously, analogous to the well-known \u201csimultaneous alignment and folding\u201d of RNAs. While this implies much higher flexibility compared to ExpaRNA, ExpaRNA-P has the same very low complexity (quadratic in time and space), which is enabled by its novel structure ensemble-based sparsification. Furthermore, we devise a generalized chaining algorithm to compute compatible subsets of ExpaRNA-P\u2019s sequence-structure motifs. Resulting in the very fast RNA alignment approach ExpLoc-P, we utilize the best chain as anchor constraints for the sequence-structure alignment tool LocARNA. ExpLoc-P is benchmarked in several variants and versus state-of-the-art approaches. In particular, we formally introduce and evaluate strict and relaxed variants of the problem; the latter makes the approach sensitive to compensatory mutations. Across a benchmark set of typical non-coding RNAs, ExpLoc-P has similar accuracy to LocARNA but is four times faster (in both variants), while it achieves a speed-up over 30-fold for the longest benchmark sequences (\u2248400nt). Finally, different ExpLoc-P variants enable tailoring of the method to specific application scenarios. ExpaRNA-P and ExpLoc-P are distributed as part of the LocARNA package. The source code is freely available at http://www.bioinf.uni-freiburg.de/Software/ExpaRNA-P.ExpaRNA-P\u2019s novel ensemble-based sparsification reduces its complexity to quadratic time and space. Thereby, ExpaRNA-P significantly speeds up sequence-structure alignment while maintaining the alignment quality. Different ExpaRNA-P variants support a wide range of applications.The online version of this article (doi:10.1186/s12859-014-0404-0) contains supplementary material, which is available to authorized users. Genome-wide high-throughput transcriptomics has revealed evidence for massive transcription of eukaryotic genomes, vastly exceeding translation to proteins -3. Ultimde novo RNA-gene finders qrna  denote the probability of the structure S in the Boltzmann ensemble of A  denotes the base pair probability of , which is defined as i,j)|A] is the probability that a random structure S, drawn from the Boltzmann ensemble of A, contains the base pair .For a sequence ble of A . Pr, Pr[\u2227|A] denotes the joint probability of the stacked base pairs  and . Such probabilities are computed in slight extension of McCaskill\u2019s algorithm  denotes for i<k<j the joint probability that a structure of X contains the base pair and the unpaired base k such that  is the parent of k.Pr  denotes for i<i\u2032<j\u2032<j the joint probability that a structure of X contains the base pairs and  such that  is the parent of .Pr \u2265\u03b81 and Pr[|B]\u2265\u03b81Pr[|A]\u2265\u03b82Pr[k\u2208loop|B]\u2265\u03b82,and Pr\u2265\u03b83Pr[\u2208loop|B]\u2265\u03b83,and Pr by McCaskill\u2019s algorithm [k \u2208 loop|X] and Pr[ \u2208 loop|X] for X\u2208{A,B}. For this purpose, we introduce \u2013 on top of the McCaskill matrices \u2013 the auxiliary matrix Fundamentally, our novel sparsification technique relies on the joint probabilities of Def. 4. For sequences lgorithm . In thismentclass2pt{minimImportantly, all these probabilities are efficiently precomputed independently for each sequence. Hence, e.g. in clustering scenarios, where all pairs from a set of sequences need to be matched, this preprocessing needs to be done only once for each sequence and not for all quadratically many pairs.Figure Fundamental to our approach, all matrices and evaluations in the recursions are sparse, i.e. only entries and cases are considered where the probabilities of elements pass the respective probability thresholds cf. Def. 5). Corresponding constraints are given in the recursion equations \u2013 this is also illustrated in Figure . CorrespD score the best EPM enclosed by each base pair match ij \u223c kl, i.e. D denotes the best score of a significant EPM Ai..j and Bk..l with The matrix entries ij \u223c kl, we determine the (score of the) best or forms a (connected) significant EPM only together with the closing base pair match ij \u223c kl. The first case is covered by the single matrix L, whereas the latter case requires three matrices GA, GAB, and LR. By and large, for deriving one D-entry one starts matching from the left using L. Potentially, one introduces a gap using matrices GA and GAB and continues using matrix LR to match the part that is only connected to the right end of ij \u223c kl.Inside of the base pair match i \u223c k of the base pair match, i.e.  is empty or contains i+1 \u223c k+1. Concretely, Lijkl is such a score, where GA and GAB. In the case of j\u2032 but matches l\u2032; for l\u2032 and potentially does not match j\u2032. Finally, LRijkl is the best sum of scores of two significant EPMs i \u223c k and the second contains j\u2032 \u223c l\u2032. Intuitively, the two EPMs are separated by a gap; formally:  or .In more detail, first we determine the best score of a significant EPM L, we check whether there is a sequence match (second case) or a structure match (third case); otherwise, we assign \u2212\u221e (first case). LR is analogous to L, only allowing to close a gap left of the structure or sequence match. For this purpose, we introduce an auxiliary matrix H, which does not need to be stored. The gap itself, computed in GA and GAB, allows skipping an arbitrary number of positions in both sequences. The recursion structure ensures that such a gap is introduced at most once per loop match and sequence. To avoid ambiguity, the recursion enforces to first skip positions in A (using GA) and after that positions in B (using GAB); furthermore we enforce a gap in the matchings computed via LR by its initialization.Our recursion equations Figure  show theD in increasing order with respect to their size so that when computing some D, any D with i<i\u2032<j\u2032<j and k<k\u2032<l\u2032<l is already computed.We compute entries of D), we finally compute the matrix F. The entries F, for 0\u2264j\u2032\u2264n and 0\u2264l\u2032\u2264m, denote the maximum score of a significant EPM of j\u2032,l\u2032), i.e. with F is almost identical to the recursion for L, except for the first case, which is 0 instead of \u2212\u221e, since the EPMs in F can start at any point . Also, since the matched base pairs in EPMs of F are external (i.e. they are not enclosed by some other base pair of the EPM), we do not perform checks for the second and third condition of significant EPMs (Def. 5).Since EPMs are not necessarily closed by a base pair match . LRijkl=\u2212\u221e (first matrix entry)l\u2032>k (first matrix row)j\u2032>i (first matrix column)LR matrix with \u2212\u221e, we keep matchings represented by LR and L distinct .By initializing the F is initialized by F=F=0 for all j\u2032,l\u2032.The final matrix GA and GAB matrices.) For strict EPMs this is decided independently of the other traced strict EPMs. It suffices to check whether the strict EPM can be extended into the gap matrices, i.e. whether a sequence or structure match is possible at the borders of the gap matrices.For enumerating only maximal EPMs during suboptimal traceback, we take special care that EPMs cannot be extended at the left or right end of gaps  that satisfy To enumerate all maximal EPMs, we start such tracebacks only from entries  is a maximal strict EPM of A and B, iff Let  is not maximal for A and B . \u201c \u21d0\u201d: Let \u201c \u21d2\u201d: Let  is not maximal for A and B. Then, there is a strict EPM Assume i\u2264j\u2032<j and k\u2264l\u2032<l. However in this case, while clearly the parent of j\u2032 \u223c l\u2032 in  is \u03c8, there is a parent of j\u2032 \u223c l\u2032 in \u03c8 . This contradicts  and Consequently, to satisfy By the same argument, the forward direction holds for relaxed EPMs. Therefore, we enumerate all maximal relaxed EPMss by restricting the traceback in the same way. However, since the backward direction does not hold generally, this procedure can enumerate non-maximal relaxed EPMs. In practice, we observe this very rarely; consequently, while redundant relaxed EPMs could be removed explicitly, we let the chaining procedure handle those EPMs.\u03b81,\u03b82, and \u03b83. Consequently, we compute all DP matrices in only O(n2) time and space. We compute matrices LRijkl only for base pairs  and  that are significant |A]\u2265\u03b81 and Pr[|B]\u2265\u03b81). Furthermore, we compute only relevant entries of these matrices.ExpaRNA-P\u2019s efficiency depends fundamentally on the sparsity of the DP matrices, which we leverage through fixed thresholds j\u2032 is a candidate of  in sequence A if it is either a significant single-stranded position within , i.e. Pr[j\u2032 \u2208 loop|A]\u2265\u03b82, or contained in a significant helix of , i.e. Pr[ \u2208 loop|A]\u2265\u03b83 for some i\u2032. Analogously, we define candidates l\u2032 of  in sequence B. |B]\u2265\u03b82 or Pr[ \u2208 loop|B]\u2265\u03b83 for some k\u2032).This is best illustrated by the notion of candidates; each O(n2) entries LRijkl such that j\u2032 is a candidate of  and l\u2032 is a candidate of . Consequently, ExpaRNA-P has quadratic time and space complexity.There are only Proof sketch: By definition, only candidates j\u2032 or l\u2032 can be part of a significant EPM as defined in Def. 5; otherwise, we assign \u2212\u221e to Lijkl and LRijkl. Furthermore, in the latter case, we neither store nor compute the values for \u03b81 reduces the number of base pairs to a constant number of base pairs per sequence position; in total, quadratically many base pairs pass the filter. The thresholds on joint probabilities guarantee that each sequence position is candidate of only constantly many base pairs. In consequence, each position is considered only a constant number of times during the entire computation; this directly results in quadratic time complexity.  matrix for each hole and takes O(Hn2) time, where H is total number of holes with H\u226an2. In contrast to ExpaRNA, there may exist more than one EPM ending at each sequence position pair, i.e. there is no one-to-one correspondence between EPMs and EPM\u2019s end positions. This is why each matrix requires additional steps in the order of the number of input EPMs E in ExpaRNA-P\u2019s chaining; the complexity of the generalized chaining algorithm is O(H\u00b7(n2+E)). Since in the most general case, when we enumerate all suboptimal EPMs up to a maximal difference to the optimal score, E\u2208O(n2) is not guaranteed, we implement in addition several ways to control the number of EPMs. For example, ExpaRNA-P allows setting an ad hoc limit on this number. Furthermore, we suggest a heuristic strategy: for each sequence position pair, keep only the best EPM ending there. Consequently, typical use cases of ExpaRNA-P maintain the chaining complexity of ExpaRNA, i.e. O(Hn2).Chaining selects a non-crossing and non-overlapping subset of EPMs. Our algorithm generalizes the chaining of ExpaRNA . The chai \u223c k, considers only the optimal EPM ending at that match. Our tool supports two ways to control the EPM enumeration by the suboptimal traceback: either by defining the maximum score difference to the optimal score or the maximum number of EPMs.We implemented ExpaRNA-P and the chaining algorithm in C++. In particular, we implemented two versions of the traceback: the suboptimal traceback and a heuristic version that, for each match In order to assess the performance of ExpaRNA-P, we designed the following pipeline: In a first step we compute the significant EPMs with ExpaRNA-P and use the chaining algorithm to extract from these EPMs an optimal non-overlapping and non-crossing subset. Then we compute a sequence structure alignment that includes all matches of the chained EPMs. For this purpose, we utilize the EPMs as anchor constraints for LocARNA. Consequently, LocARNA runs much faster, since each anchor reduces the alignment space. In correspondence with the analogous idea ExpLoc , which uWe performed all benchmarks over the pairwise alignment instances of the BRAliBase 2.1 benchmark set ,45. To mheuristic traceback with exact matchesheuristic traceback with inexact structure matchessuboptimal traceback with exact matchessuboptimal traceback with inexact structure matchessuboptimal traceback with inexact structure matches and the additional second filter stepWe study five ExpLoc-P variants, where we generate anchor constraints respectively by \u03b81=\u03b82=\u03b83=0.01 to predict less false positives. Furthermore, we enumerated EPMs that have a score of at least 90 and fix the maximal number of traced EPMs in the suboptimal traceback to 100. The scoring \u2013 as defined in Eq. str_mm to \u221210 for structure mismatches in inexact modes. Furthermore we set \u03b11=1,\u03b12=5 and \u03b13=5 in order to favor structured regions. In addition to SPS and runtime, we computed the coverage for each benchmark instance \u2013 consisting of sequences A and B. For this purpose, we define coverage as the fraction of nucleotides that are matched by the best chain of EPMs In particular, we compare exact modes 1,3), which follow the strict EPM definition, and inexact modes 2,4,5), which allow mismatches at structure positions (relaxed EPMs.) The score parameters were selected ad-hoc without parameter learning; in particular, we set the cutoff probabilities to restrictive values ,3, which,4,5, whiFigure In Table We benchmarked three existing approaches: LocARNA, ExpLoc , and RAFTable The quality drop of RAF alignments at low sequence identities is strongly reminiscent of pure sequence alignment methods. Thus, we conjecture that the specific use of sequence-based heuristics by RAF, while guaranteeing sequence alignment like run-time behavior, compromises RAF\u2019s use for \u2018hard\u2019 RNA alignment instances that require structure-based alignment methods.Furthermore, we investigated the dependency of the lengths of the input sequences on the speedup  that \u2013 without being more efficient \u2013 are much less flexible, since they require a priori known or unreliably predicted structure.Due to its novel ensemble-based sparsification, the algorithm ExpaRNA-P has only a very low (quadratic) time and space complexity, equalling sequence alignment. This sparsification technique is particularly relevant, since similar techniques can likely be applied to other RNA analysis methods.We have developed two major variants of this method; one requires strict matches in all positions of an EPM (strict EPMs), the other relaxes this  to allow mismatches at structural positions. The latter supports compensatory mutations, which are highly relevant in RNA structure analysis in general.Our benchmarks study EPMs as anchor constraints to speed up RNA structure alignments . EPMs from structure ensembles have turned out to be substantially more reliable than EPMs from fixed structures. At comparable speed ups, this results in increased quality. Most importantly, the novel approach keeps up the alignment quality even for sequences of low identity, which is ultimately decisive for structure alignment. In striking contrast, the alignment quality of the similarly fast alignment tool RAF breaks down \u2013 very much like pure sequence alignment.We have implemented rigorous suboptimal traceback, which provides extensive control of the set of enumerated EPMs. For example, this level of control is required in the analysis of structural variants common to the RNAs. In addition, we have developed a heuristic traceback, which performs almost indistinguishable in our benchmark. Being much faster than the rigorous method, it offers the best speed-quality balance in such settings.Finally, we conjecture that EPM-based anchor constraints can be combined advantageously with other RNA alignment tools such as RAF. While for LocARNA the constraints yield a considerable speedup, the combination with RAF has the potential to improve RAF\u2019s poor alignment quality for low sequence similarity."}
+{"text": "Er) are known inevitable. In this mechanism, whether the first derivative of Er (shear) or the second derivative of Er (curvature) works most is decisive in determining the class of nontrivial solutions (which describe the barrier structure). Here we report the experimental identification of the essential role of the Er-curvature on the ETB formation, for the first time, based on the high-spatiotemporal resolution spectroscopic measurement. We found the decisive importance of Er-curvature on ETB formation during ELM-free phase, but there is only a low correlation with the Er-shear value at the peak of normalized ion temperature gradient. Furthermore, in the ELMing phase, the effect of curvature is also quantified in terms of the relationship between pedestal width and thickness of the layer of inhomogeneous Er. This is the fundamental basis to understand the structure of transport barriers in fusion plasmas.The turbulent structure formation, where strongly-inhomogeneous turbulence and global electromagnetic fields are self-organized, is a fundamental mechanism that governs the evolution of high-temperature plasmas in the universe and laboratory  of the H-mode in the toroidal plasmas). The roles of inhomogeneities of radial electric field ( Er, should play an important role in the mechanism of the L-H transition347910Er and significant reduction in a plasma turbulence level. It is conventionally believed that the shear of E\u00d7B drift velocity (i.e. first derivative of Er) is the main parameter that is responsible for suppression of turbulence5121314i.e. second derivative of Er) in suppressing the turbulence and turbulent transport has also been pointed out16171819Er-shear and curvature effects on the ETB formation, simultaneously, due to lack of diagnostic that can withstand up to the second derivative estimation. Whether the first derivative or the second derivative works most in turbulence suppression is decisive in determining of class of nontrivial solutions  by the drift wave (DW) turbulence  the enhanced dissipation of DW fluctuations and (2) the convergence of DW energy into coherent axial vector fields, respectively. It is also important for understanding the formation of transport barriers in toroidal confinement devices. For instance, the \u201ccurvature transition\u201d, a kind of the internal transport barriersEr curvature. The trapping of turbulence intensity in the trough of Er\u200925Er on the ETBs formation, for the first time, based on the high-spatiotemporal resolution spectroscopic measurement2728Er-shear and -curvature) effects on ETBs formation. It is shown that both the shear and curvature of Er work, but the role of curvature is inevitable in the formation of transport barrier. This discovery has a fundamental impact on our understanding of structure formation in magnetized plasmas, in addition to a substantial impact on our predictability of performance of future burning plasma experiments, since the over-all performance of toroidal plasma fusion device critically depends on the property of the ETB. For instance, the uncertainty in the fusion power amplification factor of ITER was estimated as about factor 10, and the main origin for which is the variance in the prediction of the width of the ETBSince the discovery in ASDEX tokamakThe model of turbulence intensity, in the presence of inhomogeneous radial electric field, was assessed based on the model formula for the effect of electric field shear51231where the parameters are as follows:I is the turbulence intensity , \u03c1i is the ion gyro-radius, k is a typical wavenumber for the plasma turbulence, Vd is the diamagnetic velocity (Vd\u2009\u2261\u2009T/eaB), e: elementary charge, a: characteristic mean-scalelength, B: total magnetic field), B\u03b8), and I0 is the mean intensity in the limit of Z\u2009=\u20090. The term Z1 and Z2 denote the effects of Er-shear  as Z2 has its sign dependence.Er, the temperature gradient is enhanced. If one employs the gyroBohm dependence of local thermal diffusivity, which is proportional to the temperature gradient and turbulent intensity, the heat flux is proportional to the turbulence intensity multiplied by (\u2207T)2. For fixed heat flux, one can evaluate the enhancement degree of the ion temperature gradient in terms of Z value as;In association with the turbulence reduction by the inhomogeneous k\u03c1i\u2009~\u20090.1\u2009\u2013\u20090.3\u20091, Z2, and Z are investigated. When the turbulent transport is reduced to the level of neoclassical transport, further reduction of turbulence level is less effective in increasing the ion temperature gradient.Here, the Er on the ETBs formation, Er in the transport barrier, so that their role on ETBs formation can be analyzed separately. This discharge shows a long period of secular increase in the edge ion temperature gradient after a \u201csoft\u201d L-H transition having a longer time-scale (a few hundred milliseconds) in comparison with a conventional \u201chard\u201d one having shorter time-scale (e.g. a few milliseconds or less) seen in many tokamaks. This is followed by a violent phase, where the edge plasma bifurcates between a strong-Er and a weak-Er state , until it finally settles to the conventional H-mode. The time period of 0\u2009<\u2009\u0394tL-H\u2009<\u20090.3\u2009s in Er.In examining the effect of non-uniformity of L-H\u2009<\u20090.3\u2009s), we found that theZ is from Z2, and Z1 remains small during the growth of the temperature gradient. An important caveat to this discussion is that there is only a low correlation between Z1 and r\u2009\u2261\u2009r0 as illustrated in r\u2009=\u2009r0 becomes large as the Z2 value at r\u2009=\u2009r0 increases. This shows the relative importance of nonzero second derivative effect r\u2009=\u2009r0 . It should be noted that the location at which the r\u2009=\u2009r0) is closely related to that at which the Er (and/or its curvature) has a local peak value as shown in Er-shear has almost zero value. Indeed, this fact is confirmed by a quantitative comparison for various pedestal structures obtained in JT-60U H-mode plasmas with different angular momentum injections (e.g. co- and counter-NBI plus perpendicular-NBI heating)Looking at the slow L-H transition phase (0\u2009<\u2009\u0394tn\u2009=\u20090) seems to be associated with the multi-stage Er-transitions during ELM-free H-phase as shown in fGAM\u2009\u2248\u2009Cs/2\u03c0R) is likely to that of the predicted frequency for Geodesic Acoustic Mode (GAM) known as a high-frequency blanch of Zonal flow (ZF), this observation can also support the hypothesis of ZF (and/or Er-curvature) suppression of turbulence even in the H-mode plasmas.It is interesting that a uniform toroidal MHD oscillation (i.e. \u0394tL-H\u2009=\u20090.0\u20130.32\u2009s) there is a good correlation between the r\u2009=\u2009r0. The enhancement of the gradient (by the factor of a few times) appears in the range of k\u03c1i\u2009~\u20090.1\u20130.3.The quantitative comparison between the temperature gradient and inhomogeneity effect of electric field is illustrated in Z shows a more complex (i.e. non-linear) behaviour after  \u0394tL-H\u2009=\u20090.32\u2009s, where \u0394tL-H\u2009=\u20090.32\u20130.36\u2009s, a fast (within milliseconds) and strong drop in \u0394tL-H\u2009=\u20090.36\u2009s, the Er structure from strong-Er to weak-Er are visible. These changes are similar to those at \u0394tL-H\u2009=\u20090.42\u2009s, but the changes are in opposite direction. However, this does not seem to be the same as the H-L backward transition commonly associated with the L-mode but, rather, this phase (\u0394tL-H\u2009=\u20090.36\u20130.42\u2009s) seems to be similar to the phase \u0394tL-H\u2009=\u20090.0\u20130.32\u2009s. After \u0394tL-H\u2009=\u20090.42\u2009s, the plasma changes again, with characteristics similar to the phase \u0394tL-H\u2009=\u20090.32\u20130.36\u2009s. This phase continues until the first ELM onset at \u0394tL-H\u2009=\u20090.49\u2009s.The relationship between  be seen , while tr\u2009=\u2009r0 is likely to be non-linear, especially for the later ELM-free H-phase (during \u0394tL-H\u2009=\u20090.32\u20130.36\u2009s and \u0394tL-H\u2009=\u20090.42\u20130.49\u2009s), requires further studies: Let us explain a hypothesis to understand this stimulating observation. Before the jump of electric field occurs, the suppression of turbulence is strong enough so that the ion thermal transport is reduced to the level of the neoclassical transport. The abrupt bifurcations in the edge Er to larger values , suppress the turbulence as was shown inr\u2009=\u2009r0 seems to be almost linear for the slow L-H transition phase having weak Er (\u0394tL-H\u2009=\u20090.0\u20130.32\u2009s), including another phase having weak Er (\u0394tL-H\u2009=\u20090.36\u20130.42\u2009s), as expected from The question why the dependence of Er layer. These data are determined from multiple and reproducible Edge Localized Modes (ELMs) cycles for co- and counter-NBI discharges, mapping them onto a single-time basis, as defined by the time of the measurement relative to the ELMs for improved statistics to assess the temporal behavior (in particular inter-ELM phase) of the measurementsExperimental data presented in R-RSEP\u2009\u2265\u2009\u22120.08\u2009m for co-NBI case, while it becomes narrower up to R-RSEP\u2009\u2265\u2009\u22120.06\u2009m for counter-NBI case. Looking at 1 layer (i.e. impact of the R-RSEP\u2009\u2265\u2009\u22120.07\u2009m (co-NBI) and \u22120.05\u2009m (counter-NBI), respectively, indicating about 1\u2009cm narrower than that of the pedestal width. Furthermore, there is Z2 layer of the negative value (contributing turbulence enhancement) around R-RSEP\u2009\u2248\u2009\u22120.04\u2009m in the counter-NBI case.As shown in Er (and/or its curvature) had a local peak values for both co- and counter-NBI cases as shown in solid line on Er-shear had a local peak value shift inwards from the radius where the It should be noted that we found a strong correlation between the location at which the r\u2009=\u2009r0 defined for discharge E049219) shows a similar nature to that obtained even in the ELMing phase (at the time of ELM-onset) for various locations (discharges E049228 and E049229).As a result, we found the Z-profile had almost non-zero value in the pedestal region  contains both Er-shear and Er-curvature effects, while the Er-curvature effect is dominant contributor for Z value in the former case .This result is not self-evident, since the e.g.e.g. around the pedestal-top) and H-mode pedestal  results in an up-shift of the curve in It is also noted that the improved energy confinement region  in forming the ETBs. Recalling that the non-uniform Er effect presented in this letter should have 2nd order effect of O(Er2), the Z profile is localized strongly around the location, at which the In summary, we revisited the studies of paradigm of shear suppression of turbulence as the mechanism for the ETBs formation with an improved diagnostic for the edge radial electric field from the high resolution measurement on JT-60U tokamak, examining the effects of both shear and curvature, comparing with nd order effect, leading a new prediction of the pedestal width scaling . It should be noted that the thickness in the E\u2009\u00d7\u2009Bshear layer was roughly scaled by a few times of the Indeed, this effect may be able to exude toward the pedestal top (and/or bottom) due to its 2P\u2009=\u20093\u20133.5\u2009m, the plasma minor radius, aP\u2009=\u20090.6\u20131.1\u2009m and the maximum toroidal magnetic field, BT\u2009\u2264\u20094\u2009T at R\u2009=\u20093.32\u2009m. We performed the NBI heating experiments by comparing the external momentum input directions between co-, balanced- and counter-NBI cases under a matched plasma shape condition. The plasma current, IP, was 1.6\u2009MA, and the toroidal magnetic field, BT, was 3.9\u2009T. The corresponding safety factor at the 95% flux surfaces, q95, was thus 4.2. The elongation, \u03ba, and triangularity, \u03b4, were 1.47 and 0.36, respectively, and the total plasma volume was 57\u2009m3.The JT-60U tokamak is a single null divertor tokamak device having the plasma major radius, Rr structure at the pedestal region, we measured the pressure gradient, and plasma velocity perpendicular to the magnetic field, and the Er was evaluated by the radial force balance equation.In the study of the JT-60U tokamak for the fiscal year (FY) 2007\u20132008 experimental campaign, we measured the radial profiles for the density, temperature, and poloidal/toroidal plasma flows of fully stripped carbon impurity ions by means of the Charge eXchange Recombination Spectroscopy (CXRS) diagnostic method with fast time resolution (up to 400\u2009Hz) at 59 spatial points . With regard for determining the EHow to cite this article: Kamiya, K. et al. Experimental validation of non-uniformity effect of the radial electric field on the edge transport barrier formation in JT-60U H-mode plasmas. Sci. Rep.6, 30585; doi: 10.1038/srep30585 (2016)."}
+{"text": "With the prevalence of Social Networks (SNs) and services, plenty of trust models for Trustworthy Service Recommendation (TSR) in Service-oriented SNs (S-SNs) have been proposed. The reputation-based schemes usually do not contain user preferences and are vulnerable to unfair rating attacks. Meanwhile, the local trust-based schemes generally have low reliability or even fail to work when the trust path is too long or does not exist. Thus it is beneficial to integrate them for TSR in S-SNs. This work improves the state-of-the-art Combining Global and Local Trust (CGLT) scheme and proposes a novel Integrating Reputation and Local Trust (IRLT) model which mainly includes four modules, namely Service Recommendation Interface (SRI) module, Local Trust-based Trust Evaluation (LTTE) module, Reputation-based Trust Evaluation (RTE) module and Aggregation Trust Evaluation (ATE) module. Besides, a synthetic S-SN based on the famous Advogato dataset is deployed and the well-known Discount Cumulative Gain (DCG) metric is employed to measure the service recommendation performance of our IRLT model with comparing to that of the excellent CGLT model. The results illustrate that our IRLT model is slightly superior to the CGLT model in honest environment and significantly outperforms the CGLT model in terms of the robustness against unfair rating attacks. Moreover, the integration of SNs and services has become a trend and formed a new research area known as S-SN . A larger number means a stronger trust relationship and vice versa.TR: The set of trust values among service consumers, i.e. TR = {TR}, where 1 \u2264 i, i\u2032 \u2264 M and i \u2260 i\u2032.TS(i): The set of trustworthy service witnesses in the view of SC(i), i.e. TS(i) = {SC(i\u2032)}, where 1 \u2264 i, i\u2032 \u2264 M and service witness SC(i\u2032) is trustworthy from the perspective of SC(i).SS(j): The service witness set of SR(j), i.e. SS(j) = {SC(i\u2032)}, where 1 \u2264 i\u2032 \u2264 M, 1 \u2264 j \u2264 N and SC(i\u2032) has consumed and rated for SR(j).FS(j): The fair service witness set of SR(j), i.e. FS(j) = {SC(i\u2032)} \u2282 SS(j), where 1 \u2264 i\u2032 \u2264 M, 1 \u2264 j \u2264 N and SC(i\u2032) has consumed and given a fair rating to SR(j).RT: The rating value of SC(i) to SR(j) on service aspect a, where 1 \u2264 i \u2264 M, 1 \u2264 j \u2264 N and 1 \u2264 a \u2264 A. It is represented as an integer between 0 and 4, indicating very dissatisfied, dissatisfied, general, satisfied and very satisfied, respectively.RT: The rating vector of SC(i) to SR(j), i.e. RT = , RT, \u2026, RT), where 1 \u2264 i \u2264 M and 1 \u2264 j \u2264 N.RT: The set of rating vectors, i.e. RT = {RT}, where 1 \u2264 i \u2264 M and 1 \u2264 j \u2264 N.PR: The preference weight value of SC(i) on service aspect a, where 1 \u2264 i \u2264 M, 1 \u2264 a \u2264 A and PR(i): The preference weight vector of SC(i), i.e. PR(i) = , PR, \u2026, PR), where 1 \u2264 i \u2264 M.PR: The set of preference weight vectors, i.e. PR = {PR(i)}, where 1 \u2264 i \u2264 M.RS: The synthetical rating score of SC(i) to SR(j), i.e. i \u2264 M and 1 \u2264 j \u2264 N.SN: The social network which is composed of all the service consumers and the trust relationships among them, i.e. SN = .BN: The bipartite network which is made up of all the service consumers and services as well as the service ratings and preference weights, i.e. BN = .For illustration purposes, we give the following formal representations of elements in S-SNs:SN and BN. To balance computational complexity and evaluation performance, the trust ) and service rating ) are represented as different forms. Specifically, the former is denoted as a real number in order to reduce the computational complexity of LTTE module, while the latter is denoted as a vector including the rating values on various service aspects with different user preference weights so as to improve the evaluation performance of RTE module.S-SN can be viewed as a combination of As we mentioned earlier, this module mainly takes charge of selecting out all the candidate services which satisfy the functional requirements of the active service requester. To this end, we propose a multi-QoS based filtering method and a simple example is shown in SC(1) submits a request which contains its multi-QoS requirements , every service in SR = {SR(1), SR(2), \u2026, SR(5)} is checked whether meets the multi-QoS needs of SC(1) or not. We can easily find that SR(1), SR(2) and SR(3) do not satisfy the \u201cFunction\u201d, \u201cPrice\u201d and \u201cResponse time\u201d requirements of SC(1), respectively, so they are filtered out. While both SR(4) and SR(5) meet the multi-QoS needs of SC(1), thus they are candidate services and are then sent to RTE and LTTE modules for trust evaluations.When When evaluating the local trust value of certain candidate service, only the service ratings from trustworthy service witnesses are considered, while the opinions of the other service witnesses are ignored. For the purpose of identifying all the trustworthy service witnesses, we propose an efficient MLT algorithm (i.e. Algorithm 1) to obtain the maximum local trust values of all the service witnesses.H) is considered untrustworthy. Suppose SC(p0)\u2192SC(p1)\u2192\u2026\u2192SC(pt) is the optimal trust path from SC(i) to SC(i\u2032) (where SC(p0) = SC(i) and SC(pt) = SC(i\u2032)), then the maximum local trust value MT (i.e. MT[i\u2032] in Algorithm 1) of SC(i\u2032) in the perspective of SC(i) can be derived from  (e.g. 0.1). We can find that both MT and LT range from 0 to 1. From Algorithm 1, Eqs , H, SC(i), \u03b1; /* Social network, maximum allowable hop, active service requester and trust decay parameter, respectively. */Output: MT; /* Maximum local trust values of all the service consumers in SC from the perspective of SC(i). */VS \u21d0 \u2300; /* The visited service consumer set which is initialized to an empty set. */1: MT, HP; /* The arrays of maximum local trust values and corresponding hops from SC(i), respectively. */2: MT[i] \u21d0 1;3: HP[i] \u21d0 0;4: for each SC(i\u2032) \u2208 SC \u2212 {SC(i)} do5: ifTR > 0 then6: \u2003MT[i\u2032] \u21d0 TR;7: \u2003\u2003HP[i\u2032] \u21d0 1;8: \u2003\u2003else9: \u2003MT[i\u2032] \u21d0 0;10: \u2003\u2003HP[i\u2032] \u21d0 \u221e;11: \u2003\u2003end if12: \u2003end for13: SC(i) to VS;14: Add while |VS| < |SC| do15: SC(i\u2032) \u21d0 Find the service consumer with the maximum local trust value in SC \u2212 VS;16: \u2003ifHP[i\u2032] < Hthen17: \u2003for each SC(i\u2032\u2032) \u2208 SC \u2212 VS \u2212 {SC(i\u2032)} do18: \u2003\u2003ifTR > 0 and then19: \u2003\u2003\u200320: \u2003\u2003\u2003\u2003HP[i\u2032\u2032] \u21d0 HP[i\u2032] + 1;21: \u2003\u2003\u2003\u2003end if22: \u2003\u2003\u2003end for23: \u2003\u2003end if24: \u2003SC(i\u2032) to VS;25: \u2003Add end while26: returnMT;27: www.tmall.com) for example, it is a well-known e-commerce website and the service rating consists of five grades, namely very dissatisfied, dissatisfied, general, satisfied and very satisfied, which are denoted as 1 \u223c 5, respectively. It also considers various service aspects, namely service performance, service attitude, delivery speed and logistics speed. Though it is intuitive and beneficial to potential service consumers, it is vulnerable to unfair rating attacks and neither user preference nor rating number is taken into account when calculating the reputation value of certain service.Next, we present how to calculate the reputation values of candidate services. In many reputation systems of existing e-commerce websites, the reputation value of centain service is merely a simple average of all the rating values given to it. Taking Tmall  and local trust value LT exceeds system threshold \u03bb (e.g. 0.4), then RS is filtered out as it is considered unfair (i.e. service witness SC(i\u2032)\u2209FS(j)) and vise versa. Furthermore, we also take the following two weights into consideration:SC(i), the rating score RS from service witness SC(i\u2032) is more credible if SC(i) and SC(i\u2032) have more similar preferences and vice versa. Thus we define the user preference weight GP based on the weighted Euclidean distance between PR(i) and PR(i\u2032)  (e.g. 0.1). We can easily find that GP, GN(j) and RP range from 0 to 1 due to the normalization processing. The above calculation process (i.e. Eqs (Where i.e. Eqs  \u223c 5)) i) i\u03bd is aFT of SR(j) in the sight of SC(i) can be gained fromAs mentioned earlier, this module is mainly in charge of integrating the evaluation results of LTTE and RTE modules by weighted summation and obtaining the final trust values of all the candidate services. Specifically, the final trust value \u03c9 is a parameter which ranges from 0 to 1 and controls the weights of LTTE and RTE modules in aggregation trust evaluation, thus we can easily find that the range of FT is also . Afterwards, this module can generate the top-k (where k is a parameter) recommendation list according to the final trust values of candidate services and sends it to SC(i) via SRI module. A simple example is shown in Where SR(1)\u223cSR(5) are five candidate services with diverse local trust and reputation values . Their final trust values (i.e. FT) and top-k recommendation lists (i.e. RL) change with \u03c9 as illustrated in \u03c9 equals to 0 or 1, FT is equivalent to RP or LT, respectively. In other cases, FT falls between LT and RP. If two candidate services have the same FT, the service with larger LT should be prior to the other one in the top-k recommendation list  is more credible than reputation-based evaluation (RP) in the view of service requester).To illustrate the performance of our IRLT model, we present a series of experiments and analysis in this section. In concrete terms, we deploy a synthetic S-SN based on the famous Advogato dataset, and employ the well-known DCG metric to measure the service recommendation performance of our IRLT model through comparing to the state-of-the-art CGLT model in honest environment and malicious environment with unfair rating attacks.In this work, the comprehensive experiments are implemented through Java language on a Linux server with 2.83GHz \u00d7 4 CPU and 8G RAM. Specifically, we deploy a synthetic S-SN which contains a social network SN and a bipartite network BN. In SN part, we adopt Advogato which is a famous trust network dataset consisting of 6541 nodes (i.e. service consumers) and 51127 directed edges (i.e. trust relationships among service consumers) as well as containing three kinds of different trust relationships . In BN part, we assume that there exist 50 candidate services and each service has 100 random service witnesses in SN. Each service witness provides a service rating to corresponding service and the preference weights of service consumers in SN are randomly generated. The parameters in experiments are set as illustrated in k recommendation list in terms of local trust value (i.e. LT), reputation value (i.e. RP) and final trust value (i.e. FT), respectively.In this part, we mainly illustrate the service recommendation performance of our IRLT model in honest environment  through comparing to the state-of-the-art CGLT model. As with the outstanding CGLT scheme, we adopt the well-known DCG metric to measure the service recommendation performance. Specifically, we define three kinds of DCG metrics (i.e. Eqs  \u223c 9)) t) t9)) tok is the size of recommendation list, and LT), RP) and FT) are the local trust value, reputation value and final trust value of the s-th service in the top-k recommendation list (in the opinion of SC(i)), respectively. In each experiment, we randomly choose a service requester from SN and generate the top-k recommendation list for it through utilizing the CGLT and our IRLT schemes, respectively. Afterwards, we can calculate three kinds of DCG metric values in the CGLT and our IRLT schemes when k takes different values (i.e. 1 \u223c 50), respectively. The experiment is repeated 5000 times and the average outputs are illustrated in Where k, and three kinds of DCG metric values in our IRLT model are slightly higher than those in the CGLT model, respectively. This indicates that the top-k services obtained from our IRLT model have higher local trust values, reputation values and final trust values than those derived from the CGLT model, thus our IRLT model has a little better service recommendation quality than the state-of-the-art CGLT model in honest environment.From Ballot stuffing: Malicious service providers collude with service consumers to raise their own trust values.Bad mouthing: Malicious service providers collude with service consumers to slander their honest competitors.In this part, we focus on analyzing and validating the robustness of our IRLT model against the following two kinds of unfair rating attacks , 29:BalAs we know, these two kinds of unfair ratings will bring risk to service requesters, thus an excellent TSR scheme should be able to detect and filter them out. In the outstanding CGLT model, two kinds of trust evaluations are separately made without consideration of filtering unfair ratings. While in our IRLT model, we notice that the strange service witnesses have a higher likelihood of colluding with malicious service providers than the trustworthy ones and the service ratings from the former are more likely to be unfair, thus we filter the service ratings in RTE module by utilizing the results from LTTE module. As a result, our IRLT should have stronger robustness against these two kinds of unfair rating attacks. Next we validate the above analysis through three series of experiments, in which the service ratings from trustworthy service witnesses are assumed to be fair and 50 candidate services are composed of 25 honest services and 25 malicious services.k recommendation list in each case, respectively. The experiment is repeated 5000 times and the average outputs of DCG-FT metric are shown in In this part, we mainly validate the robustness of our IRLT model against ballot stuffing attack through comparing to the outstanding CGLT model. In the ballot stuffing attack, the collusive service consumers provide high rating scores to malicious services in spite of their poor performances. In each experiment, we vary the Percentage of Collusive Service Consumers (PCSC) and calculate the three kinds of metric values of malicious services in the top-In the ideal case (i.e. PCSC = 0%, see k recommendation list is the lower, the better. Therefore, the above experiment and analysis show that our IRLT model greatly outperforms the state-of-the-art CGLT model in terms of the robustness against ballot stuffing attack.It is obvious that malicious services mean risk for service requesters, thus the total DCG-FT metric value of malicious services in the top-k recommendation list in each case, respectively. The experiment is also repeated 5000 times and the average outputs of DCG-FT metric are shown in Next, we compare the robustness of our IRLT model against bad mouthing attack with that of the CGLT model. In the bad mouthing attack, the collusive service consumers provide low rating scores to honest services in spite of their good performances. In each experiment, we vary PCSC and calculate the three kinds of metric values of honest services in the top-In the ideal case (i.e. PCSC = 0%, see k recommendation list is the higher, the better. As a result, the above experiment and analysis demonstrate that our IRLT model is vastly superior to the outstanding CGLT model in terms of the robustness against bad mouthing attack.It is well known that honest services will bring benefit to service requesters, thus the total DCG-FT metric value of honest services in the top-k recommendation list in each case, respectively. The experiment is also repeated 5000 times and the average results of DCG-FT metric are shown in In this part, we verify the recommendation performance of our IRLT model in malicious environment with both ballot stuffing and bad mouthing attacks, in which the collusive service consumers not only provide high rating scores to malicious services but also provide low ones to honest services. In each experiment, we vary PCSC and calculate the three kinds of metric values of honest services and malicious services in the top-In the ideal case (i.e. PCSC = 0%, see k recommendation list is the higher, the better, and that of malicious services is the lower, the better. Therefore, the above experiment and analysis show that our IRLT model has better recommendation performance than the excellent CGLT model in malicious environment with both ballot stuffing and bad mouthing attacks.As we mentioned earlier, honest services will bring benefit and malicious services mean risk for service requesters, so the total DCG-FT metric value of honest services in the top-k recommendation list. Furthermore, we have deployed a synthetic S-SN based on the famous Advogato dataset and adopted the well-known DCG metric to measure the service recommendation performance of our IRLT model through comparing to that of the state-of-the-art CGLT model. The results of experiments and analysis show that our IRLT model has slightly better service recommendation quality than the CGLT model in honest environment and greatly outperforms the CGLT model in terms of the robustness against two kinds of unfair rating attacks.In this work, we have proposed a novel IRLT model, which includes four modules, for TSR in S-SNs. In SRI module, a multi-QoS based filtering method is proposed to select out all the candidate services. In LTTE module, a MLT evaluation algorithm is presented to identify all the trustworthy service witnesses and only their service ratings are considered. In RTE module, the opinions of all the service witnesses are considered through filtering by the results of LTTE module to ease unfair rating attacks. Besides, the preference similarity and rating number are regarded as two important weights. In ATE module, the outputs of RTE and LTTE modules are integrated by weighted summation to calculate the finial trust values of candidate services as well as generate the top-"}
+{"text": "X be a compact metric space and X endowed with the levelwise topology, we proved that its g-fuzzification is turbulent or erratic if the given system f is turbulent or erratic correspondingly and f is g-fuzzification is Let  X be a compact metric space and f be a continuous self-map. We denote by X endowed with the levelwise topology and we define f:g-fuzzification introduced in Kupka  and its g-fuzzification. See more details in Kupka  be a compact metric space and C(X) denote all continuous functions. X with the Hausdorff metric Let (u on the space X is a function u and u (shortly: supp(u)) .Likewise, LetU,\u00a0Vbe two subsets ofandThen:Kupka : LetU,\u00a0VBefore we present the elegant results, we need to introduce some basic definitions of chaotic behavior explored in this paper.f is a turbulent function if there are disjoint nonempty closed subsets X such that:Rom\u00e1n-Flores et\u00a0al. : Let \\doRom\u00e1n-Flores et\u00a0al. : A map \\f is chaotic in the sense of Block and Coppel (in short: B-C chaos) if and only if its iterates is turbulent, i.e., there exists J,\u00a0K of X such thatRom\u00e1n-Flores et\u00a0al. : Let \\doIt should be remarkable that the erratic property is stronger than B-C chaos.f is expansive if and only if there exists a real constant Let f is In this case we claim that lco-Cano .e(U) is given here.To prove the turbulent and erratic properties, firstly, a theorem on LetUbe closed subset ofXandandThen,It can be proved by the mathematical induction.When Assume that the theorem is true for in Kupka , we haveLikewise, we can achieve the similar result on LetUbe closed subset ofXandandThen,Here, we make a point that n and Mu  for moref. These conclusions can be listed as follows:f and Rom\u00e1n-Flores et\u00a0al.  exploreds et\u00a0al.  present Ifis a turbulent function, thenis a turbulent function.f is turbulent, there exists nonempty and closed Since e(U), clearly, e(U) and e(V) are two disjoint nonempty closed subsets of By the definition of entclass1pt{minimaLetbe erratic, then,is a erratic function.f is erratic, there exists a nonempty closed subset e(U) is nonempty closed subset of Since mentclass2pt{minimLetbe erratic, then, is a B-C chaos function.e(U), it can be verified with e(U) at least is perfect for the two theorems to make sense.Because Next, we shall discuss the Letbe a continuous function andThenfisexpansive if and only ifisexpansive.f is  and f and In this paper, exploiting the turbulent and erratic properties, we develop the ideas of Rom\u00e1n-Flores et\u00a0al.  and pres"}
+{"text": "We also explore the matroidal background of our results and show that the matroids induced by the row independence of the orbit matrices of the symmetric frameworks are isomorphic to gain sparsity matroids defined on the quotient graph of the framework, whose edges are labeled by elements of the corresponding symmetry group. The proofs are based on new Henneberg type inductive constructions of the gain graphs that correspond to the bases of the matroids in question, which can also be seen as symmetry preserving graph operations in the original graph.We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral symmetry of order 2 We think of a bar-and-joint framework as a collection of fixed-length bars (corresponding to the edges of G) which are connected at their ends by universal joints (corresponding to the vertices of G). Frameworks can be used to model various structures with pairwise distance constraints and whose rigidity property is of particular interest in applications ranging from civil engineering  is connected. A connected component of F is the edge set of a connected component of G[F]. C(F) denotes the partition of F into connected components of F, and let F is called a forest if it contains no cycle and called a tree if it is a connected forest. F is called a spanning tree of a graph F is a tree with For simplicity, some properties of edge-induced subgraphs will be associated with the corresponding edge sets as follows. Let walk in G is a sequence W and W and the starting vertex of W and W followed by closed if the starting vertex and the end vertex coincide.Let It is sometimes convenient to regard the empty set as a subgroup of a group. Let In this section we shall review some basic properties of gain graphs. We refer the reader to , 31, 32 gain graphgain functionG is, in some sense, arbitrary, and is used only as a reference orientation: the orientation of each edge may be changed, provided that we also modify g in one direction then it has gain G and the underlying undirected graph and use notations introduced in Sect.\u00a0Let mentclass2pt{minimW be a walk in gain of W is defined as W, and for a backward edge Let v. Similarly, for v and using only edges of X, where Let X relative to v is defined as Let e, e.g., , p.\u00a088 fswitching operation atvwithg changes the gain function E(G) as follows.E(G) is equivalent to another gain function E(G) if For The following two facts are fundamental  if E(G) is balanced (resp.\u00a0cyclic), respectively.In the same way, an edge subset X, in analogy with the fact that the cycle space of a graph is spanned by fundamental cycles. For a connected T of the edge induced graph G[X]. By Proposition\u00a0W by v to T. Then observe Proposition\u00a0T of G[X], suppose that (i)X is unbalanced if and only if there is an edge in (ii)X is cyclic if and only if all gains of For a connected The following technical lemmas will be used in the proof of our main theorem.X and Y be connected edge subsets such that the graph X and Y are balanced, then If X is balanced and Y is cyclic, then If X,\u00a0Y are cyclic and If Let T in G[X], G[Y], and Since the graph X and Y are balanced, Lemma\u00a0If X is balanced, then every label in Y is cyclic. This implies (2).If X,\u00a0Y are cyclic and X and Y are cyclic, Lemma\u00a0If X and Y be connected balanced edge subsets. If the number of connected components of the graph Let T of G[X]. Since the number of connected components of Y into three subsets We take a spanning tree X and Y are balanced, we have Y is balanced. Therefore By Proposition\u00a0E be a finite set. A function submodular if monotone if induces a matroid on E, where Let Dilworth truncation of For a monotone submodular function ids, see  for moreNow we consider the union of two matroids induced by monotone submodular functions G. The 2-dimensional generic rigidity matroid is the one induced by As an example, consider the union of two copies of the graphic matroid of a graph k and l with G is called -sparse if k,\u00a0l)-count matroid on G. If l times. See e.g. . It is known that, in the generic 2-rigidity matroid, an independent set F with Suppose further that see e.g. ). \\documLet Without loss of generality, assume Let Let If =3, then  implies X and Y are connected by Lemma\u00a0Therefore we assume Y is balanced and, again, Lemma\u00a0(Case 1) If =2, then  implies ities of  and 15)\\document(Case 2) If 0-3c1 by . By \\docThis completes the proof. X and Y be Let e are contained in V(X), implying X or Y is not cyclic, then we have Since X and Y are cyclic, and they are connected by Lemma\u00a0T in G[Y] such that G[X]. By Proposition\u00a0Y is balanced. Since We hence assume that E. We shall also characterize the rank function of this matroid.We are ready to prove that the family of E. Then E. The rank of a set Let For a partition F. Consider the family J. Since each edge F and Let F is a maximal subset of J with Based on sparsity matroid of The matroid which was introduced and denoted by G has a vertex of degree at most 3 if and only if G is not 4-regular. Thus we shall take special care with 4-regular We now present a constructive characterization of maximum admissible if the resulting graph is Before looking at 4-regular graphs and vertices of degree four, we consider the 0-extension, 1-extension, and loop-1-extension operations. Recall that the corresponding inverse operations are called reductions. A reduction is Let v of degree 2 or 3, the 0-reduction, loop-1-reduction, or some of the 1-reductions at v are admissible if Conversely, for any vertex The proof of the first claim is exactly the same as the proof of Lemma\u00a0v of degree three, we just need to observe that each circuit of v. To see that some reduction is admissible at a vertex extensions and loop-2-extensions for constructing 4-regular Besides 0-extensions, 1-extensions and loop-1-extensions, we shall introduce 2-extension, we take two existing edges v. More precisely, a 2-extension removes e and f, inserts a new vertex v with four new edges, v for each In a 2-$f=v_3,v_$$\\end{doloop-2-extensions, we remove an existing edge v, a new loop l at v and two new edges, v for each e is a loop or not, we have two cases as shown in Fig.\u00a0In a The following lemma shows that these operations preserve G by a 2-extension or a loop-2-extension is Let e and f and the new edges by e to f to G since Suppose that In the same manner, it can be easily checked that a loop-2-extension also preserves v and two incoming non-loop edges u to w with gain We shall define the inverse moves of these operations. Recall that, for a vertex v be a vertex of degree four, not incident to a loop, and v, assuming that all of them are oriented to v. The 2-reduction (at v) deletes v and adds one of reduction atvthroughandv and adds Let v be a vertex of degree four, incident to a loop l, and v, assuming that all of them are oriented to v. The loop-2-reduction (at v) deletes v and adds Let admissible if the resulting graph is A 2-reduction or a loop-2-reduction is said to be near-cyclic 4-regular graphs.Our main theorem asserts that these operations are sufficient to construct all 4-regular trivial graphs, fancy triangles, and fancy hats. A trivial graph is a The first group consists of three types of special fancy triangle is a A hat is a graph obtained from fancy hat is a A double cyclen vertices by replacing each edge by two parallel edges as shown in Fig.\u00a0k of the underlying dihedral group The second group consists of near-cyclic graphs, which, intuitively speaking, are the near-cyclic if there is an edge e such that The third group consists of The following lemma shows how to construct near-cyclic graphs.e having a gain in Let F is cyclic, either (i) Suppose that F is connected, and clearly the endvertices of e are contained in V(F). Moreover, every cycle in e has a gain not contained in e is not in By Lemma\u00a0base graph if it is a trivial graph, a fancy triangle, a fancy hat, or a near-cyclic graph.We are ready to state our constructive characterization of 4-regular Let We have proved that these operations preserve Combining Theorem\u00a0Let k is odd, in which case every The theorems can be strengthened if Then, at least one of Let r along a line. Suppose that Since r, then consider k has to be even which is a contradiction. Thus If C, then consider rC are non-identity and reflections, if they generate a cyclic group, then k. If Let v be a vertex, and we denote the edges incident to v by v, Let v through G, it is easy to check that We first perform the 2-reduction at G is unbalanced, a and v with Suppose that v. In each reduction, the resulting underlying graph is We now consider the remaining two possible 2-reductions at To see that Combining Theorem\u00a0Let k. See Fig.\u00a0k.Lemma\u00a0In this section we discuss our combinatorial characterization of symmetry-forced infinitesimal rigidity with dihedral symmetry. We begin with a necessary condition based on Lemma\u00a0H,\u00a0p) be a generic H,\u00a0p) is symmetry-forced infinitesimally rigid, then the quotient gain graph contains a spanning maximum Let H and p. By Theorem\u00a0Let Since k is even.In Sect.\u00a0Our goal of this subsection is to prove the following characterization of symmetry-forced infinitesimal rigidity.H,\u00a0p) be a generic H,\u00a0p) is symmetry-forced infinitesimally rigid if and only if the quotient gain graph contains a spanning maximum Let Necessity follows from Lemma\u00a0p appropriately. (i) will be solved in Lemma\u00a0k in these lemmas.By Theorem\u00a0k-gon, which consists of k-fold rotations around the origin and reflections along (fixed) lines. For a line L through the origin, we denote by L, that is, the line orthogonal to L and through the origin. We first note an elementary fact from geometry.In the rest of this section, we identify g is the reflection along a line L, then If g is a rotation, then If Let Let v be the vertex. Take p(v) does not lie on reflection lines L in (Case 1) Suppose that p randomly and computing the rank of p deterministically).(Case 2) Suppose that ,p) (see  for finde such that (Case 3) Suppose that By Theorem\u00a0L, in which case there is a m does not satisfy the equation associated with L. Then \u27e9=0,  becomes\\The next two lemmas show that loop-2-extensions and 2-extensions preserve the independence.Let p is G by a loop-2-extension, by removing an existing edge e, adding a new vertex v with new non-loop edges l incident to v . Suppose that R. Since R is orthogonal to L, we deduce that We take a point h is a rotation, and l is a zero vector in d is a vector linearly independent from L contains the origin, and d. Thus, Case (2). Suppose that d. To see the perturbation more precisely, for each l in l in t. This in turn implies that To avoid the situation where This completes the proof of the lemma. Let p is G by a 2-extension, by removing two existing edges e and f and adding a new vertex v with new non-loop edges v  No three points among L and (ii) If The first claim follows from the proof of Claim\u00a0L and For the second claim, suppose that p implies that L and In case (i), the C. Moreover, since e and f are loops attached to a vertex  of Fig.\u00a0G.In case (ii), L is the line through Now, L and (ii-1) If k-gon inscribing C. Since p is generic, if L, k-gon, and hence (ii-2) If L is the line through L can have any slope, by moving L and p, then L and In case (iii), L is the line through L and p is generic.In case (iv), C be the circle whose center is the origin and which passes through Let C. We shall relocate L and q and q or p is generic, L and (iv-1) Suppose that C as shown in Fig.\u00a0C. We shall relocate L is the tangent of C at q and L and q is the antipodal point of L and through the origin. When p is generic, L is not parallel to any reflection lines in (iv-2) Suppose that see Fig.\u00a0b. Then, Recall that tradicts . \\documeFollowing the statement of Claim\u00a0L and q be the intersection of L and v. Then, e and f. Consider the rows associated with q is on L, e in L and (Case 1) Suppose that L and q be any point on L with v. Then, the orbit rigidity matrix is described as follows:q is on the line L, L and q is on L, but not on (Case 2) Suppose that Combining Theorem\u00a0k. Therefore, we obtain the following statement even for a dihedral group k: for a generic H,\u00a0p) with even k and a free action H,\u00a0p) is symmetry-forced infinitesimally rigid if the quotient gain graph can be constructed from a disjoint union of base graphs by 0-extensions, 1-extensions, loop-1-extensions, 2-extensions and loop-2-extensions. However, as we have seen in Fig.\u00a0Notice that all the lemmas given in the last subsection are independent of the parity of i and For r and Then, for any n is odd.Let x- and y-coordinates, respectively. For each i, we subtract the first row from the second row and then multiply the first row by an appropriate scalar. We then have, for each n is even. Let See Fig.\u00a0essential if it is In this section we prove Theorem\u00a0Any essential u,\u00a0v) from u to v is simply denoted by uv, and a For simplicity, in the subsequent discussion we omit gain functions special vertices (C2)G is not cyclic.The following fundamental properties of 4-regular graphs will be frequently used.G is connected, then G is (i)G is not 4-regular and condition (C1) is satisfied, or(ii)G is 4-regular and conditions (C1) and (C2) are satisfied.If G is not connected, then G is Let G is connected, we have G is 4-regular and If the maximum degree is at most 4, almost near-cyclic if there are two incident edges e and f such that Thus, to prove Theorem\u00a0v be a vertex in G that is not incident to a loop. Let v, and suppose that In particular, G is almost near-cyclic.Let v with G is not cyclic, we must have Let special if it is incident with a loop or two parallel classes of edges with The following technical lemma is one of the key observations. A vertex in a 4-regular graph is called v be a vertex in G that is not special, and v. If G is near-cyclic.v is a cut-vertex in G and Let For simplicity, we denote We claim that there are an equivalent gain function G is neither cyclic nor near-cyclic, we have To see this, first observe that if Note that Let us consider F such that V(F) contains the endvertices of s and t be the endvertices of F contains a path from s to t that does not pass through v is special in G, contradicting the assumption of the lemma.Case 1: If (C1) is violated, then v is not a cut-vertex. Note that, since C, whose gain is included in s and t be the endvertices of P from s to a vertex in V(C). We consider a closed walk P starting at s, then goes around C, and comes back to s through s and t. The concatenation of s with v is a cut-vertex in G.Case 2: We next consider the case when (C2) is violated in G, Suppose that special graph. Special graphs are classified into the following three classes n vertices by replacing each edge by two parallel copies; n vertices, each of which is incident to a loop; n vertices by replacing each edge by two parallel copies and adding one loop to each endvertex of the path.Recall that a vertex is said to be special if it is incident with a loop or two parallel classes of edges. A graph which consists of only special vertices is called a mentclasspt{minimaLet Since l. The resulting graph is G except for the loop l is in G is essential.Suppose that the underlying graph is l. The resulting Suppose that the underlying graph is G except for the loop l is included in a cyclic subgroup G is essential.If G is balanced, and G turns out to be a fancy triangle, contradicting the fact that G is essential. It can be easily observed that The next lemma solves the case when the graph is not 2-connected.G is not 2-connected. Then a 2-reduction is admissible at some vertex.Let G is not equal to G has a cut-vertex v which is not special. We show that a 2-reduction at v is admissible. Note that G. Let v, all of them are directed to v. From the 2-edge-connectivity of G, we can assume, without loss of generality, that the endvertices of By Lemma\u00a0v through v is not special. Since the endvertices of F such that V(F) contains both endvertices of Consider the 2-reduction at v. Suppose that v through G is not near-cyclic since G is essential). Therefore, if G has a special vertex not incident to a loop.Thus, in the subsequent discussion, we may focus on 2-connected graphs. The next lemma solves the case when G has a special vertex not incident to a loop. Then, G has a vertex at which a 2-reduction is admissible.Let w be a special vertex not incident to a loop. By definition of special vertices, w is incident to two parallel classes of edges. Since G contains two adjacent vertices u and v such that v is not special and u is special and not incident to a loop . Depending on the size of Let u by v to u and u. We perform the 2-reduction at u through u, then Let us denote the edges incident to v through G is not near-cyclic and v is neither a cut-vertex nor a special vertex, Lemma\u00a0v is admissible. Let G is almost near-cyclic.The next lemma solves the case when G is almost near-cyclic. Then a 2-reduction or a loop-2-reduction is admissible at some vertex in G.Let G is almost near-cyclic, there are two edges v and Since v is not special. Then, since v is not a cut-vertex, a 2-reduction is admissible at v by Lemma\u00a0v is special. If v is not incident to a loop, then Lemma\u00a0v is incident to a loop.Suppose that v with e not incident to v. This implies that if we remove v from G, the resulting graph is cyclic. In other words, it suffices to consider the case when Suppose that both v. Let v, where G is essential. Therefore, v adds the edge We hence assume that By using Lemma\u00a0G is not essentially 4-edge-connected. Then, G has a vertex at which a 2-reduction or a loop-2-reduction is admissible.Let G is 2-edge-connected and is not essentially 4-edge-connected, there exists a subset X of V for which G is not B(X) contains a vertex v not incident to a loop, where B(X) denotes a set of vertices of X adjacent to some vertices of v is not a cut-vertex. Hence, denoting the four edges incident to v by X while Since v is a vertex of degree 3 in v is admissible in v in Note that v. Let F is 2-edge-connected if F for which V(F) contains both endvertices of F such that V(F) contains both endvertices of F, denoted by f, is incident to X and f turns out to be a cut-vertex of G, contradicting the 2-connectivity of G. Thus, We now consider adding G is almost near-cyclic, and we can apply Lemma\u00a0v. If G has a vertex v with The final special case is when G has a vertex v with Let v is special, Lemma\u00a0If v is not special, then there are three parallel edges between v and a neighbor of v. By the 4-regularity, if G is not essentially-4-edge-connected, and thus Lemma\u00a0If G is equal to the graph  and  is not admissible. Then there is an edge subset (i)F is balanced tight with (ii)F is balanced tight with (iii)F is sub-tight with Suppose that the 2-reduction through  and ) if F satisfies (i) or (ii) of Lemma\u00a0F is called an obstacle of type 2 if F satisfies (iii).Since the first and the second cases of the statement of Lemma\u00a0v, through  and , through  and , and through  and . By Lemma\u00a0X,\u00a0Y,\u00a0Z. We now investigate properties of these obstacles.As noted above, we have three possible ways for a 2-reduction at We begin with a property of type 2 obstacles.X is an obstacle of type 2 for the 2-reduction through  and . Then, the following holds for X:There is an equivalent gain function Suppose that By definition, v with g if necessary, we may assume that G. Thus, Since In the same manner we also have the following technical lemma.X and Y be obstacles for the 2-reduction through  and  and through  and , respectively. Suppose that X is type 2 and Let X is balanced and v, we may assume that Since By the definition of the obstacles (whether type 1 or type 2), The following lemmas describe different relations among obstacles.X and Y be obstacles for the 2-reduction through  and  and through  and , respectively. If Let Suppose for a contradiction that X and Y are of type 1, G.(Case 1) If both X is type 2. By definition of obstacles (whether type 1 or type 2), (Case 2) Let us consider the case when X and Y be obstacles for the 2-reductions through  and  and through  and , respectively. If Let G, each vertex of N(v) has degree three in X and Y are type 1 with a.Without loss of generality, we assume X is type 2, then Y is type 1, then c or d.If X and Y are type 2, then d. If both X, Y, Z be obstacles for the 2-reductions through  and , through  and , and through  and , respectively. If there is no hat subgraph containing the star of v, then Let X,\u00a0Y and Z are not singleton sets, then the lemma follows from Lemma\u00a0Note that a type 2 obstacle consists of more than one edge. If two of X is also a singleton set. Let (Case 1) Let us first consider the case when v is included in a hat subgraph. Indeed, if denoting without loss of generality X,\u00a0Y and Z are obstacles, we have In case (I), the star of G, as a balanced In case (II), without loss of generality, we assume X is type 1 or type 2.(Case 2) Next, we consider the case when X is type 2, then g. Since Y and Z are obstacles, we have g. In other words, G.If X is type 1. Without loss of generality we assume ac or bd and ad or bc, it suffices to consider the following two cases by symmetry: (i)The remaining case is when a as In subcase (i), E. Therefore, this case does not occur and the proof is complete. In subcase (ii), notice that, obstacles for a 2-reduction at a vertex v with v denotes a vertex with v. Without loss of generality, we assume that there are parallel edges v and a, and we denote In this subsection we shall investigate v. In each case, there exists an obstacle if the operation is not admissible. The proof of the following claim is identical to that of Lemma\u00a0We again have three possible ways for a 2-reduction at (i)F is balanced tight with (ii)F is balanced tight with (iii)F is sub-tight with Suppose that the 2-reduction through bv,\u00a0vc), we encounter an even simpler situation.For the 2-reduction through bv,\u00a0vc) is not admissible. Then there is a balanced tight set Suppose that the 2-reduction through G is almost near-cyclic, which contradicts our assumption on G. If F with Note that the type of an obstacle as in the previous subsection. Lemma\u00a0bv,\u00a0vc). The next two lemmas are counterparts of Lemmas\u00a0According to Lemmas\u00a0X and Y be obstacles for distinct 2-reductions at v. If X is type 2 and Let X and Y be obstacles for distinct 2-reductions at v. Then, if Let To prove the counterpart of Lemma\u00a0Z is an obstacle of type 1 for the 2-reduction through bv,\u00a0vc). Then, there is an equivalent gain function Suppose that v with X be an obstacle of type 2 for the 2-reduction through Let Let a and b, a,\u00a0b,\u00a0c. This means that X contains an edge linking from a to c, denoted by Suppose that Therefore, X, Y, Z be obstacles for the 2-reductions through bv,\u00a0vc), respectively. Then, Let We split the proof into two cases depending on whether a type 1 obstacle exists for the 2-reduction through X is type 2. By Lemma\u00a0a since b or c.(Case 1) Suppose that there is no type 1 obstacle for the 2-reduction through In a symmetric manner, we are done in the case when a type 1 obstacle does not exist for the 2-reduction through X and Y are type 1. If X or Y is 2-connected, and hence a as a to b. Also, by Lemma\u00a0a to c or (ii) a to b  We now consider the case when both see Fig.\u00a0.Fig. 16PE in the underlying In case (i), we have b as Z is type 1 and v,\u00a0a and b have degree four. So, if c becomes a cut-vertex, contradicting the 2-connectivity of G. On the other hand, if G becomes the graph shown in Fig.\u00a0G is almost near-cyclic, a contradiction. Let us consider case (ii). If v. Then we have three obstacles X, Y and Z for the three possible 2-reductions at v. Suppose further that the star of v is not contained in a hat subgraph. Then, by Lemmas\u00a0Suppose that no 2-reduction is admissible at G is essentially 4-edge-connected. We then have G.If Therefore we haveX and Y are connected and balanced, Lemma\u00a0If the number of connected components in Thus the number of connected components in Hence by  and 22)\\documenttight by .X and Y are type 1, then X or Y is type 2, and Lemmas\u00a0X or Y is type 2) we obtain G, If both  Also by  and \\docG is near cyclic, as u is incident to a loop and two non-loop edges by 4-regularity. Observe that removing this loop and one of the two non-loop edges results in a cyclic graph. This means that G is almost near-cyclic.If G turns out to be almost near-cyclic, which contradicts the assumption on G. This completes the proof. In both cases We are now ready to prove Theorem\u00a0G is 2-connected, essentially 4-edge-connected, not special, and not almost near-cyclic. Also, by Lemma\u00a0v with By Lemmas\u00a0G is not special, G has a vertex v that is not incident to a loop. Then v is admissible or the star of v is contained in a hat subgraph H. Suppose the latter holds. We denote the vertices of H by H (and hence v). Since H is balanced, we may assume that all labels in H are identity. Moreover, since G is not a fancy hat, we may assume that Since H.We prove that some 2-reduction at We claim that If G. Consequently, the 2-reduction at Consequently, without loss of generality, we may assume that k. This can be done by computing the rank of the quotient graphs in the corresponding matroids The main results of this paper Theorems\u00a0 and 8.2 E is independent if and only if (i) G is -sparse and (ii) every nonempty balanced subset k,\u00a0l)-sparsity for any pair of integers k,\u00a0l, see e.g. [G satisfies (ii) if and only if every minimally non--sparse graph -circuit or an M-circuit) is unbalanced. Suppose that G satisfies (i) and consider one of its M-components, i.e. a subgraph H of G induced by a connected component of the -sparsity matroid of G (see [M-components). Each -circuit is a subgraph of some M-component, so we may deal with them separately. The key observation is that within H the complements of the -circuits are pairwise edge-disjoint. Since the M-components are pairwise edge-disjoint, this shows that the number of -circuits in G is O(n) and they can easily be enumerated. Then it remains to test whether each of these circuits is unbalanced, which can be done by switching and using Lemma\u00a0Let entclass1pt{minimasee e.g. , so checentclass1pt{minimaf G (see  for moreE is independent if and only if (i) G is -sparse and (ii) every cyclic subset G satisfies (ii) if and only if every minimally non--sparse graph -circuit) is non-cyclic. Suppose that G satisfies (i). Then it is easy to see that these circuits are edge-disjoint, which shows that we have O(n) circuits to check. As above, they can easily be enumerated, and we can use switching and Lemma\u00a0G satisfies (ii) as well. As above, it remains to check whether every -circuit is unbalanced. Let H be an M-component of G. It is not hard to see that Next consider"}
+{"text": "Our study shows that the above results can be used not only to measure the electric-field vector and its spatial distribution in some electrostatic devices, such as the Stark decelerator, Stark velocity filter and electrostatic trap and so on, but also to survey the orientation degree of cold linear molecules in a strong electrostatic field.We calculate the pendular-state spectra of cold linear molecules, and investigated the dependences of \u201cQ-branch\u201d integrated intensity of pendular spectra on both electric-field strength and molecular rotation-temperature. A new multi-peak structure in the \u201cQ-branch\u201d spectrum is appearing when the Stark interaction strength  Particularly, cold/ultracold polar molecules can be used to study their quantum-state controlled pendular spectrum. Currently, they can be prepared and manipulated by using some electrostatic devices, such as Stark decelerator2328\u22121. Also, the measurements of externally-added the electrostatic field vector and its spatial gradient as well as the orientation degree  of cold heavy-atom molecules (such as YbF303132\u22121) to a moderate one (\u223c103\u2009V cm\u22121) by using electro-optic probe3640\u221215 T to 103 T353637383940in situ the E-field vector and its spatial distribution in the electrostatic devices2223242526303132The accurate amplitude and direction of the electrostatic fields and their spatial distributions play important roles in the preparation and investigation of cold/ultracold molecules using above electrostatic devices222324252622232425263 with P-, R-branches. The Q-branch transition of (HCCCN)3 is forbidden due to the selection rule. However, a so called \u201cQ-branch\u201d transition of the linear (HCCCN)3 will appearing in an external electric field due to the mixture of the wavefunctions . Generally, polar molecules in a strong electric field will be oriented and converted from pinwheeling rotors into pendular liberators confined to oscillate over a limited angular range along the field direction. In this case, the corresponding rotation eigenstates become the pendular states. Molecules with a low rotational temperature, T, a large dipole moment, and a small molecular constant, B, are very easy to be implemented into the pendular state under a weak electric field. The pendular-state spectra were first investigated experimentally by Miller\u2019s group\u03c9\u2009=\u2009\u03bcE(r)/B was used to govern the extent of hybridization of the rotor states. The Schr\u00f6dinger equation of a rigid linear molecule in an E-field is given byThe pendular states are linear combinations of the field-free rotor states, J2 is the squared angular momentum operator, M is the projection of the angular momentum J along the E-field vector direction, and \u03b8 is the angle between the molecular axis and the E-field vector, and where aJM(\u03c9) is the coefficient, which specifies the eigenfunction as linear combination of all rotational levels in a vibrational state. For any fixed value of the good quantum number M, the range of J involved in this coherent superposition or hybrid wavefunction increases with the \u03c9 parameter. The eigenstates are labeled by M and the nominal value of where And the corresponding normalized integrated intensity of the Q-branch spectra is given byv is the vibratioanl transition frequency; J\u2032 and J\u2033 states give rise to non-zero transition probabilities between the states that differ by more than unity in their nominal q  designates the spherical components in the space-fixed frame of the E-field vector of the radiation. q\u2009=\u20090 means that the polarization of the probe beam is parallel to the direction of the E-field vector; q\u2009=\u2009\u00b11 means that these two directions are orthogonal each other. The relative strength IQ of the \u201cQ-branch\u201d can be calculated by using 0 is the band origin. \u00b1SQmin and \u00b1Smin are the minimum values of the \u201cQ-branch\u201d and entire ro-vibrational spectra\u2019s both sides. The spectrum line profile was considered as Gaussian function, its full width at half maximum (FWHM) was set as B/4where v1 vibrational mode of C-H stretch of linear cyanoacetylene trimer (HCCCN)3E\u2009=\u20090) were calculated by using 3 molecule are similar to the experimental ones of (HCN)3\u20093\u20092H4\u2009The spectra of possible rovibrational transitions of the 3 under the parallel transition (the transitions of \u0394MJ\u2009=\u20090) and the perpendicular transition (the transitions of \u0394MJ\u2009=\u2009\u00b11) are showed in We can see from 3 in different electric fields. In the left side of 3 with a MRT of 1\u2009K and rise with increasing the E-field strength, which is due to the slight difference of the electric dipole moments, \u03bc, and molecular constants B of the upper and lower vibrational ground states, v and v\u2033. To our knowledge, this multi-peak spectral structure is the first finding in the world. It is clear that such a multi-peak spectral structure can be used to precisely measure the electric dipole moments \u03bc and B constants of the selected molecules. In the right side of 3 under different E-field strength were calculated, and the dependence of the normalized intensity of the \u201cQ-branch\u201d of (HCCCN)3 with different MRT on the E-field strength E was studied by using \u22121, the intensity of the \u201cQ-branch\u201d of (HCCCN)3 with a MRT of 0.25\u2009K will be increased faster than that with a MRT of 5\u2009K, and the low-energy rotational levels will be easily mixed in the E-field. This is because most of cold molecules are populated in lower rotational levels dominantly, thus the colder molecules will reach its saturation in the external E-field quickly, and has stronger relative intensity factor of Q-branch compared with that of a higher molecular temperature. In particular, when T\u2009=\u20090.25\u2009K, the Q-branch integrated intensity of cold (HCCCN)3 will be increased from 0 to about 0.95 when the E-field strength is increased from 0 to 10\u2009kV cm\u22121; while T\u2009=\u20095\u2009K, it will be increased from 0 to ~0.90 with increasing E-field strength from 0 to 100\u2009kV cm\u22121.The integrated intensity of the Q-branch of (HCCCN)2\u20092 will be increased from about 0.3 to 0.95 when the E-field strength is increased from 50\u2009kV cm\u22121 to 1000\u2009kV cm\u22121; while T\u2009=\u200910\u2009K, it will be increased from about 0.35 to 0.90 with increasing the E-field strength from 100\u2009kV cm\u22121 to 1000\u2009kV cm\u22121. Also, we can see from 2 will be increased from about 0.35 to 0.98 when the E-field strength is increased from 5000\u2009kV cm\u22121 to 105\u2009kV cm\u22121; while T\u2009=\u2009300\u2009K , it will be increased from about 0.3 to 0.92 with the increase of the E-field strength from 7500\u2009kV cm\u22121 to 105\u2009kV cm\u22121. These results show that it is suitable to observe the Q-branch spectrum of cold linear (HCCCN)3, HCN-N2 and the room temperature HCl in a weak, moderate and strong E-field, respectively.We also investigate the dependence of the normalized integrated intensity of the Q-branch on the E-field strength for HCN-N3 Q-branch on the MRT T, and shows that for a certain E-field strength, with the reduction of the MRT, the intensity of Q-branch will be first increased and then slowly reached to a saturation value. Particularly, when T\u2009\u2264\u20091\u2009mK, the E-field measurement value of ultracold (HCCCN)3 can reach \u223c\u20090.01\u2009V cm\u22121, even a smaller value. This is because the lower the MRT T is, the higher the population of lower rotational levels will be, and when the MRT T is low enough, the population of the lowest rotational level will reach its highest value, and then the integrated intensity of the Q-branch will reach its saturation value. This result shows that the lower the MRT is, the weaker the needed E-field will be, and ultracold linear molecules in a weaker E-field can be used to obtain a higher sensitivity for the observation of the Q-branch integrated intensity.\u03bc and B constants of different vibration states of cold linear molecules.First, we can see from 3 with a temperature of lower or higher than 1\u2009mK is suitable to measure a weaker E-field strength within 10\u22125\u2009\u223c\u2009100\u2009kV cm\u22121, cold HCN-N2 and heat HCl from 77\u2009K to 300\u2009K are suitable to measure a moderate E-field strength (1\u2009\u223c\u2009103\u2009kV cm\u22121) and a strong one (102\u2009\u223c\u2009105\u2009kV cm\u22121) by using the pendular Q-branch spectra of the linear molecule, respectively. The measurement principle and method will be introduced in some detail as follows: in our proposed scheme, the space of the measured E-field will be filled with the selected cold linear molecule gas, which can be generated by using buffer-gas cooling and Stark velocity filter23\u03b7coll, and the quantum efficiency \u03b7Det of the detector were assumed as a constant near the band origin v0, the photoelectric current of the detected fluorescence intensity of the \u201cQ-branch\u201d can be given bySecondly, it is clear from B(v0)\u2009=\u2009AP0\u03b7coll\u03b7det, A is the system coefficient, P0 and V are the power of the probe beam and the effective probing volume, respectively. From where k is the proportional coefficient, which can be determined by the Q-branch intensity of cold linear molecules in a homogeneous E-field generated by a pair of plate electrodes, that is, it can be determined by the calibration curve of the resulting Q-branch intensity of a plate capacitor. \u03c1(r) is the spatial density distribution of cold molecules and will be easily affected by the E-field environment, but this problem can be solved by using a CCD camera to obtain the fluorescent intensity distribution from the molecule sample, which is proportional to the spatial density distribution of cold molecules in an entire measurement region. This is similar to the measurement method of cold atomic density used in the MOT or BEC experiments.where EX of the measured E-field vector can be obtained by measuring the photon current iQX from the corresponding LIF intensity IQX of the Q-branch. If the direction of the probe-beam polarization is changed as the Y direction [see EY of the measured E-field vector will be obtained by measuring iQY from the corresponding IQY. Then, the magnitude EZ of the measured E-field vector can be determined by using similar measurement method, and then we can obtain the E-field vector The basic principle for measuring the direction of the E-field vector can be simply described as follows: the magnitude and direction of the E-field vector in a two-dimensional (2D) plane (such as in XOY plane) can be measured by changing the direction of the probe-beam polarization two times. That is, from tion see , the Y cFinally, it is well known that the stronger the electric field is, the higher the orientation degree of cold linear-molecules will beSimilar to the derivation of measurement sensitivity expression in refs \u03b7c is the fluorescence collecting efficiency, n is the density of a supersonic molecular beam, and \u03ba the front factor of E2. The effective detected volume within probe laser beam can be assumed as a spheroid, it\u2019s volume Veff equals to w0 is the waist radius, and f represents the Rayleigh length of the Gaussian beam. When the fluorescence collecting efficiency of detection system is \u03b7c\u2009=\u200910%, the rotational temperature of a supersonic (HCCCN)3 beam is 5\u2009K, and the waist radius of the focused probe beam is w0\u2009=\u200910\u2009\u03bcm, we obtain a static electric-field sensitivity of 2.05\u2009\u00d7\u200910\u22127 V/cm48. It is clear that when SNR\u2009=\u20091, the relative measurement error  reaches 100%. So in order to obtain a 1% relative measurement error (a relative uncertainty), the SNR should be equal to 100, and the corresponding practical sensitivity is E\u2009=\u20092.05\u2009\u00d7\u200910\u22125\u2009V/cm, which is far lower than ones (5\u2009V/cm\u2009~\u2009100\u2009V/cm) of other methods3638where 3, and given reasonable physical explanations. Our study shows that the proposed measurement method can cover an ultrawide range of about 10\u22125\u2009V\u2009cm\u22121\u2009~\u2009105\u2009kV\u2009cm\u22121 theoretically, and the corresponding practical measurement sensitivity is 2.05 10\u22125\u2009V\u2009cm\u22121. So it is clear that such a high-sensitive and ultrawide-range method can be used to realize the nonintrusive, in-situ measurement of the E-field vector and its spatial distribution in Stark decelerator23303132We have calculated pendular-state spectra of cold linear molecules, and studied the dependences of the integrated intensity of the Q-branch on both the E-field strength and the MRT of cold linear molecules, and found that these dependences can be used to sensitively measure the E-field vector and its spatial distribution by changing the polarization directions of the focused probe-beam as well as the orientation degree of cold linear molecules. Also, we have found some new physical phenomena as follows: (1) the saturation effect of the integrated intensity of the Q-branch in a strong E-field; (2) the similar saturation effect occurred at an ultralow temperature of the linear molecules, and (3) a multi-peak structure in the Q-branch spectrum as well as its appearing condition How to cite this article: Deng, M. et al. Dependences of Q-branch integrated intensity of linear-molecule pendular spectra on electric-field strength and rotational temperature and its potential applications. Sci. Rep.6, 26776; doi: 10.1038/srep26776 (2016)."}
+{"text": "To be exact, we employ entangled states prepared by m-bonacci sequences to detect eavesdropping. Meanwhile, we encode m-bonacci sequences in Lagrange interpolation polynomials to generate the shares of a secret with reverse Huffman-Fibonacci-tree coding. The advantages of the proposed scheme is that it can detect eavesdropping without joint quantum operations, and permits secret sharing for an arbitrary but no less than threshold-value number of classical participants with much lower bandwidth. Also, in comparison with existing quantum secret sharing schemes, it still works when there are dynamic changes, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants. Finally, we provide security analysis of the new hybrid quantum secret sharing scheme and discuss its useful features for modern applications.With prevalent attacks in communication, sharing a secret between communicating parties is an ongoing challenge. Moreover, it is important to integrate quantum solutions with classical secret sharing schemes with low computational cost for the real world use. This paper proposes a novel hybrid threshold adaptable quantum secret sharing scheme, using an  Secret sharing is an important and powerful tool for protecting confidentiality and integrity of sensitive information, such as missile launch codes, bank account information, medical information and encryption keys. Secret sharing can be categorized into two broad classes: classical and quantum. Secret sharing was invented in its classical form simultaneously by Shamir3456et al.m, n)-threshold quantum secret sharing (QSS), which is the generation of quantum key distribution (QKD)910et al.\u2019s work, many quantum secret sharing schemes14151617181920212223242526et al.m and n is restricted while in CSS, the parameters can be arbitrarily selected as long as n\u2009\u2265\u2009m. In particular, in a -threshold QSS, the parameters m, n must satisfy the condition, 2m\u2009\u2212\u20091\u2009>\u2009n, which is imposed by the quantum no-cloning theoremm and n to be flexible and scalable. Therefore, it is very challenging to develop a new -threshold QSS scheme, whose parameters m and n are not restricted.To address the eavesdropping problem, Hillery m and n and therefore it is suitable for many real-world applications. We employ entangled states prepared by m-bonacci sequences to detect eavesdropping, which can be done by any subset of participants that contains at least x) members. That is to say, not all participants are required to reach a consensus in order to reveal eavesdropping. We use m-bonacci sequences encoded in Lagrange interpolation polynomials to generate the secret, with no restrictions imposed on the parameters m, n. Given that m-bonacci numbers can be represented by Fibonacci numbers, we use the structure of the Huffman-Fibonacci tree with the greedy algorithm to encode m-bonacci sequences, i.e., the higher the frequency at which a Fibonacci number appears in m-bonacci sequences, the longer the block of binary codes. Therefore, our scheme can greatly improve the coding capacity, thus reducing the use of entangled photons, which are expensive and difficult to prepare. In real-world applications, some changes may occur when a new participant joins or alternatively, an existing participant leaves or there is a sudden disruption of some quantum channels. The new scheme has the capability to deal with such changes since the m-bonacci-number coding can be easily modified to reflect changes in secret sharing.In this paper, we propose a hybrid quantum secret sharing scheme to address this challenge. The new scheme is free from any restrictions on the parameters m-bonacci sequences, as shown in m\u2009+\u20091 participants to recover the sequence. The one-time-pad encryption is done by a collection of m\u2009+\u20091 classical participants. The decryption can be done by any other collection of m\u2009+\u20091 classical participants. There are three phases in the proposed scheme:share generation and distribution \u2013 the dealer phaseeavesdropping detection phasesecret reconstruction phaseIn this section, we first describe a new hybrid quantum secret sharing based on Then its security is analyzed and compared with other related QKD protocols.m-bonacci sequence which is used in our later scheme. The m-bonacci sequence of order m\u2009\u2265\u20092 denoted by First, we introduce the generalized Fibonacci sequencem\u2009\u2212\u20092 initial terms set to 0 and the (m\u2009\u2212\u20091)th initial term set to 1. In particular, the 2-bonacci sequence is the usual Fibonacci sequencem-bonacci numbers when m\u2009=\u20092, 3, 4, 5, 6.with the first a dealer,m (which is the same as m in m-bonacci numbers) participants who hold quantum shares (quantum participants),Adversaries.Then, we present the entities used in our secret sharing, which are as follows:Dealer is a party who is trusted by all quantum and classical participants. It is responsible for the initialization of the secret sharing. It generates shares and distributes them to all the participants. It is assumed that after finishing its tasks, the dealer \u201cforgets\u201d all the parameters of the scheme together with the secret.Quantum participants hold their quantum shares. Each quantum participant owns one quantum share. Their task is to detect eavesdropping. This guarantees unconditional security of the scheme.Classical participants hold their classical shares. There are q (q\u2009\u2265\u2009m\u2009+\u20091) classical participants can recover the key (secret) using their classical shares (after eavesdropping detection).Adversaries includes the outsider and at most m insiders. The former has no valid share, while the latter is actually a legal participant with a valid share.Finally, the proposed hybrid Definition 1 (Hybridthreshold QSS). There are m  Dealer first prepares entangled states using the m-bonacci number source as shown in et al.\u2019s work31m entangled photons with smaller m-bonacci values. Each red circle dot represents an orbital angular momentum (OAM) shifter that takes the OAM in that branch to zero. Each place where lines split or cross is implied to have a beam splitter. The portion shown has OAM values from m, which is as follows:An OAM-entangled outgoing state depends on m runs through the allowed m-bonacci numbers in the pump beam: m quantum participants receives one entangled photon from the entangled states. In the lab of each quantum participant, there are two types of detection sorters , directing the entangled photon to one of them at random. The Ei sorter is made up of an OAM sorterFi sorter is used to distinguish different superpositions of the form. The states obtained in the Ei- and Fi- type measurements are nonorthogonal to each other. Therefore, the security of our proposed scheme is based on the fact that nonorthogonal states are indistinguishableEi-type measurement form a mutually orthogonal set among themselves, while those in the Fi-type measurements are not all orthogonal to each other but form a chain, where each state is nonorthogonal to the two adjacent states in the chain. Moreover, for orbital angular momentum, it is not necessary for quantum states that are orthogonal in Hilbert space to associate to orthogonal vectors in the physical space. Likewise, it is not necessary for quantum states that are nonorthogonal in Hilbert space to associate to nonorthogonal vectors in the physical space. That is the second fact for our scheme\u2019s security.where the index Ei or the sorter Fi at random, where i\u2009\u2208\u2009{1, 2, \u00b7\u00b7\u00b7, m}. Quantum participants B1, B2, \u00b7\u00b7\u00b7, Bm record the sorter to which the photon goes and the detected OAM value.(2) The beam splitter in the quantum participant\u2019s laboratory, sends the entangled photon to either the sorter m-bonacci numbers to produce new secret shares in terms of the mentioned flow of participants. This is a novel feature of our threshold adaptable secret sharing scheme.(3) Dealer allocates Next the dealer uses the following algorithm to encode the secret:Algorithmp, Choose a prime Randomly and uniformly generate a number f\u2009(x) at A1\u2009=\u2009f(1), A2\u2009=\u2009f\u2009(2), \u2026, i\u2032, Ai\u2032), for Sample i\u2032, Ai\u2032) to appropriate classical participants, where Finally, the dealer communicates Pe is larger than the preset threshold t between Dealer and participants, they abort this communication and return to the Dealer\u2019s phase. Otherwise, the communication continues to obtain a secure key for encrypting the shared secret, until the dealer sends an error notification or stops sending secret shares. The details are given below.m\u2009+\u20091 classical participants use their shares Any m\u2009>\u20092) of B1, B2, \u00b7\u00b7\u00b7, Bm quantum participants can detect eavesdropping, by comparing the detected values with the values recovered by the m\u2009+\u20091 classical participants. We take m\u2009=\u20092 for example to illustrate how eavesdropping is detected. Suppose that an adversary Eve is eavesdropping on the quantum channel between B1, B2. Clearly, she does not know which type of a detection measurement (the sorter Ei or the sorter Fi) took place in Bi\u2019s laboratory (1\u2009\u2264\u2009i\u2009\u2264\u2009m). So, Eve has to guess. If the entangled photon goes to the Ei sorter in Eve\u2019s laboratory when going to the Fi sorter in Bi\u2019s laboratory, or the entangled photon goes to the Fi sorter in Eve\u2019s laboratory when going to the Ei sorter in Bi\u2019s laboratory, then the Bi measurement is going to be erroneous with the probability of B1, B2, \u00b7\u00b7\u00b7, Bm when they compare their scheme transcripts. More precisely, we have the following two cases to consider:Ei-type measurement on a photon, which is actually in the eigenstate Bi. If Bi receives one of these superpositions and makes an Fi-type measurement, she will read out one of the values Eve makes an Fi-type measurement on a photon, which is actually in the superposition state Bi. If Bi receives one of these eigenstates and makes an Ei-type measurement, she will obtain one of the superpositions Eve makes an Any During the process of secret share distribution, when there is a mismatch in the entangled state photons, and if the error rate \u03b7 (fraction of times Eve interferes) of the trials, the fraction of times Eve guesses wrong basis is B1 compares her results with B2\u2019s, they will find that their outcomes are inconsistent a fraction f of the time, which isIn both cases, if Eve eavesdrops with a fraction m\u2009>\u20092. This is because we can apply the recovered m-bonacci numbers with classical shares, to verify its consistency with the m-bonacci numbers carried by entangled states. Furthermore, with the detected values from the entangled photons, we can assess the security of the quantum channel .Note that in our scheme, each entangled photon binds the classical share together. Moreover, not all quantum participants are needed to detect eavesdropping when t, they abort the communication and postpone the secret reconstruction phase. Otherwise, any m\u2009+\u20091 classical participants can use their classical shares to recover values m\u2009+\u20091 classical participants can recover and further share the secret.If the participants detect eavesdropping and the error rate is higher than the preset threshold value m-bonacci sequences can be used to encode the final key. That is, m is changeable for the key, which can address the problems of restricted quantum sources in certain settings and the membership change of participants, such as the joining of a new participant or departure of existing participants. Therefore, our scheme is more practical compared the other quantum secret sharing schemes.In this scheme, we use quantum coding to generate the key for encrypting messages. Moreover, various et al.3132First, using the technique of Simon Theorem 1 (Insiders attacks). Given the hybrid k\u2009<\u2009m\u2009+\u20091 insiders  is P(\u22c5) on the secret space S. That is, for any p0 such that for any p\u2009>\u2009p0 with H(s) is the entropy of s, the conditional entropy s conditioned on s generated by the knowledge of where Proof. It is worth noting that our proposed hybrid d (d\u2009=\u2009|Kd|\u2009<\u2009m\u2009+\u20091) insiders. d classical shares i1 is the public information of d\u2009=\u2009m, i.e., the upper bound of si\u2032 obtained by the recovered Lagrange polynomial is less than p, then we can have a0 is chosen at random in Fp and thus Next, we only need to consider the case of p\u2009\u2192\u2009+\u221e, k\u2009<\u2009m\u2009+\u20091 classical participants, our proposed hybrid P(\u22c5) on the secret space S. \u25a1That is to say, when Theorem 2 (Outsider attacks). Given the hybrid Q with |Q|\u2009=\u2009m, and an outsider has already known any subset P(\u22c5) on the secret space S. That is, for any p0 such that for any p\u2009>\u2009p0 with H(s) is the entropy of s, the conditional entropy H(s|Qk) denotes the entropy of s conditioned on Qk, and \u0394 denotes the entropy loss of s generated by the knowledge of Qk.where Proof. First, there are m\u2009+\u20091 (m\u2009>\u2009t\u2032) classical participants {C1, C2, \u00b7\u00b7\u00b7, Cm+1} and t\u2032 quantum participants {B1, B2, \u00b7\u00b7\u00b7, Bt\u2032}. Suppose that an outsider has already known m-bonacci number, there is still an m-fold uncertainty about the m-bonacci number other parties detect in ref. s\u2032 and s are actually independent of each other.On the one hand, for the party who detects a particular et al.\u2019s QSSs\u2032\u2009=\u2009s.On the other hand, the quantum participants\u2019 shares are independent of the classical participants\u2019 shares. Moreover, the quantum participants\u2019 shares are used for eavesdropping detection rather than key generation. Consequently, outsiders cannot use their quantum shares directly as they do in Cleve Second, as we know, the classical shares are allocated in Shamir\u2019s SSp\u2009\u2192\u2009+\u221e, \u0394\u2009\u2192\u20090. Hence, our proposed hybrid S. Here, That is to say, when m-bonacci-value-entangled photon, according to the quantum no-cloning theorem, she is unable to clone any other undetected m-bonacci-value-entangled photon.Our scheme is based on the fact that the nonorthogonal states are indistinguishable, so it is immune against cloning and impersonation attacks. Even if Eve successfully detects the value of an m-bonacci-value-entangled photon and send a fake m-bonacci-value-entangled photon, say m-bonacci-value-entangled photon from the fake state Bi. However, due to the particular encoding used in our scheme, the m-bonacci-value-entangled photon varies and the impersonation attack is easy to be detected. For example, if she detects that the value of entangled photon is 2 from Let us consider impersonation attacks. A possible strategy Eve can use is to capture the original m-bonacci sequences for preparing m-bonacci-sequence entangled states, the quantum and classical shares change accordingly. Moreover, due to the use of varying m-bonacci numbers to prepare entangled states, Eve cannot know which m-bonacci sequence is really used every time. For example, suppose that for the fourth subkey, 3-bonacci sequences are used, however, 6-bonacci sequences are used for the fifth subkey. As a result, it is impossible to launch an impersonation attack by inserting the used m-bonacci sequences for the subkey. Therefore, our scheme is immune to replay attacks.Our scheme is immune against replay attacks. A replay attack is such an attack that a valid data transmission is maliciously or fraudulently repeated or delayed. Because we use adaptable m-bonacci number, there is still a m-fold uncertainty about the m-bonacci number other parties detect. Suppose that the eavesdropper Eve, is in possession of an entangled state analyzer for the m-bonacci-value entangled states. If so, she will be able to distinguish m-bonacci-value entangled state according to the result of her m-bonacci-value entangled state analysis. In order to detect the eavesdropper, we should consider what happens if, for instance, the state m-bonacci-value entangled state perfectly. In the remaining B1, B2, \u00b7\u00b7\u00b7 Bm together with any m\u2009+\u20091 classical participants. By adding all the probability of causing an error becomes A man-in-the-middle attack is an attack, in which Eve intercepts the transmitted entangled photons and replays other entangled photons. We now show that our scheme provides resistance against the man-in-the-middle attacks. First, quantum channels are authenticated; second, for the party who detects a particular et al.m-bonacci sequences into both quantum and classical coding, with reverse Huffman-Fibonacci-tree coding, to achieve higher-capacity and lower-bandwidth hybrid threshold adaptable QSS scheme.Simon m-bonacci values can be chosen to achieve the lower error rates and longer distances. Hence, we propose to use Huffman coding tree to encode m-bonacci numbers with the greedy algorithm, which can greatly improve the coding capacity, thus reducing the use of entangled photons. To be exact, for fixed m-bonacci number sets, we use binary representations of m-bonacci numbers based on Fibonacci numbers of order m\u2009\u2265\u20092  the m-bonacci values are encoded in Lagrange polynominal, and as a result, any t\u2032 quantum participants and any m\u2009+\u20091 classical participants can recover the secret. Due to the no-cloning theorem and its impact on parameters, for QSS schemes142426t\u2032 must satisfy the requirement of t\u2032 quantum participants are fixed, other quantum participants are unable to participate in the recovery of the secret. However, in our scheme, the parameters t\u2032 can be arbitrary, and our scheme is robust when a new participant joins or an existing participant leaves.Besides the information capacity, 1424m-bonacci sequences, the detection is possible by any subset that contains at least m-bonacci number are significantly improved, from four bits at most to more than ten bits using a similar experimental setup. Consequently, our scheme can greatly improve the coding capacity, thus reducing the use of entangled photons which are expensive and difficult to prepare. Moreover, to generate the secret, the m-bonacci sequences encoded in Lagrange interpolation polynomials and the Huffman-Fibonacci coding are applied. So, compared with the CSS in ref. m-bonacci sequences such as m\u2009=\u20092, 3, 4, 5, 6 can be used in our proposed scheme, the pump values in Unlike eavesdropping detection in QSS schemes1424m quantum and P and p (P\u2009\u226b\u2009p) be primes, then the communication overhead in ref. n|P| bits, where |P| and |p| denote the bit number of P and p. It can be known that the size of the key is |P|, so, |P| photons are prepared. In ref. n|P| qubits. The ref. For the communication overhead, there are m\u2009+\u20091 provided that m-bonacci numbers, aiming at improving the coding capacity greatly, and thus incurring a low communication overhead. When compared to the existing QSS schemes, there is an improvement in sharing the secret without joint quantum operations. Meanwhile, our scheme still works when there are dynamic changes in comparison with existing quantum secret sharing, such as the unavailability of some quantum channel, the arrival of new participants and the departure of participants.In conclusion, we combine the Huffman-Fibonacci quantum coding with Lagrange polynomials to achieve threshold adaptable QSS. The key point of our scheme is that it does not suffer from the restriction derived from the quantum no-cloning theorem, because it permits secret sharing for arbitrary values of parameters m-bonacci number can be represented by a binary string of length r, cr, cr\u22121, \u2026, c2, c1 such thatFraenkel and Kleinm-bonacci values.When one uses the following procedure to produce it, the m\u2009+\u20091 classical participants encode the reconstructed m-bonacci value based on the fact that the higher the frequency at which Fibonacci numbers appear in m-bonacci values, the longer the set of binary codes, which is opposite to the idea of Huffman coding. Let the binary codes of m-bonacci values decrease, the coding is as follows ."}
+{"text": "A frequent bottleneck in interpreting phylogenomic output is the need to screen often thousands of trees for features of interest, particularly robust clades of specific taxa, as evidence of monophyletic relationship and/or reticulated evolution. Here we present PhySortR, a fast, flexible R package for classifying phylogenetic trees. Unlike existing utilities, PhySortR allows for identification of both exclusive and non-exclusive clades uniting the target taxa based on tip labels  on a tree, with customisable options to assess clades within the context of the whole tree. Using simulated and empirical datasets, we demonstrate the potential and scalability of PhySortR in analysis of thousands of phylogenetic trees without a priori assumption of tree-rooting, and in yielding readily interpretable trees that unambiguously satisfy the query. PhySortR is a command-line tool that is freely available and easily automatable. Here, phylogenetic trees in flat files  are sorted  based on text-pattern matching. This principle is not to be confused with the tructure . Currenttructure  and SICLtructure  screen ay; SICLE  specificy; SICLE  do not asortTrees function, allowing for screening (within a tree) for \u201cExclusive\u201d clades that contain only the target leaves and/or \u201cNon-Exclusive\u201d clades that include a defined portion of non-target leaves. Using simulated data, we assess the runtime of PhySortR based on the number of trees and the number of leaves within a tree, and demonstrate the potential of PhySortR in the analysis of multiple, large-scale empirical datasets.Here we present PhySortR, a fast, flexible R package for screening and sorting phylogenetic trees. The command-line package provides the quick and highly flexible Z; the first tree  are named consistently across all input trees; this is a simple string-matching exercise, i.e., the terms specified here determine taxon-level resolution of targets. In the examples shown in target.groups = \u201cRhodophyta,Viridiplantae,Stramenopiles.\u201d The minimum support for a clade (min.support) can refer to bootstrap, Bayesian posterior probability, or any other measure of support. Here, no prior assumption of tree root is made , thus clade membership on both sides of each node is considered. For instance, the node support for Clade Z (bootstrap 99%) in rst tree  is an emrst tree , on whicrst tree \u20131D are bZ in Z in Z  present in a clade relative to the total number of target(s) found in a tree. The default value of min.prop.target is set at 0.7 as guidance. At 1.0, a strict monophyletic relationship of the target group is enforced . When the value is set too low , one would identify a target clade that is more-narrowly defined  a robust 24-member clade , the minimum proportion of target leaves within a \u201cNon-Exclusive\u201d clade is 0.9, thus the maximum proportion of non-target leaves allowed in the clade is 0.1 . For instance, the proportion of target leaves within Clade Z (0.79) in clade.exclusivity of 0.9; this clade is therefore not considered as \u201cNon-Exclusive\u201d at the default setting. This option accepts any value <1.0, and is applicable only for sorting \u201cNon-Exclusive\u201d clades (see below); at 1.0 , the clade is considered \u201cExclusive\u201d.Alternatively, the user may wish to screen for a robust clade that contains the target groups and a small proportion of \u201cinterrupting\u201d non-target leaves, e.g., a 24-member clade consisting of 23 leaves from the targets Rhodophyta, Viridiplantae, and Stramenopiles, as well as one from a non-target leaf, Haptophyceae  and must be sufficiently specific in the dataset for the purpose of the screening. For instance, \u201cplantae\u201d and \u201cViridiplantae\u201d might not be appropriate in a single query because all tips that are identified by \u201cViridiplantae\u201d will also be identified by \u201cplantae.\u201dThe arameter  is the omode argument, the function will always return a list of the trees that have been identified as containing clades that meet the specified criteria. If the move (mode = \u201cm\u201d) or copy (mode = \u201cc\u201d) command is given, subdirectories will be created in out.dir that contain trees with a particular clade, i.e., the directory out.dir/Exclusive/ will be created for the trees with \u201cExclusive\u201d clades and out.dir/Non_Exclusive/ for trees with \u201cNon-Exclusive\u201d clades. If the function is instructed to search for \u201cExclusive\u201d trees it will also return trees that contain only target leaves, termed \u201cAll Exclusive\u201d trees. These trees are a subset of \u201cExclusive\u201d trees and will be transferred to a subdirectory (if the move/copy parameter is given) within the \u201cExclusive\u201d directory i.e., out.dir/Exclusive/All_Exclusive.Regardless of which parameters are passed to the clades.sorted parameter can be used to change the types of clades that the function will search for. For example if clades.sorted = \u201cE\u201d is given, the function will only search for trees that have \u201cExclusive\u201d clades, but if the default value of clades.sorted = \u201cNE,E\u201d is given, the function will search for both \u201cExclusive\u201d and \u201cNon-Exclusive\u201d clades. During each run the function will create a log file, called \u201cout.dir.log,\u201d in the in.dir directory. This file will contain information about each identified clade, e.g., the names of the leaves in the clade, the support for the clade, the proportion of \u201cinterrupting\u201d leaves, and so forth.The http://evolution.genetics.washington.edu/phylip/newick_doc.html) that has been widely adopted in phylogenetic software. This format was later modified to incorporate more-complex network information such as hybrid nodes, in the form of extended Newick (eNewick) format; see convert.eNewick function that takes a single phylogenetic tree in eNewick format and returns the same tree in Newick format. This function in isolation can be used as a general-purpose tool for converting phylogenetic trees in eNewick format into a format that is usable by the popular phylogenetic packages in R, ape  and leaves per tree (X); see X = 100, we used a base phylogenetic tree with 1.05X tips, i.e., 105 tips. An \u201cExclusive\u201d 20-leaf target clade  is defined, tip labels of other non-target leaves are swapped (at random), following which 0.05X  of the overall tree branches  chosen at random were removed using phytools, resulting in the final tree of size X. This tree was then replicated up to N number of trees as per our experimental design below.To test the scalability of the PhySortR package we simulated benchmarking datasets composed of a given number of trees  at tree size X = 100, 200, 300, 400 and 500 . The R script for simulating these topologies and the corresponding templates are available as Simulation of trees at different eplicate . All benhttp://phylosort.sourceforge.net/), we screened for trees that contain a strongly supported (bootstrap \u2265 90%) exclusive clade of Viridiplantae + Stramenopiles. The closest equivalent parameter settings were used for PhySortR  and PhyloSort (Taxa regexp =([\u2227_] + _[\u2227_] + ).\u2217, query taxa group 1 = all Viridiplantae leaves, query taxa group 2 = all Stramenopiles leaves, Min bootstrap = 90, Exclusive mode). For PhyloSort, independent analysis was done with the option Root by outgroup (PhyloSort-root hereinafter) and without (PhyloSort-no-root).As input, here we used 897 empirical protein trees from an earlier study . Using Pape  to be sorted and the number of leaves (X) within a tree. As with any utility , and sorting through 1,000 trees of X = 500 took <350 s (\u223c5.8 min). We observed negligible differences in runtime with negative controls (trees containing no identifiable clades) as input, compared to the test set in  utility , the runy with N  and supeith N (X . In the Unlike PhyloSort, no prior assumption of tree-rooting is made in PhySortR. To illustrate the impact of tree-rooting assumption on the sorting process, we performed sorting among 897 empirical protein trees  using PhFurthermore, the algorithm of PhySortR  is distiape (phytools (ape and phytools accept only Newick as input, PhySortR accepts tree files in both Newick and eNewick (PhySortR is an R implementation based on the basic sorting principles of ape  and phytphytools , allowin eNewick  formats. eNewick  is open 10.7717/peerj.2038/supp-1Data S1Click here for additional data file.10.7717/peerj.2038/supp-2Data S2Click here for additional data file.10.7717/peerj.2038/supp-3Data S3Click here for additional data file.10.7717/peerj.2038/supp-4Text S1Click here for additional data file.10.7717/peerj.2038/supp-5Figure S1Click here for additional data file."}
+{"text": "The purpose of this paper is to present the definition of  In fact the study of such spaces received an impetus with the pioneering work of Schweizer and Sklar  is a binary operation T on  which satisfies the following conditions:T is associative and commutative;T is continuous;A triangular norm  where E is a nonempty set, T is a continuous t-norm and F is a mapping from F at the pair , the following conditions hold:(MPM-1) (MPM-2) (MPM-3) A Menger probabilistic metric space is a triple  be a Menger probabilistic metric space.E is said to converge to A sequence E is called a Cauchy sequence if for any A sequence E,\u00a0F,\u00a0T) is said to be M-complete if each Cauchy sequence in E converges to some point in E. is said to be G-complete if each G-Cauchy sequence is convergent in E.(ii)(iii)(iv) into it-self:M-complete Menger probabilistic spaces, they have proved a generalized F is triangular:Kutbi et\u00a0al.  proved tThe purpose of this paper is to present the definition of We denote by E,\u00a0F,\u00a0T) be a Menger probabilistic space and f satisfying condition  be a Menger probabilistic space and f satisfying condition  be aG-complete Menger probabilistic space andbe acontractive mapping. Assume thatThenfhas a unique fixed point.p, we getG-Cauchy sequence. Since  is G-complete, there exists a point v such that For any mentclass2pt{minimG-complete Menger probabilistic space. Meanwhile, they need to add the uniqueness condition of fixed point  be aG-complete Menger probabilistic space andbe acontractive mapping. Assume thatThenfhas a fixed point. denotes the set of all fixed points of a mapping f.In order to get the uniqueness of fixed point, authors added the following condition:Adding conditionto the hypotheses ofTheorem\u00a0we obtain uniqueness of the fixed point. be aG-complete Menger probabilistic space andbe acontractive mapping. Assume thatThenfhas a unique fixed point, whereT is also a From Theorem\u00a0Is the following property right?Let  be aG-complete Menger probabilistic space andbe acontractive mapping. Assume thatThenfhas a unique fixed point.The property  is rightIt is not hard to show that, the property  is equivNow we proveThis completes the proof. Let  be a metric space,be a mapping satisfying the following condition:whereis a constant. LetThenis a Menger probabilistic metric space;Tis acontractive mapping, whereTis also acontractive mapping, where(1) We prove (2) From  we have\\T is also a (3) By using Theorem\u00a0Let  be a metric space,be a nonexpansive mapping. Letis a Menger probabilistic metric space;Tis acontractive mapping, whereTis also acontractive mapping, whereT is nonexpansive, let T is also a (1) It is a conclusion of Theorem"}
+{"text": "Objective: Prepulse inhibition (PPI) is an operational measure of sensory gating. PPI of cortical response to a startling pulse is known to be modulated by attention. With a time-frequency analysis, we sought to determine whether goal-directed and stimulus-driven attention differentially modulate inhibition of cortical oscillations elicited by a startling pulse.Methods: An electroencephalogram (EEG) was recorded in 26 healthy controls performing an active acoustic PPI paradigm. Startling stimuli were presented alone or either 400 or 1000 ms after one of three types of visual prepulse: to-be-attended , unexpected (stimulus-driven attention) or to-be-ignored (non-focused attention). We calculated the percentage PPI for the auditory event-related spectral perturbation (ERSP) of theta (4\u20137 Hz), alpha (8\u201312 Hz), beta1 (13\u201320 Hz) and beta2 (20\u201330 Hz) oscillations and changes in inter-trial coherence (ITC), a measure of phase synchronization of electroencephalographic activity.Results: At 400 ms: (i) PPI of the ERSP of alpha, theta and beta1 oscillation was greater after an unexpected and a to-be-attended prepulse than after a to-be-ignored prepulse; and (ii) PPI of beta2 oscillations was greater after a to-be-attended than a to-be-ignored prepulse. At 1000 ms: (i) PPI of alpha oscillations was greater after an unexpected and a to-be-attended prepulse than after a to-be-ignored prepulse; and (ii) PPI of beta1 oscillations was greater after a to-be-attended than a to-be-ignored prepulse. The ITC values did not vary according to the type of prepulse.Conclusions: In an active PPI paradigm, stimulus-driven and goal-directed attention each have differential effects on the modulation of cortical oscillations. Filtering out irrelevant information is a crucial way of protecting the cognitive resources required for goal-directed activities. One of the physiological indices of these protective neural processes is referred to as prepulse inhibition . It corresponds to the attenuation of the amplitude of a startle reflex to an intense stimulus  when a weaker, non-startling stimulus (the prepulse) precedes the pulse by approximately 30\u2013500 ms. The prepulse attenuates not only motor responses  but also cortical responses to a sound pulse, such as the N100 and P200 components of the auditory evoked potential  activity can be described in a \u201ctime-frequency domain\u201d using two measures: event-related spectral perturbation (ERSP) and inter-trial coherence  have been linked to focused attention  years). All underwent a semi-structured interview and those with a history of neurological or psychiatric disorders were excluded, as well as those taking psycho-active drugs, including tobacco or cannabis. Subjects with a history of visual or auditory impairments were excluded from the study. All participants gave their written informed consent to participation. The study protocol was approved by the local institutional review board .The study population was the same as in our previous study  presented during 29 ms, with a mean 1400 ms inter-stimulus interval (range: 1300\u20131500 ms). Ten pulses were randomly delivered during the presentation, with an inter-pulse interval ranging from 18 to 30 s (mean: 24 s). The pulses were not temporally related to the visual stimuli.After the control task, participants performed two blocks of 360 trials of the startle-CPT task Figure . During The mean response time (in ms), the number of hits and the number of false alarms were recorded.\u00ae 128 AgCl electrode cap (ANT Software BV) placed according to the 10/05 international system  software  for data acquisition. The EEG and EOG signals were digitized at a sampling rate of 1024 Hz. Electrode impedances were kept below 5 K\u03a9.An EEG was recorded continuously from 128 scalp locations, using a DC amplifier  and a Quick-cap\u00ae software. The EEG signal was band-pass filtered between 0.1 and 30 Hz, and ocular artifacts were detected and removed off-line using the software\u2019s principal component analysis procedure.The EEG data were analyzed with ASAf and latency t relative to the pulse onset. Typically, for n trials, if Fk  is the spectral estimate of trial k at frequency f and time t, then:ERSP was measured using the EEGLab toolbox for MATLAB software , calculation was based on Morlet wavelet decomposition. Using the settings in EEGLab, cycles were set to , i.e., 2.5 cycles at the lowest frequency (4 Hz) with and 9.375 cycles at the highest frequency (30 Hz). A baseline-normalized ERSP was obtained during the control task and for each lead interval (400 and 1000 ms) after each type of prepulse  during the startle-CPT task. Ten trials per condition were considered.Following calculation of the ERSP, the ITC was computed in order to: (i) evaluate the effect of the prepulse on intertrial phase variability; and (ii) determine whether any abnormalities in ERSP power were due to impairments in phase variability. To compute ITC, the complex output of the baseline-normalized ERSP was divided by its complex norm , which was then averaged across trials. The complex norm of this averaged value yields the ITC for different time and frequency points. Using the same notation as above, the ITC is defined as:where \u2223 \u00b7 \u2223 represents the complex norm.ITC was obtained during the control task and for each lead interval (400 and 1000 ms) after each type of prepulse  during the startle-CPT task. Ten trials per condition were considered.2/Hz). Indeed, to calculate the percentage PPI of the power for a given frequency domain, we chose to use the absolute value of the power in mV2/Hz  because the baseline period  differed between the control session and the startle-CPT session. The percentage PPI of the absolute power for the frequency domains was calculated according to the following equation:Apart from the baseline-normalized spectral power value (expressed in dB), the spectral power was also expressed as an absolute value , for each type of prepulse.The following frequency domains were assessed: theta (4\u20137 Hz), alpha (8\u201312 Hz), beta1 (13\u201320 Hz), and beta2 (20\u201330 Hz).p < 0.05. Thereafter, we analyzed the signal on the location where the amplitude of the response was maximum.For time-frequency mapping, we used EEGLab to perform permutation tests with four conditions . The threshold for statistical significance (after Holm\u2019s correction) was set to \u00ae SPSS\u00ae, Armonk, New York, NY, USA).All other analyses were performed with SPSS 16.0 for Windows software  were performed separately for each lead interval and each frequency domain, with the prepulse  as the within-subject factor for the PPI of ERSP and  for the ITC. When required, p < 0.05 for all analyses.The significance threshold was set to p < 0.01, for all analyses). By consequence, further analyses were not adjusted.All data were normally distributed and are presented as the mean and SD. Mean %PPI values did not significantly differ according to sex (The mean reaction time was 369 (43) ms, the mean percentage of correct answers was 99% (2.5) and the mean number of false alarms was 0.15 (0.37).Time-frequency values of the ERSP are displayed as scalp topographies maps during the control session  and during the startle-CPT task [when the pulse is preceded by an \u201cA\u201d, \u201cO\u201d or \u201csymbol\u201d prepulse with a lead interval of 400 ms Figure  and 1000As displayed on the maps, an occurrence of a pulse was followed by a higher synchronization of cortical rhythms that predominated on the central area and was mainly visible in the theta and alpha frequency bands and to a lesser extent, in the beta1 and beta2 frequency bands. When a prepulse preceded occurrence of the pulse, this synchronization was clearly attenuated but much more when the prepulse was a to-be-attended (\u201cA\u201d) or an unexpected (symbol) stimulus than a to-be-ignored (\u201cO\u201d) stimulus. This phenomenon was observed for both lead intervals, but in an attenuated manner at long-lead interval (1000 ms). Moreover, at short-lead interval (400 ms), when the prepulse was a to-be-attended (\u201cA\u201d) stimulus, a desynchronization was observed 200 ms after the pulse occurrence, mainly in the alpha frequency band and, to a lesser extent, in the beta1 frequency band.As activity largely predominated on the central scalp area, further analyses and PPI measures were performed only on the Cz location  = 13.42, p < 0.001). Further comparisons (Bonferroni-corrected) revealed that the PPI of the theta rhythm was greater after a prepulse \u201cA\u201d than \u201cO\u201d (t(25) = 5.18, p < 0.001), and greater after a \u201csymbol\u201d than after a \u201cO\u201d (t(25) = 3.84, p = 0.001). There was no significant difference between the \u201cA\u201d and \u201csymbol\u201d prepulses (t(25) = 0.96, p = 0.34).For the theta band, an ANOVA revealed a significant main effect of prepulse type  = 10.7, p < 0.001). Further comparisons (Bonferroni-corrected) revealed that the PPI was greater after a prepulse \u201cA\u201d than \u201cO\u201d (t(25) = 5.7, p < 0.001) and greater after a \u201csymbol\u201d than \u201cO\u201d (t(25) = 2.7, p = 0.01). There was no significant difference between the \u201cA\u201d and \u201csymbol\u201d prepulses (t(25) = 1.23, p = 0.22).For the alpha band, an ANOVA revealed a significant main effect of prepulse type  = 13, p < 0.001). Further comparisons (Bonferroni-corrected) revealed than the PPI was greater after a prepulse \u201cA\u201d than \u201cO\u201d (t(25) = 5, p < 0.001) and greater after a \u201csymbol\u201d than \u201cO\u201d (t(25) = 3.2, p = 0.003). There was no significant difference between the \u201cA\u201d and symbol prepulses (t(25) = 1.47, p = 0.15).For the beta1 band, an ANOVA revealed a significant main effect of prepulse type  = 3.89, p = 0.02). Further comparisons (Bonferroni-corrected) revealed that the PPI was greater after a prepulse \u201cA\u201d than \u201cO\u201d (t(25) = 2.8, p = 0.009). There was no significant difference between the \u201cA\u201d and \u201csymbol\u201d prepulses (t(25) = 1.92, p = 0.06) nor between the \u201cO\u201d and \u201csymbol\u201d prepulses (t(25) = 0.8, p = 0.42).For the beta2 band, an ANOVA revealed a significant main effect of prepulse type  = 5.43, p = 0.008). Further comparisons (Bonferroni-corrected) revealed that the PPI was greater after a prepulse \u201cA\u201d than \u201cO\u201d (t(25) = 2.63, p = 0.014), and greater after a \u201csymbol\u201d than \u201cO\u201d (t(25) = 3.1, p = 0.005). There was no significant difference between the \u201cA\u201d and \u201csymbol\u201d prepulses (t(25) = 0.8, p = 0.43).For the alpha band, an ANOVA revealed a significant main effect of prepulse type  = 3.2, p = 0.05). Further comparisons (Bonferroni-corrected) revealed that the PPI was greater after a prepulse \u201cA\u201d than \u201cO\u201d (t(25) = 2.7, p = 0.01). There was no significant difference between the \u201cA\u201d and \u201csymbol\u201d prepulses (t(25) = 1.3, p = 0.2) nor between the \u201cO\u201d and \u201csymbol\u201d prepulses (t(25) = 1.14, p = 0.26).For the beta1 band, an ANOVA revealed a significant main effect of prepulse type  = 7.75, p < 0.001). Further comparisons revealed than the ITC was greater when the pulse was presented alone (during the control session) than after a \u201cA\u201d (t(25) = 3.2, p = 0.003), \u201cO\u201d (t(25) = 3.8, p < 0.001) or \u201csymbol\u201d prepulse (t(25) = 3.97, p < 0.001). The other differences were not significant (p > 0.05).For the 400 ms prepulse-pulse interval, there was no significant effect of the condition for the theta, beta1 and beta2 bands, although an ANOVA revealed a significant main effect of condition type for the alpha band  = 9.3, p < 0.001). Further comparisons revealed than the ITC was greater when the pulse was presented alone (during the control session) than after an \u201cA\u201d (t(25) = 3.67, p = 0.001), \u201cO\u201d (t(25) = 4.35, p < 0.001) or \u201csymbol\u201d prepulse (t(25) = 3.82, p < 0.001). The other differences were not significant (p > 0.05).For the 1000 ms prepulse-pulse interval, there was no significant effect of the condition for the theta, beta1 and beta2 bands, although an ANOVA revealed a significant main effect of condition type for the alpha band  changed when the said information was preceded by an attention-focusing prepulse.Our results show that at a prepulse-pulse interval of 400 ms, inhibition of spectral power for the theta, alpha, and beta1 bands was greater after a to-be-attended prepulse and an unexpected prepulse than after a to-be-ignored prepulse. Moreover, inhibition of spectral power in the beta2 band was greater after a to-be-attended prepulse than after a to-be-ignored prepulse, with a trend toward a greater inhibition after a to-be-attended prepulse than after an unexpected prepulse. At a prepulse-pulse interval of 1000 ms, inhibition of spectral power for the alpha band was greater after a to-be-attended prepulse and an unexpected prepulse than after a to-be-ignored prepulse. Inhibition of spectral power for the beta1 was also greater after a to-be-attended prepulse than after a to-be-ignored prepulse. The ITC values did not differ significantly as a function of the type of prepulse.Hence, by studying brain oscillations, we showed that inhibition of cortical responses produced by an irrelevant stimulus is modulated by attention. Our first starting hypothesis was thus confirmed: inhibition of spectral power in various frequency domains is dependent on the type of prepulse, with a greater inhibition after a prepulse on which attention is focused than after a to-be-ignored prepulse. Regarding our second hypothesis (that inhibition would be greater after a to-be-attended prepulse than after an unexpected prepulse), we only observed a trend towards such an effect for the beta2 frequency band, without significant difference for the other bands. As phase synchrony did not change with respect to the type of prepulse, it can be argued that PPI here is due to a reduction of the number of neurons discharging synchronously.One of the strengths of our study was its novel design, which enabled us to control for the respective effects of goal-directed attention and stimulus-driven attention.At a prepulse-pulse interval of 400 ms, we found that the effects of goal-directed attention and stimulus-driven attention on PPI of the brain oscillations were the same for the theta, alpha and beta1 bands, whereas inhibition of brain oscillations for the beta2 band was greater after a to-be-attended prepulse  than after an unexpected prepulse (involving stimulus-driven attention). Given that spectral power reflects the number of neurons that discharge synchronously, our results suggest that both stimulus-driven attention and goal-directed attention reduce the number of synchronous discharges in response to an irrelevant stimulus for the theta, alpha and beta1 frequency bands. Moreover, goal-directed attention may reduce the number of neurons that discharge synchronously for the beta2 band. Hence, by using a time-frequency analysis, we confirmed the previous reports  or preceded by a prepulse (of whatever type). An effect of attention on ITC was only observed for the alpha band (regardless of the prepulse type). This partially counter our hypothesis in which the prepulse would impair phase synchronization. The lack of attentional modulation of ITC for the theta, beta1 and beta2 bands is not in agreement with the spectral power results\u2014suggesting that inhibition of power is not due to an impairment in intertrial phase variability. This is in line with the fact that the ITC is independent of changes in EEG power . At a short-lead interval, stimulus-driven attention and goal-directed attention both modulate auditory-elicited theta, alpha and beta1 oscillations, whereas beta2 oscillations are preferentially inhibited when goal-directed attention is engaged. Our results also highlighted the impact of selective attention processes on sensory gating at long-lead intervals. Overall, it comes out of our results that auditory-elicited oscillations are globally modulated by attention whatever the frequency band, but that goal-directed attention has a specific effect on alpha and beta oscillations, with even a late desynchronization in the alpha frequency band. Our present findings do not suggest that phase synchronization of EEG activity is specifically modulated by attention. Given that PPI has been shown to be a useful index of sensory gating impairments in basal ganglia disorders [e.g., schizophrenia and Parkinson\u2019s disease (Perriol et al., Conception and design of the work, acquisition, analysis or interpretation for the work: AA, J-LB, CT, KD. Drafting the work or revising it critically for important intellectual content: AA, J-LB, AD, PB, CT, PD, KD. Final approval of the version to be published: AA, J-LB, AD, PB, CT, PD, KD. Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved: AA, J-LB, AD, PB, CT, PD, KD.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "High-entropy alloys (HEAs) are new alloys that contain five or more elements in roughly-equal proportion. We present new experiments and theory on the deformation behavior of HEAs under slow stretching (straining), and observe differences, compared to conventional alloys with fewer elements. For a specific range of temperatures and strain-rates, HEAs deform in a jerky way, with sudden slips that make it difficult to precisely control the deformation. An analytic model explains these slips as avalanches of slipping weak spots and predicts the observed slip statistics, stress-strain curves, and their dependence on temperature, strain-rate, and material composition. The ratio of the weak spots\u2019 healing rate to the strain-rate is the main tuning parameter, reminiscent of the Portevin-LeChatellier effect and time-temperature superposition in polymers. Our model predictions agree with the experimental results. The proposed widely-applicable deformation mechanism is useful for deformation control and alloy design. A series of new tensile deformation experiments is presented, which are performed at slow strain-rates on metals ranging from conventional alloys  to high-entropy alloys (HEAs)12345678910111213141516171234567891011121314151617Here we present new experimental results on alloys exposed to slow tensile deformation. We compare the results to the predictions of an analytic model that explains the observed serration statistics and the time-series properties of the slips. The model predicts how the scaling behavior of the slip-size distribution and related statistical properties can be changed by tuning temperature, strain-rate, or alloy composition. The experimental results agree with the model predictions. As explained below, both the experiments and the model show that the deformation mechanism of HEAs differs from that of conventional alloys. In the following sections, we discuss (1) the experiments, (2) the model, its predictions and applicability range, and (3) the comparison of the experimental results to the model predictions. Potential applications of the newly-proposed deformation mechanisms, include materials testing, evaluation, and the design of new alloys with improved deformation properties.We perform experiments on HEAs123456789101112131415161719201023HEAs are defined as alloys that have a mixing entropy higher than 1.5R, where R is the gas constant. In addition, medium-entropy alloys (MEAs) are defined as having the mixing entropy between 1R and 1.5R, and low-entropy alloys (LEAs) as being below 1R. Most conventional alloys are LEAs. However, some stainless steels, superalloys, and bulk metallic glasses are MEAs because of their high concentrations of alloying elements.In our experiments, a series of metals, containing Ni, CoNi, CoFeNi, CoCrFeNi, and CoCrFeMnNi, were designed specifically because they all have a solo face-centered-cubic (FCC) structure, thus providing a common basis for the comparison of serration phenomena. Their mixing entropies, approximately represented by the configurational entropy, are 0R, 0.69R, 1.1R, 1.39R, and 1.61R, respectively. With this range of entropies, the alloy series covers LEAs, MEAs, and HEAs. We observe changes in the serration phenomena from FCC-LEAs to FCC-HEAs, as temperature is tuned. As we will show, the measurements confirm the predicted effects on the serration statistics, of tuning temperature, strain-rate, and alloy composition.\u22125/s to 1\u2009\u00d7\u200910\u22122/s and temperatures from 300\u2009\u00b0C to 700\u2009\u00b0C. Each experiment was repeated 3 to 4 times to ensure the reliability of the test results. The slip statistics were extracted from the measured stress-time curves and, then, compared with the new predictions of the above statistical model. Details on the experiments are given in the Methods Section.In our experiments, the five metals, Ni, CoNi, CoFeNi, CoCrFeNi, and CoCrFeMnNi, were slowly deformed under tension at different strain-rates from 1\u2009\u00d7\u200910\u22124/s, and indicates the occurrence or nonoccurrence of serration behavior. Among the 31-analyzed samples at different temperatures, 14 samples display sudden slips, or stress-drops, called \u201cserrations\u201d, which are reminiscent of the Portevin-LeChatellier (PLC) effect that is well studied for conventional materials25262728293031323334353637383940large) serrations that occur less regularly than in the type-C PLC-bands, along with smaller slips that may have a fairly-broad size distribution, and type-A PLC-bands252627282930313233343536373839252627282930313233343536Tensile test results have shown that the present FCC alloy series of CoCrFeMnNi have good elongation between 15% and 50% in the range of test temperatures and strain-rates. 252627282930313233343536\u22124/s, the Ni metal and CoNi alloy do not display serrations from 300\u2009\u00b0C to 700\u2009\u00b0C. The CoFeNi alloy has serrations from 400\u2009\u00b0C to 500\u2009\u00b0C. CoCrFeNi has serrations from 300\u2009\u00b0C to 600\u2009\u00b0C. CoCrFeMnNi has serrations from 300\u2009\u00b0C to 620\u2009\u00b0C. Note that over the temperature ranges we explored, we observed serrations only in the ternary, quaternary, and quinary alloys. Additionally, the temperature range of serrations broadens, as the number of elements increases. As for the evolution of serration types, the quinary alloy displays the whole span evolving from type A at low temperatures to type B at medium temperatures and to type C at high temperatures, which is consistent with the general observation from conventional alloysIn C(S), which gives the fraction of serrations that are larger than size, S. Here S is defined as the total stress drop observed during a serration. In the following sections, we first describe a simple model that explains (1) the observed time series properties of the serrations  and (2) the observed scaling behavior of the serration-size distributions and their dependence on temperature, strain-rate, and composition.To quantify the serration statistics, The simple coarse-grained modelN lattice points, the local stress, \u03c4l, at a lattice point, l, is given by42If the material has F is the applied stress, J is the elastic-coupling constant, and um is the cumulative slip of the weak spot at the site, m. Each point fails, when the local stress, \u03c4l, exceeds its local failure threshold (slip stress), \u03c4f,l. When site, l, fails, it slips by an amount, \u0394ul, thereby reducing the stress to a sticking stress, \u03c4a,l. The associated stress drop is \u03c4f,l\u2009\u2212\u2009\u03c4a,l\u2009~\u20092G \u0394ul, where G\u2009~\u2009J is the elastic shear modulus.where \u039b. Specifically, after a weak spot has slipped, the local failure stress, \u03c4f,l, drops from its initial value, \u03c4s,l, to a lower value, \u03c4d,l, by an amount given by the weakening parameter, \u03b5\u2009\u03c4s,l\u2009\u2212\u2009\u03c4d,l)/\u03c4s,l. It remains at this weakened value until the slip avalanche is completed. Afterwards, \u03c4f,l is increased to its initial value, \u03c4s,l, at the temperature-dependent healing rate, \u039b, until the weak spot slips again during a new avalanche, and the process repeats.For HEAs, the model assumes that weak spots are weakened even further upon slipping to model how dislocations break free from the surrounding pinning atoms. This assumption is reminiscent of the Portevin-LeChatellier (PLC) effect or dynamic strain aging2530383940The re-strengthening of the weak spots models the rearrangement of atoms around arrested dislocations, leading to the (re-)\u201cpinning\u201d or anchoring of stationary dislocations in place. The weakening process models the dislocation breaking free from the pinning atoms around it. While the dislocation is free, it can slip more easily; when it meets obstacles, it is pinned again.As we discuss below, for the alloys discussed here, the weakening, \u03b5, depends on temperature and strain-rate. \u03b5, that grows with the ratio, \u039b/\u03a9, of the healing rate, \u039b, relative to the strain-rate, \u03a9. For sufficiently-low temperatures, it is reasonable to assume that pinning of the dislocations involves activated processes. Consequently, the healing rate, \u039b, follows an Arrhenius-like temperature (T) dependence, \u039b\u2009~\u2009exp(\u2212B/T), where B is a material-dependent constant. In close analogy to a similar mechanism in polymers, known as time-temperature superposition\u039b/\u03a9\u2009~\u2009exp(\u2212B/T)/\u03a9, i.e., similar slip statistics are expected for temperatures, T, and strain-rates, \u03a9, for which exp(\u2212B/T)/\u03a9\u2009=\u2009constant. As discussed in the experimental section, this prediction is consistent with the experimental data  for the PLC effect2530383940As a result, the strengthening  rate, \u039b, in the PLC effect for MEAs and HEAs is much higher than that in the conventional PLC effect.However, there is a key difference between our proposed strengthening mechanism for medium-entropy alloys (MEAs) and high-entropy alloys (HEAs) and the conventional DSA mechanism in the PLC effect. In MEAs and HEAs, the \u201cpinning\u201d of dislocations originates from abundant sources of solutes in the whole-solute matrix. \u03a9, either by tensile deformation or by compression. The model can be solved in the mean-field theory (MFT) approximation4244i.e., in a particular temperature and strain-rate regime, the material produces small and large avalanches. The small avalanches are much smaller in extent than the sample size, so that they are not affected by sample boundaries. In contrast, the large avalanches span the system, touching opposite sample boundaries. The large avalanches recur almost periodically, while the small avalanches occur at random times between the large avalanches. The large avalanches are predicted to show crack-like scalingS\u2009~\u2009R3, of the avalanche size, S, with its radius, R. The reason for the crack-like scaling behavior is that for the large slips, the model predicts that the total amount of slip at a point grows with the radius R of the slipping area, so that the total slip integrated over the entire area scales as R3. The large avalanches typically have a Gaussian size-distribution. Their average avalanche size grows with increasing weakening, \u03b5. In contrast, for small avalanches, the model predicts S\u2009~\u2009R2. The reason is that small avalanches are more pulse-like, where the amount of slip in each slipping patch is fixed, i.e., it does not grow with the radius, R, of the slipping areaD(S), of the small slip-avalanche sizes, S, scales asThe model predicts the serration statistics for experiments in which the material is sheared at a slow strain-rate, \u03ba\u2009=\u20091.5, g is a material-specific constant, and Smax is the expected cutoff size of the power-law scaling regime of D(S)Smax\u2009~\u20091/\u03b52, decreases with the inverse square of the weakening parameter, \u03b5. The complementary cumulative distribution function (CCDF), defined as S. For the smaller slips that occur between the almost periodically-recurring largest slips, C(S) scales as4245where \u03ba\u2009=\u20091.5, andwhere again, A as a material-dependent parameter.is another quickly-decaying scaling function42\u03b5, in the model:For sufficiently-slow imposed strain-rates , the weak spots have sufficient time to fully re-heal after a slip avalanche. Consequently, the weakening, \u03b5, upon slipping again is large in this case, and the small avalanches may be almost undetectably small, because Smax\u2009~\u20091/\u03b52 is small. Strong weakening also implies almost regularly-recurring large slips with a narrowly-peaked size distribution. In this strain-rate regime, only the periodically-recurring large slips are large enough to be detectable2530383940In the intermediate strain-rate regime , there is less time to pin the dislocations between avalanches. Consequently, the dislocations cannot be pinned as strongly before they move again, making the weakening, \u03b5, smaller than in the first case. As a result, the largest small avalanche, Smax\u2009~\u20091/\u03b52, is larger than in the previous case. In contrast, the almost periodically-recurring large avalanches are smaller than before. Additionally, these large avalanches occur less regularly than in case (1). Because the small avalanches are now larger, they are more easily detectable in this regime than in the first case2530383940large) slips that occur less regularly than in the above type-C PLC-bands, and along with many broadly-distributed small slips , there is very little time for the dislocations to be re-pinned after they slip. Consequently, the model assumes that in this regime, the effective weakening, \u03b5, is small. The reason is that a slipping weak spot frees a dislocation from a much weaker pinning potential than in the other cases, because the weak spots have effectively no time to re-strengthen between slips.  In this case, one may expect Smax\u2009~\u20091/\u03b52 to be large. As we show below, in the experiments presented here, this regime is observed at the lowest tested temperatures, where the pinning atoms move more slowly than in the other two regimes, and, therefore, do not have sufficient time to strongly pin the dislocations. The resulting reduced pinning of the dislocations can reduce Smax to a smaller value46Smax the distribution will show power law scaling in the range S\u2009<\u2009Smax  the deformation rate is slow, compared to the healing rate of the weak spots , (2) the deformation rate is comparable to the healing rate [in this case the pinning of the dislocations by solute atoms is not as strong as in case (1)], and (3) the deformation rate is fast, compared to the healing rate . As explained below, these three cases correspond to different values of the weakening parameter, \u03b5, is the key parameter that determines whether the serrations in the model are of type-A, B, or C PLC-bands. The weakening, \u03b5, is determined by how much time the atoms have to pin the dislocations, before they slip again in the next avalanche. Consequently , \u039b\u2009~\u2009exp(\u2212B/T), where B is a material-dependent constant.  Larger numbers of elements are also expected to lead to faster healing rates, as they provide more mobile atoms that can move to stick to the dislocations to pin them more strongly in place.The healing rate, In summary, by tuning the temperature, strain-rate, and/or the number of elements in the alloy, the serration behavior can be tuned between the three different regimes discussed above.\u039b, first increases and, then, decreases again. The weakening, \u03b5\u2009~\u2009\u039b/\u03a9, follows the same trend. As a result, the model predicts that at fixed, low strain-rates, \u03a9, smaller serrations with a broad power-law size distribution are observed only in a specific temperature regime. This temperature range is set by the condition that that \u03b5 must be sufficiently small so that the power-law-distributed events of the maximum size, Smax\u2009~\u20091/\u03b52, are large enough to be detected in the experiments (such as in types-A and B PLC-bands). As a consequence, the model predicts that for increasing temperature, the serrated stress-strain curves are expected to move from type-A to B to C PLC-bands. At temperatures far above the serration regime, all serrations are washed out by thermal fluctuations, and the stress-strain curves look smooth. At temperatures far below this regime, serrations are not observed either, because of the lack of sufficient pinning of the dislocations by the surrounding atoms on experimental time scales in this regime. The range of temperatures that shows a broad range of serration sizes is predicted to be material specific, since the healing rate is determined by the material-specific diffusion constants of atoms.For increasing temperature, the healing rate, The model also predicts the dependence on the strain-rate and composition of the temperature window in which serrations are observed: The ratio, \u039b/\u03a9, of the healing rate to the strain-rate is the key parameter determining the temperature range where serrations are observed. We already saw that \u039b decreases with decreasing temperatures. The model, then, predicts that for smaller strain-rates, serrations are observed for a smaller window of healing rates, and, thus, for a smaller range of temperatures. The dependence of the serration statistics on \u039b/\u03a9 implies that at fixed temperatures and increased strain-rates, HEAs are predicted to move from type-C to B to A PLC-bands, to no serrations at all.\u039b/\u03a9), thereby widening the temperature range over which serrations are observed. In the following section, we compare the theoretical predictions to the experimental results.Increasing the number of components also increases the healing rate and, thus, the ratio . cted see .S, follows a power-law, S\u03ba\u2212, over a wide range of sizes, S, consistent with the model predictions of \u03ba\u2009=\u20091.5, predicted by the mean-field model for type-A bands is consistent with the observations   S, folloions see .\u22122/s for higher temperatures, except for the experiments at 300\u2009\u00b0C. This fact demonstrates that the pinning of dislocations is fast. Thus, the pinning mechanism of such alloys differs from that in conventional alloys with low solute contents, for which the pinning of dislocation is much slower. The difference in the pinning mechanisms will be quantified in future work.Furthermore, we find that the PLC effect of CoCrFeMnNi remains at greater strain-rates up to 10in-situ pin) at a relatively-fast healing rate between avalanches. In addition, as temperature is increased, the healing rate, \u039b, of the weak spots increases to a maximum at a certain temperature, and, then, quickly decreases. As a result, six phenomena are observed that are consistent with the proposed model:i.e., the healing rate, \u039b, of the weak spots increases with temperature). However, a limiting temperature is reached, when the thermal vibration of atoms is too large to settle down the effective locking . The experiments show that the working temperature range to observe serration behavior at a strain-rate of 10\u22124/s covers from around 300\u2009\u00b0C to 620\u2009\u00b0C for the present quinary alloy (CoCrFeMnNi). At temperatures above 650\u2009\u00b0C, no serrations are observed prior to the critical failure \u039b, increases and decreases again with temperature). This trend explains why the quinary alloy has the largest range, while the ternary alloy has the narrowest range. Ni and CoNi alloys are lacking sufficient sources and size differences and, accordingly, show no PLC effect , compared to conventional PLC-pinning mechanisms.The PLC effect of CoCrFeMnNi remains at higher strain-rates up to 10S, of the small stress drops follows a power law, S\u03ba\u2212, with an exponent, \u03ba, that is consistent with the theoretical value of \u03ba\u2009=\u20091.5. The range over which a power law can be observed depends on temperature, strain-rate, and material composition. The model predicts that the power law distribution is multiplied by an exponentially-quickly decaying roll-off function, which cuts off the power law at a largest slip size, Smax for the largest slip sizesSmax, where the exponential roll-off is observed depends on the temperature and the number of elements in the material. For type-B bands in a certain temperature range, Smax, is so small that the power law range is not visible and only the exponential roll-off is seen because it dominates over the power law decay for the measured slip sizes  are expected for temperatures, T, and strain-rates, \u03a9, chosen such that \u039b/\u03a9\u2009~\u2009exp(\u2212B/T)/ \u03a9\u2009=\u2009constant, or equivalentlyAs argued in the Model Section, for a given HEA material, The striking agreement of the serration statistics and the observed PLC-bands with the predictions of the model for slip avalanches shows that the serrations can be explained as avalanches of slipping weak spots. In MEAs and HEAs, the weak spots  weaken upon slipping and re-strengthen ) versus 1/T for the temperatures, T, in \u03a9, T)\u2009=\u2009, \u2009=\u2009, and \u2009=\u2009. As predicted, within the accuracy of the temperature step size in the experiments, the data points in Here \u22124/s. The effect of varying the strain-rates from 1\u2009\u00d7\u200910\u22125 to 1\u2009\u00d7\u200910\u22122/s on the serration behavior was examined. The PLC effect is observed in a specific range of temperatures and strain-rates for MEAs and HEAs, and not in LEAs representing the conventional substitutional alloys.The effect of changing temperatures and adding elements to alloys ranging from FCC-LEAs to FCC-HEAs has been studied to investigate the PLC effect at a strain-rate of 10in-situ pin) at a relatively fast healing rate between avalanches, compared to conventional alloys. In addition, the PLC effect is more pronounced in HEAs than in MEAs.As shown in the above six observations, the experimental results agree with the model introduced above. Although the pinning mechanism of such alloys is different from that in conventional alloys with low solute contents, their serrations can be explained as avalanches of slipping weak spots. The main difference is that in MEAs and HEAs, the weak spots (or dislocations) weaken upon slipping and re-strengthen  trigger other weak spots to slip, resulting in slip avalanches typically detected as sudden stress drops. During slip avalanches, the participating weak spots are weakened from their original strength to a lower strength, but they are re-strengthened during the time intervals between slip avalanches. Re-strengthening or healing of weak spots between slip avalanches is temperature-, strain-rate-, and composition-dependent. More abundant sources of solute atoms give higher healing rates. The healing rate reaches a maximum at a material-specific temperature and strain-rate. For the temperature regime in which type-A PLC-bands are observed, the healing rate has an Arrhenius-type temperature dependence. For a given HEA material, similar slip statistics are observed for experiments at similar ratios of the healing rate to strain-rate, thereby revealing an underlying deformation mechanism that is analogous to the time-temperature superposition in polymersIn the present series of experiments on LEAs (Ni and CoNi), MEAs (CoFeNi and CoCrFeNi), and HEA (CoCrFeMnNi) with a single FCC structure, serration phenomena are only found in MEAs and HEA. The experimental results are in remarkable agreement with the predictions of a simple MFT model. The model predicts that the critical exponent, The results provide us with a new understanding of the deformation mechanisms of LEAs, MEAs, and HEAs and a simple mechanism for the PLC effect in general. The observed serration statistics are related to the more general phenomenon of crackling noise and/or avalanches in many other systems, ranging from HEAs, conventional alloys, bulk metallic glasses, nanomaterials and magnets to earthquakes and other systems3642444546\u22124/s and a data-acquisition frequency of 20\u2009Hz. Each alloy was tested at different temperatures:, 300\u2009\u00b0C, 400\u2009\u00b0C, 500\u2009\u00b0C, 600\u2009\u00b0C, and 700\u2009\u00b0C. The CoCrFeMnNi alloy had additional samples tested at 275\u2009\u00b0C, 325\u2009\u00b0C, 350\u2009\u00b0C, 375\u2009\u00b0C, 620\u2009\u00b0C, and 650\u2009\u00b0C, with additional strain-rates of 10\u22122/s, 10\u22123/s, and 10\u22125/s for detailed investigations. For each condition, 3 or 4 test specimens were used. The stress versus time data was recorded during the experiment. The complementary cumulative distribution function, C(S), of stress-drop sizes for each condition was extracted from a representative curve of three or four measured curves45The five experimental alloys were vacuum arc-melted from the starting elements with purities higher than 99.9 weight percent (wt. %). Each sample was re-melted and re-solidified at least four times to assure the uniform composition under the protection of argon. The alloys were, then, cast into a slab of dimensions, 10\u2009mm\u2009\u00d7\u200920\u2009mm\u2009\u00d7\u200940\u2009mm. After surface machining on cast slabs, a cold-rolling reduction of 65% was performed from the initial thickness of 8\u2009mm to a thickness of 3.2\u2009mm. The alloys were subsequently subjected to a homogenization treatment at 1,100\u2009\u00b0C for 6\u2009hours and follow-on quenching in water. The sheets were wire cut by the electrical discharge machine into tensile specimens with dimensions shown in How to cite this article: Carroll, R. et al. Experiments and Model for Serration Statistics in Low-Entropy, Medium-Entropy, and High-Entropy Alloys. Sci. Rep.5, 16997; doi: 10.1038/srep16997 (2015)."}
+{"text": "A number of alignment tools have been developed to align sequencing reads to the human reference genome. The scale of information from next-generation sequencing (NGS) experiments, however, is increasing rapidly. Recent studies based on NGS technology have routinely produced exome or whole-genome sequences from several hundreds or thousands of samples. To accommodate the increasing need of analyzing very large NGS data sets, it is necessary to develop faster, more sensitive and accurate mapping tools.HIA uses two indices, a hash table index and a suffix array index. The hash table performs direct lookup of a q-gram, and the suffix array performs very fast lookup of variable-length strings by exploiting binary search. We observed that combining hash table and suffix array (hybrid index) is much faster than the suffix array method for finding a substring in the reference sequence. Here, we defined the matching region (MR) is a longest common substring between a reference and a read. And, we also defined the candidate alignment regions (CARs) as a list of MRs that is close to each other. The hybrid index is used to find candidate alignment regions (CARs) between a reference and a read. We found that aligning only the unmatched regions in the CAR is much faster than aligning the whole CAR. In benchmark analysis, HIA outperformed in mapping speed compared with the other aligners, without significant loss of mapping accuracy.Our experiments show that the hybrid of hash table and suffix array is useful in terms of speed for mapping NGS sequencing reads to the human reference genome sequence. In conclusion, our tool is appropriate for aligning massive data sets generated by NGS sequencing.The online version of this article (doi:10.1186/s13015-015-0062-4) contains supplementary material, which is available to authorized users. Recent studies based on next-generation sequencing (NGS) technology have produced hundreds or thousands of exome or whole genome sequences with decreasing cost of NGS experiments . As the All HT-based alignment tools use the same seed-and-extend strategy , 12, whiSupport of long-read alignment, high speed, accuracy, and sensitivity are essential features of the current NGS mapping tools. Here, we tried to merge the advantages of HT-based and suffix tree-based alignment in a tool that satisfies these requirements. To this end, we developed a genome mapper using hybrid index-based sequence alignment (HIA).In this article, we describe the HIA tool, and show the results of comparisons of performance on simulated and real read data between HIA and the other four popular alignment tools including BWA, Bowtie2, SOAP2 and SeqAlto. The results of the benchmark analysis demonstrate that HIA outperforms the other aligners, especially in speed.0s1 \u2026 sm\u22121 be a string over \u03a3. Let |S|\u00a0=\u00a0m be the length of S, S[i]\u00a0=\u00a0si be the i-th symbol of S, S\u00a0=\u00a0si \u2026 sj be a substring, and Si\u00a0=\u00a0S be a suffix of S. We define a q-gram as a substring of S with length q. In the context of DNA sequence, the alphabet \u03a3 consists of the four nucleotides A, C, G, and T, i.e., \u03a3\u00a0=\u00a0{A, C, G, T}. We assign A, C, G, and T to the numbers 0, 1, 2, and 3, respectively. Thus, each q-gram is encoded as an unsigned integer with two bits per nucleotide. However, most reference genome sequences contain a nucleotide other than {A, C, G, T}, such as \u2018N\u2019. This occasionally happens with NGS read sequences as well. We replace \u2018N\u2019 with a uniform random nucleotide such as BWA and many other tools do.Let \u03a3 be an alphabet and S\u00a0=\u00a0sq\u00a0+\u00a01. Given a q-gram, HT[x] is the first position of the q-gram in SA, where x is the numeric value of the q-gram. We define the range (R) of the q-gram in SA by  is empty.In terms of a hybrid index, SOAP2 implements a hash table on the FM-index which is a compressed SA. On the other hand, our hybrid index consists of a reference sequence, a suffix array (SA), and a hash table (HT), as in Fig.\u00a0The procedure for constructing the hybrid index consists of four processes, as follows: 1) packing the reference sequence in a 2-bits per base format (Sequence); (2) counting each q-gram in the sequence and set the range of q-grams in SA (HT); (3) inserting the sequence positions of each q-gram into its range of SA; and (4) sorting the range for each q-gram (SA) lexicographically. Based on the heuristic determining the final positions of most of the suffixes using only the first few symbols of each suffix , the SA  packing Retrieving positions of a query Q in the sequence is implemented in two steps: HT lookup and binary search of the SA. If the prefix of Q of length q (q-gram) is a substring of the sequence, we find the range (R) in which the q-gram belongs in the SA, using Eq.\u00a0. OtherwiHybrid mapping follows the same seed-and-extend approach used by all HT-based tools. A MR (matching region) is a common substring between the reference sequence and the read. Let \u2018sp\u2019 be the starting position in the reference sequence where the MR occurs. We will indicate each MR as 3-tuple <dv, ro, L>, where \u2018ro\u2019 (read offset) is the starting position in the read where the MR occurs, \u2018dv\u2019  is defined as dv\u00a0=\u00a0sp\u00a0\u2212\u00a0ro, and \u2018L\u2019 is the length of the MR. Given a length-m\u2032 MR, there are (m\u2032\u00a0\u2212\u00a0q\u00a0+\u00a01) q-grams having the same diagonal values and consecutive read offsets. Diagonal values having same values implies that the corresponding MRs are close each other in the reference sequence. A CAR  is a list of MRs, which are close each other and ordered by \u2018ro\u2019. We define a CAR as a seed and align only the unmatched regions in CAR.I.Retrieve range of SA of each q-gram using HT and SAThe procedure for finding MRs and CARs of a read is as follows: 1) retrieving range of SA of each q-gram using HT and SA; (2) computing diagonal values; (3) sorting by diagonal value and offset; (4) grouping MRs with same diagonal value and successive offsets; (5) merging the adjacent MRs into CARs; (6) sorting the CARs by matched bases in descending order. For example, given a read (r\u00a0=\u00a0GCCATG) and q-gram length (q\u00a0=\u00a02) and the hybrid index constructed in Fig.\u00a0 retrievi0-th q-gram positions: 1-th q-gram positions: (CC: SA[8])2-th q-gram positions: 3-th q-gram positions: II.Compute diagonal values4-th q-gram positions: (TG: SA[15])III.Sort by diagonal value and offset, , , , , , , IV.Group MRs with same diagonal value and successive offsets, , , , , , , MR0:  \u2190 MR1:  \u2190 , , MR2:  \u2190 V.Merge the adjacent MRs into CARs and set matched basesMR3:  \u2190 , , CAR0: CAR1: VI.Sort the CARs by matched basesCAR2: CAR1: CAR0: CAR2: .Although diagonal values of two adjacent MRs are different, they could be located in a same CAR if there were inserted or deleted bases between them. In the case of CAR1, the difference value between diagonal value of MR1 and diagonal value of MR2 is 1 and there is one inserted base (C) between MR1 and MR2. We refer to this value as adjacency and we use the value in order to set the permitted size of insertion and deletion between MRs.In order to find MRs and CARs efficiently, we apply three heuristics. Let the read length and the error rate be m and \u03b5, respectively. The first heuristic is that there is a common substring of length at least m/(k\u00a0+\u00a01) between two reads of length m with k differences . Let \u03bb\u00a0=The formula  is the cSecondly, since a q-gram that occurs in many regions in the sequence is not a good discriminator, such q-gram was given less weight than one that occurs in few regions. This heuristic is based on the inverse document frequency (IDF) commonly used in the field of information retrieval. The IDF is a measure of whether or not the term is common across all documents . ApplyinFinally, given a read (r) and two strings, S1 and S2, both of length m, if the number of matched bases between r and S1 is greater than the number of matched bases between r and S2, then the number of differences between r and S1 is smaller than the number of differences between r and S2. This heuristic can be used to rank CARs by the number of matched bases and to filter out the lower-ranked CARs.To align the top-ranked CARs, we simply align the unmatched regions in each CAR, because the MRs are already aligned (matched). We classify the unmatched regions into three groups: leftmost unmatched region (LMUR), which is the left unmatched region of the first MR in a CAR; rightmost unmatched region (RMUR), which is the right unmatched region of the last MR in a CAR; and unmatched regions between two MRs (MRURs). The matched and unmatched region can be separated because of mismatch, insertion and deletion. We analyze these split causes such as Fig.\u00a0There are also many split causes of MRUR like as Fig.\u00a0Hybrid mapping might miss some CARs and result in the failure of mapping (unmapped). The main reasons for missed CARs might be one of following reasons: (1) too many errors in a read; (2) too many highly frequent q-grams in a read; and (3) many high-ranked CARs. In the first case, a long q-gram based on the first heuristic approach results in empty q-gram ranges. In the second case, the second heuristic approach causes highly frequent informative q-grams to be missed. In the third case, the lower-ranked but informative CARs are lost because of the third heuristic approach. We applied extended hybrid mapping to the unmapped, which uses shorter q-grams including some highly frequent q-grams, and extends ranked CARs further. Together, these modifications increase the sensitivity of the technique.We implemented HIA on Java to support multiple platforms , Unique (%), Q10 (%) and Time (s). The Aligned (%) denotes the percent of aligned reads over total reads and indicates the overall mapping rate. The Unique (%) measures the percent of uniquely aligned reads over total reads and refers to MAPQ\u00a0\u2265\u00a01. The Q10 (%) measures the fraction of mapped reads MAPQ\u00a0\u2265\u00a010. The Time is the elapsed time (seconds) including both the index loading time and the alignment time. In the case of the simulated datasets, the %Err measures the percent of wrong aligned reads over the reads satisfying Unique (%) or Q10 (%). We adopt the concept of a correct alignment from Langmead and Salzberg , who detTo evaluate the performance of HIA, we compared HIA to BWA, Bowtie2, SOAP2 and SeqAlto on six simulated datasets and two real datasets. In all tests, we used the GRCH37 build of the human genome as the reference sequence used in alignment. We performed the alignments using a computer with two Intel Xeon 6-Core X5670 2.93-GHz processors and 48\u00a0GB RAM. All alignment tools were run with a single thread for alignment except for multi-thread tests.Table\u00a0In the perspective of SA construction, we performed several tests of index generation and compared the results from our index generation algorithm and the divsufsort that is one of the best SA construction algorithms . It was We ran six of the aligners with various parameter settings for 100, 150, 250 and 400\u00a0bp single-end reads. All results can be found in the Additional file Table\u00a0We also ran six of the aligners with the same parameter settings as in the single-end reads for 100 and 150\u00a0bp paired-end reads. All results can be found in the Additional file Table\u00a0We ran six of the aligners with various parameter settings for one paired-end reads and two single-end reads. All results can be found in the Additional file Table\u00a0We ran six of the aligners with 6 threads and 12 threads modes for the whole of the paired-end HiSeq reads. All results can be found in the Table\u00a0We developed a new sequence alignment tool for aligning short and long reads to a reference genome. HIA has two indexes, a HT index and a SA index. The HT is capable of direct lookup of a q-gram, and the SA can very rapidly look up q-grams of variable length. Our experiments show that the hybrid of HT and SA is useful, from the perspective of speed, for mapping NGS sequencing reads to a reference genome sequence. HIA also supports the multithreading of mapping. In particular, HIA is much faster than all of the other aligners; therefore, our tool is appropriate for aligning massive data sets generated by NGS sequencing.The accuracy of alignment is very important in re-sequencing because the main purpose of alignment is to discover the variants relative to a reference genome. Although these variants (or sequencing errors) cause sequencing reads within them to match inexactly to the reference, alignment tools should nonetheless correctly map these reads to the reference. Considering the results of the benchmark analysis, we can conclude that HIA performs comparably to four popular alignment tools.Project name: HIAhttp://biomi.cdc.go.kr/hia/Project home page: Operating systems: Platform independentProgramming languageLicense: GNU GPLAny restrictions to use by non-academics: none."}
+{"text": "PMS receives as input n strings and two integers \u2113 and d. It returns all sequences M of length \u2113 that occur in each input string, where each occurrence differs from M in at most d positions. Another formulation is quorum PMS (qPMS), where the motif appears in at least q% of the strings. We introduce qPMS9, a parallel exact qPMS algorithm that offers significant runtime improvements on DNA and protein datasets. qPMS9 solves the challenging DNA -instances  and . The source code is available at https://code.google.com/p/qpms9/.Discovering patterns in biological sequences is a crucial problem. For example, the identification of patterns in DNA sequences has resulted in the determination of open reading frames, identification of gene promoter elements, intron/exon splicing sites, and SH RNAs, location of RNA degradation signals, identification of alternative splicing sites, etc. In protein sequences, patterns have led to domain identification, location of protease cleavage sites, identification of signal peptides, protein interactions, determination of protein degradation elements, identification of protein trafficking elements, discovery of short functional motifs, etc. In this paper we focus on the identification of an important class of patterns, namely, motifs. We study the ( It returns all possible biological sequences M of length \u2113 such that M occurs in each of the input strings, and each occurrence differs from M in at most d positions. Any such M is called a motif.The Planted Motif Search (PMS) problem, also known as the  motif search is the Closest Substring problem. The Closest Substring problem is essentially the PMS problem where the aim is to find the smallest d for which there exists at least one motif. These two problems have applications in PCR primer design, genetic probe design, discovering potential drug targets, antisense drug design, finding unbiased consensus of a protein family, creating diagnostic probes and motif finding . In qPMS we are interested in motifs that appear in at least \u2113-mer) M is generated and \u201cplanted\u201d at a random location in each input string (or in q% of the input strings for qPMS). Every planted instance of the motif is mutated in exactly d positions.The Closest Substring problem is NP-HardDefinition 1.An  instance is defined to be achallenging instanceif d is the largest integer for which the expected number of motifs of length \u2113 that would occur in the input by random chance does not exceed a constant . According to the above definition, the challenging instances for PMS are , , , , , , , , , , etc.Intuitively the more we increase \u2113-mers coming from distinct input strings. In the pattern driven stage, the algorithm generates the common d-neighborhood of the \u2113-mers in the tuple. Each such \u2113-mer becomes a motif candidate. The size of the tuple is usually fixed to a value such as 1 . For any string T, we denote the substring of T starting at position i and ending at position j by T[i..j].We start by defining the PMS and qPMS problems more formally. A string of length Definition 2.1, s2, \u2026, sn, over an alphabet \u03a3, and two integers \u2113 and d, identify all \u2113-mers M, M \u2208 \u03a3l, such that \u2200i, 1 \u2264 i \u2264 n, \u2203ji, 1 \u2264 ji \u2264 |si| \u2212 l + 1, such that Hd \u2264 dThe PMS problem: Given n sequences s.Definition 3.The qPMS problem: same as the PMS problem, however the motif appears in at least q% of the strings, instead of all of them. PMS is a special case of qPMS for which q = 100%.d-neighborhood. Given a tuple of \u2113-mers T = , the common d-neighborhood of T includes all the \u2113-mers r such that Hd \u2264 d, \u00b51 \u2264 i \u2264 s.Another useful notion is that of a \u2113-mer and the consensus total distance for a tuple of \u2113-mers. The consensus \u2113-mer for a tuple of \u2113-mers T =  is an \u2113-mer u where u[i] is the most common character among  for each 1 \u2264 i \u2264 \u2113. If p is the consensus \u2113-mer for T then the consensus total distance of T is defined as \u2113-mers.We now define the consensus \u2113-mers  are generated, where it is an \u2113-mer in iS. Then, in the pattern driven part, for each tuple, its common d-neighborhood is generated. Every \u2113-mer in the neighborhood is a candidate motif. In PMS8k is variable. By default, a good value for k is estimated automatically based on the input parameters , where it is an \u2113-mer from string is, \u2200i = 1..k, are generated based on the following principles. First, if T has a common d-neighborhood, then every subset of T has a common d-neighborhood. Second, for a motif to exist, there has to be at least one \u2113-mer u in each of the remaining strings ks + 1, ks + 2, \u2026, ns such that T \u222a {u} has a common d-neighborhood. We call such \u2113-mers u \u201calive\u201d with respect to tuple T. As we add \u2113-mers to T we update the alive \u2113-mers and reorder the strings in increasing order of the number of alive \u2113-mers. This reordering reduces the running time because it leads to generating fewer tuples overall.In the sample driven part of PMS8, tuples T be the current tuple of \u2113-mers and let u be an alive \u2113-mer with respect to T. If we add u to T, then the consensus total distance of T increases. We compute this additional distance Cd(T\u222a{u}) \u2212 Cd(T). For each of the remaining strings, we compute the minimum additional distance for any alive \u2113-mer in that string. Then we sort the strings decreasingly by the minimum additional distance. Therefore, we give priority to the string with the largest minimum additional distance. If two strings have the same minimum additional distance, we give priority to the string with fewer alive \u2113-mers. The intuition is that larger additional distance could indicate more \u201cdiversity\u201d among the \u2113-mers in the tuple, which means smaller common d-neighborhoods. The pseudocode for generating tuples T is given in GenTuples where the matrix R contains all the \u2113-mers in all the input strings, grouped as one row per string.In qPMS9 we change the criteria by which the strings are reordered, as follows. Let T, obtained as described in the previous section, we generate the common d-neighbors of the \u2113-mers in the tuple. In qPMS9, the neighbor generation uses the same process as in PMS8For every tuple T =  of \u2113-mers, we want to generate all \u2113-mers M such that Hd \u2264 d, \u2200i = 1..k. We traverse the tree of all possible \u2113-mers. A node at depth r, which represents an r-mer, is not explored deeper if certain pruning conditions are met. Necessary and sufficient conditions for 2 and 3 \u2113-mers to have a common neighbor are given in Ref. \u2113-mers to have a common neighbor. The interested reader is referred to the PMS8 paperGiven a tuple \u2113-mer in a given string by adding it to the tuple T and recursively calling the algorithm for the remaining strings. For the qPMS version we have an additional step where, if the value of q permits, we skip the current string and try \u2113-mers from the next string. At all times we keep track of how many strings we have skipped. The pseudocode for this algorithm is given in QGenerateTuples where R contains all the \u2113-mers in all the strings.We extend the algorithm to solve the qPMS problem. In the qPMS problem, when we generate tuples, we may \u201cskip\u201d some of the strings entirely. This translates to the implementation as follows: in the PMS version we successively try every alive m = |s1| \u2212 \u2113 + 1 independent subproblems P1, P2, \u2026, mP, where iP explores the d-neighborhood of \u2113-mer s1[i..i + \u2113 \u2212 1]. In the parallel implementation, processor 0 acts as both a master and a worker, the other processors are workers. Each worker requests a subproblem from the master, solves it, then repeats until all subproblems have been solved. Communication between processors is done using the Message Passing Interface (MPI).In PMS8q version. We split the problem into subproblems P1,1, P1,2, \u2026, P2,1, P2,2, \u2026, rP,1, rP,2, \u2026, r = n \u2212 Q + 1 and iPj, explores the d-neighborhood of the j-th \u2113-lmer in string is and searches for \u2113-mers M such that there are Q \u2212 1 instances of M in strings is+1, \u2026, ns. Notice that Q is fixed, therefore subproblems iPj, get progressively easier as i increases.In qPMS9, we extend the previous idea to the \u2113-mer M as a motif and plant modified versions of it in q% of the n strings. Each planted instance is modified in d random positions.As mentioned in the introduction, PMS algorithms are typically tested on datasets generated as follows. 20 strings of length 600 each are generated from the i.i.d. We choose an \u2113-mer u is within distance at most d from another \u2113-mer v isIt is useful to estimate how many \u201cspurious\u201d motifs (motifs expected by random chance) will be found in a random sample. For that, we make the following observations. The probability that a random \u2113-mer is within distance d from any of the \u2113-mers in a string S of length m is:The probability that an \u2113-mer is within distance d from at least q out of n strings of length m each is:The probability that an \u2113Q. Based on these formulas, we compute for every \u2113 the largest value of d such that the number of spurious motifs does not exceed 500. These values are presented in Therefore, the expected number of motifs for a given qPMS instance is: |\u03a3|q = 100% we compare all three algorithms, for q = 50% we compare only the algorithms that solve the quorum PMS problem: TraverStringRef and qPMS9. All programs were executed on the Hornet cluster at the University of Connecticut, which is a highend, 104-node, 1408-core High Performance Computing cluster. For our experiments we used Intel Xeon X5650 Westmere cores. Most results refer to single core execution, unless specified otherwise.In this section we analyze the running times of PMS8q = 100%. In In q = 50%. In q = 50%.In \u2113 and d with \u2113 up to 50 and d up to 25, with q = 100%. In \u2113 and d with \u2113 up to 30 and d up to 21, with q = 100%.In \u2113 and d such as  for DNA data or  for protein data.We have presented qPMS9, an efficient algorithm for Quorum Planted Motif Search. The algorithm is based on the PMS8 algorithm\u2113-mers for Hamming Distances could benefit for the work in Ref. For future work, one of our reviewers kindly pointed out that our approach of filtering"}
+{"text": "This paper addresses the budget constrained and delay-bounded placement problem (BCDP) for roadside units in vehicular ad hoc networks. There are two types of RSUs: cable connected RSU (c-RSU) and wireless RSU (w-RSU). c-RSUs are interconnected through wired lines, and they form the backbone of VANETs, while w-RSUs connect to other RSUs through wireless communication and serve as an economical extension of the coverage of c-RSUs. The delay-bounded coverage range and deployment cost of these two cases are totally different. We are given a budget constraint and a delay bound, the problem is how to find the optimal candidate sites with the maximal delay-bounded coverage to place RSUs such that a message from any c-RSU in the region can be disseminated to the more vehicles within the given budget constraint and delay bound. We first prove that the BCDP problem is NP-hard. Then we propose several algorithms to solve the BCDP problem. Simulation results show the heuristic algorithms can significantly improve the coverage range and reduce the total deployment cost, compared with other heuristic methods.In vehicular  A vehicormation ,3, geocaormation  and dataormation ,6. Meanwormation \u20139, conteormation \u201313, and ormation ,15. In aSeveral RSUs or AP placement algorithms have been proposed \u201319. MostThe problem of our concern is as follows. We are given a set of candidate sites in a region, each of which can be installed a c-RSU or a w-RSU (or none). The candidate site is usually located at the intersection of roads or along the road, such as a lamp post or a tree. Given a budget constraint and a specified delay bound, the problem is how to place the c-RSUs and w-RSUs with the maximum delay-bounded coverage, such that a message sent from the c-RSUs can be disseminated to more vehicles in the region within the delay bound.We propose a delay-bounded coverage model for RSUs placement, in which each candidate site has an attached delay-bounded coverage by installing a RSU. This model inherently provides a good balance between delay and coverage. Base on this model, we formulate the BCDP problem to a budgeted maximum coverage problem and prove that this problem is NP-hard.We develop two heuristic algorithms under delay-bounded coverage model. In this model, we greedily find the optimal candidate site with a maximum delay bounded coverage gain and utility until no further installing can be made due to the budget constraint.We conduct an extensive simulation study over different data to evaluate the performances of the proposed methods. Simulation results show our heuristic algorithms can significantly improve the coverage range and reduce the total installation cost, compared with other heuristic methods.There are several challenges for solving the budget constrained and delay-bounded problem in a VANET. First, we consider the placement of hybrid RSUs, that for each candidate site we need to decide what type of RSUs to choose, which is more complicated than the placement of the same type of RSUs; Second, we study the placement of RSUs for the delay bounded information dissemination, which is required by many real-time applications in vehicular networks. The main contributions of the paper are as follows:The rest of this paper is organized as follows. Previous studies are summarized in Section 2. We present the system model and assumption in Section 3. The detailed description of our delay-bounded coverage model and our greedy algorithms are in Sections 4 and 5, respectively. In Section 6, we evaluate our proposed approaches by comparing them with different simulation environment. Our conclusion is in Section 7.2.2.1.ad hoc networks [et al. [et al. [et al. [et al. [et al. [et al. [et al. [et al. [Recently, the research have attracted a lot of attention on the data delivery and message dissemination in vehicular networks \u201325. As tnetworks \u20137,26,27. [et al.  investig [et al.  exploite [et al. ,9, the a [et al.  studied  [et al.  exploite [et al.  proposed [et al. \u201330. Skor [et al.  addresse [et al. , the aut2.2.et al. [et al. [There are some published work about the node and AP placement problem in wireless sensor networks \u201338. Theset al.  propose et al.  also stu [et al.  investiget al. [et al. [et al. [et al. [Previous work addressed the problem of relay nodes placement in homogeneous wireless sensor networks. Han et al.  addresseet al. ,37, the  [et al.  addresse [et al. \u201341. Zhan [et al.  studied 2.3.ad hoc networks [Meanwhile, there are some published work related to the problem of RSUs or stationary relay nodes placement in vehicular networks \u201319,42\u201345networks , authorsnetworks , where tnetworks , the autnetworks , the autnetworks ,45 are mnetworks  studied The difference between the above work with ours is that, we consider the delay-bounded placement problem, rather than minimize the number of RSUs in vehicular networks. Meanwhile, we consider the optimal placement scheme for the both infrastructure-based and infrastructure-less RSUs. To the best of our knowledge, our work is the first to study this problem in the literature.3.We assume all c-RSUs have the same communication range, and the communication range is larger than the w-RSUs. The warning information, such as traffic accident or vehicle jam, disseminates from the traffic control center(TCC) to all c-RSUs firstly. TCC is a centralized controller that maintains the city's traffic. Then, the message spreads to the w-RSUs through wireless link. In the end, the message floods from c-RSUs and w-RSUs to all the vehicles.In the case of c-RSUs, we assume the information delay from TCC to all c-RSUs doesn't take any time (there is no delay). The assumption is acceptable as all c-RSUs have the wired network connectivity to the TCC, and the information delay almost can be ignored.In the case of w-RSUs, we further assume that a w-RSU only receives the message from a nearby c-RSU or w-RSU, but never gets the message from a passing vehicle. Once receiving a message, a w-RSU would broadcast the message immediately. Thus, a w-RSU is connected to other RSUs to serve as an effective extension to the backbone formed by c-RSUs.For information dissemination, the vehicle receives a message from an RSU when it passes the RSU, and retrieves the \u201cfresh\u201d messages stored in the RSU and carry it forward for further dissemination. A moving vehicle on the road can also pass its messages to other vehicles via the OBUs equipped them. In this case, we call it the carry-and-forward delay. Due to carry-and-forward delay several orders of magnitude longer than the communication delay, we assume that the communication delay also approximately equals 0. The assumption is acceptable as the unit of carry-and-forward delay is a second and the unit of communication delay is a millisecond.A VANET system consists of a set of vehicles equipped with on-board units (OBUs) and a set of roadside units (RSUs) that are installed at the road side. The system model and assumption are as follows:G = , while the vertex set V (G) = {v1, v1, \u2026, mv} consists of all candidate sites, and the number of candidate sites is m; the edge set E(G) = {e1, e1, \u2026, ne} consists of the entire road segments, and the number of road segments is n. Each edge is associated with a delay weight ijd, which is the expected delay from iv to its adjacent vertex jv. That means iv is connected to jv an edge in a road graph, and we call iv and jv are neighbors. According to the [R is the wireless transmission range, ij\u03c1 is the vehicle density between road e, c is the average one-hop packet transmission delay, ijl is the Euclidean distance of road e, and s\u0304 is the average vehicle speed on road e.We model a road network as a undirected weighted road graph g to the ,25, we hBv and Ev.As shown in 4.In this section, we present the delay-bounded coverage model based on the road graph. In the model, we discuss in detail how to calculate the delay-bounded coverage by installing RSUs. Then, we formally formulate the BCDP problem based on the delay-bounded coverage model.4.1.i associated with the delay-bounded coverage, we calculate the information propagation delay first. Let ijD denote the expected information dissemination delay for broadcasting a message to all vehicles on the path between any candidate sites i and j. When iv and jv are neighbors, ijD equals to the delay ijd. If i and j do not have a road directly connecting them, ijD is the shortest path between iv and jv. Notice that ijD is calculated by assuming there is no RSU installed in the middle along the route between i and j. Let N(i) denote all the neighbors of node i, we calculate ijD as follows:As the benefit of candidate site Next, we introduce the calculation of delay-bounded coverage for installing a i-RSU or a w-RSU, respectively. Then, we calculate the placement cost.4.2.Now we calculate the delay-bounded coverage for installing an RSU. We give some definitions as follows.i, denoted byCommunication Set of vertex v(i), i, any vertex inis a set of vertex that if we install an RSU in site v(i) is within the communication range of the vertex vi.iv, and the candidate site jv is within the communication range of iv, then we have jv \u2208 (i). We denote c(i) and w(i) as the communication set of installing a c-RSU and a w-RSU at site iv, respectively.If we install an RSU in site i, denoted byDelay-bounded Coverage of a vertex v(i), i, a vehicle at any edge eis a set of edge that if we install a c-RSU in site v \u2208 i would receive the message within the delay bound T.According to Definition 2, we havec(i) and w(i) as the delay-bounded coverage of installing a c-RSU and a w-RSU at site iv, respectively. We denote c and w as the c-RSUs placement set and w-RSUs placement set, respectively. We denote  = c \u222a w as the RSUs placement set. Then we give the following definition.We denote Communication Set of placement set, denoted by, is a set of placement setthat the expected end \u2013 end propagation delay from one vertex to any other vertex which are both in setis zero. of placement set  iteratively. We denote (k) as the communication set value of k-th iteration. Initially, the placement set  = \u2205 and the communication set  = \u2205. When we place an RSU at site i, the placement set  = {iv}. The communication set  equals to the communication set of iv. That is j, then the placement set  = {i, vjv}. Due to that we don't consider the delay between wired line, site i receives the information from site j in no time. Therefore, the communication set  equals to the union set of transmission range set of jv, that is According to the Definition 3, we calculate the communication set Delay-bounded Coverage of placement set, denoted by, is a edge set of placement setthat a vehicle at any edge e \u2208 would receive the message within the delay bound T.According to the Definition 4, we have:(k) as the delay-bounded coverage of the k-th iteration. v1 to v9, and we model the system as a undirected weighted road graph G. In graph G, each edge has the information dissemination delay of weight 1 unit and each RSU has also 1 unit communication range. Then, we could use v1, and we obtain the placement set  = c = {v1}. Since vertex v1, v2 and v4 are within the communication range of v1, the communication set T = 1 unit. Then, we could derive the delay-bounded coverage v6 as shown in v1 and v6 due to cable connected between them. As the placement set is  = {v1, v6} and the communication set of v6 is c(6) = {v3, v5, v6, v9}, we iteratively derive the communication set v6 is c(6) = {e, e, e, e, e, e, e}, and the delay-bounded coverage of this iteration is  = c = {v1, v6}. As shown in w = {v2} and c = {v1}, and the black thick lines are the delay-bounded coverage road segments in this iteration.Where 4.3.Given a budget constraint B, a delay bound T, a set of candidate sites, our goal is to find a candidate sites optimal set such that provides maximum delay-bounded coverage in a delay bound T with the given budget constraint B.Our problem can be viewed as a Budget Constrained and Delay-bounded RSUs Placement problem (BCDP for short) over road graphs, that is: ic and i to be installed a c-RSU and a w-RSU respectively Obviously, the placement cost of installing c-RSUs or w-RSUs is totally different. It is known that each c-RSU installation with power and wired network connectivity can cost as high as US$5000 [X = {x1, x2, \u2026,nx} denote whether site i will be installed a c-RSU or not. If site i is selected to install a c-RSU then ix = 1, otherwise ix = 0. In a similar way, we denote Y = {y1, y2,\u2026,ny} whether site i will be installed a w-RSU or not.We denote  US$5000 . Let X =Therefore, our objective is to maximize the delay-bounded coverage of placement RSUs in the region, that is:B. Constraint x, y as binary. Constraint Constraint The BCDP problem is difficult to solve, as shown in the following theorem.The BCDP problem is NP-hard.To provide the evidence of NP-hardness, we provide a polynomial reduction from a budgeted maximum coverage problem  to the BU; S; c): Let U = {e1, e2, \u2026ne} denote a set of n elements, S consists of finite sets S1, S2, \u2026, kS \u2286 U, and a cost function c : S \u2192 Q+. The objective is to find a subset S\u2032 \u2286 S, such that the total cost of elements in S\u2032 does not exceed a given budget B, and the total weight of elements covered by S\u2032 is maximized.A budgeted maximum coverage problem  and wg(i) as the delay-bounded coverage gain of installing a c-RSU and a w-RSU at site i, respectively. Then, we have:As proven in Theorem 1, we reduce the BCDP problem to the budgeted maximum coverage and prove that the problem is NP-hard. Due to the monotonicity of maximum delay-bounded coverage, the greedy algorithm is a competitive candidate. As our first greedy algorithm, we can select the candidate sites that maximise the delay-bounded coverage gain in each iteration. When we consider to install an RSU at site ijD between any two candidate sites in Line 2, then we calculate the delay bounded coverage gain of all candidate sites for both installing c-RSUs and w-RSUs. This is accomplished in Line 4\u20136 and Line 7\u20139, respectively. After that, we find best node which has the maximal delay bounded coverage gain. This is accomplished in Line 10. Then, we determine which type of RSUs installation. In Line 11\u201313, we install the c-RSUs as the delay-bounded gain of the selected c-RSU is the maximum one and the total cost is not exceed the budget. If the total cost is exceed the budget, the algorithm chooses a maximal delay-bounded gain for w-RSU installation in Line 14\u201316. In Line 18\u201320, we install the w-RSUs as the delay-bounded gain of the selected w-RSU is the maximum one and the total cost is not exceed the budget. After that, we add the best node to the set of placement RSUs, and remove all the delay-bounded coverage from the set of candidate sites in Line 21\u201324. Finally, in line 26, we identify the placement RSUs set of our solution.Our gain greedy algorithm for BCDP problem is presented as Algorithm 1. The major steps of Algorithm 1 are as follows. First, we compute the expect information dissemination delay Algorithm 1 Gain greedy algorithmInput:G = : The weighted road graph;T: The delay bound;B: The budget constraint;Output:c: The placement set of installing c-RSUs;w: The placement set of installing w-RSUs;1: = \u2205,  = \u2205;2:i, j \u2208 V, initial ijD according to For all 3:while the placement cost is not exceed the budget Band \u2260 |E| do4:for all unselected iv \u2208 Vdo\u20035:cg(i) according to \u2003\u2003Calc c-RSUs delay-bounded coverage gain 6:end for\u20037:for all unselected iv \u2208 U and iv is with the transmission range of an existing RSU do\u20038:wg(i) according to \u2003\u2003Calc w-RSUs delay-bounded coverage gain 9:end for\u200310:v* = {iv \u2223 max{cu(l), wu(k)}, \u2200iv \u2208 V };\u200311:if install a c-RSU and the placement cost is not exceed the budget Bthen\u200312:c = c \u222a{v*};\u2003\u2003 13:else\u200314:if install a c-RSU and the placement cost is exceed the budget Bthen\u2003\u200315:v* = {iv \u2223 max{wu(k)}, \u2200iv \u2208 V };\u2003\u2003\u2003 16:end if\u2003\u200317:end if\u200318:if install a w-RSU and the placement cost is not exceed the budget Bthen\u200319:w = w \u222a{v*};\u2003\u200320:end if\u200321:if install a c-RSU or w-RSU and the placement cost is not exceed the budget Bthen\u200322:V = V \\ {v*};\u2003\u200323: =  \u222a v*;\u2003\u2003 24:end if\u200325:end while26:returnc, w5.2.In the gain greedy algorithm, we aim at finding the maximum delay-bounded coverage gain candidate site to install an RSU. However, the placement cost of each candidate sites is also important. This is because, although a candidate site may offer a large delay-bounded gain, it may also have a huge cost such that other candidate sites cannot be installed any c-RSU.ic and iu as the cost and delay-bounded coverage utility of installing a c-RSU in site i, respectively. Then, we have:Consequently, our second greedy algorithm is to calculate the gain per unit cost for each iteration. We call it delay-bounded coverage utility. We denote In utility greedy algorithm, we aim at finding the maximum delay-bounded coverage utility candidate site to install an RSU. Therefore, our utility greedy algorithm for BCDP is presented as Algorithm 2.Algorithm 2 Utility Greedy algorithmInput:G = : The weighted road graph;T: The delay bound;B: The budget constraint;Output:c: The placement set of installing c-RSUs;w: The placement set of installing w-RSUs;1: = \u2205,  = \u2205;2:i, j \u2208 V, initial ijD according to For all 3:while the placement cost is not exceed the budget Bdo4:for all unselected iv \u2208 Vdo\u20035:cu(i) according to \u2003\u2003Calc c-RSUs delay-bounded coverage utility 6:end for\u20037:for all unselected iv \u2208 U and iv is with the transmission range of an existing RSU do\u20038:wu(i) according to \u2003\u2003Calc w-RSUs delay-bounded coverage utility 9:end for\u200310:v* = {iv \u2223 max{cu(l), wu(k)}, \u2200iv \u2208 V };\u200311:if install a c-RSU then\u200312:c = c \u222a {v*};\u2003\u200313:end if\u200314:if install a w-RSU then\u200315:w = w \u222a {v*};\u2003\u200316:end if\u200317:V = V \\ {v*};\u200318: =  \u222a v*;\u200319:end while20:returnc, wG has 36 candidate sites (v0 \u223c v35), which are numbered from the left to the right and from the top to the bottom. Graph G includes 60 road segments. Suppose the deployment cost of c-RSU and w-RSU is 2.5 and 1, respectively. The transmission range of a c-RSU and w-RSU are set to two road segments and one road segment, respectively. We assume the placement budget constrain is 5. We further assume that the expected carry-and-forward delay of each road segment is 1min, and the delay bound \u0394 is also set to 1min. v14 is selected to install a c-RSU, since the corresponding delay-bounded gain g(14) = 34 and delay-bounded coverage utility u(14) = 34/2.5 are both the maximum one. The 34 black thick lines are the road segments included in v14}{. So in the first iteration, we choose v14 to instal a c-RSU greedily for both Algorithms 1 and 2. v22 is chosen to install a c-RSU as the delay-bounded gain g(22) = 14 is the maximum one, where the red thick lines are the newly delay-bounded covered road segments. Meanwhile, the placement cost for installing this two c-RSUs is 5 and it is not exceed the budget. v16 is chosen to install a w-RSU, where the red thick lines are the newly delay-bounded covered road segments. Now the total cost is 3.5 and it is not over the budget. Note that if the budget is set to 4, the cost will be over budget for gain greedy algorithm in the second iteration. Therefore, we should not choose c-RSU to install but choose w-RSU to install. That is, we will choose v16 to install a w-RSU for gain greedy algorithm as shown in 5.3.OPT as the optimal delay-bounded coverage. Let c(k) as the placement cost of the k-th iteration. Before we derive the approximation ratio, we have following lemma first.Next, we analyze the approximation ratio of the Algorithm 2. We define After each iteration k, k = 1, \u2026, l + 1, the following inequality holds.After each iteration k, k = 1, \u2026, l + 1, the following inequality holds.The detailed proof of Lemmas 1 and 2 can be found in .The approximation ratio of the Algorithm 2 is (1 \u2212 1/e).l-th iteration. In the (l + 1)-th iteration, the placement cost is c(l + 1). As adding the c(l + 1) to B, we have:Let l + 1)-th round, according to l + 1)-th iteration, we get:As our greedy algorithm runs  \u00b7 L), where |V| is the number of candidate sites, |E| is the number of road segments and L is running rounds of Algorithm 2.ijD. The time complexity of ijD is O(|V|3) as we use Floyd-Warshall algorithm to compute the shortest path between any two candidate sites. The size of all unselected candidate sites is no more than |V|, the calculation of delay-bounded coverage will run L rounds and the calculation of delay-bounded coverage gain is no more than |E|. Therefore, The time complexity of Line 4\u20136 is O(|V| \u00b7 |E| \u00b7 L). In Line 7\u20139 of Algorithm 2, the time complexity is also O(|V| \u00b7 |E| \u00b7 L) as the number of candidate sites for w-RSUs is no more than |V|. Next, it iteratively chooses the site which has the maximum delay-bounded coverage utility in line 10 and the time complexity is O(|V|2 \u00b7L). Therefore, the total time complexity is O(|V|3 + |V| \u00b7 (|V| + |E|) \u00b7 L).Line 4\u20136 of Algorithm 2 computes the cost effectiveness for c-RSU placement. The calculation of delay-bounded coverage needs to compute 6.In this section, we evaluate the performance of our proposed algorithms, and present the simulation results of the algorithms in different situations.6.1.G. The candidate sites number is |V|, and the number of road segments is |E|. The length of road segment is set to 500 m, which is regarded as the length unit in the simulation. Therefore, a 10 \u00d7 10 network means the region has 10 \u00d7 10 evenly distributed candidate sites, with all sides 500 m \u00d7 10 = 5000 m long. The expected carry-and-forward delay of each road segment is set to 5 min. Since we consider the epidemic forwarding messages, we assume there is no transmission conflict and both vehicles and RSUs have infinite buffer to store packets. We define delay-bounded coverage ratio as the as the percentage of road segments that can be delay-bounded covered by the placed RSUs. We first study the delay-bounded coverage ratio, delay-bounded utility and number of RSUs under different candidate sites, different budget constraint, different cost ratio, different delay bounds and different transmission ranges ratio. We consider several algorithms as follows.In the synthetic simulation, we model the street layout of urban areas by a grid graph Random algorithm for hybrid RSUs installation (Random): In this algorithm, we randomly choose to install either c-RSUs or w-RSUs. In each iteration, we randomly install an RSU.Greedy-based algorithm for only c-RSUs installation (c-RSUs): In this algorithm, we greedily install and only install c-RSUs.Our gain greedy algorithm (Gain): Our proposed delay-bounded gain greedy algorithm for BCDP problem, and we greedily choose the maximum gain to install either c-RSUs or w-RSUs.Our utility greedy algorithm (Utility): Our proposed delay-bounded greedy algorithm for BCDP problem, and we greedily choose the maximum utility to install either c-RSUs or w-RSUs.6.2.We investigate how the changes of candidate sites impact the performance of the different algorithms. 6.3.6.4.We investigate how the changes of cost ratio impact the performance of the different algorithms. 6.5.We investigate how the changes of delay bound impact the cost, and the number of RSUs in 6.6.The transmission range ratio is defined as the ratio between the transmission range of c-RSUs and the transmission range of w-RSUs. 6.7.In the realistic simulation, we use the SUMO(Simulation of Urban MObility)  to conve6.8.m, the transmission range of c-RSUs is 1 km, the cost ratio is 10 and the delay bound is 5 min. As placement cost of installing a c-RSU is 10 unit, we could only install one c-RSU for the only installing c-RSUs algorithm. So we install a c-RSU with maximum gain as shown in Next, we plot the RSUs placement result under different budget constraints. We first plot the RSUs placement result of three algorithms when budget constraint is set to 15. As shown in Then, we plot the RSUs placement result when budget constraints is set to 25 unit in full coverage. Then, we do not need to place any more RSUs. Therefore, we place one c-RSU and eighteen w-RSUs at the end of the utility greedy algorithm.In full coverage for our the gain greedy algorithm when budget is over 45.In full coverage in full coverage. Obvious, the c-RSUs algorithm to cover boundary road segments is not very cost-effective. For our gain greedy algorithm, we have two placement strategy. As shown in full coverage. While budget is 51 or above 51, we place five c-RSUs and one w-RSU and we also obtain the full coverage as shown in Finally, we plot the RSUs placement result with 7.ad hoc networks, which finds maximum delay-bounded coverage and meanwhile a message sent from the c-RSUs can be disseminated to more vehicles in a given delay bound. First, we propose a delay-bounded coverage model for RSUs placement, which inherently provides a good balance between delay and coverage. Next, we formulate BCDP problem to the budgeted maximum coverage problem and prove that this problem is NP-hard. Finally, we propose two heuristic algorithms to solve the BCDP problem. Simulation results show effectiveness of our methods under different environments. As a future work, we will explore how to effectively deploy RSUs in VANET under different forwarding models.In this paper, we investigate the budget constrained and delay-bounded RSUs placement problem in vehicular"}
+{"text": "We also analyze the average SNR condition such that the multiuser diversity gainis fully exploited for two-hop transmission. The proposed two-step scheduling algorithm exhibits thequite comparable achievable rates to those of the optimal one using full feedback information, while itsrequired feedback information is reduced by half of the optimal one.We introduce an efficient multiuser scheduling method using amplify-and-forward relaying in relay-aideddownlink systems, consisting of one base station (BS), one relay station, and multiple mobilestations (MSs). In our scheme, the BS opportunistically selects both the transmission mode, that is, eitherone- or two-hop transmission, and the desired user . Closed-form expressions forthe average achievable rates are derived for the two transmission modes with multiuser scheduling, andits asymptotic solutions are also analyzed in the limit of large number of MSs. Based on the analysis, wepropose a  Cooperative relaying transmission techniques have widely been studied owing to the advantages of both enhancing the end-to-end link quality in terms of system capacity and extending the coverage . One of In wireless systems with many users, a multiuser diversity gain can be exploited to further improve the system throughput by utilizing the usefulness of fading since there are a large number of MSs in multiuser environments: opportunistic scheduling , opportuN MSs. As a combination of the traditional broadcast channel and relay channel, it matches several scenarios such as the downlink cellular environment with relay and wireless network with backbone nodes. To show the fundamental limits of such a relay-aided downlink system, in the literature  and C denote the expectation and the field of complex numbers, respectively. CN represents a zero-mean circularly symmetric complex Gaussian distribution with variance x. Unless otherwise stated, all logarithms are assumed to be to the base 2.Throughout the paper, N MSs. The channel model deals with the problem that one BS communicates with one selected MSs with or without the help of one RS. Hence, we do not assume that the BS sends different data packets to multiple MSs simultaneously since it requires the use of sophisticated multiuser detection schemes at the receivers.As illustrated in nth MS is given byhbm,n \u2208 C is the complex channel coefficient between the BS and the nth MS, Pb is the transmit power at the BS, x is the transmit signal, and wm,n denotes the complex additive white Gaussian noise (AWGN) at the nth MS, which follows CN.For one-hop transmission, we perform a direct transmission from the BS to a certain selected MS. Then, the received signal at the nth MS is then given byhrm,n \u2208 C and hbr \u2208 C are the complex channel coefficients between the RS and the nth MS and between the BS and the RS, respectively, g is the amplification factor at the RS, and wr denotes the complex AWGN at the RS, following the distribution CN. The channel coefficients hbm,n, hrm,n\u2009\u2009, and hbr are independent and identically distributed (i.i.d.) and are frequency-flat fading, where all the distributions are assumed to be CN. In our model, the amplification factor g at the RS is represented as [Pr is the transmit power at the RS.For two-hop transmission, communication is performed from the BS to one MS through the RS. We assume that the RS operates in simple half-duplex, that is, the RS is not assumed to receive and transmit data packets simultaneously, and AF mode. Then, at the first time slot, the BS transmits its data to the RS, and at the second time slot, the RS amplifies and forwards the received data to the corresponding MS. For simplicity, we do not consider a direct path from the BS to MSs for two-hop transmission since two-hop transmission is required when the links between the BS and MSs are relatively poor. The received signal at the given byy2,n=hrm,In this section, we propose a multiuser scheduling method that efficiently reduces the amount of feedback information for instantaneous SNRs from the MSs to the BS. The BS decides both the transmission mode  and the desired MS based on a scheduling criterion.Ri denote the average achievable rate for i-hop transmission  when an MS with the maximum instantaneous SNR is selected among N MSs. Suppose that all links between the BS and the MSs experience the same average SNR. All links between the RS and the MSs are also assumed to experience the same average SNR . Let Ri is expressed as a function of the average SNRs PbhbFor comparison, the optimal multiuser scheduling, based on full feedback of the instantaneous SNRs, is also considered. In this case, both the transmission mode and the desired user are selected simultaneously in the sense of maximizing the instantaneous achievable rate for a given channel realization. In N.In this section, the average achievable rates of both one- and two-hop transmissions with the proposed multiuser scheduling are analyzed. A closed-form expression for the average achievable rates is first derived, and its asymptotic behavior is then shown in the limit of large number of R1 for one-hop transmission is given byFrom , the avegiven byR1=Elog\u20611R1 is derived asE1(x) = \u222bx\u221e(et\u2212/t)dt is the exponential integral function.Suppose that the one-hop transmission with our multiuser scheduling is used. Then, the average achievable rate The proof essentially follows the derivation of the selection combining scheme in .R1 is expressed as a function of both the average SNR of the BS-MS link, N. For large N, the average achievable rate R1 in  with respect to \u03b3rm,n is always greater than 0 sinceThe first derivative of R2 for two-hop transmission is given byThus, the average achievable rate given byR2=E12logR2 is written asE1(x) = \u222bx\u221e(et\u2212/t)dt is the exponential integral function.Suppose that the two-hop transmission with our multiuser scheduling is used. Then, the average achievable rate p\u03b3br(x) of the random variable \u03b3br is exponentially distributed and thus is given byp\u03b3rm,max\u2061(y) of the random variable \u03b3rm,max\u2061\u225cmax\u2061n{\u03b3rm,n} is given byx and y, we haveJ = ln\u2061(1 + x) \u2212 ln\u2061\u2061(1 + (x/(1 + y))). Using (4.337.2) in [E1(x) = \u2212Ei(\u2212x)\u225c\u2212\u222bx\u2212\u221e(et\u2212/t)dt, the term Q in (The probability density function (PDF) atistics  of an exgiven byp\u03b3brx=1\u03b3\u00afgiven byp\u03b3rm,max\u206137.2) in  and the  we haveR2=N2ln\u20612e obtain  by applyrm Q in  = \u222bx\u221e(et\u2212/t)dt is the exponential integral function. Here, \u03b2 = 1 if \u03b2 < 1 if\u2009\u2009C0 > 0. Note we use the following notation: (i) f(x) = O(g(x)) means that there exist constants C and c such that f(x) \u2264 Cg(x) for all x > c; (ii) f(x) = o(g(x)) means lim\u2061x\u2192\u221e\u2061(f(x)/g(x)) = 0; (iii) f(x) = \u03a9(g(x)) if g(x) = O(f(x)); and (iv) f(x) = \u03c9(g(x)) if g(x) = o(f(x)) [Suppose that the two-hop transmission with our multiuser scheduling is used. When the number of MSs, e R2 in  and (14b o(f(x)) .N is sufficiently large, the maximum value of an exponential random variable, max\u2061n{|hrm,n|2}, scales as ln\u2061N with high probability [N tend to zero with high probability under the condition x simply yield  for some constant C1 > 0. It thus follows that 0 < \u03b2 \u2264 1. Here, if C1 = 0. Otherwise   N is sufly yield . Now letsults in , which cN, that is, N, beyond a certain value is not beneficial in terms of performance on the achievable rate. Specifically, when N), the rate R2 is bounded by a constant even for large N. Hence, we may conclude that it may not be desirable for all the MSs to feed back their instantaneous SNR of the BS-RS-MS link to the BS. On the other hand, if N, that is, From the result of in as in . In thisIn this section, to verify our analytical results in 3 times for each system parameter.The analytic results are based on closed-form expressions for the average achievable rates of one- and two-hop transmissions, shown in , 14a), , 14a), aN, when we perform either one- or two-hop transmission with multiuser scheduling. We assume that N = 1,\u2026, 30. The system performance is examined according to various average SNRs\u2014it is assumed that the average SNR of the BS-RS link, N = 1, the average achievable rate for two-hop transmission is higher than that for one-hop transmission. However, as N increases, performance on the achievable rate for one-hop transmission case becomes higher owing to more multiuser diversity gain. The analytical results are also illustrated in this figure, where they almost match well with the simulation results for any average SNRs and N. Their asymptotic behaviors for large N are examined as follows: we obtain the rate 4.5 (bits/s/Hz) from (\u03b2 = 1 is assumed in this case). Interestingly, when N increases over 10 for N \u2265 5.Hz) from  while thned from   R1 > R2, the optimal scheduling may select two-hop transmission according to some link conditions. This phenomenon occurs only for the case where there exists a crossover between two curves. However, it is easily seen that the proposed two-step scheme always outperforms either one- or two-hop transmission. On the other hand, for cases 2 and 3, the proposed two-step scheduling scheme shows nearly the same performance as that of the optimal one. In these cases, the achievable rates for the optimal scheduling are also nearly identical to those for either one- or two-hop transmission. This is because there is no crossover point between two curves of one- and two-hop transmission under the assumed link conditions. It in turn means that the proposed scheduling method works well when one transmission mode is dominant over all values of N. In other words, our two-step scheduling method based on efficiently reduced feedback information can be either optimal or suboptimal in terms of achievable rates, depending on link conditions (e.g., the average SNRs of the three links, denoted by Moreover, to see the fundamental limit of our multiuser scheduling, the comparison for the average achievable rates between the optimal and proposed two-step multiuser scheduling is performed in N. Furthermore, we analyzed the link condition such that the multiuser diversity gain is fully exploited. Finally, it was examined that the proposed algorithm has almost the same achievable rate as that of the optimal one, while its required feedback is fairly reduced by half of the optimal one.The multiuser scheduling method, opportunistically selecting both the transmission mode and the desired MS, was proposed for relay-aided downlink systems using half-duplex AF relaying. The scheduling criterion, based on efficiently reduced feedback information, was designed by showing the closed-form expression for the average achievable rates and its asymptotic behaviors for large"}
+{"text": "E-index (earliness-index), which cumulatively measures the earliness degree to which a variable (or a dynamic trait) increases or decreases its value. Theoretical proofs and simulation studies show that E-index is more general than functional mapping and can be applied to any complex dynamic traits, including those with logistic curves and those with nonmonotonic curves. Meanwhile, E-index vector is proposed as well to capture more subtle differences of developmental patterns.While it is a daunting challenge in current biology to understand how the underlying network of genes regulates complex dynamic traits, functional mapping, a tool for mapping quantitative trait loci (QTLs) and single nucleotide polymorphisms (SNPs), has been applied in a variety of cases to tackle this challenge. Though useful and powerful, functional mapping performs well only when one or more model parameters are clearly responsible for the developmental trajectory, typically being a logistic curve. Moreover, it does not work when the curves are more complex than that, especially when they are not monotonic. To overcome this inadaptability, we therefore propose a mathematical-biological concept and measurement,  Whether there are different genes responsible for the formation of a trait and how these genes regulate the trait are of fundamental importance biologically, agriculturally, and/or medically. Quantitative traits, or characteristics varying in degree, can be attributed to the effects of genes and their environment . Lander  infinite-dimensional characters in , a < b. {pi}i=0n is a sequence of points, p0 = a, pn = b, 0 \u2264 i < j \u2264 n. Also suppose that f(t) is differentiable on the open interval , i = 1,2,\u2026, n, and that f\u2032(t) is its derivative function. Then we define the E-index of the growth curve as follows:Suppose that the growth curve is a continuous function f\u2032(t), the growth rate at time point t, is undefined on each inner split point. But this would not change the integration result, even if we set the growth rate at such point to be any value. For simplicity, we denote Eab(f) as E(f).It should be noted that f\u2032(t) occurs is our key concern for growth, and the expression f\u2032(t)(b \u2212 t) in (f\u2032(t)(b \u2212 t) is, the earlier the growth or development occurs. In this sense, the E-index measures how early growth occurs in the whole process by accumulating the product along the time.How early or how late the growth rate  \u2212 t) in  quantifiE-index's properties which are to be discussed in the form of propositions. However, their proofs are all omitted since they can be found in calculus textbooks or related literature.From the definition above, we can derive several of f(t) defined on the closed interval  is strictly monotonically increasing and is globally differentiable, then its E-index can be calculated with the following equation:If the growth curve function E-index and reveals to us the relations between the integrations along horizontal direction and along vertical direction.The conclusion of y = f(a), which is the conclusion we wanted.We can illustrate the proof with The conclusion of E-index with  is defined on  and f(a) \u2264 f(t) \u2264 f(b), then 0 \u2264 E(f) \u2264 1.If the growth curve function E(f) may get a value greater than 1 if, for some t,\u2009f(t) is greater than f(b) or even be a negative value if, for some t, f(t) is less than f(a).But E-index, and we can design a growth curve function whose E-index is any designated value in the range.E-index can be easily calculated with integration operation stated in ,,E-index r in the 2 bunches of growth curves can differentiate the curves, as is illustrated in E-index is capable of doing so, and the results are shown in The function parameter r in E-index of the corresponding growth curve function is calculated with , i = 1,2,\u2026, m, and that of the jth sample of B is vjB = , j = 1,2,\u2026, n. The computation steps are as follows, using t-test of (m + n \u2212 2) degrees of freedom to discover the significance.(a)viA and vjB, we can use spline interpolation to get continuous functions (curves) fiA(t) and fjB(t).For each (b)E-index of the curves, namely, EiA and EjB, respectively, for i = 1,2,\u2026, m and j = 1,2,\u2026, n. And we denote that EA =  and EB = .Then  is emplo(c)EA and EB H0 will be rejected ifH0 will be accepted, where t is the computation result of (t\u03b1(m + n \u2212 2) is the t-distribution value with the confidence level \u03b1 and (m + n \u2212 2) degrees of freedom.We can test the null hypothesis that the two groups of samples are not significantly different:esult of  and t\u03b1  r in (2)E-indices for genotypes A and B,\u2009\u2009sA = 0.0428 and sB = 0.0597, respectively. We have by  = 2.896, which means that there is sufficient evidence to indicate that the genotypes are clearly responsible for the developmental processes of the organs.But using the statistical framework given in E-index is sometimes capable of differentiating growth curves, it is after all only one characteristic value revealing one aspect of information. Therefore, it is natural for us to extend E-index into E-index vector.As is mentioned earlier, a curve may theoretically provide infinite amount of information about growth. Though the E-index insufficient to differentiate growth curves? An example from Figures Where and why is E-index value (0.5). This is mainly due to the fact that the effect caused by the higher growth rate in Comparing the sizes of shade in Figures E-index does not work in some cases to differentiate growth curves. Consequently, we have to move forward for a more sophisticated tool. Naturally we will extend E-index into E-index vector.This example indicates that f(t) describing a growth curve is continuous on a closed interval , a < b. And suppose that Q = {pi}i=0n is a prescribed sequence of points, p0 = a, pn = b, pi < pj, 0 \u2264 i < j \u2264 n. Then the E-index vector of f(t) according to Q is defined as follows:Suppose that VQ(f) is denoted as V(f) for simplicity and (nEp0p1(f), nEp1p2(f),\u2026, nEpn\u22121pn(f)) as (E1(f), E2(f),\u2026, En(f)).E-index vectors of the growth curves in Figures E-index vectors, , , and , are apparently different, as is also illustrated with shaded areas in The f(t) and g(t) are two functions defined on a closed interval, describing two growth curves with the same prescribed sequence of points Q = {pi}i=0n. Then the growth dissimilarity between f(t) and g(t) is defined as follows:Suppose It is easy to prove that growth dissimilarity satisfies distance axioms; that is,f1(t), f2(t), and f3(t), respectively. According to  is more similar to f1(t) than it is to f3(t), which is consistent with what is observed in The results above show that, in the growth perspective of earlier and later halves, Wi denoted as the ith weight:Different weights can be designated to differently important phases of growth according to specific problems. So the growth dissimilarity defined in  can be aE-index vector to help differentiate two growth curves. What is more important, however, is to differentiate a set of growth curves or to divide them into groups or clusters, which will be discussed in the next subsection.Equation  enables More and more growth traits are available and they can be described by growth curves. Studies  indicateIn order to identify genes with growth traits, we are required to divide into groups all growth curves that are as similar as possible in the same group while being as dissimilar as possible in different groups. But a common situation we are encountering is that it is difficult for us to obtain reasonable groups.E-index, E-index vector, and the growth dissimilarity definition based on these two concepts may help us to group or cluster the growth curves.E-index vectors, we can define describing rules for a curve group. Take the growth curves in Figures E-index vector is greater than 0.6 and the second less than 0.4.\u201d And the second rule is defined as \u201cthe first component is less than 0.6 and the second greater 0.4.\u201d These two rules describe and define two groups, with growth curve (d) in the first group and growth curves (b) and (e) in the second one.With the Though describing rules are capable of grouping growth curves, human experts are involved in prescribing the rules, and thus the rules, consequently the grouping results, may be different from person to person.k-mean algorithm, and its variations are almost automatic. It is a recursive algorithm with k randomly selected centers. To cluster the growth curves, the growth dissimilarities between each growth curve and each center are calculated with E-index is capable of differentiating growth curves (such as logistic curves) as function parameters are in the applications of functional mapping. Like functional mapping, E-index is good at differentiating growth trajectories with the same values of mature state, which traditional QTL takes as the same. In this sense, E-index generalized functional mapping.(ii)E-index is sometimes unavailable according to its primitive definition given in E-index is as biologically meaningful as the important curve parameters employed in functional mapping.(iii)E-index. In fact, a cubic spline  approxi(iv)E-index provides limited information. As an extension of E-index, E-index vector is focused on the growth in different phases, the number of which may vary, and the time spans for the same vector may not be of equal length, according to the application background and requirements.Being a key and general characteristic value though, (v)k-mean algorithm.By extracting the growth information in a curve and forming a vector, we can use well developed techniques for analysis, such as describing rules and (vi)E-index vector helps us reveal detailed characteristics in growth curves. It may be looked on as a microscope employed to observe a desired level of growth detail.In order to generalize functional mapping and overcome the shortages of it,"}
+{"text": "Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, \u201cexcitable\u201d systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only. This includes quasi-solitons of fixed shape (like KdV solitons) or envelope quasi-solitons (like NLS solitons). This can happen in systems with more than two components, and can be explained by effective cross-diffusion, which emerges via adiabatic elimination of a fast but diffusing component. We describe here a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems. Reaction-diffusion systems are an important mathematical tool in studying dissipative structures. For the properties of solutions of these systems, diffusion is as important as is reaction. For instance, Turing structures are possible only if there is significant difference in the diffusion coefficients between activator and inhibitor speciesThere is a large variety of interesting regimes in systems with nonlinear kinetics and cross-diffusion instead of or in additional to self-diffusionOriginally, these regimes have been discovered in models motivated by population dynamics, where (nonlinear) cross-diffusion appears naturally as taxis of micro- or macro-organisms with respect to each other\u2019s population density3This question encounters a number of obstacles due to physical constraints. Firstly, the cross-diffusion must always be nonlinear in order to preserve positivity of chemical concentrations92113effective. Pattern-forming reactions are supposed to be supported by a source of energy, say in the form of constant supply of a reagent which is consumed in the reaction, whereas the Second Law applies to closed systems. Although this source of energy  in the spatially-extended context can be used to reconstruct full (fuller) reaction-diffusion systems with purely self-diffusing reagents, from reduced reaction-diffusion systems with cross-diffusion. We apply this procedure to produce examples of self-diffusion systems that manifest quasi-soliton solutions. Since the fast-slow analysis is an asymptotic procedure, i.e. is formally valid in certain parametric limits but has to be applied for fixed parameter values, it inherently has limited accuracy. The procedure we exploit here is valid when the spatial scale of the solutions is large compared to the diffusion length of the fast species, and the reduced equations become non-local when this is not fulfilled. To relax this restriction, we suggest a euristic procedure which enhances the accuracy of the reduction/reconstruction for particular wave-like solutions.The structure of the paper is as follows. In section \u201cMethods: Fast-slow reduction for reaction-diffusion systems\u201d we discuss the process of adiabatic elimination of a fast reacting species in the spatially-extended context, and show how the diffusivity matrix may be affected by that elimination. In section \u201cResults\u201d we present a simple application of this theory: namely, by \u201cworking backwards\u201d the adiabatic elimination, we construct a three-component reaction-diffusion system with self-diffusion only, which corresponds to a two-component system with cross-diffusion and quasi-soliton solutions of various kinds. We conclude by discussing possible implications of our findings for future research.Our asymptotic argument is based on two assumptions. Firstly, we consider a reaction-diffusion system, which has a fast and a slow subsystem,u and the fast subsystem v. We assume that the fast subsystem (2) has a unique globally stable equilibrium for v\u2009=\u2009g(u) at any fixed u of interest,where The second assumption, to be clarified and formalized later, is that the solutions of interest are sufficiently smooth in space.Linearizing and considering the limit 2u is small and therefore the resulting \u03bc is a  small parameter. Then we can formally resolve At this point we see that our solutions should be so smooth that \u2207v into Substitution of the thus found Fu\u2009=\u2009\u2202vfu|v=g(u), andwhere We see that the diffusion in the reduced system (5) is not only different from the full system, but is typically nonlinear even if the original diffusion was fully linear.g(u)\u2009=\u2009Gu, G\u2009=\u2009const, andIn the system (5) we have dropped wereandk, so thatThe second-order approximation (6) contains a biharmonic operator. We can approximately replace it with a reaction-diffusion system for solutions which are approximately oscillatory in space with one dominant wavenumber Then we havewhere Do parametric search in the reduced system, which has fewer parameters and often is easier to compute, as it is less stiff;k for it, say as the maximum of the power spectrum of the spatial profile;Once an interesting regime is found, estimate the dominant wavenumber Use the inverse transformation to obtain parameters for the full system corresponding to the found parameters of the reduced system;See what solutions the full system with these parameters will produce.The direct transformation from system  veq) to system (5) or (9), and its inverse, can be used for searching for nontrivial regimes in the full system, based on the existing experience of nontrivial regimes in the analogues of the reduced systems:As a simple example, we now consider a three-component extension of a two-component system with nonlinear kinetics, where a third component is added, which has fast linear kinetics and linked to the other components in a linear way:In terms of which leads to the reduced system (9) in the formwhereandIt is easy to see that the resulting diffusivity matrixdepends on the reaction kinetics parameters and does not have to have real eigenvalues or even be positive definite .\u03b3, Dw, Dv, and for given parameters of (11) , obtain the remaining parameters of (10) viaDw via Du \u2265 0. The latter will be satified if Dv is chosen so that either Dv\u2009\u2264\u2009DuuDvv/(Du\u2009+\u2009Duu) or Dv \u2265 Dvv.and Numerical illustrations of some nontrivial regimes obtained in the two-component system, and corresponding nontrivial regimes found in the reconstructed three-component system are presented in \u03b5\u2009=\u20090.01, k1\u2009=\u200910, Duu\u2009=\u2009Dvv\u2009=\u20090.025, Duv\u2009=\u20091, Dvu\u2009=\u2009\u22121, \u03b3\u2009=\u200930, Dv\u2009=\u20090.001, Dw\u2009=\u20090.04, and a selection of values of a as shown to the left of the panels in k for the inverse transform were obtained as the position of the maximum of the power spectrum of the signal z(x)\u2009=\u2009u\u2009+\u2009iv of a selected solution  of the two-component system, taken at a selected fixed t. Specifically, we had k\u2009=\u20090.864 for a\u2009=\u20090.07, k\u2009=\u20090.879 for a\u2009=\u20090.25 and k\u2009=\u20090.942 for a\u2009=\u20090.35. For simulations, we used the same numerical methods as those described in refs x\u2009=\u20090.1. Time differencing was first-order, explicit in the reaction terms and implicit in the cross-diffusion terms, with time step \u0394t\u2009=\u20092.5\u2009\u22c5\u200910\u22124 for the two-component system, and fully explicit with time step \u0394t\u2009=\u20092\u2009\u22c5\u200910\u22125 for the three-component system. The space interval was x\u2009\u2208\u2009, where L was different in different simulations, as shown in x-axis labels in u\u2009=\u2009usH(\u03c3\u2009\u2212\u2009x), v\u2009=\u20090, w\u2009=\u20090 to initiate a wave starting from the left end of the domain. Here H is the Heaviside function, the wave seed amplitude was typically chosen as us\u2009=\u20092 and length as \u03c3\u2009=\u20094. To simulate propagation \u201con an infinite line\u201d, L\u2009=\u2009\u221e, for \u03b4x2\u2009=\u200920 away from the boundary each time the pulse, as measured at the level u\u2009=\u20090.1, approached the boundary to a distance smaller than \u03b4x1\u2009=\u200940, and filled in the new interval of x values by extending the u, v and w variables at constant levels. The profiles in x\u2009\u2212\u2009xc, where xc\u2009=\u2009xc(t) is the center of mass of v2 at the time moment t, that is, and the corresponding three-component system (10). We used the parameter values a\u2009=\u20090.35 and a\u2009=\u20090.25, both 2-component and 3-component systems support propagation of a solitary pulse with oscillating front and monotonous back. These shapes are steady: as one can see in the top four panels of a\u2009=\u20090.35, the pulses annihilate upon collision with a bondary, \u2014 or, rather, reflect but lose their magnitude, cannot recover and eventually decay. Whereas for a\u2009=\u20090.25, the pulses in both systems successfully reflect from boundaries. One can see in \u03c3\u2009=\u20092, \u03c3\u2009=\u20098 and \u03c3\u2009=\u200912 were indistinguishable from those shown in For a\u2009=\u20090.07 is different: the shape of the pulse changes as it propagates. These are \u201cenvelope quasisolitons\u201d, similar to those previously reported in in refs The behaviour for Since the speed and shape of quasi-solitons are typically fixed, the reflections and collisions, when they happen, are always quasi-elastic, if one is to use the terminology from the conservative wave theory. That is, the properties of the solitons fully recover after collisions, even though, as can be seen in a\u2009=\u20090.03, and even then the reflected wave takes much longer to fully recover. In this aspect, the quasi-solitons are also different from the true solitons, e.g. in the NLS. A formal way to understand this difference is to observe that NLS is symmetric with respect to inversion of the sign of its complex field. Hence one can arrange two identical but counter-propagating solitons on an infinite line so that their nonlinear superposition at a certain point remains exactly zero at all times. Then replacing the problem with the one at half-line and zero boundary condition at that point will yield a solution in the form of a soliton reflecting from the boundary with a 180\u00b0 change of phase. This construction does not work for the FitzHugh-Nagumo kinetics (14) which is not invariant with respect to the inversion \u2009\u2192\u2009, unless a\u2009=\u2009\u22121, but in the latter case the system is no longer excitable. A more intuitive way to explain this is: for the pulse way to propagate, the u field must exceed the threshold a, and the boundary condition u\u2009=\u20090 makes it much more difficult for the reflected wave to satisfy this.Finally, we emphasize that the reflection from boundaries shown in not constraint by the thermodynamic restrictions of symmetry and positive definiteness. We believe that application of such reduction, accounting for the emergence of effective cross-diffusion, may lead to finding new interesting regimes in systems that have traditionally been studied without cross-diffusion, e.g. Brusselator30It has been traditionally believed that a definitive property of waves in excitable media is that they annihilate when collided. Although soliton-like interaction was observed in some reaction-diffusion systems with excitable kinetics, both in numerical simulations1921623242627How to cite this article: Biktashev, V. N. and Tsyganov, M. A. Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law. Sci. Rep.6, 30879; doi: 10.1038/srep30879 (2016)."}
+{"text": "Although positive incentives for cooperators and/or negative incentives for free-riders in social dilemmas play an important role in maintaining cooperation, there is still the outstanding issue of who should pay the cost of incentives. The second-order free-rider problem, in which players who do not provide the incentives dominate in a game, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players\u2019 incentives. The critical assumption of our model is that players who tend to provide incentives to other players for their cooperative or non-cooperative behavior also tend to provide incentives to their incentive behaviors. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We find that the second-order free-rider problem is completely resolved without any third-order or higher (meta) incentive under the assumption. To do so, a second-order costly incentive, which is given individually (peer-to-peer) after playing donation games, is needed. The paper concludes that (1) second-order incentives for first-order reward are necessary for cooperative regimes, (2) a system without first-order rewards cannot maintain a cooperative regime, (3) a system with first-order rewards and no incentives for rewards is the worst because it never reaches cooperation, and (4) a system with rewards for incentives is more likely to be a cooperative regime than a system with punishments for incentives when the cost-effect ratio of incentives is sufficiently large. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives. Although social dilemmas can be resolved if punishing non-cooperators or rewarding cooperators works, such rewards and punishments, i.e., external incentives, entail certain expenses. As a result, a cooperative player who shirks his or her duty to provide an incentive to other players will emerge, and he or she will be more advantageous than an incentive-provider. In fact, the problem of excluding such cooperative incentive-non-providers, or second-order free-riders, is a well-known academic challenge. In order to meet this challenge, we devise and analyze a meta-incentive game that integrates positive incentives (rewards) and negative incentives (punishments) with second-order incentives, which are incentives for other players\u2019 incentives. In this paper, we solve the replicator dynamics for a simple version of the game and analytically categorize the game types into four groups. We show that second-order incentives for first-order reward are necessary for cooperative regimes. This solution is general and strong in the sense that the game does not need any centralized institution or proactive system for incentives. Even though society is based on cooperation, achieving cooperation in social dilemmas is still a big challenge. The free-rider problem, for example, hinders cooperation. Many studies have addressed this problem, and the methods proposed for solving it include giving players sufficient ability to remember their direct  or indirA meta-analysis of reviews on reward and punishment systems using a common framework  revealedFirst, many studies have focused on either individually-dealt-with punishments or rewards. While some studies \u201316 have Second, should a free-rider be punished and/or should a contributor be rewarded? Experimental studies , 25 haveThird, in the approach we took, the focus is on meta-level incentives. When the incentive for cooperation is either a punishment or reward, there is still the second-order free-rider problem. The effort made to maintain a cooperative society is a cost that must be defrayed by someone. Generally, a player who contributes to a game but never defrays the cost for providing incentives is more evolutionarily adaptive than one who contributes to the game and does pay the cost. This means that eventually no one defrays the cost of maintaining the incentive system. The second-order free-rider problem can come down to the problem of costly incentives . One solThe pioneering work on meta-level incentives was performed by Axelrod . He atteThe C-FO-linkage issue is a relationship between two behaviors which differ qualitatively. Considering this point, the relationship between first-order incentives and second-order incentives is an alternative issue because they are both incentives. Kiyonari and Barclay  focused We have developed a model of a meta-incentive game (MIG) that has second-order incentives, i.e., incentives for other players to provide incentives. This analytical model can describe the carrot-and-stick issue uniformly and comparatively. The model targets an individual incentive system that integrates a positive side (reward) and a negative side (punishment) . The incMIG players first play donation games and then provide incentives in answer to their actions in the games. Incentives are provided not only for or against the others\u2019 cooperative or non-cooperative actions but also for the others\u2019 incentive behaviors or lack thereof on third-party players.Players are divided into three sorts of strategist: a cooperative incentive-provider (CI), a cooperative incentive-non-provider (CN), and a non-cooperative incentive-non-provider (NN). x, y, and z be the frequencies of CI, CN, and NN, respectively. Naturally, x+y+z = 1. The equations are formulated asUCI, UCN, UNN, and The population is infinitely large and well-mixed. The frequencies of the three strategies follow replicator dynamics describing a natural law whereby the higher one\u2019s payoff is the more frequent one\u2019s strategy becomes. Let c be the cost of donation, b be the receiver\u2019s benefit, F1 be the fine imposed as a first-order punishment, P1 be the cost of a first-order punishment, A1 be the amount of a first-order reward, R1 be the cost of a first-order reward, FP be the fine for freeriding for the first-order punishment, PP be the cost for freeriding for the first-order punishment, AP be the amount of the reward for the punisher, RP be the cost of the reward for the punisher, FR be the fine for freeriding for giving a reward, PR be the cost for freeriding for giving a reward, and AR be the amount of rewarding a rewarder, and RR be the cost of rewarding a rewarder. All these values should be non-negative constants.Now let us describe the parameter notations needed to calculate a player\u2019s (expected) payoff. Let \u03bc), which represents the proportion of a fine or award that incentive-receivers should pay or receive relative to its cost, and the discount factor of costs on the level of incentive (\u03b4), whereWe will avoid analytical difficulties due to the usage of many parameters by defining a simple meta-incentive game (S-MIG) using two parameters: the incentive cost-effect ratio .We assume that Finally, before analyzing our model, we define all 24 possible configurations of MIG in x > 0) emerges by analyzing the replicator dynamics on different types of S-MIG. As shown in Methods, the dynamics of S-MIGs can be classified into four groups. x, y, z) =  of all types, and We explore the conditions under which a cooperative equilibrium incentive. In our model, moreover, incentives are performed ex-post and individually, and thus the system does not need a centralized institution or ex-ante commitment. Many studies on non-meta-level incentives have shown that punishment is more effective than a reward. We have identified a possible explanation as to why people prefer second-order rewards to second-order punishments. Kiyonari and Barclay\u2019s experimental study  supportsWhich incentive should a designer of an MIG choose? If the cost-effect ratio of incentives is sufficiently large, even a handful of cooperative incentive-providers can beat non-cooperative incentive-non-providers if the designer uses a system with rewards for incentives instead of a system with punishments for incentives.Our work differs from Sasaki et al\u2019s model of integrating rewards and punishments, which was designed for an institutional system with a compulsory entrance fee and thus no option of second-order free riders . Kendal The asymmetry of the effects of rewards and punishments might be evident in the cost-effect ratio. Although it may be natural that a fine handed out as punishment should be larger than its cost, can the reward be larger than its cost? We believe that this balances out the risk of second-order free-riders emerging. Of course, we leave open the possibility of incorporating asymmetric reward and punishment effects as a future extension of a system.In this section, we analyze a meta-incentive game (MIG) by solving replicator equations. The expected payoffs of the players areUCI. The first term represents the benefit of donation, whereas the second term gives the cost of donation (because one is a cooperator) in the DG stage. The third term represents the costs of the first-order incentivization: rewarding a cooperator and punishing a non-cooperator. The fourth term represents the first-order reward for cooperating. The fifth term represents the costs of the second-order incentivization and consists of four parts, i.e., rewarding those who have rewarded a cooperator, punishing those who have not rewarded a cooperator, rewarding those who have punished a non-cooperator, and punishing those who have not punished a non-cooperator. Finally, the last term describes the second-order rewards for rewarding a cooperator and punishing a non-cooperator. Similar explanations can be applied to the other expected payoffs, UCN and UNN.Let us explain the terms of Using Eqs , 2), an, an2), ax, y, z) in S-MIG in the following subsection, and thus, here, it is enough to conduct an analysis of the borders. Moreover, there is no equilibrium at any point on the line x = 0, except two corners  = , ). This is because, x = 0, and thus, y always decreases. Hence, we will only deal with the y = 0 and z = 0. On those two lines, that function is calculated as We prove that there is no equilibrium at any internal point (f(x) and g(x). In the type, F1, P1, FP, PP, AP and RP should be zero because there has no incentive system on the punishment side. Moreover, using c = 1 and definitions of \u03bc and \u03b4, R1 = \u03b4, A1 = \u03bc\u03b4, RR = PR = \u03b42 and AR = FR = \u03bc\u03b42. Substituting them into f1 in In order to exemplify how to analyze each type of the S-MIG, we deal with the RB type as a representative and derive their equations of Therefore, we derive x, y, z) = . If x, y, z) =  is asymptotically stable, and thus, a cooperative regime emerges. The dynamics of each type of S-MIG are classified into four groups. In what follows, we will deal with one representative type in each group. The remainder can be similarly derived.x, y, z) = , so cooperation is never achieved regardless of the values of . The R, P+R, PP+R, PR+R, and PB+R types belong in the first group. Each type of this group has a globally stable point . In one, all the fixed points on the line z = 0 are unstable, and thus, there is a globally stable point , as in the first group. In the other, some of the fixed points are stable if x, y, z) =  on y = 0. Let us verify the PR case as a representative example. f(x) is an increasing function. Moreover, f(1) = \u22121+\u03bc\u03b4 > 0 implies that the point  =  is asymptotically stable. Even in the second pattern, however, the point  is not stable for a long time. This is because, the whole line z = 0 consists of fixed points, and thus, neutral drift is possible. Occasionally, x moves to an unstable equilibrium, and this type eventually reaches . The phase diagram of the PP-type S-MIG is shown in The P, PP, PR, and PB types belong in the second group. The whole line \u03bc, \u03b4). In one, there is a globally stable point , as in the first group. In the other, another locally asymptotically stable point  can exist. This group has three existence conditions for the basin of attraction on the point  = : z = 0, on one hand, are bistable and y = 0 depends on f(x). f(0) < 0 and f(1) = \u22121\u2212\u03b4\u2212\u03b42+2\u03bc\u03b4(1+\u03b4) > 0 when the existence condition for the basin of attraction on the point  =  is satisfied. Therefore, the dynamics on y = 0 are also bistable, and The third group, consisting of types which include either the RP or RR, and P+RB, PP+RB, PR+RB, and PB+RB (Full) types, has two patterns of behavior depending on the values of  on the line z = 0. \u03bb1\u03bb2 = \u2212y* \u03b42(1+\u03b4) < 0. Moreover, in the case of the RR-type S-MIG, \u03bb1\u03bb2 = \u2212x* y* \u03b42 < 0. The other cases are omitted.The final group, consisting of only the RB type, is the same as the third except for the direction of the dynamics in the internal space of the basin of attraction for cooperation see . In thisx of the basins of attraction for cooperation  =  on y = 0. Let fD(x) and xD be x of the basin of attraction on the line y = 0 in the D-type S-MIG for D \u2208 {P, R, \u2026, PB+RB}. Basically, the more complex the type is, the lower its lower limit of x becomes. For example, we will prove xP+RB < xP+RR. fP+RB(x) = \u22121\u2212\u03b4+2\u03bc\u03b4x\u2212\u03b42x+2\u03bc\u03b42x2 and fP+RR(x) = \u22121\u2212\u03b4+2\u03bc\u03b4x\u2212\u03b42x2+\u03bc\u03b42x2 are in fD(xD) = 0. fP+RB(xP+RR) = \u03b42xP+RR[xP+RR(1+\u03bc)\u22121] and fP+RB(xP+RR) > 0. Therefore, xP+RB < xP+RR. Moreover, some equivalence relations can be derived. For example, let us compare xRR with xRP. fRR(x) and fRP(x) are increasing functions because their partial derivatives are positive in 0 < x < 1. fRR(xRP) = \u03b42xRP(1\u22122xRP) and xRR < xRP.\u03bc0 > \u03bc10 > \u03bc11 > \u03bc12 > \u03bc13.Finally, we compare the lower limits of y is set to zero and all the parameters for the second-order incentives are also zero (FP = PP = AP = RP = FR = PR = AR = RR = 0), this new version, or an incentive game (IG), can be regarded as a model of the C-FO-linkages. We denote the three possible IG configurations as the P-type, R-type, and P+R type. The replicator equation of IG isThe MIG assumes FO-SO-linkages. In this subsection, we analyze the replicator dynamics of a model that assumes C-FO-linkages instead of FO-SO-linkages. Accordingly, cooperators automatically provide first-order incentives, and thus, there is no CN, and no second-order incentive is needed in the MIG. When \u03bc, \u03b4, and c = 1. All S-IG types have two patterns of behavior depending on the values of . In one, there is a globally stable point  = . In the other, another locally asymptotically stable point  =  can exist. The existence condition for the basin of attraction at the stable point  is We can devise a simple incentive game (S-IG) by using x, y, z) : x, y, z \u2265 0, x+y+z = 1}. Assume that  is an internal equilibrium. On that point, x*  is not zero, and thus, the function x*. Using In this subsection, we prove that there is no equilibrium at any internal point on the 2-dimensional simplex \u0394 = { around the equilibrium point . Let \u03b5x = x\u2212x*, \u03b5y = y\u2212y* and \u025b = T, where T means transposition. As a result of the linearization of the dynamics, \u03bcx*\u22121 = 0. The eigenvalues of M are \u03bb = 0, z*(3\u22122x*). These are non-negative, and thus, any internal equilibrium is non-isolated and unstable. The eigenvalues in the case of the RB type are \u03bb = 0, z*+2(x*+y*)(y*+z*), and thus, the same conclusion is reached.Now let us analyze the local stability of the point  =  leads to \u03b5x = x\u2212x*, \u03b5y = y\u2212y*, \u025b = T, andAs is shown in the previous subsection, the linearization of the dynamics around the equilibrium point  when The eigenvalues of"}
+{"text": "In particular, we generalize the Rellich\u2013Wittich-type theorem and Malmquist-type theorem about differential equations to the case of q-difference differential equations (system).By using the Nevanlinna theory of value distribution, we investigate the existence of solutions of some types of non-linear  In receThe following two results had been proved by F. Rellich and H. Wittich, respectively.Let the differential equation be the following formIff(w) is transcendental meromorphic function ofw, then Eq. is the transcendental meromorphic function ofw, then the Eq.  has no non-constant entire solution., the difference equationhas a non-trivial entire solution.,the difference equationhas a non-trivial meromorphic solution in the complex plane..In the present paper, we mainly study the above Rellich\u2013Wittich-type theorem of q-difference differential equation (system) if a equation (system) contains the q-difference term f(qz) and differential term f(z) at the same time.We call the equation a q-difference differential equation of the formz and f of degree m,z, and obtain the following results.We consider the system of For system  is defined asIf Eq.  is defined as in Theorem\u00a09. If Eq.  is defined asP andQ are irreducible polynomials inw, coefficientsare rational functions ofz. IfEq.  is defined as in Theorem\u00a011. If Eq.  be a meromorphic function. Then for all irreducible rational functions inf,with meromorphic coefficientsthe characteristic function ofR) satisfieswhereand be a transcendental meromorphic function of zero order and q be a nonzero complex constant. Thenandon a set of logarithmic density 1.(Zhang and Korhonen Letf(z) be a nonconstant zero-order meromorphic function andThenon a set of logarithmic density 1 for all r outside a possible exceptional set of logarithmic density 0. be a nonconstant meromorphic function in the complex plane andlbe a positive integer. Then(see Yi and Yang Letandf(z) be a nonconstant meromorphic function with zero order. Then for any positive finite integerk, we haveandIt follows from Lemma\u00a015 thatSuppose that f system  with zerSince orem and , 11), w, w\\docummentclasspt{minimaWe firstly choose a constant \u22600, then  can be rw(z) is a transcendental meromorphic solution of equation (Suppose that equation  with zern of Eq. . We willIf If This completes the proof of Theorem\u00a011."}
+{"text": "We theoretically show that in a crystal with a helical lattice structure, orbital and spin magnetizations along a helical axis are induced by an electric current along the helical axis. We propose a simple tight-binding model for calculations, and the results can be generalized to any helical crystals. The induced magnetizations are opposite for right-handed and left-handed helices. The current-induced spin magnetization along the helical axis comes from a radial spin texture on the Fermi surface. This is in sharp contrast to Rashba systems where the induced spin magnetization is perpendicular to the applied current. Recent discovery of novel physics due to an interplay between electricity and magnetism such as multiferroics12356791011b3\u2009=\u2009\u2212b1\u2009\u2212\u2009b2, where a is a constant. The layers are stacked along the z-direction with the primitive lattice vector c is the interlayer spacing. The Hamiltonian isFirst, we consider an orbital magnetization in a helical crystal. Here, we introduce a three-dimensional tight-binding model with a right- or left-handed helical structures. The lattice structure of this model is composed of an infinite stack of honeycomb lattice layers with one orbital per site. We consider the honeycomb lattice as shown in t1, t2 and \u0394 are real and we set t1\u2009>\u20090 for simplicity. The first term is a nearest-neighbor hopping term within the xy plane. The second term represents \u201chelical\u201d hoppings between the same sublattice in the neighboring layers. This term is different between a right-handed and a left-handed helices as shown in \u03bei is +1 and \u22121 for the sites in A and B sublattices, respectively. The space group of our model is P321, with Cy2 and Cz3 symmetries. Only when \u0394\u2009=\u20090, the space group becomes P622, having additional Cx2 and Cz6 symmetries.where ed helix  the direkzc (\u2212kzc) with a Aharonov-Bohm phase \u03d5 in the second-neighbor hopping in the Haldane model. We also note that the time-reversal symmetry is present in our model, while it is absent in the Haldane model for \u03d5\u2009\u2260\u20090. Hence the band structure of our model is easily obtained from that of the Haldane modelk\u2009\u22c5\u2009bi\u2009=\u2009\u22122\u03c0/3 (2\u03c0/3) on the kz\u2009=\u20090 plane, and the H (H\u2019) point is similarly defined on the kz\u2009=\u2009\u03c0/c plane.We note that the Hamiltonian for the right-handed (left-handed) helix becomes the Haldane model on a honeycomb latticeT\u2009\u2192\u20090, it is calculated from the formula14151617181920Using this model, we calculate the orbital magnetization induced by an electric field along the helical axis. In the limit of zero temperature n denotes the band index, fnk is the distribution function for the eigenenergy \u03b5nk, \u03b5F is the Fermi energy, and the prefactor 2 comes from the spin degeneracy. The orbital magnetic moment of the Bloch electrons is defined by21mnk and \u03a9nk are allowed to have nonzero values for any k. However, in equilibrium, due to the time-reversal symmetry Morb is zero because in Eq. k and that from \u2212k cancel each other. To induce the orbital magnetization, we apply an electric field along the z axis. For a metal it induces a charge current accompanied by nonequilibrium electron distribution, and orbital magnetization is expected to arise. Within the Boltzmann approximation, the applied electric field Ez changes fnk intowhere the integral is performed over the BZ, \u03c4 is the relaxation time assumed to be constant, and vn,z\u2009=\u2009(1/\u0127)\u2202\u03b5nk/\u2202kz is the velocity in the z direction. Substituting fnk into Eq. Morb, which is along the z-axis by symmetry. Because of time-reversal symmetry, the Morb. In the T\u2009\u2192\u20090 limit, \u2202f/\u2202\u03b5 has a sharp peak at \u03b5F. Therefore, for a band insulator, the induced orbital magnetization Morb is zero. This is in contrast to multiferroics. Furthermore, the Berry-curvature term , the current-induced orbital magnetization appears. In this case, the induced magnetization is largely enhanced around \u03b5F\u2009\u2243\u2009t1. This is attributed to an enhanced orbital magnetic moment mnk near the Dirac points appearing on the K-H or K\u2019-H\u2019 lines. The orbital magnetization in the left-handed helix . The second term is a spin-dependent nearest-neighbor hopping term within the xy plane. The third and fourth terms involve spin-dependent helical hoppings between the neighboring layers as shown in k-component of a vector pointing from site j to site i. The space group of this model is the same as that of the model (1).The first term is a spin-independent nearest-neighbor hopping term within the xy plane, on the Fermi surface around the H point at \u03b5F\u2009=\u20090.68t1. In fact, the spin around the H point has not only the xy-component but also the z-component. Because of the spin-orbit interaction, the two spin-split Fermi surfaces appear, having the opposite spin orientations. Remarkably, unlike Rashba systems, the spin is oriented radially, and rotates once around the H point. \u03b5F\u2009=\u20090.68t1. In this case, one of the spin-split Fermi surface is open. Nevertheless, the inner Fermi surface have a radial spin texture. This spin texture results from crystal symmetries. Namely, the K-H lines are three-fold rotation axis and hence the spin on these lines are parallel to these K-H lines. Furthermore, the absence of mirror symmetries is crucial for the radial spin textures; if a mirror plane including the xy plane or the z axis were present, the spins should be perpendicular to the mirror plane, and a radial spin texture would not appear. For example, Te and Se have helical crystal structure, and as expected, they have been predicted to show a radial spin texturez-component of Mspin for several parameters is numerically calculated as shown in \u03bbxy\u2009=\u20090.05t1, \u03bbz\u2009=\u20090.05t1, and \u0394\u2009=\u20090.4t1. As is expected, for a metal, the spin magnetization parallel to the current is induced by the current. Similar to the orbital magnetization, the spin magnetization in the left-handed helix and that in the right-handed helix are opposite.We now calculate current-induced spin magnetization in the present system. It is known that in Rashba systems the current-induced magnetization is perpendicular to the current, because of the tangential spin texture in the spin-split Fermi surfaces242526We have shown that in systems with helical structure, the orbital and spin magnetizations are induced by an electric current along the helical axis, using a simple tight-binding models. When an electric field is applied along the helical axis, the orbital magnetization is induced by the orbital magnetic moment on the Fermi surface, as a consequence of broken inversion symmetry. Similarly to the Berry curvature, the orbital magnetic moment is enhanced near band crossings. Therefore, when the Fermi energy lies near the band crossing, the orbital magnetization is enhanced as well. We have also shown that, in the helical crystal with spin-orbit interaction, a current induces the spin magnetization along the helical axis due to the radial spin texture. The absence of mirror symmetry allows to have the radial spin texture, which is completely different from Rashba systems with a tangential spin texture.e2Ez\u03c4t1/\u01272, which is about 150 gauss for Ez\u2009=\u2009104\u2009V/m, \u03c4\u2009=\u200910\u221212\u2009s and t1\u2009=\u20093\u2009eV. In eEz\u03c4\u03bcB/\u0127a2, which is about 7 gauss for Ez\u2009=\u2009104\u2009V/m, \u03c4\u2009=\u200910\u221212\u2009s and a\u2009=\u20090.5\u2009nm. It is multiplied by a numerical factor in \u03bb/t1. Thus, the size of the spin-orbit coupling limits the size of the current-induced spin magnetization. On the other hand, the orbital magnetization does not require spin-orbit coupling, and it can be enhanced by appropriate choice of materials with helical crystal structure. Te and Se consist of weakly coupled helices, and therefore they may have large current-induced orbital magnetization.We have presented a toy model for a helical structure. From a symmetry viewpoint, the present effect of longitudinal current-induced magnetization appears for chiral crystals without inversion and mirror symmetries. Real helical crystals, such as Se and Te, also lack inversion and mirror symmetries. From symmetry consideration, we expect that orbital and spin magnetizations along the helical axis can be induced by an electric current in these crystals by doping carriers. Magnitudes of the induced magnetizations can be estimated from our results. The induced orbital magnetization scales with Our results also provide a new building block of spintronics and will pave the way to spintronics application of helical crystals. For example, consider a ferromagnet on a helical crystal. By injecting current into the helical crystal, the induced magnetization exerts a torque on the ferromagnet, thus leading to current-induced magnetization reversal.Ez induces the spin magnetization asWithin the Boltzmann approximation, the electric field \u03bcB is the Bohr magneton and the electron spin g-factor g\u2009\u2248\u20092. In the present model (4), for \u03bb\u2009=\u20090 the spin magnetization always vanish, because of a cancellation between the contribution from  and that from . This cancellation can be avoided by adding either spin-dependent hoppings within the xy plane ."}
+{"text": "More recently, this approach has been extended to non-Hermitian scenarios characterized by spatially-modulated distributions of optical loss and gain, in order to allow the removal of higher-order modes as well. In this paper, we apply this approach to the design of non-Hermitian optical couplers with higher-order mode-selection functionalities, with potential applications to mode-division multiplexing in optical links. In particular, we highlight the critical role of the coupling between non-Hermitian optical waveguides, which generally induces a phase transition to a complex eigenspectrum, thereby hindering the targeted mode-selection functionality. With the specific example of an optical coupler that selects the second-order mode of a given waveguide, we illustrate the aforementioned limitations and propose possible strategies to overcome them, bearing in mind the practical feasibility of the gain levels required.Supersymmetry has been shown to provide a systematic and effective framework for generating classes of  Though seemingly unrelated, classical optics and quantum mechanics exhibit profound formal analogiesRecently, new levels of sophistication have been added to the above analogies through the intriguing concepts of \u201csupersymmetry\u201d (SUSY) and \u201cparity-time\u201d  = V*(x)  could exhibit entirely real eigenspectra. However, beyond some non-Hermiticity threshold in the potential, an abrupt phase transition from a real eigenspectrum  to a complex eigenspectrum  may occur, which is typically referred to as spontaneous symmetry breakingpassive configurations162232On the other hand, the et al.Interestingly, the SUSY and mode division multiplexing approaches, which offer a new dimension to increase the capacity of optical links via the capability to manipulate the multiplicity of modes that can propagate in optical waveguides. The key feature in such schemes is an efficient mode (de)multiplexing through a judiciously identification of appropriate procedures for selectively populating and extracting specific modes in an integrated fashion. Originally put forward in connection with optical fibers35Y - junctions373839These ideas may find disrupting applications to n = 2, in Against this background, here we explore the application of SUSY-inspired schemesIt is important to stress that our results are not a direct consequence of the study in Ref. b\u03b5 denoting a real-valued constant background value, and \u0394\u03b51 a complex-valued variation satisfying the symmetry conditiony-directed electric field) with exp(\u2212i\u03c9t) time-harmonic dependence, and capitalizing on the translational invariance, the electric field pertaining to a guided mode can be factorized as42\u03b21 is the modal propagation constant, and the dependence on the transverse variable is governed by the Helmholtz equationk0 = \u03c9/c0 = 2\u03c0/\u03bb0 denotes the vacuum wavenumber . As in Ref. unbrokenX \u2261 x/w denoting a dimensionless coordinate scaled with respect to a characteristic dimension w  of the waveguide. Following Miri et al.j, which is removed. It can be shown  = 0.1 and |Im(\u0394\u03b51)| = 0.015. While this choice does not directly correspond to a specific material, it allows to illustrate the basic phenomenology in terms of moderately-sized structures . Nonetheless, we also discuss the implications of different, more realistic choices of material parameters.Particularly critical is the choice of the loss/gain level: on one hand, it should be sufficiently low, so as not to dramatically affect the mode orthogonality, and to maintain all the modes in the unbroken phase. On the other hand, an exceedingly small level of non-Hermiticity in the original waveguide may result in a superpotential cf.  with sinn = 2 eigenvalue, we compute the superpotential W(2)  only occurs beyond a critical non-Hermiticity threshold. It this regime, it can be shown (see i\u03bd (with \u03bd > 0) in the SUSY*-partner waveguide only, it is possible to drive all supermodes in the exponential-attenuation (] > 0) regime, with the exception of the desired m = 3 supermode which may instead exhibit exponential amplification ] < 0).For more quantitative assessments, we focus on the particular case of w = 2\u03bb0, D = 1.02, |Im (\u0394\u03b51)| = 0.015, and \u03bd = 0.0032) excited with a linear combination of the three modes of the original waveguide  are in line with the values reported in the literature for semiconductor-based devices46\u22121 and of 6.8 \u00b7 104\u2005cm\u22121 have been reported for InGaAs single and double quantum well laser structuresBL ~ 1100\u03bb0.Finally, we stress that the specific profiles and parameters in the our case-study are essentially chosen in order to facilitate the illustration of the physical aspects and phenomena, in line with the main scope of this prototype theoretical study. This implies that the structure is not optimized having in mind fabrication-related implications. Nevertheless, we highlight that the required gain values  power gain coefficient would decrease to levels ~102\u2005cm\u22121, which are compatible with media made of polymeric matrix and glasses doped with quantum dots or other dopants5051Alternatively, we could also reduce the (complex) contrast, so as to tradeoff lower levels of gain with longer structures. For instance, by reducing the contrast of an order of magnitude, say, \u0394All numerical simulations in our analysis rely on the finite-element-based commercial software package COMSOL Multiphysics.\u03bb0, discretized with steps of 0.002\u03bb0, and terminated with Neumann-type boundary conditions.More specifically, for the study of the supermodes of the compound structures cf. , we util\u03bb0 \u00d7 700\u03bb0 computational domain, discretized with a maximum mesh-element size of 0.12 \u03bb0, and terminated by an ad-hoc perfectly-matched layer.For the study of the propagation of a given multimode input profile cf. , we utilM.P., M.C., A.C. and V.G. conceived the idea of this study. M.P. and G.C. developed the theory, designed the structures and carried out the numerical simulations, with inputs and feedback from all the other authors. A.C. and V.G. supervised the project. M.P. and V.G. wrote the manuscript with inputs and revisions from all the other authors.Supplementary information"}
+{"text": "In this paper, we prove a fixed point theorem and a common fixed point theorem for multi valued mappings in complete b-metric spaces. Fixed point theory plays one of the important roles in nonlinear analysis. It has been applied in physical sciences, Computing sciences and Engineering. In 1922, Stefan Banach proved a famous fixed point theorem for contractive mappings in complete metric spaces. Later, Czerwik , 1998 haX and Y be nonempty sets. T is said to be multi-valued mapping from X to Y if T is a function for X to the power set of Y. we denote a multi-valued map by:Nadler  Let X anT if Nadler  A point T is a multi-valued mapping iff for each Tx is non-empty for each Joseph  Every siX,\u00a0d) be a metric space. A map Banach  Led  be a metric space. We define the Hausdorff metric on CB(X) induced by d. That isCB(X) denotes the family of all nonempty closed and bounded subsets of X and Nadler  Let  be a metric space. A map Nadler  Let  is called a b-metric space.Aydi et\u00a0al.  Let X beBoriceanu  The spacb-metric space if we take Boriceanu  The spacAydi et\u00a0al.  Let \\docX,\u00a0d) be a b-metric space. Then a sequence X is called Cauchy sequence if and only if for all Boriceanu  Let  b-metric space. Then a sequence Boriceanu  Let be aOur first result is the following theorem.X,\u00a0d) be a b-metric space with constant Let  be a completeb-metric space with constantLetbe a multi valued generalized contraction mapping. Then T has a unique fixed point.Fix any Now,X,\u00a0d) is a complete b-metric space, it follows that Now,mentclass2pt{minimu is the unique fixed point of T. Assume that v is another fixed point of T. Then we have Now we show that Letbe a complete b-metric space with constantLetbe a multi valued mapping satisfies the condition:for all x,yX andwithThen T and S have a unique common fixed point.Fix any entclass1pt{minimaz is a common fixed point of T and S.We shall prove that Similarly, z is the unique fixed point of S and T. Now,We show that X,\u00a0d) is a complete Let Define Therefore, Many authors have contributed some fixed point results for a self mappings in b-metric spaces. In this paper, we have proved the existence and uniqueness of fixed point results for a multivalued mappings in b-metric spaces. Our contraction mappings also generalize various known contractions like Hardy Roger contraction in the current literature."}
+{"text": "The correct sentence is: For the CG-based estimate, e.g., the \u03c7There are errors in"}
+{"text": "The hyperreactive malarial splenomegaly (HMS) represents a chronic, potentially fatal complication of malaria. Case definition includes: gross splenomegaly, high level of anti-malarial antibody and IgM, response to long-term anti-malarial prophylaxis. In this study, a large series of patients not fully meeting the case definition was tentatively classified as early hyperreactive malarial splenomegaly (e-HMS). The main research questions was: does \u201ce-HMS\u201d tend to evolve to the full-blown syndrome? And if so, what are the main factors influencing this evolution?Retrospective, longitudinal study. The patient database was searched to retrieve all potentially eligible patients. e-HMS was defined by splenomegaly of any size (with or without raised IgM), high anti-malarial antibody titre and exclusion of other causes of splenomegaly. The clinical outcome at following visits was analysed in relation to re-exposure to malaria, and to treatment . The association of the outcome with the main independent variables was first assessed with univariate analysis. A stepwise logistic regression model was then performed to study the association of the outcome with the main independent variables.One hundred and twenty-six subjects with e-HMS were retrieved. Eighty-one had at least one follow-up visit. Of 46 re-exposed to malaria for a variable period, 21 (46\u00a0%) had progressed, including 10/46 (22\u00a0%) evolving to full-blown HMS, while of 29 patients not re-exposed, 24 (93\u00a0%) had improved or cured and five (7\u00a0%) progressed (p\u00a0<\u00a00.001). At logistic regression re-exposure was confirmed as a major risk factor of progression  while treatment at initial visit was protective .e-HMS should be regarded as a clinical condition predisposing to HMS. Although the case definition may include false positives, e-HMS should be treated just as the full-blown syndrome. A single anti-malarial treatment is probably adequate, followed by effective prophylaxis for patients exposed again to malaria transmission.The online version of this article (doi:10.1186/s12936-015-1015-6) contains supplementary material, which is available to authorized users. Plasmodium falciparum is by and large the predominant species in the countries where the syndrome has been described [The hyperreactive malarial splenomegaly (HMS), previously referred to as tropical splenomegaly or tropical splenomegaly syndrome (TSS) is a chronic complication of malaria. Patients have high levels of anti-malarial antibody , 2, as aescribed . A histoescribed , 6 diffeAt the very beginning patients might not have any symptoms. If HMS is not cured most patients report unspecific symptoms like asthenia, abdominal discomfort and other. Patients adapt physiologically to chronic anaemia, which develops due to hypersplenism , 8 and bAfter excluding other known causes of splenomegaly, \u201ctropical splenomegaly syndrome\u201d (the former name of HMS) was defined as a separate entity and Fakunle set clear diagnostic criteria in 1981 , that weAt the centre for tropical diseases (CTD), in the last 25\u00a0years, a relevant number of cases have been observed, both in immigrants from malaria endemic areas and in Italian citizens who had lived for a prolonged period in such areas. Furthermore, over the years it has been also observed that some patients, who initially had only some of the case definition criteria of the HMS , once examined again after a further stay of variable duration in endemic areas, developed all the HMS criteria. It was, therefore, supposed that it is possible to identify and diagnose an early stage of HMS, here below defined as \u201cearly HMS\u201d (e-HMS). As the latter was not considered in medical literature, these patients were usually not treated, unless malaria parasites were identified in blood . Once the early syndrome was hypothesized, a number of patients considered potentially affected were then treated for malaria and advised to follow an effective prophylaxis in case they had to go back to endemic areas.to assess if e-HMS, that has not been so far considered as a nosological entity, tends to evolve to the full-blown HMS;if so, if the evolution of e-HMS is significantly different between patients re-exposed and not re-exposed to malaria transmission, andif the evolution of e-HMS is significantly different between patients who are treated for malaria versus those who are not.The main objectives of this research were:anti-malarial antibody titre (IFAT-Biom\u00e9rieux)\u00a0>\u00a01/160, PLUS:splenomegaly  AND/ORhigh IgM level (\u22652.5\u00a0g/L), ANDno other identified causes of splenomegaly or of raised IgM, such as: schistosomiasis, HBV, HCV, HIV, brucellosis, leishmaniosis, autoimmune disease, cirrhosis, haemoglobinopathies, and other haematological conditions, such as leukemia, lymphoma, Waldenstrom disease.Retrospective, longitudinal study aiming to identify patients with e-HMS observed from 1 January 1990 to 31 January 2014 and subsequently visited at follow-up . The population included in the analysis had to be selected according to the following case definition of e-HMS:Patients with splenomegaly or with raised IgM, observed during the study period, and without any of the mentioned alternative diagnoses, were retrieved from the CTD patient database as indicated below. Those with anti-malarial antibody titer\u00a0\u2265160, and/or with history of\u00a0\u22653\u00a0years stay in malaria-endemic areas and reporting\u00a0\u226510 acute malaria episodes, were initially included. Patients meeting the case definition of full-blown HMS as outlined above were excluded. The remaining subjects, meeting the tentative case definition of e-HMS, were retained for further analysis. The main epidemiological, clinical and laboratory findings were recorded at baseline. From baseline, patients were then traced prospectively for any further visit and, in case any follow-up contacts were recorded, follow up data was included in the study file. For all patients having at least a follow-up visit after initial observation, the last follow-up visit was considered for the outcome assessment in relation with re-exposure or not to malaria-endemic areas and to treatment or not at initial visit, as well as with the other main independent variables.CTD patient database . Echography of the upper abdomen, as well as immunoglobulin dosage and anti-malarial antibody testing, were part of the routine screening of patients with a history of a long stay (>1\u00a0year) in a malaria endemic country and reporting several malaria episodes.(T1) baseline;(T2) short-term follow up visits (1\u20136\u00a0months after first observation);(T3) long-term follow up visits (\u22656\u00a0months after first observation).Data was exported to a pre-structured Excel file  titre\u00a0\u2265\u00a01:160. In the few cases of missing serology, a prolonged stay in an endemic area (\u22653\u00a0years) and over 10 malarial episodes reported, was considered equivalent to a high anti-malarial antibody titer.Serum IgM level, two standard deviations above the local mean, corresponding to\u00a0\u22652.5\u00a0g/L.Cured: absence of splenomegaly and normal IgM titer;Improved:\u00a0\u22650.5\u00a0cm decrease of the spleen diameter, or unchanged spleen diameter and\u00a0\u22650.5\u00a0g/dL decrease of IgM level;Unchanged:\u00a0<0.5\u00a0cm or no variation of the spleen diameter and\u00a0<0.5\u00a0cm or no variation of IgM level;Progressed:\u00a0\u22650.5\u00a0cm increase of the spleen diameter, or unchanged spleen diameter and\u00a0\u22650.5\u00a0g/dL increase of IgM level;HMS: patients with e-HMS at initial visit, meeting the case definition of full-blown HMS (as resumed in Introduction) at follow-up.Plasmodium using one of the following methods: QBC Malaria Test  or Malaria antigen Rapid Detection Test (RDT) . For all positive results, confirmation with microscopy was also carried out.Patients were screened for 2 test. The Fisher exact test was used if appropriated. A stepwise logistic regression model with forward selection was performed to study the association of the main dependent variable (outcome at follow-up) with the independent variables such as: sex; ethnicity; re-exposure to malaria; presence/absence of symptoms and of malaria parasites at first visit; treatment or not at first visit; age; time elapsed between the first observation and follow-up. Potential interaction among the variables was also studied with the same model. Significance values for entry in (pe)/removal from (pr) the model were set at 0.10 and 0.15, respectively.Data was analysed using the software STATA IC 14  . For catSubjects were anonymously coded in the database, unlinked from any information identifying the source individuals. Although the study was retrospective and no action on patients was involved, the study protocol was nevertheless submitted to the Ethics Committee of the Coordinating Site  for approval. The latter acknowledged the study protocol and formally authorized the study .The patient flow is resumed in Fig.\u00a0Most of the subjects included met the main case definition criteria as outlined in \u201cTable\u00a0Most subjects (46/78 or 59\u00a0%) were re-exposed to malaria transmission before follow-up (this data was missing for three patients). Table\u00a06/\u00b5L, p\u00a0=\u00a00.042), but the Hb value was similar in the two groups.The median age of re-exposed subjects was higher: 54\u00a0years versus 37.5\u00a0years (p\u00a0=\u00a00.003). Most patients re-exposed were Caucasian . There was no significant gender difference. The average duration of exposure to malaria before observation was similar and so were most clinical and laboratory findings. The median diameter of the spleen was higher in not re-exposed subjects  and so was the median RBC count .The characteristics of the e-HMS subjects who received/did not receive an anti-malarial treatment are summarized in Table\u00a0Most of the patients were symptomatic at first observation. Asthenia was the most frequently reported symptom, present in 44/97 Caucasians (45\u00a0%) and in 7/29 non-Caucasians (24\u00a0%). Fever (most often low-grade) was present in 37/97 Caucasians (38\u00a0%) and in 8/29 non-Caucasians (28\u00a0%).Plasmodium was searched in 87 subjects out of 126 (59.2\u00a0%), with a positive result  in 36/87 (41.4\u00a0%). P. falciparum was the species involved in all cases, but for one case of Plasmodium malariae and one of Plasmodium vivax, both in Caucasians. Among Caucasians, positive results were 27/67 overall, of which 3 (11\u00a0%) had only a positive RDT or QBC (with negative blood film), and of the remaining 24, 12 (50\u00a0%) had a parasite density\u00a0<1000/\u00b5L (of which 3 with\u00a0<50/\u00b5L). The highest value of parasite density was 10,500/\u00b5L, roughly corresponding to 0.25\u00a0%. Among non-Caucasians, positive results were 9/20 overall (45\u00a0%), of which 2 (22\u00a0%) had only a positive RDT or QBC, and of the remaining 7, 5 (71\u00a0%) had a parasite density\u00a0<1000/\u00b5L (of which 2 with density\u00a0<50/\u00b5L). The highest value of parasite density was 21,500/\u00b5L, roughly corresponding to 0.5\u00a0%.Overall, The results of univariate analysis are reported in Table\u00a02\u00a0=\u00a00.2137) suggesting the need of confirming the results with a higher number of observations and/or with the association of other possible predictors, if any. Variables significantly associated with outcome in the final model . Patients were more likely to be treated if malaria parasites were found in blood, which is by no mean unexpected. All potentially confounding variables were included in the log regression model.As 1/3rd of the study subjects were lost at follow-up, it was first assessed if this group was similar for the main baseline characteristics to the group of subjects with follow-up, which was indeed the case Table\u00a0, with a This retrospective, longitudinal study aimed to describe the clinical evolution of subjects presenting a history of long term exposure to malaria transmission and a splenomegaly (any spleen size), with or without a raised IgM level in blood. After excluding other possible causes of splenomegaly, a tentative definition of e-HMS was devised, as described in the \u201cIt has been reported that the development of HMS can be influenced by various aspects, including genetic predisposition \u201318, but Returning to an endemic area for malaria proved to be a risk factor for the evolution of the syndrome. Almost half of all the subjects re-exposed to malaria progressed, versus none of those who remained in Italy until follow-up. Even more importantly, almost a quarter of the re-exposed group evolved to a full-blown HMS. Therefore, although the case definition of e-HMS may not be specific and may include patients with other  causes of splenomegaly, the risk of evolution to HMS, a severe disease with high mortality, justifies in itself the recognition of the early stage of the disease, that should be properly treated. Treatment appeared to be independently protective against evolution of e-HMS to full-blown HMS.loss at follow-up of several patients: the follow-up data was obtained retrospectively from the patients returned  to the observation after the first contact; anyway for about 2/3rd of the study subjects follow-up data was available, moreover as mentioned above the baseline characteristics of the two groups were in all similar;not uniform follow-up time, for the same reasons outlined above; however, this variable was duly included in the log regression model;differences between the two main groups of re-exposed/not re-exposed and of treated/not treated for some characteristics as discussed above;on logical grounds, for treatment at initial observation to be really effective, long term prophylaxis and/or frequent/intermittent anti-malarial treatment are also necessary , 20. UnfThe main limitations of this study are inherent to the retrospective study design, in particular:However, at multivariate analysis including most potential predictors, the main findings  was robust. Asthenia was the only symptom seemingly influencing the risk of evolution, although it cannot be excluded a chance association.It\u2019s possible to identify an early stage of HMS, which has been defined as e-HMS, that tends to evolve into a full-blown HMS if malaria antigenic stimulus persists and if subjects are not treated for malaria. e-HMS is characterized by a spleen size\u00a0\u226512\u00a0cm, even in the absence of high values of IgM level, or by raised IgM without splenomegaly, in subjects with a history of long term exposure to malaria transmission, and with high titre of anti-malarial antibodies. The case definition of the syndrome should be updated in order to include criteria to diagnose e-HMS, that should be recognized and treated. Although the diagnostic criteria of e-HMS may not be highly specific and include false positive subjects , treatment is warranted even if diagnostic certitude is lacking, considering the risk of evolution to HMS and its complications.A randomized controlled trial would be the best way to rigorously assess the efficacy of initial anti-malarial treatment, followed by prophylaxis or possibly by intermittent anti-malarial treatment in case of re-exposure, on the evolution e-HMS. However, undertaking a similar trial may prove difficult in the field, also considering the necessarily long follow-up time. On the other hand, a multicentre retrospective study on a larger series of patients observed in non-endemic countries could corroborate the findings of this research and lay a more robust basis for its conclusions."}
+{"text": "Howev as well , that th as well . This pr as well . Interes"}
+{"text": "There has been a rapid increase in the retail availability of e-cigarettes in the UK and elsewhere. It is known that exposure to cigarette point-of-sale (POS) displays influences smoking behaviour and intentions in young people. However, there is as yet no evidence regarding the relationship between e-cigarette POS display exposure and e-cigarette use in young people.This cross sectional survey was conducted in four high schools in Scotland. A response rate of 87\u00a0% and a total sample of 3808 was achieved. Analysis was by logistic regression on e-cigarette outcomes with standard errors adjusted for clustering within schools. The logistic regression models were adjusted for recall of other e-cigarette adverts, smoking status, and demographic variables. Multiple chained imputation was employed to assess the consistency of the findings across different methods of handling missing data.Adolescents who recalled seeing e-cigarettes in small shops were more likely to have tried an e-cigarette (OR 1.92 99\u00a0% CI 1.61 to 2.29). Adolescents who recalled seeing e-cigarettes for sale in small shops (OR 1.80 99\u00a0% CI 1.08 to 2.99) or supermarkets (OR 1.70 99\u00a0% CI 1.22 to 2.36) were more likely to intend to try them in the next 6\u00a0months.This study has found a cross-sectional association between self-reported recall of e-cigarette POS displays and use of, and intention to use, e-cigarettes. The magnitude of this association is comparable to that between tobacco point of sale recall and intention to use traditional cigarettes in the same sample. Further longitudinal data is required to confirm a causal relationship between e-cigarette point of sale exposure and their use and future use by young people. There is increasing concern about the rising prevalence of e-cigarette use among children and young people in particular, that e-cigarette use is increasing among young people who have never smoked (never smokers) . AlthougIt has been clearly demonstrated that increased availability of cigarettes is associated with higher consumption. For example, a higher tobacco retail outlet density in a young person\u2019s home environment increases the probability of current smoking and ever smoking  and the The e-cigarette market is undergoing a period of substantial growth internationally  and the The regulatory environment for e-cigarettes is very different to that for tobacco. While most tobacco advertising and promotion is prohibited in the UK  and saleYoung people are not only exposed to e-cigarette adverts through POS displays but also from TV, billboards, print media and the internet. Experimental research has shown that exposure to e-cigarette TV adverts increases the likelihood that adolescents will intend to try e-cigarettes in the future .This Scottish study examines the relationship between the recall of e-cigarette POS displays and children\u2019s use and future intention to use e-cigarettes controlling for exposure to online advertising of e-cigarettes, e-cigarette advertising via other media, smoking status and demographic factors. In order to compare the size of effects we also examine the relationship of cigarette point of sale exposure to intention to smoke cigarettes in the same sample. To our knowledge information on young people\u2019s recall of e-cigarettes in retail outlets and use and intention to use e-cigarettes has not been collected in any other survey to date so this is the first and currently the sole source of information on this important and policy relevant topic.The data presented here were collected as part of an ongoing 6-year multi-modal study designed to assess the impact of Scottish legislation banning tobacco POS displays on young people\u2019s smoking-related attitudes and behaviours . The infThe results reported here are based on data collected between January and March 2015 after the implementation of the tobacco point of sale ban in large supermarkets but before its implementation in small shops. Questionnaires were administered to pupils in Secondary 1 through to Secondary 6  by teachers during class time under examination conditions. Information regarding the survey was sent out to parents two weeks prior to the survey date. Parents could withdraw their child from the survey by returning the opt-out form to the school. Young people could decline to take part in the survey or withdraw from the survey at any point. Ethical approval for the study, including the consent procedures, was obtained from the University of St Andrews, School of Medicine Ethics Committee.This study aimed to examine the relationship between e-cigarette point of sale recall  and e-cigarette use. Previous e-cigarette use and intention to use e-cigarettes in the next 6\u00a0months were the dependent variables. E-cigarette POS recall in large supermarkets and small shops were the explanatory variables. Recall of other sources of e-cigarette advertisement was included in the adjusted models to control for the potentially confounding effects of exposure to other types of e-cigarette advertisement. In addition, demographic factors such as age, sex, and family affluence were included as control variables. Tobacco smoking is known to be a predisposing factor to e-cigarette use therefore previous tobacco use was also included in the adjusted models as a control variable in order to test whether e-cigarette POS sale influenced e-cigarette uptake in never smokers (never tried tobacco cigarettes).Respondents were asked their gender, ethnic group, and date of birth. Ethnic group was dichotomised to white ethnic group versus other responses. Individual family material well-being was assessed through the Family Affluence Scale (FAS)  which isRespondents were asked whether they had heard of e-cigarettes and could respond \u2018yes\u2019, \u2018no\u2019, or \u2018don\u2019t know\u2019. Respondents who answered \u2018yes\u2019 were directed to the question \u2018which ONE of the following is closest to describing your experience of e-cigarettes?\u2019, to which they could respond \u2018I have never used them\u2019, \u2018I have tried them once or twice\u2019, \u2018I use them sometimes (more than once a month)\u2019, or \u2018I use them often (more than once a week)\u2019. This variable was dichotomised to \u2018ever tried-1\u2019 versus \u2018never tried-0\u2019. The next question was \u2018Do you think that you will try e-cigarettes in the next 6\u00a0months?\u2019 to which they could reply \u2018yes I do\u2019, \u2018no I don\u2019t\u2019 or \u2018don\u2019t know\u2019. This response was also dichotomised to \u2018yes\u2019 -1 versus \u2018no\u2019 or \u2018don\u2019t know\u2019-0. In the original coding of the e-cigarette variables participants who responded that they did not know what an e-cigarette was or missed this question were coded as \u2018missing\u2019 on all other e-cigarette questions. Another alternative coding method was employed to minimise missing data where participants who did not know what an e-cigarette was, were assumed not to have tried one and not to intend to try one. Results are presented for both versions of the e-cigarette dependent variables.Ever smoking was assessed with the question: \u2018Have you ever smoked cigarettes, even if it is just one puff?\u2019 to which they could respond \u2018yes\u2019 or \u2018no\u2019. Negative responses were used as our variable for \u2018never smoked\u2019. To assess intention to smoke respondents were asked \u2018Do you think you will smoke a cigarette or hand-rolled cigarettes (roll-ups) at any time during the next year?\u2019 To which they could answer \u2018definitely yes\u2019 \u2018probably yes\u2019 \u2018probably not\u2019 \u2018definitely not\u2019. This was dichotomised to \u2018yes\u2019-1 or \u2018no\u2019-0.Respondents were asked \u2018During the past 30\u00a0days, have you noticed any adverts  for (a) cigarettes or hand rolled cigarettes (roll-ups), or (b) electronic cigarettes (e-cigarettes)?\u2019 To which respondents could answer \u2018Yes\u2019, \u2018no\u2019 or \u2018don\u2019t know\u2019. This response was also dichotomised to \u2018yes\u2019-1 versus \u2018no\u2019 or \u2018don\u2019t know\u2019-0.Respondents were asked \u2018When you are using the internet, how often do you see adverts for (a) tobacco products or pictures of people smoking, or (b) electronic cigarettes (e-cigarettes) or people smoking them?\u2019 To this pupils could respond \u2018I don\u2019t use the internet\u2019, \u2018most of the time\u2019, \u2018some of the time\u2019, \u2018hardly ever\u2019, \u2018never\u2019. Responses of \u2018I don\u2019t use the internet\u2019 were recoded as \u2018never\u2019. All responses were dichotomised to \u2018never\u2019 -0 versus other responses-1.Respondents were asked whether in the past 30\u00a0days, when they had been in (a) large supermarkets and (b) small shops, they could remember seeing (i) cigarette or tobacco packs or (ii) electronic cigarettes displayed for sale. To this they could respond \u2018yes\u2019, \u2018no\u2019 or \u2018don\u2019t know\u2019. This response was also dichotomised to \u2018yes\u2019 -1 versus \u2018no\u2019 or \u2018don\u2019t know\u2019-0.Data analysis and imputation was conducted in Stata version 14. Analysis was by logistic regression with standard errors adjusted for clustering by school. Where the prevalence of the outcome was low  was not a significant predictor of previous e-cigarette use or intention to use in the adjusted models. This indicates that once recall of point of sale and internet e-cigarette adverts is included in the models, recalling seeing adverts in billboards, newspapers or magazines or on TV does not account for any additional variance in uptake of e-cigarettes by adolescents. Recall of e-cigarettes in small shops and supermarkets contributes independently to the prediction of intention to use e-cigarettes. Recall of e-cigarette displays in small shops and on the internet is associated with previous e-cigarette use. Thus, e-cigarette advertising may be influencing adolescents from two sources \u2013 the physical spaces in which they live their lives and their online experience.Small shops may be important as a source of e-cigarette point of sale exposure because they are frequently visited by young people. They also represent part of young people\u2019s formative environment. Display of e-cigarettes in local small shops may indicate normality and social acceptability to young people . The preThe other key source of e-cigarettes advert exposure is the internet. A recent report on children\u2019s use of online technologies in Europe highlights \u2018how embedded the internet has become in young people\u2019s lives\u2019 and that \u2018most young people find the internet to be a necessity for life in modern society\u2019 . The data, in this study, are cross-sectional so no firm conclusions can be drawn regarding causality. Therefore, we do not know whether young people plan to try e-cigarettes because they have noticed e-cigarette displays in shops or on the internet, or whether they notice e-cigarette displays because they are favourably disposed towards trying e-cigarettes. However, even if e-cigarette experimentation makes users more likely to notice displays, seeing displays in the local environment may well further reinforce that inclination . FurtherAnother limitation is that the sample is not representative of the population of Scotland, as a fully randomised sampling process was not employed and there was 13\u00a0% non-response to the survey. However, demographic variables have been included in the adjusted models to control for these factors.This is the first study to suggest that there is an association between young people\u2019s exposure to and recall of POS displays for e-cigarettes and their stated intentions to use e-cigarettes. Longitudinal data, which will be provided by this study in the future, will allow us to establish whether this relationship is causal. The possibility that e-cigarette POS displays may be linked to likelihood of uptake by young people is of concern, given that forthcoming EU legislation will state that e-cigarettes should be an adult-only product. There is some evidence, from animal models, that nicotine has long term effects on the adolescent brain including permanent changes to connectivity and neurotransmitter receptivity in neural reward-systems. These are the brain circuits associated with addictive behaviours , 33. TheOur findings suggest that young people\u2019s recall of e-cigarettes POS displays in small shops is associated with use of, and intention to use, e-cigarettes. Further research is required on how to balance the promotion of e-cigarettes as a cessation aid while preventing the initiation of e-cigarette use among young people who have never smoked."}
+{"text": "This usually causes the sparse problem and reduces the classification accuracy. To solve this problem, we add gaps into k-mer and introduce a new feature called gapped k-mer (GKM) for identification of recombination spots. By using this feature, we present a new predictor called SVM-GKM, which combines the gapped k-mers and Support Vector Machine (SVM) for recombination spot identification. Experimental results on a widely used benchmark dataset show that SVM-GKM outperforms other highly related predictors. Therefore, SVM-GKM would be a powerful predictor for computational genomics.Recombination is crucial for biological evolution, which provides many new combinations of genetic diversity. Accurate identification of recombination spots is useful for DNA function study. To improve the prediction accuracy, researchers have proposed several computational methods for recombination spot identification. The k-mer feature is one of the most useful features for modeling the properties and function of DNA sequences. However, it suffers from the inherent limitation. If the value of word length  Recombination plays an important role in genetic evolution, which describes the exchange of genetic information during the period of each generation in diploid organisms23et al.et al.181920et al.23To improve the predictive accuracy, researchers have proposed several computational methods for recombination spot identification, which are based on some well known machine learning techniques, such as support vector machine (SVM)579111213k neighboring residues. By using this feature, the local sequence composition information can be extracted. Typically, the value of k is set to 6 or 7, and the length of their corresponding feature is 46\u2009=\u20094096 or 47\u2009=\u200916384. Actually, larger k values are preferred, because more sequence composition information can be incorporated. However, large k values (k\u2009>\u20096) will lead to extremely sparse feature vectors, which may cause a severe over-fitting problem. In order to find a tradeoff between the sparse feature space problem and more sequence composition information, the gapped k-mer has been proposed, and successfully applied to enhancer identification33All these computational methods could yield quite encouraging results, and each of them did play a role in stimulating the development of recombination spot identification. However, further study is needed due to the following reason. Among the aforementioned features, k-mer628293031In this study, we apply the gapped k-mer to recombination spot identification, and propose a new computational predictor called SVM-GKM via combining GKM with Support Vector Machines. Experimental results on a widely used benchmark dataset show that SVM-GKM outperforms the two state-of-the-art methods in the field of recombination spot identification, and some interesting patterns can be discovered by analyzing the discriminative features in SVM-GKM.et al.Here, we employ a benchmark dataset taken from Liu + contains recombination hotspots, negative subset \u2211\u2212 contains recombination coldspots, and symbol \u222a represents the \u201cunion\u201d in the set theory. There are 490 hotspots in \u2211+ and 591 coldspots in \u2211\u2212. The codes of the 1081 DNA samples as well as their detailed sequences are given in the where positive subset \u2211k, the method based on k-mers could cause the sparse problem. This is because many k-mers are not appeared in one DNA sequence, and thus its feature vector may contain a large amount of zero values. To overcome this disadvantage caused by k-mers, Ghandi et al.With the increase of word length m to stand for is the length of matches, so the length of gaps is k\u2212m. Then feature vector f\u2009S of a given sequence S can be defined asFirst, each training sample is represented as a series of k-mers, where k is the length of subsequence. The key to calculate the GKM kernel matrix is to compute the number of mismatches between each pair of sequences for all pairs of k-mers. Here, we define a variable i\u2212th gapped k-mer in the sequence S, b is the alphabet size. For DNA sequence, b\u2009=\u20094. Then the kernel function between two sequences S1 and S2 can be defined aswherem increases, direct calculation of Since the number of all possible gapped k-mers grows extremely rapidly as n(n\u2009\u2264\u2009k\u2009\u2212\u2009m) is the number of mismatches between two k-mers x1 and x2. x1 is from S1 and x2 is from S2, Nn is the number of pairs of k-mers with n mismatches in sequences S1 and S2, hn is the corresponding coefficient. hn is defined as follows:where hn when calculating the mismatch for two sequencesIn order to reduce the error caused by corresponding coefficients, the following equation is used to get n1is the mismatch number that k-mer x1 contains, n2is the mismatch number that k-mer x2 contains, and t is the mismatches number, which exists at the k\u2009\u2212\u2009n mismatch positions for both x1 and x2. The remaining mismatches r\u2009=\u2009n2\u2009\u2212\u2009t\u2009\u2212\u2009(n\u2009\u2212\u2009n1\u2009\u2212\u2009t) are among the the n mismatch positions for k-mer x2.where In this paper, a tree structure is employed to count mismatchesti) stands for the path from the root to node ti with depth d. d means that the corresponding sub-sequence has a length of d. For a tree, its maximum depth is k, i.e. the length of the k-mer. Therefore, for a terminal leaf node of the tree, the leaf node represents a k-mer. A terminal leaf node can also hold the list of training sequence labels, which contains the information of appeared k-mers and the number of these k-mers in each sequence. We use depth-first search (DFS)35ti at depth d and also store the number of mismatches between two paths s(ti) and s(tj). Differing from this method, our method only needs to store the values of the terminal leaf nodes and does not need to store the information of all nodes. Thus, at the end of one DFS traversal of the tree, the mismatch profiles for all pairs of sequences are completely determined. k\u2009=\u20093. The tree is generated by sequences S1, S2, and S3. We can see that for node t6, s(t6)\u2009=\u2009\u2018AAA\u2019. Sequence S1 contains two counts of substring s(t6), but sequence S2 and sequence S3 do not contain this substring. For our experiments, we used the gkm-SVM software v1.3http://www.beerlab.org/gkmsvm/.The tree is generated by training samples and we construct it by adding a path for every k-mer. Assume that s(The support vector machine (SVM) method is a widely used method for classification problems3438394041434445K-fold cross-validation is a widely used method for evaluating the performance of a computational predictor47Here, we use four metrics, sensitivity (Sn), specificity (Sp), accuracy (Acc), and Mathew\u2019s correlation coefficient (MCC) to test the predictor485051N+ is the total number of the tested recombination hotspots sequences, N\u2212 is the total number of the tested recombination coldspots sequences, where k (see method section for details) on the performance of SVM-GKM. k from 8 to 15 with match length m set as 7. The performance of SVM-GKM increases significantly with the growth of k values, and SVM-GKM achieves the best performance when k\u2009=\u200913. These results are not surprising, because for larger k values, more sequence order information can be incorporated into the predictor, contributing to higher performance for recombination spot identification.The SVM-GKM predictor is constructed by only using the gapped k-mer as a feature. We first evaluate the impact of the parameter word length n is set as 0, and the tree structure is also employed so as to reduce the computational cost. The performance of these two methods on the benchmark dataset with different parameters is shown in The k-mer is a widely used feature considering the local sequence order information along the DNA sequences. GKM is an improvement of k-mer by introducing the gaps into k-mers. For comparison, a predictor called kmer-SVM is constructed based on k-mers. The kmer-SVM can be viewed as a special case of GKM-SVM without gaps. Therefore, the implementation of kmer-SVM is the same as that of SVM-GKM except that the gap number k\u2009>\u20099). We can also see that parameter k does not have significant impact on the performance of SVM-GKM, and SVM-GKM achieves its highest accuracy (86.57%) when k\u2009=\u200913. In contrast, kmer-SVM achieves its highest accuracy (82.31%) when k\u2009=\u200910 and then its performance decreases significantly. This is because when k is larger than 10, the dimension of the feature vectors is very large and many values are zeros, leading to extremely sparse problem. For example, when k\u2009=\u200913, the dimension of the feature vectors generated by kmer-GKM is 413\u2009\u2248\u20096.7\u2009\u00d7\u2009107. In contrast, for the same word length, the length of feature vectors generated by SVM-GKM is only 6, which is much smaller than that of kmer-SVM, and therefore, GKM can efficiently avoid the sparse problem. As shown in et al.We also compare SVM-GKM with other two highly related methods, including iRSpot-PseDNCIt is interesting to explore if the gapped k-mers can reflect the characteristics of the recombination spots or not. Therefore, the discriminative power of different gapped k-mers in SVM-GKM are calculated by using the Principal Component Analysis (PCA)5455As a widely used feature in the field of recombination spot identification, k-mer only incorporates the local sequence composition information of DNA sequences. In order to overcome this disadvantage, gapped k-mer (GKM) has been proposed to incorporate the long range sequence order information and reduce the length of the feature vectors. GKM successfully overcomes the sparse problem caused by k-mers via introducing the gaps into the k-mers, and has been successfully applied to enhancer identification. In this study, we apply the concept of GKM to the field of recombination spot identification, and demonstrate that this approach can obviously improve the predictive performance. These results are not surprising, because previous studies485859Besides k-mer and gapped k-mer, palindrome structure, relatively high GC content, dinucleotides bias, and consensus DNA motifs have been showed useful for recombination spot identification. Our future study will focus on exploring various feature combinations to construct a computational predictor. Performance improvement can be expected by using some neural-like computing strategies, such as spiking neural models611616263How to cite this article: Wang, R. et al. Recombination spot identification Based on gapped k-mers. Sci. Rep.6, 23934; doi: 10.1038/srep23934 (2016)."}
+{"text": "F\u2009=\u20092.28, p\u2009=\u20090.10. In addition, the results demonstrated that both groups were immersed and present in the environment. The results on posttreatment measures of CH  demonstrate the efficacy of IBT in terms of symptom reduction. Overall, these results suggest that the creation of a virtual environment may be effective in the treatment of CH by helping the compulsive hoarders take action over their clutter.The present study evaluated the efficacy of adding a virtual reality (VR) component to the treatment of compulsive hoarding (CH), following inference-based therapy (IBT). Participants were randomly assigned to either an experimental or a control condition. Seven participants received the experimental and seven received the control condition. Five sessions of 1\u2009h were administered weekly. A significant difference indicated that the level of clutter in the bedroom tended to diminish more in the experimental group as compared to the control group  Though classified in DSM-V as a distinct disorder, compulsive hoarding (CH) was long considered a subtype of OCD. Also new in DSM-V is that OCD is no longer considered an anxiety disorder. CH and OCD are now considered separate disorders, part of the Obsessive Compulsive and Related Disorders category. Regardless, the experience of intense anxiety when required to get rid of personal objects and difficulty in taking action are part of the diagnostic criteria for CH . The majn\u2009=\u200913) corroborates the results of the other meta-analysis and reports an average effect size of 1.11 for VR, as compared to a control condition  validated in an individual format 1-There will be a statistically significant difference between the experimental and control conditions on measures of clutter, such as the Clutter Image Rating scale.2-The participants in the experimental condition will experience clinically greater levels of anxiety than participants in the control condition during the sessions with immersion in the VR environment.3-The non-immersive virtual environment will elicit a state of presence and immersion in all of the participants.4-IBT will lead to clinically and statistically significant improvement in symptoms of (a) CH, (b) anxiety, and (c) depression.The hypotheses:Participants were recruited using advertisements posted in universities, hospitals, CLSC\u2019s, and community organizations in the region of Montr\u00e9al, as well as Fernand Seguin research centre\u2019s website. Twenty-five participants were evaluated in the context of this project. Of these, nine were excluded following the initial evaluation, and two dropped out over the course of treatment, one in each group. Of the 14 participants who took part in the project, 2 were males and 12 were females. Demographic data are reported in Table neuroVR 2.0 platform (www.neurovr.org) was used to create the environments. A digital camera was used to take photographs of the CH\u2019s home environments and Corel Paint Shop Pro Photo X2 software was used to treat the images. This procedure was validated at the Universit\u00e9 du Qu\u00e9bec en Outaouais (UQO) in a sample of six participants , which is freely accessible online. In the experimental condition, objects that belong to the hoarders were inserted into the apartment environment created using this platform. In the control condition, images depicting objects were selected from the internet and inserted into the apartment environment. To create the experimental virtual environments, approximately 30 photos taken by participants of their homes were selected. The objects in these images were cut out using Corel Paint Shop Pro Photo X2 and inserted in the apartment environment. The objective was to recreate the participant\u2019s apartment, mainly their living room, kitchen, and bedroom. The objects were placed in piles as represented in their pictures. The objects that were eventually selected to be used in VR procedure were cut out individually so that the participant could select them.All of the virtual environments were created using the neuroVR 2.0 platform , post-IBT treatment, and post-VR. The clinical interviews were administered by an evaluator trained in the administration of CH measures. The evaluation lasted for 4\u2009h.Structured Clinical Interview for DSM-IV for Axis I disorders [SCID-I; French version; Ref.   .Overvalued Ideas Scale (OVIS) (r\u2009=\u20090.86), and inter-rater reliability (r\u2009=\u20090.88).The e (OVIS)  is an 11Evaluation of Primary Inferences Scale (EPIS) (The e (EPIS)  was deveEvaluation of Secondary Inferences Scale (EPIS) (The e (EPIS) . With thSaving Inventory-Revised (SIR)  , is compSaving Cognitions Inventory (SCI) (The ry (SCI)  is a queClutter Image Rating (CIR) (The ng (CIR)  is a serBeck Depression Inventory (BDI-II) (r\u2009=\u20090.93).The (BDI-II)  is a 21-Beck Anxiety Inventory (BAI) (r\u2009=\u20090.63) (The ry (BAI)  contains\u2009=\u20090.63) .Inferential Confusion Questionnaire \u2013 Expanded Version (ICQ-EV) (r\u2009=\u20090.90).The (ICQ-EV)  is compr(ICQ-EV) . This meImmersive Tendencies Questionnaire (ITQ) (The Canadian adaptation of the re (ITQ)  is comprre (ITQ)  demonstrre (ITQ) .Presence Questionnaire (PQ-F) (The French Canadian adaptation of the e (PQ-F)  consistsThe French Canadian translation of the Simulator Sickness Questionnaire (SSQ-F)  was alsoFinally, the therapist asked the participants to rate their level of anxiety and discomfort during the VR tasks. For example, when the client had to discard a virtual object, the therapist asked the client to rate their level of anxiety and discomfort on a scale from 0 to 10 and took note of the rating. This allows for measure of the difficulty of the task and also to verify if the VR elicited the expected emotions.Fourteen participants with a diagnosis of CH took part in this project. The participants were randomly assigned to one of two of the following conditions: active control condition and experimental condition.All of the participants received IBT administered by psychologists trained in this approach. The treatment protocol used was developed by O\u2019Connor et al.  and adapAfter receiving IBT, five sessions of 1\u2009h were given to participants in both conditions. These sessions were administered by psychologists trained in the use of neuroVR 2.0 and the established treatment protocol. These sessions were also audio recorded and verified by an independent person involved with the project to ensure the integrity of the steps of the VR sessions was respected. In addition, the participants had no contact with one another between VR sessions. The first session allowed participants in the experimental condition to familiarize themselves with the virtual environment and to change elements of the environment to make them resemble, as much as possible, their actual environment at home. The second session was aimed at helping participants begin to sort through their homes by establishing a plan of action based on the elements present in the virtual environment. In the last three sessions, participants took action virtually by disposing of objects already selected based on the degree of subjective distress they reported. Once an object was selected, the participants were supposed to put it in a virtual, 3D garbage can. They were then asked to re-evaluate their degree of anxiety and discomfort on a scale of 0 to 10. At the beginning of each session, the therapist evaluated if some objects were sorted or taken out from home by the participant. The last session was also used to discuss relapse prevention and to establish a plan of action for the coming months. The client was asked to identify at-risk situations for relapse and to write a plan of action with the therapist as a way to ensure the client had all of the tools that may be needed in the future. Finally, measures of presence and VR sickness were completed at the end of each VR session.For control participants, the steps of treatment were the same. The only difference was that the objects selected when sorting and discarding did not belong to them. Their level of anxiety and discomfort on a scale from 0 to 10 was still evaluated to determine the presence of any emotions toward these objects. With regards to the task completed at home, participants were asked to discard one object, without specifying which one. The point of this exercise was to see if they would dispose of an object that was similar to the one discarded in the virtual environment.T-test were conducted on all normal variables. Non-parametric analyses were conducted when variables did not meet the assumptions of normality or had a small sample size. The variables for which non-parametric analyses were conducted are the following: the subscale \u201ccontrol\u201d of the SCIR and the \u201cacquisition\u201d and clutter subscales of the SIR. The non-parametric analyses of these variables will be presented following the presentation of the parametric analyses. Additionally, a significance level of 0.10 was chosen because of the small sample size. Even though we used a cut-off point of 0.10, we nonetheless corrected for multiple comparison analysis.Normality was verified for all variables and the analyses were conducted by taking into consideration whether the assumptions were met or not. Analysis was conducted on completers. Repeated measures ANOVAs and p\u2009>\u20090.05). Also, there were no significant differences between the groups at pretreatment on clinical measures.Univariate (age) and chi-square  analyses did not find any significant differences between the groups \u2009=\u20092.28, p\u2009=\u20090.10. It is possible to qualify this interaction because of the significance level. Contrasts indicated a linear interaction between the two groups for the pre-VR and post-VR F\u2009=\u20097.80, p\u2009<\u20090.001. This interaction demonstrates that the participants\u2019 results for the series of images of the bedroom in the experimental group had a tendency to decrease over time as compared to the control group. There were no interactions observed for the other rooms depicted in the CIR, the kitchen F\u2009=\u20090.16, p\u2009=\u20090.85 and the living room F\u2009=\u20090.90, p\u2009=\u20090.42.Repeated measures ANOVAs were conducted on the main measure of clutter, the CIR. With regards to the images of the bedroom, a significant interaction was observed t-tests were conducted in order to determine if there was a difference between the mean level of anxiety before and after action was taken in the two groups. A significant difference was observed for the experimental group t(6)\u2009=\u200917.67, p\u2009<\u20090.001 as well as for the control group t(6)\u2009=\u20098.00, p\u2009<\u20090.001. An independent t-test was conducted, and a significant difference was found between the groups before action was taken in VR t(12)\u2009=\u20093.36, p\u2009<\u20090.05 and after the VR task t(12)\u2009=\u20093.35, p\u2009<\u20090.05.Paired sample F\u2009=\u20095.32, p\u2009<\u20090.05, but no interaction effect, for the \u201cemotional\u201d subscale of the SCIR F\u2009=\u20090.97, p\u2009=\u20090.39. There was also a main effect of time for the \u201cresponsibility\u201d subscale of the SCIR F\u2009=\u20094.20, p\u2009<\u20090.05 and the \u201cmemory\u201d subscale F\u2009=\u20097.76, p\u2009<\u20090.05, but no significant interaction effects between groups (p\u2009>\u20090.05). A Greenhouse\u2013Geisser correction was applied to these variables. Finally, a main effect of time was observed for the SCIR total score F\u2009=\u20099.46, p\u2009<\u20090.001, but there were no interaction effects.A repeated measures ANOVA demonstrated a main effect of time F\u2009=\u20092.38, p\u2009=\u20090.15 or for the SIR total score F\u2009=\u20091.68, p\u2009=\u20090.22. As the \u201cclutter\u201d and \u201cacquisition\u201d subscales did not meet the assumptions of normality, non-parametric analyses were conducted. There is no test equivalent to a 2\u2009\u00d7\u20092 repeated measures analysis. As such, a composite score between post-RV and pre-IBT was calculated and a Mann\u2013Whitney U test was conducted in order to determine if there was a significant difference between groups. No difference was observed for the \u201cclutter\u201d subscale for the experimental group  and the control group , U\u2009=\u200920.00, z\u2009=\u2009\u22120.58, p\u2009=\u20090.56, r\u2009=\u20090.14. Also, there was no difference for the \u201cacquisition\u201d subscale for the experimental group  and control group , U\u2009=\u200914.00, z\u2009=\u2009\u22121.35, p\u2009=\u20090.18, r\u2009=\u20090.36.As previously mentioned, a main effect of time from pre-IBT to post-RV was found for the SIR total score and its three subscales. A repeated measures ANOVA did not find an interaction between the groups for the \u201cdiscarding objects\u201d subscale F\u2009=\u20093.56, p\u2009<\u20090.05, and no interaction effect F\u2009=\u20090.16 p\u2009=\u20090.85. A main effect of time was also observed for the \u201cobsessions\u201d subscale F\u2009=\u20094.19, p\u2009<\u20090.05 but not for the \u201ccompulsions\u201d subscale F\u2009=\u20091.13, p\u2009=\u20090.31. No interaction was observed between the groups for either subscale. A repeated measures ANOVA found no main effect F\u2009=\u20092.39, p\u2009=\u20090.11 or interaction F\u2009=\u20090.24, p\u2009=\u20090.24 for the OVIS. There was, however, a linear trend across time for both groups. Essentially, the total score demonstrated a tendency to decrease for the two groups. The results do not demonstrate a main effect for the BDI F\u2009=\u20090.02, p\u2009=\u20090.98 or the BAI F\u2009=\u20090.22, p\u2009=\u20090.80. There was also no interaction observed for the BDI F\u2009=\u20091.81, p\u2009=\u20090.19. There was, however, an interaction found for the BAI F\u2009=\u20093.17, p\u2009<\u20090.10. The BAI scores for the control group had a tendency to decrease over time, while that of the experimental group increased from pre-IBT to post-IBT, and decreased at post-VR. A Mann\u2013Whitney U test did not find any difference between the groups on the ICQ-EV at post-VR: experimental group  and control group , U\u2009=\u200919.5, z\u2009=\u2009\u22120.22, p\u2009=\u20090.83, r\u2009=\u20090.06. See Table A repeated measures ANOVA found a main effect of time for the total score on the YBOCS between pre-IBT, post-IBT, and post-RV F,24\u2009=\u20093.5t-tests found no significant difference between groups on any of the subscales of the presence questionnaire. The scores demonstrated a high degree of presence for both groups according to the French-language norms of the questionnaire; experimental group M\u2009=\u200990.96, SD\u2009=\u20093.07; control group M\u2009=\u200986.98, SD\u2009=\u200920.94. The SD is much larger for the control group than for the experimental group. An independent t-test did not find any difference between the two groups for the Simulator Sickness Questionnaire. Furthermore, each group obtained scores that were below the average reported in the norms for the questionnaire .Independent We also compared the results of this study with a non-concurrent data collected from another group. Five participants were recruited in the same way as the participants in the present study\u2019s sample and participated in the first therapy group given at the Fernand Seguin research center, before the virtual environments were created. They received the same treatment protocol (IBT), and it was the same therapist who animated the sessions.z\u2009=\u20090.00, p\u2009=\u20091.0; kitchen: z\u2009=\u2009\u22121.00, p\u2009=\u20090.32; living room: z\u2009=\u20090.00, p\u2009=\u20091.00. This was also the case for measures from post-IBT to 6-month follow-up: bedroom: z\u2009=\u20090.00, p\u2009=\u20091.0; kitchen: z\u2009=\u2009\u22121.41, p\u2009=\u20090.20; living room: z\u2009=\u20090.00, p\u2009=\u20091.00. The results for the three rooms decreased.Measures were taken at pretreatment, posttreatment, and at 6\u2009months following completion of the treatment. The results demonstrate no clinical or statistical difference on measures of clutter (CIR) from pre-IBT to post-IBT; bedroom: z\u2009=\u2009\u22121.6, p\u2009<\u20090.10, with a large effect size (r\u2009=\u20090.57). The median score decreased from pre-IBT (Md\u2009=\u200921.50) to post-IBT (Md\u2009=\u200917.00). The \u201cobsessions\u201d subscale decreased significantly z\u2009=\u2009\u22121.83, p\u2009<\u20090.10, with a large effect size (r\u2009=\u20090.65). The median score decreased from pre-IBT (Md\u2009=\u200911.00) to post-IBT (Md\u2009=\u20098.50). No change, however, was observed for the \u201ccompulsions\u201d subscale z\u2009=\u2009\u22120.38, p\u2009=\u20090.71. There was no significant difference for the total YBOCS score from post-IBT to 6-month follow-up z\u2009=\u2009\u22120.00, p\u2009=\u20091.00.With regards to the secondary measures, scores on the YBOCS decreased significantly from pre-IBT to post-IBT z\u2009=\u2009\u22120.37, p\u2009=\u20090.72 and BDI: z\u2009=\u2009\u22120.92, p\u2009=\u20090.36. There was a significant difference on the ICQ-EV z\u2009=\u2009\u22121.60, p\u2009<\u20090.10, with a large effect size (r\u2009=\u20090.60). The median score decreased from pre-IBT (Md\u2009=\u200976.00) to post-IBT (Md\u2009=\u200965.50).There was no significant difference from pre-IBT to post-IBT on the OVIS: z\u2009=\u2009\u22121.83, p\u2009=\u20090.06, with a large effect size (r\u2009=\u20090.65). The median score decreased from pre-IBT (Md\u2009=\u200916.50) to post-IBT (Md\u2009=\u20097.00). There was no significant difference on any of the questionnaires from post-IBT to 6-month follow-up.A significant difference on the BAI was also observed z\u2009=\u2009\u22121.63, p\u2009<\u20090.10, with a large effect size (r\u2009=\u20090.62). The median score decreased from pre-IBT (Md\u2009=\u20092.00) to 6-month follow-up (Md\u2009=\u20090.00). No measures were taken at post-IBT in this sample, as they were in the present study.With regards to the secondary CH measures, no significant decrease on the SIR total score and the \u201cclutter\u201d and \u201cdiscarding objects\u201d subscales was observed between pre-IBT and 6-month follow-up. A significant difference was observed on the \u201cacquisition\u201d subscale z\u2009=\u2009\u22121.63, p\u2009<\u20090.10, with a large effect size (r\u2009=\u20090.62). The median score decreased from pre-IBT (Md\u2009=\u20092.00) to post-IBT (Md\u2009=\u20090.00). No significant difference was observed from post-IBT to the 6-month follow-up for the SCIR and its subscales.With regards to the SCIR, no significant difference was observed from pre-IBT to post-IBT for the total score or for its three subscales: \u201cemotional,\u201d \u201cresponsibility,\u201d and \u201cmemory.\u201d A significant difference was observed for the \u201ccontrol\u201d subscale from pre-IBT to post-IBT t-tests were conducted to measure change on measure of CH from pre-IBT to post-IBT. Unfortunately, the SIR was not completed at post-IBT because of an omission in the questionnaire package given to participants. As such, the only measures available for the SIR are at pre-IBT and post-VR. A significant difference was observed from pre-IBT to post-VR for the SIR total score t(13)\u2009=\u20094.79, p\u2009<\u20090.001 and the \u201cdiscarding objects\u201d subscale t(13)\u2009=\u20095.44, p\u2009<\u20090.001. A Wilcoxon test of signed-rank showed a statistically significant decrease on the \u201cacquisition\u201d subscale from pre-IBT to post-VR z\u2009=\u2009\u22122.64, p\u2009<\u20090.005, with a large effect size (r\u2009=\u20090.50). The median score on the \u201cacquisition\u201d subscale decreased between pre-IBT (Md\u2009=\u200921) and post-VR (Md\u2009=\u200915). No significant difference was observed for the \u201cclutter\u201d subscale between pre-IBT and post-VR z\u2009=\u2009\u22121.03, p\u2009=\u20090.31.Paired sample t(13)\u2009=\u20094.59, p\u2009<\u20090.001, and for its three subscales: \u201cemotional\u201d t(13)\u2009=\u20092.82, p\u2009<\u20090.05; \u201cresponsibility\u201d t(13)\u2009=\u20093.07, p\u2009<\u20090.05; and \u201cmemory\u201d t(13)\u2009=\u20096.07, p\u2009<\u20090.001.A significant difference was found for the SCIR total score from pre-IBT to post-IBT, z\u2009=\u2009\u22122.80, p\u2009<\u20090.005, with a large effect size (r\u2009=\u20090.53). The median score decreased between pre-IBT and post-TBI (Md\u2009=\u200915.46).A Wilcoxon signed-rank test demonstrated a statistically significant decrease for the subscale \u201ccontrol\u201d of the SCIR from pre-IBT to post-IBT t(13)\u2009=\u20091.14, p\u2009=\u20090.27; kitchen: t(13)\u2009=\u20091.30, p\u2009=\u20092.22; living room: t(13)\u2009=\u20090.54, p\u2009=\u20090.60).No significant difference was found between the different images on the CIR between pre-IBT and post-IBT (bedroom: p\u2009>\u20090.05).A repeated measures ANOVA was conducted comparing the two groups  for all measures of CH from pre-IBT to post-IBT and no significant interaction was observed between the two groups \u2009=\u20093.21, p\u2009<\u20090.05, and for the \u201cobsessions\u201d subscale t(13)\u2009=\u20092.77, p\u2009<\u20090.05. Also, a significant difference was observed for the \u201ccompulsions\u201d subscale t(13)\u2009=\u20093.21, p\u2009<\u20090.06. There was no significant difference on the OVIS t(13)\u2009=\u20091.37, p\u2009=\u20090.20, BDI t(13)\u2009=\u20091.00, p\u2009=\u20090.34, or BAI t(13)\u2009=\u2009\u22120.09, p\u2009=\u20090.93. To better understand these results, a repeated measures ANOVA was conducted and the results demonstrated that for the BAI, an interaction effect was present between the two groups F\u2009=\u20098.64, p\u2009<\u20090.05. The scores of the experimental group increased, whereas those of the control group decreased. As the assumption of sphericity was not met, the Greenhouse\u2013Geisser correction was applied. As the ICQ-EV was not normally distributed and also not transformable, a Wilcoxon signed-ranked test was conducted. There was no significant difference from pre-IBT to post-IBT for the ICQ-EV z\u2009=\u2009\u22120.72, p\u2009=\u20090.47.Paired sample As expected, the results on measures of VR demonstrated a good state of presence during the experimentation, good immersion, and very little VR sickness. These results confirm the hypothesis that non-immersive virtual environments allow for the creation of a feeling of presence and immersion, which can contribute to the eliciting of emotions, when using the virtual environment.It was observed that both groups experienced anxiety during the VR sessions, a finding that is contrary to the initial hypothesis that stipulated that the control group would not experience significant anxiety. A significant difference, however, was found between the groups. Specifically, the participants in the experimental group experienced significantly more anxiety than the control group during the action taking task completed in the virtual environment. Following the VR task, the control group was significantly less anxious than the experimental group. This may be explained by the fact that the virtual environment in the experimental condition used participants\u2019 personal objects, whereas the virtual environments in the control condition did not. For this reason, the feeling of attachment toward the objects was not the same for participants in each condition.Following VR sessions, there was an interaction between the groups on the main measure of clutter, that is, for the images of the bedroom. The level of clutter in the experimental group showed a tendency to decrease, as compared to a tendency to increase in the control group. This may signify that taking action in VR allowed participants in the experimental group to discard significantly more objects in their bedroom. It does not seem that action taken in the control group allowed participants to discard objects in the same room, as their scores actually increased. It should be noted, however, that for participants in the experimental group, the majority of selected pictures were of their bedroom.Following VR, there was also a decrease over time in cognitions related to the CH symptoms \u201cresponsibility,\u201d \u201cemotional,\u201d and \u201cmemory\u201d as well as for the total score. The SIR total score as well as the \u201cacquisition\u201d and \u201cdiscarding objects\u201d subscales also decreased over time, as well as the \u201cobsessions\u201d subscale of the YBOCS. Overvalued ideas also evinced a tendency to decrease over the three time points, pre-IBT, post-IBT, and post-VR. Finally, a significant interaction was observed between the groups on a measure of anxiety. The results of the experimental group increased slightly at post-IBT and decreased at post-VR, whereas anxiety in the control group consistently decreased over time. This may be explained by the fact that individuals in the experimental group had to submit pictures of their home so that their virtual environment could be created. This may have caused anxiety as many of the participants in this group reported worries about what was going to happen in the VR sessions.Finally, the comparison of the experimental group with the control group and non-concurrent comparison group suggest that the VR condition is an accessible and interesting tool that may help the participant take action at home. The results also demonstrate that IBT is a promising approach in the treatment of CH as it was possible to observe improvements in CH symptoms in the participants. It may also be possible to use VR as a preventative measure to impede the development of compulsive behavior .After receiving IBT, participants in all three groups evinced a significant improvement in their CH-related cognitions. The same can be said for the measures of obsessions and compulsions, as these scores significantly decreased as well for both groups included in the present study. No differences were observed, however, on measures of depression or inferential processes. Also, no differences were observed on the measure of clutter (CIR). These results are in line with other studies that have reported that hoarders have difficulty in taking action when it comes to their clutter. With regards to the measure of depression, the participants expressed that they would have appreciated additional sessions. The majority of them reported feeling discouraged regarding the clutter of their homes and did not see any progress in this respect. With regards to overvalued ideas, even though the scores on the OVIS did not significantly decrease, the clinical scales demonstrated a decrease of 40% in the primary doubt. This pattern of results may be attributable to the fact that the OVIS considers only one overvalued idea, whereas the clinical scales are more exhaustive, taking into account all of the overvalued ideas reported by the participant.The limitations of the present study are mainly the small sample size and the absence of a passive control group. Also, it would have been preferable to have additional time points, such as at 3- and 1-year follow-up. Following the clinical evaluations post-VR, some participants indicated they had experienced difficulties during the IBT and the VR. As such, it would have been of interest to have included qualitative measures and analyses. For example, participants reported problems, such as bankruptcy, sickness or death of a loved one, eviction, and loss of employment. These elements were also corroborated by the participants\u2019 psychologists. The participants as well as the psychologists identified these events as obstacles to progress in treatment. It is, therefore, important to consider these life events as they can have a considerable impact on the success of treatment.Other elements should also be considered for future research. Indeed, it would be interesting to compare the experimental condition to a passive control condition or a wait list. Though the results were compared to a non-concurrent control group that did not receive VR, these participants were not randomly assigned to this condition. Also, as many studies include home visits, it would be of interest to have an active control condition comparing VR to home visits. In addition, it may be that five sessions of VR is insufficient to observe significant results on CH measures. As the home environments are extremely cluttered, they require a lot of work to achieve satisfactory results.In conclusion, it seems that non-immersive VR is accessible and elicits a state of presence and immersion in participants suffering from CH. VR also elicits emotions during sorting tasks and when virtually discarding objects. Personalization of the virtual environment seems to help hoarders clean out their environment, as was the case in the bedroom in the context of this study. Only two participants dropped out of treatment, which is very little compared to the majority of studies conducted with this population. It may be that VR is less overwhelming. Finally, the participants reported that virtually sorting and discarding objects helped them to take action and experience less distress and anxiety at home. They were also generally satisfied with the IBT and VR.The present article was part of M-E St-P-D\u2019s thesis. Dr. KO was supervising the entire research.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Dear Editor,Hepatitis E virus (HEV), a member of the genus Hepevirus, is a non-enveloped virus with a positive stranded RNA genome that is approximately 7.2 kb in length . It has"}
+{"text": "Ornithodoros brasiliensis Arag\u00e3o is an endemic tick to Brazil, restricted to highlands of the state of Rio Grande do Sul[de do Sul. It is ade do Sul. To builde do Sul-5. The r"}
+{"text": "Microscale soft-robots hold great promise as safe handlers of delicate micro-objects but their wider adoption requires micro-actuators with greater efficiency and ease-of-fabrication. Here we present an elastomeric microtube-based pneumatic actuator that can be extended into a microrobotic tentacle. We establish a new, direct peeling-based technique for building long and thin, highly deformable microtubes and a semi-analytical model for their shape-engineering. Using them in combination, we amplify the microtube\u2019s pneumatically-driven bending into multi-turn inward spiraling. The resulting micro-tentacle exhibit spiraling with the final radius as small as ~185\u2009\u03bcm and grabbing force of ~0.78\u2009mN, rendering itself ideal for non-damaging manipulation of soft, fragile micro-objects. This spiraling tentacle-based grabbing modality, the direct peeling-enabled elastomeric microtube fabrication technique, and the concept of microtube shape-engineering are all unprecedented and will enrich the field of soft-robotics. Spiraling tentacles are widely utilized in nature for grabbing and squeezing objects. There have been continuous soft-robotic efforts to mimic them with pneumatic tube actuators325121431Our approach is two-stepped. In the first, we fabricate easily deformable elastomeric microtubes as the platform structure. High deformability is ensured by the thinness of the microtube itself (100\u2212125\u2009\u03bcm in inner diameter) and its tube-wall (8\u221232\u2009\u03bcm). Making such a subtle structure at a length exceeding several millimeters has been deemed unfeasible. We accomplish it with a new, direct peeling-based soft-lithographic technique. It also allows significant asymmetrization of the microtube\u2019s cross-sectional shape which leads to bending up to a single-turn. In the second step, we apply shape-engineering to the microtube to amplify the bending into multi-turn spiraling. Using a semi-analytical model, we establish a design rule which enables such a spiraling with a simple hump . The outin situ thermal solidificationPast reports testify that the biggest issue in using liquid-phase poly(dimethylsiloxane) (PDMS) for building long and thin structures, such as pillars or wires, is its tendency to beadL reaching 5\u22128\u2009mm. The main factor limiting L was the inevitable increase in the friction and wrinkling during the peeling process. Despite their high aspect-ratios  and thin walls, the microtubes did not sag or collapse, even when no air pressure was applied.The completed PDMS microtube is robust enough to be peeled directly from the template with a polymer jacket remover, a standard tool in fiber-optics . The pro38t1 and t2 of 31.8\u2009\u00b1\u20094.9 (s.d.) and 7.9\u2009\u00b1\u20091 (s.d.) \u03bcm, respectively. The coating thickness can also be made uniform by rotating the template during curing.The solidification process can also be controlled for additional tailoring of the microtube\u2019s cross-sectional shape. Slowing it down prolongs gravitational impact on the coating, resulting in an increase in the tube\u2019s cross-sectional asymmetry, as shown in As shown in We connected the microtubes directly to blunt syringe needles for pneumatic actuation. Owing to their high aspect-ratio, thin tube-wall, and inherent softness of PDMS, the microtubes bent significantly upon applying air pressure, as shown in L, di, t1, and t2 at 5600, 104, 35.6, and 7.7\u2009\u03bcm, respectively. As the characterization sample, we used the one in Regardless of the pressure or cross-sectional asymmetry, plain microtubes with no cross-sectional change along in the axial direction failed to achieve spiraling. Conventionally, such an insufficient bending has been amplified into spiraling through the use of bi-material composite structures34Instead, we enabled the spiraling motion in the PDMS microtube actuator by adding a simple hump to it as shown in x, y) of the deformed base curve can be described by an integration:s \u2208  is the natural coordinate of the beam of length L, and f is a cosine (sine) function for u\u2009=\u2009x (u\u2009=\u2009y). E is the material\u2019s Young\u2019s modulus, and I is the second moment of area. At this specific instant, it is plausible to assume that a plain microtube has a constant I along its length, and that a humped microtube has a step-wise distribution of I, as shown in I with increasing pressure would call for analyses of hyperelastic deformations and plasticity at extreme cases, which is beyond our scope. The bending moment Mo \u2261 \u03c0\u00b7r2\u00b7p\u00b7de wherer is the radius, p the current pressure, and de the distance between the microtube's neutral axis and void hole's center. y\u2009>\u20090. In light of the simple harmonic functions in x and y to 0, thereby impeding the desired spiraling.We investigated the hump\u2019s role in promoting the spiraling motion using the Euler-Bernoulli beam theory3141I as shown in I, the integration in I1 and I0 are the values of I in the hump and non-hump sections, respectively, as shown in I0\u2009<\u2009I1. By adjusting the levels of the phase-shifts in x and y, we can control re-entry point to the first quadrant. A simple criterion can be derived by assuming With the hump, we can modulate the microtube\u2019s geometry and, hence, the values of L) affects the level of bending as a function of its position. We used a microtube model with its characteristics approximately matching those of MT1. With I0 and I1 at 5.1\u2009\u00d7\u200910\u221216 and 8.6\u2009\u00d7\u200910\u221215\u2009m4, respectively, the inward spiraling can be obtained when 0.024\u2009<\u2009\u03b1\u2009<\u20090.524. We set the \u03b1 value of Hump B at an improper value of 0.55 while setting that of Hump A to the proper value of 0.21, as indicated by arrows in Hump A did achieve inward spiraling with the final y\u2009>\u20090. Hump B, on the other hand, performed even worse than the plain, un-humped microtube, resulting in y\u2009<\u20090.L, di, t1, and t2 at 5800, 104, 33, and 7.4\u2009\u03bcm, respectively, and compared its bending behaviors before and after adding a hump at an obviously improper position of 0.78\u00b7L. To experimentally confirm the prediction above, we fabricated another PDMS microtube with structural characteristics very similar to those of MT1 with L, di, t1, and t2 at 5470, 105, 34.6, and 8.2\u2009\u03bcm, respectively, and its hump installed at 0.17\u00b7L point exhibited spiraling with two full turns, achieving the final RoC of 210\u2009\u03bcm. RoC as low as 185\u2009\u03bcm has been obtained.hg to the optical fiber cantilever. The standard beam deflection theory relates the force F and the deflection \u03b4c at hg as41I\u2009=\u2009\u03c0r4/4, r the radius of the optical fiber cantilever, and E the Young\u2019s modulus of fused silica.The spiral formed by the PDMS micro-tentacle is ideal for grabbing and holding microscale objects. To estimate its grabbing force, we configured it to deflect a cantilever as shown in the inset of L, di, t1, and t2 at 5000, 107, 39.1, and 7.2\u2009\u03bcm, respectively. Its minimum spiraling diameter was 370\u2009\u03bcm and the corresponding maximum achievable deflection \u03b4c,max was 200\u2009\u03bcm. c as a function of hg at the pressure level of 9.8\u2009psi. Each represents the average of five measurements. We omitted the error bar since the standard deviations were\u2009<1% of the average values. The force F, estimated through curve-fitting, was approximately 0.78\u2009mN. We retained only the first four points in the curve-fitting since \u03b4c approached its maximum possible value and began to saturate beyond hg ~ 7.5\u2009mm.For this measurement, we used a micro-tentacle with L, di, t1, and t2 at 5000, 104, 31.5, and 6.9\u2009\u03bcm, respectively. Our first target was the egg of Mallotus villosus which deforms and bursts easily when manipulated with hard tweezers. We initially placed multiple eggs on a glass slide and then used the micro-tentacle\u2019s bending motion to separate one egg. Then we grabbed the egg by winding the micro-tentacle around it. The optical micrographs in Thanks to the softness of PDMS and the spiraling motion, the micro-tentacle can function as a soft-robotic grabber of micro-objects that can easily be deformed or damaged under hard material-based grippers. As practical examples, we attempted to grab biological objects. We utilized a micro-tentacle with et al. exhibited 10\u221250\u2009mN of forceet al. and Wakimoto et al. also exhibited force levels of 3\u2009mN11 and 2.2\u2009mN3, respectively. The force-volume ratio of our micro-tentacle is 8.4\u2009mN/mm3 which is higher or comparable to those listed above. It indicates that our micro-tentacle produced force very efficiently with a simple and small structure. In fact, our micro-tentacle can be regarded as the bridge between the conventional, larger micro-actuators producing mN-level force and biological micro-organisms such as C. elegans capable of producing 62\u2009\u03bcN of forceThe cantilever deflection measurement revealed that the spiraling micro-tentacle\u2019s grabbing force is in the vicinity of 0.78\u2009mN at 9.8\u2009psi pneumatic pressure. In absolute sense, this force is weaker than those of existing elastomer-based pneumatic micro-actuators. For example, the PDMS/polyimide-based pneumatic balloon actuator by Konish in situ thermal solidification of PDMS dip-coated around a cylindrical template and direct peeling of the cured structure. Its capability to asymmetrize the microtube\u2019s cross-sectional shape enabled the microtube to bend up to a single turn. But we went further to amplify the bending into a life-like, multi-turn spiraling motion. To that end, we established a semi-analytical model to shape-engineer the microtube and turn it into a micro-tentacle. The optimized micro-tentacle exhibited a spiraling motion with two full turns and ~200\u2009\u03bcm inner radius, which is ideal for grabbing micro-objects.To conclude, we have demonstrated elastomer-based soft-robotic micro-tentacles capable of winding around and holding microscale objects. To realize the thin, highly deformable microtubes, we established a new fabrication technique based on in vivo biomedical manipulation or surgery714Experimental confirmation of the feasibility of such a winding motion in elastomer-based microscale pneumatic actuators is another of this work\u2019s contribution. The spiraling capability will render the micro-tentacle particularly useful for manipulating fragile or easily deformable objects since it will allow the micro-tentacle to grab and hold a delicate object either by winding around it conformally or by forming a ring that can scoop up the object without squeezing. Thanks to the use of PDMS for its construction and also to its microorganism-level force, our micro-tentacle is fully compliance-matched to biological structuresAs depicted in For grabbing force measurement, we utilized a 15\u2009mm-long section of 125\u2009\u03bcm-diameter communication-grade fused silica optical fiber  as the cantilever. As the support for applying the grabbing force, we also installed a 155\u2009\u03bcm-diameter stainless steel wire  in parallel with the fiber. Then we measured the deflection of the fiber under an optical microscope  as the micro-tentacle wound around both the metal wire and optical fiber.How to cite this article: Paek, J. et al. Microrobotic tentacles with spiral bending capability based on shape-engineered elastomeric microtubes. Sci. Rep.5, 10768; doi: 10.1038/srep10768 (2015)."}
+{"text": "Z-numbers based formalization of information (Z-information) represents a natural language (NL) based value of a variable of interest in line with the related NL based reliability. What is important is that Z-information not only is the most general representation of real-world imperfect information but also has the highest descriptive power from human perception point of view as compared to fuzzy number. In this study, we present an approach to decision making under Z-information based on direct computation over Z-numbers. This approach utilizes expected utility paradigm and is applied to a benchmark decision problem in the field of economics.Real-world decision relevant information is often partially reliable. The reasons are partial reliability of the source of information, misperceptions, psychological biases, incompetence, and so forth.  Decision making is one of the attractive research areas in the last decades. The complexity and uncertainty are persistent phenomenon in the real world, and the fuzzy set \u20133 is widZ-number is a sufficient formalization of real-world information that should roughly be considered in light of its reliability. The critical issue is that the reliability of information is not considered properly. Zadeh has proposed a new notion Z-number which is more appropriate to describe the uncertainty. Z-number takes both restraint and reliability. In comparison with the classical fuzzy number, Z-number has more ability to describe the real information of human   Z-numberdered in . Z-numbeested in , 9. In  is a discrete fuzzy number if its support is finite; that is, there exist x1,\u2026, xn \u2208 \u211b with x1 < x2 < \u22ef<xn, such that supp\u2061(A) = {x1,\u2026, xn} and there exist natural numbers s, t with 1 \u2264 s \u2264 t \u2264 n satisfying the following conditions:(1)\u03bcA(xi) = 1 for any natural number i with s \u2264 i \u2264 t;(2)\u03bcA(xi) \u2264 \u03bcA(xj) for any natural numbers i, j with 1 \u2264 i \u2264 j \u2264 s;(3)\u03bcA(xi) \u2265 \u03bcA(xj) for any natural numbers i, j with t \u2264 i \u2264 j \u2264 n.A fuzzy subset A be a discrete fuzzy number. A probability measure of A denoted by P(A) is defined asLet ested in \u201314, 16, \u03b1-cut is given as  as a mental factor which influences a choice of a preferred Z-number. The degree of pessimism is submitted by a human observer who wishes to compare the considered Z-numbers but does not completely rely on the results obtained by the above mentioned fuzzy optimality approach. In this viewpoint, given do(Zj) \u2264 do(Zi), we define for two Z-numbers Z1 and Z2 [The suggested approach may be considered as basis of a human-oriented ranking of  and Z2 (19)rZi,Zi = Zj otherwise [Thentherwise .\u03b2 is submitted by a human being and adjusts ranking of Z-numbers to reflect human attitude to the computed do. This attitude may result from the various importance of Z-numbers for a human being and other issues [The degree of pessimism r issues .Real-world decision relevant information is imprecise, uncertain, and partially reliable. Therefore, results of decision analysis based on such information are also partially reliable. This fact should prevent decision makers relying much on decision analysis results even when a very careful mathematical modeling was used.Z-information may help achieve a more realistic decision analysis technique and, at the same time, use a simple form of the utility function.A well-known approach to decision making under uncertainty is the use of expected utility function . However\ud835\udcae = {S1, S2,\u2026, Sn} be a set of states of nature and let \ud835\udcb3 = {X1,\u2026, Xl}, k = 1,\u2026, l, be a set of Z-valued outcomes. Denote by \u2131\ud835\udcae a \u03c3-algebra of subsets of \ud835\udcae. Then consider \ud835\udc9c = {f \u2208 \ud835\udc9c\u2223f : \ud835\udcae \u2192 \ud835\udcb3}, the set of Z-valued actions, as the set of all \u2131\ud835\udcae-measurable Z-valued functions from \ud835\udcae to \ud835\udcb335,32.Let ZPl of the states of nature is represented by Z-valued probabilities Si:Linguistic information on likelihood \ud835\udcb3 are Z-valued outcomes; elements of \ud835\udc9c are Z-valued acts; elements of \ud835\udcae are states of nature; elements of \u2131\ud835\udcae are events.In the suggested framework, we extend a classical neo-Bayesian nomenclature as follows: elements of Z-information can be formalized as a 4-tuple . The problem of decision making with Z-valued information on the basis of EU consists in determination of an optimal act f* \u2208 \ud835\udc9c: find f* \u2208 \ud835\udc9c for which ZU(f*) \u2265 ZU(f), \u2200f \u2208 \ud835\udc9c.A framework of decision making with ZU(f) is a Z-valued expected utility defined asHere Z-numbers, without converting them to fuzzy and/or crisp numbers. This allows preserving available imprecise and partially reliable information and using it in the final comparison of alternatives.The suggested approach is based on direct computations with In this application section, we intend a problem of decision making in the field of economics. The analyzed data are obtained from Techware Incorporated in . Two newZ-numbers. The set of alternatives isf1 denotes introducing product 1, f2 denotes introducing product 2, and f3 denotes introducing both products (1 and 2).Let us proceed to formal description of the considered decision problem. The partially reliable linguistic decision relevant information in the considered problem will be described by S1 denotes strong national economy, S2 denotes fair national economy, and S3 denotes weak national economy. The probabilities of states of nature are ZP(S1) = , ZP(S2) = .The set of states of nature isThe set of outcomes isThe partially reliable linguistic information for the probabilities of states of nature and the utilities of each alternative taken at different states of nature is shown in Z-number based representation is shown in The corresponding decision matrix with Z-numbers for probabilities and utilities from The membership functions of the first and the second components of Z-number based probability ZP(S3) = Z43 =  on the basis of ZP(S1) = Z41 and ZP(S2) = Z42. As ZP(S3) is completely determined by ZP(S1) and ZP(S2), its reliability B43 will be the same as reliabilities B41 and B42. Therefore, to complete determination of Z43 =  it is needed to compute A43 on the basis of A41 and A42. For computation of A43 we used the approach suggested in [Z43 =  is shown in Let us proceed to solving the problem. First it is needed to determine unknown ested in . The detZ-number based data we compute the expected utility for each of the alternatives f1, f2, f3 as follows:Z-numbers described in Based on the previous The results of computation of expected utilities for all the alternatives are shown in Figures Z-number valued utilities is needed. For comparison we will use the approach suggested in Now determining the best alternative by comparing the computed \u03b2 = 0.3.As one can see, the second alternative is not Pareto optimal. Now it is needed to compare the first and the third alternatives. Suppose that the pessimism degree in comparison of these alternatives is Then we havef1.Therefore, the best action is Z-numbers opens a door for applications in many areas, especially in decision making theory. The goal of the present study is to develop an approach for decision making under Z-information described in NL. The suggested approach utilizes the paradigm expected utility based on a direct computation of Z-numbers. The advantage of the approach is its ability to account for imprecision and partial reliability of information and relative simplicity of computations. The approach is applied to solve a benchmark decision problem in the field of economics. The obtained results show validity of the approach.The concept of"}
+{"text": "A serial femtosecond crystallography based method has been proposed, which enables simultaneous X-ray phase identification and structure solution for multiphase polycrystalline samples. Test results from simulating calculations are encouraging. CrystFEL. Identification according to the primitive unit-cell volume determined from individual snapshots was able to separate the whole set of snapshots into two subsets, which correspond to the two zeolites in the sample. Monte Carlo integration in CrystFEL was then applied to them separately. This led to two sets of three-dimensional single-crystal diffraction intensities, based on which crystal structures of the two zeolites were solved easily by direct methods implemented in the program SHELXD.Serial femtosecond crystallography (SFX) is capable of collecting three-dimensional single-crystal diffraction data using polycrystalline samples. This may dramatically enhance the power of X-ray powder diffraction. In this paper a test has been performed using simulated diffraction patterns. The test sample is a mixture of two zeolites with crystal grain sizes from 100 to 300\u2005nm. X-ray diffraction snapshots by SFX were simulated and processed using the program suite  For those snapshots that passed through the indexing, their primitive unit-cell volume was calculated. Then numbers of snapshots were plotted against the unit-cell volumes as shown in Fig. 23. In addition to these two peaks, there are a number of much smaller peaks with their unit-cell volumes equal to N times or 1/N (N is a simple integer) of either 3800 or 5500\u2005\u00c53. Peaks related to the volume of 3800\u2005\u00c53 are coloured in red, while those related to the volume of 5500\u2005\u00c53 are in blue. As seen, the red and blue peaks form the majority of peaks in Fig. 1indexamajig in CrystFEL near the unit-cell volume at 3800 and 5500\u2005\u00c53 are as follows:In this section, no preliminary knowledge concerning either chemical composition or crystal structure of the sample was assumed. The critical step here is to find out how many different crystalline phases are contained in the sample. First, indexing of each diffraction snapshot was tried by the program a = 13.67, b = 14.25, c = 22.37\u2005\u00c5, \u03b1 = 89.90, \u03b2 = 89.89, \u03b3 = 61.81\u00b0.Red phase: a = 17.29, b = 17.33, c = 19.49\u2005\u00c5, \u03b1 = 88.02, \u03b2 = 88.02, \u03b3 = 70.85\u00b0.Blue phase: et al., 2010CrystFEL was applied to these two data sets separately and produced two sets of three-dimensional diffraction intensities of the red and the blue phases. Finally the program XPREP  was applied to the two sets of three-dimensional diffraction intensities separately. The space groups were thus determined and the unit-cell parameters were converted according to crystallographic conventions. The results are as follows:The whole set of test data was re-indexed by specifying the primitive unit-cell parameters of the red phase. 164\u2005571 snapshots among the total 1\u2005000\u2005000 passed through the indexing. They were then separated to form the diffraction data set of the red phase. Similarly a set of 714\u2005025 snapshots was separated to form the diffraction data set of the blue phase. Monte Carlo integration  are shown in Figs. 3From the previous section we now have two sets of three-dimensional diffraction intensities and the corresponding space group and unit-cell parameters. Based on these, the crystal structure of the red and the blue phases can be easily solved by standard single-crystal methods. The only additional information we need is the chemical composition of the two phases  technique based on a third-generation synchrotron radiation source can do the same, since Stellato  al. 2014 and Both al. 2014 showed t"}
+{"text": "In order to acquire radiation-tolerant characteristics in integrated circuits, a dummy gate-assisted n-type metal oxide semiconductor field effect transistor (DGA n-MOSFET) layout was adopted. The DGA n-MOSFET has a different channel shape compared with the standard n-MOSFET. The standard n-MOSFET has a rectangular channel shape, whereas the DGA n-MOSFET has an extended rectangular shape at the edge of the source and drain, which affects its aspect ratio. In order to increase its practical use, a new aspect ratio model is proposed for the DGA n-MOSFET and this model is evaluated through three-dimensional simulations and measurements of the fabricated devices. The proposed aspect ratio model for the DGA n-MOSFET exhibits good agreement with the simulation and measurement results. According to a recent report , the dumW and length L. Furthermore, this simple geometry enables easy calculation of its aspect ratio. The current density of the standard n-MOSFET is constant along its length [W by L. When the integrated circuit is designed using standard MOSFETs, the circuit characteristics are determined using adjustments of each aspect ratio of W/L in the MOSFETs. Circuit designers can adjust only the aspect ratios in order to obtain specified circuit characteristics because the other parameters are determined in the device fabrication process. Therefore, the aspect ratio of the MOSFET is the most important parameter in the circuit design.The standard n-MOSFET, which is shown in s length . TherefoThe channel shape of the DGA n-MOSFET is presented in According to previous reports , 4, the For the practical use of the DGA n-MOSFET in circuit design, this study proposes a simple aspect ratio model by adopting several reasonable approximations. It is expected that the proposed simple aspect ratio model simplifies the estimation of the aspect ratio of the DGA n-MOSFET. The proposed aspect ratio model is evaluated using a three-dimensional simulation with the SILVACO ATLAS simulation tool. Furthermore, the proposed aspect ratio model is also evaluated through device fabrication and its measurement.LT, WT, and\u2009\u2009\u03b8 are the channel length, half of the source side channel width, and corner angle, respectively [\u03b8 was specified in order to determine whether to place an additional rectangle between the two trapezoid transistors. Thus, it was determined that if (LD \u00b7 tan\u2061\u03b8)/2 > D, a rectangle is added between the two trapezoid transistors. LD, D, and \u03b8 are the channel length, extended width, and corner angle, respectively. This approximation was developed based on two assumptions. The first assumption is that the current density at the corner regions of the DGA n-MOSFET channel can be negligible. It is intuitively known that the electric field will not reach the corner regions; consequently, the series association of the two trapezoidal structures substitutes the DGA n-MOSFET channel region. The second assumption is that the corner angle \u03b8 of the substituted trapezoid structure will be constant regardless of the length LD, extended width D, and width WD, because the spreading angle of the current at the edge of the source is expected to be constant. The behavior of the current spreading is determined by the contact shape between the electrodes and channel region. In the DGA n-MOSFET, the source and drain edges are always positioned in the middle of the upper and lower sides of the channel region.The channel region of the DGA n-MOSFET is approximated using the series association of two trapezoidal transistors. Moreover, the value of the corner angle WD, extended width D, and corner angle \u03b8 have the same values; however, the length LD has different values and it increases in order of the figure number. LD \u00b7 tan\u2061\u03b8)/2 < D.The final approximated channel shapes are presented in LD, WD, and\u2009\u2009\u03b8 are the channel length, channel width, and corner angle, respectively.In this case, the series association of the two trapezoidal transistors replaces the channel area of the DGA n-MOSFET. Moreover, a space exists between the bottom vertexes of the upper trapezoid and both left and right sides of the original channel area. The effective aspect ratio for the approximated structure shown in LD \u00b7 tan\u2061\u03b8)/2 = D. In this case, the series association of the two trapezoidal transistors also replaces the channel area of the DGA n-MOSFET. However, the bottom vertexes of the upper trapezoid encounter both left and right sides of the original channel area. The effective aspect ratio for the approximated structure shown in LD( = 2Lcri), WD, and\u2009\u2009\u03b8 are the channel length, channel width, and corner angle, respectively.LD \u00b7 tan\u2061\u03b8)/2 > D. In this case, the series association of the two trapezoidal transistors and one rectangle replaces the channel area of the DGA n-MOSFET. The rectangle is added between the two trapezoidal structures. The effective aspect ratio for the approximated structure shown in LD, WD, D, and\u2009\u2009\u03b8 are the channel length, channel width, extended width, and corner angle, respectively. Moreover, A and B indicate the aspect ratio formula for the trapezoidal structure and rectangle, respectively, as shown in \u03bcm process technology using the SILVACO ATLAS simulation tool. For both the standard and DGA n-MOSFETs, the gate oxide thickness, body thickness, and body doping density were 7\u2009nm, 6\u2009\u03bcm, and 8e16\u2009#/cm3, respectively. For the DGA n-MOSFET, the side p+ doping density was 1e19\u2009#/cm3. Moreover, the isolation structure was adapted using local oxidation of silicon (LOCOS). Five different widths  and three different lengths , which resulted in fifteen different structures, were simulated. For the DGA n-MOSFET, the extended width D was fixed to 2\u2009\u03bcm.The standard n-MOSFET structure and DGA n-MOSFET structure were designed to be compatible with the commercial 0.35\u2009WD and extended width D were 2\u2009\u03bcm. The length LD increased in order of the figure number as 0.5\u2009\u03bcm, 1\u2009\u03bcm, and 3\u2009\u03bcm. In order to evaluate the proposed effective aspect ratio model for the DGA n-MOSFET, the current densities are presented using rainbow colors in a linear scale relative to each maximum current density. From \u03b8 was determined using comparisons of the proposed effective aspect ratio model with the simulation results. When the corner angle\u2009\u2009\u03b8 was 0.977, the proposed effective aspect ratio model had the best agreement with the simulation results. The approximated channel area with a corner angle\u2009\u2009\u03b8 of 0.977 is indicated in The corner angle\u2009\u2009Wdrawn,\u2009\u2009Weff,\u2009\u2009Ldrawn,\u2009\u2009Leff, \u03bcn, Cox, and\u2009\u2009\u03bb are the drawn width, effective width, drawn length, effective length, electron mobility, gate oxide capacitance per unit area, and channel length modulation parameter, respectively. Moreover, the superscripts \u201cDGA\u201d and \u201cSTD\u201d refer to the DGA n-MOSFET and standard n-MOSFET, respectively. When calculating the effective aspect ratios, it was assumed that the DGA n-MOSFET and standard n-MOSFET have the same electrical parameters for the \u03bcnCox and channel length modulation parameter\u2009\u2009\u03bb. The transconductance gm was adopted at a Vds of 0.05\u2009V in order to minimize the effects induced by the channel length modulation parameter\u2009\u2009\u03bb difference between the DGA n-MOSFET and standard n-MOSFET. Furthermore, the transconductance gm was used at a Vgs of 1.5\u2009V in order to use a saturated gm.In the simulation, the effective aspect ratios for the DGA n-MOSFETs were extracted using the following equations: Weff and effective length Leff, the \u0394W and \u0394L were extracted from the simulation results of the standard n-MOSFETs. From the simulation results, the extracted \u0394W and \u0394L were 0.05\u2009\u03bcm and 0.005\u2009\u03bcm, respectively.Moreover, in order to acquire the effective width \u03bcm technology with a gate oxide thickness of 7.3\u2009nm and LOCOS for the isolation of the active areas. Three different widths  and three different lengths , which resulted in a total of nine structures, were fabricated. For the DGA n-MOSFET, the extended side channel width D was fixed to 2\u2009\u03bcm.The standard n-MOSFET and DGA n-MOSFET were fabricated using the MagnaChip and Hynix 0.35\u2009Vg-Id curves were measured and were then differentiated by Vg in order to acquire the transconductance gm curve. When measuring the Vg-Id curves, the Vds was set to 0.05\u2009V. Moreover, all transconductance values gm used to extract the aspect ratios were chosen at a Vgs of 1.5\u2009V.The fabricated devices were measured using an Agilent 4156A semiconductor parameter analyzer. The W and \u0394L were 0.15\u2009\u03bcm and 0.05\u2009\u03bcm, respectively.As in the simulation case, in order to extract the effective aspect ratios for the DGA n-MOSFETs,  were alsLD \u00b7 tan\u2061\u03b8)/2 > D, the rectangular structure was added between the two trapezoidal structures.For practical use of the radiation-tolerant DGA n-MOSFET in designing a radiation-tolerant integrated circuit, an effective aspect ratio model of the DGA n-MOSFET was proposed. In the proposed effective aspect ratio model, the channel area of the DGA n-MOSFET was approximated using a trapezoidal structure and a rectangular structure. When (The proposed effective aspect ratio model was evaluated using a three-dimensional simulation and through measurement of the fabricated devices. Compared with the simulation results, the proposed effective aspect ratio model had an error range between \u22120.4% and 1.4%. Moreover, compared with the measurement results, the proposed effective aspect ratio model had an error range between \u22123% and 5.4%. Therefore, it can be concluded that the proposed effective aspect ratio model is well matched with the simulation and measurement results."}
+{"text": "Multi-Agent Reinforcement Learning (MARL) algorithms face two main difficulties: the curse of dimensionality, and environment non-stationarity due to the independent learning processes carried out by the agents concurrently. In this paper we formalize and prove the convergence of a Distributed Round Robin Q-learning (D-RR-QL) algorithm for cooperative systems. The computational complexity of this algorithm increases linearly with the number of agents. Moreover, it eliminates environment non sta tionarity by carrying a round-robin scheduling of the action selection and execution. That this learning scheme allows the implementation of Modular State-Action Vetoes (MSAV) in cooperative multi-agent systems, which speeds up learning convergence in over-constrained systems by vetoing state-action pairs which lead to undesired termination states (UTS) in the relevant state-action subspace. Each agent\u2019s local state-action value function learning is an independent process, including the MSAV policies. Coordination of locally optimal policies to obtain the global optimal joint policy is achieved by a greedy selection procedure using message passing. We show that D-RR-QL improves over state-of-the-art approaches, such as Distributed Q-Learning, Team Q-Learning and Coordinated Reinforcement Learning in a paradigmatic Linked Multi-Component Robotic System (L-MCRS) control problem: the hose transportation task. L-MCRS are over-constrained systems with many UTS induced by the interaction of the passive linking element and the active mobile robots. The transportation problem The transportation of a hose by a team of robots is a paradigmatic instance of the tasks that can be performed with Multi-Component Robotic Systems (MCRS)  is a probabilistic transition function P giving the probability of observing state s\u2032 after executing action a in state s, and R:S \u2192 \u211d is the expected immediate reward after reaching state s. The set of terminal states \ud835\udce3 is defined as the set of states having null outgoing transition probabilities, i.e. \ud835\udce3 = {sS\u2223\u2200s\u2032 \u2260 s, a;P = 0}. The action selection policy is usually modeled as the probability distribution \u03c0:S \u00d7 A \u2192  of taking action a in state s.In RL algorithms, the interaction between an agent and its environment is modeled as a Markov Decision Process (MDPs), defined as a tuple < valueV\u03c0(s) of state s is the expected accumulated reward obtained from that state following policy \u03c0. It can be expressed asE\u03c0 denotes the expected return from time step t following policy \u03c0 thereafter, ri represents the reward received at time i, and \u03b3 \u2208  is a discount-rate parameter decreasing the weight of the reward at each time-step. Bellman equation forV\u03c0  is the probabilistic state transition function P that defines the probability of observing state s\u2032 after all agents execute the joint action a \u2208 A in state s, and R:S \u00d7 A \u00d7 S \u2192 \u211dN are the expected rewards received by agents after transition .When the system is composed of several interacting autonomous agents, the Multi-Agent Reinforcement Learning (MARL) problem consists of the search for the joint optimal policies maximizing the reward for each and all agents . In the an = T \u2208 A, ai, k \u2208 Ai. As a consequence, the rewards also depend on the collective action. The local policy of each agent \u03c0i:S \u00d7 Ai \u2192  gives the probability of the ith agent executing action a in state s. The local policies are composed into a global joint policy\u03c0 = {\u03c01, \u2026, \u03c0N}.In the multi-agent case, state transitions are the result of the concurrent joint action cooperative when the local rewards are identical for all agents R1 = R2 = \u2026 = RN,The SG is fully ai \u2208 Ai and i = 1, \u2026, N. When there are more than one optimal action choice, the optimal policy is achieved by a consensus protocol.If a centralized learner exists, the task could be mapped to an MDP, whose centralized Q-function could be expressed asTeam Q-Learning (Team-QL) , i = 1, \u2026, N is the state transition function Pt that defines the probability of observing s\u2032 after agent \u03b4(t) executes, at time t, action a from its local action repertoire A\u03b4(t).R:S \u00d7 \u222aAi \u00d7 S \u2192 \u211d is the shared scalar reward signal Rt received by all agents after executing a local a action from A\u03b4(t).\u03b4:\u211d \u2192 {1, \u2026, N} is the turn function implementing the Round-Robin cycle of agent calling for action execution. \u03b4(t) gives the index of the agent allowed to execute an action at time t (times are relative to the start of the episode). This function is cyclic, \u2200t \u2208 \u2115;\u03b4(t) = \u03b4(t + N), therefore, agents are always visired in the same order, so that without loss of generality, we can denote i + 1 the agent that will be visited after i.The state value function V\u03c0 gives the value of being in state s for agent i \u2208 {1, \u2026, N} under joint policy \u03c0, and it is the expected accumulated discounted rewards following the joint policy \u03c0. The Bellman equation for a joint policy \u03c0 in a C-RR-SG isE\u03c0 represents the expectation from time t onwards, following joint policy \u03c0. The optimal state value V* is given by:\u03c0 can be expressed asi isThe straightforward approach to learn the optimal policy for a C-RR-SG is applying the single-agent Q-Learning update:Proposition 1Q* if each agent fulfills the conditions for convergence of the single agent Q-learningA centralized single-agent Q-Learning training of a C-RR-SG by the rule of .Proof. If we are able to map the C-RR-SG into an MDP, then the proof of the proposition follows from the convergence of single agent Q-learning. The map is as follows: The MDP state space S is the same of the C-RR-SG, since it is defined by a set of global variables visible by all agents. The MDP set of actions is the union of the local sets of actions P = P, s\u2032), that is, actions are sequenced according to the turn function. The MDP reward function is built by R(s\u2032) = R, s\u2032), that is, we record the reward at the arriving state. The C-RR-SG turn function removes the uncertainty and concurrency about the joint agent actions, therefore the MDP policy can be stated as \u03c0(st) = \u03c0\u03b4(t)(st), that is, we apply at each time the local policy of the agent selected by the turn function. The MDP Q-table is built by collapsing all the agent Q-tables into a monolithic one by applying the turn function, i.e. Qt = Q). Single-agent Q-Learning converges to optimal Q* values under two conditions . Null action \u2205 is defined as the action that does not perform any state transition: \u2200s;P = 1.where joint-action discounted rewards of a joint-action a = , ai \u2208 Ai, are approximated by the sequential execution of agents\u2019 actions following RR scheduling \u03b4:P \u2243 P, a\u03b4(2)\u2026a\u03b4(N), s\u2032)R \u2243 R, a\u03b4(2)\u2026a\u03b4(N), s\u2032),The transition probabilities and P, a\u03b4(2)\u2026a\u03b4(N), s\u2032) and R, a\u03b4(2)\u2026a\u03b4(N), s\u2032) denote the probability of reaching state s\u2032 after executing actions specified in a in the sequence established by \u03b4, and the expected reward of this transition, respectively. Under this assumption, Q-values for joint-actions can be approximated by composition of the transition and reward functions of local actions. The state-action value for composed joint-actions can be defined asa = [a1a2\u2026aN], ai \u2208 A\u03b4(i). Note that rewards inside a joint-action are weighted as in the C-RR-SG.where Greedy selection of optimal joint policy The combinatorial optimization problem of chosing the best ordering of the local actions has been tackled as a greedy variable selection process  with is the greedy solution to the following minimization problem:Generalizing this process, agent For completeness, terminal states must be taken care of, because we are composing cycles of actions. If a terminal state is reached, there will not exist transition probability information from this state onwards. We can address this potential implementation issue by leaving unaltered the entries in the incoming messages for which no transition probability is available, so that the remaining agents will perform no action at all.Proposition 3The action selection policy defined by Eq (8).Proof. The transition and reward functions are approximated by \u03c0D(s) \u2243 \u03c0*(s).T\u222aG,Ae,P,R >.This approximation has been tested experimentally in environments with delayed rewards, with positive results. Unlike the technique presented in , where tN time-steps to perform N local actions instead of a single joint-action, and the execution time will grow linearly to the number of agents. Nevertheless, this is neglectable in the case of overconstrained environments, where learning in an effective manner Ae(s) is critical.An additional advantage of D-RR-QL is that it allows us to use MSAV in a multi-agent environments. Since we assume that a joint-action is approximately the same as the equivalent sequence of local actions, agents can veto actions on their local action space. Agents take actions one by one during the cycle of execution and thus have no interference from the rest of agents. Of course, this requires taking Modular State-Action Vetoes). Let the state be defined i-th Veto-Module, and let the joint-action space be defined A = Aj \u00d7 A\u2212, where Aj is j-th agent\u2019s local action space, and A\u2212 = A1 \u00d7 Aj\u22121 \u00d7 Aj + 1 \u00d7 \u2026 \u00d7 AN. Whenever an agent vetoes a state-action pair in its own state-action subspace, it is effectively vetoing \u2223SX \u00d7 A\u2212 \u2223 state-action pairs in the joint state-action space. The multi-agent Safe-MSAV architecture can be expected to avoid UTS much faster than any other exploration strategy operating on the complete state space S.The speed boost introduced by the use of MSAV in such multi-agent environments is even bigger than in the single-agent case  and the environment is reset to the initial setting  for the first robot).The relative positions of the Self-position in absolute coordinates. Each robot perceives its own absolute position.Four flag variables indicating whether there is an obstacle  in each of the four possible directions a robot can move.Benchmark algorithms  only use robot relative positions because the remaining state variables are a linear function of them and these algorithms cannot benefit from the additional information provided by the extended set of variables. For instance, it is of no use to include the obstacle flag variables because they are a function of the relative positions of the robots and thus, can only take one value for any given set of relative positions. In order to best learn how to avoid breaking a physical constraint corresponding to an UTS, we used three Veto-modules within each agent\u2019s MSAV policiy, each of which in charge of a specific physical constraint:Overstretching the hose. This module receives a negative reward every time a hose segment is overstretched, and its local state space encompasses the relative positions of the robots preceding and following the robot which executed the action that led to over-stretching its hose segment.Collisions. Every time a robot takes an action that makes it collide with any other, this module receives a negative reward. The local state space is composed by the obstacle flag variables.Simulation bounds. This last module uses only its robot\u2019s absolute position and receives a negative reward every time a robot gets out of the simulation grid.Each of the four generated negative rewards was fed to a specific module learning the veto of specific undesired state-actions using the value of the relevant state variables [Linked Multi-Component Robotic Systems (L-MCRS) are over-constrained systems which can benefit from the use of D-RR-QL with MSAV. The hose transportation task is a paradigmatic application of L-MCRS: A set of n robots . This si setting . The sysariables .ne. D-RR-QL with MSAV was run using the Safe Soft-Max policy \u03f5 \u2212 greedy policies but the experiments yielded slightly worse results and thus, will not be reported here. Initially, the temperature parameter was set \u03c4 = 10 and decreased at the end of each episode with \u25b3\u03c4 = \u221210/ne. Starting from episode number 500, the learnt policy was evaluated using greedy action selection each 500 episodes. This is the reason why data plots start from episode 500 instead of episode 0. Each experiment was run 3 times and the results were averaged. The performance was measured using two different criteria: (a) the accumulated discounted rewards, which is the typical performance measurement in the RL field, and (b) the number of cells reached with the tip of the hose, which allows us to intuitively assess how effective the exploration of the state-space is.Because the amount of episodes and the degree of exploration is key to this particular kind of tasks, experiments were run with different number of episodes http://www.ehu.es/ccwintco/index.php?title=D-RR-QL.We implemented ourselves these experiments in C/C++. The source code used in our experiments and can be accesed publicly at: ne = {104,2 \u22c5 104}. Figs even reaching the goal cell a single time.In this first experiment, we tested two different values of Figs ne = 5 \u22c5 105 and ne = 106). We only report the number of reached cells with the tip of the hose, because the accumulated discounted rewards are similar to those obtained in the previous experiment, and offer no farther information. Both Soft-Max and \u03f5 \u2212 greedy policies were tested and, in this case, slightly better results were obtained by using \u03f5 \u2212 greedy. Initially, \u03f5 = 1 and every episode it was decreased with \u25b3\u03f5 = \u22121/ne. This is paradoxical considering the better results obtained by Soft-Max policies in the previous experiment. Our educated guess is that this is due to using the same decay schedule for the two exploration parameters \u03f5 and \u03c4. While they have a similar function, \u03f5 is the probability of exploring each time-step and \u03c4 shapes the probability distribution of the action selection algorithm. Moreover, as the Soft-Max algorithm depends on the magnitude on the actual estimations of the value function, the efficiency of the exploration algorithm needs not improve linearly to the number of episodes allowed to the agents.In order to get a clearer idea of how far the benchmark algorithms are from the goal of learning a greedy policy that reaches the goal position, we ran a second set of experiments where agents were allowed much more time for exploration of the environment  policies which improve performance in over-constrained environments. First, we have presented agent interaction model as a Cooperative Round Robin Stochastic Game (C-RR-SG), in which agents select and take actions following some predefined order. A communication-free distributed implementation called Distributed Round Robin Q-learning (D-RR-QL) has been proposed, providing a proof of its convergence to the optimal policy on a C-RR-SG. We have also presented a message-based procedure to obtain the optimal policy for the original cooperative stochastic game (C-SG) from the local policies learned by D-RR-QL. We give a consensus-based implementation for the decentralized determination of RR turns that may allow fully distributed implementation of the D-RR-QL.O(1) messages each step if communications are used, 0 messages otherwise) and to obtain the global policy deciding a joint-action (each action requires O(N) messages) are minimal when compared to coordinated multi-agent approaches such as Coordinated-QL. As a line of future work, we need to study the equivalence between C-SG and C-RR-SG to determine the degree of approximation that can be obtained when there is no C-RR-SG equivalent to a C-SG. We also plan to investigate more general ways to learn how to avoid reaching undesirable terminal states. On the other hand, the degree of abstraction used in our experiments limits the applicability to real robot control problems. This approach can be directly applied in real environment as long as low-level controllers and sensors provide this kind of abstract actions and states, but the coarseness of the state-action space representation limits the optimality of the learned policies. Therefore, we plan to use continuous state-action spaces in our future research.Computational experiments show that D-RR-QL using MSAV policies can provide a valid joint-action policy approximating the optimal policy faster than D-QL, Team-QL, and Coordinated-RL in over-constrained systems. Furthermore, the D-RR-QL convergence is not limited to deterministic MDPs, it can also cope with stochastic environments. Communication requirements to learn local Q-values ("}
+{"text": "On top of the q-group index we introduce PEANUT, a highly parallel GPU-based read mapper. PEANUT provides the possibility to output both the best hits or all hits of a read. Our benchmarks show that PEANUT outperforms other state-of-the-art read mappers in terms of speed while maintaining or slightly increasing precision, recall and sensitivity.We present the  A read mapping algorithm has to be error tolerant because of mutations and sequencing errors. The optimal solution to this problem is to calculate alignments of each read against the reference. Since this would incur an infeasible running time , various filtering methods and approximations have been developed. These can be roughly classified into methods based on backward search using the Burrows\u2013Wheeler transform  data analysis projects, e.g., for variant calling or gene expression analysis, is mapping the obtained DNA reads to a known reference . The orm BWT; , e.g., Borm BWT;  or Bowtiorm BWT; , and metRazerS 3 . Both teAmong the best alignments of a read, it is sometimes not obvious which one represents the true origin of the read. In the following, the candidate origins of a read reported by a read mapper are called hits. q-gram index on a GPU is not a common choice because of its large size. Therefore, to the best of our knowledge, q-gram index based mappers so far only use the GPU for calculating the alignments and keep the index on the CPU, e.g., Saruman  for read mapping has become popular and GPU-based BWT-read-mappers appeared, e.g., SOAP3 , SOAP3-d Saruman  and Next Saruman .q-group index, a novel data structure for read mapping which is a variant of the classical q-gram index with a particularly small memory footprint. The q-group index comes with efficient parallel algorithms for building and querying, targeted towards modern GPUs. To the best of our knowledge, the q-group index is the first feasible implementation of q-gram index functionality on the GPU. On top of the q-group index we present PEANUT , a GPU-based massively parallel read mapper. PEANUT provides both an all-mapping and a best-mapping mode and is the first GPU-based all-mapper. With both a recent and a four years old NVIDIA\u2122 Geforce GPU, we show that PEANUT outperforms other state of the art best-mappers and all-mappers. For all-mapping, PEANUT is 4\u201310 times faster. PEANUT shows a slightly higher precision and recall than other best-mappers and an improved sensitivity compared to other all-mappers at default parameters.Here, we present the q-group index to maximize parallel GPU usage (\u201cDesigning for efficient GPU usage\u201d). Then, we describe the q-group index data structure (\u201cThe q-group index\u201d) and present the PEANUT approach of read mapping with the q-group index . The \u201cResults\u201d section shows benchmark results on speed, precision, recall and sensitivity of PEANUT. A brief discussion concludes the paper.This article is structured as follows. We first discuss the GPU architecture and its implications for designing the thread block size it can be controlled how threads are distributed among the SMs. One thread block is executed on one SM and continues resident until all threads in the block are completed. Once a thread block has finished, another will be scheduled to the SM if any blocks are left. An SM can execute 32 threads in parallel (restricting the thread block size to be a multiple of 32); such a group of threads is called a warp or wavefront. At any time, each of these threads has to execute the same instruction in the code, but may do so on different data, a concept which is called single instruction, multiple threads (SIMT). Hence, conditionals with diverging branches should be avoided, since threads taking an if-branch have to wait for threads taking the corresponding else-branch to finish and vice versa. All SMs may access a slow common global memory (about \u22643 GB on most of today\u2019s GPUs) in addition to their fast on-chip cache and memory. While the size of the fast cache is extremely limited, accesses to the global memory are slow and should be minimized. However, the memory latency can be reduced by coalescing the access, i.e., letting threads in a warp access contiguous memory addresses, such that the same memory transaction can serve many threads. In addition, an SM can execute a different warp while waiting on a transaction to finish, thereby hiding the latency. For the latter, threads should minimize their register usage such that the number of warps that can reside on an SM is maximized. Finally, data transfers from the main system memory to the GPU global memory are comparatively slow. Hence it is advisable to minimize them as well.We use the terminology of NVIDIA\u2122, while the general concepts are also applicable to competitors like AMD\u2122. A GPU is partitioned into streaming multiprocessors (SMs), each of which has its own on-chip memory, cache and processing cores. By adjusting the parallel prefix scans, a special case of which is the computation of a cumulative sum, which at first appears to be a serial process, or filtering an index set. Parallel prefix scans are used to solve these problems in a data parallel way with a minimum amount of branching, thus nicely fitting the above considerations; A useful programming pattern that is used extensively in the algorithms presented in this work are q-group index presented in this work is designed with above considerations in mind: The data structure supports simple access patterns that minimize the register usage. This allows to hide latency caused by not coalesced memory accesses. We evaluate this in \u201cGPU resource usage\u201d. The parallel algorithms presented in this work further minimize the data transfers necessary between their steps to constant amounts of data . Where appropriate, we discuss architecture specific considerations in the text.The q-gram index of a text T stores, for each string of length q over the alphabet, at which positions in T the q-gram occurs and allows retrieving these positions in constant time per position. It is commonly implemented via two arrays that we call the address table A and the position table P.A classical DNA Q-grams are encoded as machine words of appropriate size with two subsequent bits encoding one genomic letter . Unknown nucleotides  are converted randomly to A, C, G or T, and larger subsequences of Ns are omitted from the index. Hence, a q-gram needs 2q bits in hardware and is represented (encoded) as a number g\u2208{0, \u2026, 4q\u22121}. The address table provides for each (encoded) q-gram g a starting index A[g] that points into the position table such that P[A[g]], P[A[g] + 1], \u2026, P[A[g + 1]\u22121] are the occurrence positions of g.q-gram length q entails a tradeoff between specificity of the q-grams and the size of the data structure. Array A needs 4q integers and thus grows exponentially with q, while array P needs |T| integers, independently of q. Larger values of q lead to fewer hits per q-gram that need to be validated or rejected in later stages. Further, the choice of q determines the sensitivity or error-tolerance of the search via the pigeonhole principle (q-gram lemma): only if there are e < (n + 1)/q\u22121 errors, we can guarantee that a q-gram match exists.Deciding about the q-group index is to have the same functionality as the q-gram index , but with a smaller memory footprint for large q. This is achieved by introducing additional layers in the data structure. In the following, we always consider a q-gram as its numeric representation g\u2208{0, \u2026, 4q\u22121}.The idea of the qq-grams into groups of size w, where w is the GPU word size . The q-gram with the number g is assigned to group number \u230ag/w\u230b. Thus the ith group is the set iG = {g|\u230ag/w\u230b = i} of w consecutive q-grams according to their numeric order. The set of all q-groups is ijg for the jth q-gram in iG.We divide all 4q and text T, the q-group index is a tuple of arrays I consists of w bits each , and bit j of I[i] indicates whether ijg occurs at all as a substring in the text, i.e., For a given O corresponds to the position table P of a regular q-gram index: it is the concatenation of all occurrence positions of each q-gram in sorted numeric q-gram order. To find where the positions of a particular q-gram g begin in O, we first determine the group index i and the q-gram number j within the group, such that g = ijg. With the bit pattern of I[i], we determine whether ijq occurs in T. If not, there is nothing else to do. If yes, i.e., I[i]j = 1, we determine the j\u2032 such that bit j is the j\u2032th one-bit in I[i].The array S contains, for each group i, an index into another address array S\u2032, such that S\u2032[S[i] + j\u2032] is the starting index in O where the positions of ijg can be found; see The address array q-gram index, access is in constant time per position: For a given q-gram g, to determine  such that g = ijg, we simply compute i = \u230ag/w\u230b and j = g\u2212wi = jmodw. To compute j\u2032, i.e., find how many one-bits occur up to bit j in I[i], we use the population count instruction with a bit mask: x) returns the number of 1-bits in x.Similar to a plain I is created from the q-grams of the text (line 2). Then, S is calculated as the cumulative sum over the population counts of I (line 6). Next, the number of occurrences for each q-gram is calculated (line 10) and S\u2032 is created as the cumulative sum over these counts (line 14). Finally, the q-gram positions are written into the appropriate intervals of O (line 16).Algorithm 1 shows how the index is built. The outline of of the algorithm is as follows. First, 1https://www.khronos.org/opencl kernels. The cumulative sums are implemented with parallelized prefix scan operations (see \u201cDesigning for efficient GPU usage\u201d). Importantly, the algorithm needs hardly any branching (hence maximizing concurrency) and makes use of coalescence along the reads in order to minimize memory latency. All major data structures are kept in GPU memory.Each step is implemented on the GPU with parallel OpenCLq-group index, we note that both I and S consist of \u23084q/w\u2309 words, S\u2032 contains an index for each occurring q-gram and hence of min{4q, |T|} words in the worst case, and O is a permutation of text positions consisting of |T| words. Thus the q-group index needs up to 2/w\u22c54q + min{4q, |T|} + |T| words, compared to a conventional q-gram index with 4q + |T| words. To evaluate how the worst case size of the q-group index behaves compared to the size of the q-gram index, we consider the ratio K between the possible q-grams and the text size, i.e., 4q = K|T|.To determine the worst case size of the q\u2a85|T|, the conventional q-gram index has a small advantage because each q-gram occurs (even multiple times). In fact, assuming w = 32, if K \u2264 1, the size ratio between q-group index and q-gram index is K = 1 (or |T| = 4q), this means a small size disadvantage of 3% for the q-group index.If 4q becomes larger for fixed text size (such that q-grams become sparse), the q-group index saves memory, up to a factor of 16: For K > 1 the size ratio is (K/16 + 1 + 1)|T|/((1 + K)|T|) = (2 + K/16)/(1 + K), which tends to 1/16 for large K. The break-even point is reached for K = 16/15.If, on the other hand, q = 16 because a bit-encoded DNA 16-mer just fills a 32-bit word and q = 16 offers reasonable error tolerance and high specificity. In this regime, with current GPU memory size, we use |T| = 108 (processing 100 million nucleotides at a time), so the size ratio is K = 42.95, and the q-group index needs only 10% of the memory of the conventional q-gram index. K.In practice, we use q-group index further by sampling every second  position of S and adding another population count and addition instruction to the code for odd positions.Without noticable increase in access time, we can reduce the memory usage of the q between each read and each reference  and only computes alignment scores where such matches are found. In total, the PEANUT algorithm for read mapping consists of the three steps (1) filtration, (2) validation and (3) postprocessing. The first two steps, filtration and validation, are handled on the GPU, while postprocessing is computed on the CPU.PEANUT uses the filtration plus validation approach: It first quickly detects exact matches of a given length The steps are conducted on a stream of reads. Reads are collected until buffers of configurable size are saturated. Then, any computation is done in parallel for all buffered reads see .q-group index. Next, the potential hits are validated using a variant of Myers\u2019 bit-parallel alignment algorithm  between the reference and the reads.The filtration step aims to yield a set of potential hits, e.g., associations between a reference position and a read. For this, we seek for matching q-group index is created on the GPU on the fly (see Algorithm 1). If the index was built over the reference, either repetetive large data transfers or on-line rebuilding of the index would be necessary for each set of buffered reads and each chromosome. Hence\u2014inspired by RazerS 3  that returns, for a q-gram g, an index pair  such that the occurrence positions in the indexed text are all O[k] with kstart \u2264 k < kend, where O is from the q-group index built with Algorithm 1. Given the q-group index , the function Indexpair(g) is implemented as follows. Let \u2254Group-And-Bit(g) and j\u2032\u2254Grouprank. Then kstart = S\u2032[S[i] + j\u2032] and kend = S\u2032[S[i] + j\u2032 + 1]. We assume that there is a function Indexpair. In the following, only positions with at least one hit are considered (line 5). The cumulative sum of the counts generates an interval for each position, that determines where its hits are stored in the output array of the algorithm (line 6). Finally the occurrences for each reference q-gram are translated into hits that are stored in the corresponding interval of the output array (loop in line 8). We translate the position inside the index of concatenated reads into a read number (line 12) and a \u201chit diagonal\u201d that denotes the putative start of the read in the reference  uses parallelized prefix scan operations (see \u201cDesigning for efficient GPU usage\u201d). All data structures reside in GPU memory; between the steps, at most constant amounts of data have to be transferred between host and GPU .Again, each step of Algorithm 2 is implemented on the GPU with parallel OpenCL kernels. The filtering of P of reference positions to investigate and the reference sequence are retrieved from a precomputed HDF5-based reference index.2http://www.hdfgroup.org/HDF5.Hierarchical data format version 5,  First, this speeds up access to the reference. Second, we omit exceedingly frequent q-grams from the set P, as these only yield uninformative hits when using q-gram index based algorithms. Finally, P is sorted in numerical order of the q-grams. This increases the memory coalescence when accessing the q-group index, since subsequent threads will have a higher probability to access the same region in the index and hence the same memory bank in the global GPU memory.The set The validation step takes the potential hits of the filtration step and calculates the edit distance  between a read and the reference sequence at its putative mapping position. If the edit distance is small enough, the hit is considered to be correct and will be postprocessed in the next step.E between reference sequence and read, which contains one column for each reference base and one row for each read base. The value ijE is the minimal edit distance between the read prefix of length i and any substring of the reference that ends at position j. Interpreted as a graph with a node for each matrix entry, a path in E from the top to the bottom row denotes a semi-global alignment between read and reference. Myers\u2019 algorithm calculates the edit matrix column-wise. The state of the current column is stored in bit vectors. A transition from one column to the next is achieved via a constant amount of bit-parallel operations on the bit vectors. In iteration j, the minimal distance between the read and any substring of the reference that ends at position j can be retrieved. If the accepted error rate is limited, only a part of the edit matrix is needed to calculate the optimal edit distance. Our implementation of the algorithm follows a banded version that calculates only the relevant diagonal band of the edit matrix (w (currently 32 bits). Thereby it provides a complexity of r| being the read length. While the reduction to the diagonal band restricts the maximum insertion or deletion size in a single alignment, mismatches are not affected. Hence, the procedure allows to discover partial matches of the read, as needed for split read mapping. Large indels can be rescued later when calculating the actual alignment if a sufficiently large portion of the read aligns in this step.The edit distance is calculated with Myers\u2019 bit-parallel algorithm  that simt matrix . The imppercent identity is obtained which we define here in compliance with RazerS 3 as (|r|\u2212k)/|r|, where |r| is the read length and k is the edit distance. Hits with a percent identity less than a given threshold are discarded. The default for this threshold is 80 percent which provides a decent sensitivity in our benchmarks (see \u201cResults\u201d). Decreasing it has moderate impact on performance, since more hits have to be postprocessed and written to disk.Similar to q-grams), sorts the remaining hits by percent identity, pairs mates in case of paired-end alignment, estimates a mapping quality and calculates the actual alignment of each hit. For the latter, either local or semi-global alignments can be chosen. In contrast to the previous steps, postprocessing is done on the CPU. This allows us to postprocess the hits in parallel to filtration and validation.The postprocessing of a read removes duplicate hits  that the hit position p is not the true origin of the read r in the reference. p|r) in a Bayesian way as P being the set of all reference positions and approximate the likelihood Pr(r|p) of a read r to be sampled from position p  as product of the miscall probabilities of mismatching bases as obtained from the sequencer. In practice, Pr(p|r) is approximated roughly using the best and second best hit  we can approximate the posterior probability Pr(p|r) as P\u2032 being the validated hit positions of the read r. The PHRED-scaled mapping quality is then obtained as min{\u221210log10(1\u2212Pr(p|r)), 60}. Per default, we cap the mapping quality at 60 and force it to 0 in case of ambiguous hits  in order to generate values comparable to other read mappers like BWA  from false positives is needed. PEANUT reports alignments in the SAM  format, best hit . PEANUT like BWA . This isWe evaluate PEANUT in terms of its efficiency of GPU resource usage, its accuracy and its speed. We also evaluate the ability of the mapping quality measure defined in \u201cPostprocessing\u201d to separate true hits from others.occupancy, that is the fraction of active warps among the maximum number of warps on an SM. The more active warps exist on an SM, the higher is the chance that latency can be hidden by executing another warp. q-group index (create_queries_index) and the filtration step (filter_reference), it even reaches 1.0 which illustrates the benefit of the q-group index being tailored towards the GPU architecture.In order to maximize utilization of the GPU hardware, idle cores have to be avoided. The two most important reasons for idle cores are branching and memory latency (see \u201cDesigning for efficient GPU usage\u201d). The latter can be hidden if the SM is able to execute a different warp while waiting on the transaction. The capability to do so can be measured with the q-group index) to detect all alignments up to a given error rate. For this, we use the Rabema , such that using 16-grams appears to be a reasonable default choice in practice.In general, we advise to set the percent identity threshold to be slightly more permissive than the expected error rate. This is because the replacement of We compare the PEANUT algorithm with other state of the art read mapping algorithms in terms of run time and accuracy. The evaluation is conducted on 4 datasets:1.5 million simulated Illumina HiSeq 2000 reads;2.5 million real Illumina HiSeq 2000 reads from the human exome;3.10 million real paired-end Illumina HiSeq 2000 reads from the human exome;4.50 million real paired-end Illumina HiSeq 2000 reads from the whole human genome.5http://ftp.ensembl.org/pub/release-74/fasta/homo_sapiens/dna/ version 37 with Mason (see \u201cSensitivity\u201d). The read length is set to 100 and all other parameters of Mason are left at their default values, such that reads with a typical error profile and mutation rate are generated. The second and third datasets are generated from real paired-end exome sequencing reads6http://www.ebi.ac.uk/ena/data/view/ERR281333, 07/2014.Available at the European Nucleotide Archive under   were created from the ENSEMBL human reference genome07/2014.  of lengtparallel (the time for merging the resulting output was not included into the run time). NextGenMap was used in GPU mode, such that it makes maximum use of the available hardware. All read mappers were configured to output alignments in SAM format  with an NVIDIA Geforce\u2122 780 GPU  and a 7200 rpm hard disk. We evaluated two modes of PEANUT. First, PEANUT was configured to find the best stratum of semi-global alignments (best-stratum mode) for each read. Second, PEANUT was configured to find all semi-global alignments  for each read. For comparison, we benchmarked the newest generation of BWA , no working installations of SOAP3 , SOAP3-dIn the following, we distinguish between all-mappers and best-mappers . Best-mappers only strive to find the single origin of a read on the reference sequence of a single organism. All-mappers provide all alignments of a read down to a given error rate. Hence, all-mapping is computationally more intensive.Run time performance is measured three times as the overall wall clock time for processing a dataset on the test system. 9http://www.bioplanet.com/gcat, 08/2014. benchmark provides an alternative, less formal approach to measure the accuracy of a mapper by testing whether a mapped read is within 5 base pairs of its known origin in given datasets simulated with DWGSIM.10https://github.com/nh13/DWGSIM, 08/2014. For comparison, we provide GCAT results in 11http://www.bioplanet.com/gcat/reports/3499-acxvkaiakl/alignment/100bp-se-small-indel/peanut/compare-26-35, 08/2014. (2) 100bp-se-large-indel,12http://www.bioplanet.com/gcat/reports/3522-twmulhzdnt/alignment/100bp-se-large-indel/peanut/compare-28-32, 08/2014. (3) 100bp-pe-small-indel13http://www.bioplanet.com/gcat/reports/3500-rzzjxccatd/alignment/100bp-pe-small-indel/peanut/compare-23-18, 08/2014. and (4) 100bp-pe-large-indel,14http://www.bioplanet.com/gcat/reports/3498-dqxwpnmjyn/alignment/100bp-pe-large-indel/peanut/compare-87-25, 08/2014. consisting of about 12 million 100 basepair reads each. The comparison is limited to those of our considered read mappers for which public results are available in GCAT . The full reports are available via the GCAT web service under the URLs provided in the footnotes.The accuracy of the obtained alignments is assessed using Rabema . For best-mappers, using the simulated dataset 1, we measure precision and recall with Rabema as defined by All-mappers are compared by their ability to find all alignments of a given error rate. Here, we again use the sensitivity provided by Rabema (see \u201cSensitivity\u201d). This involves creating a gold standard with RazerS 3 configured to full sensitivity, which is computationally expensive. We therefore perform this on only 1,000 reads simulated with the same parameters as dataset 1. The gold standard is calculated for an error rate of at most 15%. While PEANUT requires at least 2.5 GB of GPU memory for filtration and validation, it is not restricted to running on high-end GPU models like the Geforce 780 used above: q, the corresponding probability \u03bb and C of the approximation (see \u201cPostprocessing\u201d) can be configured to different values to achieve a closer fit for a particular reference or dataset. Despite that, the defaults provide a reasonable way to distinguish between true and false positives without the computational overhead needed for calculating concrete alignments of many suboptimal hits (see \u201cPostprocessing\u201d).Finally, we evaluate the mapping qualities provided by PEANUT. For each PHRED-scaled mapping quality q-group index, a novel data structure for read mapping, along with parallel algorithms for index building and querying. The algorithms fit nicely to the GPU architecture by using a combination of element-wise and prefix scan operations over large arrays and requiring hardly any data transfer between the host and the GPU. We showed that the q-group index needs significantly less memory in practical scenarios than a conventional q-gram index while maintaining constant access time. The q-group index has been adopted by NVIDIA\u2122 and is provided as part of the NVBIO library.15http://nvlabs.github.io/nvbio/We presented the q-group index we implemented the read mapper PEANUT. The q-group index enables the mapper to be the first implementation of the filtration and validation approach that works completely on the GPU. The benefit of this is illustrated by PEANUT showing supreme speed over state of the art read mappers like BWA, Bowtie 2, RazerS 3, CUSHAW3 and MrFast, as well as the GPU based read mappers NextGenMap and CUSHAW2-GPU. This holds for both the high-end GPU NVIDIA\u2122 Geforce 780 and a four years old NVIDIA\u2122 Geforce 580. PEANUT is 4\u201310 times faster than other all-mappers. Further, it is faster than all other best mappers; in particular, it is 2 times faster than the fastest best-mapper on the most realistic dataset. The speed improvements do not come at the cost of mapping quality. In fact, PEANUT is even slightly more sensitive than other all-mappers at default parameters and provides an at least comparable precision and recall compared to other best-mappers in our Rabema-based benchmarks.On top of the 16http://www.python.org software package. Filtration and validation were implemented in OpenCL, using the PyOpenCL package (http://peanut.readthedocs.org, where we further provide a Snakemake (PEANUT is distributed under the MIT license as an open source Python package  and post package . Documennakemake  workflow"}
+{"text": "Most psychological research on Bayesian reasoning since the 1970s has used a type of problem that tests a certain kind of statistical reasoning performance. The subject is given statistical facts within a hypothetical scenario. Those facts include a base-rate statistic and one or two diagnostic probabilities. The subject is meant to use that information to arrive at a \u201cposterior\u201d probability estimate. For instance, in one well-known problem Eddy,  the subjThe probability of breast cancer is 1% for a woman at age forty who participates in routine screening. If a woman has breast cancer, the probability is 80% that she will get a positive mammography. If a woman does not have breast cancer, the probability is 9.6% that she will also get a positive mammography. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer? __ %.H as the focal hypothesis, \u00acH as the mutually-exclusive hypothesis, and D as datum: P(H), the prior (often equated with the base-rate) probability of the hypothesis; P(D|H), the true-positive rate; and P(D|\u00acH), the false-positive rate. In the mammography problem, P(H) = 0.01, P(D|H) = 0.80, and P(D|\u00acH) = 0.096. Furthermore, P(\u00acH) = 1 \u2013 P(H) = 0.99. The estimate queried is P(H|D).The information in such problems can be mapped onto common expressions that use Bayes' theorem states:Thus, it yields a posterior probability of 0.078 in the mammography problem. Yet even the majority of physicians who were queried by Eddy  gave estWell-established findings such as these have supported the view that expert and na\u00efve subjects alike are non-Bayesian , which they are asked to estimate, with P(D|H), which is provided  = 0.80. The inverse fallacy can also explain patterns of deviation from Bayes' theorem in tasks that hold constant base rates for alternative hypotheses , and researchers typically do not collect multiple \u201cprior\u201d and \u201cposterior\u201d  probability assessments.A remarkable feature of the standard approach to studying Bayesian reasoning is its inability to reveal how people P(H), which the subject updates in light of \u201cnew\u201d evidence, D. It is somewhat ironic that advocates of base-rate neglect have not noted  that, if people ignore base rates, it may be unwise to assume they represent the subject's prior probability. Would that not imply that the subject ignores his or her own prior probability?It is instead conveniently assumed that the base rate represents the subject's prior belief, P(H), is in fact a conditional probability corresponding to one's personal probability of H, given all that they know prior to learning D , b = f (H \u2229 \u00ac D), c = f (\u00ac H\u2229 D), and d = f (\u00acH \u2229 \u00acD). Going from left to right, the four boxes in the lowest level of the frequency tree in Figure a\u2013d, which have received much attention in the causal induction literature /(a + b + c + d), a/(a + b), and c/(c + d). That is, frequencies a\u2013c support the easy computation of a/(a + c). However, those improvements in performance, which pertain to static coherence constraints  ranged from 0 to 1 over seven probability levels across the problems. Subjects exhibited a form of conservatism , causing an underweighting of relevant information.For example, Williams and Mandel  presented Mandel  found thThe issues I have raised, non-exhaustive as they are, draw attention to some important problems with the conventional approach to studying Bayesian reasoning in psychology that has been dominant since the 1970s. Rather than fostering pessimism, I hope my comments illustrate that there are good opportunities for future work to advance our understanding of how people revise or update their beliefs.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "One fundamental yet longstanding issue in materials science is how local inelasticity arises within an amorphous structure before yielding occurs. Although many possible scenarios were postulated or predicted by theories and simulations,however, direct experimental evidence has been lacking today due to the lack of a sensitive way to detect nano-scale inelasticity. Through the carefully designed microcompression method as coupled with the state-of-art nano-scale electric resistance measurement, we here unfold a stochastic inelastic deformation process in a Zr-based metallic glass, which takes place via the recurrence of two types of short-lived inelastic events causing structural damage and recovery, respectively, prior to yielding. Our current findings reveal that these stochastic events not only self-organize into sub-critical events due to elastic coupling, but also compete with each other in a way that enables the whole amorphous structure to self-heal as well as to sustain local damage. Amorphous materials are ubiquitous in our everyday lifeOver the past decades, it is the long-sought issue with regard to the origin of flow in amorphous solids that has been attracting tremendous research interest of materials scientists and physicists234567891011121314153481011Here, a coupled nano-scale electro-mechanical system was used to tackle this problem. As seen in the later text, this system is proven to be extremely sensitive in resolving the structural signals that result from inelastic events occurring during the apparent 'elastic' deformation of a metallic glass. As compared to a conventional mechanical test, the nano-mechanical module of this system is based on the recently developed Hysitron TI950 nanoindentation platform, which possesses the resolution of ~0.1\u2005nm in displacement and ~1\u2005\u03bcN in force; in addition, the coupled nano-electric module is based on the state-of-art Nano-Electric-Contact-Resistance (NanoECR) technique, which possesses the resolution of 10\u2013100\u2005pA in current and 0.1\u2005mA in voltage See . The cou55Cu30Ni5Al10 (in at. %). Its structural amorphousness was confirmed using the X-ray diffraction method and high-resolution transmission electron microscopy  and electric current (I) data, as a function of time (t), measured simultaneously from the microcompression test. It should be emphasized here that, due to the surface roughness effect and the settling of the nanoindenter on the micropillar, there is a period of 1\u20132 seconds before an electric Ohm's contact could be established  and the electric current I. In the above relation, \u0394 represents an incremental change of a physical quantity and \u03b5 = 0h/H, where 0H denotes the initial height of a micropillar. Here it should be noted that, due to the ultrahigh sensitivity of our testing system, the noise-to-signal ratio for the calculated \u0394\u03c1/\u03c1 is very low and about 1 \u00d7 10\u22124  of the metallic glass can be extracted from the measured displacement (h) and current (I) data. \u0394\u03c1/\u03c1 and h versus time t as the micropillar was compressed to a peak stress of ~2000\u2005MPa. Before reaching this peak stress, a few pop-in events can be witnessed on the h-t curve. Note that, for the sake of consistency, a displacement pop-in event is herein defined as a displacement jump greater than ~2\u2005nm in size. In accord with the pop-in events, a few pronounced resistivity spikes can be also observed on the \u0394\u03c1/\u03c1 -t curve. As seen in the inset of 45\u0394\u03c1/\u03c1| greater than 5 \u00d7 10\u22124, which is about fivefold of the maximum experimental error that could occur to the derived resistivity change. As such, we believe that these secondary spikes are the manifestation of real structural alteration caused by the local inelastic events in the metallic glass.With the above equation, the relative change in the electric resistivity  the structure factor, and \u03bc(q) the pseudo-potential which can be replaced by a scattering matrix when the above model is applied to metallic glasses. In the 1980s, Kelton and Spaepen\u0394\u03c1, of a metallic glass can be directly related to the variation in its atomic packing density \u0394\u03be through \u0394\u03c1 = C\u0394\u03be. Here C is the pre-factor that depends mainly on the structural factor S(q) of the metallic glass  with thermal annealing if \u03b1 < 5 \u00d7 10\u22125\u2005K\u22121 or otherwise increases with thermal annealing. On the other hand, based on the data from 13 types of metallic glasses with different glass transition temperatures gT, Kato and co-workersg\u03b1\u03a4 ~ 8.24 \u00d7 10\u22123 for metallic glasses. As the gT of Zr-based metallic glasses are around 700\u2005K, the corresponding \u03b1 should be about 1.2 \u00d7 10\u22125\u2005K\u22121. This suggests that the electric resistance of Zr-based metallic glasses should decrease with thermal annealing or structural ordering, which is consistent with the previous result reported by Bai and co-workers\u0394\u03c1/\u03c1 of the Zr-based metallic glass to structural disordering while the decrease to structural ordering. In other words, the recurrence of these p- and n-type spikes indicates that the atomic structure of the metallic-glass micropillar was repeatedly experiencing damage and recovery even though the applied stress was far below the yielding point.Physically, the resistivity, h increases with time t during loading [h-t curves, agreeing with the \u2018elastic' character of the overall deformation in the metallic glass. In sharp contrast, the corresponding curves of \u0394\u03c1/\u03c1 versus t display many spike-like features. Compared to those prominent spikes at displacement pop-in, these spikes occurring in the \u2018elastic' regime appear much shorter and last only for a short period of time. Due to the limit of our data acquisition rate (~103 points per second), the measured duration times d\u0394t for these secondary spikes range from ~1 to ~1.5\u2005ms and appear to be independent of the spike heights and the applied stresses  and densely-packed (solid-like) atoms8910232425262729302933p for the net transition of local structural configurations along the stress direction at time t and shear stress \u03c4, it can be proved that p satisfies the following dynamic equation in order to retain the total free energy of the system29\u03c9 is the attempt frequency; \u0394G is the energy barrier and \u03a9 is the activation volume of the local inelastic event. For a constant shear stress \u03c4 at load hold, we obtain: Rt is the average relaxation time of these inelastic events, which equals Rt/t goes to infinity, the \u2018memory' of the MG about the stochastic inelastic events at t = 0 will die out while the probably p for the net transition along the stress direction will approach a steady-state value p(\u03c4) = \u03c4\u03a9/kT. Note that \u03a9 should be p(\u03c4)f(\u03a9)d\u03a9, where f is the probability density function of the activation volume for an inelastic event. If the \u2018liquid-like cell' model of Cohen and GrestLLRp is the volume fraction of the liquid-like cells, c\u03a9 as the smallest activation volume. In such a case, the following cumulative probability can be obtained for the constant stress activation of the local inelastic events with their activation volumes greater than \u03a9: Assuming a probability With int\u0394t ahead of the event. Experimentally, int\u0394t can be measured as the time interval between two consecutive spike events of the same kind. int\u0394t obtained for the holding stresses of 296\u2005MPa and 592\u2005MPa, respectively. Consistent with our theory, the general trend of the waiting times int\u0394t clearly shows the distribution of an exponential decay. Meanwhile, as the holding stress is doubled, it appears that longer waiting times could be detected, which also agrees with our prediction. However, it needs to point out that this agreement is only in a qualitative manner. Rather than the strong linear stress dependence, the stress dependence of the accumulative probability, as seen from our data, is very weak. A similar behavior could be observed at other holding stresses. This weak stress dependence suggests that the simple mean-field anelastic model we proposed needs further development. One possible way of improvement is to include a term of elastic coupling into the mean-field modeling. In such a case, we can study how the variation of the stress field is coupled with the variation of the local properties, which may explain the weak stress dependence shown by our experimental data. The related theoretical work is under progress and will be discussed in our future work. Despite the weakness of the mean-field modeling, it is still worth mentioning that, with the mean-field model and d\u0394t~ 1\u2005ms, we can estimate an average activation energy of ~0.5\u2005eV for these local inelastic events, which agrees with the previous results obtained from nanoindentation29The Estimation of Activation Energy' in the To verify the above thinking, let us follow the recent analysis of Krisponeit et al.\u22123), is likely to be caused by the avalanches triggered through elastic coupling. Nevertheless, we envision that the latter mechanism due to the de-caging effect is also feasible for the high-magnitude spikes; however, the probability for its occurrence must be very low.Next, we would like to further address the following questions: in what cooperative way these chain-like inelastic events occur? And even if the occurrence of these events is stochastic in nature, are their outcomes, such as the structural relaxation and damage, also stochastic? In principle, these local inelastic events may occur in an isolated manner as pictured in the previous mean-field theories15Finally, let us discuss whether the outcome of the inelastic events, i.e. structural damage versus relaxation, is stochastic. As seen in 736To conclude, it is demonstrated in this Letter that, with the state-of-art NanoECR technique, the local inelastic events hidden, otherwise, in the overall elastic response of the metallic glass could be revealed. Due to the elastic coupling, these local inelastic events take place cooperatively, exhibiting a self-organized behavior as seen in their magnitude distribution. In contrast to the classic model, it is also shown that the effects of these inelastic events are twofold: it can either damage or heal the amorphous structure. Depending on the applied stress and stress rate, the competition of the local events can lead to overall damage or recovery of the amorphous structure. These intriguing and multi-scaled deformation characters as seen in the metallic glass are parallel to those already known phenomena observed for earthquakes, sand pile avalanches, dislocation slip dynamics and a variety of other dynamic systems36The Zr-based metallic-glass micropillars were prepared by FEI Quanta 3D 200\u2005FIB/SEM dual beam system. Following the ion-milling method detailed in Ref.C.T.L. and Y.Y. designed the project. S.W. and Z.Y.L. carried out the experiments. X.L.F., B.A.S., Y.F.Y., Y.Y. and C.T.L. analyzed the data. Y.Y. and X.L.F. wrote the manuscript.Supplementary Information"}
+{"text": "K-means method is applied to segment 1,462 patients into twelve clusters. The average values of L, R, and F excluding monetary covered by national health insurance program are computed for each cluster. In addition, customer value matrix is used to analyze customer values of twelve clusters in terms of frequency and monetary. Customer relationship matrix considering length and recency is also applied to classify different types of customers from these twelve clusters. The results show that three clusters can be classified into loyal patients with L, R, and F values greater than the respective average L, R, and F values, while three clusters can be viewed as lost patients without any variable above the average values of L, R, and F. When different types of patients are identified, marketing strategies can be designed to meet different patients' needs.This study combines cluster analysis and LRFM  model in a pediatric dental clinic in Taiwan to analyze patients' values. A two-stage approach by self-organizing maps and  The medical care industry in Taiwan has become very competitive when the national health insurance (NHI) program with a mandatory, single-payer social health insurance system was launched by the government in Taiwan since March 1995 . Under sMarket segmentation is very useful to identify different customer needs and then to provide the management to customize the products or services to fulfill the needs . Data mi L, R, and F values compared with the overall average values of L, R, and F values, different types of patients, such as loyal patients, potential patients, and lost patients, can be identified. In addition, in order to evaluate customer values, customer value matrix proposed by Marcus [This study intends to combine data mining techniques  and LRFM model in a pediatric dental clinic for market segmentation. When all patients are grouped into clusters, the characteristics for each cluster are to be observed and described. By observing the average values ofy Marcus  by consiy Marcus  by takinThis paper is organized as follows.  K-means method are commonly used for cluster analysis.Huang et al.  stated tSOM, an unsupervised neural network method, uses clustering, visualization, and abstraction to solve problems and market screening \u201315. The K-means method, a nonhierarchical approach, is one of the very popular approaches to perform cluster analysis due to its simplicity of implementation and fast execution [ K-means method using Euclidean distance has two major steps. First, place the instances in the closest class (the assignment step). Second, recalculate class centroids from the instances assigned to the class (the reestimation step) [xecution . K-meanson step) , 17. K-means method is very sensitive to the choice of a starting point to partition the items into K initial clusters [ K-means method has been proposed and widely applied to improve the weakness [ K-means method to perform cluster analysis of the data set in the second stage.Self-organizing maps method has the advantages over other traditional cluster analysis methods but it does not provide measures for validation for the cluster analysis results . In contclusters , 19, 20.weakness , 20, 21.LRFM model was developed based on RFM model, which is a well-known method to analyze customer values for market segmentation , 22. TheThe traditional approach to use RFM model is to sort the customer data and then divide the data into five equal segments for each dimension of RFM . The topL) into consideration, where L is defined as the number of time periods (such as days) from the first purchase to the last purchase in the database.Reinartz and Kumar  addresse R is redefined as the number of days since the last visit when the first day of the specified time period is set to one. That is, R value belongs to the larger-is-better scenario, and larger R value indicates that the customer has visited the organization more recently, which is different from the traditional definition of recency. By further taking into account the strategic positioning of customer clusters, four major types of customers can be grouped in terms of RFM symbols, that is, lost customers with\u2009\u2009R \u2193F \u2193M \u2193 and R \u2193F \u2191M \u2191, new customers with R \u2191F \u2193M \u2193, loyal customers with R \u2191F \u2191M \u2191, and promising customers with R \u2191F \u2193M \u2191.Ha and Park  used aveL \u2191R \u2191F \u2191M \u2191, L \u2193R \u2191F \u2191M \u2191, L \u2191R \u2193F \u2191M \u2191, and L \u2193R \u2193F \u2191M \u2191), frequent customers , spender customers , and uncertain customers . Moreover, sixteen combinations of LRFM model can be classified into five major groups such as core customers, potential customers, lost customers, new customers, and resource-consumption customers. Specifically, core customers include L\u2191R\u2191F\u2191M\u2191, L\u2191R\u2191F\u2191M\u2193, and L\u2191R\u2191F\u2193M\u2191. Potential customers consist of L\u2191R\u2193F\u2191M\u2191, L\u2191R\u2193F\u2191M\u2193, and L\u2191R\u2193F\u2193M\u2191. Lost customers are composed of L\u2193R\u2193F\u2191M\u2191, L\u2193R\u2193F\u2191M\u2193, L\u2193R\u2193F\u2193M\u2191, and L\u2193R\u2193F\u2193M\u2193. New customers comprise L\u2193R\u2191F\u2193M\u2193, L\u2193R\u2191F\u2191M\u2193, L\u2193R\u2191F\u2193M\u2191, and L\u2193R\u2191F\u2193M\u2193. Finally, resource-consumption customers are L\u2191R\u2191F\u2193M\u2193 and L\u2191R\u2193F\u2193M\u2193.Chang and Tsay  based on F and M values, four quadrants as shown in F\u2191M\u2191), spender customers (F\u2193M\u2191), uncertain customers (F\u2193M\u2193), and frequent customers (F\u2191M\u2193). On the other hand, Chang and Tsay [ L and R to explain the characteristics of lost customer and loyalty by proposing customer relationship matrix depicted in L\u2191R\u2191), potential relationship (L\u2191R\u2193), lost relationship (L\u2193R\u2193), and establishing relationship (L\u2193R\u2191).Marcus  proposedand Tsay  used L aWhen different LRFM combinations are identified, customers can be classified into appropriate groups such as core customers, potential customers, lost customers, new customers, and resource-consumption customers. In addition, the customer value matrix enables the management to classify customers into best, spender, uncertain, and frequent customers in terms of frequency and monetary. Customer relationship matrix helps the management identify the characteristics of four different types of the relationships between the organization and the customers through length and recency. In other words, customer values can be evaluated by customer value matrix and customer relationship matrix. More importantly, different marketing strategies can be designed to meet different customer needs.This pediatric dental clinic started its operation since 17 September 1995. By definition, the patients must be less than 18 years old. This study collects the data set with 1,462 effective patients who visited this clinic with the total of 7,957 times from 1 July 2009 to 30 June 2011. The demographic information for each patient consists of the membership number, gender, birth date, and the visiting dates, where the frequency can be measured by counting the number of visits during the time period. Monetary value for each patient is excluded in this study since the majority of the income from a dental clinic is from the fixed copayment and registration fee per visit by national health insurance program in Taiwan [The descriptive statistics of length, recency, and frequency are summarized in  K-means method is performed for cluster analysis.  L, R, and F, average age and gender of the patients, and the symbol(s) of L, R, and F greater than the averages of L, R, and F. Most of the patients are in Clusters 3, 4, 8, 9, 10, and 12. Patients in Clusters 4 and 8 are younger children. More detailed analyses regarding gender and age group are reported in To perform cluster analysis, IBM SPSS Modeler 14.2 is the software, and the \u201cKohonen node\u201d (viz. SOM) with default values is used. In addition, the Kohonen mode is set to \u201csimple\u201d for cluster analysis. The result generated by SOM suggests that the best number of clusters among 1,462 patients is twelve as shown in  L, R, and F values greater than the average L, R, and F values. Patients in Cluster 8 have larger R and F values. Clusters 1, 5, and 7 have higher L value compared with the average L value. Cluster 4 has larger R value, while Cluster 11 has larger F value. Finally, L, R, and F values in Clusters 3, 10, and 12 are smaller than the average L, R, and F values.From To further analyze patients' values, twelve clusters can be plotted by customer value matrix in terms of frequency and monetary. It is worth noting that monetary is assumed to be fixed in our study such that the original vertical axis (monetary) in  K-means method, along with LRFM model to cluster a total of 1,462 pediatric patients into twelve groups. From managerial viewpoints, patients in Cluster 11 belong to new customers. In addition to Cluster 11, patients in Cluster 8 are new customers with recent visits. The only difference between Cluster 11 and Cluster 8 is that patients in Cluster 8 have higher frequency to visit the dental clinic. In order to maintain a long-term relationship, the dental clinic needs to interact with the patients more often. In contrast to new customers, patients in Clusters 2, 6, and 9 belong to loyal customers. In order to increase the number of the visits, the dental clinic can provide better after-medical care activities. Finally, patients in Clusters 3, 10, and 12 with low length, recency, and frequency values might not be the focal point for marketing strategy since these patients contribute less to this dental clinic. More resources can be deployed elsewhere to create more profits for this clinic.This study uses a two-stage approach, namely, self-organizing maps and L, R, and F in From the viewpoints of customer value matrix, Clusters 2, 6, 8, 9, and 11 are the best customers. By directly observing the symbols of"}
+{"text": "In ball sports, we are taught to follow through, despite the inability of events after contact or release to influence the outcome . Here we \u2022Future movements determine which motor memory is currently active and modifiable\u2022Skills that otherwise interfere can be learned if each has a unique follow-through\u2022A single skill is learned faster if its follow-through is consistent\u2022Selection of motor memories depends on both lead-in and follow-through movements For a motor skill to be learned, its motor memory must be stored, protected from interference, and reactivated for modification during practice. Howard et\u00a0al. demonstrate that future movement determines which motor memory is currently active and that a consistent follow-through constrains skill acquisition to a single memory, thereby speeding up learning. For a motor skill to be learned over a prolonged period of time, the motor memory of the skill must be stored, protected from interference by intervening tasks, and reactivated for modification when the skill is practiced. Given the widespread notion of the importance of a consistent follow-through in many sports , here we1,7\u00a0= 16.8; p\u00a0= 0.005; hand paths shown in 1,7\u00a0= 17.706; p\u00a0= 0.004) reaching around 40% of full compensation over a session. In contrast, when a second group of participants were presented with the final target, which again was predictive of the field direction, but did not follow-through to the target , suggesting that participants solely used non-specific co-contraction to reduce their error [1,124\u00a0= 7.388; p\u00a0= 0.08) and force compensation , indicating that interference was strongly reduced in the follow-through group.Participants grasped the handle of a robotic interface  and madeir error . FinallyThese results show that . However, significantly faster learning was observed for the consistent, compared to the variable, follow-through group for both kinematic error  and force compensation  as shown using an ANOVA across all exposure trials with the main effects of experimental group and trial number. The same analysis, performed on the first one-third of the exposure trials, showed significantly faster learning for the consistent compared to the variable follow-through group for both kinematic error  and force compensation . By the end of the session, there were no significant differences in either the kinematic error  or force compensation  , showing that both groups eventually learned the same amount for this simple skill.We tested this prediction in two groups who experienced a single force field whose direction was fixed across all trials. Both groups made a movement in the force field to a central target followed by an unperturbed follow-through movement to a final target A. For onfast p\u00a0< 0.001 between groups, other parameters non-significant), suggesting that variable follow-through leads to decreased retention across trials [We used a dual-rate model to examine whether changes in the parameters that govern learning might account for the differences that we observed in skill acquisition rate, but not final level of learning. The time course of learning novel dynamics is well accounted for by two interacting processes: a fast process that adapts and decays quickly and a slower process that adapts and decays more gradually . Each prs trials .Could our results on simple force-field learning over the course of an experimental session apply to real-world learning taking place over much more extended periods? In real-world tasks, such as a tennis or golf stroke, the lead-in to the movement is critical for task success, as it will determine characteristics such as variability at contact . Moreove1,5\u00a0= 36.750; p\u00a0= 0.002) and increase in force compensation  to around 50%. Participants learned to access the motor memories based on the nonlinear rule as shown by the force compensation being of the appropriate sign for all four possible movements  have a very limited ability to separate motor memories , dynamicAlthough we have shown that consistent follow-through leads to faster learning through selection of a single memory, this does not preclude other potential advantages of the follow-though, such as injury reduction or other biomechanical advantages . AlthougI.S.H., D.M.W., and D.W.F. designed the study. I.S.H. ran the experiments. I.S.H., D.M.W., and D.W.F. performed the data analysis. I.S.H., D.M.W., and D.W.F. wrote the paper."}
+{"text": "Banach  establisBanachX,\u00a0d) be a complete metric space and f has a fixed point.Banach Let  be a complete metric space and T has a fixed point.Kannan Let b-quasi-metric family if Generating space of (2)b-dislocated metric family if Generating space of (3)b-dislocated-quasi metric family if Generating space of If y Banach .X,\u00a0d) be a metric space. If we put d for all Let .Let open ball of radius x.Let closed ball of radius x.The set Now, we state some propositions and corollaries in In a n Kumari , Sarma an Kumari .LetthenIf we writeforthe operationsatisfies Kuratowski\u2019s closure axioms of Kelley (b) be a metric space. Ifis a self mapping andx,\u00a0ybe any elements ofX. Now consider the following contractive conditions:RhoadesThere exist nonnegative functionsa,\u00a0b,\u00a0csatisfyingRhoades There exsuch that, for eachCiric.1  be a complete metric space and ifis a self continuous mapping which satisfies:for allandThenThas a unique fixed point inX.We now give an example to illustrate the above corollary.Let d is a complete metric on X. Define the self mapping Clearly T.For Three eminent conditions (1), (2) and (3) are made significant contribution in the area of fixed point theory and applications. After these three results, a huge number of papers have been written by several authors to those results either improve or generalize some of the conditions (1), (2) or (3), or even the three conditions simultaneously.In 1972, Zamfirescu ((Zamfirescu1972) There exists real numbers Then T has a fixed point.In Rhoades , RhoadesRhoades 19a,\u00a0b,\u00a0c satisfying is a complete metric space. Ifbe a self continuous mapping satisfying any of the conditions either Rhodes or Zamfirescu or Ciric.1. ThenThas a unique fixed point.T has a unique fixed point. In Rhoades , Rhodes Letbe a complete-family with the parametersandIfis a self continuous mapping which satisfiess-h generating b-quasi-contraction, i.e.for allandIf for some positive integeris continuous, thenThas a unique fixed point inX.u in X.We can construct a sequence u. Also we have,Thus its subsequence u is a fixed point of Which yields that Now we shall prove that l be a smallest positive integer such that Let If Similarly,Thus Which is a contradiction.Hence u is a fixed point of T.Which yields X such that Now if there exists another point u is a unique fixed point of T in X. Hence If we take parameter Letbe a complete generating space of quasi-metric family andis a continuous mapping which satisfies:for allandIf for some positive integeris continuous, thenThas a unique fixed point inX.If we takethen we get following corollary.Let  be a complete metric space and ifis a continuous mapping which satisfies:for allandIf for some positive integeris continuous, thenThas a unique fixed point inX.Zamfirescu Contraction, we introduce the following definition in the setting of Based on the definition of Then f is called \u201cs-z generating b-quasi-contraction\u201d.Let Letbe a complete-family with the parametersIfbe a continuouss-z generating b-quasi-contractionthenfhas a unique fixed point inX.Put Now we prove that m,\u00a0n are positive integers such that To do this,let Now considerThus Which implies there exist some f is continuous, we get Since u is a fixed point of f. Suppose there exists another point X such that Thus u is a unique fixed point.Since We now give an example to illustrate the above theorem. Let f satisfies the condition(1) of Theorem 34 but f doesn\u2019t satisfy condition(2) of Theorem 34.Hence f in X.SinceIf we take parameter Letbe a complete generating spaces of quasi-metric family. Ifbe a continuous mapping such that for eachat least one of the following is true.Thenfhas a unique fixed point.If we takethen we get following corollary.Let  be a complete metric space. Ifbe a continuous mapping such that for eachat least one of the following is true.Thenfhas a unique fixed point.Open Question What are the additional conditions as needed in order to establish the existence of a unique fixed point satisfying the condition for any Conclusion In this work, we introduced a new concept of s-h generating b-quasi-contraction., s-z generating b-quasi-contraction.. Also, we derived the existence of fixed point theorems for generating spaces of b-quasi-metric family. Moreover, some examples are provided wherever necessary. Our results may be the motivation to other authors for extending and improving these results to be suitable tools for their applications."}
+{"text": "Quality end-of-life care depends on understanding patients\u2019 end-of-life choices. Individuals and cultures may hold end-of-life priorities at different hierarchy. Forced ranking rather than independent rating, and by-person factor analysis rather than averaging may reveal otherwise masked typologies.n\u2009=\u2009120) rank-ordered 47 opinion statements on end-of-life care following a 9-category symmetrical distribution. Statements\u2019 scores were analyzed by averaging analysis and factor analysis (Q-methodology).We explored Saudi males\u2019 forced-ranked, end-of-life priorities and dis-priorities. Respondents ; 52\u00a0% reported average religiosity, 88 and 83\u00a0%\u2009\u2265\u2009very good health and life-quality, respectively, and 100\u00a0%\u2009\u2265\u2009high school education. Averaging analysis revealed that the extreme five end-of-life priorities were to, be at peace with God, be able to say the statement of faith, maintain dignity, resolve conflicts, and have religious death rituals respected, respectively. The extreme five dis-priorities were to, die in the hospital, not receive intensive care if in coma, die at peak of life, be informed about impending death by family/friends rather than doctor, and keep medical status confidential from family/friends, respectively. Q-methodology classified 67\u00a0% of respondents into five highly transcendent opinion types. Type-I  and Type-V  reported the lowest and highest religiosity, respectively. Type-II  and Type-III  reported the best and worst life-quality, respectively. Type-I respondents were the oldest with the lowest general health, in contrast to Type-IV . Of the extreme 14 priorities/dis-priorities for the five types, 29, 14, 14, 50, and 36\u00a0%, respectively, were not among the extreme 20 priorities/dis-priorities identified by averaging analysis for the entire cohort.1) Transcendence was the extreme end-of-life priority, and dying in the hospital was the extreme dis-priority. 2) Quality of life was conceptualized differently with less emphasize on its physiological aspects. 3) Disclosure of terminal illness to family/close friends was preferred as long it is through the patient. 4) Q-methodology identified five types of constellations of end-of-life priorities and dis-priorities that may be related to respondents\u2019 demographics and are partially masked by averaging analysis.The online version of this article (doi:10.1186/s12904-015-0064-5) contains supplementary material, which is available to authorized users. Quality end-of-life care is increasingly viewed as a global public health problem as well as health systems problem in need of better information , 2. ThisSeveral North American and European studies explored end-of-life priorities from the point of view of patients with life-limiting illness, \u201321 outpaThree instruments have been widely used to evaluate the dying experience and explore end-of-life priorities, namely, Quality of Dying and Death (QODD), , 39, 40 The aims of this study were to explore Saudi males\u2019 opinions regarding end-of-life priorities and the usefulness of Q-methodology in this setting.This exploratory cross-sectional study was conducted in accordance with the ethical principles contained in the Declaration of Helsinki after approval of the Research Ethics Committee (REC) of the King Faisal Specialist Hospital and Research Center (KFSH&RC). All respondents provided verbal informed consent before participating in the study.The study instrument (Q-set) was developed, validated, and piloted by the authors. The initial Q-concourse (collection of opinion statements to represent possible end-of-life priorities) was constructed in Arabic language based on published conceptual frameworks , 13 and n\u2009=\u200910). Qualitative evaluation of Q-sorts after assuming extreme point of view as well as focused probing indicated that the Q-sorts reflected sorters\u2019 point of view.Criterion validity does not apply to Q-methodology because of its subjective nature. Content validity was examined thorough literature review and by eliciting domain experts\u2019 advice. Reliability was studied through test-retest assessment, re-sorting after assuming certain extreme points of view , and focused probing in an interview session following completion of Q-sorts. Participants were asked to Q-sort the same Q-set three times: first according to their point of view, then after assuming a certain extreme point of view, and finally according to their point of view for a second time (without prior knowledge that the Q-sorting will be repeated). The aim was to ensure that the results are reproducible and reflect the point of view of the sorter rather than being a function of the particular Q-set used. Intra-individual correlation coefficient was consistently more than 0.8 (n\u2009=\u20097), treatment preferences (n\u2009=\u20095), whole-person-concerns (n\u2009=\u20098), moment of death (n\u2009=\u20095), family/friends (n\u2009=\u20096), achieving sense of completion/spirituality/religiosity (n\u2009=\u20095), preparation for death (n\u2009=\u20095), and relationship with healthcare professionals (n\u2009=\u20096). The first three domains are most related to life quality vs quantity concerns, the fourth and fifth to connectedness, the sixth to transcendence, the seventh to coping, and the eighth to information-disclosure and decision-making. An English translation (accuracy confirmed by back translation) of the final Q-set is available in Additional file The developed Q-set and sorting instructions were piloted on 20 Saudis of different demographics. The primary emphasis was to identify statements that are ambiguous, unclear, or leading, as well as to identify potential areas that were not covered by the initial Q-set. The Q-sorts used for validation or pilot testing were not included in this report. The final Q-set consisted of 47 statements in 8 thematic domains: symptoms and personal control  was checked and respondents were asked to correct any identified mistake.Sample size was based on convenience and practicality, consistent with Q-methodology exploratory nature. KFSH&RC Saudi employees as well as patients and patients\u2019 companions attending outpatient clinics were invited to participate through direct contact and advertisement. Saudi adults (\u226518\u00a0year old) who had completed at least a high school education, who were able to understand the purpose and procedures of the study, and who provided informed consent, were eligible to participate. The study recruited both males and females, however, due to limitation of the statistical program used for Q-methodology analysis (maximum 120 Q-sorts), and the fact that analyzing mixed male and female Q-sorts obscured important gender differences; male and female Q-sorts were analyzed separately; only the results of males are reported here.The following data were also collected: age, self-declared religiosity , general health , life quality , employment status , living arrangement , and death experience in family/close friends . Respondents also rated six statements related to attitude toward death and one statement related to life satisfaction on a 5-point scale .p\u2009<\u20090.01) loading\u2009\u2265\u20090.38 on one, and only one, factor were considered definer Q-sorts for the factor. A model Q-sort for each factor was composed from statements\u2019 scores calculated as weighted (based on factor loading) average across definer Q-sorts. This idealized Q-sort represented how a hypothesized respondent with 100\u00a0% loading on the factor would have ordered all the Q-set statements. Interpretation of factors involved comparing composite statement scores across factors and reviewing respondents\u2019 post-sorting comments. Respondents who loaded significantly on one of the identified factors were compared as groups, in regards to their age, sorting time, religiosity, general health, life quality, employment status, living arrangement, death experience in family/close friends, attitude to death, and life satisfaction. Wilcoxon Signed Ranks, student t, Mann\u2013Whitney, Kruskal-Wallis, and Fisher exact test were used to compare opinion types based on the variable examined (IBM SPSS Statistics 20). Two-tailed p values are reported.Data were verified by double entry and validity checks. As pre-specified in the study protocol, due to complexity of sorting the Q-set into nine categories, Q-sorts that took <20\u00a0min were not considered valid and were excluded from analysis. Q-sorts were analyzed by by-person centroid factor analysis , using PCQ for Windows . Data analysis in Q-methodology involves sequential application of correlation, factor analysis, and computation of factor scores . Mean (SD) sorting time was 38.2 (16.6) minutes.Main demographic data of respondents are summarized in Table\u00a0Respondents ranked 47 end-of-life opinion statements on a 9-point scale  following a systematic forced distribution , 8.7 (0.9), 6.5 (1.8), and 6.4 (1.9), respectively). Three statements in the whole-person-concerns domain: \u201cI want to die maintaining my dignity.\u201d (6.8 (1.7)), \u201cI want to die without having my body exposed.\u201d (6.3 (1.8)), and \u201cI want to die clean.\u201d (5.9 (1.7)); and one statement in the symptoms and personal control domain: \u201cI want to die free of pain.\u201d (5.7 (2.0)) also received priority scores.Four statements related to life quality/quantity, \u201cIf I go into coma, I do not want to be placed in an intensive care unit.\u201d, \u201cI want to die at the peak of my life.\u201d, \u201cI want to have no tubes inserted into my body.\u201d, and \u201cI want to live longer regardless of my medical condition.\u201d received dis-priority scores (3.5 (1.8), 3.5 (2.1), 3.9 (1.9), and 3.9 (2.0), respectively). Two statements in the family/friends domain, \u201cI want my family/friends, rather than my doctor to inform me about my impending death.\u201d and \u201cI want my medical status to be kept confidential from my family/friends.\u201d also received dis-priority scores (3.5 (1.6) and 3.5 (1.7), respectively).In the moment of death domain, one statement \u201cI want to have my family/friends with me at my last moments.\u201d received a priority score (5.9 (1.9)) and one statement \u201cI want to die in hospital.\u201d received the most extreme dis-priority score (3.0 (1.7)).Finally, three statements in the preparation for death domain, \u201cIf I have a fatal illness, I don\u2019t want to know.\u201d, \u201cI want to discuss my fears about dying with my physician.\u201d, and \u201cI want to discuss my fears about dying with my family/friends.\u201d received dis-priority scores (3.7 (2.1), 3.9 (1.6), and 4.08 (1.7), respectively). However, statement, \u201cI want to have my financial affairs in order before I die.\u201d received a priority score (6.0 (2.2)).Using the 120 Q-sorts as variables, we were able to extract 9 factors with eigenvalues higher than 1. However, it was not practical to apply all these factors for factor rotation or to meaningfully interpret them. By inspecting the scree plot  for areas of sudden decrease in eigenvalues and by logically analyzing the results after extracting 3 to 9 factors, we determined that the appropriate number of factors to extract was five. This five-factor solution accounted for 44\u00a0% of the total variance and 67\u00a0% of the 120 Q-sorts. Of the remaining Q-sorts, ten did not have significant loading on any of the factors, and 30 were confounded (loaded significantly on more than one factor).There were three consensus statements and three differentiating statements. All the five factors (opinion types) gave the most extreme priority (rounded score 9) to \u201cI want to die at peace with God.\u201d and to \u201cI want to die being able to say the statement of faith.\u201d Respondents\u2019 justification included \u201cWithout peace with God my life is worth nothing.\u201d, \u201cWe are created to worship Him\u201d, \u201cIf God is pleased, people will be pleased, so I will die with peace of mind.\u201d, \u201cIt is the dream of every Muslim.\u201d, \u201cBecause of my sins.\u201d, and \u201cTo go to Paradise.\u201d Some respondents cited the following verses from The Quran \u201cI have only created Jinns and humans, that they may serve Me. No Sustenance do I require of them, nor do I require that they should feed Me. For Allah is He Who gives  Sustenance, \u2212 Lord of Power,- Steadfast (for ever).\u201d  and some cited Prophet Muhammad\u2019s saying \u201cHe, whose last words are: there is no God but Allah will enter Paradise.\u201d All opinion types gave the same dis-priority (rounded score 2) to \u201cI want my medical status to be kept confidential from my family/friends.\u201d Statement, \u201cI want to have an Islamic clergy with me at my last moments.\u201d differentiated opinion type I from the rest , statement, \u201cI want to die being able to bathe and feed myself.\u201d differentiated opinion type III from the rest , and statement, \u201cI want to die being able to control my bladder.\u201d differentiated opinion type V from the rest .To facilitate interpretation of results, we considered that an issue was important to respondents belonging to a particular opinion type if its related statement received one of the seven highest (priority) or seven lowest (dis-priority) scores  in the model Q-sort of the opinion type. Issues related to the rest of the statements were considered non-priority. As shown in Table\u00a0The eigenvalue and explained variance for opinion type I were 8.9 and 7\u00a0%, respectively. Thirteen respondents belonged to this opinion type only; 9 respondents belonged both to this and other opinion types.In addition to the two common transcendence priorities, resolving conflicts before dying was a priority for opinion type I (in common with 2 out of the 4 other types). Respondents\u2019 justifications included \u201cSo that I would forgive/be forgiven by those whom I aggrieved/who aggrieved me.\u201d, \u201cI don\u2019t want any conflict after death.\u201d, and \u201cGood deeds/worships would not be accepted without forgiveness by others.\u201d However, in variance with the other four types, having an Islamic clergy at time of death and receiving care from religiously trustworthy professionals were the most extreme dis-priorities. Justifications included, \u201cWhat is the benefit?\u201d, \u201cIt will make me feel depressed.\u201d, \u201cI think healthcare professionals have their own code of ethics regardless of their religions.\u201d, and \u201cThere is no relation between religion and health issues.\u201d Opinion type I could be described as family-caring, since it assigned priority scores to avoiding emotional and financial burdens to family/friends and dis-priority scores to \u201cI want my family/friends rather than my doctor to inform me about my impending death.\u201d, \u201cI want my doctor to discuss any concerns related to my illness and care in the presence of my family/friends.\u201d, and \u201cI want my medical status to be kept confidential from family/friends\u201d; suggesting that they would rather inform family/friends themselves in a way that would ease their emotional burden. Justifications included \u201cThey are believers, but I want to tell them in my own way.\u201d This together with assigning a dis-priority score to \u201cIf I have a fatal illness I don\u2019t want to know.\u201d indicated a monitoring style of coping. Finally, opinion type I was life-quality-concerned, assigning priority scores to \u201cI want to die maintaining dignity.\u201d and \u201cI want to die without having my body exposed.\u201d, and dis-priority score to \u201cI want to live longer regardless of my medical condition.\u201d Justifications included, \u201cGod gave me dignity, I should maintain it.\u201d, \u201cIf I die with dignity everything else is easy, everything follows dignity and respect.\u201d, and \u201cLong life with good deeds is good thing, but life just for staying alive is not important at all.\u201d; suggesting that for this opinion type, transcendence is part of life quality.It is of note that avoidance of emotional and financial burdens to family/friends, two priorities for this opinion type, were not among the ten priorities identified by averaging analysis for the entire cohort. Further, its two most extreme dis-priorities, having an Islamic clergy at the last moments and receiving care from religiously trustworthy professionals, were not among the ten dis-priorities for the entire cohort.The eigenvalue and explained variance for opinion type II were 12.4 and 10\u00a0%, respectively. Seventeen respondents belonged to this type only; 16 respondents belonged both to this and other opinion types.This opinion type was also highly transcendent. However, in variance with opinion type I, it was described as rituals-apt as it gave priority scores to \u201cI want my religious death rituals to be respected\u201d and \u201cI want to have an Islamic clergy with me at my last moments.\u201d Justifications for the later included, \u201cTo remind me and presage me.\u201d, \u201cHis presence will remind me of the statement of faith and to ask for forgiveness.\u201d, and \u201cGood thing to have, maybe he will help me (after God), to ease death and prepare to meet God.\u201d Opinion type II could be described as family-dependent, as it gave priority score to \u201cI want to have my family/friends with me at my last moments.\u201d and dis-priority scores to \u201cI want to die in the hospital.\u201d and \u201cI want my medical status to be kept confidential from my family/friends.\u201d Justifications included, \u201cI just want my family with me. It is not important where I die.\u201d and \u201cThe opposite is true, they should know everything.\u201d This opinion type strongly opposed \u201cIf I have a fatal illness I don\u2019t want to know.\u201d and strongly embraced \u201cI want to have my financial affairs in order before I die.\u201d; indicating a monitoring coping style. Justifications included, \u201cI want to be prepared.\u201d, \u201cTo the contrary, I should know.\u201d \u201cI need to know to seek treatment.\u201d, \u201cIllness is a test just as health is, knowing will rejuvenate faith.\u201d, and \u201cFatal illness is a test and there would be big rewards for people who are patients.\u201d for the first and \u201cIt affects my next life.\u201d, \u201cI will be questioned about it.\u201d, \u201cI don\u2019t want conflict between my children.\u201d, \u201cIt is a debt in my neck.\u201d, \u201cFinancial matters may be a burden on me in my next life and in my grave.\u201d, and \u201cDebt is the most important thing one leaves after death, we will be stopped in front of God till the debt is given back.\u201d for the second. Finally, it reacted strongly against \u201cI don\u2019t want to be kept on life support when there is little hope for a meaningful recovery\u201d, \u201cI want to have no tubes inserted into my body\u201d, and \u201cIf I go into coma, I don\u2019t want to be placed in an intensive care unit.\u201d Justifications included, \u201cI don\u2019t care, I want cure at any price.\u201d; \u201cIt is not a shame.\u201d, \u201cIt is not important what is inserted in the body.\u201d; \u201cIt is the doctor decision not mine.\u201d, \u201cIt provides better care.\u201d, and \u201cWhen in coma, the decision is to the first of kin.\u201d This opinion type even gave dis-priority score to \u201cI want to die free of pain\u201d (justified as \u201cPain would be expected when the soul departs from the flesh.\u201d), indicating a strong life-quantity concern.Having an Islamic clergy present at the last moments, a priority for this opinion type, and no life support with little hope, the most extreme dis-priority for this opinion type, were not among the 20 priorities and dis-priorities identified by averaging analysis for the entire cohort. Further, this opinion type gave dis-priority score to \u201cI want to die free of pain\u201d, which received a priority score by averaging analysis.The eigenvalue and explained variance for opinion type III were 17.2 and 14\u00a0%, respectively. Thirty one respondents belonged to this type only; 24 respondents belonged both to this and other opinion types.Despite being also highly transcendent, opinion type III was silent (gave non-priority scores) regarding \u201cI want my religious death rituals to be respected.\u201d and \u201cI want to have an Islamic clergy with me at my last moments.\u201d It could be described as self/family-neutral, as it was also silent regarding \u201cI want to have my family/friends with me at my last moments.\u201d, \u201cI want to avoid being an emotional burden to my family/friends.\u201d, and \u201cI want to avoid being a financial burden to my family/friends.\u201d; and gave weak dis-priority scores to \u201cI want my family/friends, rather than my doctor to inform me about my impending death.\u201d and \u201cI want my medical status to be kept confidential from my family/friends.\u201d It reacted strongly against \u201cI want to discuss my fears about dying with my family/friends.\u201d and \u201cI want to discuss my fears about dying with my physician.\u201d and was silent regarding \u201cif I have a fatal illness, I don\u2019t want to know.\u201d; suggesting an avoidance coping style. In clear contrast to the other opinion types, the third highest priority for opinion type III was to be able to self bathe and feed. In addition, it gave priority scores to \u201cI want to die maintaining my dignity.\u201d, \u201cI want to die free of pain.\u201d, \u201cI want to die being able to control my bowels.\u201d, and \u201cI want to die without having my body exposed.\u201d and dis-priority score to \u201cI want to die in hospital.\u201d; suggesting a strong life-quality concern. Justifications included, \u201cI don\u2019t want to appear weak in the eyes of others.\u201d, \u201cI don\u2019t want to be a burden on others.\u201d, \u201cExposing the body is forbidden for Muslims.\u201d, \u201cI want to die at home.\u201d, \u201cRarely people get out alive, more suffering in hospital.\u201d, and \u201cI want to die at home but near a hospital.\u201d However, it also gave dis-priority scores to \u201cIf I go into coma, I do not want to be placed in an intensive care unit.\u201d and \u201cI want to die at the peak of my life.\u201d and were silent regarding \u201cI want to live longer regardless of my medical condition.\u201d; suggesting an equally strong life-quantity concern as well. Justifications included, \u201cIt is the doctor who knows and should decide.\u201d, \u201cI want to use my life to worship God and obey my parents.\u201d, \u201cIt is my goal to see my grandchildren and provide them with good life.\u201d, and \u201cI want to live longer.\u201dThis opinion type contributed the largest number of respondents to the entire cohort. Nevertheless, its third and sixth highest priorities (being able to self bathe and feed and being able to control bowels) were not among the ten priorities identified by averaging analysis.The eigenvalue and explained variance for opinion type IV were 8.6 and 7\u00a0%, respectively. Nine respondents belonged to this opinion type only; ten respondents belonged both to this and other opinion types.In communality with the other four opinion types, this opinion type was highly transcendent. In agreement with opinion type II, it gave priority score to \u201cI want my religious death rituals to be respected.\u201d It also gave priority score to \u201cI want to die clean.\u201d, and thus was classified as rituals-apt. Justifications included, \u201cBecause cleanliness originates from/is part of belief.\u201d Nevertheless, they were silent in regard to \u201cI want to have an Islamic clergy with me at my last moments.\u201d and gave dis-priority score to \u201cI want to die well dressed.\u201d Justifications included, \u201cI wish I will die pure not well-dressed because I will go into soil.\u201d, and \u201cIn the last moments, what is important is the inside (essence) not the outside (appearance).\u201d; indicating different conceptualization of death rituals. Opinion type IV can be described as self-centered; it gave dis-priority scores to \u201cI want to die at home.\u201d, \u201cI don\u2019t want to die alone.\u201d, and \u201cI want to avoid being an emotional burden to my family/friends.\u201d, and \u201cI want to die in hospital.\u201d and was silent in regards to \u201cI want to resolve any conflict before I die.\u201d and \u201cI want to avoid being a financial burden to my family/friends.\u201d Justifications included, \u201cPlace is not important, what is important is how to die.\u201d, \u201cDeath in any place is the same death.\u201d, and \u201cDeath is unavoidable; I wish I will die before my father, sibs, and friends.\u201d Interestingly, in agreement with the other four opinion types, it gave dis-priority score to \u201cI want my medical status to be kept confidential from my family/friends.\u201d, probably here in order for the family/friends to be available to help. It gave priority score to \u201cI want the doctor to inform me about my impending death before informing my family.\u201d and dis-priority score to \u201cI want my family/friends rather than my doctor to inform me about my impending death.\u201d; suggesting a strong monitoring coping style. Finally, although it gave priority scores to \u201cI want to receive medical care with compassion.\u201d and to \u201cI don\u2019t want to be kept on life support when there is little hope for a meaningful recovery.\u201d it was otherwise silent to issues related to life quantity and quality.Three priorities  and four dis-priorities  for this opinion type were not among the 20 priorities and dis-priorities identified by averaging analysis for the entire cohort.The eigenvalue and explained variance for type V were 6.9 and 6\u00a0%, respectively. Ten respondents belonged to this opinion type only; five respondents belonged both to this and other opinion types.In agreement with opinion types II and IV, opinion type V was described as rituals-apt. Respondents justifications included, \u201cEvery human wants to be shrouded and buried according to his religion.\u201d and \u201cBecause Islam respects the dead body.\u201d Opinion type V was described as family-centered (both family-dependent and family-caring), as it embraced both \u201cI want to have my family/friends with me at my last moments\u201d and \u201cI want to die knowing that my family /friends are prepared to accept my death\u201d. Justifications included, \u201cTo pray for me and to forgive me.\u201d, \u201cTo be comfortable.\u201d, \u201cI want to end with my family as I started with them.\u201d, and \u201cI expect to be happier with them.\u201d It was silent in regards to coping style and information disclosure. However, it reacted strongly against \u201cI want to die being able to control my bladder\u201d, \u201cI want to die well dressed.\u201d, \u201cI want to have no tubes inserted into my body.\u201d, \u201cIf I go into coma, I don\u2019t want to be placed in an intensive care unit.\u201d, \u201cI want to die being able to control my bowels.\u201d, \u201cI want to die at the peak of my life.\u201d, and \u201cI want to die maintaining my sense of humor.\u201d; indicating a strong life-quantity-concern. Justifications included, \u201cControlling bladder does not mean anything to me.\u201d, \u201cWhen on death bed appearance is not important.\u201d, \u201cI want tubes inserted in my body to continue my treatment.\u201d, and \u201cControlling bowels is not important at time of death.\u201d Nevertheless, it gave priority score to \u201cI want to die free of pain.\u201dOne priority (having family/friends prepared to accept death) and four dis-priorities  for this opinion type were not among the 20 priorities and dis-priorities identified by averaging analysis for the entire cohort.Contrasting normalized scores for each of the 47 statement among the five opinion types supported our interpretation of the factors. For example, normalized score differences between opinion type I  and opinion type II (life-quantity-concerned) in relation to \u201cI do not want to be kept on life support when there is little hope for a meaningful recovery.\u201d, \u201cI want to die free of pain.\u201d, \u201cI want to die maintaining my dignity.\u201d, and \u201cI want to die free of depression.\u201d were 1.79, 1.61, 1.07, 1.01, respectively. Similarly, score differences between opinion type I and opinion type V (life-quantity-concerned) in relation to \u201cI want to die maintaining my dignity.\u201d and \u201cI want to live longer regardless of my medical condition.\u201d were 1.52 and \u22121.57, respectively; and between opinion type II and type III  in relation to \u201cI want to die free of pain.\u201d, \u201cI want to die having no difficulty breathing.\u201d, \u201cI want to die free of anxiety.\u201d,, and \u201cI want to die being able to bathe and feed myself.\u201d were \u22121.84, \u22121.18, \u22121.15, and \u22121.08, respectively.In the same vein, differences in normalized scores between opinion type I  and opinion types II, IV, and V  in relation to \u201cI want an Islamic clergy with me at my last moments.\u201d, and \u201cI want to receive care from healthcare professionals whom I religiously trust\u201d were \u22122.76 and \u22121.79, \u22122.01 and \u22121.75, and \u22121.91 and \u22121.90, respectively. Similarly, differences in normalized scores between opinion type III (avoidance-coping) and opinion types I, II, and IV (monitoring-coping) in relation to \u201cI want to discuss my fears about dying with my family/friends\u201d were \u22120.44, \u22121.03, and \u22121.04, respectively.Although all five opinion types were highly transcendent there were quantitative differences. Opinion types I, II, and III were more transcendent than opinion types IV and V .Table\u00a0p\u2009>\u20090.11). There was no significant difference in sorting time (ANOVA p\u2009=\u20090.42) and borderline significant difference in age , which was due to a significant difference between opinion types I and IV (p\u2009=\u20090.04). Using Kruskal-Wallis test, there were no significant differences (p\u2009>\u20090.27) among the five opinion types in relation to religiosity, general health, life quality, life satisfaction, or death attitude, except in regard to statement \u201cI often think about dying.\u201d (p\u2009=\u20090.08). For this statement, there were significant differences (Mann\u2013Whitney U test between opinion types II and I (p\u2009=\u20090.007), II and III (p\u2009=\u20090.04), and II and V (p\u2009=\u20090.02), with opinion type II having stronger agreement with the statement than the other 3 types. Further, there were significant differences between opinion types I and IV in life satisfaction and general health .There were no significant differences among the five opinion types in relation to employment status, living arrangement, or death experience in family/close friends  by averaging analysis, the extreme ten priorities were to, be at peace with God, be able to say the statement of faith, maintain dignity, resolve conflicts, have religious death rituals respected, not have the body exposed, have financial affairs in order, die clean, have family/ friends at last moments, and die free of pain, respectively. The extreme ten dis-priorities were to, die in the hospital, not receive intensive care if in coma, die at peak of life, be informed about impending death by family/friends rather than the doctor, keep medical status confidential from family/friends, not know if one has a fatal illness, not have tubes inserted in one\u2019s body, live longer regardless of medical condition, discuss fears about dying with the physician, and discuss fear about dying with family/friends, respectively. 2) Q-methodology analysis classified 67\u00a0% of the respondents into five opinion types: rituals-averse transcendent, family-caring, monitoring-coping, life-quality-concerned; rituals-apt transcendent, family-dependent, monitoring-coping, life-quantity-concerned; rituals-silent transcendent, self/family-neutral, avoidance-coping, life-quality & quantity-concerned; rituals-apt transcendent, self-centered, monitoring-coping, life-quality/quantity-neutral; and rituals-apt transcendent, family-centered, neutral-coping, life-quantity-concerned. 3) Out of the extreme 14 priorities/dis-priorities for the five types, 29, 14, 14, 50, and 36\u00a0%, respectively, were not among the extreme 20 priorities/dis-priorities identified by averaging analysis for the entire cohort. 4) Eleven issues were identified as non-priority both on averaging analysis and Q-methodology analysis: to die having no breathing difficulty, anxiety, or depression, to receive all available treatments no matter what the chances of success are, to be able to communicate with others and referred to as a person, to avoid being a financial burden to society, to die instantaneously, to make own medical decisions, to have doctors available to answer questions, and to receive medical information regularly.Religious traditions often provide a framework for understanding death and dying as well as norms for end-of-life care. Islamic traditions, in common with Judeo-Christian traditions, view life as sacred and a mean to prepare the soul, and death as inevitable and a transition to another life. Our respondents were highly transcendent, eight of the top ten end-of-life priorities were clearly  or arguably  in the transcendence domain. In contrast, in a North American study, coming to peace with God was ranked the second or third (after freedom from pain and presence of family), depending on the subgroup studied,  and in aAccording to Islamic traditions, when a person is dying, close relatives/friends kindly remind him/her of the vast Mercy of Allah and to say the statement of faith (there is no God but Allah). Dying rituals include having the dying person to lie or sit facing toward Mecca. After death, the body is ritually washed (modesty preserved), anointed, shrouded , prayed over, and buried with a simple rite. In this study, the importance of rituals to respondents was variable. Although three opinion types were rituals-apt, one was rituals-silent and one was rituals-averse, suggesting that to some, resolving issues of faith within oneself may be more important than social or interpersonal expressions of spirituality. Further, having religious death rituals respected, but not having an Islamic clergy at the last moments, was one of the overall priorities. Furthermore, respondents who belonged to the rituals-averse and rituals-silent opinion types had lower self-declared religiosity, which is likely related to ritual practices rather than strength of beliefs or inner piety, as these two opinion types had higher normalized factor scores for \u201cI want to die at peace with God.\u201d and \u201cI want to die being able to say the statement of faith.\u201d than two of the three rituals-apt opinion types. Interestingly, in a North American study, having funeral arrangements planned received stronger importance rating from patients compared to physicians, , 13 and Arguably, sanctity of life is related not only to its intrinsic value but also to some of its qualities, such as self-consciousness, ability to establish relationship, and ability to derive pleasure . At the In our study, three out of the extreme ten dis-priorities indicated preference for life-quantity ; and one dis-priority  and four out of the extreme ten priorities  indicated preference for life-quality. Our results may be a reflection of the Islamic views of life sanctity, life as a mean to develop the soul, mandating relief of suffering whenever possible, and enduring and accepting irrelievable suffering as a spiritual reward. Nevertheless, Q-methodology showed that our respondents were not homogeneous in this regard. We were able to stratify respondents into life-quality-concerned, life-quantity-concerned (2 opinion types), life-quality and quantity-concerned, and life-quality/quantity-neutral. Preference for life quality was qualitatively associated with lower self-declared life quality, life satisfaction, and religiosity. A North American study on patients with advanced heart failure identified two distinct groups independent of functional or symptoms status, one preferring treatments that prolonged survival time and another that favored strategies that improved quality of life but reduced survival time . HoweverConceptualizing what constitute life quality may differ among individuals, individuals in different roles, and cultures. Interestingly, to die free of pain was the tenth priority for our respondents, while other physiological  and psychological  indicators of life-quality were non-priorities. Further, to die free of pain was a priority for only two of the five opinion types, and in fact a weak dis-priority for one. On the other hand, to be able to self bathe and feed, to be able to control bowels, to die clean, and to die without having body exposed were variably among the top seven priorities of the five opinion types. The importance of having pain free death has been documented in previous studies. Freedom from pain was ranked as the most important by seriously ill patients, recently bereaved family, physicians, and non-physician care providers,  higher oOne of the extreme ten priorities (to have family/close friends at last minutes) and two of the extreme ten dis-priorities  indicated the importance of connectedness to our respondents overall. Q-methodology analysis was able to group respondents into, family-caring, family-dependent, family-centered (both caring and dependent), self-centered, and self/family-neutral. A study on terminally ill men revealed heterogeneity in views about presence of others at the very end of life . WantingOverall, to die in the hospital was the most extreme dis-priority for our respondents, whereas to die at home was a non-priority. However, there was clear heterogeneity, to die in the hospital was a dis-priority for three opinion types, to die at home was a dis-priority for one opinion type, and two opinion types were silent as to the preferred place of death. Rather constant with our results, 51\u00a0%  to 84\u00a0% (Netherland) of European general public,  51\u00a0% of Five of the extreme 10\u00a0dis-priorities were related to information disclosure and coping style , indicating that overall respondents wanted to be informed about their fatal illness (but not to discuss it), to inform their family/friends about their medical condition, and to be informed before their family/friends. Nevertheless, the following were non-priorities, being able to communicate with others, having the doctor available to answer questions, and receiving medical information regularly. Our results are consistent with results in other cultures. In a North American study, preparation for the end of life was consistently rated as important by seriously ill patients, recently bereaved family, physicians, and non-physician care providers,  and abouDenying one\u2019s death fits with a medical culture that defines death as a negative outcome in the fight against disease (rather than a transition to another life); therefore, one would fear that disclosing information about a terminal illness would remove hope and may not be favored over hiding it . On the Although not to know if one has a fatal illness was a dis-priority, making own medical decisions was a non-priority for our respondents. People value the right to not have their physical, emotional, and dispositional privacy invaded (negative liberty); however, the value of decisional privacy (positive liberty) is less certain . FurtherDevelopment of an optimal instrument for studying end-of-life care continues to be a work in progress , 54. SevWe hypothesized that there are latent constellations of end-of-life choices that may be masked by averaging analysis. Indeed, we found that 29, 14, 14, 50, and 36\u00a0% of the extreme 14 priorities/dis-priorities for the five opinion types, respectively, were not among the extreme 20 priorities/dis-priorities identified by averaging analysis for the entire cohort. Using a smaller Q-set of 34 statements, a study on 37 South Korean university students\u2019 perception of good death identified four types, a resolute acceptance type, a reasonable, natural life span type, a relational, sentimental type, and an altruistic, satisfied type .This study had a number of limitations. First, it was based on convenience sampling and performed at a single tertiary healthcare institution in a major metropolitan city. Further, because forced-ranking is mentally demanding, only educated and committed individuals were suitable for the study. Thus our results could be generalized only with caution even though the institution is a governmental referral center for the entire country.Second, the study confronted rather healthy individuals with a hypothetical scenario. Responses to hypothetical scenarios may not accurately indicate what people would choose in real-life situations. However, such responses have enriched our understanding of end-of-life choices, , 32\u201337 aThird, Q-methodology is exploratory and not exhaustive in nature. Opinion types are defined as prototypical exemplars rather than as discrete categories; Q-methodology assumes neither discontinuous data nor clear cut-off points between categories. Thus the five opinion types extracted in this study should be seen as impressionistic conclusions. Further, it is likely that there are opinion types other than those identified in the study. Moreover, the prevalence of the identified opinion types among the larger population requires large sample surveys and standard analytic methods.Despite these limitations, our data support four main conclusions. 1) In young adult Saudi males transcendence was the extreme end-of-life priority, and dying in the hospital was the extreme dis-priority. 2) Quality of life was conceptualized differently with less emphasize on its physiological aspects. 3) Disclosure of terminal illness to family/close friends was preferred as long it is through the patient. 4) Q-methodology identified five types of constellations of end-of-life priorities and dis-priorities that may be related to respondents\u2019 demographics and are partially masked by averaging analysis. The results emphasize the need to consider broader quality of life meanings as well as patients\u2019 faith and religion to achieve the goal of quality death and dying. Patient-centered approaches to end-of-life care needs to take into account the identified priorities, dis-priorities, and typologies to sensitize health workers caring for Muslims/ Middle Eastern patients. This is the first study, to our knowledge to assess end-of-life priorities in such cultures; our findings need to be expanded and confirmed. The results also emphasize diversity in prioritizing end-of-life issues; one average opinion profile may not be useful as concerns can appear in varying combinations and hierarchy."}
+{"text": "Acta Cryst. (2016), E72, 976\u2013979.Erratum to  et al. , the name and affiliation of one of the authors is incorrect.In the paper by \u00c7elik"}
+{"text": "Moreover, we propose a D-delay transmission strategy to ensure that every packet can be delivered to its destination nodes with limited delay. Different from most existing network schemes, our network model has a novel two-tier architecture. The existence of helping nodes greatly improves the network capacity. Four types of mobile networks are studied in this paper: i.i.d. fast mobility model and slow mobility model in two-dimensional space, i.i.d. fast mobility model and slow mobility model in three-dimensional space. Using the virtual channel model, we present an intuitive analysis of the capacity of two-dimensional mobile networks and three-dimensional mobile networks, respectively. Given a delay constraint D, we derive the asymptotic expressions for the capacity of the four types of mobile networks. Furthermore, the impact of D and m to the capacity of the whole network is analyzed. Our findings provide great guidance for the future design of the next generation of networks.This paper investigates the capacity problem of heterogeneous wireless networks in mobility scenarios. A heterogeneous network model which consists of  Their finding implies that as the size of the network goes to infinity, the per-node throughput will decrease to zero. Following this work, extensive studies have been conducted to achieve a tighter capacity bound . We have the following theorem:Theorem\u00a02.\u00a0In two-dimensional i.i.d fast mobility model, without considering relaying progress, we can bound the number of bits directly delivered to destination nodes as:Proof.\u00a0Consider inequality Equation (3), according to the Cauchy-Schwarz inequality, we have:Now we investigate the throughput capacity contributed by iX and jX, let dist(t) denote their distance in time slot t. Based on the assumption that the mobility model are i.i.d, we have:The inequality above gives a bound on the expected distance which the bits take. For two arbitrary nodes T time slots, we have:In W1 bits in single time slot, hence we can obtain:The network can carry at most According to the inequalities above, we have:By Jensen\u2019s inequality, combining inequality Equation (4) and inequality Equation (5), we can obtain the following inequality:Let E[\u039bd[T]]. \u25a1Simplify the inequality above, we can obtain Theorem\u00a03.\u00a0In two-dimensional i.i.d fast mobility model, if packet relaying exists, the bound on the number of bits transmitted to the destination number through relay nodes is:D is delay constant.Proof.\u00a0T time slots, let \u039br[T] denote the number of bits which are transmitted from relay nodes to destination nodes in T time slots, we have \u039b[T] = \u039br[T] + \u039bd[T]. According to Cauchy-Schwarz inequality and inequality Equation (3), we obtain:In Theorem 2 has given number of bits directly delivered to destination nodes. Now we consider the scenario where packets can be relayed in the networks.B, let Bd denote its destination node and Be denote the node storing bit B. We assume that from time slot Bt to time slot Bt + D \u2212 1, the minimum distance between Bd and Be is BL. Then we have:Consider bit B which is in the set R[T], we have:For an arbitrary bit According to Taylor\u2019s formula, equality Equation (14) can be expressed as:Therefore, we obtain:Obviously, we have:Combining Equations (7) and (8), we have:Hence, we can obtain the following inequalities:According to Jensen's inequality, combining inequality Equation (6) and inequality Equation (9), we have:E[\u039br[T]]. \u25a1Theorem\u00a04.\u00a0In two-dimensional i.i.d. fast mobility networks, the ad hoc transmission mode capacity is:Proof.\u00a0Combining Theorems 2 and 3, we have:Let In the meaning of order, the throughput capacity contributed by relaying nodes plays a dominating role compared with the throughput without relaying node. Thus, we have Theorem\u00a05.\u00a0In two-dimensional networks, the per-node throughput helping transmission mode contributes is:Proof.\u00a0p, q) as the source and the helping node on  as the destination. In our network model, two neighbor helping nodes can communicate directly, hence the minimum number of hops is h = |p \u2212 i| + |j \u2212 q|. Summing up all the possible h, we have:E[|p \u2212 i|] can be obtained by the following equation:Since the node distribution is i.i.d., each helping node is chosen as a source or a destination with the same probability. We randomly choose the helping node on  and (12) into Equation (10), we have:W2, for each helping node, it can carry at most W2 bits in each time slot. Thus, we have:H\u03bb is the per-node throughput capacity of backbone helping node.Since the bandwidth of uplink sub-channel is iY, its interference region is a circle with radius (1 + \u0394H)Hr. Each helping node occupies a region of iY is:For an arbitrary helping node iY is bounded by c8 = c7 \u2212 1. It implies that there exists a temporal and spatial scheduling strategy that every helping node can obtain at least one slot to communicate in every (1 + c8) slots. Therefore, we have:Hence the number of nodes interfered by Combining Equations (14) and (15), we can obtain the per-node throughput capacity of backbone:\u03bb = A\u03bb(n) + H\u03bb(m). According to Theorems 4 and 5, we can obtain Theorem 6 as follows:Theorem\u00a06.\u00a0In two-dimensional i.i.d. fast mobility networks, under protocol model, the network capacity is:Proof.\u00a0Combining Theorems 4 and 5, we can prove the theorem above. \u25a1Since the total throughput capacity is contributed by multi-hop mode and helping mode, we have Theorem\u00a07.\u00a0In two-dimensional i.i.d. slow mobility networks, we have the following inequalities:Proof.\u00a0Similarly with the proof of Theorem 1, we can prove the theorem above. \u25a1Similar to the fast mobility model, we can calculate the throughput capacity of slow mobility model. First we present some important inequalities, as shown in Theorem 7:Theorem\u00a08.\u00a0In two-dimensional i.i.d. slow mobility networks, if relaying progress is not allowed, the number of bits directly delivered to destination nodes is bounded as follows:Proof.\u00a0According to Theorem 1 and the Cauchy-Schwarz inequality, we have:First we consider the case that all the packets are directly transmitted to the destination nodes without relaying.Since Similar to the analysis in Theorem 2, the following inequality can be obtained:Combining inequality Equation (18) and inequality Equation (19), we have:Let Theorem\u00a09.\u00a0In two-dimensional i.i.d. slow mobility network model, if packet relaying is allowed, the bound on the number of bits which are transmitted successfully from relay nodes to destination nodes is as follows:Proof.\u00a0Similar to the steps in capacity analysis of network capacity of two-dimensional i.i.d. fast mobility networks, we have:Simplify the inequality above, we can obtain Theorem 8. \u25a1Therefore, we can obtain the following inequalities:Combining inequality Equation (18) and inequality Equation (20), we have:Theorem\u00a010.\u00a0In two-dimensional i.i.d. slow mobility networks, the throughput capacity contributed by ad hoc transmission mode is:Proof.\u00a0Combining Theorems 9 and 10, we have:Let Inequality Equation (21) then follows the proof of Theorem 4. \u25a1Theorem\u00a011.\u00a0In two-dimensional i.i.d. slow mobility networks, under protocol model, the capacity is:Proof.\u00a0Combining Theorems 5 and 10, we can prove the theorem above. \u25a1Theorem 5 has given the throughput capacity contributed by backbone networks. Combining the results of Theorems 5 and 10, we can obtain the network capacity of two-dimensional i.i.d. slow mobility networks:Theorem\u00a012.\u00a0In three-dimensional i.i.d fast mobility model, we have:Proof.\u00a0The proof progress is similar with Theorem 1. \u25a1Theorem\u00a013.\u00a0In three-dimensional i.i.d fast mobility model, we can obtain that the bounds on the number of bits directly delivered to destination nodes by ad hoc transmission mode:Proof.\u00a0According to the Cauchy-Schwarz inequality, we can obtain the following inequality:Inequality Equation (1) and inequality Equation (2) which hold in two-dimensional networks are also suitable for three-dimensional networks. However, in three-dimensional i.i.d fast mobility model, we should modify inequality Equation (3) to analyze the network capacity of the networks.Since the node distribution is i.i.d in a three-dimensional space, according to the knowledge of Probability Theory, we have that:According to the inequality above, we conclude that:W1 bits. Hence we have:In single time slot, each node can carry at most Taking expectation on the inequality above, we have:Combining inequality Equation (23) and inequality Equation (24), we have:Let Then Theorem 14 can be proved by simplifying the inequality above. \u25a1ad hoc mode considering relaying progress.Theorem\u00a014.\u00a0In three-dimensional i.i.d fast mobility networks, if relaying exists, we can obtain the bound on the number of bits successfully delivered to the destination nodes through relay nodes as follows:D is the delay constant.Proof.\u00a0According to the Cauchy-Schwarz inequality and inequality Equation (48), we have the following inequalities:Next we study the throughput contributed by B, in time , let Be and destination node Bd, i.e.:Consider bit Since the node distribution is i.i.d in each time slot, we have:Using the Taylor formula, we can obtain the following inequality:Then we can get the bound on the expectation of the number of bits which satisfy Since Furthermore, we have:Combining inequality Equation (25) and inequality Equation (26), we can obtain the following inequalities:Let ad hoc transmission mode:Theorem\u00a015.\u00a0In three-dimensional i.i.d. fast mobility networks, the ad hoc transmission mode capacity is:Proof.\u00a0ad hoc transmission mode as follows:Based on Theorems 13 and 14, we have the total number of bits transmitted by Combining Theorems 13 and 14, we can obtain the capacity contributed by ad hoc transmission mode:According to the definition of order, we can obtain the capacity contributed by Theorem\u00a016.\u00a0In three-dimensional networks, the per-node throughput capacity contributed by the backbone network is:Proof.\u00a0p, q, u) and the helping node on  as source and destination respectively. Hence we have that the expectation of the hops is E[h] = 3E[E[|p \u2212 i|]].In three-dimensional backbone network, we randomly choose the helping node on  in Theorem 7 is suitable for the three-dimensional i.i.d. slow mobility network. Besides, we have the following inequality which will be used in the following analysis:Now we consider the three-dimensional i.i.d. slow mobility networks. Similar to the method used in network capacity analysis of two-dimensional i.i.d. slow mobility networks, we first calculate the bounds on the number of bits which are directly transmitted from source nodes to destination nodes without packet relaying. Furthermore, we analyze the number of bits which are delivered successfully from relay nodes to destination nodes.Hence, we have:As Similar to the steps in Theorem 8, we have:Therefore, we can conclude that:Theorem\u00a019.\u00a0In three-dimensional i.i.d. slow mobility networks, if packet relaying is allowed, we have the following inequality:Proof.\u00a0Similar to the proof process, we have:Let Hence, we have the following inequalities:Based on the argument of Theorem 1, we have:Hence, we have:Theorem\u00a020.\u00a0In three-dimensional i.i.d. slow mobility networks, the capacity contributed by ad hoc transmission mode is:Proof.\u00a0Similar to the proof of Theorem 4, we have:Let Hence we have Theorem\u00a021.\u00a0In three-dimensional i.i.d slow mobility networks, under the protocol model, the capacity is:Proof.\u00a0Combining Theorems 16 and 20, we can prove the theorem above. \u25a1Theorem 16 implies that in three-dimensional networks, the capacity contributed by helping transmission mode is We have obtained the capacities of the four types of heterogeneous mobile networks in this section. By analyzing these capacity expressions, we will get some interesting conclusions. The analysis is presented in the following section.n, D and m to the network capacity. Firstly we list the capacity contributed by ad hoc transmission mode as follows: in two-dimensional i.i.d. fast mobility model, we have A\u03bb(n) of the four types of networks. In the Section above we have obtained the throughput capacity of the four types of mobile networks. In this section we analyze the impact of some important parameters such as A\u03bb(n) and n is shown in n goes to infinity, the number of mobile nodes offers many opportunities for source nodes to meet destination nodes, even in slow mobility networks. Hence, if the number of mobile nodes is large enough, the capacities of the four types of networks are similar.The relationship of D = \u03a9(n2), we have A\u03bb = \u0398(1). In this case, the four types of mobile networks have the same capacity, which is \u0398(1). It means that in delay tolerant networks, the network capacity can achieve constant order, and the price is that the delay will go to infinity. Of course, the delay constraint D is approximated in the analysis above. Concretely, in two-dimensional mobile network model, D = \u03a9(n); in three-dimensional mobile network model, D = \u03a9(n2). However, since n is assumed to be large enough, D is not limited in both the two cases.Let D = O(n), we have A\u03bb = 0. In this case, the capacity will decrease to zero as n goes to infinity. Concretely, in two-dimensional mobile network model, D = O(n); in three-dimensional network model, D = O(n2). It implies that if the delay is assumed to be very small, the number of bits transmitted by ad hoc transmission mode is very little. Our analysis is shown in Let D falls in between O(n) and \u03a9(n), there is a positive correlation between A\u03bb and the delay constraint. Theorems 5 and 16 offer the throughput capacity of backbone networks. When (1)In two-dimensional networks:Combining the analysis above, we reach the following conclusions:D = \u03a9(n), the capacity is m = \u03a9(n), most of packets can be delivered to the destination nodes with the help of backbone network. It implies that if the number of helping nodes is large enough, network capacity can stay constant order, and the delay can be limited, too. Similarly, if m = o(n), most of the packets will be transmitted by ad hoc transmission mode. It means that if the number of helping nodes is small, though the capacity is also constant order, the delay can not be ensured.If the delay is allowed to be larger than some fixed constant D = \u03a9(n)), the network capacity is (2)In three-dimensional mobile networks:If the delay is limited , which means that the network capacity of the whole network can achieve a constant order. If D is constrained, the capacity contributed by ad hoc mode is almost zero and most of packets have to be delivered by helping transmission mode.We can reach similar conclusions to two-dimensional mobile networks. According the analysis above, we can conclude that the number of helping nodes in the network is a key factor which affects the throughput capacity. If the number of helping nodes is large enough, the capacity can stay constant with the help of the backbone network. In this case, the time delay can be ensured. If the number of helping node is small, most of the packets have to be delivered in multi-hop fashion. In this case, though the throughput capacity can achieve constant order too, the delay will go to infinity. The delay constraint D is not limited and D is limited, where D is the delay constraint. We find that if D is not limited, the capacity contributed by ad hoc transmission mode can achieve constant order, while the price is that the delay will go to infinity. If D is limited, the capacity contributed by ad hoc transmission mode will decrease to zero. Hence there is a positive correlation between the throughput capacity and D. We also find that the number of helping nodes in the network is an important factor on the network capacity greatly. If the number of helping nodes is large enough, most of packets can be transmitted by helping transmission mode. In this condition the network capacity can achieve constant order without a long time delay. If the number of helping nodes is small, most of packets have to be transmitted by helping transmission mode, and the time delay can not be ensured.In this paper we propose a new heterogeneous mobile network architecture, which is composed of normal nodes and more powerful helping nodes. Four types of mobile network model are investigated: two-dimensional i.i.d. fast mobility model, two-dimensional i.i.d. slow mobility model, three-dimensional i.i.d. fast mobility model and three-dimensional i.i.d. slow mobility model. First we provide a brief description of our network model. We analyze the throughput capacity of the four types of network model intuitively by virtual channel systems. Then we obtain the network capacity by strict mathematical proof respectively. We find that the throughput capacity is"}
+{"text": "Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron\u2019s probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as \u201csingle-spike information\u201d to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex. A popular approach to the neural coding problem is to identify a low-dimensional linear projection of the stimulus space that preserves the aspects of the stimulus that affect a neuron\u2019s probability of spiking. Previous work has focused on both information-theoretic and likelihood-based estimators for finding such projections. Here, we show that these two approaches are in fact equivalent. We show that maximally informative dimensions (MID), a popular information-theoretic method for dimensionality reduction, is identical to the maximum-likelihood estimator for a particular linear-nonlinear encoding model with Poisson spiking. One implication of this equivalence is that MID may not find the information-theoretically optimal stimulus projection when spiking is non-Poisson, which we illustrate with a few simple examples. Using these insights, we propose novel dimensionality-reduction methods that incorporate non-Poisson spiking, and suggest new parametrizations that allow for tractable estimation of high-dimensional subspaces. The neural coding problem, an important topic in systems and computational neuroscience, concerns the probabilistic relationship between environmental stimuli and neural spike responses. Characterizing this relationship is difficult in general because of the high dimensionality of natural signals. A substantial literature therefore has focused on dimensionality reduction methods for identifying which stimuli affect a neuron\u2019s probability of firing. The basic idea is that many neurons compute their responses in a low dimensional subspace, spanned by a small number of stimulus features. By identifying this subspace, we can more easily characterize the nonlinear mapping from stimulus features to spike responses \u20135.K, such that the probability of response r given a stimulus s depends only on the linear projection of s onto these filters, i.e., p(r|s) \u2248 p(r|K\u22a4s). Existing methods differ in computational complexity, modeling assumptions, and stimulus requirements. Typically, moment-based estimators have low computational cost but succeed only for restricted classes of stimulus distributions, whereas information-theoretic and likelihood-based estimators allow for arbitrary stimuli but have high computational cost. Previous work has established theoretical connections between moment-based and likelihood-based estimators [Neural dimensionality-reduction methods can be coarsely divided into three classes: 1) moment-based estimators, such as spike-triggered average (STA) and covariance (STC)  moment-b\u20138; (2) mtimators , 19, 23,timators , 21, 24.Here we focus on maximally informative dimensions (MID), a well-known information-theoretic estimator introduced by Sharpee, Rust & Bialek . We showThe connection between the MID estimator and the LNP model makes clear that MID does not incorporate information carried by non-Poisson statistics of the response. We illustrate this shortcoming by showing that MID can fail to find information-maximizing filters for simulated neurons with binary or other non-Poisson spike count distributions. To overcome this limitation, we introduce new dimensionality-reduction estimators based on non-Poisson noise models, and show that they can be framed equivalently in information-theoretic or likelihood-based terms.Finally, we show that a model-based perspective leads to strategies for overcoming a limitation of traditional MID, that it cannot tractably estimate more than two or three filters. The difficulty arises from the intractability of using histograms to estimate densities in high-dimensional subspaces. However, the single-spike information depends only on the ratio of densities, which is proportional to the nonlinearity in the LNP model. We show that by restricting the parametrization of this nonlinearity so that the number of parameters does not grow exponentially with the number of dimensions, we can obtain flexible yet computationally tractable estimators for models with many filters or dimensions.Linear-nonlinear cascade models provide a useful framework for describing neural responses to high-dimensional stimuli. These models define the response in terms of a cascade of linear, nonlinear, and probabilistic spiking stages see . The lin\u03b8 = {K,\u03b1} denote the parameters of the LNP model, where K is a  matrix whose columns contain the stimulus filters , and \u03b1 are parameters governing the nonlinear function f from feature space to instantaneous spike rate. Under this model, the probability of a spike response r given stimulus s is governed by a Poisson distribution:\u03bb denotes the stimulus-driven spike rate  and \u0394 denotes a time bin size. The defining feature of a Poisson process is that responses in non-overlapping time bins are conditionally independent given the spike rate. In a discrete-time LNP model, the conditional probability of a dataset D = {}, consisting of stimulus-response pairs indexed by t \u2208 {1,\u2026,N}, is the product of independent terms. The log-likelihood is therefore a sum over time bins:rt!) is a constant that does not depend on \u03b8. The ML estimate for \u03b8 is simply the maximizer of the log-likelihood: Let Iss, is the the average information that the time of a single spike (considered independently of other spikes) carries about the stimulusThe maximally informative dimensions (MID) estimator seeks to find an informative low-dimensional projection of the stimulus by maximizing an information-theoretic quantity known as the single-spike information . This qup(s) denotes the marginal or \u201craw\u201d distribution over stimuli, and p(s|spike) is the distribution over stimuli conditioned on observing a spike, also known as the \u201cspike-triggered\u201d stimulus distribution. Note that p(s|spike) is not the same as p(s|r = 1), the distribution of stimuli conditioned on a spike count of r = 1, since a stimulus that elicits two spikes will contribute twice as much to the spike-triggered distribution as a stimulus that elicits only one spike.Although first introduced as a quantity that can be computed from the peri-stimulus time histogram (PSTH) measured in response to a repeated stimulus, the single-spike information can also be expressed as the Kullback-Leibler (KL) divergence between two distributions over the stimulus  and p(K\u22a4s|spike) are the raw and spike-triggered stimulus distributions projected onto the subspace defined by the columns of K, respectively. In practice, the MID estimator maximizes an estimate of the projected single-spike information:\u00cess(K) denotes an empirical estimate of Iss(K). The columns of The MID estimator  seeks top(s) and p(s|spike), is exactly the ML estimator for the parameters of an LNP model, regardless of spike rate, the time bins used to count spikes, or the amount of data.Previous work has shown that MID converges asymptotically to the maximum-likelihood (ML) estimator for an LNP model in the limit of small time bins , 24. Herp(K\u22a4s) and p(K\u22a4s|spike). These density estimates are then used to compute \u00cess(K), the plug-in estimate of single-spike information in a subspace defined by K  that partition the range of the projected stimuli K\u22a4s. In the one-dimensional case, we typically choose these sets to be intervals Bi = [bi\u22121,bi), defined by bin edges {b0, \u2026, bm}, where b0 = \u2212\u221e and bm = +\u221e. Then let p(K\u22a4s) and p(K\u22a4s|spike), respectively, given by:xt = K\u22a4st denotes the linear projection of the stimulus st, 1Bi(\u22c5) is the indicator function for the set Bi, defined as:Let {\u011d(x) denotes the ratio of density estimates:The estimates \u011d(x) is a piece-wise constant function that takes the value q\u0302i/p\u0302i over the ith histogram bin Bi.Note that f is parametrized as a piece-wise constant function, taking the value fi over histogram bin Bi. Given a projection matrix K, the ML estimate for the parameter vector \u03b1 =  is the average number of spikes per stimulus in each histogram bin, divided by time bin width \u0394, that is:lnp denotes the Poisson log-likelihood under a \u201cnull\u201d model in which spike rate does not depend on the stimulus, but takes constant rate lnp can be considered an estimate for the marginal entropy of the response distribution, Iss can be equally regarded as \u201cLNP information\u201d.Now, consider an LNP model in which the nonlinearity kelihood :\u2112lnp, meaning that the MID estimate is the same as an ML estimate for the filters in an LNP model:Empirical single-spike information is therefore equal to LNP model log-likelihood per spike, plus a constant that does not depend on model parameters. This equality holds independent of time bin size \u0394, the number of samples \u00cess, correspond to a particular parametrization of the LNP model nonlinearity f as a piece-wise constant function over histogram bins. The ratio of these plug-in estimates gives rise to the ML estimate for f. MID is thus formally equivalent to an ML estimator for both the linear filters and the nonlinearity of an LNP model.Moreover, the histogram-based estimates of the raw and spike-triggered stimulus densities Iss and yields large errors in the filter estimate. Even with 1000 stimuli and 200 spikes, a 20-bin histogram gives substantial upward bias in the estimate of single-spike information } isK has a single filter and the nonlinearity is restricted to be a logistic function, f(x) = 1/(1+exp(\u2212x)), this reduces to the logistic regression model. Note that the spike probability \u03bb is analogous to the single-bin Poisson rate \u03bb\u0394 from the LNP model (p(r = 1) goes to zero [We can define the linear-nonlinear-Bernoulli (LNB) model by analogy to the LNP model, but with Bernoulli instead of Poisson spiking. The parameters NP model , and the to zero , 26.x = K\u22a4s and a Bernoulli spike response r \u2208 {0,1} is given by:Iss is the single-spike information  and p(x), weighted by (N\u2212nsp)/nsp, the ratio of the number of silences to the number of spikes. It is straightforward to show that empirical Bernoulli information equals the LNB model log-likelihood per spike plus a constant:\u03b8, the maximum of the empirical Bernoulli information is identical to the maximum of the LNB model likelihood, meaning that once again, we have an exact equivalence between likelihood-based and information-based estimators.Let ormation , and \u00ce0\u00ce0 > 0 and these spike absences are neglected by the single-spike information measure. Only in the limit of infinitesimal time bins, where p(r = 1) \u2192 0, does \u00ceBer converge to \u00cess[\u00cess, and the LNB filter estimate The empirical Bernoulli information is strictly greater than the estimated single-spike (or \u201cPoisson\u201d) information for a binary spike train that is not all zeros or ones, since e to \u00cess, 26. As \u03bb increases linearly as a function of stimulus angle: \u03bb = (s\u2212\u03c0/2)/\u03c0, for s \u2208  and \u00ce0 (silences) as a function of projection angle, which illustrates the relative biases of the two quantities.The first example  uses stis1 and suppressive in stimulus axis s2 . For this neuron, both stimulus axes are clearly informative, but the  axis s2 carries 13% more information than the  axis s1. However, the standard MID estimator identifies s1 as the most informative axis  carried by silences, as a function of marginal probability of a spike, p(r = 1).In the limit of infinitesimal time bins, the information carried by silences goes to zero, and the plug-in estimates for Bernoulli and single-spike information converge: p(r = 1) \u2192 0, we find that:p(r = 1) (see p(r = 1). The bound is tight in the Poisson limit, p(r = 1) \u2192 0, but is substantially loose in the limit where spiking is common p(r = 1) \u2192 1, in which all information is carried by silences. In the limit of rare spiking, For neural responses binned at the stimulus refresh rate , it is not uncommon to observe multiple spikes in a single bin. For the general case, then, we must consider an arbitrary distribution over counts conditioned on a stimulus. As we will see, maximizing the mutual information based on histogram estimators is once again equivalent to maximizing the likelihood of an LN model with piece-wise constant mappings from the linear stimulus projection to count probabilities.s with a spike count r \u2208 {0,\u2026,rmax}, where rmax is the maximum possible number of spikes within the time bin (constrained by the refractory period or firing rate saturation). The linear-nonlinear-count (LNC) model, which includes LNB as a special case, is defined by a linear dimensionality reduction matrix K and a set of nonlinear functions {f(0) \u2026, frmax)((x) = 1,\u2200x, since the probabilities over possible counts must add to 1 for each stimulus.Suppose that a neuron responds to a stimulus \u03b8 = , \u2026 \u03b1rmax) given data D = {} can be written:1j(rt) is an indicator function selecting time bins t in which the spike count is j. As before, we consider the case where fj). The Icount estimator, by contrast, is sensitive to the non-Poisson statistics of the response, and combines information from all spike counts  , 7, infowhy MID is impractical for high-dimensional feature spaces. The problem isn\u2019t the number of filter parameters: these scale linearly with dimensionality, since a p-filter model with D-dimensional stimuli requires only Dp parameters, or indeed only p(x) and p(x|spike). For histogram-based density estimators, the number of parameters grows exponentially with dimension: a histogram with m bins along each of p filter axes requires mp parameters, a phenomenon sometimes called the \u201ccurse of dimensionality\u201d.Before we continue, it is helpful to consider p(x|spike) and p(x) to a single nonlinear function f. This change in focus makes it easier to scale the likelihood approach to high dimensions for a few different reasons. First, direct estimation of a single nonlinearity in place of two densities immediately halves the number of parameters required to achieve a similarly detailed picture of the neuron\u2019s response to the filtered stimulus. Second, the dependence of the MID cost function on the logarithm of the ratio p(x|spike)/p(x) makes it very sensitive to noise in the estimated value of the denominator p(x) when that value is near 0. Unfortunately, as p(x) is also the probability with which samples are generated, these low-value regions are precisely where the fewest samples are available. This is a common difficulty in the empirical estimation of information-theoretic quantities, and others working in more general machine-learning settings have suggested direct estimation of the ratio rather than its parts [A key benefit of the LNP model likelihood framework is that it shifts the focus of estimation away from the separate densities ts parts \u201333. In Lf  instead of regularizing the estimates of stimulus densities. For example, consider an experiment using natural visual images. While natural images presumably form a smooth manifold within the space of all possible pixel patterns, the structure of this manifold is neither simple nor known. The natural distribution of images does not factor over disjoint sets of pixels, nor over linear projections of pixel values. A small random perturbation in all pixels makes a natural image appear unnaturally noisy, violating the underlying presumption of kernel density estimators that local perturbations do not alter the density much. Indeed the question of how best to model the distribution of natural stimuli is a matter of active research. By contrast, we might expect to be able to develop better parametric forms to describe the non-linearities employed by neural systems. For instance, we might expect the neural nonlinearity to vary smoothly in the space of photoreceptor activation, and thus of filter outputs. Thus, locally kernel-smoothed estimates of the non-linear mapping\u2014or even parametric choices of function class, such as low-order polynomials\u2014might be valid, even if the stimulus density changes abruptly. Alternatively, subunits within the neural receptive field might lead to additively or multiplicatively separable components of the nonlinearity that act on the outputs of different filters. In this case, it would be possible to factor f between two subsets of filter outputs, say to give f(x) = f1(x1)f2(x2), even though there is no reason for the stimulus distribution to factor p(x) \u2260 p(x1)p(x2). This reduction of f to two (or more) lower-dimensional functions would avoid the exponential parameter explosion implied by the curse of dimensionality.Third, \u2026 as the nonlinearity is a property of the neuron rather than the stimulus, it may be more straightforward to construct a smoothed or structured parametrization for f is parametrized by a quadratic form embedded in a 1D nonlinearity [f as a sum of one-dimensional nonlinearities, in which case the number of parameters grows only linearly with the number of filters.Indeed, such strategies for parametrization of the nonlinear mapping are already implicit in likelihood-based estimators inspired by the spike-triggered average and covariance. In many such cases, inearity , so thatinearity , 22, 24.inearity , parametf is parametrized using basis functions {\u03c6i(\u22c5)}, i = 1,\u2026,n\u03c6, which are linearly combined with weights \u03b1i and then passed through a scalar nonlinearity g. We refer to g as the output nonlinearity; its primary role is to ensure the spike rate \u03bb is positive regardless of weights \u03b1i. This can also be considered a special case of an LNLN model [Here we provide a general formulation that encompasses both standard MID and constrained methods that scale to high-dimensional subspaces. We can rewrite the LNP model  as folloLN model , 34, 35.g and the basis functions {\u03c6i} in advance, fitting the nonlinearity simply involves estimating the parameters \u03b1i from the projected stimuli and associated spike counts. If g is convex and log-concave, then the log-likelihood is concave in {\u03b1i} given K, meaning the parameters governing f can be fit without getting stuck in non-global maxima [If we fix l maxima .g to the identity function and the basis functions \u03c6i to histogram-bin indicator functions (denoted 1Bi(\u22c5) in i\u2019th histogram bin , cubic splines, radial basis functions, or any mixture of these bases. Alternatively, we could use non-parametric models such as Gaussian processes, which have been used to model low-dimensional tuning curves and firing rate maps , 37. TheWe propose to parametrize the nonlinearity for many-filter LNP models using cylindrical basis functions (CBFs), which we introduce by analogy to radial basis functions (RBFs). These functions are restricted in some directions of the feature space (like RBFs), but are constant along other dimensions. They are therefore the function-domain analogues to the probability \u201cexperts\u201d used in product-of-experts models  in that \u03bc and a characteristic width \u03c3:xi and is invariant along xj \u2260 i. Parametrizing f with first-order CBFs is tantamount to assuming f can be parametrized as the sum of 1D functions along each filter axis, that is f(x) = g(f1(x1) + \u2026 fm(xm)), where each function fi is parametrized with a linear combination of \u201cbump\u201d functions. This setup resembles the parametrization used in the extended projection-pursuit regression (ePPR) model [g confers some added flexibility. For example, we can have multiplicative combination when g(\u22c5) = exp(\u22c5), resulting in a separable f, or rectified additive combination when g(\u22c5) = max, which is closer to ePPR. If we use d basis functions along each filter axis, the resulting nonlinearity requires kd parameters for a k-filter LNP model.We define a \u201cfirst-order\u201d CBF as a Gaussian bump in one direction of the feature space, parametrized by center location R) model , althoug\u03bci and \u03bcj determine the center of the basis function in the  plane. A second-order basis represents f as a (transformed) sum of these bivariate functions, giving d2 basis functions for each of the k filter outputs, or merely k filters into disjoint pairs. Higher-order CBFs can be defined analogously: k\u2032th order CBFs are Gaussian RBFs in a k\u2032-dimensional subspace while remaining constant in the remaining k\u2212k\u2032 dimensions. Of course, there is no need to represent the entire nonlinearity using CBFs of the same order. It might make sense, for example, to represent the nonlinear combination of the first two filter responses with second order CBFs (which is comparable to standard MID with a 2D histogram representation of the nonlinearity), and then use first order CBFs to represent the contributions of additional (less-informative) filter outputs.We can define second-order CBFs as functions that have Gaussian dependence on two dimensions of the input space and that are insensitive to all others:To illustrate the feasibility of this approach, we applied dimensionality reduction methods to a previously published dataset from macaque V1 . This dap parameters for the nonlinearity), and a grid with 3 RBFs per dimension for the rbf-LNP model (3p parameters). By contrast, the exponentiated-quadratic nonlinearity underlying the iSTAC estimator requires O(p2) parameters.To compare performance, we analyzed the growth in empirical single-spike information (computed on a \u201ctest\u201d dataset) as a function of the number of filters. Note that this is equivalent to computing test log-likelihood under the LNP model. For a subset of neurons determined to have 8 or more informative filters (16/59 cells), the cbf-LNP filters captured more information than the iSTAC filters . This inn filters identified .Rowekampmp et al ), and deet al[f(k\u22a4s+s\u22a4Cs). This method is one-dimensional in a quadratic stimulus space  and therefore avoids the curse of dimensionality. Other work has used independent component analysis to find directions in stimulus space in which the spike-triggered distribution has maximal deviations from Gaussianity [Other proposals can be seen as assuming specific quadratic-based parametrizations for the nonlinearity, that are more restrictive than the CBF form. The iSTAC estimator, introduced by Pillow & Simoncelli , is basen et al.  considerl. [et al, 46 usedssianity .We have studied the estimator known as maximally informative dimensions (MID),  a populaEstimators defined by the optima of information-theoretic functionals have attractive theoretical properties, including that they provide well-defined and  distribution-agnostic characterizations of data. In practice, however, such agnosticism can be difficult to achieve, as the need to estimate information-theoretic quantities from data requires the choice of a particular estimator. MID has the virtue of using a non-parametric estimator for raw and spike-triggered stimulus densities, meaning that the number of parameters  can grow flexibly with the amount of data. This allows it to converge for arbitrary densities, in the limit of infinite data. However, for a finite dataset, the choice of number of bins is critical for obtaining an accurate estimate. As we show in A second kind of distributional assumption arises from MID\u2019s reliance on single-spike information, which is tantamount to an assumption of Poisson spiking. To be clear, the single-spike information represents a valid information-theoretic quantity that does not explicitly assume any model. As noted in , it is sThe distributional-dependence of MID should therefore be considered when interpreting its estimates of filters and nonlinearities. MID makes different, but not necessarily fewer, assumptions when compared to other LN estimators. For instance, although the maximum-likelihood estimator for a generalized linear model assumes a less-flexible model for the neural nonlinearity than does MID, it readily permits estimation of certain forms of spike-interdependence that MID neglects. In particular, MID-derived estimates are subject to concerns regarding model mismatch that arise whenever the true generative family is unknown .In light of the danger that these distributional assumptions be obscured by the information-theoretic framing of MID, our belief is that the safer approach is to specify a model explicitly and adopt a likelihood-based estimation framework. Where the information theoretic and likelihood-based estimators are identical, nothing is lost by this approach. However, besides making assumptions explicit, the likelihood-based framework also readily facilitates the introduction of suitable priors for regularization of suitable priors, or hierarchical models , 49, or Having clarified the relationship between MID and LNP model the, we introduced two generalizations designed to recover a maximally informative stimulus projection when neural response variability is not well described as Poisson. From a model-based perspective, the generalizations correspond to maximum likelihood estimators for a linear-nonlinear-Bernoulli (LNB) model (for binary spike counts), and the linear-nonlinear-Count (LNC) model (for arbitrary discrete spike counts). For both models, we obtained an equivalent relationship between log-likelihood and an estimate of mutual information between stimulus and response. This correspondence extends previous work that showed only approximate or asymptotic relationships between between information-theoretic and maximum-likelihood estimators , 24, 25.X stands in for any probability distribution over the neural response , and perform dimensionality reduction by maximizing likelihood for the filter parameters under this model. The log-likelihood under any such model can be associated with an information-theoretic quantity, analogous to single-spike, Bernoulli, and count information, using the difference of log-likelihoods  denotes the conditional response distribution associated with the LNX model with parameters \u03b8, and px(r|\u03b80) describes the marginal distribution over r under the stimulus distribution p(s). The empirical or plug-in estimate of this information is equal to the LNX model log-likelihood plus the estimated marginal entropy:n denotes the number of samples and \u03b80 depends only on the marginal response distribution. The maximum likelihood estimate is therefore equally a maximal-information estimate.We could analogously define arbitrary \u201cLNX\u201d models, where see also ):Ilnx\u225c\u2211Note that all of the dimensionality-reduction methods we have discussed treat neural responses as conditionally independent given the stimulus, meaning that they do not capture dependencies between spike counts in different time bins . Spike-history dependencies can influence the single-bin spike count distribution\u2014for example, a Bernoulli model is more accurate than a Poisson model when the bin size is smaller than or equal to the refractory period, since the Poisson model assigns positive probability to the event of having \u2265 2 two spikes in a single bin. The models we have considered can all be extended to capture spike history dependencies by augmenting the stimulus with a vector representation of spike history, as in both conditional renewal models and generalized linear models , 50\u201352.p(K\u22a4s) and p(K\u22a4s|spike). However, dimensionality and parameter count can be a crippling issue given limited data, and density estimation becomes intractable in dimensionalities > 3. Furthermore, the dependence of the information on the logarithm of the ratio of these densities amplifies sensitivity to errors in these estimates. The LNP-likelihood view suggests direct estimation of the nonlinearity f, rather than of the densities. Such estimates are naturally more robust, and are more sensibly regularized based on expectations about neuronal responses without reference to any regularities in the stimulus distribution. We have proposed a flexible yet tractable form for the nonlinearity in terms of linear combinations of basis functions cascaded with a second output nonlinearity. This approach yielded a flexible, computationally efficient, constrained version of MID that is able to estimate high-dimensional feature spaces. It is also general in the sense that it encompasses standard MID, generalized linear and quadratic models, and other constrained models that scale tractably to high-dimensional subspaces. Future work might seek to extend this flexible likelihood-based approach further, for example by including priors over the weights with which basis functions are combined to improve regularization, or perhaps by adjusting hyperparameters in a hierarchical model as has been successful with linear approaches [Lastly, we have shown that viewing MID from a model-based perspective provides insight into how to overcome practical limitations on the number of filters that can be estimated. Standard implementations of MID employ histogram-based density estimators for proaches , 49.In recent years, the ability to successfully characterize low-dimensional neural feature spaces using MID has proved useful to address questions relating to multidimensional feature selectivity \u201356. In a\u03c1 = p(r = 1) denote the marginal probability of a spike, so the probability of silence is p(r = 0) = 1\u2212\u03c1. Let Q1 = p(s|r = 1) and Q0 = p(s|r = 0) denote the spike-triggered and silence-triggered stimulus distributions, respectively. Let Ps = p(s) denote the raw stimulus distribution. Note that we have the Ps = \u03c1Q1+(1\u2212\u03c1)Q0. The mutual information between the stimulus and one bin of the response , the mutual information is dominated by the first (Q1) term. Here we wish to show a bound on the fraction of information carried by the Q0 term. We can do this by computing a second-order Taylor expansion of I around \u03c1 = 0, and show that their ratio is bounded below by \u03c1/2. Expanding in \u03c1, we havez\u22121) \u2265 log(z). We therefore have\u03c1 \u2192 0.In the limit of small \u03c1. For the case of Q0 and Q1. We have been unable to find any counter-examples to this , but have so far been unable to find a general proof.We conjecture that the bound holds for all values of \u00cess based on a PSTH measured in response to repeated stimuli is also a Poisson log-likelihood per spike (plus a constant). Specifically, the empirical single-spike information is equal to the log-likelihood ratio between an inhomogeneous and homogeneous Poisson model of the repeat data :\u03bb;r) denotes the log-likelihood of the repeat data r under a Poisson model with time-varying rate \u03bb.An important general corollary to the equivalence between MID and an LNP maximum likelihood estimate is that the standard single-spike information estimate rjt} denote spike counts collected during a \u201cfrozen noise\u201d experiment, with repeat index j \u2208 {1,\u2026,nrpt} and index t \u2208 {1,\u2026,nt} over time bins of width \u0394. Then T = nt\u0394 is the duration of the stimulus and N = ntnrpt is the total number of time bins in the entire experiment. The single-spike information can be estimated with a discrete version of the formula for single-spike information provided in [t\u2019th time bin in response to the stimulus sequence s, and T is long enough that an average over stimulus sequences is well approximated by the average across time.We can derive this equivalence as follows. Let {vided in  (see eq.s (as in ) that T nsp = \u2211j,trjt is the total spike count. This allows us to rewrite single-spike information (The plug-in (ML) estimator for spike rate can be read off from the peri-stimulus time histogram (PSTH). It results from averaging the response across repeats for each time bin:ormation  as:I^ssr = {rjt} given rate vector Iss is equal to the difference between Poisson log-likelihoods under an inhomogeneous (rate-varying) and a homogeneous (constant rate) Poisson model, divided by spike count . These r from unseen test data. This results in the \u201ccross-validated\u201d single-spike information:Iss evaluated on training data tends to over-estimate information due to over-fitting.A similar quantity has been used to report the cross-validation performance of conditionally Poisson models, including the GLM , 58. To A\u2019 and \u2018B\u2019, and two possible discrete stimulus sequences, s1 = AB and s2 = BA, each of which occurs with equal probability, so p(s1) = p(s2) = 0.5. Assume each sequence lasts T = 2s, so the natural time bin size for considering the spike response is \u0394 = 1s. Suppose that stimulus A always elicits 3 spikes, while B always elicits 1 spike. Thus, when sequence s1 is presented, we observe 3 spikes in the first time interval and 1 spike in the second interval; when s2 is presented, we observe 1 spike in the first time interval and 3 spikes in the second.To gain intuition for the different information measures we have considered , it is useful to consider how they differ for a simple idealized example. Consider a world with two stimuli, \u2018\u03bb1(t) and \u03bb2(t), the spike rate in response to stimulus sequence s1 and s2, respectively. For this example, \u03bb1(t), takes the value 3 during  takes values 1 and 3 during the corresponding intervals. The mean spike rate for both stimuli is \u03bb\u0304 = 2 sp/s. Plugging these into Iss = 0.19 bits/spike. This result is slightly easier to grasp using an equivalent definition of single-spike information as the mutual information between the stimulus s and a single spike time \u03c4 (see [p(s|\u03c4 = 1) attaches 3/4 probability to s = s1 and 1/4 to s = s2. The posterior entropy is therefore \u22120.25 log 0.25\u22120.75 log 0.75 = 0.81 bits. We obtain the same entropy if the spike occurs in the second interval, so H(s|\u03c4) = 0.81. The prior entropy is H(s) = 1 bit, so once again we have Iss = 1\u22120.81 = 0.19 bits/spike.Single-spike information can be computed exactly from e \u03c4 (see ). If oner takes values outside the set {0,1}, and therefore cannot have a Bernoulli distribution. To make Bernoulli information well defined, we would need to either truncate spike counts above 1  provides perfect information about the stimulus, since it occurs only in response to B.The Bernoulli information, by contrast, is undefined, since 1 , or elsr carries perfect information about the stimulus, so the mutual information between stimulus (A or B) and r is 1 bit. We defined Icount to be the mutual information normalized by the mean spike count per bin  nonlinearity. We performed joint optimization of filter parameters r = \u22a4 and \u03bb = (f(K\u22a4s1),\u2026,f(K\u22a4snt))\u22a4, where nonlinearity f = g(\u2211\u03b1i\u03c6i) depends on basis function \u03a6 = {\u03c6i} and weights \u03b1 = {\u03b1i}  stimulus design matrix, \u03a6 denotes the (nt\u00d7n\u03c6) matrix whose \u2019th entry is \u03c6j(K\u22a4st), and \u03a6i) is a (nt\u00d71) vector composed of the point-wise derivatives of the inverse-link function g at its input, and \u2018\u2218\u2019 denotes Hadamard or component-wise vector product.Let \u03bb\u2032\u2032 = g\u2032\u2032(\u03a6\u03b1) and \u03a6i,j). The spk-filter model, this resulted in 3k parameters for the nonlinearity, and (240+3)k parameters in total for a stimulus with 24 bars.The cbf-LNP model was implemented with a cylindrical basis function (CBF) nonlinearity using three first-order CBFs per filter. For a k-filter model, this resulted in 3k parameters for the nonlinearity, and 240k+3k parameters in total.The traditional MID estimator (rbf-LNP) was implemented using radial basis functions (RBFs) to represent the nonlinearity. Unlike the histogram-based parametrization discussed in the manuscript (which produces a piece-wise constant nonlinearity), this results in a smooth nonlinearity and, more importantly, a smooth log-likelihood with tractable analytic gradients. We defined a grid of RBFs with three grid points per dimension, so that CBF and RBF models were identical for a 1-filter model. For a g(\u22c5) = log(1+exp(\u22c5)), to ensure positive spike rates. We also evaluated the performance of an exponential function, g(\u22c5) = exp(\u22c5), which yielded slightly worse performance (reducing single-spike information by \u223c 0.02 bits/spike).For both models, the basis function responses were combined linearly and transformed by a \u201csoft-rectification\u201d function: \u03b8 = {K,\u03b1}. Both models were fit incrementally, with the N+1 dimensional model being initialized with the parameters of the N dimensional model, plus one additional filter . The joint likelihood in K and \u03b1 was ascended using MATLAB\u2019s fminunc optimization function, which exploits analytic gradients and Hessians. The models were fit to 80% of the data, with the remaining 20% used for validation.The cbf- and rbf-LNP models were both fit by maximizing the likelihood for the model parameters In order to calculate information contributed by excitatory filters under the cbf-LNP model , we remoMeasurements of computation time  were avehttp://pillowlab.princeton.edu/code.html.Code will be provided at"}
+{"text": "Conflict analysis has been used as an important tool in economic, business, governmental and political dispute, games, management negotiations, military operations and etc. There are many mathematical formal models have been proposed to handle conflict situations and one of the most popular is rough set theory. With the ability to handle vagueness from the conflict data set, rough set theory has been successfully used. However, computational time is still an issue when determining the certainty, coverage, and strength of conflict situations. In this paper, we present an alternative approach to handle conflict situations, based on some ideas using soft set theory. The novelty of the proposed approach is that, unlike in rough set theory that uses decision rules, it is based on the concept of co-occurrence of parameters in soft set theory. We illustrate the proposed approach by means of a tutorial example of voting analysis in conflict situations. Furthermore, we elaborate the proposed approach on real world dataset of political conflict in Indonesian Parliament. We show that, the proposed approach achieves lower computational time as compared to rough set theory of up to 3.9%. Decision making is an important aspect when we consider the information about the result that we choose among two or more alternatives. There are many approaches in decision making problems which have ability to handle uncertainty, such as Fuzzy set theory , Rough set al. [et al. [et al. [et al. [et al. [et al. [Regarding conflict problems using rough sets, the model introduced by Deja  is an enet al. , 15 prop [et al.  proposed [et al.  presente [et al. . Skowron [et al.  proposed [et al.  proposed [et al.  proposed [et al.  applied  [et al.  presente [et al.  outlined [et al. .et al. [et al. [With the ability to handle uncertainty from the conflict data set, rough set theory has been successfully used. Another new approach in handling uncertainty is soft set theory . It is pet al.  proposedet al.  introduc [et al.  introduc [et al.  defined  [et al.  proposed [et al.  defined  [et al.  investiget al. [et al. [et al. [ivn-soft sets and implemented it on decision making problems. Maji et al. [There are also works on soft set theory implemented in decision making, Feng et al.  proposedet al.  discusse [et al.  proposed [et al.  proposed [et al.  extended [et al.  introduc [et al.  presente [et al.  combinedi et al.  proposedi et al.  presentei et al.  proposedet al. [et al. [t-norm and t-conorm of fuzzy parameterized soft sets (FP-soft sets) and investigated their properties. \u00c7a\u011fman and Deli [et al. [In real life many problems are imprecise in nature, classical soft set theory is not fit of effectively dealing with such issues. Majumdar and Samanta  introducet al.  proposed [et al.  proposed [et al.  proposed [et al.  introduc [et al.  defined and Deli  defined and Deli  construcand Deli  proposed [et al.  proposedIn this paper, we present an alternative approach to handle conflict situations, based on some ideas using soft set theory. Our motivation is to improve the computational performance by the rough sets approach in handling conflict situations when determining the support, strength, certainty, and coverage of conflict situations.We propose conflict analysis based on soft set approach.The novelty of the proposed approach is that, unlike rough set theory that relies on decision rules, it is based on the concept of co-occurrence of parameters in soft set theory.We illustrate the proposed approach by means of a tutorial example of voting analysis in conflict situations.Comparative analysis of the propose approach and rough set-based approach in handling conflict of Indonesian political election is presented. Furthermore, we show the efficiency of our proposed approach in term of computational time to the rough set approach.In summary, the contribution of this work is described as follows:The reminder of this paper is organized as follows. In section 2, we review the basic concepts of soft set theory. Section 3 describes the analysis of rough set theory in handling conflict situations. In section 4, we present soft set approach for conflict analysis. In section 5, we present result and discussion. Finally, the conclusion of this work is given in section 6.U be an initial universe set and let E be set of parameters in relation to object in U. The set P(U) denote the power set of U. The definition of soft set is given as follows:In this section, we review some basic notion of soft set theory. To avoid difficulties, one must use an adequate parameterization. Let A pair  is called a soft set over U where F is a mapping given by F:E \u2192 P(U).(See ) A pair U. Every set F(e), for e \u2208 E from this family may be considered as the set of e-elements of the soft set , or as the set of e-approximate elements of the soft set.In other words, the soft set is parameterized family of subsets of the set F,E) describe the \u201cattractiveness of cars\u201d that Mr. X is going to buy. Suppose that U = {c1,c2,c3,c4,c5,c6} and E = {e1,e2,e3,e4,e5}, where there are six cars in the universe U and E is a set of parameters, ei for i = 1,2,3,4,5 standing for the parameters \u201ccostly\u201d, \u201csafety\u201d, \u201cstyle\u201d, \u201cperformance\u201d, and \u201ccapacity\u201d respectively. In this example, we consider a mapping F:E \u2192 P(U) which is given by \u201ccars(.)\u201d, where (.) is to be filled in by one of parameters e \u2208 E. Suppose that, we have the following mapping values i.e.Let be a soft set (F(e3) means car with style characteristic, whose functional value is the set {c3,c4,c5}. Thus, we can view the soft set  as collection of approximation as follows:As we can refer to the example above, the mapping F,E) can be represented as a Boolean-valued information system   See , 53). Th. ThF,E) Soft set theory can also be used to handle multi-valued information systems and in the following section, we present the notion of multi soft sets representing multi-valued information systems.S =  to |A| number of Boolean-valued information systems which is based on decomposition of A = {a1,a2,\u2026,aA||} into a single attribute {a1},{a2},\u2026,{aA||}. In the following sub-section, we recall the construction of multi soft sets.Herawan and Deris proposed the idea of multi soft sets to for representing multi-valued information systems . The ideS =  be a multi-valued information system such that for every a \u2208 A, f is a finite non-empty set and for every u \u2208 U,|f| = 1. For every ai under ith-attribute consideration, ai \u2208 A and v \u2208 Va, we define the mapping In this section, we only consider for complete multi-valued information systems. Let Si = . The information systems Si = ,1\u2264i\u2264|A| is referred to as a decomposition of a multi-valued information system S =  into |A| number of Boolean-valued information systems, as depicted in The next step, we define a Boolean-valued information system as a quadruple Based on Proposition 3.1.If  is a soft set over the universe U, then  is a Boolean-valued information system S = .Si = , for 1\u2264i\u2264|A| in a \u2208 A and for every object u \u2208 U, the |f| is a total function. Hence, the structure of multi-valued information system and |A| number of Boolean-valued information systems give the same value of attribute related to objects.From Proposition 3.1, each Boolean-valued information system S =  be a multi-valued information system and Si = ,1\u2264i\u2264|A| be a |A| Boolean-valued information systems. Then we have the following multi-soft setsFrom sub-section 3.1, in this sub-section we present the notion of multi-soft set representing multi-valued information systems. Let F,A) = ,,\u2026,) as a multi-soft sets over universe U representing a multi-valued information system S = .We further define the , where U and A are non-empty finite sets called universe, and the set of attributes, respectively. Pawlak models conflict analysis as follows:U is called objects (agents)Elements of A is set of attributes (issues).The In this section firstly we recall the concept of conflict analysis from the point of view of rough set theory. Pawlak , 11 inita \u2208 A is a total function a:U \u2192 Va, where Va is the set of values of a, called the domain of a; elements of Va will be referred to as opinions, and a(x) is opinion of agent. The domain of each attribute is restricted to three values Va = {1,0,\u22121} representing opinion of agents, where 1 means alliance, 0 means neutrality and \u22121 means conflict. In the following sub-section, we introduce an alternative soft set approach for conflict analysis.Every attribute F,A) as presented in sub-section 3.2, let S =  be a multi-valued information system and Si = , for 1\u2264i\u2264|A| be a |A| decomposed Boolean-valued information systems. A conflict situation based on multi-soft sets is modelled as a  where quadruple Si = , where U and ai are non-empty finite sets, U is called universe, ai is called attributes, V = \u222aa\u2208AVa, Va is the domain  of attribute a and element of Va is referred as opinions toward the issue, f:U \u00d7 A \u2192 V is a total function such that f \u2208 Va, for every  \u2208 U \u00d7 A.Based on the multi-soft sets , neutral, and conflict toward the issue, respectively. Therefore, here we have conflict model based on multi-soft sets as follows:On a conflict situation, we can say that is special type of multi-soft sets, because Si =  be a multi-valued information system, and Si = ,1\u2264i\u22643, ai \u2208 A, Va = {1,0,\u22121} be a conflict model Boolean-valued information systems with Va is restricted to three values Va = {1,0,\u22121} or Va = {+,0,\u2212}. Therefore, here we haveLet In the following sub-section we discuss the binary relations on agents i.e. alliance , neutrality, and conflict.F,A) be a soft set representing a Boolean-valued information system Si = . Based on the idea from Pawlak [Let f = 1, between agents x and y have the same point of view or opinion about the issue f ;That means that, if b. Neutralityf = 0, at least there is one agent x or y has neutral view to conflict issue f ;In the case of neutrality, if c. Conflict (against)f = \u22121, both agents have different opinions about conflict issue f (agents x and y are conflict on f).Finally, in the case of conflict, if F,E) can be represented as a Boolean-valued information system , in the following definition we present the notion of similarity between two parameters in . We firstly define the notion of occurrence of parameters in soft set theory.From the fact that a standard soft set  be a soft set over the universe U representing  and an object u \u2208 U. A parameter co-occurrence set of an object u can be defined as follows:coo(u) = {e\u2208E:f(e) = 1}. The following example illustrates the Definition 4.1.Obviously, Example 4.1. From soft set  in From Definition 4.1, we have the following definition of agent support.Definition 4.2.Let  be a soft set over the universe U and an agent u \u2208 U. The support of an agent u is defined byFrom Definition 4.2, we have the following definition of rules strength.Definition 4.3.Let  be a soft set over the universe U representing . The strength of a rule A1 \u21d2 A2for A1,A2 \u2282 A denoted by \u03c3x is defined byFrom Definition 4.3, we have the following definition of rules certainty.Definition 4.4.Let  be a soft set over the universe U representing . The certainty of a rule A1 \u21d2 A2for A1,A2 \u2282 A denoted by cerx is defined by\u03c0(A1(x)) = |A1(x)| / |U|.From Definition 4.4, we have the following definition of rules coverage.Definition 4.5.Let  be a soft set over the universe U representing . The coverage of a rule A1 \u21d2 A2for A1,A2 \u2282 A denoted by covx is defined bywhere \u03c0(A2(x)) = |A2(x)| / |U|.x = \u03c0x(A1|A2)Similarly, covThe algorithm for handling conflict data using multi-soft sets is given in In the following section, we present a tutorial example of voting analysis in a conflict situation.U,A,V,f) where the domain agents (universe) and the voting function f are respectively defined byIn this section, we illustrate the proposed approach through an example of a conflict data set. Let a conflict situation given by a multi-valued information system  representations as in From the decomposition of a multi-valued information system  into mulF,E) in From multi-soft sets , neutrality, and against (conflict) among the agents. From steps 4, 5, and 6 in From The flow graph associated with A \u2192 1 has the certainty factor 0.525 and coverage factor 0.206. The flow graph gives a clear insight into the voting structure of all parties. We can replace flow graph shown in From \u201capproximate\u201d flow graph depicted on A, B, C, and D form a coalition, which is in conflict with party E. This flow graph generated by using certainty factor greater than 0.5.The In the next section, we present an application of handling conflict in the problem of determining governor election model in Indonesia.In this section, we present a real world application of the proposed approach to solve the problem of determining governor election model in Indonesia i.e. direct or indirect methods. The dataset is taken from liputan6 online  and vivaFrom U,A,V,f) where the domain ag (universe U) of the voting function f is respectively defined byLet a conflict situation given by a multi-valued information system , abstention , and no (against/conflict), respectively.From F,E) representations as in From the decomposition of a multi-valued information system  into mulF,E) in From multi-soft sets . It is executed sequentially on a processor Intel Core i3 CPUs. The total main memory is 4GB and the operating system is Windows 10. The experimental results on all party supports are given in The strength, certainty, and coverage, of Indonesian parties voting result are given in The flow graph associated with From In the \u201capproximate\u201d flow graph depicted on The following graphs present the comparison of execution time between the proposed soft set based approach and rough set based approach on computing support, strength, certainty, and coverage.From From From From Conflict analysis has been used as an important tool in economic, business, governmental and political dispute, games, management negotiations, military operations and etc. In this paper we have presented an alternative approach for handling conflict situation involving uncertainty. It is based on multi-soft sets taking into account of co-occurrence of parameter related to object in universe. The novelty of the proposed approach is that, unlike in rough set theory that uses decision rules, it is based on the concept of co-occurrence of parameters in soft set theory. We have presented an illustrative example on how to handle conflict using multi soft sets. Furthermore, we elaborate the proposed approach of real world dataset of voting from political election data set from Indonesian parliament. However, we achieve lower computational time as compared to rough set approaches. In the future work, we will extend this proposed soft set-based method by refinement of the neutrosophic set , 58 and"}
+{"text": "Little is known about the effects of fear as a basic emotion on mental rotation (MR) performance. We expected that the emotional arousal evoked by fearful stimuli presented prior to each MR trial would enhance MR performance. Regarding the influence of anxiety, high anxious participants are supposed to show slower responses and higher error rates in this specific visuo-spatial ability. Furthermore, with respect to the embodied cognition viewpoint we wanted to investigate if the influence of fear on MR performance is the same for egocentric and object-based transformations. To investigate this, we presented either negative or neutral images prior to each MR trial. Participants were allocated to the specific emotion in a randomized order. Results show that fear enhances MR performance, expressed by a higher MR speed. Interestingly, this influence is dependent on the type of transformation: it is restricted to egocentric rotations. Both observation of emotional stimuli and egocentric strategies are associated with left hemisphere activation which could explain a stronger influence on this type of transformation during observation. Another possible notion is the conceptual link between visuo-spatial perspective taking and empathy based on the co-activation of parietal areas. Stronger responses in egocentric transformations could result from this specific link. Regarding the influence of anxiety, participants with high scores on the trait-anxiety scale showed poor results in both reaction time and MR speed. Findings of impoverished recruitment of prefrontal attentional control in patients with high scores in trait anxiety could be the explanation for this reduced performance. According to There is plentiful evidence that fear induced by presenting fearful stimuli affects visual perception in the ventral stream. For instance, By analyzing this special relationship, it raises the question whether affect and emotion also have an influence on mental imagery. This study tries to answer this question by investigating the influence of fear and anxiety on a certain visuo-spatial ability, specifically mental rotation (MR).MR involves the process of imagining how a two- or three-dimensional object would look if rotated away from its original upright position . In the In MR, there are two different strategies of mental transformations: object-based and egocentric transformations. In object-based transformations, the observer\u2019s position remains fixed and moves the object in relation to the surrounding environment. In egocentric transformation tasks, participants are required to change their own perspective and thus imagine rotating their own body in order to make a decision . The useLittle is known about the effects of fear as basic emotion on visuo-spatial processing in the dorsal stream assessed by MR performance. The corresponding neural system that is activated when a stimulus evokes fear is the amygdala . AccordiRegarding the influence of anxiety on MR performance, Despite the fact that the role of emotion and affect has been investigated in the context of MR performance, it is still an open question if the influence of fear and anxiety is the same for egocentric and object-based transformations. The present article addresses this issue with regard to the embodied cognition approach. The key idea of this renewed viewpoint in cognitive neuroscience is that many cognitive processes that were formerly defined as purely \u201ccognitive\u201d are also deeply rooted in body-related experiences with the environment .There is plentiful evidence that motor processes are involved in both object-based  and egocWhat does this embodiment approach mean with regard to the influence of fear and anxiety on MR performance? Next to the postulation of \u201ccognitions\u201d being embodied, there is also a strict coupling between emotion and sensory-motor integration . For exaThe present investigation differs from previous research by investigating the influence of fear and anxiety on MR performance with focus on the differentiation of egocentric and object-based transformations. Based on the work of According to Concerning the role of fear, in line with the notion of an enhanced activation of the amygdala that in turn modulates activity in parietal areas through the presentation of aversive stimuli we expected that fear primes MR performance. It is still an open question if anxiety affects MR performance and if so, to what extent, but based on the negative influence of anxiety on cognitive processes cf.  it is renegative: 23.27, SD = 4.27; mean ageneutral: 23.27, SD = 4.27), t(84) = -0.69, n.s., and the anxiety trait score , t(84) = -0.46, n.s. Regarding intelligence, they showed comparable scores , t(84) = -0.26, n.s., see Table 1. Participants were recruited through advertisement at the university. All participants received either \u20ac10 for participation or credits for psychology courses. None of the participants have participated before on MR tests. All participants gave informed consent for participation.Eighty-six adults, 43 men  and 43 women  participated and were classified into the following two types of emotion: negative and neutral. The \u201cnegative emotion\u201d group consisted of 22 men and 21 women, the \u201cneutral emotion\u201d group was composed of 21 men and 22 women with no significant difference in both age  served as between-subject factor. Since the IAPS consisted of 193 negative and 130 neutral pictures, which is not sufficient for the 336 MR trials in total, we had to choose 112 images for each block resulting in three repetitions of each image. Even if habituation and consequently a decrease of emotional response were risked, a less amount of trials would not have been arguable from the scientific viewpoint. The selection of the images was randomized. However, this selection was based on the fact that level of arousal and valence was comparable for both emotions. For this purpose, the IAPS provides a list with scores of valence and arousal. The primes were controlled for both levels. According to Before each trial pictures from the International Affective Picture System (IAPS) were presented, as illustrated in The individual test sessions lasted about 60 min and took place at a silent room at the University. At the beginning the participant completed the demographic questionnaire, the state-trait anxiety inventory and the ZVT.Later, the MR test with standardized task instruction was conducted. In the BFO and letter conditions, participants had to press the left mouse button (left-click) when the two stimuli were \u201csame\u201d and the right mouse button (right-click) when the two stimuli were \u201cdifferent.\u201d In this case \u201csame\u201d means that the stimulus on the right side was identical to the comparison stimulus, \u201cdifferent\u201d means that the stimulus on the right side was not identical to the comparison stimulus. In the BFE condition participants had to decide if the figure had the right (right mouse click) or the left arm (left mouse click) outstretched see .According to Each participant performed three blocks of 112 experimental trials, resulting in 336 trials: 3 transformation types (BFE vs. BFO vs. letters) * 2 trial types (same vs. different/left vs. right) * 7 angular disparities  * 4 repetitions of each combination * 2 stimuli per block . In each block, the order of the presentation of the stimuli was randomized.First, to exclude that the MR performance is influenced by possible IQ differences between gender and group an univariate analysis with the dependent measure IQ and the independent variables gender and group was conducted.Second, two repeated analyses of variance were conducted, with \u201creaction time\u201d and \u201caccuracy rate\u201d as dependent variables, and with \u201cangular disparity\u201d , \u201ctransformation type\u201d , \u201cemotion\u201d  as factors. The factors \u201cangular disparity\u201d and \u201ctransformation type\u201d were the within-subject factors. Because preliminary analysis revealed no relevant effect with the factor gender only the factor \u201cemotion\u201d  served as between-subject factors. The variable \u201ctrait anxiety\u201d was included as a co-variate. For reaction time, only the responses for \u201csame\u201d trials were analyzed because angular disparity is not clearly defined for mirror-reversed responses . For errThird, a repeated analysis of variance was calculated with \u201cMR speed\u201d as a dependent variable and \u201ctransformation type\u201d as within-subject factor and \u201cemotion\u201d as between-subject factor. The variable \u201ctrait anxiety\u201d was included as a co-variate. MR speed was calculated as the inverse of the slope of the regression line, calculated separately for each subject, relating RT to angular disparity and was expressed as degrees per second. A higher MR speed means that a larger angular disparity is rotated per second. According to the traditional theory of MR  claimingThe significance levels of the analyses of variance results were corrected according to the method of Greenhouse\u2013Geisser to compensate for non-sphericity of the data if necessary.F = 0.38, n.s. nor a group effect, F = 0.008, n.s. nor an interaction between both factors, F = 1.52, n.s. concerning the transformed IQ values.There were neither gender differences, F = 10.13, p < 0.001, partial \u03b72 = 0.11, and \u201cangular disparity,\u201d F = 54.68, p < 0.001, partial \u03b72 = 0.39. The covariate also reached significance and could be expressed by a significant correlation between \u201ctrait anxiety\u201d and the averaged reaction time for each transformation type . There were two positive significant correlations: (1) between \u201ctrait anxiety\u201d and \u201cBFO\u201d , 2) between \u201ctrait anxiety\u201d and \u201cletters\u201d . Regarding the significance of the factor \u201ctransformation type,\u201d Bonferroni-corrected t-tests showed that the reaction was higher for the BFO condition  compared to the letter condition, , t = 12.84, p < 0.001, and to the BFE condition, , t = -12.61, p < 0.0001. Furthermore, there was a significant difference between the reaction time in the letters and BFE condition, t = 3.21, p < 0.01. Regarding the main effect of the factor \u201cangular disparity,\u201d post hoc pair-wise comparisons showed higher reaction times for each consecutive angular disparity (p = < 0.001) except the one at 30\u00b0 which did not differ from that of 0\u00b0, t(85) = -2.34, n.s.Concerning reaction time, the analysis of variance showed three main effects for the factors \u201ctransformation type,\u201d Furthermore, there were two interactions:(1)F = 1.84, p < 0.05, partial \u03b72 = 0.02, and it is illustrated in Figure 3. Whereas reaction time in the BFO condition was overall increasing with angular disparity and higher for each consecutive angle (p = < 0.001), reaction times in the letters condition did not differ between angular disparities of 0 and 30\u00b0, t(85) = -2.06, n.s., and between angular disparities of 30 and 60\u00b0, t(85) = -1.01, n.s.. Increasing disparity in the BFE task only led to higher response times for disparities larger than 90\u00b0 (p = < 0.001). All other effects did not reach significance at the 0.05 level. Furthermore, by trend reaction time in the egocentric transformation condition surprisingly decreased between the angular disparity of 0 and 60\u00b0. That is, whereas reaction times in the object-based condition roughly increased linearly with increasing disparity as expected, they showed a U-shaped pattern for the egocentric transformation condition. The \u201ctransformation type\u201d \u00d7 \u201cangular disparity\u201d interaction was significant, (2)r = -0.21, p < 0.01; 120\u00b0: r = -0.29, p < 0.01; 150\u00b0: r = -0.28, p < 0.01; 180\u00b0: r = -0.27, p < 0.01). All other effects failed to reach significance. The interaction between the covariate \u201ctrait anxiety\u201d and \u201cangular disparity\u201d was significant, expressed by a correlation between \u201ctrait anxiety\u201d and the averaged reaction time for each angular disparity. The correlation between \u201ctrait anxiety\u201d and the angular disparities of 0, 120, 150, and 180\u00b0 reached significance  = 8.932, p < 0.001, partial \u03b72 = 0.09. Bonferroni-corrected t-tests revealed that from an angular disparity of 90\u00b0, there was a lower PR score for the following angular disparity compared to the preceding one . All other effects did not reach significance.The analysis of the PR score showed one main effect of the factor \u201cangular disparity\u201d F = 5.11, p < 0.01, and \u201cangular disparity,\u201d F = 136.28, p < 0.001. According to multiple post-hoc comparisons, participants showed higher accuracy rates in the BFE and the letters condition compared to that found in the BFO condition. Performance between the letters and BFE condition did not differ. Regarding the main effect of the factor \u201cangular disparity,\u201d the decrease of accuracy emerges for disparities larger than 90\u00b0 (p = < 0.001). All other effects did not reach the 0.05 significance level.Regarding accuracy rate, results revealed two significant main effects of the factors \u201ctransformation type,\u201d F = 5.00, p < 0.001. Whereas accuracy rate in both object-based conditions  was overall decreasing with angular disparity by trend and significant lesser for each consecutive angle from an angular disparity of 90\u00b0 on (p = < 0.001), increasing disparity in the egocentric task only led to higher error rates for disparities larger than 120\u00b0 (p < 0.001). Furthermore, by trend accuracy rate in the egocentric transformation condition surprisingly increased between the angular disparity of 0 and 60\u00b0, and between 90 and 120\u00b0. All other effects did not reach significance at the 0.05 level. Together, this small-angle advantage is more pronounced for the object-based transformations than for the BFE condition, as illustrated in Figure 4.Furthermore, the interaction between \u201ctransformation type\u201d and \u201cangular disparity\u201d was significant, F = 3.91, p < 0.05, partial \u03b72 = 0.05. Bonferroni-corrected t-tests showed that participants rotated stimuli in the BFE condition  significantly faster than those in the BFO condition , t = -5.67, p < 0.001, but not significantly faster than letters , t = -1.44, n.s.Due to negative rotation speed, two persons had to be excluded. The analysis of variance showed a significant main effect of \u201ctransformation type,\u201d Furthermore, results showed two significant two-way interactions:(1)F = 5.37, p < 0.001, partial \u03b72 = 0.07. Post-hoc comparisons showed that the rotation speed did not differ for participants who have either seen negative or neutral pictures before the MR task, both in the BFO condition, t = -0.18 n.s., and in the letters condition, t = -0.26 n.s., whereas MR speed differed between both groups in the BFE condition, t = 2.32, p < 0.05. The MR speed for the BFE condition was much higher if participants had seen negative pictures  compared to neutral ones , see Figure 5. All other effects were not significant. The interaction between \u201ctransformation type\u201d and \u201cemotion\u201d reached significance at the 0.05 level, (2)F = 4.61, p < 0.05, partial \u03b72 = 0.05 expressed by a negative correlation between \u201ctrait anxiety\u201d and the rotation speed of \u201cletters\u201d . The interaction between \u201ctransformation type\u201d and the co-variate \u201ctrait anxiety\u201d was significant, The main goal of our study was to investigate if the influence of fear on MR performance is the same for egocentric and object-based transformations. Furthermore, we wanted to examine the effect of anxiety on MR performance. The main results were a facilitation effect of fear which is restricted to egocentric transformations: participants rotated stimuli in the BFE condition more quickly after seeing an aversive image compared to a neutral one. Concerning the influence of anxiety, individuals with high scores on the trait-anxiety scale of the STAI showed both partially higher reaction times and a partially slower MR speed.In line with previous findings , we coulLike mentioned above, both types of strategies differ in a crucial point: Whereas in object-based transformations participants are asked to mentally move/rotate the object in relation to the surrounding environment, in an egocentric chronometric MR tasks people are required to change their own perspective because they have to imagine themselves rotating in order to complete the task . TherefoAnother possible explanation for the enhanced effect of fearful stimuli on egocentric transformation is based on the idea that fearful primes may prepare the body to react. We tentatively propose that this motor pre-activation has a stronger impact on the BFE condition which is suggested to be embodied to a higher extent than the object-based conditions . The notion, that the processing of emotional stimuli activates bodily reactions has already been pointed out by Another attempt to explain the egocentric-specific influence of fear could involve the meaning of the working memory (WM). We tentatively propose that fear impairs functions of the WM which affects object-based rotations to a higher extent. This assumption stems from the fact that in egocentric transformations the visual buffer being the neuronal substrate for both imaginal and perceptual visuo-spatial transformations is not that highly loaded because there is no image interference in left\u2013right judgments tasks . The widA further approach for this finding could be attributed to a conceptual link between visuo-spatial perspective taking and perspective-taking in the abstract sense, specifically empathy. Although purely speculative, it could be concluded that the presentation of aversive stimuli elicits a stronger activation of areas which are the neural correlate for egocentric transformations and therefore represent the social construct empathy in an abstract sense compared to those being activated during object-based transformations. In perspective transformations, subjects are required to transform themselves into the body of another person. There is evidence that this kind of self-other equivalence is a basic condition for empathy . AllportBased on the finding of the activation of the parietal cortex during both visuo-spatial processes and empathy , ThakkarIn contrast to their expectation, The positive correlation between \u201ctrait anxiety\u201d and \u201creaction times\u201d of letter and BFO condition and \u201cMR speed\u201d of letters in our study suggests that higher scores in the trait anxiety scale of the STAI are associated with higher reaction times of these conditions. These results are contradictory to the finding of previous research showing a facilitation effect of emotion: participants with high state-anxiety rotated objects more quickly after the presentation of fearful faces compared to neutral ones . HoweverThe findings of our study show that high anxiety scores interfere with MR performance which is in line with the negative influence of anxiety found in previous literature cf. . AccordiAccording to Interestingly, with respect to the simulation-based account the influence of anxiety is restricted to the two object-based conditions  where no motor simulation was required. This is in line with the specific effect of fearful stimuli being restricted to the egocentric transformation. Both results could provide further evidence for the importance of motor simulation in the assumed link between embodied cognitions and emotions.The investigation of the influence of fear by presenting aversive images is widespread. However, it still remains unclear to which extent this type of stimulus material elicits emotion. Furthermore, it raises the question which kind of emotion is triggered, whether it is rather disgust than fear. Even if the images were standardized regarding valence and arousal, the extent of the emotional response stays individually. This could be controlled by measuring the physiological response, specifically skin conductance response. However, this measurement still makes no statement about the quality of emotion. Conducting self-reported measurements could clarify the emotional state, but they can only be assessed after the MR task which may be a too long period after the presentation of the aversive stimuli.Furthermore, the direct comparison between egocentric and object-based transformations should be reconsidered in view of the fact that these types of transformations differ in some aspects: visual stimulation (2 stimuli vs. 1 stimulus, cf. Taken together, the explanation approaches mentioned above based on neuronal correlates still remain quite speculative at this point since no brain activity was measured in the present study. Further behavioral and neuroanatomical research is needed to clarify this specific link between emotion and cognition.Empathy seems to be associated with egocentric transformations based on the co-activation of parietal areas during visuo-spatial processes and this social construct . We hypoTo complete the emotional version of the MR task, the influence of positive images could be investigated in future. If the poor performance of anxious individuals is really stemming from an attentional deficit caused by threat-related stimuli, the adding of positive stimuli may clarify this assumption.The relationship between emotion and MR seems to be very close. The findings of our study suggest that there is a facilitation effect of fear which is restricted to egocentric transformations. To what extent empathy as social construct plays a role still remains unclear and demands a lot of future research. In contrast to The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "There is an error in the sub-heading \u201cModulation of APP Processing by RC, RS, CP, and FG and S\u201d under the \u201cResults\u201d section. The correct sub-heading for this section is:\u201cModulation of APP Processing by RC, RS, CP, and FG\u201dAdditionally, there is an error in the second paragraph of the sub-heading \u201cChromatographic Conditions\u201d under the \u201cMaterials and Methods\u201d section. There are no supplementary methods in the article, and Table S2 is incorrectly referenced as Table S1 in this paragraph. Therefore, the correct paragraph should read:Qualitative identification of 12 active compounds of HLJDT was also performed by ultra-high performance liquid chromatography with quadrupole time-of-flight mass spectrometry (UHPLC-Q-TOF-MS) analysis with positive mode ESI-MS. A database was prepared for the identification of phytoconstituents of HLJDT based upon their molecular masses, calculated m/z values and retention times (Rt) observed in the analysis (Table S2)."}
+{"text": "As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results. These distributions are those that maximise the Boltzmann-Gibbs entropy and ensure the equilibrium state. The Maxwell distribution is an instance of the equilibrium distribution for the velocities of molecules in an ideal gas. The underlying mathematical reason for this is the existence of the standard Central Limit Theorem (CLT)q\u2009\u2192\u20091. This feature permits to describe these special non-equilibrium states with the same formal framework of the equilibrium thermostatistics, known as Tsallis statisticsq attains a special limiting value (q\u2009\u2192\u20091). In this case, the underlying mathematical mechanism is the generalized CLT4q-Gaussians. Therefore, the role of q-Gaussians in Tsallis statistics is basically the same as that of Gaussians in Boltzmann-Gibbs statistics. In this work we show, for the first time, that these two cases coexist in the classical standard map, and discuss the necessary conditions under which one case prevails over the other one. This neatly illustrates the respective domains of validity of Boltzmann-Gibbs and of Tsallis statistics. The results are important not only from the statistical mechanics theoretical viewpoint but also due to their potential of being applicable to diverse fields of physics. Indeed, many physical systems can, as a first approximation, be reduced to the standard map. This is so for particle confinement in magnetic trapswhere Boltzmann-Gibbs entropy is a special case as q-Gaussians, have been observed in nature in several experimental, observational and model systems1113q-Gaussians have been found as the chaos threshold is approached using the band splitting structure obeying the Huberman-Rudnick scaling law2021Non-Gaussian distributions, particularly q-Gaussians have also been recently observed in a conservative high dimensional model\u03b1-XY model, i.e., a system of N classical localized planar rotators with two-body interactions and periodic boundary conditions, the potential is assumed to decay with distance as 1/r\u03b1, and \u03b1\u2009\u2265\u20090 is the parameter that controls the range of the interactions, short-range for \u03b1/d\u2009>\u20091, and long-range for 0\u2009\u2264\u2009\u03b1/d\u2009\u2264\u20091 .\u03b1-XY model just mentioned. Ordinary Gaussians are observed when short-range interactions (\u03b1\u2009>\u20091) are present, and q-Gaussians are observed when long-range interactions (0\u2009\u2264\u2009\u03b1\u2009\u2264\u20091) are present\u03bb asymptotically decreases as N\u03ba(\u03b1)\u2212, in a rather similar way of that observed in\u03b1-XY model and the q-Gaussian distributions that emerge are characterized by the parameter q that depends on \u03b1.Recently a generalization of the conservative one-dimensional Fermi-Pasta-Ulam model, properly modified to account for linear and nonlinear long-range interactions, has been analyzed. The range of the interactions is controlled in the same way as for the \u03bb and two regimes shall be distinguished in the thermodynamic limit (number of particles N\u2009\u2192\u2009\u221e). (i) Strongly chaotic regime corresponds to a large positive Lyapunov exponent, where the system is ergodic. The dynamics of the system evolves to an equilibrium state described by Boltzmann-Gibbs statistical mechanics, with exponential or Gaussian distributions ; (ii) Weakly chaotic regime corresponds to a very small positive Lyapunov exponent (\u03bb\u2009\u2248\u20090), where the system behaves for a very long time as non-ergodic. Distributions of the dynamical variables are not exponential or Gaussians, and the Boltzmann-Gibbs framework is not suitable for this case. q-Gaussian distributions have been observed for this case by proper time and ensemble averagesSq227All these systems appear to share in common the following scenario: ergodicity in a region is characterized by the largest Lyapunov exponent B\u2009>\u20090 is the Lagrange parameter and the q-exponential is given bywhere A]+\u2009\u2261\u2009max {0, A} and its inverse, q-logarithm, is defined by q\u2009\u2192\u20091.where /[number of points with \u03bb above \u03bbthreshold] to decrease; for fixed K, this ratio increases with increasing \u03bbthreshold, but remains almost constant for 5\u2009\u00d7\u200910\u22125\u2009<\u2009\u03bbthreshold\u2009<\u200910\u22122. The precise relation between \u03b1 and this ratio remains to be studied but it is out of the scope of this manuscript and will be addressed elsewhere. It is easily seen that, as the stability islands dominate the whole phase space, the dominant distribution is the q-Gaussian with q\u2009=\u20091.935 (case K\u2009=\u20090.6), whereas the dominant one becomes the Gaussian if the chaotic sea invades more and more the whole phase space (case K\u2009=\u20092). It is in fact a very interesting result since, although for some portion of the phase space the system is ergodic, the signature of the q-Gaussian seems not to be erased even for very large T values. Therefore, apparently, for these two different portions of the phase space, the system behaves differently and each one is as robust as the other one. This mixture of Boltzmann-Gibbs statistical behaviour with Tsallis statistical behaviour is somewhat reminiscent of what was observed in a quite different system, namely one where overdamped motion is presentWe check this hypothesis using our two appropriate cases, namely, K, the phase space is almost entirely dominated by zero Lyapunov behaviour and the distributions  are q-Gaussians. As the value of K increases the measure of the zero Lyapunov regions decreases, and we see a continuous crossing, expressed by the parameter \u03b1 in q-Gaussian distributions  and Gaussian ones (Boltzmann-Gibbs statistics) with \u03b2q\u2009\u2192\u2009\u221e and \u03b2\u2009\u2192\u2009\u03c0 as K\u2009\u2192\u2009\u221e . Remarkably enough, the distributions originated from initial conditions taken inside the region of islands, instead of over the entire phase space, yield one and the same value q\u2009=\u20091.935, independently on whether we consider one or many of these regions, and independently from K. Initial conditions taken within the chaotic sea always yield Gaussians with \u03b2\u2009=\u2009\u03c0. The variance of q-Gaussians with 5/3\u2009<\u2009q\u2009<\u20093 diverges, though they have finite width. The N-fold convolution product of independent (or quasi-independent) q-Gaussians would asymptotically yield L\u00e9vy distributionsnot the case for the standard map: indeed, the actual time-averaging involves strong correlations. As previously discussed, since the standard map can be considered as a basic model for several physical systems , the present results are expected to be valid and useful for the statistical mechanical analysis of diverse phenomena, experimentally and observationally detected.The phase space of the standard map presents regions of positive Lyapunov exponents coexisting with regions of zero Lyapunov exponents. The positive Lyapunov regions present mixing and thus the system is ergodic in those regions. For sufficiently low values of the control parameter How to cite this article: Tirnakli, U. and Borges, E. P. The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics. Sci. Rep.6, 23644; doi: 10.1038/srep23644 (2016)."}
+{"text": "Gb-metric space which is recently introduced by Aghajani et al. (Filomat 28(6):1087\u20131101, In this paper we prove the existence and uniqueness of couple fixed point theorems for three mappings satisfying some new rational contractive conditions. We prove our results in the frame work of  Due to this a flood of research work have been generated from this area. As a part of this study generalisation of metric space becomes one of the most interesting topic in which many researchers have devoted and continued working. Since the introduction of metric space by Frachet, there is a lot of generalisation of this space. Some of them which can be mentioned are 2-metric space, G-metric and b-metric and generated the new definition and named it as Gb-metric space. They also pointed out that the class of Gb-metric space is effectively larger than that of G-metric space and G-metric space becomes a particular case of Gb-metric space. They claimed that every Gb-metric space is topologically equivalent to a b-metric space. For more results on b-metric space one can study the research papers of Malhotra and Bansal  is called a G-metric space. is called a b-metric space with parameter s., Then G is called a generalized b-metric and pair  is called a generalized b-metric space or  be a G-metric space, and  be a r is be a complete symmetricmetric space with parameterand let the mappingssatisfyingfor allandwithThenS,\u00a0TandRhave a unique common coupled fixed point inX.Let DefineTherefore,X. As X is complete By property  of DefinNow we will prove that Using inequality  we have\\x,\u00a0y) is a Common coupled fixed point of S, T and R.Similarly, we can prove that p,\u00a0q) be the second common coupled fixed point of S, T and R.In order to prove the uniqueness of the coupled fixed point, if possible let   5) we haHence S, T, R have unique coupled common fixed point.Thus This completes the proof. Let  be a complete symmetricmetric space with parameterand let the mappingsatisfyingfor allandwithThenShas a unique coupled fixed point inX.Let  be a complete symmetricmetric space with parameterand let the mappingssatisfyfor allandare non-negative real numbers withThenS, T, Rhave unique coupled common fixed point.Let ThenAdding  and 8)  8) we haAlso, we can show thatBy property  of DefinSo, for X. Since X is complete Therefore Now, we will show that Therefore Which implies that Also, we can prove that x,\u00a0y) is a common coupled fixed point of S,\u00a0T and R.Hence,  be the second common copuled fixed point of S,\u00a0T and R.In order to prove the uniqueness of the common coupled fixed point of Then by using inequality  we have9But Which implies that S,\u00a0T,\u00a0R have a unique common coupled fixed point.Thus This completes the proof. Let  be a complete symmetricmetric space with parameterand let the mappingsatisfyingfor allandare non-negative realnumbers withThenShas a unique coupled fixed point.Let S,\u00a0T and R.Defineb-metric and G-metric spaces. These results may be extended to other spaces.We prove the existence and uniqueness of common coupled fixed point theorems for three mappings with a new rational contractive conditions in"}
+{"text": "Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case. Recently, more advanced methods have been presented for DOA estimation, for example, the Khatri\u2013Rao (KR) product approach. By assuming quasi-stationary sources, this concept can identify up to 2N \u2212 1 sources using an N-element uniform linear array, without computing higher-order statistics , then vec(A) = T.Notations: We denote matrices and vectors by boldfaced capital letters and lower-case letters, respectively. SuperscriptThe remainder of the paper is organized as follows. In Section 2, we present the signal model and the KR-MUSIC algorithm . Section2.In this section, we give a short summary of the KR-MUSIC algorithm (see ), preced2.1.K sources impinging on a uniform linear sensor array, consisting of N omnidirectional sensors and neglecting mutual coupling. For a signal kS(t) emitted by the k-th source, let s(t) = T denote the K \u00d7 1 source signal vector. Let N \u00d7 1 steering vector corresponding to the direction \u03b8, with d, the spacing between the N sensors and \u03bb the signal wavelength. In this paper, we fix the element spacing to d/\u03bb = 1/2. Our aim is to study the effect of random variations in the array geometry on algorithms estimating the directions of arrival k\u03b8 corresponding to the K source signals, in the presence of measurement noise. Therefore, A = [a(\u03b81) a(\u03b82) \u2026 a(k\u03b8)] describes the N \u00d7 K array manifold matrix and v(t) = T \u2208 \u2102N\u00d71 represents the spatial and temporal white noise. For the observed signal nx(t) of the n-th sensor, let x(t) = T denote the N \u00d7 1 receiver signal vector. This vector equals:Consider v(t) is white Gaussian and zero-mean wide-sense stationary with covariance matrix C \u225c E{\u2016v(t)\u20162}. It is statistically independent of the source signals.The noise k\u03b8 \u2260 l\u03b8 for k \u2260 l.All source DOAs are distinct: ks(t) are mutually uncorrected and have a zero mean.The source signals L, such that:m,kd the frame-dependent and sensor-dependent average normalized signal power. This assumption means that the second-order statistics of the source signals are time varying, but that they remain static over a short period of time. Under this quasi-stationarity assumption, we define a local covariance matrix:Each source signal is wide-sense quasi-stationary with frame length The DOA-estimation algorithms under study are the root-MUSC and KR-root-MUSIC algorithms. These algorithms rely on the following assumptions:ks(t) satisfying the above constraints, with sequence length T = 25,600 and an allowable range of the frame periods  = . Algorithm 1 is applied to generate the synthetic signals.In the remainder of the paper, we apply the DOA estimation algorithms to synthetic signals generated by the procedure proposed in  to constcurT = 0. curT is the start of a new frame of the signal;Set whilecurT < TdofL following a uniform distribution on ;\u2003Randomly generate s\u03c3 following a uniform distribution on ;\u2003Randomly generate fort = curTtocurT + fL\u2212 1 do\u2003kS(t) = Rs(t) + Ijs(t), where Rs(t) and Is(t) are independent and identically Laplacian distributed with zero mean and variance \u2003\u2003Randomly generate end\u2003curT := curT + fL;\u2003end\u2003 Algorithm 1: The algorithm to generate synthetic signals.L = 512. The number of frames is set to M = T/512 = 50.Observe that the frame intervals of the different impinging sources are not fixed and not synchronized. We apply the KR subspace methods by choosing a fixed frame period of 2.2.L, where L divides T, the KR-MUSIC algorithm proceeds as follows  \u2208 \u2102(2N\u22121)\u00d7(2N\u22121\u2212K)from U, we compute the DOA spectrum:By extracting the noise subspace matrix For a given receiver signal vector rb(z) \u220a \u21021\u00d7(2N\u2212 1) as:K largest local maxima of the DOA spectrum PKR-MUSIC(\u03b8) are the DOA estimates.Define UnHW\u20162. In the remainder of the paper, we call the resulting method the KR-root-MUSIC method.Instead of searching the peaks of the MUSIC spectrum, we can also apply the root-MUSIC method  to \u2016UnHW3.N sensor elements, where the first sensor element is placed at the origin of the xy-plane and the other elements along the x-axis of this plane. The l-th sensor element is displaced by a vector In this section, we assume that one of the sensor elements is displaced due to an unintentional movement of an element. l-th sensor are given by r\u20d7 = . Define \u03b2 = arg(r\u20d7) and r = \u2016r\u20d7\u2016, such that u\u20d7 is the unit vector with the same direction of the position vector of the source, which is located in the array's far field. The l-th row of the array manifold matrix then becomes Denote 4.In order to investigate the influence of a stochastic displacement of one of the sensor elements, we need stochastic simulation tools to characterize the statistical distribution of the DOAs due to the distribution of the random displacement vectors.A Monte-Carlo simulation for such a task requires a large amount of realizations to accurately capture the statistics of the random process. Therefore, we apply the SCM proposed in  as a mor4.1.X  is given. We want to determine the variation of the output Y = f(X) , due to the statistical variation of X. The random variable X follows the cumulative distribution XP and probability density function XdP in the sample space \u03a9. To determine the statistics of Y, we rely on the Askey scheme . We apply the synthetic signal generation procedure of Section 2.1 to generate a random source signal and use this signal vector throughout the simulations. We furthermore assume that no noise has been added to the impinging signal. We assume that one of the sensor elements has moved along the x-axis. For d between two sensor elements) of the sensor element,Consider the case of In lgorithm  estimateK peaks. We also observe that in the KR-MUSIC case, the estimated curves are almost linear as a function of the shifts. Furthermore, we observe that DOAs estimated by using the KR-MUSIC algorithm are almost the same as those estimated by the KR-root-MUSIC algorithm.In 5.2.In this section, we start from the same assumptions as in Section 5.1, concerning the impinging signal and the sensor array.x-axis pl\u03c3 = 0.08. As outlined in Section 4, we therefore apply Hermite polynomials in the GPoC expansion of Q quadrature points and a polynomial expansion of order P = Q \u2212 1) to determine the expansion coefficients for the GPoC expansion. In the bottom figure of Let P = Q \u2212 1 for pl\u03c3 = 0.2. We observe that, in the 95% confidence interval  for In P = 4.In 5.3.v(t) = R\u03c5(t) + I\u03c5(t). R\u03c5(t) and I\u03c5(t) are both Gaussian distributed with zero mean and dispersion \u03c3 = 0.3 providing an SNR = 7.78 dB. Throughout the simulations, we use this source signal vector and noise vector. We also assume that the first sensor element is displaced along the x-axis and that the relative displacement pl\u03c3 = 0.12. To obtain the cdfs, we use two different methods: Monte-Carlo (MC) simulation and SCM. We carry out an MC simulation  .In this section, we assume that the first sensor element is displaced by d,eyreld]. The relpl\u03c3 = 0.12. We have carried out an MC simulation with 10,000 realizations. The simulation time is about 128 s for the root-MUSIC algorithm and 157 s for the KR-root-MUSIC algorithm. We also apply the two-dimensional GPoC expansion P in both variables to obtain the cdfs for the DOAs. We calculate the weight coefficients using Q1 = Q2 = P \u2212 1 quadrature points in the x- and y-directions using Q = 44, Q = 99 and Q = 172, respectively, and with polynomial expansions of order P = 7, P = 10 and P = 15, respectively. The measured value of the KS test, which compares the samples of the MC method with those obtained with the cubature formulas, is also presented in \u03b1 = 0.05). Using cubature formulas, only for the estimates of the third DOA, 172 quadrature points are insufficient to satisfy the null hypothesis. For the KR-root-MUSIC algorithm, four quadrature points in each direction are sufficient. If we use cubature formulas, Q = 44 quadrature points are sufficient to satisfy the null hypothesis. We also observe that, using the SCM theory, the simulation time is reduced by a factor of about 20, and using the cubature formulas, we can reduce the simulation time by a factor of 56.For the same impinging signal as in Section 5.3, we have plotted the cdfs of the different estimated DOAs, for P = Q \u2212 1 = 13. We observe that both curves almost coincide.In pQ as the p-th percentile of the estimated DOA, meaning that p% of the estimates for the true DOA are below pQ. Define S around the true DOA. For a Gaussian distribution, the value S will correspond to the dispersion. In S as a function of pl\u03c3 for a two-dimensional displacement of the first sensor element. Again, we observe that the SCM method provides a good approximation for the estimates, both for the root-MUSIC algorithm as for the KR-root-MUSIC algorithm. Observe that for values pl\u03c3 less than 0.4, the root-MUSIC yields better estimates for the first and third DOA than the KR-root-MUSIC algorithm. However, the KR-root-MUSIC estimates the second DOA better. We furthermore observe that, for the KR-root-MUSIC algorithm, the S-values are straight lines as a function Of pl\u03c3.Define N,K) =  case with a displacement of the first sensor element and with the KR-root-MUSIC algorithm. The true DOAs to be estimated are . Observe that, with the same array configuration as in \u03b8\u03021 = \u221265\u00b0 with a large error, even for small values of pl\u03c3. The estimation error for the remainder of the DOAs starts to increase dramatically for values of pl\u03c3 larger than 0.2.In 6.In this paper, we have investigated the effect of a displacement of one of the sensor elements. We have applied the SCM formalism to efficiently predict the cdfs of the estimated DOAs, in the case that the relative displacement is Gaussian distributed. Comparison of the SCM method to the Monte-Carlo method demonstrates that SCM is an accurate method to predict the cdfs of the DOAs. For the one-dimensional case, the SCM method decreases the simulation time by a factor of more than 100. For the two-dimensional case and using cubature formulas, we can reduce the simulation time by a factor of 56. In the future, we will extend the applied method to array configurations in which more sensor elements are displaced. Moreover, the SCM will be applied to other DOA estimation algorithms and for other array configurations. The flexibility and non-intrusive character of the proposed method only requires that DOA-estimates need to be computed in the quadrature points, by use of the appropriate algorithm."}
+{"text": "G\u2032/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized ( G\u2032/G)-expansion method [G\u2032/G)-expansion method to look for travelling wave solutions of NLEEs. Zhang et al. [G\u2032/G)-expansion method and its applications. Authors of [G\u2032/G)-expansion method. Also, Bekir [G\u2032/G)-expansion method for nonlinear evolution equations. In this paper we explain the method which is called the (G\u2032/G)-expansion method to look for travelling wave solutions of nonlinear evolution equations.The general form of the Drinfeld-Sokolov-Satsuma-Hirota system that is going to be studied in this paper is given by wt\u22126wwx+wloped in . System wt\u22126wwx+wwt\u22126wwx+wloped in . Howeverloped in . Wazwaz loped in , the sinloped in \u201310, the loped in , sine-coloped in , homotoploped in , homotoploped in , 15, varloped in , 17, B\u00e4cloped in , 19, Exploped in , 21, -expansion method; we give the detailed description of the method which was first presented by Wang et al. [Another powerful analytical method is called  and dependent variable u, \u03be = x + y \u2212 ct is wave variable. Also, c is a constant to be determined later.For a given NLPDE with independent variables G(\u03be) satisfies the second order LODE in the following form: a0, ak , \u03bb, and \u03bc are constants which will be determined later, am = 0, but the degree of which is generally equal to or less than m \u2212 1; the positive integer m can be determined by considering the homogeneous balance between the highest order derivatives and nonlinear terms appearing in /G(\u03be))k , and then setting each coefficient to zero, we can get a set of overdetermined partial differential equations for a0, ai , \u03bb, c, and \u03bc with the aid of symbolic computation Maple.Substituting  and 5)  5) into ai,\u2026, am, c and general solutions of (G(\u03be) of ai,\u2026, ations of  dependin(G(\u03be) of .We now describe the generalized tanh-coth method for the given partial differential equations. We give the detailed description of the method which to use this method; we take the following steps.X =  and dependent variable u, we consider a general form of nonlinear equation \u03be = x + y \u2212 ct is wave variable. Also, c is constant to be determined later.For a given NLPDE with independent variables ak , bk , p, r, and q are constants to be determined later. But, the positive integer m can be determined by considering the homogeneous balance between the highest order derivatives and nonlinear terms appearing in =S(\u03a6)m obtained in k , and then setting each coefficient to zero, we can get a set of overdetermined partial differential equations for a0, ai , bi  p, q, and r with the aid of symbolic computation Maple.Substituting  and 9)  9) into a0, a1, b1,\u2026, am, bm, c in -expansion method, we have F = G\u2032/G and then G\u2032/G)-expansion are same as ones by the generalized tanh-coth methods. Hence we use only the generalized tanh-coth method.But from \u221218u\u2032u\u2032\u2032\u2032 in  we obtaiwt\u22126wwx+wions of (u(\u03be)=a0+ae we get 2u(v)\u221218uituting =a0+a(I) The First Set for (\u03be = x \u2212 (p2 \u2212 4qr)t. Set for . By usin(II) The Second Set for (\u03be = x \u2212 (p2 \u2212 4qr)t. By using the w = ux, v = (1/6)(ut \u2212 3(ux)2 + uxxx), can be used to get the solutions of the DSSH system (G\u2032/G)-expansion and the generalized tanh-coth methods. Also, in this paper we can see correlation between (G\u2032/G)-expansion method and tanh-coth methods. We have succeeded in identifying the equivalence of the two methods under special conditions [G\u2032/G)-expansion method is exactly the same as the solution of tanh-coth method if the conditions are satisfied. In fact, we can see that the tanh-coth method is a special case of the (G\u2032/G)-expansion method. Set for . By usinBy using u27=G\u2032/G)-expansion and the generalized tanh-coth methods which are useful methods for finding travelling wave solutions of nonlinear evolution equations. These methods have been successfully applied to obtain some new generalized solitonary solutions to the DSSH equation. These exact solutions include three types: hyperbolic function solution, trigonometric function solution, and rational solution. The generalized (G\u2032/G)-expansion method is more powerful in searching for exact solutions of NLPDEs. By comparing our results and Wazwaz's [In this paper we investigated the Drinfeld-Sokolov-Satsuma-Hirota system by using the generalized (Wazwaz's  results"}
+{"text": "Parkinson\u2019s disease (PD) is a degenerative disorder of the central nervous system, in which a small naturally unfolded protein \u03b1-synuclein plays an essential role. \u03b1-Synuclein belongs to a synuclein family comprising three members: \u03b1, \u03b2, and \u03b3-synucleins associated with neurodegenerative and neoplastic diseases and involved in development. Several studies revealed that \u03b1-synuclein is present not only in the brain, but also in the skin and other peripheral tissues. This finding open a new approach to PD diagnosis based on the assay of \u03b1-synuclein from a biological sample of a living patient. Furthermore, PD is associated with an increased risk of skin melanoma. An important posttranslational modification of \u03b1-synuclein is phosphorylation at serine-129, which may convert the protein into pathological species both in PD and melanoma. Thus, analysis of phosphorylated \u03b1-synuclein might be an important diagnostic test for both diseases providing additional information about the mechanism of pathology. Parkinson\u2019s disease (PD) is a common severe neurodegenerative disorder that affects a significant proportion of the adult population. The risk of developing PD is age dependent, affecting 1%\u20132% of the population over 65 years . The undetc. . HoweveOne of the key proteins in PD pathogenesis is \u03b1-synuclein (reviewed in ), being The use of \u03b1-synuclein as a PD marker is relatively easy, because it is present not only in the brain, but also in peripheral organ and tissues .Currently, the study of \u03b1-synuclein phosphorylation mechanism related to the PD pathology has become a research hotspot, because after phosphorylation by G-protein-coupled kinase  or other\u03b1-Synuclein is a naturally unfolded protein easily changing its conformation and only specific conformers possess toxic properties. Thus, generation of conformation-specific \u03b1-synuclein antibodies and/or antibodies distinguishing phosphorylated/nonphosphorylated \u03b1-synuclein is an important step for the improved specificity of PD diagnosis . Hopefuletc., have been made [PD diagnosis based on \u03b1-synuclein analysis may be simplified, because this protein is present not only in the brain, but also in peripheral tissues . Severaleen made ,18,19,20een made ).Initially testing of \u03b1-synuclein in CSF as early PD diagnostic tool gave promising results ,21, but in vivo biomarker for degenerative peripheral autonomic neuropathy. In a later study, the same research team applied similar method for analysis of native \u03b1-synuclein (n-syn) and misfolded phosphorylated (p-syn) \u03b1-synuclein in idiopathic Parkinson disease (IPD) attempting to define the importance of n-syn and p-syn for PD diagnosis [in vivo marker of IPD, and its analysis in skin shows that p-syn inclusions are different in PAF and IPD, pointing to dissimilar underlying pathogenic mechanisms [Recently, an important step forward in PD early diagnosis is described by Donadio and coauthors . These riagnosis . The autchanisms .in vivo, are promising because they are based on a direct, straightforward, low-priced, and minimally invasive technique with minor discomfort for the patient.Therefore, recent studies have shown that methods based on the use of n-syn/p-syn ratio analysis in skin biopsy to diagnose PD and other synucleinopathies Importantly, patients with PD have an increased risk of developing melanoma, which is the major cause of skin cancer death worldwide . It has Several putative players may be involved in this association, including tyrosine, tyrosinase, tyrosine hydroxylase, DJ-1 and melanocortin 1 receptor ,37,38,39An important ongoing international multicenter prospective study The Parkinson\u2019s Progression Markers Initiative (PPMI)  is aimedetc. However, it is usually better with p-syn than with \u03b1-synuclein. For example, Wang and coauthors [The sensitivity and specificity of p-syn analysis in skin and other peripheral tissues in some studies is not high enough to use it as a routine method of PD diagnostic ,46, whicoauthors  concludeoauthors . Some mooauthors  proposedoauthors . The devoauthors  may be aThus, Ser129 phosphorylated \u03b1-synuclein may be a more reliable marker compared to unphosphorylated protein, and its analysis demonstrates higher specificity and better prognostic value. Collecting of skin samples is inexpensive and not invasive method. Therefore, the analysis of phosphorylated \u03b1-synuclein can be used as an important diagnostic test for both diseases and provide additional information about the mechanism of pathology."}
+{"text": "Unlike the western medical approach where adrug is prescribed against specific symptoms of patients,traditional Chinese medicine (TCM) treatment has a uniquestep, which is called syndrome differentiation (SD). It is arguedthat SD is considered as patient classification because priorto the selection of the most appropriate formula from a setof relevant formulae for personalization, a practitioner hasto label a patient belonging to a particular class (syndrome)first. Hence, to detect the patterns between herbs and symptomsvia syndrome is a challenging problem; finding thesepatterns can help prepare a prescription that contributes tothe efficacy of a treatment. In order to highlight this uniquetriangular relationship of symptom, syndrome, and herb, wepropose a novel three-step mining approach. It first startswith the construction of a heterogeneous tripartite informationnetwork, which carries richer information. The second step isto systematically extract path-based topological features fromthis tripartite network. Finally, an unsupervised method is usedto learn the best parameters associated with different featuresin deciding the symptom-herb relationships. Experiments havebeen carried out on four real-world patient records  with comprehensivemeasurements. Interesting and insightful experimental resultsare noted and discussed. Traditional Chinese medicine (TCM) has a long history and has been accepted as one of the main medical approaches in China . Many ofIn recent years, interest in TCM has increased globally and the application of data mining to TCM \u20134 is alsIn general, a homogeneous information network can be derived from a heterogeneous information network, for example, an herb-herb network can be derived from a symptom-syndrome-herb network by a projection on herbs only. A heterogeneous information network is different from a homogeneous information network because it carries richer information than its corresponding projected homogeneous information networks. Therefore, it aimed to discover herb-symptom patterns, via syndromes, from a heterogeneous information network, which contains different types of attribute values associated with objects. To the best of our knowledge, this is the first attempt towards mining herb-symptom patterns in TCM utilizing heterogeneous information networks.In this research, we construct the heterogeneous information network leveraging the tripartite graph. Our heterogeneous information network contains multiple types of objects, such as herb, symptom, syndrome, and multiple types of links defining different relations among these objects, such as links existing between herbs and syndromes, between syndromes and symptoms, and between symptoms and herbs. Thus, the number of different types of objects there are in the network can be found out, as well as the identification of the possible links existing among objects. Furthermore, we can detect the patterns between herbs and symptoms.We construct the TCM heterogeneous information network utilizing the tripartite graph.We study the problem of the symptom-herb relationship prediction in TCM heterogeneous information network.We propose a novel three-step prediction approach based on the TCM heterogeneous information network to discover symptom-herb patterns.Experiments on real TCM patient records indicate that our proposed method can mine symptom-herb relationships with high accuracy.Treatments are proven to be more effective than a direct symptom-herb relationship; that is, classifying patients into different syndromes is a crucial step in TCM treatment.The major contributions of this paper are summarized.The remaining of the paper is organized as follows. We first introduce the background and preliminaries on TCM heterogeneous information networks and denote the task of symptom-herb pattern prediction in H = {h1, h2,\u2026, hn}, a set of syndromes D = {d1, d2,\u2026, dm}, and a set of symptoms P = {p1, p2,\u2026, pq}. We assume that there are n herbs, m syndromes, and q symptoms. Here, symptoms refer to something that can be observed and measured, such as fever, nausea, coughing, and weight loss. Syndrome is a special phenomenon in TCM. A TCM doctor will base upon the patient's symptoms and classify them into one or two syndromes. After that, formulas will be prescribed according to the syndrome.In this work, we need to consider three types of entities: a set of herbs We first introduce the definitions of heterogeneous information network , 8, tripG =  with an entity type mapping function \u03d5 : V \u2192 \ud835\udc9c and a link type mapping function \u03c8 : E \u2192 \u211b, where each entity v\u2286V belongs to one particular entity type \u03d5(v)\u2286\ud835\udc9c, each link e\u2286E belongs to a particular relation type \u03c8(e)\u2286\u211b, and W : E \u2192 R+ is a weight mapping from an edge e\u2286E to a real number w\u2286R+. Notice that, when the types of entities |\ud835\udc9c| > 1 and also the types of relations |\u211b| > 1, the network is called heterogeneous information network.A heterogeneous information network is denoted as a directed graph V1 \u222a V2 \u222a V3}, E\u232a can be called as tripartite, if a set of graph nodes decomposed into three disjoint sets such that no two graph nodes within the same set are adjacent; that is, V1\u2229V2\u2229V3 = \u2205.A graph TG = \u2329{X, Y, and Z, where X = {x1, x2,\u2026, xm}, Y = {y1, y2,\u2026, yn}, and Z = {z1, z2,\u2026, zq}, graph G = \u2329V, E\u232a is called a tritype information network on types X, Y, and Z, if V(G) = X \u222a Y \u222a Z and E(G) = {\u2329oi, oj\u232a}, where oi, oj \u2208 X \u222a Y \u222a Z.Given three types of objects sets Wm+n)\u2217(m+n)( = {\u2329woioj\u232a} (or Wn+q)\u2217(n+q)( = {\u2329woioj\u232a} or Wm+q)\u2217(m+q)( = {\u2329woioj\u232a}) be the adjacency matrix of links, where \u2329woioj\u232a equals the weight of link \u2329oi, oj\u232a, which is the observation number of the link, and we thus use G = \u2329{X \u222a Y \u222a Z}, W\u232a to define this tritype information network with weight. In the following, we use X, Y, and Z denoting the object set and their type name. For convenience, we decompose the link matrix into four blocks: WXX, WXY, WYX, and WYY , each denoting a subnetwork of objects between types of the subscripts. W can be denoted asLet H representing herbs, P representing symptoms, and D representing syndromes. Notations and similarity relations used in definitions as well as the rest part of the paper can be found in Notation section.This tritype information network, one of the heterogeneous information networks, denotes the rules of how entities exist and how links should be created. And, through analyzing this tritype information network, we can know how many types of objects there are in the network and where the possible links exist. In the following, we give an example of tritype information network, which is showed in G = \u2329{H \u222a D \u222a P}, W\u232a, the target type P, and a set of herbs {Hj}, our goal is to find or predict the most reasonable herbs for each symptom Pi, that is, how to predict the target relationship E(G) = {\u2329Pi, Hj\u232a}, where Pi, Hj \u2208 P \u222a H.Based on the previous definitions, our goal of this work can be summarized as follows: given a tritype network Different from symptom-syndrome patterns and syndrome-herb patterns, which are directed relationships , symptom-herb patterns are undirected relationships. Intuitively, the herb-symptom relationship detection is an implicit relationship mining, which is more difficult to detect than an explicit relationship mining. However, if new herb-symptom relationships can be discovered, they are beneficial for doctors configuring the prescriptions.In this work, our experiments were performed on four real TCM datasets: Insomnia, Infertility, Diabetes, Tourette. These four datasets were provided by Guang'anmen Hospital, China Academy of Chinese Medical Sciences. These four datasets include the symptoms, the syndromes, and prescription information of outpatients. Here, edges are formed among objects belonging to the same prescription. Properties of these four datasets are shown in In this section, we conduct following observations based on the four TCM datasets in order to get a better understanding on the symptom-syndrome-herb patterns and structural properties of TCM tripartite network.x-axis represents the 251 unique herbs, ordered by descending herb frequency. The y-axis refers to the herb frequency. As reported by other authors  to provide a range of tolerance to bad outcomes. In particular, given a relevance function R, the relevance threshold \u03b8 is used for creating the parameterized version of this relevance function, R, that is formalized as\u03b8 changes over different datasets. Ax, Ay \u2208 X \u222a Y \u222a Z and ratio = Good_Outcome(Pattern)/(Good_Outcome(Pattern) + Bad_Outcome(Pattern)). Here, Good_Outcome(Pattern) refers to the total number of this pattern working effectively, and Bad_Outcome(Pattern) is the total number of this pattern having no effect on patients. In the next section, patterns of symptom-herb that are predicted above relevance threshold \u03b8  = 1) are sorted according to predicted rating, while patterns of symptom-herb that are below \u03b8  = 0) are ignored.In this work, relevance function is used to filter out the patterns with bad outcome. Here, the relevance function is parameterized with \u201crelevance threshold\u201d K nearest entities according to the similarity measures, simPH_Path or simPDH_Path; then, we predict rating for each potential entity pair; subsequently, we get Top-n predicted patterns by ranking prediction rating; lastly, we get Top-N list by filtering the patterns of bad outcome using relevance function. The pseudocode of Tri-TSPA is shown in Up to now, we have given a systematic way to extract and build the topological features in the tripartite networks. In this subsection, we will introduce our prediction algorithm (Tri-TSPA). Our prediction method is as follows: first, we discover F measurement strategy to calculate the rating. Actually, we can replace F with JC, AW, and TfIdf, respectively. In addition, PH_Path based on symptom-herb patterns mining is shown in Line 4\u2013line 7, and PDH_Path based on symptom-herb patterns mining is shown in Line 8\u2013Line 11.In In this section, we conduct many experiments to evaluate the effectiveness of the proposed algorithm. We show that our proposed three step prediction approach can mine a reasonable set for each symptom on the TCM networks.We first convert these datasets into heterogeneous tripartite information networks. We construct four TCM networks from TCM datasets, which consist of three types of objects: symptoms, syndromes, and herbs. Links exist between symptoms and syndromes, syndromes and herbs, and herbs and symptoms.PH_Path based strategy and PDH_Path based strategy. For each strategy, we apply four different measurement methods to set each term of each matrix related to this PH_Path (or PDH_Path). By combining these two kinds of strategies and four measurement methods together, we get total 8 different predicted methods. In the following section, a series of experiments will be carried on in order to find which predicted method can get the best performance.In order to effectively mine symptoms-herbs patterns, we adopt two kinds of strategies: F, JC, AM, and TfIdf). After collecting all associated features, a training model is then built to learn the best coefficients associated with different features in deciding the symptom-herb patterns by performing multiple experiments. In the test stage, we utilize the learned coefficients to predict the potential patterns between symptoms and herbs and record whether this pattern is to appear in the test dataset.In this work, we adopt twofold cross-validation  to evaluate the performance of the prediction for each TCM network. In the training stage, we first extract two kinds of paths, symptom-herb path and symptom-syndrome-herb path. In terms of these two paths, we further build five matrices in  accordinPDH_Path from Infertility and Diabetes datasets, such as p1-d1-h1, p2-d1-h1; meanwhile, we can obtain the existing patterns based on the PH_Path from Insomnia dataset, such as p1-h1, p2-h1. Second, we can further check whether the patterns based on the PH_Path from Insomnia dataset exist in the dataset Insomnia or Tourette. If they exist , we can assume a virtual syndrome d and construct the edge between d and p1 and the edge between d and h1 (or the edge between d and p2). Otherwise, we only assume a virtual syndrome d and produce the edges between d and other symptoms (or the edges between d and other herbs). Similarly, we can construct the tripartite graph based on the Tourette dataset.In addition, the Insomnia and Tourette dataset lacks the object of syndrome and symptom, respectively. In this case, we assume some virtual objects (representing syndromes or symptoms) which can be constructed according to the next method. Here, we take the Insomnia dataset as an example to explain how to construct the virtual objects, namely, syndromes. First, we can get the existing patterns based on the N highest ranked herbs as the predicted list for a target symptom. To evaluate the prediction accuracy, we focus on how many symptoms-herbs patterns previously removed in the preprocessing step reappear in the predicted results. Therefore, we apply two popular performance metrics, namely, Precision@N and Recall@N [Our proposed algorithm computes a ranking score for each candidate herb and returns the top-Recall@N \u201320, to cN is the ratio of recovered symptoms-herbs patterns to the N predicted symptoms-herbs patterns. Recall@N is the ratio of recovered symptoms-herbs patterns to the set of symptoms-herbs patterns deleted in preprocessing. We divide the symptoms-herbs patterns into two sets: the test set Th and the Top-N set Rh. Symptoms-herbs patterns that appear in both sets are members of the hit set. Precision and Recall are defined as follows:Precision@\u03bb0, \u03bb1, \u03b1, \u03b10, \u03b11, \u03b2, \u03b20, \u03b21, \u03b8, and K. We have varied the neighborhood size from 10 to 50 by an interval of 10 and the other nine parameters from 0 to 1 by an interval of 0.1. Using the validation data (in Infertility dataset), we have found the best \u03bb0 to be 0.8, \u03bb1 to be 0.2, \u03b1 to be 0.7, \u03b10 to be 0.8, \u03b11 to be 0.2, \u03b2 to be 0.3, \u03b20 to be 0.8, \u03b21 to be 0.2, \u03b8 to be 0.5, and K to be 30. In addition, we have different values for these parameters in the other three datasets, but we get the similar experimental results. Here, we do not list all the values for these parameters because of the limitation of space.In our experiments, we divide each dataset into two parts: training set and test set. We further split the training data to validation data to optimize the parameters K as an example to explain how to install optimal value for each parameter. From N list the Precision changes over the neighborhood size K. We can further observe that when the neighborhood size K equals 30, our proposed method gets the best performance. Also, from K as 30.In PH_Path based strategy and PDH_Path based strategy by using the optimal measurement method.In this section, we first evaluate the performance of four different measurement methods for two kinds of paths. And then, we compare the performance of F, and JC, respectively. From F, and JC. Here, an interesting result is observed that JC gets the worst performance. Contrary to JC being known to be more useful to measure the similarity between two same type of objects, it may be due to the existence of different type of objects. Similarly, from It is worth noting that a comprehensive set of experiments was conducted using every measurement method in conjunction with every evaluation metric on every dataset, and the results are very consistent across all experiments. Because of the space limitations, we show the results based on the Infertility dataset in the Figures In this section, we will estimate the performance of our presented Tri-TSPA based on two kinds of paths.PDH_Path can find more symptom-herb relations than the one based on PH_Path, in general.First, we illustrate how our Tri-TSPA can serve as a powerful model for predicting potential symptom-herb relationships. The prediction processing performance results can be found in Figures PDH_Path improves Precision@30 by 10.8% compared with the one based on PH_Path. In addition, from PDH_Path improves Recall@30 by 11% when compared with PH_Path. Therefore, we can conclude that PDH_Path based prediction method gives a good performance overall. Here, we can see that when N reaches 30, the precision of both algorithms is optimal. Meanwhile, although Recall@50 of both algorithms reaches optimal value, the gap between Recall@30 of both algorithms and Recall@50 of both algorithms is very small. So we take N = 30 as an optimal value to achieve optimal prediction power for the Infertility dataset.From In addition to the Infertility dataset, we tested the proposed algorithm with other three datasets, and the same pattern is observed in the vast majority of cases.The symptoms in TCM are related to the body as a whole. A certain subset of symptoms belongs to a certain syndrome, and the typical treatment of a syndrome usually follows a therapeutic principle, which refers to the use of a certain combination of herbs .N list of herbs for each symptom  is a crucial step to a successful treatment in TCM. In the future, we intend to extend our work in the following three directions. Firstly, a new measure to estimate the performance in the proposed method should be explored. Secondly, another novel similarity measure method should be studied to capture the rich topological features. Thirdly, a new matching function to improve the predictive performance should be sought."}
+{"text": "We prove the existence and uniqueness of fixed points of T-stability for an iteration on partial cone metric space of Zamfirescu contraction. As an application, we prove a theorem for integral equation. We also give illustrative examples to verify our results. Rhoades . Further, let T. In complete metric space, the Picard iteration process Banach\u2019s contraction condition.Let us consider a self mapping entclass1pt{minimaWe shall state some of the iteration process generalising  as folloFor For Kannan  establisT, there exists For a self map atterjea  gave theT, there exists For a selfmap mfirescu  establisentclass1pt{minimamfirescu  and 6)..T, thereThen the mapping  Rhoades , 1991, L Rhoades , Yousefi Rhoades , Rhoades Rhoades , Qing an Rhoades , Asadi e Rhoades , Saadati Rhoades , Olatinw Rhoades  and refeHuang and Zhang  obtainedE be a real Banach space. A subset P of E is called a cone ifP is closed, non-empty and Let P by x\u00a0\u2264\u00a0y if and only if P).Given a cone There are two kinds of cone. They are normal cone and non-normal cone. A cone The aim of this paper is to show the existence and uniqueness of fixed points of T-stability for an iteration on partial cone metric space under Zamfirescu contraction. We give an application in integral equation. We also give illustrative examples that verifies our results.We have the following basic definitions:X be a nonempty set. Suppose the mapping  Then d is called a cone metric on X and  is called a cone metric space. such that X is non-empty set and p is a partial cone metric on X is called a partial cone metric space. We know that if p\u00a0=\u00a00, then x\u00a0=\u00a0y. But if x\u00a0=\u00a0y, then p may not be 0.Sonmez  A partiaA cone metric space is a partial cone metric space. But there are partial cone metric space which are not cone metric space. The following example verifies the statement.X, p) is a partial cone metric space which is not a cone metric space.Sonmez  Let \\docX, p) be a partial cone metric space. Let X and x and x is called a limit of Sonmez  Let  be a partial cone metric space. Let X and N such that Sonmez  Let  is said to be complete if and only if every Cauchy sequence in X is convergent.Sonmez  A partiaX, d) be a complete metric space, X. Suppose that T. Let T which is defined by f is some function. Suppose p of T. Let T-stable or stable with respect to T if and only if Olatinwo  Let  be a partial cone metric space. Let X with X and posit that In this section we establish iteration procedure in partial cone metric spaces. This is to stretch out some recent results of T-stability. Let  be a complete partial cone metric space. Let P be a normal cone with normal constant K andwith. If there existssuch thatfor allandand in addition, wheneveris a sequence withas, then Picard iteration is T-stable.Let v be another fixed point of T, thenFor uniqueness: Let T is unique. Thus the fixed point of Let  be a complete partial cone metric space. Let P be a normal cone with normal constant K andwithIf there existssuch thatfor allandand in addition, wheneveris a sequence withasthen Picard iteration is T-stable.Let v be another fixed point of T, thenFor uniqueness: Let T is unique. Thus the fixed point of Let  be a complete partial cone metric space. Let P be a normal cone with normal constant K andwith. If there existssuch thatfor allandand in addition, wheneveris a sequence withas, then Picard iteration is T-stable.Let v be another fixed point of T, thenFor uniqueness: Let T is unique. We get p be the partial cone metric on X defined by Let mentclasspt{minimaLet X\u00a0=\u00a0C, withforand letdefined bywhereis a continuous function.The partial derivativeFwith respect to y exists andfor someFor every real numberone hasfor everyLetbe a normal cone and  the complete partial cone metric space definedwhere. Then Picard\u2019s iteration is T-stable ifF satisfies of Theorem\u00a0T has unique fixed point and Picard\u2019s iteration is T-stable.Let We extend and prove the T-stability of Picard\u2019s iteration satisfying Zamfirescu contraction in partial cone metric space. Our results are more general than that of the results of metric and cone metric spaces. This result can be extended to other spaces."}
+{"text": "As a key regulatory mechanism of gene expression, DNA methylation patterns are widely altered in many complex genetic diseases, including cancer. DNA methylation is naturally quantified by bounded support data; therefore, it is non-Gaussian distributed. In order to capture such properties, we introduce some non-Gaussian statistical models to perform dimension reduction on DNA methylation data. Afterwards, non-Gaussian statistical model-based unsupervised clustering strategies are applied to cluster the data. Comparisons and analysis of different dimension reduction strategies and unsupervised clustering methods are presented. Experimental results show that the non-Gaussian statistical model-based methods are superior to the conventional Gaussian distribution-based method. They are meaningful tools for DNA methylation analysis. Moreover, among several non-Gaussian methods, the one that captures the bounded nature of DNA methylation data reveals the best clustering performance. Recentl\u03b2, at a specific genomic locus provides an estimate of the fraction of cells that have that locus methylated. Although studies have considered using the logit-transform y = log2\u03b2/(1 \u2212 \u03b2) instead of \u03b2 for subsequent statistical inferences   and canribution  and the ribution  are usuaIn the remaining part of this section, we will introduce some typical non-Gaussian distributions that can be applied in DNA methylation analysis.3.1.1.u and v. The pdf of the beta distribution is:The beta distribution is characterized by two positive shape parameters where \u0393(\u00b7) is the gamma function. The beta distribution has a flexible shape, which is shown in 3.1.2.l2 norm equals one, i.e., ||x||2 = 1. The vMF distribution contains two parameters, namely the mean direction \u03bc and the concentration parameter \u03bb. The pdf of a K-dimensional vMF distribution can be expressed as:The vMF distribution is considered a popular distribution in the family of directional distributions ,51. The \u03bc||2 = 1, \u03bb \u2265 0 and K \u2265 2 [K(\u03bb) is given by:where ||nd K \u2265 2 . The nor\u03bd(\u00b7) represents the modified Bessel function of the first kind of order \u03bd [where \u2110 order \u03bd . The pdf order \u03bd ,54. It c order \u03bd .3.1.3.x and \u2212x are equivalent. In other words, that is \u00b1x that are observed. Here, we need probability density functions for x on  which are axially symmetric, that is f(\u2212x) = f(x). In such cases, the p-dimensional observation \u00b1x can be regarded as being on the projective space \u2119p\u22121, which is obtained by identifying opposite points on the sphere .Observations on the sphere might have an additional structure, such that the unit vectors One of the simplest distributions for axial data, with a rotational symmetry property, is the (Dimroth\u2013Scheidegger\u2013) Watson distribution. The Watson distribution is a special case of the Bingham distribution , which ix \u2208 \u2119p\u22121, or equivalently \u00b1x \u2208 , has the (p \u2212 1)-dimensional Watson distribution pW , with the mean direction \u03bc and the concentration parameter \u03ba, if its probability density function is:A random vector \u03ba \u2208 \u211d, ||\u03bc||2 = 1, and 1F1 is Kummer\u2019s (confluent hypergeometric) function  reduces to the uniform density, and as \u03ba \u2192 \u221e, pW  tends to a point density. For \u03ba < 0, as \u03ba \u2192 \u2212 \u221e, the density concentrates around the great circle orthogonal to the mean direction  is drawn according to the following generative model:With the above description, we assume that the matrix x; k, \u03b8) is the gamma density with parameters k, \u03b8 defined as:where Gamma method  is appliwhich can be expressed in matrix form as:H, the reconstruction in where \u2298 means element-wise division. When placing sparsity constraints on the columns in W\u0304 is low-dimensional while retaining the bounded support constraint.Hence, the resulting pseudo-basis matrix 3.3.1.L are not corresponding to the convex region, the K-means algorithm cannot provide satisfactory clustering results. However, when mapping the data points to \u211dK space via SC, they may form tight clusters [K-dimensional space, the reduced features, each of which is K-dimensional, are extracted by taking eigenvalue analysis of an intermediate matrix M. The reduced features will then be used for clustering, with conventional methods like K-means. The feature extraction procedure via the SC method [K space.Recently, spectral clustering (SC) has become one of the most popular clustering algorithms . It is aclusters . SC analC method  is summa3.4.K-dimensional space. These data are obviously non-Gaussian distributed. It has been shown in several studies that applying a suitable non-Gaussian distribution to model the non-Gaussian distributed data can improve the corresponding performance [The ultimate goal of dimension reduction is to benefit the clustering of DNA methylation data. The dimension reduction methods introduced above yield features with special properties. The BG-NMF method provides a basis matrix see , every eformance ,26,31. T3.4.1.For the beta-valued DNA methylation data, it is natural to consider the beta distribution as a candidate to model the underlying distribution. Since the DNA methylation data that show an obvious normal/cancer status are multi-modal, a beta mixture model (BMM) can be applied for modeling. One mixture component represents one cluster. In unsupervised clustering, selecting the optimal number of clusters is a big challenge. One popular method designed for such purpose is the recursive partitioning beta mixture model (RPBMM) . The RPB3.4.2.Another way of carrying out model selection is to employ the variational Bayesian estimation framework for BMM (VBBMM). Under this circumstance, the joint posterior distribution of the weighting factors is modeled by a sparse Dirichlet distribution, so that the component with a very small weight will be pruned from the mixture model. In , the ext3.4.3.l2 norm equaling one has a directional property. The von Mises-Fisher (vMF) distribution is suitable for such a type of data [The data with its  of data ,69. In o of data . This me3.4.4.i.e., l2 norm equals one) and its axial mirror by the Watson distribution. Similarly, when such data are multi-modally distributed, a Watson mixture model (WMM) can be applied. With a variational inference framework, Taghia et al. [The Watson distribution is a simple distribution for modeling axially symmetric data on the unit hypersphere ( (Chaptera et al.  proposed4.Cancer is characterized by alterations at the DNA methylation level. A Gaussian distribution, in general, cannot describe the DNA methylation data appropriately. Hence, the Gaussian distribution-based unsupervised clustering does not provide convincing performance.For the purpose of efficiently clustering DNA methylation data, we proposed several dimension reduction methods and consequent unsupervised learning methods, which are all based on non-Gaussian distributions. They all perform better than the Gaussian distribution-based method. In the dimension reduction step, both the BG-NMF and the SC methods can remove the redundant dimensions efficiently. In unsupervised clustering, the VBBMM method, the VBvMM method and the VBWMM method can all reveal the heterogeneity of the DNA methylation data appropriately. Clustering performance demonstrates that the proposed non-Gaussian distribution-based methods are meaningful tools for analyzing DNA methylation data. Experimental results also show that the BG-NMF + VBBMM method performs the best among all of the proposed methods and is faster than the benchmarked BG-NMF + RPBMM method. Furthermore, for the reduced features inferred from both the BG-NMF method and the SC method, the consequent unsupervised clustering method needs to be improved, so that better clustering accuracy can be obtained.Moreover, the methodology introduced in this paper can be easily extended to analyze other DNA methylation data sets. Some other non-Gaussian statistical models can also be applied for such purposes."}
+{"text": "The rapid advance of DNA sequencing technologies has yielded databases of thousands of genomes. To search and index these databases effectively, it is important that we take advantage of the similarity between those genomes. Several authors have recently suggested searching or indexing only one reference genome and the parts of the other genomes where they differ. In this paper, we survey the 20-year history of this idea and discuss its relation to kernelization in parameterized complexity. With these methods, initiatives such as the 1000 Genomes Project and the 100,000 Genomes Project are now feasible. Advances in sequencing have far outstripped advances in computer processors and random-access memory, however, so it is increasingly challenging to make use of the data available. For example, while modern aligners can easily hold in memory the index for approximate pattern matching on a single human genome, they cannot handle thousands of human genomes. Schneeberger et al.  proposedWhen we are not given an upper bound on the pattern length, we can use one of the competing indexes that does not require such a bound or we can scan, with an online pattern-matching algorithm, the reference genome, and the parts of the other genomes near phrase boundaries. Wandelt and Leser  and Rahn2S is a string with S[n]\u2009=\u2009$, which is an end-of-file symbol that does not occur elsewhere in S. LZ77 works by parsing S into phrases such that, for each phrase S, S occurs in S but S does not occur in S; that phrase is stored as a triple consisting of a pointer to S\u2019s first occurrence in S , j\u2009\u2212\u2009i, and S[j]. The LZ77 encoding of S takes \ud835\udcaa (z log n) bits, where z is the number of phrases in the parse. For example, in the following verses vertical lines indicate phrase boundaries:9|9-|b|o|t|tl|e|s|-o|f|-be|er|-on|-t|h|e-|w|a|ll|-9|9-bottles-of-beer-I|f-o|n|e-o|f-t|ho|se|-bottles-s|hou|ld|-h|ap|pe|n-to|-f|all-98|-bottles-of-beer-on-the-wall-98|-bottles-of-beer-on-the-wall-98-bottles-of-beer-I|f-one-of-those-bottles-should-happen-to-fall-97|-bottles-of-beer-on-the-wall\u2009\u2026In general, the best compression of highly repetitive datasets is achieved with the LZ77 algorithm by Ziv and Lempel . Suppose Although these verses may be annoyingly similar by the standards of natural language, they are far less similar than human genomes. Indeed, most repetitive biological datasets are much too similar (as well as much too large) for us to use them as informative examples.S with \ud835\udcaa (z log n) rules. An SLP for S is a context-free grammar in Chomsky normal form that generates S and only S; it is balanced if the height of each subtree in the parse tree is logarithmic in that subtree\u2019s size. It follows from Rytter\u2019s and Charikar et al.\u2019s results that we can store S in \ud835\udcaa (z log2n) bits and support random-access reading of any substring of S with length l in \ud835\udcaa (log n\u2009+\u2009l) time. Verbin and Yu  bits and support random-access reading in \ud835\udcaa (log n\u2009+\u2009l) time. Rytter\u2019s, Charikar et al.\u2019s, and Bille et al.\u2019s constructions are not practical, but there are practical grammar-based compressors, such as those by Larsson and Moffat (S can easily be augmented to support random-access reading in \ud835\udcaa (log log n\u2009+\u2009l) time. LZ78 also works by parsing S into phrases but then each phrase must extend a previous phrase plus one character. Because of this property, the LZ78 encoding of S has \u03a9 (S\u2009=\u2009na.One drawback of LZ77 compression is that reading a character in a compressed string can be very slow. Rytter  and Charn and Yu  showed tn and Yu  showed hd Moffat  and Marud Moffat . As far d Moffat  and Gagid Moffat  are the d Moffat  does notS\u2009=\u2009na) and there are several implementations of this approach, such as those by Deorowicz and Grabowski  has length at most m\u2009+\u2009k, and any such substring that does not cross or end at an LZ78 phrase boundary must be an exact copy of an earlier one that does. They gave an algorithm for approximate pattern matching in LZ78 strings that works by extracting the m\u2009+\u2009k and m\u2009+\u2009k\u2009\u2212\u20091 characters before and after each LZ78 phrase boundary, respectively, using a technique similar to those discussed in Section Farach and Thorup  observed Ukkonen  showed hP\u2019s approximate matches in S from an SLP for S. Recently, Gagie et al. (S in \ud835\udcaa (z log n) time such that later, given P and k, we can find all P\u2019s occ approximate matches in \ud835\udcaa \u2009+\u2009occ) time. Their algorithm works by extracting the m\u2009+\u2009k and m\u2009+\u2009k\u2009\u2212\u20091 characters before and after each LZ77 phrase boundary, respectively, and then continuing as with the algorithm by Bille et al.  bits and returns the locations of all P\u2019s occ occurrences in S in \ud835\udcaa (m log m\u2009+\u2009occ log log n) time. These indexes require no assumptions about the pattern.K\u00e4rkk\u00e4inen and Ukkonen  gave the Navarro  modifiedo et al.  and Do eo et al.  gave indo et al.  and Takao et al.  gave indo et al. . Gagie eo et al.  recentlyq\u2009\u2212\u20091 characters, where q is a parameter. If P has length exactly q, then their index returns the locations of all P\u2019s occurrences in S in optimal \ud835\udcaa (m\u2009+\u2009occ) time. If we are given an upper bound M on the pattern length at construction time, then even with K\u00e4rkk\u00e4inen and Ukkonen\u2019s original version, we need keep only a kernel of the text and can use \ud835\udcaa (z log n\u2009+\u2009zM log \u03c3) bits in total, where \u03c3 is the size of the alphabet. We suspect this escaped investigation for so long because it seemed too obvious and inelegant to be theoretically interesting, and the need to index massive, highly repetitive datasets in practice has become pressing only since the development of next-generation sequencing methods.K\u00e4rkk\u00e4inen and Sutinen  gave an q-grams or seeds. Danek et al.\u2019s index for the database for the 1000 Genomes Project is the first one to fit in the memory of a commodity personal computer. Ferrada et al. (The use of kernelization for indexing was eventually investigated by Schneeberger et al. , althouga et al.  emphasizThe authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Co-occurrence of aggression and anxiety might change during adolescence, or stay stable. We studied change and stability of four types of co-occurrence regarding direct aggression and anxiety in adolescence: an anxious and non-aggressive type, an aggressive and non-anxious type, a comorbid aggressive-anxious type and a no problems type. We applied a person-centered approach to assess increases and decreases of these types, and tested various models of intra-individual change of the types: the stability, acting out and failure models. We used data from a five-wave study of 923 early-to-middle and 390 middle-to-late adolescents , thereby covering the ages of 12\u201320. We observed accelerated development in the older cohort: adolescents tended to grow faster out of the aggressive types in middle-to-late adolescence than in early-to-middle adolescence. We observed one other group-dependent pattern of heterogeneity in development, namely \u201cgender differentiation\u201d: gender differences in aggression and generalized anxiety became stronger over time. We found support for two perspectives on intra-individual change of the four types, namely the stability and the acting out perspective. The no problems\u2014and to a lesser extent the anxious\u2014type proved to be stable across time. Acting out was found in early-to-middle adolescents, males, and adolescents with poorer-quality friendships. In all three groups, there were substantial transitions from the anxious type to the aggressive type during 4\u00a0years (between 20 and 41\u00a0%). Remarkably, acting out was most prevalent in subgroups that, generally speaking, are more vulnerable for aggressive behavior, namely early-to-middle adolescents and males. We interpret acting out as the attempt of adolescents to switch from anxiety to instrumental aggression, in order to become more visible and obtain an autonomous position in the adolescent world. Acting out contributed to the explanation of accelerated development and gender differentiation. We also observed an increase of adolescents with no problems. These findings highlight that the co-occurrence of aggression and anxiety changes considerably during adolescence, but also that the anxious and no problems types are quite stable in this period. Aggression and anxiety co-occur in childhood and adolescence. According to a recent review Granic , rates oWe will focus on direct aggression  and generalized anxiety disorder . For a number of reasons, we decided to use specific conceptualizations of aggression and anxiety. For instance, many studies have shown that direct aggression differs from other forms of aggression. It is conceptually different from indirect and relational aggression  and explored a number research questions when it was not possible to formulate hypotheses.First, we addressed age, gender, and friendship differences in development of direct aggression and generalized anxiety disorder. Our first hypothesis (H1) originates from the review of research into normative development of direct aggression and generalized anxiety disorder in adolescence, and predicts a regular decrease of the aggressive type over time in adolescence, along with an increase of the anxious type in middle-to-late adolescence. We tested H1 for two cohorts: early-to-middle and middle-to-late adolescents. We explored increases and decreases of the strong co-occurrence type, the comorbid aggressive type. The second hypothesis (H2) addressed gender differences. In general, the studies of our literature review reported higher levels of direct aggression  with an average age of 12.4\u00a0years (SD\u00a0=\u00a0.59) at baseline, and a middle-to-late adolescent cohort  with an average age of 16.7\u00a0years (SD\u00a0=\u00a0.80) at baseline. Because both age groups were assessed during five measurement waves, a total age range from 12 to 20\u00a0years was available. The early-to-middle adolescent cohort consisted of 468 boys (50.7\u00a0%) and 455 girls (49.3\u00a0%), and the middle-to-late adolescent cohort consisted of 169 boys (43.3\u00a0%) and 221 girls (56.7\u00a0%). A more detailed description of the sample can be found in Meeus et al. Data for this study were collected as part of an ongoing Dutch research project on COnflict And Management Of RElationships (CONAMORE), with a 1-year interval between each of the five available waves. The longitudinal sample consisted of 1313 participants, divided into an early-to-middle adolescent cohort (2 (\u03c72/df) of 1.14, p\u00a0>\u00a0.05, which, according to Bollen  procedure. Little\u2019s Missing Completely At Random (MCAR) test produced a normed \u03c7o Bollen , indicatParticipants and their parents received an invitation letter describing the research project and goals and inviting them to participate. More than 99\u00a0% of the families who were approached signed the informed consent form. During regular annual assessments, participating adolescents completed questionnaires at school or at home. Confidentiality of responses was guaranteed. Adolescents received \u20ac10 (approximately US $13) for each wave in which they provided data.The 9-item Generalized Anxiety Disorder symptoms scale (from now on GAD) of the original 38-item SCARED  was employed in this study. This scale has been regularly used in developmental psychopathology studies of\u00a0adolescents from the general population   to 5 (more is not possible). Examples of items are \u201cDoes your best friend like or approve of the things you do?\u201d (support), \u201cDo you and your best friend get on each other\u2019s nerves?\u201d(negative interaction), and \u201cHow often does your best friend tell you what to do?\u201d(power). Internal consistencies were high, with alphas ranging across waves from .82 to .93 for support, negative interaction and power. Since we aimed to study the moderating role of best friendship quality in the development of aggression/anxiety, we used Latent class growth analysis (LCGA) to distinguish between higher- and poorer-quality friendships across the five waves. We estimated levels and linear and curvilinear changes of the three dimensions. We found a two-class solution to be superior to the one-class solution according to the bootstrapped VLMR-LMT test (p\u00a0<\u00a0.001). Entropy (E) of this solution was good, at .91. To avoid a large number of transitions with very low or zero cell frequencies in the latent transition (LTA) models, we decided to continue with the two-class solution and not to test for additional three or more class models. A majority of the 1045 respondents (79.4\u00a0%) was classified in the higher-quality friendship class, and 268 (20.6\u00a0%) in the poorer-quality friendship class. The higher-quality friendship class showed greater levels of support, lower levels of negative interaction, and lower levels of power, as compared to the poorer-friendship quality class.The Network of Relationships Inventory (NRI)  and latent transition analysis (LTA). LCA is a group-based, person-centered analytic strategy that is a confirmatory version of cluster analysis. LTA represents a longitudinal extension of LCA. LTA calculates increases and decreases in class size across time, as well as patterns of stability and change over time in the form of movement or transitions between classes . LTA offers two types of structural parameters: (a) varying numbers of participants in a class across waves, indicating increase or decrease in class size over time, and (b) transitions of individuals between classes that explain these changes in class size. Note that the transitions indicate patterns of intra-individual change in aggression/anxiety types. LTA is therefore appropriate for evaluating stability or change of the aggression/anxiety types over time, and the aggression/anxiety types transitions that explain stability and change over time.We analyzed our data in three steps. First, we applied cross-sectional LCA to explore the number of classes (aggression/anxiety types) within each of the five waves. We found four classes in each of the waves. BIC of four-class solutions was at least 257.22 lower than that of one-, two-, and three-class solutions. Second, we select the best-fitting, five-wave LTA model in a number of successive steps. We found that a stationary, three-covariate LTA model provided the best fit to the data. BIC\u2019s for the three-covariate model, and the no-covariate model were 10,541.02, and 10,677.21, respectively. This model suggests that adolescents regularly made transitions between aggression/anxiety types across waves, and with the same probability. Additionally, the regular pattern varied by age groups, gender, and best friendship groups. In sum, age groups, gender, and best friendship groups were moderators of these developmental processes. Entropy of the final model was very good (.87). Third, we applied Bayesian evaluations of the contingency tables generated by the final LTA model. LTA results can be converted into contingency tables that summarize the prevalence of classes (co-occurrence types) across waves. We use Bayesian Model Selection with (in)equality constraints between the parameters of interest .Transition probabilities of stability of the aggression/anxiety types across 4-year intervals, as found in the final stationary model, are presented in Table\u00a0early-to-middle [.05]\u00a0<\u00a0GAD\u00a0\u2192\u00a0DAearly-to-middle [.20]), whereas both failure and acting out were not apparent in middle-to-late adolescence (DA\u00a0\u2192\u00a0GADmiddle-to-late\u00a0=\u00a0GAD\u00a0\u2192\u00a0DAmiddle-to-late [\u2264.05]). We applied Bayesian Model Selection to test three alternative models of age group differences of failure and acting out in waves 1 and 5. Model 1 assumed no cohort differences in failure and acting out. Model 2 assumed probabilities of failure to be lower than probabilities of acting out in the younger age group, as compared to no differences in probabilities in failure and acting out in the older age group. Model 3, the unconstrained model, did not specify any constraints of failure and acting out across age groups. Model comparisons showed that Model 2, the \u201cacting out in early-to-middle adolescence model\u201d, was by far the best-fitting model (see Table\u00a0early-to-middle [.20]\u00a0>\u00a0GAD\u00a0\u2192\u00a0DAmiddle-to-late [.01]). A follow-up set of Bayesian models confirmed this to be the case , whereas both failure and acting out were not apparent in females  . A follow-up set of Bayesian models confirmed this to be the case , whereas both failure and acting out were not apparent in higher-quality friendships (hqf) (DA\u00a0\u2192\u00a0GADhqf\u00a0=\u00a0GAD\u00a0\u2192\u00a0DAhqf [\u2264.06]) (see Table\u00a0pqf\u00a0=\u00a0.25) than higher-quality friendships (GAD\u00a0\u2192\u00a0DAhqf\u00a0=\u00a0.06). A follow-up set of Bayesian models confirmed this to be the case  (DA\u00a0\u2192\u00a0GAD\u00a0DApqf .2), wherea\u00a0DApqf .2), whereaThe present longitudinal research set out to examine the development of co-occurring direct aggression and generalized anxiety disorder during adolescence. To what extent are adolescents aggressive, anxious, or show a combination of both high aggression and anxiety? We studied whether these co-occurrence patterns remain stable or change during adolescence. Do anxious adolescents \u201cact out\u201d and become aggressive over time, as the acting out model would suggest . Remarkably, acting out was most prevalent in subgroups that, generally speaking, are more vulnerable for aggressive behavior, namely early-to-middle adolescents and males.Acting out can be seen as a mechanism that contributes to the explanation of the two observed processes of developmental heterogeneity in aggression and generalized anxiety: accelerated development in middle-to-late adolescence and gender differentiation. Accelerated differential development was visible in accelerated decrease of aggression in middle-to-late adolescence and not in early-to-middle adolescence. Acting out indexes growing from the anxious type into the aggressive type, and therefore partly prevents a decrease of the aggressive type in early-to-middle adolescence. This prevention effect of acting out is no longer active in middle-to-late adolescence. Thus, acting out partly explains an accelerated decrease of the aggressive type in middle-to-late adolescence. Additionally, acting out was a building block of gender differentiation. Acting out was present in males and not in females. Acting out implies growing into the aggressive type, and therefore partly explains the increase of the aggressive type in males and not in females. Thus, acting out partly explains gender differences in aggression that grow during adolescence.The percentages of acting out  in early-to-middle adolescents, males, and adolescents with poorer friendships were rather substantial, and ranged between 20 and 41\u00a0%, respectively . Therefore, the aggression/anxiety types were not the outcome of overlapping and biased self-reports.A third limitation has to do with our quite specific conceptualization of aggression and anxiety behaviors. This calls for replication of the present study with various other measures of internalizing and externalizing problems.A fourth limitation is that we are unable to compare our findings on stability of the types with those of the earlier studies. This is simply due to the fact that the earlier studies did not present percentages of stability in these co-occurrence types.Clinical implications of the present study are twofold. First, generalized anxiety seems to be a more persistent risk factor for adolescents\u2019 future than aggression. We found intra-individual stability of the anxious type to already be substantial in early-to-middle adolescence (.58 across 4\u00a0years). Both findings underscore the need and possibility for early identification of generalized anxiety. This is especially because we also know that early intervention for generalized anxiety can be successful and more cost-effective than clinical treatment , whereas the anxious type increases regularly during the entire adolescent period. We found substantial support for the acting out perspective. We interpreted acting out as the attempt of adolescents to switch from anxiety to instrumental aggression (Kunimatsu and Marsee"}
+{"text": "Nucleic Acids Res. (2014) 42 (16): 10832\u201310844. doi: 10.1093/nar/gku764The authors wish to apologize for errors in the last paragraph of the DISCUSSION section in this paper. The \u201cRNA DQ\u201d should read as \u201cintramolecular RNA G-quadruplex (RQ)\u201d at its first appearance and as \u201cRQ\u201d at the followings. The \u201cDNA DQ\u201d should all read as \u201cDQ\u201d.With these corrections, the correct version appears below (starting from \u201cAlternatively\u2026\u201d).3 loop and bulge, the RQ might also be unstable as was the DQ. With the participation of G3 tracts from the DNA and RNA, the HQ of three G-quartets was much more stable and should be more competitive to form and to play a role in transcription termination.Alternatively, the RNA could also form an equivalent intramolecular RNA G-quadruplex (RQ) of three G-quartet layers by using the 13G-15G as the non-template DNA strand did in this work. However, the mutation in the 13G-15G in our work is expected to disrupt (M14/16) or promote (M3G) the formation of RQ, respectively, as to the DQ. But these showed little effect on the termination . This suggested that the RQ was largely irrelevant to the termination. On the other hand, because of the bulky T"}
+{"text": "Since high-intensity aerobic exercise depends on such physiological factors, it has been hypothesized that IPC can also improve exercise performance. Although some studies confirmed this hypothesis (Salvador et\u00a0al. 2 and muscle deoxygenation during square-wave transitions from low- to moderate-intensity and from moderate- to severe-intensity cycling exercise. Besides, authors assessed the effect of IPC on the time to exhaustion in the severe-intensity workload. Authors found that IPC increased the time to exhaustion, which supports an increase in exercise performance. Furthermore, IPC did not change the pulmonary V\u0307O2 kinetics, but changed the kinetics of muscle deoxygenation. These findings are original and advance the knowledge about the effect of IPC on exercise physiology. However, some aspects of the experimental protocol and data analysis deserve attention to interpret these findings.In this context, a recent study by Kido et\u00a0al.  examined2 kinetics. Nevertheless, repetitions of exercise transitions are crucial to increase the signal-to-noise ratio. This was proposed by Lamarra et\u00a0al. (L is a constant that depends on the value of the underlying time constant; SD is the standard deviation of the breath-by-breath fluctuation in V\u0307O2; \u0394V\u0307O2 is the V\u0307O2 amplitude above the baseline level; and n is the number of exercise transitions. Based on this equation, typically, four to eight exercise bouts are used for moderate-intensity transitions and two to four exercise bouts are used for severe-intensity transitions (Poole and Jones 2 kinetics.Authors used just one exercise transition to calculate the pulmonary V\u0307Oa et\u00a0al. , who des2, the kinetics of muscle deoxygenation was changed by IPC. Muscle deoxygenation, as measured by near-infrared spectroscopy, is a proxy of muscle oxygen extraction. Thus, a change in this variable should influence the pulmonary V\u0307O2 kinetics, which was not observed, maybe due to the aforementioned limitation on the V\u0307O2 kinetics analysis. Noteworthy, authors investigated the effect of IPC on work-to-work transitions, and it is known that the phase II of pulmonary V\u0307O2 kinetics is slowed when high-intensity exercise is initiated from a moderate-intensity work rate in comparison with a rest-to-work transition (Dimenna et\u00a0al. Despite the fact that authors did not find an effect of IPC on the kinetics of pulmonary V\u0307OSpecifically regarding the muscle deoxygenation, authors concluded that IPC accelerated its kinetics in the transition from low- to moderate-intensity exercise, but did not change the kinetics in moderate- to severe-intensity exercise. Moreover, the amplitude of the deoxy-Hb/Mb response in the low- to moderate-intensity exercise was reduced by IPC, whereas IPC did not change the amplitude in the moderate- to severe-intensity exercise. However, as the amplitude of the deoxy-Hb/Mb was reduced in the low- to moderate-intensity exercise, the baseline value for the moderate- to severe-intensity exercise was consequently reduced, which may have compromised the interpretation about the kinetics of deoxy-Hb/Mb in the moderate- to severe-intensity transition. In addition, the amplitude of deoxy-Hb/Mb response during exercise was analyzed relative to the plateau value during a 10-min arterial occlusion. But, authors did not report the values obtained during this maneuver. Were these values affected by the IPC? If these values were affect, does it explain the difference in amplitude during exercise? Alternatively, if data were normalized by the resting baseline value, would the interpretation be similar? At last, the time delay, time constant, and mean response time were calculated from data normalized by the end exercise amplitude. Would the interpretation be similar if the analysis was done from data normalized by the resting baseline value or by the plateau during the 10-min arterial occlusion?2 utilization and delivery in the microcirculation via near-infrared spectroscopy. First, Barbosa et\u00a0al. (Besides Kido et\u00a0al. , two stua et\u00a0al.  studied a et\u00a0al.  then repa et\u00a0al.  and Patta et\u00a0al.  (i.e., la et\u00a0al.  (i.e., ha et\u00a0al. . Thus, fa et\u00a0al. ."}
+{"text": "Electronic cigarettes (e-cigarettes) have risen in popularity in the U.S. While recent studies have described the prevalence and demographics of e-cigarette users, few studies have evaluated the impact of advertising on perceptions and interest in trial. This pilot study was conducted to assess whether exposure to ads for e-cigarettes or a comparison product (snus), elicited differences in interest to try e-cigarettes between smokers and non-smokers.A web-based survey was completed by 600 respondents, aged 18\u201365, recruited from an internet panel in the U.S. Respondents answered questions assessing tobacco use, and then viewed nine magazine ads for Blu e-cigarettes or Camel snus, a low-nitrosamine smokeless tobacco product, in random order. After viewing each ad, respondents were asked a series of questions about their perceptions, beliefs, attitudes, and interest in trial. At the end, respondents were asked to choose a free sample product from the following options: an e-cigarette, smokeless tobacco (SLT), pack of cigarettes, or no product.p-value\u2009<\u20090.001). Six percent of non-smokers exposed to e-cigarette ads reported interest in trying e-cigarettes. E-cigarettes were the most popular product selected to sample (34\u00a0%), followed by cigarettes (8\u00a0%) and SLT (3\u00a0%); 331 respondents (55\u00a0%) chose no product. Participants randomized to the e-cigarette ad group were significantly more likely to choose an e-cigarette at product selection . Within the e-cigarette condition, 71\u00a0% of smokers selected an e-cigarette at product selection, compared to 25\u00a0% of non-smokers; smoking status was significantly associated with sample product selection .Ad receptivity scores did not appear to be influenced by ad theme; differences existed between smokers and non-smokers. Participants exposed to e-cigarette ads more frequently reported favorable product attitudes compared to participants exposed to snus ads. Cigarette smokers in the e-cigarette condition were more likely to report interest in trying e-cigarettes compared to non-smokers in that condition  contains supplementary material, which is available to authorized users. E-cigarettes are a novel phenomenon. These devices provide nicotine to users in the form of an aerosol vapor, which is promoted as a reduced risk form of delivery. Awareness of e-cigarettes and other electronic nicotine delivery devices is increasing. Recent nationally representative studies conducted among the U.S. adult general population have shown that awareness of e-cigarettes has risen from approximately 40\u00a0% in 2010, to nearly 60\u00a0% in 2011 .The increased awareness of e-cigarettes may be linked to a corresponding increase in media presence; including ads in magazines, television, and strategic product placement of e-cigarettes in Hollywood productions. For example, e-cigarettes have been used by celebrities in commercials, print ads, movies, and television shows . AvailabWhile e-cigarettes may be beneficial for individual smokers as a harm reduction device, it is yet unclear if these devices yield a positive or negative public health impact. The use of e-cigarettes as a complete replacement for conventional cigarettes or as a quit aid could result in a net public health gain , 14. HowEvidence from multiple U.S. Surgeon General\u2019s reports support the notion that tobacco advertising and promotion can influence risk perception, trial, and use of tobacco products in both adults and youth \u201318. SuchWhile an increasing number of recently published studies have described awareness and use of e-cigarettes \u20133, very This pilot study aimed to explore issues related to e-cigarette advertising and the potential impact such advertisements may have on the public\u2019s willingness to try e-cigarettes among current smokers and non-smokers. Namely, we sought to assess whether exposure to ads for e-cigarettes or a comparison product (snus), showed differences in interest to try e-cigarettes among both cigarette smokers and non-smokers.http://www.lightspeedgmi.com/). Eligible participants answered a series of preliminary questions to confirm that they were between ages 18 and 65, current United States residents, and able to read and write in English. After determining eligibility, participants were directed to an informed consent screen, clicking a button indicating consent. Respondents completed a core series of questions adapted from a similar study assessing tobacco use, past quit attempts, use of nicotine replacement therapies, and knowledge, attitudes, and beliefs about nicotine-containing products , even once?\u201d and currently reported using the tobacco product every day or some days. \u201cEver users\u201d for a tobacco product were defined as those individuals who responded \u201cYes\u201d to the question, \u201cHave you ever used [tobacco product], even once?\u201d, and currently reported not using the product at all. \u201cNever users\u201d for a tobacco product were defined as those individuals who responded \u201cNo\u201d to the question, \u201cHave you ever used [tobacco product], even once?\u201d In analyses examining differences between current cigarette smokers versus current non-smokers, \u201cever\u201d and \u201cnever\u201d smokers were combined into one category.For each individual ad, we asked the series of statements shown in Table\u00a0We employed two different measures to assess interest in trying e-cigarettes within our sample. The first measure, \u201cintention to try\u201d, was based on the statement: \u201cBased on what I just saw, I think this product is something I want to try.\u201d . To keep our analysis succinct, we opted to recode this Likert measure into a binary variable. The answer options \u201cstrongly agree\u201d and \u201cagree\u201d were combined to indicate \u201cintention to try\u201d, while the remaining options were combined to indicate \u201cdoes not intend to try\u201d.The second measure, labeled \u201cwillingness to receive a free product\u201d, was derived from the question administered for product selection by respondents, which stated, \u201cIf we had the opportunity to send you a free sample of one of the products listed below, which of the products would you choose?\u201d .d is reported for effect sizes related to independent samples t-tests. Results are reported for four groups of interest: Smokers who viewed ads for e-cigarettes, non-smokers who viewed ads for e-cigarettes, smokers who viewed ads for snus, and non-smokers who viewed ads for snus.Descriptive analyses were performed on these pilot data. Pearson chi-square tests were conducted to assess associations between demographic variables, smoking status and main outcome measures . Demographic measures included age group , gender , level of education , and racial self-identification . Independent samples t-tests  were used in comparing mean ad receptivity scores, grouped according to cigarette smoking status (current smoker versus current non-smoker) Cramer\u2019s V is reported for effect sizes related to Pearson chi-square tests, while Cohen\u2019s \u03c72\u2009=\u2009144.692, p-value\u2009<\u20090.001; Cramer\u2019s V\u2009=\u2009.491). Current smokeless tobacco use among current cigarette smokers was 17\u00a0%, while 4\u00a0% of current non-smokers reported use of smokeless tobacco . Ten percent of the total sample reported using more than one tobacco product, while nearly 20\u00a0% of our sample consisted of individuals who have at least tried an e-cigarette one time .A total of 46,561 e-mail invitations were sent to GMI panelists, inviting them to take part in the survey. 875 individuals began the survey, of which 600 completed the survey in full Table\u00a0. Most pa\u03c72\u2009=\u200946.237, p-value\u2009<\u20090.001, Cramer\u2019s V\u2009=\u2009.278). Table\u00a0\u03c72\u2009=\u200931.117, p-value\u2009<\u20090.001, Cramer\u2019s V\u2009=\u2009.322). Similar trends were observed among smokers and non-smokers within the snus comparison condition. Among all non-smokers in either condition, more favorable perceptions were observed for e-cigarettes compared to snus.Participants were asked to respond to a set of questions assessing attitudes about the product shown in their exposure condition (e-cigarette or snus) displayed in Table\u00a0p-value\u2009<\u20090.001, Cohen\u2019s d\u2009=\u20090.872). In the snus comparison condition, the combined mean ad receptivity score for smokers was 113.41 (SD\u2009=\u200945.10), compared to 98.92 (SD\u2009=\u200945.25) for non-smokers. We observed a positive, weak relationship between snus ad receptivity and smoking status (t(298)\u2009=\u20092.561, p-value\u2009=\u2009.011, Cohen\u2019s d\u2009=\u20090.297). Mean ad receptivity scores among smokers in the snus condition ranged from 37.51-38.30, while mean ad receptivity scores among smokers exposed to e-cigarette ads ranged from 45.68-47.09.Figure\u00a0\u03c72\u2009=\u200991.95, p-value\u2009<\u20090.001, Cramer\u2019s V\u2009=\u2009.554). Among all participants in the snus comparison condition, 10\u00a0% reported that they intended to try snus and a weaker, yet statistically significant association was observed between smoking status and intention to use snus .In the combined sample, 94 respondents (16\u00a0%) reported that the product shown in their exposure grouping (snus or e-cigarettes) was \u201csomething I want to try\u201d Fig.\u00a0 Among al\u03c72\u2009=\u200910.59, p-value\u2009=\u20090.014, Cramer\u2019s V\u2009=\u2009.133). Within the e-cigarette condition, smokers more frequently selected an e-cigarette at product selection, compared to non-smokers . Within the snus condition, e-cigarettes remained the most frequently selected tobacco product among responders, with smokers more frequently reporting this choice than non-smokers. Product choice in the snus condition was significantly associated with smoking status .In the product selection task, over half of the sample (55\u00a0%) elected to not be sent a free sample product. E-cigarettes were the most frequently selected tobacco product among all participants, with 34\u00a0% reporting this choice. Selection of smokeless tobacco and cigarettes among sample members was low . Participants exposed to e-cigarettes ads were more likely to select an e-cigarette as their hypothetical free product (39\u00a0%) compared to participants who saw ads for snus (28\u00a0%). In comparing ad exposure conditions, we observed a statistically significant association between ad exposure grouping and product choice . One-quarter of non-smokers in the e-cigarette condition selected the e-cigarette as their sample product; 3\u00a0% of which previously reported intention to try the product after being shown ads for e-cigarettes. These findings among non-smokers in the e-cigarette condition were not statistically significant. In the snus comparison condition, we did not observe any significant associations between product selection and intention to try e-cigarettes among smokers. Among non-smokers in the snus condition, 5\u00a0% of non-smokers previously reported intention to try snus, while 4\u00a0% selected smokeless tobacco during product selection. Nearly 16\u00a0% of non-smokers in the snus condition chose an e-cigarette during product selection. We observed a statistically significant association between product choice and intention to try snus among non-smokers in the snus condition .In total, 16\u00a0% of respondents reported that they intended to try the product shown in their exposure condition. Forty-five percent of respondents elected to receive a sample product . Among smokers in the e-cigarette condition who reported intending to try an e-cigarette, 90\u00a0% selected the e-cigarette as their sample product, while 10\u00a0% selected another option. Among smokers in the e-cigarette condition who did not report intending to try an e-cigarette, 46\u00a0% selected the e-cigarette as their sample product, while 53\u00a0% selected another option  that may enhance appeal as a product that may reduce harm to health. Such aspects are not currently addressed by the data presented in this report, and should be studied in greater detail.These data suggest that more favorable perceptions toward e-cigarettes existed among all participants, but particularly among current cigarette smokers, who rated e-cigarette ads, interest in trial, and attitudinal measures on e-cigarettes more favorably when compared to snus, a similarly marketed harm reduction product. Smokers exposed to either form of advertising overwhelmingly chose the e-cigarette in the product selection task, yet this was much more frequently observed among smokers in the e-cigarette condition. This product selection occurred over other options, one of which was a pack of cigarettes. Such findings may suggest that e-cigarettes, often proposed as a product that may reduce harm to health, appear to be more favorable to smokers than snus, another frequently proposed harm reduction product. These pilot data do not measure specifically why this may be the case. Snus is a smokeless tobacco product, possessing a different mode of administration for nicotine than e-cigarettes, and smokeless products currently carry health warning labels as mandated by law. Our findings also support the notion of snus posing relatively low appeal to smokers for harm reduction, as demonstrated through previous studies , 35. FacWhile we observed more favorable ad receptivity scores for e-cigarette ads compared to snus among smokers, ad receptivity for either tobacco product was relatively similar among non-smokers in both conditions. Additionally, non-smokers in our study generally did not report intention to use either of the products they were exposed to, with 6\u00a0% of non-smokers in each group reporting intention to try the product after viewing ads. In the product selection task, non-smokers were more likely to reject the offer of a free sample tobacco product, compared to smokers. Interestingly, a small proportion of non-smokers who did not previously report intention to try e-cigarettes prior to the offer of a free e-cigarette opted to select a free sample e-cigarette. The broader implications of these findings among non-smokers are unclear. With the limited offering of products during product selection, coupled with the absence of measures to indicate reasons for selection of a particular product or participant follow-up over time, we cannot be sure whether non-smokers in our sample chose a free tobacco product for personal use or for some other reason. Future studies should examine such reasons in greater detail.Our data did not allude to particular advertisement themes  having a strong association with either use intention to use or willingness to receive a free product. It could be that other elements of advertisements not addressed in this study could play a determining factor in influencing interest in these products, a few of which have been demonstrated in other studies. For example, Pepper et al.  conducteThere are potential negative and positive public health impacts of widespread promotion and advertising of e-cigarettes. If e-cigarettes are deemed by the FDA as a potentially reduced exposure product or a smoking-cessation aid, then advertising targeted to smokers to switch to these products completely for harm reduction or cessation could be beneficial for overall public health. The data for this study showed that smokers were interested in receiving a free sample e-cigarette, regardless of advertising condition; the data also showed that 3\u00a0% of non-smokers in the e-cigarette condition displayed interest in trying e-cigarettes. Yet, when offered a free sample tobacco product, 25\u00a0% of non-smokers in the e-cigarette condition selected an e-cigarette. The current marketing environment for e-cigarettes is saturated with promotions and price discounts for these products. Such an environment could result in a greater proportion of non-tobacco users to consider trying e-cigarettes. While our data do not directly speak to increased uptake among non-tobacco users, our findings suggest low interest, and more extensive research is needed to determine the appeal of e-cigarettes to nonusers of tobacco.The findings from our pilot study are subject to limitations. Primarily, this study was conducted among a fairly small sample recruited from an opt-in panel of internet users. When compared to the U.S. general population, our sample members more frequently reported having a college degree , were more likely to identify as being White, non-Hispanic , and had higher rates of cigarette  and smokeless tobacco use  . This afContinued promotion and advertising may peak public interest in e-cigarettes compared to snus, and may have an impact on willingness to receive promotional products or intention to try e-cigarettes. Our study found that e-cigarette advertising may influence intention to try these products, particularly among current smokers. In addition to the absence of an established safety profile and regulation on the quality of e-cigarettes, additional considerations about product advertising should be considered in developing future regulatory actions."}
+{"text": "In the linear regime, a spiral interference pattern containing phase defects is visible. In the nonlinear (superfluid) regime, the interference disappears and eight vortices appear, minimizing the energy while conserving the quantized angular momentum. The radial position of the vortices evolves in the region between the two pumps as a function of the density. Hydrodynamic instabilities resulting in the spontaneous nucleation of vortex-antivortex pairs when the system size is sufficiently large confirm that the vortices are not constrained by interference when nonlinearities dominate the system.Exciton-polaritons are light-matter mixed states interacting via their exciton fraction. They can be excited, manipulated, and detected using all the versatile techniques of modern optics. An exciton-polariton gas is therefore a unique platform to study out-of-equilibrium interacting quantum fluids. In this work, we report the formation of a ring-shaped array of same sign vortices after injection of angular momentum in a polariton superfluid. The angular momentum is injected by a  Quantized vortices have been extensively investigated in different fields of physics, such as superconductivity4581011121315et alet alSeveral schemes to produce vortices and vortex lattices have been proposed and implemented. Liew \u2113. Note that self-ordered, same-sign vortex lattices have been theoretically predicted in Ref. In this work, as a first step towards the physics of rotating polariton quantum fluids, we theoretically propose and experimentally implement a scheme that generates stable chains of same-sign vortices in a coherently driven polariton superfluid. The global angular momentum is injected by mean of a Laguerre-Gauss (LG) laser beam with orbital angular momentum These characteristics are close to those of cold atom condensates29303126\u03c9laser \u2212 \u03c9pol, where \u03c9laser and \u03c9pol are respectively the pump and bare polariton energies at normal incidence k = 0\u2005\u03bcm\u22121. A single-mode, polarization-preserving fiber selects the TEM00 mode. The polarization is linear  after the fiber and the remaining polarization fluctuations are cut by a polarizing beam splitter (PBS). As visible in We consider a planar semiconductor microcavity in the strong coupling regime, where exciton-photon coupled states (i.e. polaritons) are created by a laser excitation. We make use of a CW single mode, frequency-locked Ti:Sa laser to resonantly excite the cavity. Resonant pumping creates a low-density exciton gas, which allows us to neglect interactions between polaritons and the exciton reservoir, in contrast with experiments performed under non-resonant pumping\u2113 = 8 and a Gaussian (G) beam of zero orbital momentum at the center. Both the spot size and the intensity of the laser beams are fully determined by the hologram. The LG-beam diameter is chosen to be larger than the waist of the G-beam. As a result, their spatial overlap is small, allowing for the interference to be very weak. To avoid spin-dependent phenomena, the  beam of orbital momentum \u03bb-GaAs planar microcavity containing three GaAs-InGaAs quantum wells, with a polariton Rabi splitting of 5.1\u2005meV. The cavity finesse is F = 3000, which results in a polariton linewidth of about 0.1\u2005meV. The cavity is wedged in one direction, providing a large choice of cavity-exciton detunings by pumping at different positions in the sample. In order to enhance the polariton-polariton interactions, we use a cavity-exciton detuning of \u03b4 = C\u03c9 \u2212 X\u03c9 = 1\u2005meV (X\u03c9C)( is the excitonic (cavity) energy at normal incidence, k = 0\u2005\u03bcm\u22121), thus increasing the exciton fraction of polaritons and, consequently, the nonlinear effects. The microcavity is cooled down to 5\u2005K in a cryostat and the measurements are taken in transmission. Above a critical value of \u0394, a bistable behavior appearspI = 300\u2005mW, we modify \u0394. We consider three different cases: low density  in 2 = 0.4\u2005meV, point (ii) in 3 = 0.7\u2005meV, point (iii) in The sample is a 2The detection is simultaneously made in energy and in real- and momentum space. An objective collects the sample emission. CCD cameras are used for direct imaging of the real- and the momentum space, while the energy (wavelength) is measured with a spectrometer. We only collect circularly-polarized light, therefore filtering out any residual spin-flip effect. The polariton phase is measured with an off-axis interferometry setup: a beam splitter divides the real-space image into two parts, one of which is expanded to generate a phase reference beam. The selection of the Gaussian part at the center of the image ensures a flat phase reference, which is used to make an off-axis interference pattern. With this method, the vortex position in the image is independent of the phase of the reference beamP(r) = LGP(r) + GP(r) with A1 and A2 are the amplitudes of the pumping lasers, with \u03c31 = 5.0\u2005\u03bcm and \u03c32 = 3.0\u2005\u03bcm. Direct comparison with the experiments is then performed by extracting the steady-state density |\u03c8|2 and phase arg(\u03c8).In order to describe the configuration under study, we numerically solve the driven-dissipative Gross-Pitaevskii equation, which in the parabolic approximation reads1 \u2248 0\u2005meV), we observe - both experimentally (2 = 0.4\u2005meV (point (ii) in 20\u2113 single-charged vortices from a pump with angular momentum \u2113 is a manifestation of the quantum nature of the polariton fluid, in analogy to the formation of the Abrikosov lattice from a single highly-charged vortex.In the linear regime  = \u03c11/2[P1(r)/A1 + P2(r)/A2] is the Thomas-Fermi density profile induced by the pump, ri = R is the position of each vortex in the chain, and R that minimizes the energy, R0, can then be extracted by minimizing the total energy E[R] = Ekin + Eint and taking the physically relevant solution of the condition \u03b4E/\u03b4R = 0, whereE as a function of R for different values of \u03be ~ \u03c1\u22121/2. We observe that R0, the value of R that minimizes the energy, increases as the value of \u03be (\u03c1) is decreased. Since \u03c1 increases with \u0394, \u03be decreases with \u0394; it follows that R0 increases with \u0394. R0 as a function of \u03c1 calculated by this method and the comparison with experimental data. As expected, the higher the density, the further from the center the vortices migrate. This behavior and the agreement between the variational method and experiment are a clear indication of the phase freedom obtained when interactions dominate, a feature that is independent from the optical interference.It is important to remark that the spatial freedom of the vortices provides a quantitative test of the model given below. As predicted by our model, we observe that the vortices in the nonlinear case exhibit a radial phase freedom, while their azimuthal position is locked by the pump phase. Their radial position is modified as the density 3 = 0.7\u2005meV (point (iii) in \u03be, we observe the spontaneous nucleation of vortex-antivortex pairs. Four pairs are experimentally visible in \u2113 = 0 caseIn the upper bistability branch, the polariton energy is renormalized through self-interaction to the pump energy, so that the pumping is resonant and yields high polariton densities. This is not the case in the lower bistability branch, where the pumping is not resonant and thus inefficient. For large \u0394, the low pump intensity regions in the lower bistability branch are off-resonant, as can be seen in In the present work, we resonantly inject polaritons with a given total angular momentum and observe the formation of a ring of quantized single-charged vortices. For the first time, a regular ring pattern of elementary vortices of the same sign is reported in a polariton superfluid. In the superfluid regime, the radial position of each vortex is not determined by the pump but rather depends on the polariton density. Experimental and theoretical indications of this behavior, due to strong nonlinear interactions, are provided through the system hydrodynamical characteristics. The mechanism leading to the creation of vortex chains results from the combination of the saturation of the radial counterflow instability with the injection of angular momentum in a limited region of space. Let us note that this general behavior was experimentally and theoretically verified to be the same if the number of injected vortices is changed, whether odd or even. We expect that the present scheme will pave the stage to study a series of new vortex collective phenomena that have been observed in cold atom BEC3435\u03c6LG = \u2113\u03c6 [2\u03c0], where  are the polar coordinates in the SLM plane. However, imposing this phase on the SLM produces a superposition of \u03c6LG + G = \u2113\u03c6H(r \u2212 r0) + \u03c0(1 \u2212 H(r \u2212 r0)), where H(r) is the Heaviside distribution and r0 is a constant determining the LG/G intensity ratio. The resulting hologram is presented in Collimated Laguerre-Gauss beams are a class of modes possessing a simple phase profile with radial invariance. The phase profile of a \u03c0). This vertically deviates the first order reflection forming the pump, allowing us to block the zero-order reflection. The final hologram is presented in A small fraction of the light is not modified by the SLM, for which it acts like a mirror. To separate this from the desired mode a grating hologram (T.B. performed the experiment, analyzed the data and wrote the manuscript. H.T. and D.S. performed the simulations and wrote the manuscript. Q.G. and E.G. participated to the manuscript. A.B. supervised the experiment. G.M. developed the theoretical model. All authors reviewed the manuscript."}
+{"text": "All-optical switching is the foundation of emerging all-optical (terabit-per-second) networks and processors. All-optical switching has attracted considerable attention, but it must ultimately support operation with femtojoule switching energies and femtosecond switching times to be effective. Here we introduce an all-optical switch architecture in the form of a dielectric sphere that focuses a high-intensity photonic nanojet into a peripheral coating of semiconductor nanoparticles. Milli-scale spheres coated with Si and SiC nanoparticles yield switching energies of 200 and 100\u2009fJ with switching times of 10\u2009ps and 350\u2009fs, respectively. Micro-scale spheres coated with Si and SiC nanoparticles yield switching energies of 1\u2009pJ and 20\u2009fJ with switching times of 2\u2009ps and 270\u2009fs, respectively. We show that femtojoule switching energies are enabled by localized photoinjection from the photonic nanojets and that femtosecond switching times are enabled by localized recombination within the semiconductor nanoparticles. The terabit-per-second rates of optical fibres exceed the capability of electronics, but all-optical switches are needed to alleviate the bottleneck in these networks. Here, Born et al. describe such a switch using dielectric spheres, yielding femtojoule switching energy and femtosecond switching times. Logic operations are at the core of data processing, and switching is the key mechanism for logic operations. Switching is typically realized via electronics, with transistors relaying the flow of data, but there is pressure to introduce switches that can operate at optical fibre transmission rates13The AOS is a photonic analogue to the electronic transistor, as it enables nonlinear mixing of optical beams, but all-optical switching must be implemented with consideration to demands for low switching energies and ultrafast switching times5678910et al.et al.Early AOS studies focused on the development of semiconductor materials for ultrafast switching times\u2014ideally on a femtosecond level. Charge-carrier photoinjection and recombination were applied in semiconductors having simple planar topologies, that is, bulk wafers, so the all-optical switching times were limited by bulk recombination lifetimes. It was later found that semiconductors with ultrashort lifetimes could establish ultrafast switching between coincident control (pump) and signal (probe) beams. For example, Ganikhanov et al.et al.et al.More recent AOS studies have focused the development of device geometries for low switching energies\u2014ideally on a femtojoule level. Increased beam intensities, and enhanced mixing of beams, have been introduced through many  devices. Almeida In this study, the demands of all-optical switching, being AOS activation with femtojoule switching energies and AOS recovery with femtosecond switching times, are addressed through the development of a non-resonant AOS architecture. A nanojet focal geometry is introduced, in the form of a dielectric sphere, to focus high-intensity photonic nanojets into a semiconductor nanoparticle material system that coats the sphere. It is found that the localized photoinjection of charge carriers by the nanojet supports AOS activation with femtojoule switching energies, and the localized recombination of charge carriers in the semiconductor nanoparticles supports AOS recovery with femtosecond switching times. A milli-scale AOS architecture is demonstrated\u2014in support of emerging optical fibre front-end systems, such as optical time-division multiplexingT, is a result of perturbations to the surface transmission, Ts, and bulk transmission, Tb. The result is seen as a transient on the total differential transmission, \u0394T(t)/T\u2248\u0394Ts(t)/Ts+\u0394Tb(t)/Tb, with opposing polarities for the surface and bulk contributions. According to Drude theory, the pump-induced generation of the charge-carrier density, N, increases the differential surface transmission, \u0394Ts(t)/Ts, and decreases the differential bulk transmission, \u0394Tb(t)/Tb. This occurs because N decreases the refractive index near the surface, \u0394ns(t), and increases the absorption coefficient in the bulk, \u0394\u03b1b(t), which modulates the total differential transmission according to18Semiconductor charge carriers that are photoinjected by a pump beam can be used to modulate a coincident probe beam. The pump-induced modulation to the probe beam's total transmission, ns is the refractive index near the surface, and \u03b4z is the photoinjection depth of charge carriers into the bulk.where ns(t) and \u0394\u03b1b(t) evolve in proportion to the charge-carrier density, N, which varies through time, t, along the normal dimension to the semiconductor surface, z, according toBoth \u0394\u03b4(t). The initial distribution for N is an exponential decay into the semiconductor, with an initial charge-carrier density of N0 at the surface and a 1/e photoinjection depth of \u03b4z into the bulk. The photoinjection depth, \u03b4z, is defined here as a general parameter that can be less than or equal to the semiconductor's penetration depth. Given a suitable focal geometry, with tight focusing and a short depth of focus penetrating into the semiconductor, \u03b4z can be made to be less than the semiconductor's penetration depth. The boundary condition for N at the semiconductor surface adheres to D\u2202N/\u2202z=SvN, for a diffusion coefficient, D, and surface recombination velocity, Sv. Given a suitable material system, with a high density of surface states, this boundary condition can reduce the overall charge-carrier lifetime, \u03c4, to a value below the bulk charge-carrier lifetime, \u03c4b.where the three terms on the right-hand side characterize the respective processes of photoinjection, recombination, and diffusion. Photoinjection from an ultrashort laser pulse is applied by way of the time-varying delta function, Ep, that is needed to establish the initial charge-carrier density, N0=Ep\u03b7/(\u0127\u03c9pV), in the first term of \u0127 is the reduced Planck's constant, \u03c9p is the angular frequency of the pump beam, and V\u2248A\u03c6\u03b4z is the photoinjection volume set by the pump beam's cross-sectional photoinjection area, A\u03c6, and photoinjection depth, \u03b4z. In this study, localized photoinjection is applied by way of a nanojet focal geometry, to yield a reduced focal spot size, that is, photoinjection area, and reduced depth of focus, that is, photoinjection depth. This leads to reduced photoinjection volumes and high initial charge-carrier densities.Localized photoinjection can enable AOS activation with femtojoule switching energies, by minimizing the pump pulse energy, \u03c4, as a result of \u03c4=1/\u03c4b+SvR. An increase in the surface recombination velocity, Sv, or the specific surface area, that is, surface-to-volume ratio, R, has \u03c4 decrease below the bulk charge-carrier lifetime, \u03c4b. Our prior work has shown that nanoscale cylindricalR, increases the surface state density and decreases the charge-carrier lifetime. In this study, localized recombination is applied by way of a nanoparticle material system. It is typically advantageous to apply both a material system with an increased surface state density and a focal geometry that localizes photoinjection in the region of high surface state density\u2014and this two-fold approach is taken here.Localized recombination can enable AOS recovery with femtosecond switching times, by promoting surface recombination and thus minimizing the overall charge-carrier lifetime, The all-optical switching results of this study are defined with respect to nominal tests using a standard focal geometry with a microscope objective and targets comprised of the well-established semiconductors, semi-insulating GaAs, float-zone Si and 6H-SiC, with respective wafer thicknesses of 350, 280 and 330\u2009\u03bcm. These semiconductors are particularly advantageous for this study, given their wide range of bulk lifetimes and surface recombination velocities.T/T, for the three semiconductor targets. The negative signal polarities indicate that pump-induced modulation to the probe beam is dominated by absorption in the bulk for all three semiconductor targets, which agrees with the observed long bulk lifetimes. GaAs exhibits a picosecond-scale bulk lifetime of \u03c4b=280\u2009ps, Si exhibits a nanosecond-scale bulk lifetime\u03c4b=20\u2009ns and SiC exhibits a microsecond-scale bulk lifetime\u03c4b=20\u2009\u03bcs. The fast transient at the onset of the SiC response is due to charge-carrier scattering. Details on the SiC charge-carrier dynamics are given in the Methods section. All three materials exhibit unacceptably slow recovery times for AOS operation, as minimal contributions are seen from surface recombination in the GaAs, Si and SiC targets, despite their wide range of surface recombination velocities, Sv=1.2 \u00d7 104\u2009m\u2009s\u20131, Sv=500\u2009m\u2009s\u20131 and Sv=4,000\u2009m\u2009s\u20131, respectively20A\u03c6, and depth, \u03b4z, of the pump beam in the semiconductor establish a reduced photoinjection volume, V\u2248A\u03c6\u03b4z. This leads to a large initial charge-carrier density, N0, and a small charge-carrier lifetime, \u03c4, if the photoinjection is preferentially applied at a semiconductor surface. The nanojet focal geometry must be implemented with careful consideration to the properties of the sphere, however, as there is an inherent relationship between the photonic nanojet's intensity and the sphere's diameter, d, and refractive index, n. With this in mind, the properties of the sphere that yield the optimal nanojet are studied by way of theoretical analyses across two regimes of scale.Localized photoinjection is considered in this section, for enhanced AOS activation, by way of a nanojet focal geometry. A high-intensity photonic nanojet25n<2 for diameters d>100\u2009\u03bcm. The curve shows that high-intensity focusing at the exit interface of the sphere is brought about the refractive index of n\u22482. An intensity colourmap for this milli-scale regime is generated from the Ray theory curve and is shown at the top of the figure. The peak intensity for n\u22482 is shown in white. These findings agree with limiting case of a ball lens in the thick-lens formulan\u22482.In the milli-scale regime, with sphere diameters that are much larger than the wavelength, focusing is well-described by Ray theory. et al. Mie theory simulations are carried out to identify the maximum intensities at the exit interface of the sphere, intersecting with the optical axis, as a function of the sphere refractive index, n, and diameter, d. The full distribution of intensities from Mie theory is shown for the micro-scale regime as an intensity colourmap map in d<30\u2009\u03bcm and 1.5<n<2. The trendline for maximum intensities is shown as a solid blue curve. The curve rises from a low refractive index at small diameters, n\u22481.75, toward the Ray theory result at large diameters, n\u22482. The highest intensities are seen as a broad band of intensities that peak at n\u22481.75 for small d then rise toward n\u22482 for sufficiently large d, where the Mie theory and Ray theory results merge.In the micro-scale regime, with sphere diameters that are comparable to the wavelength, it is necessary to implement a rigorous three-dimensional electromagnetic analysis. This can be done efficiently for a spherical geometry using Mie theory. Given the optical responses of Resonance manifests itself as two patterns of interferometric fringes in the intensity colourmap map for the micro-scale regime in n\u22482, has a 42% reduction in the (transverse) spherical aberration, compared with that of a sphere with a refractive index of n\u22481.5.Spherical aberration manifests itself as imperfect focusing at the exit interface of the sphere. This leads to an increased demand on the switching energy, as the incident beam power must be increased to compensate for the reduced intensity. Note that spherical aberration can be compensated, to some degree, in that a sphere, being approximated as a plane-parallel plate between two plano-convex lenses, will have spherical aberration be over-corrected by the plane-parallel plate and under-corrected by the lensesT/T, is shown in n=1.51, (b) n=1.76, (c) n=1.83 and (d) n=1.98. The experimental curves are shown with corresponding theoretical curves, having been generated by a Drude/charge-carrier dynamical model. The model couples the Drude theory characteristics for probe beam transmission from The measured differential transmission, \u0394n=1.51 sphere exhibits decreased probe transmission from pump-induced changes primarily to the absorption coefficient in the bulk\u2014like that seen for the nominal semiconductor tests with a microscope objective. In contrast, the increasingly positive curves of the n=1.76, 1.83 and 1.98 spheres exhibit increased probe transmission from pump-induced changes primarily to the refractive index near the surface. For increasing sphere refractive indices, the preferential deposition of charge carriers near the semiconductor surface is also seen by way of reducing charge-carrier lifetimes. Charge-carrier lifetimes of \u03c4=210, 120, 60 and 10\u2009ps are measured for the sphere refractive indices of n=1.51, 1.76, 1.83 and 1.98, respectively. The decreasing charge-carrier lifetimes come about from a diminishing depth of focus and the corresponding preferential deposition of charge carriers at the semiconductor surface\u2014where there exists a high surface state density and appreciable surface recombination velocity, Sv=1.2 \u00d7 104\u2009m\u2009s\u20131. Curve-fitting of the Drude/charge-carrier dynamical model results to the experimental results confirms that the increasing sphere refractive indices reduce both the pump beam's photoinjection area, A\u03c6, and photoinjection depth, \u03b4z. For sphere refractive indices of n=1.51, 1.76, 1.83 and 1.98, the respective photoinjection depths into the semiconductor decrease, according to \u03b4z=480, 300, 180 and 70\u2009nm, and this leads to an increase in the initial charge-carrier densities.It is apparent from the experimental and theoretical results of d=2.0\u2009mm and refractive index of n=1.98, can support all-optical switching with femtojoule switching energies and picosecond switching times. The implementation tested here, with a GaAs target beyond the sphere, yields an \u223c10-fJ switching energy  and a 10-ps switching time. It is worth noting, however, that further reductions in the switching time can be met by enhancing surface recombination, and such enhancements are explored in the following section.Given these experimental findings, it is apparent that a nanojet focal geometry, with a sphere diameter of R=12/d for a sphere. This maximization of surface-to-volume hastens the charge-carrier recombination rate, according to 1/\u03c4=1/\u03c4b+SvR. The charge-carrier lifetime, \u03c4, can ideally be reduced to a value well below the bulk semiconductor lifetime, \u03c4b.Localized recombination is considered in this section, for enhanced AOS recovery, by introducing a semiconductor nanoparticle material system. The introduction of semiconductor nanoparticles increases the specific surface area to its highest theoretical limit, being \u03c0 steradians solid angle of the sphere.The nanoparticle material system is integrated with the nanojet focal geometry, by coating nanoparticles over the entire surface of the dielectric sphere, to form the complete AOS architecture. An AOS architecture such as this enables ease of alignment, in that the geometry inherently overlaps the coincident pump and probe foci within the nanoparticles at the exit interface of the sphere, and it also enables omni-directionality, in that the coincident pump and probe beams can be incident over the full 4The Si and SiC nanoparticles that are used have approximate diameters of 20 and 50\u2009nm, respectively.  Spheres in the micro-scale regime, with diameters ranging from 1 to 30\u2009\u03bcm, will require the sphere to have a refractive index along the blue curve of n\u22481.75 and n\u22481.83. The spheres used in the AOS architecture must be selected with careful consideration to their refractive index, Given the considerations above for nanoparticles and dielectric spheres, the AOS architecture is tested with spheres in both the milli- and micro-scale regimes using nanoparticle coatings of both Si and SiC.d=2.0\u2009mm, being at the upper limit of the milli-scale regime, and are comprised of S-LAH79 glass, with a refractive index of n=1.98\u00b10.02 The figure insets show a Mie theory simulation and scanning electron microscope (SEM) image of the nanoparticles.Experimental results for the milli-scale AOS architecture are shown in T/T, for all-optical switching between pump and probe beams, with Si nanoparticles. The applied Si nanoparticles have a relatively low surface recombination velocity, Sv=500\u2009m\u2009s\u20131, but a noteworthy decrease in AOS recovery time is still observed\u2014being approximately two thousand times faster than that of bulk Si. This rapid recovery is due to the promotion of surface recombination from the increased specific surface area of the nanoparticles. Ultimately, the milli-scale AOS architecture with the d=2.0-mm sphere and Si nanoparticles yields a switching time of 10\u2009ps and switching energy estimated to be 200\u2009fJ.T/T, for all-optical switching between pump and probe beams, with SiC nanoparticles. The applied SiC nanoparticles have a relatively high surface recombination velocity, Sv=4,000\u2009m\u2009s\u20131, so a dramatic decrease in recovery time is observed\u2014being approximately sixty million times faster than that of bulk SiC.  Ultimately, the milli-scale AOS architecture with the d=2.0-mm sphere and SiC nanoparticles meets the demands for all-optical switching, as it yields a switching time of 350\u2009fs and switching energy estimated to be 100\u2009fJ.d=30\u201340\u2009\u03bcm, being at the upper limit of the micro-scale regime, and are comprised of N-LASF9 glass, with a refractive index of n=1.83\u00b10.02 The figure insets show a Mie theory simulation and an SEM image of the nanoparticles.Experimental results for the micro-scale AOS architecture are shown in T/T, for all-optical switching between pump and probe beams, with Si nanoparticles. The applied Si nanoparticles again produce a noteworthy decrease in the AOS recovery time\u2014being even faster than that of the d=2.0-mm sphere in +\u2009nm, particles that are seen to be interspersed among the 20-nm nanoparticles in SEM images. The milli-scale AOS architecture, with its larger focal spot area is unable to avoid the aggregates of larger particles, which have a smaller specific area and longer charge-carrier lifetime, and this leads to its longer recovery time. Ultimately, the micro-scale AOS architecture with the d=30\u201340-\u03bcm sphere and Si nanoparticles yields a switching time of 2\u2009ps and switching energy estimated to be 1\u2009pJ.T/T, for all-optical switching between pump and probe beams, with SiC nanoparticles. The applied SiC nanoparticles produce a dramatic decrease in AOS recovery time\u2014being even faster than that of the d=2.0-mm sphere in d=30\u201340-\u03bcm sphere and SiC nanoparticles meets the demands for all-optical switching, as it yields a switching time of 270\u2009fs and switching energy estimated to be 20\u2009fJ.An AOS architecture was introduced in this work. A guiding principle of localization was used in the design and analysis to facilitate AOS activation with femtojoule switching energies and AOS recovery with femtosecond switching times. The AOS architecture applied a nanojet focal geometry, in the form of a dielectric sphere, to focus high-intensity beams into a nanoparticle material system, in the form of a coating of semiconductor nanoparticles. The AOS architecture was implemented on milli-scale dimensions, with Si and SiC semiconductor nanoparticles, to yield respective switching energies of 200 and 100\u2009fJ, with respective switching times of 10\u2009ps and 350\u2009fs. The AOS architecture was then implemented on micro-scale dimensions, with Si and SiC semiconductor nanoparticles, to yield respective switching energies of 1\u2009pJ and 20\u2009fJ, with respective switching times of 2\u2009ps and 270\u2009fs.It was found that the AOS architecture could establish localized photoinjection of charge carriers, to enable femtojoule switching energies, and it could establish localized recombination of charge carriers, to enable femtosecond switching times. The AOS architecture met practical considerations for coupling, including beam alignment, directionality and capture cross-section, as well as practical considerations for stability, including physical and temperature sensitivity. Future applications of the AOS architecture may be implemented with consideration to coupling of the spheres to waveguides and/or fibres. Optical micro-electro-mechanical systems packaging can facilitate this integration, by way of on-chip spherical mounts based on V-grooves33353738T/T, of the probe beam is measured by time-resolved sampling as a function of the time delay between pump and probe pulses. The data are acquired with a lock-in amplifier (SR830) using a 100-ms time constant. The GaAs and Si targets use pump and probe pulses with respective wavelengths of 780 and 1,550\u2009nm . The SiC target uses pump and probe pulses with respective wavelengths of 390 and 1,550\u2009nm . The 780\u20131,550-nm pump\u2013probe experiments with d=2.0-mm spheres use a pump\u2013probe power ratio of 1:2. The 390\u20131,550-nm pump\u2013probe experiments with d=2.0-mm spheres use a pump\u2013probe power ratio of 1:20. The 780\u20131,550-nm pump\u2013probe experiments with d=30\u201340-\u03bcm spheres use a pump\u2013probe power ratio of 3:1. The 390\u20131,550-nm pump\u2013probe experiments with d=30\u201340-\u03bcm spheres use a pump\u2013probe power ratio of 1:1. For these pump\u2013probe conditions, the pump photon energy is above-bandgap and the probe photon energy is below-bandgap. This leads to probe-power-independence for all reported results, that is, multi-photon contributions from the probe beam are not observed.The pump\u2013probe experimental configuration, seen in A tabletop pump\u2013probe experimental set-up such as this characterizes the impulse response of the AOS architecture. For future applications, seeking compact device profiles and ultrashort laser pulses, the AOS architecture can be integrated with a sub-millimetre ultrashort pulsed laser, such as a mode-locked laser diodeExperimental results are collected for focusing through spheres into a GaAs target and into nanoparticle coatings.d=2.0\u2009mm. They are mounted in the pump\u2013probe experimental set-up by bonding the spheres to a 22-gauge needle tip with ultraviolet-curable polymer. The GaAs target is positioned in the focal plane of the spheres by collimating the back-reflected beams, as collimated back-reflected beams indicate that the reflective GaAs target is positioned in the focal plane of the sphere. Ultimately, the spheres with refractive indices of n=1.51, 1.76, 1.83 and 1.98 will be separated from the GaAs target by 480, 160, 100 and <1\u2009\u03bcm, respectively. The respective sensitivities for these positions, being 1.1, 0.7, 0.6 and <0.5\u2009\u03bcm, are dictated by each sphere's depth of focus.For the experiments that focus into a GaAs target, the spheres have a diameter of d=2.0\u2009mm and d=30\u201340\u2009\u03bcm. The d=2.0-mm spheres are mounted as stated above. The d=30\u201340-\u03bcm spheres are mounted on a planar glass substrate. The nanoparticles are applied to the surface of the sphere with a dry-coating processFor the experiments that focus into (Si or SiC) nanoparticle coatings, the spheres have diameters of N, and it is these time constants that witness pronounced effects from the increased specific surface area of the nanoparticles. Short-recovery time constants are observed at \u223c3\u2009ps for the bulk and at 350 and 270\u2009fs for the SiC nanoparticles on the micro- and mill-scale architectures, respectively. The short-recovery time constants are attributed to ultrafast charge-carrier dynamics in the SiC bandstructureM-sidevalley and then undergo intervalley and intravalley scattering. The scattering yields femtosecond and picosecond transients for the effective mass and mobility. The effective mass and mobility transients form ultrafast transients on the refractive index near the surface, \u0394ns(t), and absorption coefficient in the bulk, \u0394\u03b1b(t), respectively, and this is ultimately seen as an ultrafast modulation on the differential transmission of the probe beam, according to 3948The bulk SiC results of How to cite this article: Born, B. et al. Integration of photonic nanojets and semiconductor nanoparticles for enhanced all-optical switching. Nat. Commun. 6:8097 doi: 10.1038/ncomms9097 (2015)."}
+{"text": "Face recognition is challenging especially when the images from different persons are similar to each other due to variations in illumination, expression, and occlusion. If we have sufficient training images of each person which can span the facial variations of that person under testing conditions, sparse representation based classification (SRC) achieves very promising results. However, in many applications, face recognition often encounters the small sample size problem arising from the small number of available training images for each person. In this paper, we present a novel face recognition framework by utilizing low-rank and sparse error matrix decomposition, and sparse coding techniques (LRSE+SC). Firstly, the low-rank matrix recovery technique is applied to decompose the face images per class into a low-rank matrix and a sparse error matrix. The low-rank matrix of each individual is a class-specific dictionary and it captures the discriminative feature of this individual. The sparse error matrix represents the intra-class variations, such as illumination, expression changes. Secondly, we combine the low-rank part (representative basis) of each person into a supervised dictionary and integrate all the sparse error matrix of each individual into a within-individual variant dictionary which can be applied to represent the possible variations between the testing and training images. Then these two dictionaries are used to code the query image. The within-individual variant dictionary can be shared by all the subjects and only contribute to explain the lighting conditions, expressions, and occlusions of the query image rather than discrimination. At last, a reconstruction-based scheme is adopted for face recognition. Since the within-individual dictionary is introduced, LRSE+SC can handle the problem of the corrupted training data and the situation that not all subjects have enough samples for training. Experimental results show that our method achieves the state-of-the-art results on AR, FERET, FRGC and LFW databases. Face recognition has been an active topic in machine learning, computer vision and pattern recognition research due to its potential value for applications and theoretical challenges. Face recognition is widely applied in real life, such as online image search, law enforcement, access control for secure facilities , security surveillance, and etc. Many face recognition approaches have been proposed, such as, Eigenfaces , Fisherfet al.  8] [8]et al [8]et alet al.  12]  \u2208 Rm\u00d7in consists of training images belonging to the ith subject and X =  \u2208 Rm\u00d7n denotes the training images matrix by concatenating all training samples. Given the training samples in X, the aim of face recognition is to classify a query image y \u2208 Rm.Firstly, let us present a typical face recognition problem. Assume there are Recent research has proved that linear regression based algorithms, e.g. Nearest Feature Subspace (NFS) , Linear y \u2208 Rm belonging to class i, if given sufficient training samples of class i, we havei\u03b2 =  \u2208 Rni is the coefficient vector corresponding to Xi. Of course, this class-specific subspace is embedded in the linear space spanned by all the training images. Hence, y can be cast as the linear combination of all training samples, i.e.\u03b2 \u2208 Rn is a coefficient vector. Actually, we don\u2019t know which class the query image y comes from. Hence, the goal of sparse representation is to represent y using as few training images as possible, which is computed by solving the following minimization problem:\u03f5 is a pre-specified small constant and \u2225\u22c5\u22250 means \u21130-norm. The above problem is NP-hard and it can be solved by approximating the \u21130-norm with \u21131-norm based convex relaxation. Hence, problem \u21131-norm regularizer, i.e.\u03bb is a scalar constant. In the ideal case, the entries of X from the ith class. In practice, this is not real, the recovered coefficient vector y is assigned to the class which has the minimum reconstruction residual.Sparse representation has attracted broad interest in various domains due to its great success in image processing. The basic idea of sparse representation is to represent a given test sample correctly with as few training samples as possible. SRC assumes that training samples from each subject lie on a linear subspace spanned by the training images from the given subject. Therefore, for a test sample et al.  [11 [11et alet al.  13]. Ho. Hoet ali.e., occlusions, lighting variations, facial expressions) violate the linear subspace assumption. Furthermore, due to insufficient number of training images, the query images of the ith class may be not lie on the subspace spanned by training images Xi. Therefore, the performance of SRC will deteriorate in these two situations. In order to handle the small sample size problem, leave-one-class-out subspace model is proposed  and E = . Di contains the structured patterns and discriminative feature of the ith subject. Therefore, Di has a better representative ability than the original data Xi in describing the face images of the ith subject  \u2208 Rm\u00d7n for c subjects and the query image y, parameters \u03bb1, \u03bb2.Output: Class label of the query image y.Step 1: Learning class-specific dictionary and intra-class variant dictionary by low-rank matrix recovery.\u2003fori = 1: cdo\u2003Di,Ei \u2225Di\u2225* + \u03bb1\u2225Ei\u22251\u2003s.t.Xi = Di + Ei\u2003\u2003minend for\u2003Step 2: Building supervised dictionary and Within-individual variant dictionary.\u2003D =  is make up of the class-specific sub-dictionaries Di. The within-individual variant dictionary E =  is builded by integrate all the sparse error matrix of each subject. However, for each column of E, if the norm is less than a threshold \u03b7 (e.g. \u03b7 = 10\u22123), it is removed from E.\u2003The supervised dictionary Step 3: Finding sparse representation of the query image y in term of new dictionary [D\u2003E].\u2003\u21131-norm minimization problem\u2003Solving the \u2003Step 4: Classification\u2003fori = 1: cdo\u2003\u2003\u2003end for\u2003Identity(y) = argminie(i)\u2003ith subject as Si. Thus, we havey, we assume that it comes from the ith class. If we have observed a sufficient number of training images per subject, then the query image can be well reconstructed by the training images belonging to the ground-truth class of it. Therefore, y \u2208 Si. Obviously, SRC has achieved very promising results in this situation.In this section, the justification of our method and the difference with SRC will be discussed. Linear regression based algorithms assume that the images from a single subject lie on a linear subspace. We denote the subspace spanned by the training images from the ith class to cover the variations of the test image y, i.e., y \u2209 Si. However, for large scale face recognition problems where the training sets contain large number of subjects, some training images from other subjects can be used to describe the test image y. Therefore, in this paper, we suppose that the test sample lies on the subspace spanned by all training samples, i.e., y \u2208 S = span{X1, \u2026, Xc} and y \u2209 Si. For SRC, the training samples, which are the most similar with the query image y, are selected to represent y. Since y \u2209 Si, there exist training samples y. Certainly, y can\u2019t be modeled accurately by training images just from others because there must be some unique patterns owned by the ith class. So, we haveXi\u2212 represents all training samples except for the ith subject. According to y can be written as:\u03b1ij and \u03b2j are the coefficients. Obviously, \u03b1 =  \u2260 0 and \u03b2 =  \u2260 0. Without loss of generality, assume that kth (k \u2260 i) subject. If the contribution of training data belonging to the ith class is small, it is possible that y as the kth class. For example, the query image in y which might be caused by illuminations, expressions, or occlusions. However, SRC can\u2019t separate these components  from the original training samples, hence, SRC treats them as discriminative feature of each subject.In practice, facial images might suffer from expression, illumination variations and even occlusions, there isn\u2019t adequate number of training images for the Si, i.e., the subspace of Subject i, can be modeled asi and it is the discriminative component of this subject, while ei1, ei2, \u2026, eini are basis vectors for the within-individual subspace and explain why training images of Subject i do not look identical. Hence, the basis vectors of subspace Si can be divided into two categories: The first one is the discriminative vector for each class; the other one is within-individual variant vector. However, in practical scenarios, facial images are affected by many factors, it\u2019s not appropriate to describe the class-specific information of Subject i by just one basis Di as representation basis matrix of Subject i and Si is the subset of space spanned by Di and Ei, i.e.,dij and eij represent the jth  column of Di and Ei, respectively. We denote span{ei1, ei2, \u2026, eini} represents the noise or within-individual variance of Xi. We combine the sparse error matrices of all subjects into a within-individual variant dictionary E = , which can be used to model the intra-class variations lighting conditions, expressions or occlusions. Therefore, W = span{e11, \u2026, en11, \u2026, ecnc} is a within-individual subspace. From ith subject, it lies in the linear subspace y in i, but it may be lie in y belongs to Subject 84. However, y \u2209 S84 due to the occluded regions. By taking advantage of low rank matrix recovery, we obtain the within-individual subspace W. The query image y can be represented by the class-specific subspace W. Hence, LRSE+SC can alleviate the small sample size problem and the problem of the corrupted data.According to the theories of linear subspace and \u03bb1 tends to infinity, all the atoms of within-individual dictionary E are zeros. In this situation, our method LRSE+SC is equivalent to SRC.From \u21131-regularized least squares problem. The feature-sign search algorithm is very fast and achieves high performance .There are two parameters, tions in , the cor\u03bb1, \u03bb2 over recognition accuracy, we perform two experiments on AR database. \u03bb1, \u03bb2. These two examples demonstrate that the optimal values of \u03bb1, \u03bb2 are correlated with training samples and test samples. However, when \u03bb2 = 0.001, 0.0005, LRSE+SC achieves good performance. It is easy to see that LRSE+SC can achieve good performance when the value of \u03bb1 in the neighborhood of 0.023.In order to study the influences of parameters In this paper, we have introduced a novel face recognition framework by utilizing low rank matrix recovery. In this mechanism, we try to decompose the original images into the class-specific feature and within-class variant feature. We have demonstrated theoretically and experimentally that the within-class variant feature which is separated from the original images is very important to deal with small sample size problem.Our method leverages low-rank and sparse error matrix decomposition technique and sparse representation scheme. Firstly, we recover the low-rank matrix of each subject by removing the sparse error in the training images. Then the low-rank matrix can be used as supervised dictionary to coding the test samples. Our algorithm regards the sparse error matrix of all subjects as sparse within-class variant dictionary to represent the variants of the test image and training images from the same class, which may be caused by illuminations, expressions and disguises. Experiments confirm that LRSE+SC approach outperforms SRC and ESRC for small sample size problem."}
+{"text": "Such torsional excitation is a form of parametric pumping in the system, which results in the breakage of the time-reversal symmetry. We report that, in quasi-static sense, the system shows topologically non-trivial band-gaps. However, in a dynamic regime where the pumping effect is significant, these band-gaps become asymmetric with respect to the frequency and wavenumber domains in the dispersion relationship. By using numerical simulations, we show that such asymmetry has a direct correspondence to the topological invariant, i.e., Chern number, of the system. We propose that this asymmetry, accompanied by selective inter-band transition, can be utilized for directional isolation of the stress wave propagating along the phononic crystal.We present an active, purely mechanical stress wave isolator that consists of short cylindrical particles arranged in a helical architecture. This phononic structure allows us to change inter-particle stiffness dynamically by controlling the contact angles of the cylinders. We use  A wide variety of researchers have been striving to attain the ability to control the flow of energy in media for centuries. In particular, one-way transmission of electrical energy by semiconductor diodes and transistors has revolutionized the modern era. On the similar lines, one-way propagation of light, heat, and sound have captured the attention of the scientific community, leading to the invention of novel devices, namely photonic5in-situ tunability of wave transmission direction is desired, a linear medium would take the precedence over a non-linear one. This is because the allowed direction of wave propagation can be reversed simply by flipping the external bias, which is not the case with passive settings of non-linearity-based isolators. Moreover, the isolation characteristics could be tuned by adjusting the magnitude of the external bias directly, thereby making such systems active. One could use different types of biases in these active systems. For example, in an acoustic domain, external moving fluid can serve as a bias10121314One of the most common ways to realize one way transmission in a mechanical system is to break the time-reversal symmetrylongitudinal wave by having a direct control over the torsional modes. In particular, we use a torsional travelling wave to induce a specific spatio-temporal modulation of the system\u2019s stiffness, which resembles the sliding lattice potential of the topological Thouless pump in quantum mechanicsbulk wave propagation along the phononic crystal. In this study, we show the topological invariants that we calculate for our one-dimensional system quantify the amount of asymmetry in the dispersion of such bulk waves, in contrast to a two-dimensional system in which those invariants tend to be related to the number of edge modes.In this study, we propose a one-dimensional phononic crystal that consists of a chain of cylinders, to achieve the stress wave isolation in a purely mechanical manner. The array of cylinders has shown extraordinary tunability in terms of tailoring the stress wave propagation through them1617Inspired by the mechanics of the Hertzian contact, the architecture of the helix, and the physics of the Thouless pump, this study claims three-fold novelty as following. First, in terms of design, we propose a purely mechanical system that utilizes a strong coupling between two mechanical wave modes to break the time-reversal symmetry. This implies the control of one mechanical wave mode via another, without resorting to external bias/field. Second, in terms of the fundamental physics of a time-dependent, one-dimensional mechanical system, we show that this system is topologically non-trivial and can be characterized by the topological invariant in two-dimensions, i.e., Chern numberThe phononic crystal to be investigated in this study consists of short cylindrical particles stacked helically as a one-dimensional chain . Each cyet al.i-th cylinder asBased on the previous work by Li \u03b10 is the contact angle between any two cylinders at equilibrium; A\u03b1 is the dynamic perturbation in the contact angle caused by a travelling torsional wave; k\u03b1\u2009=\u20092\u03c0/N represents a wavenumber with N being the spatial period of the contact angle variation; f\u03b1 denotes the frequency of the travelling torsional wave; and forward and backward direction of the travelling torsional wave, respectively.where \u03b1i(t)\u2009=\u2009\u03b1i+\u20091(t)\u2009\u2212\u2009\u03b1i(t). Using the Hertz\u2019s contact law, instantaneous contact force between i-th and (i\u2009+\u20091)-th cylinders would be \u03b2i(t)\u03b43/2, with \u03b4 as the relative longitudinal displacement between two cylinders. The time-dependent stiffness coefficient \u03b2i(t) is of the following form19We can define the contact angle, i.e., relative angle between two cylinders, as \u0394Y, \u03bc and R denote Young\u2019s modulus, Poisson\u2019s ratio, and the radius of a cylinder. Ke(t) and Ee(t) represent the complete elliptical integrals of the first and second kinds, respectively. The elliptical contact area has eccentricity a and b as its semi-major and semi-minor axes, respectively. b/a is equal to [(1\u2009+\u2009cos\u2009\u0394\u03b1i(t))/(1\u2009\u2212\u2009cos\u2009\u0394\u03b1i(t))]\u22122/3, approximatelyHere, n cylinders of equal masses m. We fix the longitudinal motion and keep the torsional motion free at both ends of the chain. Let xi(t) represent instantaneous longitudinal displacement of the i-th cylinder, and \u03b4i be the initial deformation between i-th and (i\u2009+\u20091)-th cylinders under static pre-compression. For a generic scenario, under the excitation forces p1(t) and pn(t) applied to the first and last cylinders of the chain, respectively, we write-Once we have formulated the instantaneous contact stiffness between constituents elements, we can now write the equations of motion for the system consisting of For small instantaneous displacements X(t), stiffness matrix K(t), mass matrix M, and forcing vector F(t) are expressed as-where displacement vector K(t) and a forcing vector F(t), which make the system dynamics fairly complex yet interesting. K(t) imbibes spatio-temporal modulation of contact stiffness in the system, whereas the forcing term F(t) has an external forcing component as well as a component dependent on stiffness modulation. Under no external force p(t) applied to the system, we can easily deduce that a travelling torsional wave as in K(t)\u2009=\u2009K(t\u2009+\u2009T) and F(t)\u2009=\u2009F(t\u2009+\u2009T), where T\u2009=\u20091/f\u03b1. This periodic evolution of K(t) represents parametric pumping in the system caused by torsional wave. The mechanism is analogous to the pumping action performed, for example, when one wants to change the amplitude of oscillation of a swing without exerting an external force. Instead, one changes the center-of-mass and thus vary the effective swing length with timeK(t) acts as such a time varying parameter in this case, which is pumped with frequency f\u03b1 of the torsional wave.Let us now look at the f\u03b1\u2009=\u20090, we see that the second component of F(t) vanishes, and this equation reduces to the familiar standard form: independentK. We can easily analyse it further to obtain eigen-frequencies and Bloch states. However, due to a non-zero f\u03b1, simultaneous space-time stiffness modulation is enforced, and a time-periodic set of equations with a period T represents our system. This period is dictated by the pumping frequency f\u03b1 of the torsional wave. In this way, our system not only supports the Bloch states caused by spatial variation of parameters, but also allows us to tailor them by an additional degree of freedom, i.e., time, hence taking us to the realm of Floquet-Bloch engineeringNote that this parametric pumping has direct consequences on the vibrational modes the system supports. If the perturbation in contact angles were to depend solely on space but not time, i.e., To understand the system dynamics, we start with analysing the normal modes of vibration in the system. We would take the homogenized form of K(t\u2009+\u2009T)\u2009=\u2009K(t). This time-periodic system of equation resembles the well studied Mathieu\u2019s equation, and it can be solved using Floquet theoryadiabatic topological quantum pumpquasi-static scenario, and then extend the key characteristics to explain dynamic scenario of pumping. With regard to quasi-static evolution over time, we assume that the variation in the stiffness matrix K(t) with respect to time is significantly small, such that the natural modes of vibration can be calculated directly from the matrix at any time instant. Natural frequencies corresponding to such quasi-static evolution of system are named as static frequenciesk\u03b1 in f\u03b1, i.e., the pumping frequency, causes temporal variations in stiffness, and is the measure of how quickly static frequencies are varied over time. If we understand how static frequencies evolve over time, that would give us direct insights into the actual system dynamics for quasi-static pumping. It would also be useful to decipher the complex dynamics in case of rapid pumping  where secondary mode of vibration with frequency offsets, namely frequency cascadeswhere Under the quasi-static assumption, we can convert fL|s denotes the static frequency of the longitudinal waves, which should not be confused with pumping frequency f\u03b1 of the torsional waves. For the analysis, we choose \u03b10\u2009=\u200910\u00b0, A\u03b1\u2009=\u20092\u00b0, N\u2009=\u20096, and n\u2009=\u2009300. We take geometrical dimensions and material properties of quartz cylinders from our previous experimental studies f\u03b1\u2009=\u20090.1\u2009kHz of the forward propagating torsional wave.Here t\u2009=\u20090. In general, we expect five band-gaps in frequency spectrum for the spatial period (N\u2009=\u20096) of stiffness variation. However, the perturbation A\u03b1 in contact angles is small, and therefore we notice only three prominent band-gaps, labelled as 1, 2, and 3 (insets show zoomed view). We then calculate how these frequencies evolve over time due to the quasi-static pumping of torsional wave. Since the pumping is periodic, we expect evolution of the eigen-frequencies to be periodic as well. In T. It is important to note that only frequencies on the edges of band-gaps evolve quite distinctly over time. Frequencies corresponding to global modes do not evolve as distinctly as the edge modes. This is intuitive if we rely on the following argument: spatio-temporal stiffness variation in our system is equivalent to a sliding potential, so at each time instant, stiffness variation is just spatially shifted from the one at last time instant. Quasi-statically speaking, this only reflects as a change in the edge modes of a finite lattice, not the global modes. Hence, the modulation is only evident for the modes on the edges. It is also important to note that all three band-gaps evolve distinctly over time with a different number of degeneracies (crossings). We will now shed light on the same in more detail, and establish their non-trivial topological characteristics.In bulk-boundary correspondence indicates breaking for time-reversal symmetry; and it is the classical analogue of the topological band-gaps of the sliding lattice first proposed by Thouless in 1983Such non-trivial topological nature of band-gaps manifests the quantization of pumped charge in a time-dependent, one-dimensional quantum mechanical system. The average charge/photon flow in one period of pumping cycle can be quantified using a topological invariant in two dimensions, i.e., Chern number2733small pumping frequency, f\u03b1\u2009=\u20090.01\u2009kHz. In right end \u2013 evolves to a global mode. The other instance  from both left and right ends of the chain separately and see how the pulse propagates in the medium. We send these pulses at the two different time points 1 and 2, and solve We now verify the results obtained through quasi-static analysis, and demonstrate the implications of the bulk-boundary correspondence in the system by carrying out full numerical simulations at a \u03c0f\u03b1t in It should be also noted that if we flip the sign of the pumping frequency , time-reversal symmetry is broken, and we notice asymmetry in the dispersion curves . However, the most remarkable observation is that each band-gap, on the primary mode branch, shows a unique asymmetry with respect to positive and negative wavenumber axes. Those are not only distinct in terms of the magnitude of frequency and wavenumber offset but also in their directional shifts. For example, band-gap 1 shifts up for positive wavenumbers, whereas band-gap 3, even though showing the same frequency offset, shifts down for the positive wavenumbers. Band-gap 2, however, shows entirely distinct offset with double the magnitude compared to those of band-gap 1 and 3.On the other hand, as we introduce a significant pumping frequency  \u2013 which occurs during the time evolution of eigen-frequencies  \u2013 essentf\u03b1\u2009=\u20092\u2009kHz, we focus on the widest and highest band-gap 3. We choose a longitudinal travelling pulse with frequency fL\u2009=\u200916.78\u2009kHz, such that it lies inside and outside of the band-gap of the primary mode for the right and left branches of dispersion curve, respectively. We use 0.8\u2009ms long Gaussian pulse , and a frequency higher than the band-gap region propagates in the opposite direction (right). These are indicated as the tips of the arrow marked in f\u03b1 for the current band-gap. Hence, we see the modes travelling in opposite directions lie on different bands of the dispersion curve ; and hence the term inter-band transition is justified.This is indeed a peculiar type of wave dynamics we observe in our system. Though, an input wave can propagate in In this study we have proposed a purely mechanical device based on a helical phononic crystal, which shows non-reciprocity in terms of stress wave propagation. We used the coupling of two mechanical waves \u2013 longitudinal and torsional modes \u2013 to achieve the breakage of time-reversal symmetry. We related such symmetry breaking to the topological nature of band-gaps induced by spatio-temporal variation of system parameters. In this phononic crystal, the topological characteristics represented by the Chern number directly dictate the level of asymmetry associated with each band-gap in the dispersion curves. Notably, the asymmetry in the dispersion curve can be used to achieve the inter-band transition at a specific frequency range. Towards the practical significance, if the higher frequency mode in such asymmetric wave propagation can be filtered, e.g., by using the fact that it would attenuate more in the presence of material dissipation or by taking advantage of its slower wave propagation speed, the current system would serve the purpose of stress wave isolator, allowing stress waves only in one-direction. Moreover, the allowable direction as well as general characteristics of the longitudinal wave can be simply controlled by fine-tuning the torsional wave parameters, thereby making the proposed system active and tunable.How to cite this article: Chaunsali, R. et al. Stress Wave Isolation by Purely Mechanical Topological Phononic Crystals. Sci. Rep.6, 30662; doi: 10.1038/srep30662 (2016)."}
+{"text": "The study of various living complex systems by system identification method is important, and the identification of the problem is even more challenging when dealing with a dynamic nonlinear system of discrete time. A well-established model based on kernel functions for input of the maximum length sequence (m-sequence) can be used to estimate nonlinear binary kernel slices using cross-correlation method. In this study, we examine the relevant mathematical properties of kernel slices, particularly their shift-and-product property and overlap distortion problem caused by the irregular shifting of the estimated kernel slices in the cross-correlation function between the input m-sequence and the system output. We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance of kernel-slice overlapping. An instance of third-order Wiener nonlinear model is simulated to justify the proposed method. Living systems usually exhibit complex and nonlinear behaviors \u20133, whichThe kernel estimation for such nonlinear system usually requires the input signal to be a long Gaussian white noise to completely activate the underlying system. Under such conditions, Lee and Schetzen proposed a convenient cross-correlation method widely used to estimate the kernel functions , 8.In several circumstances, particularly for a variety of living biosystems, input signals are constrained as a series of impulse trains instead of continuous signals, such as the Gaussian white noise , 10. ForUsing the m-sequence approach, Sutter studied the binary kernel for identifying multifocal retinosystem through electroretinography and explained the visual function using the binary kernels . Shi andHowever, the binary kernel slices\u2014derived by making use of the shift-and-product property of the m-sequence\u2014are all laid in the first-order cross-correlation function between the m-sequence input and the system response, that is, the observed output. The specific location of any kernel slice in the cross-correlation function is determined through a complex shift function that cannot be explicitly determined. If the kernel slices are improperly arranged such that overlaps among neighboring slices occur, then the kernel estimation is inevitably distorted. A straightforward approach to solve this problem is to multiply the length of the input m-sequence, which is unfavorable for living systems with more or less time-varying property. Another approach to alleviate the overlap issue is to sparsify the impulse train of the m-sequence at risk of suffering the underestimation caused by the reduced number of available kernel slices .In this study, we addressed the overlap problem through a new strategy using an inverse-repeat (IR) m-sequence. We will drive the estimation equations for the binary kernel slices corresponding to the IR m-sequence, through which the odd- and even-order kernel slices can be separately estimated and thus reduce the chance of slice overlapping. Last, a third-order nonlinear system is simulated to demonstrate the process of the proposed method.b[n] consisting of digit \u22121 and +1 that pseudorandomly occurred can be generated through the output of a linear circular shift register. The structure of which is determined through a primitive polynomial of degree r, which is also the degree of the periodical m-sequence . The exact value of a shift function depends on the shifting lags of the m-sequences to be multiplied. This property indicates that the product of the m-sequences with different circular shifts is also the same m-sequence circular shifting to a lag determined by a shift function fp that is unknown a priori. A straightforward approach to calculate the specific value of a shift function is to compare bit-by-bit the original m-sequence b[n] and the resulting k-bit shifting version b[n \u2212 k] until b[n] = b[n \u2212 k], such that fp = k.(i) Shift-and-product propertyj1 = \u22ef = jp\u22121 = 0, that is, the product of the same j\u2009\u2009m-sequences, it yieldsFor p \u2265 3), the m-sequence should be selected with caution in case invalid results occur for the kernel estimation.Equation  providesbnbn\u2212j1\u22efb\u03d5bb[n] is a periodical real value function with the same minimal period of L; that is, (ii) The autocorrelation function that is, \u03d5bbn=1L\u2211\u03c4y[n] of a general Qth-order nonlinear dynamic system in response to the input b[n] can be modeled by a Volterra series expansion  and output y[n] is k = k1 and\u2009 li = ki+1 \u2212 ki, and then . Therefore, if the shift functions of two neighboring slices satisfys and another kernel slice of order q is less than the length of the prior slice, then a slice overlap occurs. The kernel slices overlapping condition is illustrated in To estimate the Volterra kernel for Gaussian white noise, input is not theoretically feasible for the difficulty of nonorthogonality. Instead, it is preferred to estimate thexpansion . This metimation , 16. A pgiven by wpk1,k2,\u2026 y[n] is \u03d5bpy,\u03d5bpy is twice as that of b[n], and a[n] satisfies the inverse repeatability, that is, (i) The minimal period of y[n] of a nonlinear system in response to the input a[n] can also be modeled by Volterra series expansion. If we dichotomize y[n] into an odd-order response yo[n] = \u2211\u210bpb[n],\u2009\u2009p = odd, and even-order response ye[n] = \u2211\u210bpb[n], p is even, they satisfy,(ii) The output a[n] and b[n] is zero, that is, (iii) The cross-correlation function of a[n] isL is odd, then \u03d5aa[n] = \u2212\u03d5aa[n + L]; that is, \u03d5aa[n] is also inversely repeated. The proof of property (iv) is given in (iv) The autocorrelation of a[n] also has the following shift-and-product property, (v) IR m-sequence a[n] be the input of the system, and then the output of the Qth-order nonlinear system expressed in terms of Volterra series expansion is k = k1 and li = ki+1 \u2212 ki, and, using IR m-sequence property (v), the Volterra operator on the input a[n] becomesb[n] and odd-order Volterra series term \u210bpa[n], (p = odd), is zero and that the cross-correlation function between IR m-sequences a[n] and even-order Volterra series term \u210bpa[n] (p = even) is also zero; that is, Based on the above properties of the IR m-sequences, we can derive the binary kernel slices in response to an IR m-sequence. Let ploiting  for the that is, \u03d5bHp[n]=1pth-order cross-correlation for IR m-sequence input a[n] with the same approach as that of getting  to  to pth-omember is\u03d5apy=12L\u2211lices as wp, output signal y[n], and cross-correlation \u03d5by[n]. The estimated kernel slices are plotted in solid trace superimposed on the cross-correlation signal (in dashed trace). The red trace segments indicate the occurrence of slice overlaps. According to the overlap condition defined in  and proposed IR m-sequence (in blue traces) methods are shown in l1 = 4 show a slightly opposite behavior that needs to be accounted for, because no overlap occurs at these affected kernel slices. This inconsistency is only observable at a significantly small scale (see the amplitude scales in A series of third-order kernel slices are shown in The shift-and-product property of the m- and IR m-sequence is crucial in the derivation of new properties to address the overlap problem for short-length m-sequence. It is apparently not beneficial to use a redundantly higher order m-sequence or to sacrifice the number of the estimated slices using sparse m-sequence. In this study, we alternatively propose an approach by introducing the IR m-sequence. We provide and prove several relevant properties of the IR m-sequence allowing the estimation of the binary kernel slices. By examining the special shift-and-product properties of the IR m-sequence derived for odd and even shifts, the odd- and even-order kernel slices can be separately represented in the cross-correlation functions, such that the chance of overlapping significantly decreases. Furthermore, this separation will be useful in some special applications where only odd- or even-order kernel slices might be of significant interest."}
+{"text": "Segmentation of injured or unusual anatomic structures in medical imagery is a problem that has continued to elude fully automated solutions. In this paper, the goal of easy-to-use and consistent interactive segmentation is transformed into a control synthesis problem. A nominal level set PDE is assumed to be given; this open-loop system achieves correct segmentation under ideal conditions, but does not agree with a human expert's ideal boundary for real image data. Perturbing the state and dynamics of a level set PDE via the accumulated user input and an observer-like system leads to desirable closed-loop behavior. The input structure is designed such that a user can stabilize the boundary in some desired state without needing to understand any mathematical parameters. Effectiveness of the technique is illustrated with applications to the challenging segmentations of a patellar tendon in MR and a shattered femur in CT. Segmentation is the task of identifying and localizing salient structures in the image volume. Since there is an abundance of raw image data that is not analyzed due to the infeasible time and cost of manual segmentation, automated methods for segmentation are the subject of much recent medical computing literature [Microwave-frequency Magnetic-Resonance-Imaging (MRI)  and X-Raterature \u20137]. How. Howsegmterature \u201310]. In. Insegmetime; a partial differential equation (PDE) is used to model the space-time relationship between image data and segmentation boundaries . Gi. Gitime;undaries \u201320]. It. Ittime;blem; in \u201323], us, ustime;blem; in , 24],  by byut+ddxents. In , the inv u \u201334]; e.; e.ut+ddUsing a PDE formulation guarantees that the computational complexity is fixed and that the segmentation result changes continuously over time. By incorporating control-theoretic tools, it is shown that the steady state segmentation can be driven to an ideal reference boundary. Input from the human user indicating locations where the current state does not match the desired reference state is processed and used as feedback in the PDE. An approach similar to backstepping , 35] is is35] isThe remainder of this paper is as follows.Image segmentation based on the narrow-band level-set method is reviewed in Section II. Following an approach similar to back-stepping, a controller is proposed in Section III that stabilizes a labeling-error term, assuming exact knowledge of a reference state. An auxiliary observer-like system is designed in Section IV to process a user input signal and estimate the reference state. Application of the technique to interactive segmentation of CT and MRI volumes is demonstrated in Section V, using images that are difficult to segment with existing methods. The proposed algorithm is compared to related methods in Section VI. Section VII summarizes the results and applicability of the approach. Key components of the final closed-loop system and corresponding paper sections are visualized in level set method, reviewed in Section II-A. Section II-B describes the limitations of open-loop segmentation, thus motivating the feedback control model of interactive image segmentation in Section III-A.The class of open-loop systems considered in this work are PDE-based segmentation algorithms using the popular n to be the spatial domain and x a coordinate in \u03a9. Labeling assignments are represented with an implicit function \u03d5 : \u03a9 x . D. D37]. DF in In \u201cvariational level set methods\u201d \u201340], th, th40], artificial time parameter t, which arises solely due to an iterative minimization of t corresponds to a physical time since the human user watches a time-varying visualization of \u03d5 to decide where and when to provide input.As pointed out in , many imt\u03d5| > 0 only in a neighborhood of the moving zero level set . Th. Th\u03d5t| > method\u201d  update \u03d5exterior and interior regions by a regularized version of the Heaviside step function denoted by \u03b5, illustrated in \u03b5\u03b4 are defined as\u03a9 is divided into This paper considers systems described by narrowband level-set PDEs with the general formG(\u00b7) in \u03ba(F), where F is a smooth function with non-vanishing gradient defined on x \u2208 \u03a9.Application-specific goals, such as minimization of a functional, dictate the choice of image-dependent \u03d5 to a signed distance function  mi mi\u03d5 to ap1, p2, and \u03ba0 are fixed constants for a given re-distancing method. These bounds are helpful for control synthesis in Section III.where n-dimensional non-parametric density estimates ..n-dimensI(x) in the interior (\u03d5 > 0) and exterior (\u03d5 < 0) regions areNevertheless, a recurring problem is that many objects of interest do not coincide with minima of a proposed functional. As an example, consider segmentation via the \u201cmean-alignment\u201d system . The weiA gradient flow for the functionalgives the following narrowband open-loop system:I(x) in the course of minimizing E(t).\u03d5 in agreement with a desired segmentation.Rather than having the human user give up on the PDE system and manually outline the desired region of interest, the PDE can be augmented with a user-driven control input. A control solution is sought due to limitations in the efficacy of open-loop system \u03c8 denote the ideal reference segmentation. A human user could manually trace the level set \u03c8(x) = 0 if given unlimited time. We seek to drive \u03d5 towards an explicit estimate of \u03c8, while maintaining closed-loop stability and minimizing burden placed on the user. User-driven control effort should preserve the advantages of the narrowband formulation noted in Section II-A; therefore, an admissible control signal f will act only on the |\u03d5| \u2264 \u03b5 subdomain of \u03a9. The closed-loop system then becomesLet \u03c8(x) is assumed known; a control is synthesized to drive \u03d5 such that it matches \u03c8. Later in Section IV, a coupled system that estimates \u03c8 from available user input is formulated.In this section, \u03be and , respectively:Define the pointwise and total labeling error as \u03c8 is known and available, regulation of (t) is straightforward with the following two theorems in this section. The regulatory control uses known bounds on the image-dependent G term of GM(x), G\u0305M to be upper bounds such that for any segmentation state \u03d5,If Theorem III.1 Using a spatially-varying U(x), a control for 0 > 0, \u03bb1 > 0, \u03c1 \u2208 , a sufficient condition for boundedness of  isGiven constants \u03bb\u03be is large in the sense ofFurthermore, when the error the rate of convergence is bounded byProof: Re-arranging terms in \u2032 and integrating by parts making use of \u03b5\u03b4 \u2218 \u03d5 = 0 on \u2202\u03a9:L1 guarantees the existence of a constant r such thatThe Poincar\u00e9 inequality in r is at most half the diameter of \u03a9  whe whe53] wI(x). To do so, open-loop dynamics are chosen to use the localizing active contours of  be beU(x) fIt is emphasized that the closed-loop control formulation in this paper does not seek to replace existing curve evolution algorithms but rather to augment them. The control-theoretic approach enables a user to reach the desired segmentation at steady-state; running the level set evolution for a longer time will not cause the boundary to \u201cbleed-through\u201d or contract.Two orthopedic images are used as test data to quantitatively compare the method presented in this paper with the popular GrabCut algorithm . The useActuated voxels after initialization are plotted in Y -axis) and the number of newly actuated voxels (X-axis). Each mark corresponds to one iteration when new user input was applied. Linear regression lines are overlaid on the data. The two algorithms have a similar dynamic response in the epiphysis segmentation, shown in Predictability of how the segmentation changes in response to mouse strokes is a criterion for practical ease of use. Two scatterplots quantify the predictability in This paper has presented a modeling approach that enables control-theoretic analysis and design for interactive medical image segmentation. Results shown for a synthetic image (Section IV-D) and real medical volumes (Section V) agree with theoretical expectations of system performance. Section V illustrated two qualitatively different situations: (1) gradual expansion of the boundary to bound the entire femur fragment and (2) prevention of \u201cbleed-through\u201d or over-segmentation with the patellar tendon. In both situations, the user is able to drive the segmentation to a desired steady state and to do so with much less effort in terms of actuated voxels than manual segmentation. In summary, the PDE control formulation enables us to guarantee a user's ability to reach a reference segmentation state while also absolving them of the need to understand mathematical details or use precise mouse movement.Successful use of the closed-loop algorithm by medical students motivates several future extensions. If a single image contains several objects of interest, they would need to be extracted sequentially in the current framework. Such a sequential de-coupled approach does not address natural constraints of the geometry and involves re-editing common boundaries. A coupled formulation using an open-loop system of PDEs such as in  together"}
+{"text": "In this commentary we note that, where relevant but non-redundant features are binary, they inevitably lead to a classifier capable of capturing only a linear relationship between structural features and activity. If, instead, we were to use relevant but non-redundant real-valued features, the resulting predictive model would be capable of describing a non-linear structure-activity relationship. Hence, we suggest that real-valued features, where available, are to be preferred in this scenario.It is common in cheminformatics to represent the properties of a ligand as a string of 1\u2019s and 0\u2019s, with the intention of elucidating,  One of the major goals of cheminformatics is to predict the relationship between a ligand\u2019s chemical structure and its bioactivity . If thisTo devise an adequate model describing this relationship, the cheminformaticist typically follows a standard approach; starting with a large number of ligand attributes or features considered important for representing the underlying characteristics of the ligand, and relevant to its bioactivity. Then, through feature selection techniques, one selects the ligand attributes deemed to have statistically minimum interdependence among themselves (given the ligand bioactivity), while also showing strong association with the ligand bioactivity \u20135. With L-dimensional vector k, where k = 1, 2, ..., K with K being the total number of classes of interest.Typically the ligand\u2019s chemical structure is represented by an x without errors is generally impossible. Usually both x and k are treated as random variables such that for a given x we have a distribution x to the class minimising the probability of misclassification is induced from given prototype samples (a training dataset) [Identifying the relevant features mentclass2pt{minim classes . In pracdataset) , 9.p(k)), evidence  and absence (0) of these features\u2014i.e., L relevant features whose relationship with the bioactivity is statistically significant, but whose class-conditional interdependency is statistically insignificant\u2014i.e., retain features that are statistically non-redundant .It is common practice nowadays to assume that the xl\u2208{0,1} . In pracxl\u2208{0,1} , 5 that xl\u2208{0,1} , one migxIn our probabilistic setting, ernoulli , 12, 13,4 of ref ):4\\documcument}\u2032 , 12, 13\u2014k in xHowever, the situation can be different if non-redundant real-valued features are utilised to represent the chemical structure of the ligand. In this scenario the entclass1pt{minimaependent . Thus, fIn this commentary it has been noted that, when ligand features are represented by a string of binary numbers, one must end up with a linear model for describing the dependency (if any) between the chemical structure of a ligand and its bioactivity of interest\u2014albeit in a classification setting. Such a linear model may be severely biased and limited in its predictivity. It was also pointed out that, where relevant real-valued features are used, the resulting model can be unbiased as it can adequately capture both linear and non-linear structure-activity relationships."}
+{"text": "In consideration of capacity constraints, fuzzy defect ratio, and fuzzy transport loss ratio, this paper attempted to establish an optimized decision model for production planning and distribution of a multiphase, multiproduct reverse supply chain, which addresses defects returned to original manufacturers, and in addition, develops hybrid algorithms such as Particle Swarm Optimization-Genetic Algorithm (PSO-GA), Genetic Algorithm-Simulated Annealing (GA-SA), and Particle Swarm Optimization-Simulated Annealing (PSO-SA) for solving the optimized model. During a case study of a multi-phase, multi-product reverse supply chain network, this paper explained the suitability of the optimized decision model and the applicability of the algorithms. Finally, the hybrid algorithms showed excellent solving capability when compared with original GA and PSO methods. Many scholars have been devoted to the study of positive supply chains, for instance \u20135, howevShih  discusseThus, this paper focuses on the reverse supply chain and constructs an optimized decision model for the selection of supply chain partners as well as determination of production and distribution quantities. Multiechelon logistics issues could be regarded as a Knapsack of a multiple selection portfolio, and resource distribution as a NP-hard issue ; howeverGAs have been widely used in solving real-world complex optimization problems \u201316 and MFuzzy theory, first proposed by Zaden in 1965 as an extension of a general set, is a numerical control methodology for imitating human thought and addressing the inaccuracy of all physical systems. According to Fuzzy Theory, the thought logic of human begins as fuzzy and is intended for judgment, even if conditions and data are uncertain, while modern computers feature bipolar logic, that is 0 or 1, different from the logic of humans. However, fuzzy logic theory can represent the degree of fuzzy concepts with values between 0 and 1, namely, \u201cmembership function.\u201dKarkowski  indicatef = , where fl, fm, and fu are lower bound, mode, and upper bound values, respectively. f.The triangular fuzzy number can be represented as In addition, it is essential for practical applications that a fuzzy number should be transformed to a numerical value. The transform process is called \u201cdefuzzification.\u201d Associated ordinary number (AON) is a simple method in defuzzification and many researches have employed it directly and effectively \u201343. In tThis paper analyzed the reverse distribution activities of defective products in a complex supply chain network, and explored a method of feeding these products back to the manufacturing partners, with consideration of the capacity constraints of suppliers, and the demands of multi-phase, multi-product production and planning. Moreover, the partners shall be selected based on total objective functions , in addition, the fuzzified production defect ratio and transport loss ratio are taken into account. Given the fact of numerous suppliers in a supply chain network, with different production characteristics and resource allocation capabilities covering their capacity and yield, it is crucial to select proper suppliers in a complex supply chain network.T-treatment for data integration [T-treatment formula  \u2192 P(2.1) represents the transport path from the first partner of the first hierarchy to the first partner of the second hierarchy, Gene value is an integral number representing the quantity of partner product transported on the distribution path.romosome  and the Step\u2009\u20092. Generate a random initial population according to the final customer demands of the partners, restrict the population for meeting the demand constraint (nstraint ~12), an, anStep\u2009nstraint . Step\u2009\u20093. Use Roulette Wheel method to select the chromosomes. Calculate selection probability of every chromosome, of which the chromosomes of better fitness function have a higher probability. Step\u2009\u20094. Randomly select two chromosomes from the population for crossover, and generate random crossover points, then exchange the genes of the chromosome, as shown in xc, the number of chromosomes is yc, the crossover quantity is xc \u00d7 yc = nc; a better efficiency could be achieved if crossover rate is 0.75~0.95 [.75~0.95 . Step\u2009\u20095. Randomly select a chromosome for mutation with its position; if the mutation rate is xm, and the number of genes is ym, the mutation number is xm \u00d7 ym = nm, as shown in Step\u2009\u20096. When the chromosomes of best offspring are superior to those of worst population, this population will be replaced as a new one.Step\u2009\u20097. Repeat Steps\u2009\u20092 to 6 until the stop conditions are satisfied.Step\u2009\u20091. Set the particle number, iteration number, maximum speed, learning factor, and inertia weight. Step\u2009\u20092. Randomly generate the initial speed and position of every particle, with the range specified in the constraint (nstraint ~12). . Step\u2009\u20092Step\u2009\u20093. Substitute the particles of population into the objective function equation , and c1 and c2 are learning factors. where Step\u2009\u20095. Substitute the updated particle position into the constraint (nstraint ~12); re; reStep\u2009nstraint ~(12). Step\u2009\u20096. Compare the particle's objective function value with updated particle position and its Pbest. If the objective function value is superior to the Pbest, the Pbest of this particle will be replaced by its objective function value with updated particle position. Step\u2009\u20097. Compare the Pbest and Gbest. If the best value of particle is superior to Gbest, the Gbest will be replaced by the best value of the particle. Step\u2009\u20098. Repeat Steps 2 to 7 until meeting the stop conditions or reaching the set iteration number.Steps\u2009\u20091~3. Perform Steps 1~3 of PSO solving model. Step\u2009\u20094. Perform Step\u2009\u20093 of GA solving model to select the particle positions of better fitness functions stored in the library. With this selection mechanism, there is a higher probability that the particle position of better fitness functions will become Gbest; another new Gbest could be obtained through recombination, and the particles could be evaluated and properly deleted, of which the worst individuals are replaced by optimum individuals, after sequencing of fitness functions. Step\u2009\u20095. Obtain a new group of good populations using the selection mechanism, then perform Steps 1~3 of PSO solving model and obtain the new Pbest and Gbest. Step\u2009\u20096. Perform Step\u2009\u20095 of GA solving model to randomly select mutation particles for single-point mutation and generate a new population. Step\u2009\u20097. Perform Steps 4~7 of PSO solving model to obtain the new Pbest and Gbest of the new population. Step\u2009\u20098. Repeat Steps 2 to 7 until stop conditions are met.Steps\u2009\u20091~6. Perform Steps\u2009\u20091~6 of PSO solving model. Step\u2009\u20097Substep\u2009\u20097.1. Set start temperature (Tstart), end temperature (Tend), cooling rate (\u03b1), and length of Markov Chain (M).Substep\u2009\u20097.2. Disturb the updated particle under current temperature T, and generate a neighboring solution k. Substep\u2009\u20097.3. Calculate the objective function, perform disturbance mechanism under current temperature to generate a neighboring solution k, and then substitute it into the objective function equation (f(X) and the difference of the fitness function \u0394f(n) = f(X\u2032) \u2212 f(X). Obtain initial solution X, and through iteration of random disturbances neighboring reasonable solutions, obtain a new solution X\u2032; every particle runs across the length of Markov Chain M several times at start temperature Tstart; a fitness is obtained every time (energy function \u0394f(n)). equation , and calSubstep\u2009\u20097.4. Judge if this neighboring solution is accepted through probability function, using probability function ; if r \u2264 P(n), it will disturb the neighboring solution k; replace the particle and its fitness function; if r > P(n), it will not replace the particle. A new disturbance solution will generate if not accepted, until the termination of set search times.Substep\u2009\u20097.6. Repeat Substeps\u2009\u20097.2\u20137.5 through Markov Chain (M) until M times, and then perform the cooling steps, indicating that a stable state is reached under this temperature. Substep\u2009\u20097.7. Implement the cooling procedure at the set-cooling rate of \u03b1 through a cooling mechanism T = T \u00d7 \u03b1. Substep\u2009\u20097.8. Judge if the cycling is finished through the set end temperature Tend, if T \u2264 Tend, perform the next step; if T > Tend, repeat Substeps 7.2 to 7.7 until T \u2264 Tend. Step\u2009\u20098. Repeat Steps 2 to 7 until reaching the desired iteration number.Steps\u2009\u20091~5. Perform Steps 1 to 5 of GA solving model. Step\u2009\u20096. Perform Substeps 7.1 to 7.8 of PSO-SA solving model. Step\u2009\u20097. Generate new offspring through genetic evolution; if optimum fitness function of offspring is superior to that of the population will be replaced as a new one otherwise, maintain the chromosomes of original population for next-generation evolution. Step\u2009\u20098. Repeat Steps 3 to 7 until the set stop conditions are met.In a complex supply chain network, even a leading manufacturer cannot guarantee 100% yield during the production process, or prevent any defect during the transport process. However, the defect ratio and loss ratio are not fixed; thus, fuzzy defect ratio and fuzzy transport loss ratio are applied in this paper.X products for final customer requirements amount to 400, 350, 450, and Y products amount to 250, 150, 200, and Z products amount to 100, 200, and 250. Q), fuzzy defect ratio (FDR), fuzzy transport loss ratio (FTR), and maximum and minimum capacity (Max.\u2009CAP. and Min.\u2009CAP.). Since the production defect ratio and transport loss ratio are fuzzy sets with triangular fuzzy number, (P(2.1), its fuzzy number of defect ratio is , then its FDR is 2% according to . Then, the fitness value, execution time, and convergence time of the algorithms were compared using Scheffe's multiple comparison method, with Scheffe's equation as follows:In Tables k is group freedom, F\u03b1(k\u22121)(n\u2212k) is critical value, MSE is intergroup MS, ni, nj is number of samples.where Fitness\u03bcPSO-GA = Fitness\u03bcGA-SA = Fitness\u03bcPSO-SA < Fitness\u03bcPSO = Fitness\u03bcGA; that is, PSO-GA, GA-SA, and PSO-SA are all better than PSO and GA, and there are no clear differences in the fitness values of the three algorithms. The comparative result of system execution time is shown in ET\u03bcPSO < ET\u03bcPSO-GA < ET\u03bcPSO-SA < ET\u03bcGA-SA < ET\u03bcGA is the PSO is superior to other solving models. The convergence times of the algorithms are shown in CT\u03bcPSO-GA < CT\u03bcPSO < CT\u03bcPSO-SA < CT\u03bcGA-SA < CT\u03bcGA PSO-GA < PSO < PSO-SA < GA-SA < GA; that is, PSO-GA, has faster convergence speed than PSO, PSO-SA, GA-SA, and GA. The results show that PSO-GA performs better in fitness value, execution time, and convergence time. Then, the PSO-GA is employed to make the distribution plan of three periods reverse supply chain and the results are shown in Tables This paper focused on analyzing the issues of returning defective products to original manufacturers in a reverse supply chain system. Fuzzy defect and fuzzy transport loss ratios were considered, and an optimized mathematical model was developed. This model combined cost and quality with T-technology and described how to plan a reverse supply chain on the precondition of meeting customer demands and realizing the capacity of partners. To solve the problems efficiently, three hybrid algorithms were applied to this reverse model, including PSO-GA, PSO-SA, and GA-SA; then, the performances of these algorithms were compared. The experimental results show that if the fitness value, execution time, and convergence time are considered, PSO-GA has the minimal value, which means that PSO-GA has the qualities and capabilities for dealing with the production planning and distribution of a multi-phase, multi-product reverse supply chain."}
+{"text": "A long sample-to-detector distance, 160.5\u2005m, can be used at this beamline and a small-angle resolution of 0.25\u2005\u00b5m Rubber containing nanoparticles is such a system; the hierarchical structure of the nanoparticles in rubber has a close relationship with reinforced mechanical and viscoelastic properties of filled rubber (reinforcement effect)  which corresponds to a small-angle-scattering resolution of 4.2\u2005\u00b5m in real space. There is still a need to measure lower-angle X-ray scattering for clarifying the higher-order structure in a hierarchical structure. In the present study, we used lower-energy X-rays and a smaller beam stop to measure scattering in a much smaller angle. In this paper, we present the details of the USAXS set-up.To overcome the difficulty, we have developed a two-dimensional ultra-small-angle X-ray scattering (USAXS) set-up using a long sample-to-detector distance at BL20XU, SPring-8 . The glancing angle was set to 3.39\u2005mrad, at which the intensity of higher-energy X-rays was reduced as shown in Fig. 2b); in this way, higher harmonic X-rays such as 24\u2005keV X-rays were removed. Parasitic scattering from the mirrors was removed by using another set of guard slits that was placed just downstream of the mirrors. The specimen was placed just behind the guard slits. There were air gaps of approximately 1\u2005m upstream and downstream of the specimen. In the second hutch, a beam stop was set just downstream of the exit window of the vacuum pipe. The diameter of the beam stop was 2\u2005mm. There was another vacuum pipe of 1\u2005m downstream of the beam stop and an X-ray detector was set just behind the exit window of the pipe. An imaging plate (IP)  (Suzuki 3.q-range of 0.25\u201310\u2005\u00b5m\u22121 is recorded. The crossed pattern originates from the form factor of the rectangular grid hole. The FWHM of each diffraction spot was 0.83 (H) \u00d7 0.75\u2005mm (V). There are two factors that broaden the spot size: one is the direct beam size that is determined due to the angular divergence of X-rays and the opening size of the rectangular aperture. As shown in a previous study using 23\u2005keV X-rays, the beam size at the detector position depends on the rectangular aperture size due to the diffraction from the rectangular aperture , where d is the pitch of the periods. In the present case, the FWHM of the spot is larger than the FWHM of the direct beam, and is divided into the contribution from the size of the direct beam and the broadening due to the width of the Laue function. Based on the assumption that the broadening of a spot is expressed as the root-mean square of the two contributions, the maximum transverse length inside which coherent scattering takes place is estimated to be 0.84 \u00d7 102\u2005\u00b5m (H) \u00d7 1.0 \u00d7 102\u2005\u00b5m (V). These values are consistent with the transverse coherence length estimated from the size of the rectangular aperture, the X-ray wavelength and the distance between the aperture and the sample: 93\u2005\u00b5m. Also, the values are equivalent to the beam size. From the above discussion, we conclude that (i) the beam at the sample is nearly full-coherent, and (ii) a reduction in the beam size at the detector position is required for both minimizing the measurable q and \u0394q values. Further optimization of the mirrors is expected to enhance the performance significantly.Fig. 3q should be combined. Fig. 4et al., 2007et al., 2011q-range 2.5 \u00d7 10\u22124\u20131.0\u2005nm\u22121 was recorded: this corresponds to 6\u2005nm\u201325\u2005\u00b5m in real space. The one-dimensional scattering intensity profiles were obtained by azimuthally averaging two-dimensional data. Detailed structural analysis based on the scattering intensity profile is beyond the scope of the present article; analysis of the anisotropic structural distribution of aggregates/nanoparticles in rubber will also be presented elsewhere. The intensity profiles measured using 8\u2005keV X-rays at BL20XU show significant fluctuation. This fluctuation originates from the speckle observed in this setting owing to the coherence of X-rays  approximation. The applicability of the RG approximation has been discussed greatly for small-angle light scattering (Kerker et al., 1963i.e. that \u03b4 ka\u03b4 k is the wavenumber of the X-ray beam and a\u00a0is the radius of the sphere. In the present case, where \u03b4 is of the order of 10\u22126 and k is 40.8\u2005nm\u22121, the condition is expressed as aq-range, it is of great importance to study the applicability of the RG approximations as in studies of the light scattering of aggregates (Farias et al., 1996et al., 2007The q = 0.25\u2005\u00b5m\u22121. An optimization of the mirrors is expected to enhance the performance significantly. The applicability of the RG approximation needs to be carefully examined. Combination of this two-dimensional USAXS technique and an X-ray imaging technique (Kishimoto et al., 2013In conclusion, a small-angle scattering resolution was extended to"}
+{"text": "This paper establishes the computational complexity status for a problem of deciding on the quality of a committee. Starting with individual preferences over alternatives, we analyse when it can be determined efficiently if a given committee  \u2022We focus on the complexity to decide if a committee satisfies a Condorcet criterion.\u2022For Borda voting this decision problem is \u2022For approval voting, we draw the separation line between hard and easy instances.\u2022It is  Centuries ago, Condorcet committee as a committee that is preferred to every other committee by a majority of voters. In contrast, Condorcet winning set if for each element A natural generalization of a Condorcet winner to committees, i.e., sets of alternatives of a given size, is proposed by Other approaches, however, are taken by In recent papers, the problem of selecting committees is extended by additionally taking into account weight constraints; see, e.g., Similarly to 1.2computationally tractable problems), and into the class of problems for which polynomial algorithms seem unlikely to exist .In line with, e.g., In the literature, multi-winner (or committee) selection problems in proportional representation voting schemes have been considered from a computational point of view, the main attention drawn to the schemes of Monroe and Chamberlin\u2013Courant. Typically, the misrepresentation of a voter is evaluated by means of numerical scores used in positional voting rules, with particular focus on approval and Borda scores  of committee of size -committee. In what follows, the voters\u2019 preferences are assumed to be additively separable. This reflects the idea that, when choosing between two committees, a voter prefers the one for which the sum of the voter\u2019s scoresGiven Definition\u00a02.4Let  With abuse of notation, we abbreviate Definition\u00a02.5Let  Clearly, a strong Condorcet committee is also a weak Condorcet committee. To simplify notation, for Example\u00a01Given the voter preference profile However, 2.3We are now ready to state the weak Condorcet Definition\u00a02.6GIVEN: Set QUESTION: Is  The problem SCC is defined by simply replacing in the above definition \u201cweak Condorcet\u201d by \u201cstrong Condorcet\u201d.RemarkNote that CC and SCC belong to the class A natural problem related to these problems is the task of deciding whether there exists a weak respectively strong Condorcet Definition\u00a02.7GIVEN: Set QUESTION: Is there a weak Condorcet  Analogously, in the problem SCC-Existence we ask if there exists a strong Condorcet CC-Existence and SCC-Existence.In the next section, we present a detailed computational complexity study of CC and SCC. In Section\u00a0 3Min 2-Sat-3 problem, which is known to be In this section, we use the computational complexity status of the Definition\u00a03.1GIVEN: Set QUESTION: Is there a truth assignment  Note that in any instance of Min 2-Sat-3 as defined above the clauses are made up of variables and not of literals. I.e., there are no negated variables in an instance of Min 2-Sat-3.In what follows, we identify a truth assignment Remark\u00a01Min 2-Sat-3, and let satisfying truth assignment for Let  since otherwise Remark\u00a02Min 2-Sat-3 to the decision problem In this paper, we prove the  We begin the analysis of the complexity status of CC and SCC by considering Borda voting. Next, we state results for CC and SCC under approval voting, and conclude Section\u00a0 3.1First, let us consider the case that the voters\u2019 preference relations are strict orders on Theorem\u00a03.1The CC problem under Borda voting is-complete, even if the preference profile consists of strict orders.ProofMin 2-Sat-3. Let We prove the theorem by a polynomial transformation from an arbitrary instance \u2022for every variable \u2022we introduce \u2022\u2013the two variables that make up \u2013the third to the \u2013the last for every clause king see : \u2013the tw\u2022\u2013for each of these voters, the ranking restricted to the last \u2013putting for all when restricted to the we introduce the voters n2\u2212k see  such tha\u2022we introduce the voters From That is, in instance Claim\u00a01a satisfying truth assignmentforwithIn instancethere is a-committeesuch that, i.e.,\u00a0a majority of voters prefersto.Proof of Claim\u00a01\u201c\u201cLet Thus,  Note that Min 2-Sat-3 can be polynomially reduced to the complement of CC under Borda voting, which implies the  An analogous hardness result for SCC follows immediately.Theorem\u00a03.2The SCC problem under Borda voting is-complete, even if the preference profile consists of strict orders.ProofCreate instance  The negative results of Lemma\u00a03.3In instance, eitheris a weak Condorcet-committee or a weak Condorcet-committee does not exist.ProofIt is sufficient to show that for any 3.2In this section, we investigate the complexity of CC and SCC in the case that the voters are allowed to distinguish between \u201cgood\u201d and \u201cbad\u201d candidates only .First, let each voter approve of exactly one candidate as it is the case in plurality voting.Proposition\u00a03.4CC under plurality voting can be solved in polynomial time. In addition, a weak Condorcet-committee can be found intime.ProofWe prove the second part of the proposition first. Rank the candidates Let thm\u00a0see\u00a0 , the timFor the first part of the proposition, let  With analogous arguments, we get a positive, i.e.,\u00a0computational tractability result if each voter votes against exactly one candidate.Proposition\u00a03.5CC under antiplurality can be solved in polynomial time. In particular, a weak Condorcet-committee can be found intime.Corollary\u00a03.6Under plurality voting and antiplurality voting, SCC can be solved in polynomial time.ProofFollows straightforward from the proof of RemarkIt should be noted that in the cases of plurality and antiplurality voting a weak Condorcet  Therewith, if each voter is allowed to choose only one \u201cgood\u201d or one \u201cbad\u201d candidate, CC and SCC are easy to solve. However, this changes drastically if a voter is allowed to choose two \u201cgood\u201d or two \u201cbad\u201d candidates, as the following theorems show.Theorem\u00a03.7Under \u00a02-approval, both CC and SCC are-complete.ProofMin 2-Sat-3 with We prove the theorem for CC first. Let \u2022introducing, for every variable \u2022introducing candidates From \u2022for every clause \u2022for each \u2022we introduce \u2022for every pair Thus, the set of candidates is see also : \u2022for evLet Claim\u00a02a satisfying truth assignmentforwithIn instancethere is a committeeof sizesuch that.Proof of Claim\u00a02\u201c\u201c\u2022at most \u2022due to the fact that the number of occurrences of each variable is bounded by three, at most Assume prefer  where the fourth inequality follows from Now, Note that Since  Note that in instance Min 2-Sat-3 is polynomial due to Min 2-Sat-3.\u00a0\u25a1For SCC, consider instance  We can derive a lemma to be used in Section\u00a0 \u2260F imply 1\u2264p\u2264k\u22121. Lemma\u00a03.8In instance, eitheris a weak Condorcet-committee or a weak Condorcet-committee does not exist.Proof holds for any For  In addition, from Corollary\u00a03.9Both CC and SCC are-complete in the strong sense. As a consequence of Corollary\u00a03.10Both CC and SCC are-complete under-approval for any fixed.ProofWe prove the corollary for CC . The case For We show that Claim\u00a03such thatinsuch thatin.Proof of Claim\u00a03\u201c\u201cI.e., Finally, there cannot exist two or more elements in  Turning our attention to CC and SCC under 2-veto, it turns out that the problems show the same computational complexity behaviour as in the case of 2-approval.Theorem\u00a03.11Under \u00a02-veto, both CC and SCC are-complete.ProofMin 2-Sat-3 with a set Min 2-Sat-3 remains \u2022for every variable \u2022candidates \u2022for each \u2022for each We give a proof for CC first. Let Note that we have Claim\u00a04a satisfying truth assignmentforwithIn instancethere is a committeeof sizesuch that.Proof of Claim\u00a04\u201c\u201cAgain, let Case 1:  where the second inequality trivially follows from Case 2: (11) Recall that  Because in instance Min 2-Sat-3 is polynomial, which completes the proof.Min 2-Sat-3 iff For SCC, construct instance Lemma\u00a03.12In instance, eitheris a weak Condorcet committee or such a committee does not exist.Proof where the last inequality holds for any Let Corollary\u00a03.13Both CC and SCC are-complete under-veto for any fixed.ProofCeteris paribus, the proof follows from the one of 3.3In the two previous sections, computational complexity results for CC and SCC under Borda voting and approval voting have been presented. In particular, the cases that individual preferences are expressed by linear orders and dichotomous preferences have been considered, and a complete analysis in terms of complexity results of the latter case has been established.However, using ry voter .top class and bottom class respectively.Within this section, for Corollary\u00a03.14Both CC and SCC are-complete if the voters have multichotomous preferences, even if each,, induces the same numberof preference classes for some.ProofWe prove the corollary for CC; the hardness of SCC follows analogously. The case \u2022introduce \u2022let, for Let Let the instance Claim\u00a05The following two decision problems are equivalent:(P1)GIVEN: Instanceofunder \u00a02-approval (as in the proof ofTheorem \u00a03.7)QUESTION: Is there a committeeof sizesuch that, where?(P2)GIVEN: Instanceofunder ruleQUESTION: Is there a committeeof sizesuch that?Proof of Claim\u00a05Let  From the above claim we can conclude the theorem by the proof of  For trichotomous preferences, we may consider the following voting rule.Definition\u00a03.2Let  In case of trichotomous preferences, from (the proof of) 4CC-Existence and SCC-Existence belong to the class CC-Existence is SCC-Existence is In this section, we consider the problems of deciding whether or not a weak respectively strong Condorcet Theorem\u00a04.1SCC-Existence is-hard, even under Borda voting or approval voting. In particular, for approval voting SCC-Existence is Corollary\u00a04.2SCC-Existence isFor approval voting, -complete.ProofSCC-Existence is in SCC-Existence with set SCC-Existence reduces to the problem of deciding if SCC-Existence is in Due to Theorem\u00a04.3CC-Existence is-hard, even under Borda voting or approval voting. In fact, it turns out that CC-Existence is both CC-Existence and SCC-Existence show a different computational complexity behaviour.Theorem\u00a04.4CC-Existence is-hard, even under \u00a02-approval voting.ProofIndependent Set (IS). The IS problem is the following decision problem: Given an undirected graph We provide a reduction from c graphs .CC-Existence as follows: Set For an instance If If  Our results have shown that CC-Existence is both SCC-Existence is CC-Existence under approval voting already\u2013but we do not have a proof.5With respect to classic voting schemes adapted from Social Choice Theory, we have analysed the computational complexity involved in deciding if a given committee is at least as good as (resp.\u00a0better than) every other committee in a pairwise majority comparison. In particular, we have established the sharp separation line between computationally tractable and intractable instances. As our results show, if the voters vote for or against exactly one candidate it can be determined efficiently if a given committee is a weak or strong Condorcet SCC-Existence is CC-Existence is both As it turns out, also the problem"}
+{"text": "K, and R a classical maximal K. We study sets of lengths of factorizations of cancellative elements of R into atoms (irreducibles). In a large majority of cases there exists a transfer homomorphism to a monoid of zero-sum sequences over a ray class group of R. If K, we prove that in the remaining cases no such transfer homomorphism can exist and that several invariants dealing with sets of lengths are infinite.Let  Then the monoid of divisorial two-sided ideals is a free abelian monoid. If H is commutative , this gives rise to the construction of a transfer homomorphism G of H. Transfer homomorphisms preserve sets of lengths, and if Sets of lengths  are among the most investigated invariants in factorization theory. So far research has almost been entirely devoted to the commutative setting, and it has focused on commutative noetherian domains, commutative Krull monoids, numerical monoids, and others cf. . Recall Only first hesitant steps were taken so far to study factorization properties in a non-commutative setting . Any approach to study sets of lengths, which runs as described above and involves divisorial two-sided ideals, is restricted to normalizing Krull monoids Let Theorem 1.1Letbe a holomorphy ring in a global field K, A a central simple algebra over K, and R a classical maximal-order of A. Suppose that every stably free left R-ideal is free. Then there exists a transfer homomorphism, whereis a ray class group of, andis the monoid of zero-sum sequences over. In particular,1.The set of distancesis a finite interval, and if it is non-empty, then.2.For every, the union of sets of lengths containing k, denoted by, is a finite interval.3.There is ansuch that for everythe set of lengthsis an AAMP with differenceand bound M.R-ideal is free, we obtain a transfer homomorphism to a monoid of zero-sum sequences over a finite abelian group. Therefore, sets of lengths in R are the same as sets of lengths in a commutative Krull monoid with finite class group.Thus, under the additional hypothesis that every stably free left A satisfies the Eichler condition relative to R-ideal is free by Eichler\u02bcs Theorem. In particular, if K is a number field and A satisfies the Eichler condition relative to A is a totally definite quaternion algebra. Thus in this setting R-ideal is free is indeed necessary.If Theorem 1.2Letbe the ring of algebraic integers in a number field K, A a central simple algebra over K, and R a classical maximal-order of A. If there exists a stably free left R-ideal that is not free, then there exists no transfer homomorphism, whereis any subset of an abelian group. Moreover,1..2.For every, we have.H is a commutative Krull monoid with an infinite class group such that every class contains a prime divisor, then Kainrath showed that every finite subset of The proof of  lengths , whence 2Let Throughout the paper there will be many statements that can be either formulated \u201cfrom the left\u201d or \u201cfrom the right\u201d, and most of the time it is obvious how the symmetric statement should look like. Therefore often just one variant is formulated and it is left to the reader to fill in the symmetric definition or statement if required.2.1H be a small category. In the sequel the objects of H play no role, and therefore we shall identify H with the set of morphisms of H. We denote by Let H is a semigroup if and only if A semigroup may be viewed as a category with a single object (corresponding to its identity element), and elements of the semigroup as morphisms with source and target this unique object. In this way the notion of a small category generalizes the usual notion of a semigroup  with j to be the inclusion map, and we call category of right fractions of H with respect to D. If D also admits a left calculus of fractions, then The notion of semigroups of fractions generalizes to categories of fractions with analogous conditions monoid is a cancellative semigroup satisfying the left and right Ore condition  from Let 2.2G is a small category in which every element is a unit . If A groupoid vertex group or isotropy group of G at e. If a: If G is connected  and satisfies the ACC on divisorial two-sided ideals. A prime Goldie ring R is a Krull ring if it is completely integrally closed and satisfies the ACC on divisorial two-sided ideals  and transfer homomorphisms in the setting of cancellative small categories.Throughout this section, let H be a cancellative small category.H is reduced if atom (or irreducible) if H, and call H atomic if every H is a subset H is defined similarly. A principal left (right) ideal of H is a set of the form Ha (aH) for some H is a commutative monoid, then prime element if Proposition 3.1If H satisfies the ACC on principal left and right ideals, then H is atomic.ProofH is cancellative, this implies Claim AIf, then there existandsuch that.We first note that if Proof of Claim AaH with aH in \u03a9 implies Assume the contrary. Then the setHa with We proceed to show that every rigid factorization) in a cancellative small category. It is modeled after a terminology by Cohn The following definition provides a natural notion of an ordered factorization For all,implies.(b).is called right-saturated if these equivalent conditions are fulfilled.Proof(a) \u21d2 (b): Let (b) \u21d2 (a): Let Definition 3.6B be a reduced cancellative small category. A homomorphism transfer homomorphism if it has the following properties:(T1)(T2)If Let The notion of a transfer homomorphism plays a central role in studying sets of lengths. It is easily checked that the following still holds in our generalized setting  with differenceand bound M.ProofG. By the previous lemma it is sufficient to show these statements for the monoid of zero-sum sequences The description in 4\u03b7, and as the main result in this section, we present a transfer homomorphism to a monoid of zero-sum sequences in In this section we introduce arithmetical groupoids and study the factorization behavior of integral elements. In Section Definition 4.1G together with a relation \u2a7d on G such that for all 1.2.3.A lattice-ordered groupoid G, and \u2227 and \u2228 do not represent meet and join operations on the entire set G in the order-theoretic sense.)If a of a lattice-ordered groupoid is called integral if G.An element Definition 4.2G is called an arithmetical groupoid if it has the following properties for all 1)(PFor 2)(P3)(PIf 4)(PFor every non-empty subset 5)(P6) , 2., henWe summarize some basic properties that follow immediately from the definitions.Lemma 4.3Let.1.holds if eitheror. In particular, forthe following are equivalent: (a) .2.Let. Ifandare integral, thenand.3.If,and, then(i)andif,(ii)andif.4.Letand. Ifexists, then alsoexists, and. Moreover, then alsoexists and. Analogous statements hold forand.5.,,and in particularare conditionally complete as lattices.6.The setof all integral elements forms a reduced wide subcategory of G, andis the groupoid of (left and right) fractions of this subcategory.7.For every, there existandwithand.Proof3, 1 this is equivalent to 3 this is equivalent to 1. Assume first 1. For (a) \u21d4 (c) set (a) \u21d4 (b) and (c) \u21d4 (d) by P3. Similarly, 2. Since 3 implies x from the left gives 3. We show (i), (ii) is similar. Since xc is an upper bound for xM. If xM, then 4. Let For 4, and 5. We show the claim for 4), to ensure that the supremum lies in The proof for G. If a is integral. Since 6. By 2 and the fact that every 5 there exist integral 7. By PFor If Definition & Lemma 4.4Forthe following are equivalent:(a)u is maximal in,(b)u is maximal in,(c).An elementsatisfying these equivalent conditions is called maximal integral.Proofu is maximal in u in the first set, therefore u is maximal in the second set.(a) \u21d2 (b): By definition, u in (b) \u21d2 (c): Assume v and (c) \u21d2 (a): Let Lemma 4.5Let U be an l-group. Forthe following are equivalent:(a)p is maximal integral,(b)p is a prime element in,(c).Proofe be the identity of U.(a) \u21d4 (c) is shown as in p be maximal in (a) \u21d2 (b): Let p be a prime, (b) \u21d2 (c): Let Proposition 4.61.If G is a group , and projectivity is an equivalence relation. Note that in a modular lattice perspective intervals are isomorphic Lemma 4.8If a, b, c are as in the definition of transposability, thenfor someand c is transposable to d.Proofd with Since Lemma 4.9If two lattice intervalsandofare projective, then the integral elementsandare projective to each other in the sense of the previous definition.ProofIt suffices to show that if the lattice interval Definition & Lemma 4.10For every,and we writefor this set. The lower bound is defined by.ProofLet \u03a6 and the notation of Section Lemma 4.11Let.1.Iforwith, then. In particular, if, then.2.If,then. If moreover, then, and if furthermoreandare coprime, then.3.If, thenis prime.4.Letbe projective elements. If, then, and.With the definition of Proof\u03a6.1. Immediate from the definition of 2. Observe that a, b be integral. Then 1 implies Let now 3. By (e)+) by , 3.. Assv is maximal integral, and may assume that either u is transposable to v or v is transposable to u. Let u is transposable to v via v is maximal integral. If v is transposable to u, one argues along similar lines.4. We first show that u is transposable to v . Let again For the remainder of the claim we may now assume that The converse of Proposition 4.121.The categoryis half-factorial. Explicitly: Everypossesses a rigid factorizationwithandand the number of factors,, is uniquely determined by a. Moreover, ifis another rigid factorization with, then there exists a permutationsuch thatis projective tofor all. In particular,for all.2.Any two rigid factorizations ofcan be transformed into each other by a number of steps, each of which only involves replacing two successive elements by two new ones.3.Transposition.) Ifwithand,,, then there exist uniquely determinedsuch that,and. by  and u\u2032=vUniqueness. If Explicit formulas. Since The equalities 4. Write Corollary 4.13Ifis a subcategory, thenis finite and non-empty for all. If for every primeand all  the setis finite, thenis finite for all.Proof6 that H satisfies the ACC on principal left and right ideals, and hence k is bounded by the length of the factorization of a in Using that H is a commutative monoid and The properties that all sets of lengths, respectively that all sets of factorizations, are finite have been studied a lot in the commutative setting. Note, if Definition & Lemma 4.14There exists a unique groupoid epimorphismsuch thatfor all. We call \u03b7 the abstract norm of G.Proofa (G is the category of (left and right) fractions of \u03b7 extends to a unique groupoid homomorphism We need to show existence and uniqueness of such a homomorphism. Let ned by a , it foll\u03b7 is surjective, let first To verify that \u03a6 need not be a homomorphism, but from a the prime factorizations of In general Theorem 4.15Let G be an arithmetical groupoid,the abstract norm, H a right-saturated subcategory of, and. Forset, and. Assume that1.forwith,if and only if,2.for everyand, there exists an elementsuch thatand.Then there exists a transfer homomorphism.Proofa, and not on the particular rigid factorization into maximal integral elements chosen. Let \u03b7). Therefore Let \u03b8 is a homomorphism: Obviously b into maximal integral elements, then ab. ThusWith this definition \u03b8 has properties T1 and T2.We still have to check that a possesses an empty factorization into maximal elements, hence If \u03b8 is surjective: a is integral in G and H is right-saturated in \u03b8 satisfies T2: Let H is a left-saturated subcategory of \u03b8 one then first chooses The theorem remains true if Remark 4.16G is a group, then H is therefore a reduced commutative Krull monoid If is A(G+) . As a saH be a normalizing Krull monoid. Then H, which form the free abelian monoid of integral elements in the free abelian group of divisorial ideals of H. In this way we recover the well-known transfer homomorphism for Krull monoids as given for example in Conversely, let We continue the discussion of normalizing Krull monoids in 5In this section we develop a divisorial one-sided ideal theory in semigroups. This follows again original ideas of Asano and Murata and generalizes the corresponding theory in rings and the theory of divisorial two-sided ideals in cancellative semigroups  fractions of H.A semigroup Lemma 5.1Let Q be a quotient semigroup, anda subsemigroup.1.If H is an order in Q, thenand.2.If, thenand H is an order in Q.3.If H is an order in Q,is a subsemigroup of Q and there existwith, thenis an order in Q.ProofH is a right order in Q, there exist H. Then H is a left order it follows in the same way that a is right-cancellative in 1. It suffices to show 2. It again suffices to show H is an order in Q, there exist 3. It suffices to show that every For the remainder of this section, let Q be a quotient semigroup.H and Q, then H is (Asano-)equivalent to Q. An order H is maximal if it is maximal within its equivalence class with respect to set inclusion.If H, one has to study the ideal theory of all maximal orders in its equivalence class at the same time.A feature of the non-commutative theory is that often there is no unique maximal order in a given equivalence class, and in fact in the most important cases we study there are usually infinitely many, but only finitely many conjugacy classes of them. In studying the divisorial one-sided ideal theory of a maximal order X is a left H-module if right-module if module if it is a left H- and a right H-module is an Let Lemma 5.2Let H,be subsemigroups of Q and let X be an-module.1.andare-modules.2.and.3.andare subsemigroups of Q.4..5.if and only ifif and only if.Proof1. 2. 3. Clearly 4. We show 5. Immediate from the definitions of Definition 5.3For Definition 5.4H and Q.1.fractional left H-ideal is a left H-module I such that A 2.fractional right-ideal is a right I such that A 3.I is a fractional left H-ideal and a fractional right I is a fractional-ideal.If 4.fractional H-ideal is a fractional A 5.I is a left H-ideal if it is a fractional left H-ideal and right-ideal is defined analogously.6.I is a left H-ideal and a right I is an ideal.If 7.H-ideal is an An 8.H-ideal I is integral if A fractional left Let H is a maximal order, then the notions of a left H-ideal and that of an integral fractional left H-ideal coincide  H-ideal, or two-sided to emphasize that it is indeed a fractional H-ideal.If H-ideals and first observe the following.We recall some properties of fractional left Lemma 5.5If H is an order in Q and I is a fractional left H-ideal, thenandare orders. I is a fractional-ideal.ProofH is an order and I is a fractional left I is also a fractional right Let I to be a fractional H-ideal .(b)There exists a fractional-ideal.(c)There exists a fractional-ideal.ProofQ, 1. There exist 2. Using I is an I is a fractional 3. (a) \u21d2 (b): By (b) \u21d2 (a): By H and (a) \u21d4 (c) follows by symmetry, swapping the roles of Lemma 5.8Let H be an order in Q. The following statements are equivalent.(a)H is a maximal order.(b)If I is a fractional left H-ideal, thenand if J is a fractional right H-ideal, then.(c)If I is a fractional H-ideal, then.(d)If I is an H-ideal, then.Proof(a) \u21d2 (b): By (b) \u21d2 (c) \u21d2 (d): Trivial.H and I is an H-ideal, and J is again an H-ideal (we use (d) \u21d2 (a): Assume Lemma 5.9Let H be a maximal order in Q, let I and J be fractional left H-ideals, and let K be a fractional left-ideal.1.,is a fractional right H-ideal withandis a fractional left H-ideal withand. Moreover,.2.If, then Ha is a fractional left H-ideal with,and. Ha is integral , if and only if.3.Ifthenand.4.,and.5..6..7.Ifandare also maximal, then.ProofH-ideal. By the symmetric statement of what we just showed for fractional right H-ideals, therefore H-ideal. Applying the first part of the statement to 1. By Ha is a fractional left H-ideal. Certainly Ha is a left H-ideal if and only if it is integral due to maximality of H, and 2. Since H-ideals with H-ideals to obtain 3. If H-ideal with H-ideal with 4. By 5. 6. 7. We use Kv) from . We have\u2282IvKv by . By 3, tTo prove the claim it suffices to show \u22121 using  again. MDefinition 5.10H be an order in Q. A fractional left or right H-ideal I is called divisorial if Let I is a fractional left H-ideal for a maximal order H, then it is not necessarily true that H-ideals with H maximal, already both, v-product, by J is a divisorial fractional left v-invertible, i.e., invertible with respect to this operation.If Proposition 5.11Let H be a maximal order in Q. Let I be a fractional left H-ideal. Then:1.is a maximal order. In particular,is a maximal order.2.and ifis also maximal, then.3.If I is a divisorial fractional left H-ideal, J a divisorial fractional left-ideal and K a divisorial fractional left-ideal, thenProofH is maximal, J is an integral left 1. Because H is maximal, it suffices to show We claim J, Therefore, from the definition of Now 2. We have to show 3. Using Corollary 5.12If H is a maximal order, then every orderwithis contained in a maximal order equivalent to H.ProofI. Then By Corollary 5.13Let \u03b1 denote an equivalence class of maximal orders of Q. LetandThenis a lattice-ordered groupoid, with identity elements the maximal orders in \u03b1. If I, J are inwithor, thenand. Moreover,is the subcategory of integral elements.Proofv-product v-product is associative when it is defined  by , and cleDefinition & Lemma 5.14An order H is bounded if it satisfies the following equivalent conditions:(a)Every fractional left H-ideal and every fractional right H-ideal contains a fractional (two-sided) H-ideal.(b)Every left H-ideal and every right H-ideal contains a (two-sided) H-ideal.(c)For allthere existsuch thatand.(d)For allthere existsuch thatand.(e)For all, HaH is a fractional (two-sided) H-ideal.(f)For allthere exists a fractional (two-sided) H-ideal I with.(g)Ifandwith, then there existwithand.Proof(a) \u21d2 (b): Trivial.Hc contains an H-ideal J. If (b) \u21d2 (c): Let (c) \u21d2 (d): By (c) applied to HaH is an (d) \u21d2 (e): (e) \u21d2 (f): Trivial.H-ideal, there exists (f) \u21d2 (g): I be a fractional left H-ideal and HbH is a fractional H-ideal contained in I  \u21d2 (a): Let Lemma 5.151.Let H andbe orders in Q. If H is bounded and, thenis also bounded.2.Let H andbe bounded equivalent maximal orders of Q. Then there exists an-ideal I.ProofH is bounded, there exist 1. Because H and H and 2. We show: If H and Clearly Proposition 5.16Let \u03b1 be an equivalence class of maximal orders in Q.is an arithmetical groupoid if and only if allequivalently, onesatisfy the following three conditions:1) H-ideals is modular\u201d, as the property for the other side then holds automatically.From the discussion after 2.H be a normalizing monoid. By definition of a monoid, H satisfies the left and right Ore condition, hence it is an order in its quotient group. H-ideal is in fact already a two-sided H-ideal, and thus H is bounded.Let H is a normalizing Krull monoid. Then H-ideals is then modular, even distributive Assume that Definition 5.18H satisfying A1\u2013A3 an arithmetical maximal order. If \u03b1 is its equivalence class of arithmetical maximal orders, then we denote by We call a maximal order Let from here on H be an arithmetical maximal order in Q, and let \u03b1 be its equivalence class of arithmetical maximal orders.Ha with H-ideal with inverse v-product coincides with the usual proper product on H determines \u03b1) we denote the subcategory of H. Explicitly,H are conjugate. Again the inclusion By H and The following simple lemma gives a correspondence between Lemma 5.19Let.1.Ifwith, thenwith.2.Ifandwith, then there existwith,and.3.Ifwithand, then there existwithand.In particular, forwe haveif and only if.Proof1. The multiplication is defined because 2. Since 3. Since Observe that we may view a rigid factorization Proposition 5.20Let. For everythere is a bijection, given byIfis a transfer homomorphism to a reduced cancellative small category B and having the additional property thatfor alland, then it induces a transfer homomorphismgiven by.ProofThe claimed bijection follows by iterating the previous lemma.\u03b8 is a transfer homomorphism and first check that \u03b8 is a homomorphism: For We need to verify that Remark 5.21B is necessarily a semigroup.The condition Let Lemma 5.221.Ifand, then.2..ProofI, then 1. It suffices to verify the claim for maximal integral \u03b7 is a homomorphism)2. The first equality is immediate from 1. For the second equality, note that if H.Applying Theorem 5.23Let Q be a quotient semigroup, H an arithmetical maximal order in Q, and \u03b1 its equivalence class of arithmetical maximal orders.1.For all,is finite and non-empty. If, for every maximal divisorial H-ideal P, the number of maximal divisorial left H-ideals I withis finite, thenis finite for all.2.Let,, and. Assume:(i)A divisorial fractional left H-ideal I is principal if and only if.(ii)For alland allthere exists a maximal divisorial left-ideal with.Then there exists a transfer homomorphism.ProofBy 1. This follows immediately from I be a fractional left I is principal if and only if the fractional left H-ideal 2. Let Remark 5.241.H be a normalizing Krull monoid. Then H-ideals, while We continue our discussion from C is the divisorial class group of H, and H-ideal. The second condition of the theorem is trivially true by virtue of In the previous theorem we therefore have 2.H is a maximal order satisfying only A1 and A3, then 5 and P6, and still obtain \u03a6, which can only be defined in the presence of P5). This is possible because P6 is only used to show existence of a rigid factorization of a. A sufficient condition for H satisfies A1, then H) satisfy the ACC, and as in If 5.1R is a ring-theoretic order in Q, then a fractional left R-ideal I in the semigroup-theoretic sense is a fractional left R-ideal in the ring-theoretic sense if and only if Suppose that Let for the remainder of this subsectionbe a quotient ring.Lemma 5.25Let H be an order in the multiplicative semigroupand I a fractional left H-ideal (in the semigroup-theoretic sense). Consider the following statements:(a).(b)is a subring of Q.(c)is a subring of Q.Then (a) \u21d2 (b) and (a) \u21d2 (c). If H is a maximal order and I is divisorial, then (a) \u21d4 (b) \u21d4 (c).ProofAssume that (a) holds. We show (b): Let H is maximal, Assume now that Lemma 5.26A ring-theoretic order R in Q is maximal in the ring-theoretic sense if and only if it is maximal in the semigroup-theoretic sense.ProofR is maximal in the ring-theoretic sense, then it is maximal in the semigroup-theoretic sense, as the other direction is trivial. Let I be a fractional left R-ideal in the semigroup-theoretic sense. Then R-ideal in the ring-theoretic sense, and using R in the ring-theoretic sense implies J is a fractional right R-ideal in the ring-theoretic sense then R is maximal in the semigroup-theoretic sense. \u2003\u25a1We show that if \u03b1 be an equivalence class of maximal orders of As before let Lemma 5.27Letand assume that H is a subring of Q .1.Everyis a subring of Q (and therefore an order in Q in the ring-theoretic sense).2.If I is a divisorial fractional left H-ideal and J is a divisorial fractional left-ideal, theni.e., the semigroup-theoretic v-product coincides with the ring-theoretic one.3.If I and J are divisorial fractional left H-ideals, then.ProofI. By maximality of H and 1. By H-ideals (in the semigroup-theoretic sense). Therefore 2. Write H-ideals  R-modules is modular, thenis an arithmetical maximal order inin the semigroup-theoretic sense. In particular, the conclusions ofhold for R.Proofv-product, meet and join coincide, and hence By E, that are prime and satisfy the ACC on divisorial two-sided E-ideals, but do not satisfy the ACC on divisorial left E-ideals or the ACC on divisorial right E-ideals. In fact , the orders E are not even atomic. However, these orders are not Goldie, as they are not of finite left or right uniform dimension, and do not satisfy the ACC on left or right annihilator ideals.In Before going to maximal orders in central simple algebras, we discuss principal ideal rings.Example 5.29R be a bounded order in a quotient ring Q. Assume that every left R-ideal and every right R-ideal is principal. By the characterization in R is then already a maximal order, and it satisfies A1\u2013A3. Thus D is a division ring and Let Q be a quaternion algebra over a field K with X, thereforeK is infinite. , then \u03b7 of Section But the aim of this subsection is to restrict to the situation where the base ring Lemma 5.31Letand let T be a classical-order in A. The following are equivalent:(a)I is a fractional left T-ideal in the ring-theoretic sense I is a finitely generated-module withand.4If T is maximal, then in addition the following statements are equivalent to the previous ones:(c)I is a divisorial fractional left T-ideal in the semigroup-theoretic sense (.ic sense .(d)I is a divisorial fractional left T-ideal in the ring-theoretic sense  \u21d2 (b): Recall that (b) \u21d2 (a): Certainly T be maximal. (d) \u21d2 (a) is trivial, and (a) \u21d2 (d) follows because T is a Dedekind prime ring, and hence every fractional left T-ideal (in the ring-theoretic sense) is invertible , and therefore divisorial.Let now (c) \u21d4 (d) follows from T-ideal in T-ideal in the sense of T-ideal in the ring-theoretic sense with T is maximal, then the extra condition A subset v-product coincides with the usual proper product of ideals: A in Reiner\u02bcs terminology  R-modules.To be able to apply our abstract results we still have to check that AWriting Lemma 5.32Ifand, thenand there is a canonical bijectioninducing an isomorphism of free abelian groups. The inverse map is given bywhereis the unique maximal (two-sided) R-ideal lying over. If R is unramified at, then.If all residue fields ofare finite, andis the abstract norm homomorphism, then.ProofM a maximal integral left All but the last statement follow from 6Throughout this section, let K be a global field andbe a holomorphy ring in K.5Furthermore, let A be a central simple algebra over K, and R a classical maximal-order.Setting Lemma 6.1Let r be as in. Then r induces an isomorphismwhere.ProofBy Lemma 6.2For all classical maximal-orders, and all, there exist infinitely many maximal left-ideals I with.ProofLet M with For each )]=[p]=g . \u2003\u25a1R-ideals, i.e., In the following equivalent characterizations of the first condition of Lemma 6.3The following are equivalent.(a)A fractional left-ideal withconjugate to R is principal if and only if.(b)A fractional left R-ideal is principal if and only if.(c)Every fractional left R-ideal I withis principal.(d)For the map of finite setsit holds that.(e)Every stably free left R-ideal is free.(f)Every finitely generated projective R-module that is stably free is free.ProofR is hereditary noetherian.The equivalence of (a), (b), (c) and (d) is trivial. The remaining equivalences follow from standard literature: (f) \u21d2 (e) is true because R-module. Then R-ideal I and I is stably free and hence free by (e), but then so is M.(e) \u21d2 (f): Let and n\u2208N0 . I is stR-modules of rank one, i.e., the map To see (d) \u21d4 (e) it suffices to recall that see e.g.  and thatProof of Theorem 1.1R is an arithmetical maximal order in Q. We verify conditions (i) and (ii) of I be a fractional left R-ideal. By R-ideal is free, this is the case if and only if I is principal, thus condition (i) holds. Condition (ii) holds due to By Remark 6.4K, then there is a transfer homomorphism to either I with If more generally 7Throughout this section, letbe the ring of algebraic integers in a number field K, A a central simple algebra over K, and R a classical maximal-order in A having a stably free left R-ideal that is not free. Furthermore, the discriminant of A is denoted byR-ideal that is not free implies that A is a totally definite quaternion algebra and that K is totally real.  We proceed in three subsections.The aim of this section is to prove 7.1We state two propositions and show how they imply Proposition 7.1There exists a totally positive prime element, a non-empty subsetand for everyan atomsuch thatWe emphasize that E does not depend on l.)Proposition 7.2Ifand, then.Proof of Theorem 1.2 (based on Proposition 7.1 and Proposition 7.2)Claim AIfand, then.We first show that there is no transfer homomorphism ProofLet By p and E be as in In order to show Let 7.2Algebraic number theory. Our notation mainly follows Narkiewicz K, a. Completion at a prime Quaternion algebras. We follow T of A is called a classical Eichler-order if it is the intersection of two classical maximal T takes the form T. Furthermore, because A is totally definite, we have A classical R-ideals, and Proposition 7.3Let. Letwith, and such thatThen, for everywith, there exist at least C maximal left (right) R-ideals of reduced normand class c. Hereis the narrow class number, and w and M are constants depending onsee.onD see.As in the previous section, ProofAlthough not explicitly stated in this way, this is proved by Kirschmer and Voight in Optimal embeddings. Let T a classical Eichler A of squarefree level L, every embedding \u03b9 is an optimal embedding if T is still bounded by a constant times h(O) see . Since  cf. . The numQ]\u22121 cf. , withdL=q with q being locally represented everywhere by the norm form, \u03b7 small enough, say By Remark 7.7T of A there are infinitely many pairwise non-associated totally positive primes T. This can easily be seen as follows: Let T. If T. But there are infinitely many pairwise non-associated such primes, because every class of the ray class group q of the required form correspond exactly to the trivial class in For any classical Lemma 7.8Let q be a totally positive prime element of. Let I be a non-principal right R-ideal withfor some, and J be a left-ideal withfor somesuch that: as left S-ideals) and I (respectively J) is not contained in any principal left S-ideal except S itself, and not contained in any principal right-ideal  exceptrespectivelyitself.Assume further thatwithand.1.For all,is a principal right R-ideal and an atom of. In particular,for all.2.if it is primitive. In particular ifand, then.ProofI is not contained in any principal right R-ideal, it is in particular not contained in qR, hence primitive. Similarly, J is primitive. Let I and J.Since S-ideals, I, J and a, this is the only rigid factorization of 1. Since I and J are both maximal left S-ideals), then 2. By primitivity,Lemma 7.9Let I be a left R-ideal,, and. Thenwith the left-most and the right-most expressions being proper products ofThe products have to be read in ascending order with \u201c\u201d to the very left.)ProofThe formulas are clear, and so is that the products are proper ones. The key point is that these one-sided ideals are indeed integral. But this is so because Lemma 7.10Let M be a maximal left R-ideal, and N a maximal left-ideal. If, then.ProofSince Proof of Proposition 7.1R If Case 4.Case 4a.J is non-principal. If Case 2. In the case that Case 3 in the same situation.)If Case 4b.If Finally, if If Case 5.Case 2.If Case 6.Case 1.If For Case 1. For Case 4 gives at least one factorization with length in Case 2, Case 3, and Case 4 depends only on the principality of certain one-sided ideals, and not on l. Thus we have shown that there exists a set p a totally positive prime element of R. \u2003\u25a1Since there is at least one Remark 7.111.T.In the proof, the classical 2.q with q is a square in a a non-square in If K)\u21921 cf. , it suffeals cf. .3.a in the proof, we can replace A at all  at some position. Thus, for each ax in a of length l. \u2003\u25a1It suffices to prove the claim for"}
+{"text": "While for s polarization, the G-H shift is a constant value for any incident angle.Light reflection and refraction at an interface between two homogeneous media is analytically described by Snell's law. For a beam with a finite waist, it turns out that the reflected wave experiences a lateral displacement from its position predicted by geometric optics. Such Goos-H\u00e4nchen (G-H) effect has been extensively investigated among all kinds of optical media, such as dielectrics, metals, photonic crystals and metamaterials. As a fundamental physics phenomenon, the G-H effect has been extended to acoustics and quantum mechanics. Here we report the unusual G-H effect in zero index metamaterials. We show that when linearly polarized light is obliquely incident from air to epsilon-near-zero metamaterials, no G-H effect could be observed for  Such a lateral displacement is called the Goos-H\u00e4nchen (G-H) shift2357841416e.g, the plasmonic materials at optical frequencyi.e. the s polarized light with its electric-field vector perpendicular to the incident plane, and the p polarized light with its electric-field vector parallel to the incident plane. It is shown that there is no G-H effect for p polarized light, while for s polarization, the G-H shift is a constant value, independent of the incident angle. Such a unique behavior has not yet been revealed in previous study on the G-H effect.Recently, zero index metamaterials (ZIMs) have drawn much attention for their intriguing electromagnetic (EM) properties181920212223242526x-y plane separates two semi-infinite media. Region 1 is air, and region 2 is ENZ metamaterial with parameters \u03bc2 = 1 and \u03b52 \u2248 0 . A linearly polarized light with incident angle in\u03b8is incident from air onto ENZ metamaterial. As known, the ENZ metamaterial can be regarded as optically thinner medium compared to air, and the critical angle for total reflection to occur is given by s and p polarizations, will be totally reflected by the ENZ metamaterial for any incident angles excluding the normal one.Our configuration is shown the schematically in s polarization. Suppose the incident linearly polarized light with an angular frequency \u03c9 is given as xk = k0 sin in\u03b8, zk = k0 cos in\u03b8, and k0 = \u03c9/c is the wave number in air, c is the velocity of light in air. For simplicity, the time dependence exp(\u2212i\u03c9t) will be omitted throughout this work. After reflection by ENZ metamaterial, the reflected light is z = 0, the reflected coefficient is calculated as \u03b52 is close to zero, i.e.\u03b52 \u2248 0, the G-H shift is sd = \u03bb/\u03c0, a constant value for any incident angle. Meanwhile, we can work out that the phase of reflected light is s\u03d5 = \u22122in\u03b8 from For G-H effect, however, both polarizations have different responses during such a total reflection process. First, let us consider the p polarized light. In this case, electric-field in y direction in the above equations should be changed into magnetic field. In region 1 of air, the incident and reflected light can be written as p polarized light is given as \u03b52 \u2248 0, the G-H shift is pd = 0 for any incident angle. From \u03c0, which means there is a half-wave phase lag for p polarized light after total reflection. Such a feature is analogous to the propagation of the s polarized light reflected by the perfect electric metal. With that in mind, the ENZ metamaterial could be regarded as a perfect magnetic conductor (PMC) for p polarized light. From the perspective of intrinsic property of ENZ metamaterial, we know that as the permittivity \u03b52 tends to zero, the right term H2 = Const. Then, following the continuous conditions of the magnetic fields at the boundary z = 0, we get (rH + H)exp(xxik) = Const. For the p polarized light obliquely incident onto the ENZ material, we have xk \u2260 0. To keep the above boundary condition valid for arbitrary coordinate x, the only satisfaction is that rH + H = 0. It also means that the magnetic field inside ENZ metamaterial is exactly zero. Consequently, the reflected coefficient is p = Hr\u03c1/H = \u22121 and its reflected phase is \u2212\u03c0. Such understanding from the intrinsic property itself is more straightforward, and gives the same results on G-H effect for p polarized light.A similar procedure can be implemented for e.g. the ENZ metamaterial). The time averaged energy flow can be calculated by applying s polarized incident light, we have l = 1/\u03ba. It implies that the incident EM energy will enter into ENZ metamaterial, and the energy will go back into air when it arrives at z = l. Moreover, the G-H shift from the view of geometric optics, is d \u2248 2l sin in\u03b8 = \u03bb/\u03c0 when \u03b52 \u2248 0. For p polarized light, however, the corresponding averaged energy flow is The G-H effect can also be interpreted from the point of view of an energy flow along the interface in the optically thinner mediums and p polarized light. For an absorptive medium, the m = s and p)in\u03b8. Combining \u03b52] \u2260 0, where Re[\u03b52] and Im[\u03b52] represent, respectively, the real part and imaginary part of the permittivity of loss ENZ metamaterial. As usual, the imaginary part indicates the loss.We considered a lossless ENZ metamaterial in above theoretical analysis. However, for a real ENZ metamaterial, such as the noble metal at plasma frequency or doped semiconductors at terahertz28\u03b52] = 10\u22124, and the solid and dashed lines are corresponding to s and p polarizations, respectively. As shown by the blue lines, the G-H shifts for both polarized light of s and p are sd = \u03bb/\u03c0 and pd = 0, respectively, for any incident angle except the vicinity of the critical angle. It is noted that when the incident angles vary across the critical one, the reflection phase will experience an abrupt change, usually leading to quite an obvious G-H effecte.g. Im[\u03b52] = 0.01, for s polarized light, as shown by the black solid line, there is a region where the G-H shift gradually changes from zero to \u03bb/\u03c0. Such a property stems from the fact that the added losses make the reflection phases deviate from the linear relationship of s\u03d5 = \u22122in\u03b8. In particular, the deviation is quite notable at small incident angle. For p polarized light, however, the situation is more complicated. Generally, for an absorptive medium, there is an abrupt change of phase across the (pseudo) Brewster angle when a p polarized light is reflected by it. As a result, such an abruptly changed phase induces a negative G-H shift around the (pseudo) Brewster angle\u03b52] = 0.01, as shown by the black dashed line, a resonance for G-H shift could be observed. Further, we use a larger loss with Im[\u03b52] = 0.1, as shown by the red lines. The gradually changing region of G-H shift for s polarized light is enlarged (see the red solid line), while for p polarized light, the resonance position is shifted to a larger angle (see the red dashed line). Nevertheless, for an incident angle large enough, the G-H shifts for the loss cases will approach those of the situation without loss, i.e., for s polarized light, it is almost \u03bb/\u03c0, while for p polarized light, it is close to zero. The larger the loss is, the narrower the range of the working incident angle is. In particular, the working incident angle range for Im[\u03b52] = 0.01 is at about  = 0.1, it changes into  to the G-H shift, \u03b52] increases to 10\u22122. For the lossless case, the critical angle becomes larger, then the working angle for both polarizations is accordingly shifted to a larger angle, as shown by the blue lines. When the same levels of losses are involved, the black and red lines are corresponding to those of Im[\u03b52] = 0.01 and 0.1, respectively. Similar results can be observed including the gradually changed regions of G-H shifts for s polarized light and the resonances of G-H shifts for p polarized light. Although the real part of the permittivity is larger, the working incident angle ranges do not vary that much if we compare \u03b52] increases from 10\u22124 to 10\u22122. However, the amplitudes of resonances change a little bit. Generally, for an absorptive dielectric, the amplitudes of resonances decrease as the ratio of Im[\u03b52]/Re[\u03b52] increasesIn order to examine the sensitivity of the small values of Re[\u03bb. Because of the small G-H shift, it is easier to observe the lateral shift L = sd/cos(in\u03b8). s polarization, the lateral shift L is about 0.5\u03bb, as shown in p polarization, the shift is zero, as shown in \u03bb for s-polarization. Considering the fact that the incident beam is not a plane wave, such a deviation is acceptable. Moreover, p polarization, the symmetry axis of the field distribution (the red line) is located at the original point x = 0, as shown by the dotted line. While for s polarization its symmetric center is shifted to the left. Such a contrast further verifies our theoretical prediction that the G-H shift exists only for s polarization. Lastly, we compare the numerical results L for different incident angles with the analyzed results, as shown in L = sd/cos(in\u03b8), while the five blue points are the numerical results for incident angles with 15\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 75\u00b0, respectively. In the plot, the numerical results fit well with the analytical curve.To give a comprehensive understanding and to verify the above theoretical analysis, we perform the numerical simulations of G-H shifts, where we consider a beam with a spatial Gaussian profile incident from air to ENZ metamaterial, and the half-width of the beam is 7.5e.g., mu-near-zero (MNZ) metamaterials, matched impedance zero-index metamaterials (MIZIMs), and anisotropic ZIMs. For MNZ metamaterials, we predict based on current results that the G-H shift is a constant for p polarized light, independent of the incident angle. Yet, there is no G-H shift for s polarization. For MIZIMs, there are no G-H shifts for both polarizations of s and p because the oblique incident light cannot enter into MIZIMs at all.Finally, it is worth mentioning that we only focus on the ENZ metamaterials here. In fact, the zero index metamaetrials can be further categorized, s or p polarization is obliquely incident onto the ENZ metamaterial from air. We have shown that for lossless ENZ material, there is no G-H shift for p polarization, which indicates that it obeys exactly the prediction by the geometrical optics. While for s polarization, the G-H shift is a constant value, independent of the incident angle. We also have explored analytically the influence of loss of ENZ metamaterials on the G-H shift for both polarizations and we found that the novel features still hold for a broad range of angles. Analogous deviations of G-H effect are expected for acoustic waves, quantum matter waves and so on. In addition, we have shown that the reflected phase of p polarized light is p\u03d5 = \u2212\u03c0, while for p polarized light, the reflected phase obeys that linear relationship s\u03d5 = \u22122in\u03b8. Due to such different responses, we believe that the ENZ metamaterial can be utilized to manipulate the polarization states of reflected light, by only adjusting the incident angle. We expect our work to contribute some new notions to the manipulation of the polarization states of light at the THz region.We have investigated the G-H effect of reflected light, when a linearly polarized light of either x axis from \u22128\u03bb to 8\u03bb. Due to the interference effect, the field amplitudes are oscillating along z direction. The line plots are located at the first peak close to the interface between air and ENZ metamaterial. Meanwhile, we zoom in the line plot of |yE| enough to get the distance between its symmetric axis and x = 0, which indicates the lateral shift L. The numerical results in The numerical simulation results shown in Y.X. and H.C. conceived the idea. Y.X. did the theoretical calculations and the numerical simulations. H.C. and C.T.C. helped with the theoretical analysis. H.C. supervised the whole project. All the authors wrote the manuscript."}
+{"text": "We apply the well-known Condorcet criterion from voting theory outside of its classical framework and link it with spanning trees of an undirected graph. In situations in which a network, represented by a spanning tree of an undirected graph, needs to be installed, decision-makers typically do not agree on the network to be implemented. Instead, each of these decision-makers has her own ideal conception of the network. In order to derive a group decision, i.e., a single spanning tree for the entire group of decision-makers, the goal would be a spanning tree that beats each other spanning tree in a simple majority comparison. When comparing two dedicated spanning trees, a decision-maker will be considered to be more satisfied with the one that is \u201ccloser\u201d to her proposal. In this context, the most basic and natural measure of distance is the usual set difference: we simply count the number of edges the spanning tree has in common with the proposal of the decision-maker. In this work, we show that it is computationally intractable to decide (1) if such a spanning tree exists, and (2) if a given spanning tree satisfies the Condorcet criterion. Dating back more than two centuries\u00a0 or a crucial supply network such as a gas or oil pipeline. These networks are generally designed as spanning trees connecting all countries represented by vertices in a graph. The decision-makers could be the countries themselves, or board members of some EU institution. For political and historical reasons involving trust, self-interest, or stability concerns, different decision-makers have different perceptions which links  between the countries should be used in order to establish the whole network. In particular, the decision-makers could have different conceptions of the entire network because of political relations and alliances , or due to concerns regarding the security of supply and political stability. In addition, different decision-makers could base their conceptions on different criteria, which typically results in differing networks. Finding a plausible solution which takes into account the interests of all the decision-makers in such a setting is clearly an important aggregation task.T such that for each other spanning tree T beats (is not beaten by) In principle, we are thus concerned with the aggregation of spanning trees of an undirected graph into a single spanning tree. Hence, this work is somewhat related to the axiomatically motivated work of\u00a0Endriss and Grandi , where, The first question is related to the work of\u00a0Darmann , where iThe second question is in the spirit of the seminal paper by\u00a0Bartholdi et\u00a0al. , who sho\u00a0Darmann  focuses \u00a0Darmann  providesentclass1pt{minima\u00a0Darmann  is close\u00a0Darmann  the agen\u00a0Darmann  it follo\u00a0Darmann  and, to \u00a0Darmann  by showiV and a set E of two-element subsets of V. We call the elements of V vertices and the elements of E edges. A subset spanning tree of G, if  contains no cycle. Note that for any two spanning trees G we have We briefly introduce the formal framework of this paper. An undirected graph A be a set of agents. For each agent G. Then, a spanning tree T of G is called a Condorcet tree if for all spanning trees G, T of G is called a weak Condorcet tree, if for all spanning trees G, Let In the first decision problem considered in this paper we ask for the existence of a Condorcet tree.Condorcet-Tree)  Condorcet tree.Condorcet-Tree Winner)  clauses made up of exactly 3 literals ; the task is to decide if C is unsatisfiable, i.e., if there is no truth assignment for X that satisfies all the clauses in C. 3-Unsat remains Sat is known to be 3-Unsat is We provide a reduction from the ns\u00a0Tovey ; obvious3-Unsat, with Z be the set of literals, i.e., Let Step I: Constructing instanceof Condorcet-Tree. From Condorcet-Tree as follows.Step Ia: Defining the graph. Let t and q respectively. Identifying a literal with an edge of the same label, we formally defineG consists ofmentclass2pt{minimStep Ib: Introducing the agents. We introduce a set G. Note thatH is contained in the spanning tree T proposed by each edge in the set B is contained in all but each edge in D is contained in at most one proposed spanning tree andeach edge in Z is contained in at most each edge in From these observations, it is easy to conclude that T is the unique maximum spanning tree w.r.t. the edge weights for each for each for each for each Step II: Proving the reduction. We complete the proof by showing that the following claim holds:The agent set mentclass2pt{minim3-Unsat if and only if Condorcet-Tree.Condorcet-Tree. As a consequence, T is the unique Condorcet tree. Assume that 3-Unsat, i.e., there is a truth assignment C. We show that this leads to the conclusion that T is not a Condorcet tree in .\u201cA:agents in t. Hence, for each agents in agents in On the other hand, the agents in T. Hence, we getT is not a Condorcet tree. Hence there is no Condorcet tree in 3-Unsat.Recall that Condorcet-Tree. Thus, T is not a Condorcet tree, i.e., there must be a spanning tree \u201cFirst, we show that we can assume thatG from G. Obviously, H, we have(i) Second, we show thatholds. By construction, (ii) If entclass1pt{minimatated in\u00a0.n from the sets Hence, mentclass2pt{minimtradicts\u00a0. Thus, \\Third, we show thatholds for eacht, n from the sets (iii) mentclass2pt{minimn from the sets n of the voters Analogously, tradicts\u00a0.Finally, fromwe derive a truth assignmentthat satisfies all clauses inC. Let for each agent for each agent for each agent As a result, due to C, i.e., 3-Unsat. (iv) mentclass2pt{minim satisfy\u00a0 each ageWeak-Condorcet-Tree.In the following theorem, we state an analogous result for Weak-Condorcet-Tree is The proof follows from the one of Theorem\u00a0We now turn to the problems of deciding whether a given spanning tree is a (weak) Condorcet tree. These problems turn out to be Condorcet-Tree Winner is T. Thus, in instance T a Condorcet tree?\u201d is \u201cYes\u201d. It is hence straightforward that Condorcet-Tree Winner is In the proof of Theorem\u00a0Condorcet-Tree Winner, where we ask if Finally, membership in Analogously, with (the proof of) Theorem\u00a0Weak-Condorcet-Tree Winner is Condorcet-Tree and Weak-Condorcet-Tree only provide lower bounds for their computational complexity. A finer placement of these problems in terms of their computational complexity is an interesting open question.We have shown that both deciding if a (weak) Condorcet tree exists and deciding if a given spanning tree is a (weak) Condorcet tree, are computationally difficult problems. While the latter problems turn out to be"}
+{"text": "Large reorientations of the line of sight, involving combined rotations of the eyes, head, trunk and lower extremities, are executed either as fast single-step or as slow multiple-step gaze transfers. In order to obtain more insight into the mechanisms of gaze and multisegmental movement control, we have investigated time-optimal gaze shifts (i.e. with the instruction to move as fast as possible) during voluntary whole-body rotations to remembered targets up to 180\u00b0 eccentricity performed by standing healthy humans in darkness. Fast, accurate, single-step movement patterns occurred in approximately 70\u00a0% of trials, i.e. considerably more frequently than in previous studies with the instruction to turn at freely chosen speed (30\u00a0%). Head-in-space velocity in these cases was significantly higher than during multiple-step transfers and displayed a conspicuously regular bell-shaped profile, increasing smoothly to a peak and then decreasing slowly until realignment with the target. Head-in-space acceleration was on average not different during reorientations to the different target eccentricities. In contrast, head-in-space velocity increased with target eccentricity due to the longer duration of the acceleration phase implemented during trials to more distant targets. Eye saccade amplitude approached the eye-in-orbit mechanical limit and was unrelated to eye/head velocity, duration or target eccentricity. Overall, the combined movement was stereotyped such that the first two principal components accounted for data variance almost up to gaze shift end, suggesting that the three mechanical degrees of freedom under consideration  are on average reduced to two kinematic degrees of freedom . Synchronous EMG activity in the anterior tibial and gastrocnemius muscles preceded the onset of eye rotation. Since the magnitude and timing of peak head-in-space velocity were scaled with target eccentricity and because head-on-trunk and trunk-in-space displacements were on average linearly correlated, we propose a separate controller for head-in-space movement, whereas the movement of the eye-in-space may be, in contrast, governed by global, i.e. gaze feedback. The rapid progression of the line of sight can be sustained, and the reactivation of the vestibulo-ocular reflex would be postponed, until gaze error approaches zero only in association with a strong head-in-space neural control signal. Upright human subjects reorient to angularly distant targets (\u226590\u00b0) by assembling fairly stereotypical, simultaneous, combined movements of the eye, head, trunk and lower extremities Land . Such laDuring the less time-efficient multiple-step gaze transfers, target acquisition takes at least 100\u2013300\u00a0ms longer. It has been suggested that the higher the head-in-space velocity during this task, the more likely that a single-step gaze shift pattern will be elicited  of such gaze reorientations is characterized by tight segmental coupling, as the three mechanical degrees of freedom available  are reduced to two kinematic degrees of freedom , turning at natural, freely chosen speeds , mean age 27\u00a0\u00b1\u00a01.2\u00a0years. No one wore spectacles, and selection ensured excellent physical condition. The study was approved by the Imperial College Riverside Ethics Committee in accordance with the Declaration of Helsinki, and all subjects provided informed consent.Details have been given previously .In contrast to all our previous studies with this paradigm, where Ss were given no instruction as to the speed of the movement required, here Ss were instructed to accomplish turns as soon and as fast as possible.Head-in-space, upper trunk and feet horizontal (yaw plane) movements were recorded using a Polhemus Fastrak motion analysis system . Markers were placed on a light, adjustable helmet, on the spinous process of the seventh cervical vertebra and dorsally on each foot. Horizontal eye-in-orbit rotations were recorded using bi-temporal DC electrooculography (EOG) with a flat response to 90\u00a0Hz. EMG activity was collected by adhesive surface disc electrodes  placed at a distance of 3\u00a0cm near the motor point of the following muscles on the right side: anterior tibial, gastrocnemius, biceps femoris and external oblique.sgolayfilt), while head and trunk velocities were calculated after subjecting the position signals to moving mean linear filtering . Movement onset/offset for the various segments was calculated from the time derivative. Gaze (eye-in-space) displacement was obtained by adding EOG and head signals after appropriate scaling. Subtracting the trunk from the head signal resulted in an estimate of head-on-trunk movement. Biphasic deflections in the eye velocity trace were thought to represent blinks , so that the first and the last PCs, respectively, account for maximal and minimal amount of variance in the original data. The PCs combine linearly with the original  variables, and if the three elemental variables are totally uncovaried, three statistically significant PCs will account for data set variability. In contrast, if two of the variables covary, then only two significant PCs account for data set variability and the space defined by the three elemental variables is reduced by one dimension, i.e. variation in the data set under consideration can be described by a plane . Similarly, if all three variables covary, then only one significant PC accounts for data set variability and the space defined by the three variables is reduced by one further dimension (i.e. to a straight line). Thus, the number of significant PCs and the percentage of data variance they account for stand for the degree of covariation among the variables.We applied PC analysis to examine and quantify statistically the relationships among a set of 3-covarying variables (channels), i.e. eye-in-orbit, trunk-in-space and head-on-trunk, of mth sample of the trial, m\u00a0=\u00a01, \u2026, n. For the purpose of PC analysis, raw position data were used (i.e. before filtering), and EOG was resampled at 30\u00a0Hz. Increasing time intervals, starting always with the onset of gaze, was analysed (\u2018sliding\u2019 approach). Data centring and auto-scaling were carried out by subtracting the arithmetic means Percentages of the variation in the original set of variables, which the principal components account for, equal the normalized eigenvalues eig. For each data set , the eigenvalue k\u00a0=\u00a01, \u2026, N, are calculated. Further, by averaging across all trials, the mean eigenvalue Eigenvalues Bartlett\u2019s test of sphericity was used to validate the hypothesis that the first principal component was significantly different from all those of lower importance, i.e. both second and third. This has to be accepted if the test statistic function j\u00a0=\u00a01, 2), a test for proportion of total variance was applied post hoc. A desired proportion of total variance at 99.0\u00a0% was selected and excluded all principal components, which accounted for <1\u00a0% of the total variance; one-sample independent t test was performed for the arithmetic means of variance proportion of second and third PCs and tested whether they were significantly >1\u00a0%. When normality failed according to a one-sample Kolmogorov\u2013Smirnov nonparametric test, a binomial nonparametric test for the median value was carried out instead.N-trials, separately for various target eccentricities and time intervals from gaze onset . Outbound turns and visually guided gaze shifts  will not be considered further here.Inbound or \u2018return\u2019 reorientations to targets \u226590\u00b0 consisted predominantly of single-step displacements of the visual axis covering at least 85\u00a0% of target eccentricity Fig.\u00a0. Here, wAs already reported in the literature for large saccades with the head free to move , and the line of sight was stabilized, in darkness, quite near the memorized centrally located target. Ss sometimes made a corrective small saccade after the LED was turned on.F\u00a0=\u00a026.1 p\u00a0<\u00a00.0001 and F\u00a0=\u00a025.1 p\u00a0<\u00a00.0001, respectively). In contrast to head-in-space, the dynamic trajectories of trunk-in-space, and most particularly head-on-trunk motion, were more variable , confirming that the Ss generally tried to comply with the instruction \u2018go as fast as you can\u2019. Noteworthy, in reorientations made by means of the multiple-step pattern . In many instances, the premature termination of primary gaze shift long before reaching the position of the centrally located remembered target was signalled by an abrupt deceleration break in the, up to this point, monotonically increasing head-in-space velocity trace . However, even if interrupted by variable periods of stationary gaze, the displacement of the visual axis was terminated again very close to the remembered target.Head-in-space movement resulted from the sum of head-on-trunk and trunk rotation in space. The dynamic trajectory of head-in-space velocity was conspicuously monophasic, increasing smoothly to a peak and then decreasing slowly until realignment with the memorized gaze direction . Single-step transfers were approximately 100\u2013300\u00a0ms faster than multiple-step gaze displacements . Finally, head-in-space oscillations  did not increase with the amplitude of head-on-trunk movement (R2\u00a0=\u00a00.24).As already reported in the literature , we examined how the timing of peak head-in-space velocity was associated with the end of the gaze shift in single-step movement patterns Fig.\u00a0. If headN\u00a0>\u00a015) of trials for statistical analysis were available. The first PC was significant  and accounted for almost 90\u00a0% of variance in all analysis time windows. The second PC was also significant overall and accounted approximately for about 10\u00a0% of variance (p\u00a0<\u00a00.001). In contrast, the third PC was non-significant in all time windows and target eccentricities, accounting for <1\u00a0% of variance. Variance up to half a second after movement initiation could be thus accounted for by essentially the first two PCs (i.e. the sum of their percentages was approximately 100\u00a0%), suggesting that the three mechanical degrees of freedom under consideration are reduced to two kinematic degrees of freedom. Visualization of these relationships is exemplified in Fig.\u00a0x and y axes give mean PC scores, units are normalized as a consequence of auto-scaling, c.f. \u201cMean\u00a0\u00b1\u00a0standard deviations of percentages of variance accounted for by individual principal components (PCs) are shown in Table\u00a0\u03b8 and \u03c6. Note from Table\u00a0\u03b8 is often close to 90\u00b0 while \u03c6 is mostly larger than 45\u00b0. Because \u03b8 is mostly close to 90\u00b0, the covariation plane is approximately perpendicular  to the plane defined by the axes head-on-trunk and trunk-in-space. In consequence, head-on-trunk and trunk-in-space displacements are linearly correlated, i.e. they lay approximately upon a regression line and can be replaced by one variable, for example, head-in-space. The slope of this relationship is larger than unity as \u03c6 is mostly >than 45\u00b0. In this way, trunk-in-space is on average larger than head-on-trunk displacement throughout the gaze transfers. Of note, these relationships do not apply during \u2018multistep\u2019 (nystagmic) transfers. Here, three derived significant PCs account for the data variance . There was not any statistical difference in the onset of EMG activation from the right tibial and gastrocnemius muscles, both for inbound and for outbound reorientations, i.e. they were activated on average synchronously. Not unexpectedly, EMG activity in these muscles decreased as the right foot started to rotate rightwards.Ss activated the right anterior tibial and gastrocnemius muscles approximately 30\u00a0ms on average before starting to rotate gaze (i.e. the eye) rightwards to the centrally located remembered target Fig.\u00a0. Biceps Ss were instructed to move as fast as possible and were thus able to attain high head and trunk velocities. In the remaining 30\u00a0% of trials, however, the progression of the line of sight was interrupted by one or more variable intervals of stable gaze . All the same, gaze displacement ended again close to the remembered target. Multiple-step gaze shifts were characterized by significantly low head-in-space velocity. High head-in-space velocity during task execution thus increases the probability of eliciting single-step gaze shifts and quickly acquiring a predetermined direction of the visual axis, as hypothesized in previous studies . This presumably presents the CNS with a simpler control task.A conspicuous, central feature of large, single-step reorientations to remembered targets was the high peaked monophasic head-in-space velocity traces Fig.\u00a0, suggestA further salient finding of our study in favour of separate control for head-in-space is that command timing does not relate to gaze displacement but, instead, head-in-space displacement Fig.\u00a0. If the Why did Ss frequently choose to move head-on-trunk far below 60\u201370\u00b0 (i.e. the limit of the so-called neutral zone, McClure et al. Separate control signals for the eye and head have been proposed by several researchers because of the variability in the relative timing of the start of eye and head movements and the effect of initial eye-in-orbit position on the contribution of the eyes and head to gaze displacement (for a review, see Freedman The fact that high head-in-space velocity and single-step gaze shifts are interconnected makes sense biologically when target acquisition occurs under \u2018as soon as you can\u2019 conditions, but how are these two variables associated mechanistically? It is clear from our findings that reemergence of the VOR and gaze stabilization does not depend solely on gaze error, as most gaze models propose (cf. Galiana and Guitton Foot rotations in this experimental paradigm are extremely variable and start mostly considerably later than movements of the eye, head and trunk (on average 350\u00a0ms later than the eye, Anastasopoulos et al."}
+{"text": "Statistics in Medicine published by John Wiley & Sons, Ltd.Estimating the size of hidden or difficult to reach populations is often of interest for economic, sociological or public health reasons. In order to estimate such populations, administrative data lists are often collated to form multi-list cross-counts and displayed in the form of an incomplete contingency table. Log-linear models are typically fitted to such data to obtain an estimate of the total population size by estimating the number of individuals not observed by any of the data-sources. This approach has been taken to estimate the current number of people who inject drugs (PWID) in Scotland, with the Hepatitis C virus diagnosis database used as one of the data-sources to identify PWID. However, the Hepatitis C virus diagnosis data-source does not distinguish between current and former PWID, which, if ignored, will lead to overestimation of the total population size of current PWID. We extend the standard model-fitting approach to allow for a data-source, which contains a mixture of target and non-target individuals . We apply the proposed approach to data for PWID in Scotland in 2003, 2006 and 2009 and compare with the results from standard log-linear models. \u00a9 2013 The Authors.  Estimating population sizes using two (or more) data lists has a long history Traditionally, log-linear models Log-linear models have been extended to allow additional (discrete) covariates to be incorporated The fact that a cell count of the table is unknown, or missing, may motivate us to consider the missing data mechanism only observe members of the target population or are able to identify whether an individual is a member of the target population. However, this may not always be the case. For example, for the data that we introduce in Section 1.1, we are interested in the current number of people who inject drugs (PWID) in Scotland. Four data-sources are used to observe such individuals, including the Hepatitis C virus (HCV) diagnosis database. Individuals are identified as being PWID on this database, but their status as \u2018current\u2019 or \u2018former\u2019 injector is not recorded. Thus, this data-source records not only current PWID but also former PWID who do not belong to the target current PWID population of interest. A previous analysis of one\u2009year of these data by King et al. In this paper, we relax the standard assumption that all individuals recorded by the given data-sources belong to the population of interest or \u2018target\u2019 population. Typically, data-sources are chosen so that they et al. In the last decade, data from multiple administrative data-sources have been repeatedly used to estimate the total number of current PWID in Scotland. We shall consider the data collected in the last three studies, corresponding to years 2003, 2006 and 2009. Four data-sources were used corresponding to social enquiry reports S1), hospital records (S2), Scottish Drug Misuse Database  and HCV diagnosis database (S4). The HCV diagnosis database contains epidemiological data (including risk group and date of first diagnosis) on all individuals who have been newly diagnosed with HCV in Scotland. In addition, a range of covariates was recorded for each individual, including age (C1), gender (C2) and region (C3). For each study, age is categorised into two levels . For 2003, region was categorised into the two levels, Greater Glasgow and Rest of Scotland, whereas in 2006 and 2009, the two levels were Greater Glasgow and Clyde, and Rest of Scotland. This change was to conform with the National Health Service board regions, which altered between the 2003 and 2006 studies. See King , hospita7 contingency table, with 8 (\u2009=\u200923) unknown cell counts. However, as discussed by et al. et al. The number of individuals observed by each combination of data-sources and cross-classified across covariates can be presented in the form of an incomplete 2In this paper, we investigate, in further detail, the issue of individuals observed by the HCV diagnosis data-source including both target and non-target individuals. The main contribution of the paper is the development of a new modelling strategy to incorporate this complexity, without excluding the HCV diagnosis data-source, and hence, potentially, discarding a significant amount of information. The additional advantages of this strategy over the approach of The outline of the paper is as follows. Section 2 describes the new modelling strategy in detail and includes a simulation study to test the strategy's efficacy. In Section 3, we apply the strategy to the Scotland PWID multi-list data, for 2003, 2006 and 2009, to provide the aforementioned estimates. We end with Section 4 discussing future work and epidemiological conclusions of the results in Section 3.In this section, we discuss the assumptions relating to the modelling approach before describing the notation that will be used and the new model-fitting approach to deal with the HCV diagnosis data-source's potential for recording both former and current PWID.only the HCV diagnosis data-source  for each cross-classification of covariate values may contain non-target individuals. The corresponding cell entries can then be regarded as an upper bound on the true cell count (i.e. true number of current PWID observed by only the HCV diagnosis data-source), leading to left censored cells.We assume that the HCV diagnosis data-source may record individuals from both current and former PWID  but that each of the other data-sources only records current PWID. This implies that individuals recorded by the HCV diagnosis data-source and any other data-source are a current injector. Thus, only the observed cells corresponding to being recorded by n cells in the incomplete contingency table, of which nU are unobserved and nC are censored. For each year of these data, n\u2009=\u200927\u2009=\u2009128, nU\u2009=\u200923\u2009=\u20098 (corresponding to being unobserved by each data-source for the 8 covariate cross-classifications) and nC\u2009=\u200923\u2009=\u20098 (corresponding to being recorded by only the HCV diagnosis data-source for the 8 covariate cross-classifications). We label each cell from 1,\u2009\u2026\u2009,n, such that cells i\u2009=\u20091,\u2009\u2026\u2009,nC correspond to the censored cells and cells i\u2009=\u2009nC\u2009+\u20091,\u2009\u2026\u2009,nC\u2009+\u2009nU to the unobserved cells. For i\u2009=\u20091,\u2009\u2026\u2009,n, we let yi denote the true number of current PWID in cell i. Further, we let yO,zC}are the observed data, whereas {yU,yC}are parameters to be estimated so that the total population size \u03b2 denote the set of log-linear parameters in the model (we return to the issue of model uncertainty later).Notationally, we assume that there yi, has an independent Poisson distribution, that is, for i\u2009=\u20091,\u2009\u2026\u2009,n, \u03bci has the form,\u03b2 denotes the (q\u2009+\u20091)\u2009\u00d7\u20091 vector of (identifiable) log-linear parameters, \u03b20,\u03b21,\u2009\u2026\u2009,\u03b2q, and xi the (q\u2009+\u20091)\u2009\u00d7\u20091 design vector relating to cell i\u2009=\u20091,\u2009\u2026\u2009,n. The term \u03b20 corresponds to the intercept term, whereas \u03b21,\u2009\u2026\u2009,\u03b2q correspond to the main-effect and log-linear interaction terms. For parameter identifiability, we use the standard sum-to-zero constraints for the log-linear main-effect and interaction parameters. Because each data-source and covariate only has two levels, each element of xi is equal to\u2009\u00b1\u20091. Finally, we let X denote the n\u2009\u00d7\u2009(q\u2009+\u20091) design matrix with ith row, xi.We use a special case of a generalised linear model (GLM), where we assume that each (true) cell count, y\u2009=\u2009{y1,\u2009\u2026\u2009,yn}is to set, An alternative  model specification for ith element of p is given by \u03bci given by Equation 2. This is the model specification considered by N, to be directly incorporated through a prior distribution on N.where the yU, yC and all model parameters, denoted by \u03b8, given the observed data yO and zC, can be written in the form, y\u2009=\u2009{yO,yC,yU}, and \u03c0(\u2009\u00b7\u2009) and \u03c0(\u2009\u00b7\u2009|\u2009\u00b7\u2009) represent marginal and conditional probability density/mass functions, respectively. This result is derived because we assume that the observed cell entries yO are independent of zC, yU and yC, given \u03b8; and the observed censored cells zC are independent of yU, given the log-linear parameters \u03b8 and true cell entries yC. The term \u03c0(y\u2009|\u2009\u03b8) corresponds to the complete data likelihood for the full set of cell entries, y, as specified by Equation 1 and \u03c0 the distribution of the observed upper bound for the censored cells, given the log-linear parameters and true cell entries. For these data, we assume non-informative censoring. In other words, zi\u2009|\u2009yi\u2009\u223c\u2009U[yi,\u2009\u221e\u2009), independently, for i\u2009=\u20091,\u2009\u2026\u2009,nC \u2009=\u2009\u03c0(zC\u2009|\u2009yC)). In Section 4, we discuss an alternative distribution for zi, which can be used to incorporate individual prior information on the proportion of individuals observed by the HCV diagnosis data-source who are current PWID.Given a log-linear model (in terms of the interaction terms present in the model), the posterior distribution of \u03b8m denote the parameters present within model \u03c0(m) denotes the prior model probability for model To allow for additional model uncertainty, in terms of the log-linear interaction terms that are present in the model, we extend the posterior distribution given in Equation 5. We treat the model indicator as a discrete parameter and form the joint posterior distribution over both parameters and model space. Let \u03b8m and m, into the analysis via the prior distributions, \u03c0(\u03b8m\u2009|\u2009m) and \u03c0(m). However, we assume there is weak prior information on the model parameters and so need to specify a prior distribution, which reflects this position. In general, care must be taken when specifying prior distributions on the model parameters under weak prior information in the case of model uncertainty due to Lindley's paradox \u03b2m. To counter this issue, we use the idea of \u2018default prior distributions\u2019 \u03b2m, we drop the subscript m, for notational simplicity. Because the intercept, \u03b20, is present in all models, we assume \u03c0(\u03b20)\u2009\u221d\u20091. Let the matrix Y be formed from X by removing the first column of ones corresponding to \u03b20. The GHGP for the remaining elements, \u03b1\u2009=\u2009, of \u03b2 is given by \u03b1\u2009|\u2009\u03c32\u2009\u223c\u2009N , where \u03c32\u2009>\u20090 is an unknown hyperparameter. The GHGP extends the Zellner g-prior \u03b1 and an imaginary sample of size 1\u2009/\u2009\u03c32, which is referred to as the \u2018prior sample size\u2019 by \u03c32\u2009=\u20091, thus giving a prior sample size of one. This is intuitively appealing because the amount of information the prior provides is directly interpretable. Sabanes-Bov\u00e9 and Held \u03c32 be unknown by assuming a gamma hyperprior distribution with parameters a\u2009/\u20092 and b\u2009/\u20092, so that, on the inverse scale Within the Bayesian approach, we can incorporate any available prior information on the model parameters, a\u2009=\u2009b\u2009=\u200910\u2009\u2212\u20093 so that the hyperprior on 1\u2009/\u2009\u03c32 is vague but centred at one. However, in Section 3, we investigate the sensitivity of the resulting analysis to these values of a and b. The inverse-gamma hyperprior distribution assumed earlier also has the minor computational advantage of being conditionally conjugate (see step 1 in Section 2.4) meaning the full conditional distribution of \u03c32 is also an inverse-gamma distribution. Because, in our case, all of the data-sources and covariates have two levels, under sum-to-zero constraints, the GHGP corresponds to the elements of \u03b1 being independent with variance given by \u03c32.where IG denotes the inverse-gamma distribution. We specify m is given by \u03b8m\u2009=\u2009{\u03b2m,\u03c32}.Finally, we specify a uniform prior over all admissible models, that is, yU, yC, \u03b8m and m under the Poisson specification is identical to that obtained using the multinomial model formulation when \u03c0(N)\u2009\u221d\u2009N\u2009\u2212\u20091, corresponding to Jeffreys\u2019 prior The joint posterior distribution of N (obtained by combining the estimated number of injecting drug related death rates with an estimated associated death rate). Thus, the posterior distributions for the total population size ignoring the censored cells for 2003 and 2006 will be slightly different to those published in The aim of this paper is to consider the impact of censored contingency cells, and so, to maximise consistency across years, we specify the same default prior from above on the parameters for each dataset. The previous analyses of the Scotland PWID multi-list data have used the alternative multinomial model specification in order to specify an informative prior on the total population size, N. Under the multinomial model formulation, and for the subset of decomposable models, Madigan and York p, which gives a closed form expression for the marginal posterior distribution of the total population size. However, as Dellaportas and Forster The priors we have specified earlier are not conjugate. In fact, for hierarchical log-linear models, conjugate priors do not exist. This means it is necessary to employ the computational methods, described in Section 2.4, to evaluate the marginal posterior distribution of the total population size, yU, yC, \u03b8m and m, given by Equation 5. The algorithm employed is an example of data-augmentation and, as such, can be viewed as iterative multiple imputation yU and yC, update the parameters and model, \u03b8m and m.Step 1 Conditional on the current values of the unknown and censored cell counts, \u03b8m and m, update the unknown and censored cell counts, yU and yC.Step 2 Conditional on the current parameters and model, In this section, we describe the computational algorithm used to generate an MCMC sample from the posterior distribution of We consider each step in turn.\u03b2m, and model, m, are updated using the reversible jump (RJ) algorithm m remains unchanged, and we update only the log-linear parameters, \u03b2m. Previous approaches, including the study of King and Brooks m. We use an alternative algorithm that utilises the iterated weighted least squares implementation of the Metropolis\u2013Hastings algorithm for GLMs The log-linear parameters, \u03c32. The inverse gamma prior distribution for \u03c32 is conditionally conjugate so that we update the parameter using the closed form of the full conditional distribution, that is, \u03b2m\u2009=\u2009.Now consider the hyperparameter, yi\u2009|\u2009\u03b2m\u2009\u223c\u2009Poisson(\u03bci). Similarly, to update the true cell entries for the censored cells, yi\u2009|\u2009\u03b2m,zi\u2009\u223c\u2009Poisson(\u03bci)I(yi\u2a7d zi), where I denotes the indicator function.To update the unobserved cell entries The computational approach described in this section is implemented in the R In this section, we conduct a small simulation study to assess the efficacy of the proposed modelling strategy and to compare this against other methods. The simulation study attempts to match the observed properties of the Scotland PWID multi-list data introduced in Section 1.1 and its inferred properties from Section 3.yU, is completely unknown; one cell count, yC, is unknown but bounded from above by zC; and the remaining 14 cell counts, yO, are observed. We consider three different true total population sizes N\u2009=\u200910000,15000 and 20000. Additionally, we consider two different forms for the true data-generating model: (i) a model with non-zero interactions for S1 : S2, S1 : S4 and S2 : S4 and (ii) a model with a non-zero interaction for S1 : S2. Note that model (ii) is decomposable but model (i) is not decomposable . Table\u2009\u03b2 under each of the true data-generating models. These values were chosen so that the simulated data were consistent with the observed Scotland PWID multi-list data. For example, the negative values of the true parameters associated with the main-effect terms mean that the probability of observing an individual is less than that of not observing an individual.The simulation study is set up as follows. We assume there are four data-sources: S1, S2, S3 and S4, and that S4 is the censored data-source observing a mixture of individuals from the target and non-target populations. For simplicity, we assume that there are no covariates. This means that there are 16 cells in the table. One cell count, N, we generate the true cell counts from the multinomial distribution. We remove the cell count, yU, corresponding to not being observed by any of the data-sources. We also replace yC (the cell count corresponding to just being observed by S4) by zC, where zC is generated from a negative binomial distribution (under the parameterisation of yC and probability 2\u2009/\u20093 (so as to be consistent with the inferred properties from the observed data for PWID in Scotland). For each true data-generating model and each true total population size, we generate 1000 datasets using the aforementioned procedure. We analyse each dataset using the following four methods. INC-C The proposed modelling strategy, described in Sections 2.1 to 2.4, of incorporating the censoring mechanism, using hierarchical models.REM-C The approach of IGN-C The approach of MY-C The approach of Using the parameter values in Table\u2009yC, in the censored cell from a truncated posterior predictive distribution. Also, note that, to apply the approach of N. To maintain consistency with the three other approaches listed earlier, we assume Jeffreys\u2019 prior for N, that is, \u03c0(N)\u2009\u221d\u2009N\u2009\u2212\u20091 (Section 2.3).Note that the MY-C method of \u03c6, of individuals observed by the S4 data-source who are actually members of the target population or identify interactions involving the S4 data-source. Additionally, for this method, by removing the censored data-source, we are discarding information. The INC-C and MY-C methods actually model the censoring mechanism and will be able to provide a posterior distribution of \u03c6. Additionally, these two methods can identify interactions involving the S4 data-source. Finally, the INC-C method has the advantage over the MY-C method of considering the much more flexible class of hierarchical models. However, this advantage comes at the price of requiring more complex computational methods to evaluate the resulting posterior distributions.Before we present the results of the simulation study, we briefly contrast the relative advantages and disadvantages of the four methods. The REM-C and IGN-C methods are the simplest approaches because we do not model the censoring by either removing the data-source or ignoring the problem altogether, respectively. The REM-C method will not be able to evaluate the posterior distribution of the proportion, N, and \u03c6. These rates and lengths, averaged over the 1000 datasets, are given for each of the three true values for N, each of the two true data-generating models and each of the four methods. An entry of NA indicates that this method cannot estimate the value of \u03c6. Note that the true value of \u03c6 depends on the true cell counts generated for each individual dataset.Table\u2009N was less than the lower bound of the interval under the IGN-C method for every occurrence of the interval not covering N. This indicates that the IGN-C method over-estimates the population size under the chosen two true data-generating models. The remaining methods, INC-C, REM-C and MY-C, all perform fairly well. As expected, the MY-C method performs in a more satisfactory manner when the true data-generating model is a decomposable model, that is, for model (ii). The INC-C and REM-C methods perform very similarly. However, the INC-C method has the advantage of being able to estimate \u03c6.In terms of coverage, the IGN-C method performs poorly. Further investigation shows that the true value of In terms of the mean lengths of the intervals, the INC-C and REM-C methods perform similarly again with, typically, the INC-C intervals being slightly shorter, that is, more precise. This supports our intuition, that by removing the censored data-source, we would be discarding information. However, the actual different in mean lengths between the INC-C and REM-C methods is small. Typically, the MY-C intervals are slightly wider than the INC-C and REM-C intervals, and this difference is more obvious under the decomposable model (ii).We further compare the INC-C, REM-C and IGN-C methods using the Scotland PWID multi-list data in Section 3.\u03c72 statistic and its associated Bayesian p-value (Section 3.1). In a similar analysis of multi-list data from England, King et al. We apply the proposed methodology (INC-C) from Section 2 to the Scotland PWID multi-list data for 2003, 2006 and 2009. For comparison, we also conduct two additional analyses for each dataset: (i) the approach of p-value \u03c72 statistic on the observed cell entries, yO, as the discrepancy function. We take a pragmatic approach whereby a Bayesian p-value in the interval  indicates no lack of a goodness-of-fit to the data of the model-averaging approach. For the INC-C analyses, we obtain Bayesian p-values of 0.15, 0.44 and 0.30 for years 2003, 2006 and 2009, respectively; for the IGN-C analyses, values of 0.09, 0.27 and 0.08, respectively; and for the REM-C analyses, values of 0.06, 0.28 and 0.12, respectively. Thus, for all analyses, the Bayesian p-value suggested an adequate goodness-of-fit for each method. Therefore, these do not suggest that the IGN-C modelling approach that ignores censoring is inadequate, but these assessments use the same false assumption as the model does, that is, that all individuals observed by the HCV diagnosis data-source are current PWID.In order to assess overall goodness-of-fit of the four data-source analyses, we calculate the (model-averaged) Bayesian The corresponding posterior estimates for the total population size for current PWID are provided in Table\u2009Figure\u2009Table\u2009Table\u2009For 2003 and 2006, the IGN-C analysis lends additional support for a further one interaction terms being present (i.e. posterior model probability\u2009>\u20090.75); for 2009, a further six interaction terms have strong positive support, whereas the interaction term S2\u2009\u00d7\u2009S4  loses posterior support. For the interactions identified under the IGN-C method, the sign of the posterior mean of the data-source\u2009\u00d7\u2009data-source interactions are all positive, which leads to the increased population estimates.Finally, for all interactions where it is deemed that there is positive evidence that they are present, except the S1\u2009\u00d7\u2009S3  interaction discussed earlier, the sign of the posterior means of the interactions were consistent across all years and analyses.As stated, an advantage of the INC-C analysis over the REM-C method is that it allows us now to consider the proportion of individuals identified by the HCV diagnosis data-source as having a risk factor of injecting who are actually current PWID (i.e. members of the target population).Because of the initiative (Section 1.1) to encourage former PWID, born in 1956\u20131975, to be tested for HCV diagnosis, we consider the posterior distribution of the proportion of current PWID for the two different age groups. Table\u2009a and b, which specify the prior distribution for \u03c32 (Section 2.3), we repeat the INC-C analysis for a range of values of these hyperparameters. To do this, we fix a\u2009=\u20090.001 and vary b according to the expectation of the prior sample size 1\u2009/\u2009\u03c32. We choose b\u2009=\u20090.004,0.002 and 0.0005 corresponding to expectations of the prior sample size of 4, 2 and 0.5, respectively. Additionally, we also use the Gelman prior \u03c3 so that a\u2009=\u2009\u2212\u20091 and b\u2009=\u20090 in the full conditional distribution of \u03c32 given by 8. We compare the resulting posterior mean of the total population size under each of the four priors to the corresponding posterior mean under the prior specified in Section 2.3 where a\u2009=\u20090.001 and b\u2009=\u20090.001, for each year. In each case, the resulting posterior mean is within 4% of the corresponding mean for when a\u2009=\u20090.001 and b\u2009=\u20090.001. Note that the posterior means under the four priors are given in Table S1 of Section 4 of the Supporting information, along with 95% HPDIs.To investigate the sensitivity of the analysis to the values of the hyperparameters, Within standard capture-recapture studies, it is assumed that all individuals that are observed by the data-sources are members of the target population of interest. If this is not the case, the results obtained can lead to biased population estimates. For the data studied within this analysis, the HCV diagnosis database identified as PWID those who had listed injecting as their HCV risk factor, thus including former PWID in addition to the target population of current PWID. In such instances, one possibility is simply to remove such data-sources from the capture-recapture analyses. However, this may remove a significant amount of information that is contained within the data-source(s). In this paper, we have accounted for the possibility of censoring occurring for a single data-source  by explicitly accounting for the censoring within the modelling structure for the HCV diagnosis database.In particular, we considered estimating the total number of current PWID in Scotland in the years 2003, 2006 and 2009 allowing for censoring for the HCV diagnosis database and compared this with the analyses that ignored the potential censoring issue or removed the HCV diagnosis database and considered only three data-sources. Consistently, the analyses that ignored the issue of the HCV diagnosis database observing a mixture of former and current PWID led to significantly larger estimates for the total population size than the other two approaches that accounted for this (either by directly modelling the censoring or simply removing the given data-source). This conclusion was confirmed by the simulation study in Section 2.5.The approach of removing the HCV diagnosis data-source produced remarkably similar posterior estimates to that of incorporating the censoring. However, the analysis incorporating censoring allowed us to estimate the proportion of those present on the HCV diagnosis database with a history of drug use who are actually current PWID and identify interactions involving the HCV diagnosis data-source. Both of these are of interest to epidemiologists.We divide the remainder of this concluding section into two parts. In Section 4.1, we discuss ways in which the proposed modelling approach that incorporates censoring can be extended by considering a larger model space, p-value. This may not always be the case and we may need to consider a larger set of models, In this section, we discuss two ways in which the modelling approach, given in Section 2, can be extended. First, in Section 3, the maximal model was specified as the model containing all of the two-way interactions. This gave sufficient complexity to obtain an adequate model according to the Bayesian his case . The MCMzi, on the censored cell count, yi, for each cross-classification of covariates, is uniform, namely, Second, in this paper, we considered uninformative censoring, that is, the distribution of the upper bound, \u03c8i, of individuals, within each cross-classification, i, of covariates, observed solely by the HCV diagnosis data-source who are currently PWID. One way to incorporate this is to assume that We may actually have some prior information on the proportion, zi is the random variable of the number of trials given yi successes and a probability of success \u03c8i. In this context, the number of trials is the number of individuals observed solely by the HCV diagnosis data-source and the number of \u2018successes\u2019 is the number of current PWID. The prior information on \u03c8i may be in the form of a point estimate or encoded in a prior distribution, for example, a beta distribution.where NB denotes the negative binomial distribution We found that Scotland's number of current PWID had risen between 2003 and 2006 but decreased by 2009. This is good news in public health terms but celebration should be cautious because cessation from injecting need not mean that the individuals concerned have ceased opiate dependency. The dramatic decrease in Scotland's number of current PWID between 2006 and 2009, including among those aged 35\u2009+\u2009\u2009years ."}
+{"text": "The following information is missing from the Funding section: This study was supported by the A*MIDEX project (n\u00b0 ANR-11-IDEX-0001-02) funded by the \u00ab Investissements d\u2019Avenir \u00bb French Government program, managed by the French National Research Agency (ANR). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript."}
+{"text": "Recently, the study of the fractional formal  has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator  The subject of fractional calculus  has acquired significant popularity and major attention from several authors in various science due mainly to its direct involvement in the problems of differential equations in mathematics, physics, engineering and others for example Baskonus and Bulut , Yin et\u00a0l-Oboudi . Severaljafzadeh  investigf et\u00a0al.  gave soml-Ashwah  used S\\dz et\u00a0al.  investigz et\u00a0al.  defined z et\u00a0al.  defined In this paper, we define a generalized mixed integro-differential operator f of form (Let mentclass2pt{minima et\u00a0al.  introduca et\u00a0al. . Now, leS\u0103l\u0103gean  and whenl-Oboudi . Afterwaf, which satisfies the followingf which satisfies the followingf is said to be in the class positive real numbers, Let ivastava , Dixit aivastava  and receivastava . Let a ft}k=0 in . For \\dond Breaz . Also, tFor y Frasin .For nd Breaz .For z et\u00a0al. . In partd Pescar .For r et\u00a0al. . In partlexander .We start our first result.Letbe positive real numbers, Ifandthen the integral operatorgiven by (is in the classwhereOn successive differentiation of Let Letbe positive real numbers. Ifandthenis in the classwhereLetbe positive real numbers, We assume thatare starlike functions by orderand that isandIfthengiven by (is in the classwhereBy following same methods as in Theorem 1, we haveition in , we haveBy setting Letbepositive real numbers, We assume thatandIfIn geometric function theory, we defined and studied a new integro -differential operator"}
+{"text": "There are several methods of ITA available. The basic tool to compare such algorithms concerning their quality are large-scale simulation studies that are crucially set up on a large collection of quasi-orders. A serious problem is that all known ITA algorithms are sensitive to the structure of the underlying quasi-order. Thus, it is crucial to base any simulation study that tries to compare the algorithms upon samples of quasi-orders that are representative, meaning each quasi-order is included in a sample with the same probability. Up to now, no method to create representative quasi-orders on larger item sets is known. Non-optimal algorithms for quasi-order generation were used in previous studies, which caused misinterpretations and erroneous conclusions. In this paper, we present a method for creating representative random samples of quasi-orders. The basic idea is to consider random extensions of quasi-orders from lower to higher dimension and to discard extensions that do not satisfy the transitivity property.Dependencies between educational test items can be represented as quasi-orders on the item set of a knowledge domain and used for an efficient adaptive assessment of knowledge. One approach to uncovering such dependencies is by exploratory algorithms of  Orders play an important role in various formal theories of behavioral, social, economic, or computer sciences. Examples are in decision making and preference modeling  as a cornerstone concept in the educational or psychological theory of knowledge or learning spaces  i \u2264 j is interpreted as stating \u201cEach subject who is able to solve item j is also able to solve item i.\u201d As an example, a plausible dependency to postulate between the two algebra items \u201ca. Perform the multiplication 4x4y4\u00b7 2x \u00b7 5y2and simplify\u201d and \u201cb. Find the greatest common factor of the expressions 14t6y and 4tu5y8and simplify\u201d is to assume that the mastery of problem a is a prerequisite for the mastery of problem b. Thus, the items a and b are in relation with respect to a quasi-order \u2264, denoted by a \u2264 b.Prerequisite relations can be modeled using quasi-orders. In knowledge or learning space theory, a quasi-order \u2264 on a test or item set item tree analysis . We call X a representative subset or sample if P(\u22641 \u2208X) = P(\u22642 \u2208X) for any two quasi-orders \u22641 and \u22642 on Q, where P denotes probability. Since this definition is for arbitrary quasi-orders, as a corollary, we obtain that any such representative set X of quasi-orders must also be \u201cproportionally representative\u201d for the population distributions of quasi-order size, quasi-order width, and quasi-order height (defined below), in the sense that the corresponding sample distributions computed in X provide unbiased estimates of their population analogs. The latter distributional properties are the evaluation criteria used for assessing the extent of representativeness in this paper.Let In \u00dcnl\u00fc and Schrepp , it was In the next section, we discuss existing approaches to addressing this problem and the critical issues related with these. In a next step, the description of the proposed algorithm is given, and then simulation results are presented demonstrating the usefulness of the sampling procedure. Finally, we conclude with a summary and further related remarks.Q of n test items. The goal is to create randomly a sample, PQO(n), of quasi-orders that is representative, in the sense that each quasi-order on Q is included in the sample with the same probability.Formally, the problem we address in this paper can be described as follows. Presuppose a set R on Q (not necessarily reflexive or transitive) is denoted by a matrix (rij) with rij\u2208 {0, 1} and rij = 1 \u21d4 iRj.We use the relational matrix notation, i.e., a binary relation R mean that its corresponding relational matrix satisfies the following properties:rii = 1 for all i = 1, \u2026, n (reflexive R),rij = 1 \u2227 rjk = 1 \u2192 rik = 1) for all i,j,k \u2208 {1, \u2026, n} (transitive R)., where rii = 1 for all i = 1, \u2026, n, and the other values rij are chosen with equal probability from {0, 1}.Create a relational matrix  quasi-orders, we can see in Table n the chance to pick a transitive relation using this random process is tiny.This method, directly operating on all items simultaneously, also fails even for moderate sizes of n = 6 items requires to select ~50,000,000 random reflexive relations, i.e., 1,500,000,000 random 0\u20131-numbers. If we would be able to generate and check 1000 reflexive relations per second, it would require ~50,000 s until the process stops. It is obvious that this will not work at all for larger item numbers, for example for n = 10. In contrast, the processing times of the newly proposed procedure are feasible and the results can be found in the section Creating Quasi-orders on Bigger Item Sets.Thus, finding for example 10,000 quasi-orders on ad-hoc procedures to draw random quasi-orders. Although these methods are very flexible and virtually work for any value of n, they lack representativeness in their generation processes. The simplest method is to create a random relation on n items and to compute the transitive closure of this relation. It was found in earlier publications  such that:rii = 1 for all i = 1, \u2026, n.rij with i, j = 1, \u2026, n and i \u2260 j, the value rij is chosen randomly with probabilities P(rij = 1) = x and P(rij = 0) = 1\u2212x. The probability x itself is a realization of a normal distribution with parameters \u03bc = 0.16 and \u03c3 = 0.06. Values \u201c< 0\u201d or \u201c> 0.3\u201d are set to 0 or 0.3, respectivelyFor all rij) is the resulting random quasi-order.The transitive closure of the binary relation corresponding to  of m quasi-orders on n items and assume that PQO(n) is representative, in the sense that each quasi-order on the n items is contained in this set with the same probability. Thus, PQO(n) can be seen as a random sample drawn from the set of all quasi-orders on n items. In the induction step, we create for each quasi-order in PQO(n), subsequently represented by its relational matrix (qij), a number of z random extensions to n + 1\u2014i.e., each random extension of (qij), denoted as the matrix . Duplicates are removed, i.e., each quasi-order occurs only once in PQO(n + 1). Regarding the choice of z, note that the chance a random extension of a quasi-order on n items again yields a quasi-order on n + 1 items decreases with increasing item number n. Thus, higher values for z must be used when n is getting larger, and in particular, this number must be adjusted depending on the number of quasi-orders that should be created during simulation. A general strategy easily possible is to specify z in a way such that slightly more quasi-orders than desired are generated. In a final step of the procedure, PQO(n + 1) is reduced to a required or reasonable size, for example by keeping only m randomly selected elements from PQO(n + 1) based on simple random sampling. This step is necessary to have the number of elements of the PQO(n)'s reasonably limited, if this process is repeated several times; for instance, when creating a sample consisting of 1000 quasi-orders on 10 items starting with the set of all four quasi-orders on two items.The This inductive algorithm produces representative samples of quasi-orders.Proposition. Let \u22641 and \u22642 be any two quasi-orders on n + 1 items. Denote by P1 and P2 the probabilities that \u22641 and \u22642 are contained in the set PQO(n + 1) that is generated according to the proposed inductive procedure, respectively. Then, P1 = P2.Proof. The proof is by induction. As its anchoring, the algorithm always starts with a representative set of quasi-orders for a sufficiently small item number l. We consider the inductive step from n\u2265l to n + 1. Let \u2264i, n be the traces of \u2264i  on the n items of the predecessor construction step, that is, the quasi-orders restricted to those n items. Since PQO(n) constructed in the predecessor step n is assumed to be representative in the sense we defined (the induction hypothesis), the probabilities for the two traces to belong to PQO(n), in respective order, Pn1,  and Pn2, , are the same. Moreover, all random extensions (to the n + 1 items) of any given trace quasi-order (on the n items) are equally likely, with the same probability of 2n\u22122 and independent of the trace quasi-order considered. Thus, Pn2,  = P2.To assess the quality of the algorithm used to create random quasi-orders we performed a first simulation study. In the study, we generated 100 random samples each of (sample sizes) 100, 1000, and 5000 quasi-orders on a set of six items, which were compared with the set of all possible quasi-orders concerning their distributions of important properties.Size: The size of a quasi-order \u2264 is defined as the number of item pairs  with i \u2264 j.Width: The size of a longest anti-chain in \u2264 : An anti-chain is a subset of items {i1, \u2026, ik} with \u00ac(ix \u2264 iy) for all x, y \u2208 {1, \u2026, k} .Height: The size of a longest chain in \u2264 : A chain is a subset of items {i1, \u2026, ik} with i1 \u2264 i2\u2227 \u2026\u2227 ik\u22121 \u2264 ik.We use the following properties as the criteria for representativeness of the samples.n = 6 items. The computations reported in this paper were done with a C program that implements the described algorithm on a computer with an Intel Core i5 2.50 GHz processor.The sampling process started with the set of all four quasi-orders on a set of two items. The inductive procedure described in the last section was then employed to create random quasi-orders on If we compare the mean values of the average sizes, widths, and heights taken over the 100 generated samples, we see that the results approximate the true values calculated for the set of all quasi-orders on six items very well . For example, linear orders are a special case of quasi-orders and, as pointed out by Augustin Kelava, may be useful in the analysis of item position or item order effects in large-scale assessments. Knowledge or learning space theory combinatorial structures or computational ITA analyses could be utilized to study these effects. Future research into this issue is needed.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "The aim of the study was to verify if there is any association between exposure to Cu, Zn, Cd, Pb, As and the formation of malondialdehyde (MDA), 8-hydroxydeoxyguanosine (8-OHdG), advanced oxidation protein products (AOPP), and whether in this process cigarette smoking plays a role. The investigations were performed in the 352 smelters occupationally exposed to heavy metals and 73 persons of control group. Metals concentration was determined by atomic absorption spectrometry. MDA and AOPP concentrations were determined by spectrophotometric methods. The concentration of 8-OHdG was determined by ELISA method. It was demonstrated an increased Cu concentration in smoking smelters compared to non-smoking control group. It was noted no differences in Zn and Mg concentrations between the examined groups. Pb concentration was more than sixfold higher in the group of smoking smelters and about fivefold higher in the group of non-smoking smelters compared to the control groups (smokers and non-smokers). It was shown that Cd concentration in the blood was nearly fivefold higher in the smoking control group compared to the non-smoking control group and more than threefold higher in the group of smoking smelters compared to non-smoking. It was shown an increased As concentration (more than fourfold) and decreased Ca concentration in both groups of smelters compared to control groups. In groups of smelters (smokers and non-smokers), twofold higher MDA and AOPP concentrations, and AOPP/albumin index compared to control groups (smokers and non-smokers) were shown. Tobacco smoke is the major source of Cd in the blood of smelters. Occupational exposure causes accumulation of Pb in the blood. Occupational exposure to heavy metals causes raise of MDA concentration and causes greater increase in AOPP concentration than tobacco smoke. E (NO3\u2212) , 5. Comp (NO3\u2212) . These s. E , which is also generated in the process of biosynthesis of prostaglandins. MDA can be transmitted to distant tissues and, thanks to the possibility of forming covalent bonds with other molecules, modifies their structure, and consequently, changes its properties. MDA has high cytotoxicity, is mutagenic, and inhibits the activity of various enzymes, leading to inhibition of DNA replication, transcription, and breathing , 7. MDA Exposure of proteins to reactive oxygen species results in modification of amino acid residues, what alters protein structure and function . The chaAlbumin is a major protein of blood plasma, where it constitutes about 55\u00a0% of all proteins. This protein is also a major and predominant antioxidant in plasma . The abiThe oxidation of proteins, including albumin, leads to the formation of permanent products, which vary in terms of structure, function, and physicochemical properties. These are known as an advanced oxidation protein products (AOPP) . AlthougThe aim of the study was to verify if there is any association between exposure to metals  occurring in the work environment of smelters and the formation of MDA, 8-OHdG, and AOPP and whether in this process cigarette smoking plays a role. The influence of the exposure to heavy metals and tobacco smoke on the concentration of Ca and Mg also was analyzed.The investigations were performed in the whole blood, serum, plasma, and urine of 352 males working in the copper foundry and 73 healthy men, non-exposed occupationally to heavy metals, who were qualified as control group by clinician of primary medical care. The study protocol was approved by Local Bioethics Committee of Wroclaw Medical University (Nr KB: 469/2008). The study population was in similar age and similar BMI. Table\u00a02 , immediately gently mixed, and centrifuged . The obtained serum, plasma, and whole blood were portioned and stored in sealed tubes . Blood samples of smelters and persons of control groups were stored at \u221280\u00a0\u00b0C until analysis.Venous blood was collected in the morning, after 12-h fasting. Serum was obtained according to the standard procedure by taking venous blood for disposable trace element-free tubes  with serum clotting activator, left at 25\u00a0\u00b0C to complete thrombosis, and centrifuged . In order to obtain plasma, blood was collected into trace element-free tubes containing EDTA-KThe urine was collected in the morning, according to the standard procedure. Subjects were asked to wash their hands before supplying the urine, in order to reduce contamination. Urine samples were stored in special container containing liquid nitric acid at \u221220\u00a0\u00b0C until determination.3 for acidification) was determined by FAAS method with snap Phillips PU 9360, used for hydride generation. In this method, wavelength \u03bb\u2009=\u2009193.7\u00a0nm deuterium background correction and quartz atomization chamber were used.Concentrations of metals were determined using Solaar M6 aparatus . The Pb concentration in whole blood (Pb-B) was determined by graphite furnace atomic absorption spectrometry (GFAAS) in the graphite Massman cuvette, the absorbance measurement at wavelength \u03bb\u2009=\u2009283.3\u00a0nm, with Zieeman background correction. The reference material was used BCR-194, -195, -196, IRMM, EU. The Cd concentration in whole blood (Cd-B) and in urine (Cd-U) was determined by the same method at wavelength \u03bb\u2009=\u2009228.8\u00a0nm, with Zieeman background correction. The concentration of Zn and Cu in serum (Zn-S and Cu-S) was determined by flame atomic absorption spectrometry (FAAS) in air-acetylene flame at wavelength \u03bb\u2009=\u2009324.8\u00a0nm. The reference material was used Single-Element Zinc (Copper), standard 1000\u00a0\u03bcg/ml, CPI International. The determination of Ca and Mg concentrations in serum (Ca-S and Mg-S) was also performed by this method at wavelength \u03bb\u2009=\u2009422.7\u00a0nm for Ca and \u03bb\u2009=\u2009285.2\u00a0nm for Mg, with deuterium correction of the glass. As a reference material for these metals was used Seronorm\u2122 Trace Element Serum . The As concentration in urine (As-U) . The cotinine determination was carried out by the method described earlier , 29.5\u00a0M\u22121\u00a0cm\u22121). The MDA intensity was measured by spectrophotometric method at \u03bb\u2009=\u2009535\u00a0nm. The concentrations of MDA were expressed as micromoles per liter in plasma.Lipid peroxidation was measured in plasma by measuring the formation of thiobarbituric acid reactive substances (TBARS), quantified as malondialdehyde (MDA) equivalents, according to the method described earlier , 31. The2O. The next step, 200\u00a0\u03bcl blocking buffer was added and incubated at room temperature for 1\u00a0h. Fifty microliter of samples and 8-OHdG standards were added. After 10\u00a0min of incubation, monoclonal anti-8-OHdG was added , washed three times followed by addition of secondary antibody conjugated to horseradish peroxidase . The plate was washed three times with washing buffer and to each well 100\u00a0\u03bcl of substrate for peroxidase was added and incubated for 20\u00a0min. Followed by the addition of 100\u00a0\u03bcl of reaction stop solution. A spectrophotometric measurement of absorbance was performed at a wavelength \u03bb\u2009=\u2009450\u00a0nm. The content of 8-OHdG in the tested samples was calculated by comparison with a standard curve determined from standards treated similarly to the samples tested.To evaluate the concentration of 8-OHdG in the serum, a commercial test OxiSelect\u2122 DNA Oxidative Damage ELISA Kit was used . To 96-well plate, 100\u00a0\u03bcl of conjugate 8-OHdG/BSA was added and incubated overnight at 4\u00a0\u00b0C, and then washed with HDetermination of AOPP-P concentration was performed by spectrophotometric method developed by Witko-Sarsat et al. , based o280\u00a0nm0.1\u00a0%\u2009=\u20090.5). To make the standard curve, the standard solutions at concentrations 0, 11.3, 22.6, 33.9, 45.2, 56.5\u00a0g/l were prepared, which were obtained by the dilution of albumin in PBS.Alb-S concentration was determined by using the bromocresol purple (BCP) , which reacts with albumin in phosphate buffer saline (PBS) at pH\u2009=\u20096.8. The concentration of albumin standard  was determined using the molar absorption coefficient , serum sample, or albumin standard were added and mixed. All samples were incubated for 5\u00a0min at 25\u00a0\u00b0C. Absorbances of the standards and of the samples were measured against the blank sample (working reagent) at wavelength \u03bb\u2009=\u2009603\u00a0nm. The increase in absorbance was proportional to the concentration of albumin in the sample.p\u2009<\u20090.05.Statistical analysis was carried out using the program Statistica 10.0. Data about examined groups, BMI, age, years of work in smeltery, and cotinine concentration, were analysed using ANOVA Kruskal\u2212Wallis test. The concentration of metals , MDA-P, 8-OHdG, AOPP-P, albumin, and the value of AOPP/albumin index also using the same test were analyzed. In order to verify the association between parameters , the multiple linear regression models were performed. Statistical significance was accepted for In this study, the concentrations of Cu, Zn, Ca, and Mg in serum; Pb and Cd in whole blood; and Cd and As in urine were determined Table\u00a0. In the In both smoking and non-smoking smelters, a significant increase in the concentration of Pb in the blood (Pb-B) compared to the control group (smokers and non-smokers) was observed. In the group of smoking smelters, 6-fold increase in Pb-B concentration in comparison to the smoking control group and 7.4-fold higher in relation to the non-smoking control group were observed. In the group of the non-smoking smelters, 5.7-fold higher Pb-B concentration compared to the non-smoking control group was observed. The concentration of Cd in the blood (Cd-B) was significantly higher at smokers (both the smelters and the control group) compared to non-smokers. In the blood of smokers (both the smelters and the control group), 3.3-fold higher Cd concentration compared to the non-smoking smelters and 4.8-fold higher compared to the non-smoking control group were observed.In the group of smoking smelters, 2.5-fold higher concentration of Cd in urine (Cd-U) compared to the non-smoking control group was observed. In the urine of smoking and non-smoking smelters, As concentration (As-U) was significantly higher compared to control groups (both smokers and non-smokers). In the smelters (smoking and non-smoking), more than 4-fold higher of As-U concentration in comparison to the smoking control group and more than 4.6-fold higher compared to the non-smoking control group were observed.In the groups of smelters (smokers and non-smokers), 2-fold higher MDA-P concentration compared to control groups  was shown Table\u00a0. HoweverIn the plasma of smoking and non-smoking smelters, 2-fold higher of AOPP-P concentration in comparison to the smoking control group and 2.2-fold higher compared to the non-smoking control group was shown Table\u00a0. There wAOPP/albumin index, which is expressed in micromole as the amount of AOPP per gram of albumin, was calculated. In the group of smoking smelters, 1.7-fold increase in the value AOPP/albumin index compared to the smoking control group and 3-fold increase of this parameter compared to the non-smoking control group was observed. 2.3-fold increase in the value of AOPP/albumin index in the non-smoking smelters compared to non-smoking control group was observed . The correlation of Pb-B and AOPP-P concentrations , and the AOPP/albumin index  in this group also were shown.In the serum of non-smoking smelters, the correlation was demonstrated between the concentration of Cu-S and Alb-S  compared to controls (99.7\u2009\u00b1\u200912.1\u00a0\u03bcg\u00a0%) . Also, iBizo\u0144 et al. (2013) demonstrated that exposure to heavy metals causes an increase of Pb-B concentration . Higher Cd-B and Cd-U concentrations increase during exposure to tobacco smoke, that was observed by other scientists. Bizo\u0144 et al. (2013) demonstrated an increase in Cd-B concentration of smokers compared to non-smokers, both in the control group and the group of smelters  . In otheAn increase of As-U concentration in the group of persons occupationally exposed to heavy metals (18.9\u2009\u00b1\u200922.2\u00a0\u03bcg/g creatinine) in comparison to the control group (3.5\u2009\u00b1\u20093.0\u00a0\u03bcg/g creatinine) was observed . Bizo\u0144 eThe concentrations of Ca and Mg macroelements, which values have a significant impact on the reduction of the penetration capability of some toxic metals, such as Cd and Pb were also determined. The demonstrated differences in Ca-S concentration between the groups of smelters and control groups (both smokers and non-smokers) confirm that exposure to heavy metals causes a decrease Ca-S concentration. These results are similar to the study made by Kossowska et al., where was demonstrated a difference between Ca-S concentration in the group of smelters (90.4\u2009\u00b1\u20097.3\u00a0\u03bcg/ml) and the control group (99.3\u2009\u00b1\u20094.1\u00a0\u03bcg/ml) . In our Chronic exposure to heavy metals causes their accumulation in tissues and has the influence on the human health \u201350. It wThere was observed significantly higher plasma MDA levels (2.67\u2009\u00b1\u20090.69\u00a0\u03bcM) of workers exposed to lead than those in the control group (1.23\u2009\u00b1\u20090.61\u00a0\u03bcM) . HoweverBarbato et al. (2010) conducted a meta-analysis in environmental pollution exposed employees and in five studied groups, increase of 8-OHdG in the urine was observed, and in three studied group, there was no effect . Gar\u00e7on It should be noted that AOPP concentration depends on many physiological and environmental factors, which may influence on the examined population  \u201359. The There are some studies demonstrating the impact of cigarette smoking on the formation the changes in the structure of proteins. It was shown an increase in the amount of carbonyl groups in the molecules of proteins, which are the component of AOPP. A difference in the amount of carbonyl groups was shown between the group of persons, which were intensive smokers (4.00\u2009\u00b1\u20091.31\u00a0nmol/mg protein) and the persons not exposed to tobacco smoke (0.80\u2009\u00b1\u20091.94\u00a0nmol/mg protein) . HoweverBecause of the fact that in the composition of AOPP is mainly the products of albumin\u2019s oxidation; the determination of this protein in the serum of smelters was an important element of this study. On the concentration of AOPP, it has an influence not only in many factors discussed above, but also the concentration of albumin in the blood of the examined persons, which were in reference range (35\u201355\u00a0g/l) . For thiIn this study, it was demonstrated that an important factor influencing AOPP-P concentration is occupational exposure to heavy metals, especially Cu. The inverse correlation between Cu-S and Alb-S concentration may indicate the participation of Cu in the formation of AOPP and its oxidation effect on albumin. In the group of non-smoking smelters, it was demonstrated the correlation between the concentration of Pb-B and AOPP-P, and the value of AOPP/albumin index. This may indicate that high Pb-B concentration is an oxidation factor for proteins. These results suggest that Cu and Pb play an important role in protein oxidation. Cu can generate free radicals by Fenton reaction. Additionally, Pb can replace Cu in antioxidant enzymes that causes an increase in serum Cu concentration and intensifies an oxidative stress.In this study, it was confirmed the influence of heavy metals exposure on lipids peroxidation. It indicates that occupationally exposure can have an important role in lipid degradation and cell damage. It was not observed any effect of heavy metals exposure or cigarette smoking on oxidative modification of DNA. It was shown that cigarette smoking and occupational exposure to heavy metals have an influence on protein oxidation. These oxidizing factors of which the source is the environment seem to be important for destruction of protein molecule and limit its function.In this study, it was confirmed that tobacco smoke is the main source of Cd in the blood of smelters. The occupational exposure on heavy metals has no influence on Cd-B and Cd-U concentrations. With the increasing exposure to tobacco smoke and heavy metals, Ca concentration in serum was decreased.Exposure to heavy metals causes an increase of heavy metals concentrations in the blood, especially Pb-B, but also Cu-S and As-U of smelters. This oxidizing factor intensifies lipids peroxidation and causes an increase in MDA concentration, but they have no influence on DNA. The intensity of AOPP formation depends on the type of factor that it causes\u2014for smelters, occupationally exposure to heavy metals is a stronger oxidation factor than tobacco smoke. The strongest oxidation effect on the protein has Cu and Pb."}
+{"text": "Under a Markov model of evolution, recoding, or lumping, of the four nucleotides into fewer groups may permit analysis under simpler conditions but may unfortunately yield misleading results unless the evolutionary process of the recoded groups remains Markovian. If a Markov process is lumpable, then the evolutionary process of the recoded groups is Markovian.ad hoc test statistic, which is based on an index that is evaluated using a bootstrap approximation of its distribution; one that is based on a test proposed specifically for Markov chains; and one using a likelihood-ratio test. We show that the likelihood-ratio test is more powerful than the index test, which is more powerful than that based on the Markov chain test statistic. We also show that for stationary processes on binary trees with more than two taxa, the tests can be applied to all pairs. Finally, we show that if the process is lumpable, then estimates obtained under the recoded model agree with estimates obtained under the original model, whereas, if the process is not lumpable, then these estimates can differ substantially. We apply the new likelihood-ratio test for lumpability to two primate data sets, one with a mitochondrial origin and one with a nuclear origin.We consider stationary, reversible, and homogeneous Markov processes on two taxa and compare three tests for lumpability: one using an Recoding may result in biased phylogenetic estimates because the original evolutionary process is not lumpable. Accordingly, testing for lumpability should be done prior to phylogenetic analysis of recoded data. RY-recoded nucleotide sequences, and Gibson et al. [Y-recoded nucleotide sequences. Before these studies, other investigators had used RY-recoded nucleotide sequences to infer the evolutionary relationships among mammals [When nucleotides intentionally are recoded to a 3- or 2-state alphabet in order to focus on a subset of the possible types of substitutions  or ren et al. , who dev mammals -3 and am mammals .Recoding of nucleotides and/or amino acids has been used repeatedly in recent phylogenetic studies -31. HoweIn this paper, we take a first step by considering tests for lumpability in a Markov model of evolution for pairs of homologous nucleotide sequences  into one or two new states --in molecular phylogenetics, this procedure has been called recoding [Let recoding . Table 1e NC-IUB . The 13 n independently evolving sites, which have diverged under Markovian conditions from their common ancestor on a rooted, 2-tipped tree. Let \u03c00 denote the initial probability vector of the nucleotide frequencies, such that A, G, C, T . Over each edge of this tree, there is a substitution process, X(t) and Y(t), respectively, described by the transition probabilitiesConsider two nucleotide sequences, A and B, each with andijf(t) denote the theoretical joint probability of a site being in state i in A and state j in B at time t:Let F(t) = {ijf(t)} denote the joint probability matrix and let PX(t) and PY(t) denote the transition probability matrices of X(t) and Y(t). In practice, the two matrices cannot be identified from F(t) without some assumptions about the evolutionary processes of the sequences A and B. We assume that the processes are globally stationary, reversible, and homogeneous (SRH)  = PY(t) = P(t) and, if X \u03c0and Y \u03c0denote the equilibrium probability distributions of the processes X(t) and Y(t), take X \u03c0= Y \u03c0= \u03c00 = \u03c0 and write \u03a0 = diag(\u03c0). Then, from (1), we get F(t) = P(t)T\u03a0P(t). The transition probability matrix can be expressed by an instantaneous rate matrix R, such that P(t) = eRt, where ij \u2265 R0 for i \u2260 j, T\u03c0R = 0T, where T \u03c0is the equilibrium distribution of R [R = S\u03a0, where S is a symmetric matrix with ij \u2265 s0 for i \u2260 j, and R and P(t) can be written in terms of the eigenvector decomposition of \u03a0/21S\u03a0/21 = L\u039bLT. In other wordsNow, let ons, see -39, and,ons, see ). Given ion of R . Further4sij\u03c0j/\u03c0i. The matand\u039b is a diagonal matrix with columns containing the eigenvalues of \u03a0/21S\u03a0/21 and L is a matrix with columns containing its right eigenvectors. The joint probability matrix is then symmetric andwhere S ) and three free parameters for \u03c0 ; its expected value is thus E(N) = nF(t). Because the parameters s and \u03c0 are in a one-to-one relation with the elements of F, the maximum-likelihood estimates of s and \u03c0 can be obtained from the eigenvector decomposition of Let andwhere q <4, such that a lumped process, The following probabilities can be defined for any given and initial probabilities \u03c0, the lumped process, defined in (7), is a Markov chain whose transition probabilities do not depend on the choice of \u03c0. A necessary and sufficient condition for X'(t) to be lumpable with respect to a partition i in X'(t) is lumpable, then the transition probabilities for X'(t) for any given pair of subsets in By definition ,42, a Mae i in Sk,42. AccoP'(t) can be expressed as a matrix function of P(t) as follows:If the Markov chain is lumpable, the lumped transition matrix V is a 4 \u00d7 q matrix, where q is the number of states in the lumped process, such that the l-th column of V is a vector with 1's in the components corresponding to states in l Sand 0's otherwise, andwhere q \u00d7 4 matrix whose k-th row is a probability vector with non-zero elements corresponding to the states in is a pability ,42 isIn the case of nucleotides, the second column of Table We note that under certain conditions, such as those considered by the JC  and F81 ad hoc test based on a parametric bootstrap for an index of departure from the lumpability condition [We consider three possible tests: An ondition ; a test ondition ; and a lFrom (8), if a Markov process is lumpable, thenshould have all elements zero. Consider the index proposed in :\u03b7 \u2265 0, with \u03b7 being 0 only under lumpable Markovian processes. Then, the hypothesis that the Markov process is lumpable is equivalent to the hypothesis H0 : \u03b7 = 0. From the observed divergence matrix, N of two homologous sequences, assuming a SRH Markovian model of evolution, an estimate H0, whereIt is clear that and B matrices can be generated by simulation under conditions of lumpability, where we take b \u2208 {1, \u22ef, B}, to be independent and multinomial with parameters n and The distribution of P-value is then the probability that we obtain a value as large as or larger than the observed P-value is the proportion of The true \u03c72 test to determine whether a Markov chain is lumpable with respect to a partition ijn}, to estimate the transition probabilities ijp, where ij nrepresents the number of transitions into state j from state i in one step, so the number of steps in the Markov chain is \u2022\u2022n, where the subscript \u2022 indicates summation. Now, if we start from our divergence matrix N, where ij nrepresents the number of sites that are in state i for sequence A and state j in sequence B, and the SRH assumptions are kept, either A or B can be assumed to be the original sequence at time 0, whereas the other one can be assumed to be the observed sequence at time 2 (since we took the edge lengths to be 1). Take A as the ancestral sequence, then the divergence matrix N has the same properties as a transition count matrix, and we can proceed as described in [i to A vailable . The tesribed in . A transl = 1, ..., q. From the definition of a lumpable process (7), if the Markovian process is lumpable with respect to where k \u03b3is the number of states that are part of the subset k = 1, ..., q. Therefore, H0 : i \u2208 N, estimates il gand where andwhere nd Baran  obtainedwhereandil \u2212 eil oare a stack of q tables of size 4 l \u00d7 \u03b3of mean-corrected multinomials with row and column sums equal to zero) that the test statistic is distributed under H0 as a \u03c72 variable with and showed ((1) = exp(S\u03a0) and {ijf} = F\u03c0,s)((1). These matrices are obtained as shown in (5) and (6). We also want to estimate  under the constraints imposed by the null hypothesis of lumpablity, H0. The constraints are given in the second column of Table where {A, such thatThis maximization needs a new approach. We construct an orthogonal matrix, y is the response constraint vector, defined such that two values of y are zero corresponding to the two constraints. The matrix A will, in the case of partitions into two groups of two, contain \u03c0, so to emphasise this possible dependence, write y = g(s|\u03c0). Also write s = A\u22121y = g\u22121(y|\u03c0). Thenwhere s, if dependent of \u03c0, are optimized given the original \u03c0 set, then the \u03c0 vector is optimized given the optimized values of s. This process is repeated until convergence is achieved.The optimization process is done in two steps: the values of LR, can be calculated withFrom these two log-likelihood values, a log likelihood-ratio, \u00d7 LR is distributed as a \u03c72 variable with 2 degrees of freedom.Under the null hypothesis of lumpability, 2 In order to check the accuracy of the tests under the null hypothesis, Monte Carlo simulations were done from a set of parameters that meets the assumption of lumpability. The parameter vectors in this case wereandn = 1500, 5000 divergence matrices were calculated by Monte Carlo simulations assuming that Ni is multinomial with parameters ) for i = 1, . . . , 5000.The joint probability distribution was calculated by the steps given in (2), (3), and (4); then, assuming a nucleotide sequence of length PP plot displaying the distribution of observed P-values, obtained from each test, plotted against the expected P-values, obtained from the uniform distribution. The linear relationship between these two sets of P-values  and values of s that yield increasing values of \u03b7, as in (9), generated 3000 divergence matrices using Monte Carlo simulation, and then calculated the three test statistics and their corresponding P-values, using the procedures explained above, for each value of \u03b7. The power at the 5% level, is then equal to the proportion of observed P-values less than 0.05.The power of each test was compared for each recoding scheme under non-lumpable conditions. To do this, we used RY recoding--similar power curves were obtained for the other 12 recoding schemes (results not shown). All of these results indicate that the likelihood-ratio test is the most powerful of the tests considered, followed by the Index test and, finally, by the Markov Chain test.Figure P-values. A PP-plot with these P-values should yield a straight line when the data are lumpable, and deviations from this expectation when the processes are not lumpable. However, the observed P-values are not independent, so we need to show that this condition is not cause for concern for the dots in a PP-plot to be on a straight line. We give a simplified argument taken from [P-values P1, . . ., nP, which, if all the null hypotheses are true, are identically distributed as uniform random variables on . Let p be any value between 0 and 1, let I(j < pP) take the value 1 if j < p Pand 0 otherwise, and let P-values less than p. Then E(I(j < pP)) = P (j < pP) = p and so the expected number of P-values less than p is E(pN) = np. This implies that the plot of the observed P-values will lie approximately on a straight line. The dependence will cause some clustering of the observed P-values but the PP-plot will remain useful in indicating whether there is evidence against some of the hypotheses.For general cases involving more than 2 homologous sequences, we can test for lumpability in all pairs of sequences by using the methods described above under the assumption that the evolutionary process is SRH over the whole tree . For example, in the case of an alignment with seven sequences, there will be 21 ken from . ConsidePP-plots shown in Figure RY recoding, on the tree shown in Figure The RY), then we can obtain Fq(t) = VTP(t)V and from this, using  and (4), we can further obtain the transition matrix of the process X'(t),If a process is lumpable with respect to a given recoding scheme  is not a Markov process and, although we can calculate Pq(t), it is not the transition matrix of the process X'(t).where P'(t) = UP(t)V can be defined and, if the process X(t) is lumpable, then P'(t) = qP(t). On the other hand, if X(t) is not lumpable, the elements of P'(t) are still given as P'(t) is no longer a transition matrix of X'(t). Conveniently, we can compare P'(1), the true conditional probability matrix at t = 1, with Pq (1), the false transition matrix at t = 1, thus allowing us to examine the effect of non-lumpability.In either case, the matrix T \u03c0=  and T s= . As can be seen from the \u03c0- and s-vectors, the lumpable condition is met for RY-recoding but not for KM-recoding. Figures RY- and KM-recoding schemes.Figure RY-recoded data is shorter than the corresponding edge in the tree obtained from the original data. However, because the original process was lumpable with respect to RY-recoding, the relative length of each edge in the two trees is the same, the difference being equal to a scale factorEvery edge in the tree obtained from the KM-recoded data is also shorter than the corresponding edge in the tree obtained from the original data, but the relative length of each edge in the two trees differ, the reason being that the process generating the original data was not lumpable with respect to KM-recoding.Every edge in the tree obtained from the Figures PP-plots from tests for lumpability for RY recoding, indicating non-lumpability, and AGY recoding, indicating lumpability.In a previous study , a set oPP-plot in Figure PP-plots from the likelihood-ratio test for lumpability for RY-recoding, showing strong evidence against lumpability, and for the SW-recoding, which provided the least evidence against lumpability. It is evident that no recoding should be applied to these data.In a previous study , a ~9.3kBias in estimates of phylogenetic parameters can occur when recoding of nucleotides or amino acids is used to transform data associated with models of evolution, which are not lumpable with respect to the recoding scheme used. A test proposed in this paper, which is based on a likelihood-ratio test, can yield an indication of whether the same results for estimable parameters can be expected from fitting a given model of evolution and its recoded version to the data.The authors declare that they have no competing interests.LSJ and JR conceived the project. KWL carried out the pilot study, showing that the Index test was feasible. VAVR and JR developed the tests and wrote the manuscript with input from LSJ and KWL. VAVR wrote the codes and generated the numerical results. All authors have read and approved the manuscript."}
+{"text": "One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ordered states with nearly degenerate energies without invoking special features of the Fermi surface. All of these self-consistent solutions have a pair density wave intertwined with a charge density wave and sometimes a spin density wave. Most of these states vanish in the underdoped regime, except for one with a large d-form factor that vanishes at approximately 19% doping of the holes, as reported by experiments. Furthermore, these states could be modified to have a global superconducting order, with a nodal-like density of states at low energy. Lax2\u2212SrxCuO4) cuprate family. For other cuprate families, the evidence for bond-centred unidirectional domains was found via scanning tunneling spectroscopy36789121414Ever since the discovery of the high-Tc superconductivity, many low-energy charge-ordered states in the cuprate have been discovered. Neutron scattering experimentst\u2009\u2212\u2009J model1415t\u2009\u2212\u2009J model and the validity of replacing the oxygen hole with a Zhang-Rice singletet al.22252627The existence of these great varieties of charge-ordered states has created a great debate regarding whether the strong coupling Hubbard model or the t\u2009\u2212\u2009J type models have revealed low-energy intertwined states appearing as stripes or bidirectional charge-ordered states, such as checkerboard (CB). However, these works usually involved different approximations and parameters, which often resulted in different types of charge-ordered patterns, and these studies were mostly concentrated at a hole concentration of 1/8, which is the most notable concentration in early experiments. Hence, it is not clear if these results were the consequence of the invoked assumption or the approximation used, or if they are a generic results in the phase diagrams of cuprates. There were attempts to produce these CDWs or PDWs using a different approach, such as using a mean field theory to study a t\u2009\u2212\u2009J-like model but taking the strong correlation as only a renormalization effect of dispersion222340YBa2Cu3O\u03b46+) compoundsFor quite some time, various calculations29303132333435363738t\u2009\u2212\u2009J model has several stripe states, with nearly degenerate energy as the uniform state and, with coexistent superconductivity and antiferromagnetism. When the number of variational parameters is extrapolated to infinity, the authors concluded that the anti-phase stripe, which has no net pairing, has slightly higher energy than the in-phase stripe with a net pairing, which in turn, also has slightly higher energy than the uniform state. This result is very consistent with the result of variational Monte Carlo calculationst\u2009\u2212\u2009J model30t\u2009\u2212\u2009J model with the variational approach using GWA.Amid all this confusion, recent numerical progress achieved by using the infinite projected entangled-pair states (iPEPS) methodt\u2009\u2212\u2009J model. We find many unidirectional and bidirectional charge-ordered states with nearly degenerate energies as the uniform state, especially in the lightly doped regime; thus, it is a much more general phenomenon than previously thought. All of these states have intertwined orders of PDW, CDW and/or SDW. One of the CDW states, denoted as AP-CDW, reveals a bond order pattern with a much larger d-form factor than s\u2032 symmetry, as found in the experimentBi2Sr2CaCu2Ox8+) and NaCCOC (Cax2\u2212NaxCuO2Cl2). Furthermore, just as in the experimentd-form factor. For example, a different CDW intertwined with SDW and PDW, which is the familiar stripe reported long ago for 214122931s\u2032 form factor, as reported in the experiment2Here, we report our findings from a much more extensive examination of the renormalized mean-field theory prediction using the GWA for the hole-doped t\u2009\u2212\u2009J model. By using GWA, we can replace the strong constraint of forbidding the double occupancy of two holes on the same site in the variational wave function using Gutzwiller factors323344As mentioned above, the variational approach has been quite effective at capturing the physics of the strong correlation present in the \u03b4i, the local spin moment i is a site position and ij is the nearest neighbour bond. An iterative method is used to self-consistently solve the mean-field Hamiltonian HMF (Eq. (S7) in the \u22123 between successive iterations. All the calculations are performed on a 16 by 16 square lattice. To obtain various charge orders, specific patterns of \u03b4i, In our mean field theory, there are four variational order parameters. Besides the hole density a0), as listed in a0, with two domains of size 4a0 with opposite antiferromagnetic directions joining together. The pair field has more choices. It could always be positive, with all of its x-bond pair field being positive and y-bond pair field being negative: thus, it would have a net total non-zero pair field. This is called an in-phase (IP) state, with a period of 4a0. However, just like the spin moment, the pair field could also have two domains with opposite signs and a domain wall in between: this state is known as the anti-phase (AP) state, with a period of 8a0. Thus, we could have four possible states for each unidirectional CDW or bidirectional charge CB (cCB), as we either have an IP or AP pair field with or without SDW. However, we only have three such states in a0. Later, we will show a state with a net pairing order or IP pairing state and CDW, which occurs if we do not require solutions to be commensurate with the lattice.In addition to the two uniform solutions of a dSC state and a dSC-AFM state, there are many non-uniform charge-ordered states. For simplicity, we shall first present those charge-ordered states with a period of four lattice spaces  and reciprocal lattice vectors denoted by the \u201c+\u201d sign, the modulation wave vector is , and the vectors are shifted by the reciprocal lattice vectors. The peaks at  are determined by AS\u2032, while those at  and  are determined by AD. The ratio of AD to AS\u2032, or d/s\u2032, is approximately 7.5 in this case. This ratio is quite special for the AP-CDW state. For the IP-CDW-SDW stripe, the ratio is actually less than one. The schematic plots of the Fourier transform of IP-CDW-SDW and AP-CDW-SDW stripes are shown in d/s\u2032 is approximately 1.2. The Fourier transform of the bond orders of the AP-cCB pattern is similar to that of AP-CDW with a dominant d-form factor, as discussed in the SM.So far, we have only discussed the pair field, hole density and spin moment; now, we shall consider more carefully the bond order d-form factor with almost zero s\u2032. The Fourier transform of its bond order is schematically shown in d-form factors, and red (blue) represents a positive (negative) value. The wave vector with a large amplitude is at 5\u03c0/8a0 or its period is approximately 3.2a0. This length is close to the separation between the domain walls of the pair field shown in The nPDW stripe shown in et al.Ox and Oy sites. Just like \u03c0/2a0, 0) is larger than that at  and both have the same sign but opposite sign with respect to . In their sample there are two domains with density modulation in x and y directions, respectively.d-form factor actually vanishes at an approximately 19% hole concentration, as shown in et al.\u03c0/2a0, 0), which is associated with the density wave. The density wave disappeares at approximately 19% doping. Moreover, this 19% hole concentration is conspicuously close to the so-called quantum critical pointAnother interesting result regarding the AP-CDW stripe is that its t\u2009\u2212\u2009J model. Although they do not provide extremely accurate numbers, as many sophisticated numerical methods do, our results show that they do capture the most important physics of the strong correlation. This strong correlation provides a site-dependent Gutzwiller renormalization that produces many exotic solutions of PDW stripes and/or CBs intertwined with modulations of charge density and/or spin density. These results show quantitative agreement with some of the key experiments312kF is absent. Our model does not have the second or third neighbour hopping to provide a Fermi surface with nesting vectors or \u201chot spots\u201d2240a0 so far, our preliminary study also finds charge-ordered states with periods of 5a0 and even 3a0. States with a longer period should be possible, and they could also have degenerate energies34J/t away from 0.3.The results reported above are all based upon the well-established renormalized mean-field theoryt and J that will alter the preferences of these states. For example, a weak electron lattice interaction could make the IP-CDW-SDW stripe much more stable against the dSC-AFM stateAn important consequence of having all these charge-ordered states originating from the same Hamiltonian and physics is that these states are not the usual \u201ccompeting states\u201d we are familiar with. They do not stay in a deep local minima in the energy landscape. They are actually quite fragile and can easily evolve into each other, as we have already demonstrated with the nPDW stripe, which evolved from a mixture of AP-CDW and an uniform d-SC state. Other examples of the mixture of stripes listed in t\u2009\u2212\u2009J HamiltonianWe introduce the t, as our energy unit, is set to 1, and J is set to 0.3. \u03c3 is equal to \u00b1. Si is the spin one-half operator at site i. The Fermi surface of the uniform state is quite simple, without nesting parts, and does not intersect with the magnetic Brillouin zone boundary, thus avoiding hot spots.where nearest neighbour hopping PG) with the Gutzwiller renormalization factors. The renormalized Hamiltonian now becomesFollowing the idea of Gutzwiller32\u03b4i:where v is used to denote that these quantities are different from the real physical quantities for comparison with the experiments. Their relationship is given in Eq. (S9). As for the Gutzwiller factors, we follow the work of Yang et al.32et al.where where How to cite this article: Tu, W.-L. and Lee, T.-K. Genesis of charge orders in high temperature superconductors. Sci. Rep.6, 18675; doi: 10.1038/srep18675 (2016)."}
+{"text": "T//) and field-like (T\u22a5) spin-transfer torque terms in the Landau-Lifshitz-Gilbert simulation, reliable and deterministic magnetization reversal can be achieved at a significantly reduced current density of 5\u00d7109\u2009A/m2 under the co-action of electric field and spin-polarized current, provided that the electric-field pulse duration exceeds a certain critical value \u03c4c. The required critical \u03c4c decreases with the increase of T\u22a5 strength because stronger T\u22a5 can make the finally stabilized out-of-plane component of magnetization stay in a larger negative value. The power consumption for such kind of deterministic magnetization switching is found to be two orders of magnitude lower than that of the switching driven by current only.Effective manipulation of magnetization orientation driven by electric field in a perpendicularly magnetized tunnel junction introduces technologically relevant possibility for developing low power magnetic memories. However, the bipolar orientation characteristic of toggle-like magnetization switching possesses intrinsic difficulties for practical applications. By including both the in-plane ( E-field) effect58910121314161718Jc) as low as ~109\u2009A/m2, which becomes the most challenging issue of high density memories. Meanwhile, reducing the STT switching current is also of particular importance to lower the energy consumption192021Jc\u2009, the typical Jc of the present memory devices is still of the order of 1010\u20131011\u2009A/m2. Accordingly, new switching schemes are strongly expected for further reduction of power consumption.The effective manipulation of magnetization direction by electric current or voltage has attracted much attention for potential applications in nonvolatile spintronic devices. To date, different types of electric control methods have been developed: One is based on the spin-transfer torque (STT) effect induced by spin-polarized current1E-field effect23242526272829E-field switching scheme. For the Fe/MgO or FePt/MgO-based perpendicular tunnel junctions, the application of electric field alters the Fermi level position at the interface, which changes the orbital occupancy and interface magnetic anisotropy30313233E-field control of magnetism in principle does notE-field can be reduced by a factor of 500 when compared with the STT devicesE-field have been experimentally demonstrated in MTJs: one utilizes the coercivity change to assist magnetization reversal of the free layer26273637E-field pulse strength and duration (\u03c4), the final magnetization state of free layer in the latter scheme case can be aligned either antiparallel (AP) or parallel (P) with the magnetization of fixed layer3738E-field pulse as short as tens of picosecondsIn order to reduce energy consumption, magnetization switching driven by either spin-orbit torques45E-field effect40E-field effect. In this paper, we performed simulations to reveal the magnetization switching behaviors driven by the combined action of electric field and STT effects. We find deterministic switching occurring at a much weaker current density but a larger pulse duration region which varies with the strength of field-like STT. The parameters of E-field and STT corresponding to such deterministic switching could be used for a new switching scheme with a dramatic reduction in energy consumption.Undoubtedly, it is essential to achieve reliable deterministic magnetization switching with low power consumption for advanced perpendicular STT-MRAMs. One promising approach is to employ both the STT effect and E-field) pulse is applied between the top electrode and the magnetic free layer separated by an oxide layer for tuning the PMA of free layer. The electric current is polarized by the fixed bottom ferromagnetic layer which exerts a spin-transfer torque on the free layer. We define the positive current as the electrons flowing from the free layer to the fixed layer. In our simulations, for the case of co-action of current and E-field pulses, the pulse length of injected current is 1\u2009ns longer than the corresponding E-field pulse. Numerous studies have shown that the current-induced spin-transfer torque includes two vector components: the in-plane torque term142444546474950aJ and bj are the torque factors (see Methods). The typical material parameters are used for the CoFeB free layer0Ms\u2009=\u20091.4 T, Gilbert damping factor \u03b1\u2009=\u20090.2, thickness d\u2009=\u20091.4\u2009nm, and spin polarization P\u2009=\u20090.3.The model structure we considered is a MgO/CoFeB-based perpendicularly magnetized tunnel junction. As illustrated in Hext is applied with its out-of-plane component to completely compensate the stray field generated from the polarizer layer, and its in-plane component is denoted as Hy . As we know, under the action of voltage pulse, the effective magnetic field Heff will change due to the reduced PMA. We suppose that the magnetic anisotropy field E\u2009=\u20091.28\u2009V/nm)In this study, we suppose that an external field E-field only, STT only, or both E-field and STT. All the simulations start from an initial parallel configuration. E-field induced magnetization switching phase diagram, for which a voltage pulse of 1.8\u2009V with various pulse durations were used. As we mentioned, since the direction of effective magnetic field Heff moves from z-axis to y-axis due to the PMA reduction caused by E-field, the magnetization will precess around the new Heff direction [see z\u2009=\u2009+\u20091) or switching to the AP state (mz\u2009=\u2009\u22121). So, the final state of the free layer depends on the voltage pulse duration and external field, and this type of magnetization switching is termed as \u201ctoggle-like\u201d switching modeE-field pulse width and external field) is indispensable which holds a great challenge for experiments.We have carried out simulations on the magnetization switching driven by tion see . Once thJ and in-plane external field Hy\u2009. The current pulse duration is set as 15\u2009ns. Here both the in-plane and field-like spin-transfer torques are considered. In the simulation \u03be is chosen to be 0.02, which is proportional to the strength of the field-like torque. Clearly, a critical current Jc as high as 2.5\u00d71011\u2009A/m2, which changes slightly with the external field, is required to achieve magnetization reversal from P to AP state. Obviously, the P-to-AP switching cannot occur if the current is below Jc, for instance, J\u2009=\u20091\u00d71011\u2009A/m2, because the driving force by the STT alone with such low current cannot provide enough power to gyrate the free layer crossing over the energy barrier to another energetically favorite state. However, for the same low current density the P-to-AP switching can be achieved with the help of an additional E-field generated by a 1.8\u2009V voltage pulse, as shown in E-field and current, the parameter region of the first blue-stripe (AP state) is enlarged for both cases with [T\u22a5) of STT, implying the expected deterministic AP state can be easily realized in this parameter region. This controllable AP region can be attributed to the STT effect which favors the AP state and dominates the magnetization dynamicsT\u22a5, another even larger deterministic AP region appears at the top-right corner of Reliable and deterministic switching is vitally important for practical applications, which can be realized by applying an enough strong current through the STT effect. ses with  or withoses with  the fielT// and T\u22a5 on magnetization switching, we show in E-field and current. The only difference is that only the in-plane T// is included in T// and T\u22a5 torques. The simulation parameters are taken as Hy\u2009=\u200923\u2009mT and \u03c4\u2009=\u20098\u2009ns (1.8\u2009V in strength), corresponding to the parameter points marked as the red stars in 11\u2009A/m2 to generate the STT effect. Clearly, the STT alone in both cases cannot cause the magnetization to deviate away from its initial equilibrium state since such low current is far from enough to switch the magnetization [see t\u2009=\u20093\u2009ns, the E-field pulse is added, which modifies the effective field, leading to the magnetization of free layer away from the initial +z direction and precessing around the in-plane +y direction [see E-field is removed, no switching takes place and the free layer magnetization returns back to the P state if the field-like toque is not considered. On the contrary, the magnetization switches to the -z direction (AP state) when both T// and T\u22a5 torques are included in the simulation model.In order to distinguish the roles of the two spin torque terms of tion see . At t\u2009=\u2009tion see . As soon11\u2009A/m2, the external field of Hy\u2009=\u200923\u2009mT, and the voltage of 1.8\u2009V, but different E-field pulse durations. T// and T\u22a5 torques. We can see that the free layer magnetization goes back to the parallel configuration for the pulse duration \u03c4\u2009=\u20091.5, 3.0, 4.6 and 6.0\u2009ns, whereas it switches to the AP configuration for \u03c4\u2009=\u20092, 4, 5, and 6.3\u2009ns, respectively. This is a typical toggle-like switching mode. However, as the E-field pulse is longer than 6.3\u2009ns, the final AP state can be observed only, thus producing a deterministic magnetization switching region. This feature has been further confirmed by continuously changing the pulse duration from 0 to 30\u2009ns. The dependence of final magnetization state on the pulse duration is given in \u03c4c of E-field is 6.3\u2009ns. For comparison, we have also performed simulations with the in-plane torque only. As shown in E-field pulse duration smaller than 7.8\u2009ns, above which random magnetization switching is observed. This means that the in-plane torque alone cannot generate deterministic switching even though the E-field pulse duration is long enough to stabilize the magnetization along the in-plane direction.To further clarify that, we have performed a series of simulations using the same parameters including the current density of 1.0\u00d710\u03c4c to trigger the deterministic magnetization switching is found to be closely related to the strength of field-like STT. T\u22a5 strengths characterized by a parameter \u03be. In these simulations, the E-field pulse duration is fixed to be 13.5\u2009ns and the other parameters are the same as those in T// torque only, the out-of-plane magnetization component mz exhibits damped precession which finally stabilizes around the mz\u2009=\u20090 axis during the electric pulse duration. The final P or AP state is dominated by the fluctuated mz value at the moment when the E-field pulse is just finished, which can be either positive or negative depending on the pulse duration but not on the \u03be strength (\u03be changes from 0 to 0.3). For the positive mz [stay in the cyan region, see mz the PMA forces it to the final AP state. This result is responsible for the observed random switching state shown in T// on the new deterministic switching region is very weak and can be ignored. However, when the T\u22a5 component is included, the mz value will be shifted downwards and keeps negative when the pulse duration is over a critical value, e.g. \u03c4c\u2009=\u20096.3\u2009ns for \u03be\u2009=\u20090.02. Such shift makes the mz stabilize at a negative value, which would certainly result in a deterministic AP magnetization switching as the pulse is removed. As a result, from the oscillation curves shown in \u03c4c, over which the mz stays negative and AP state occurs. The \u03c4c value relies on the \u03be, which decreases down to 4.9 and 3.4\u2009ns as \u03be increasing up to 0.05 and 0.15, respectively. For clarity, the critical pulse durations are summarized in \u03be.The required critical pulse duration mz, i.e. the equilibrium position of mz during the action of E-field, can be qualitatively analysed from the LLG equation governed by \u03be\u2009=\u20090.02. In this case since the precession vector m is close to the y-axis, the direction of T\u22a5 is approximately along +x direction. The directions of T\u22a5 (brown arrows) and mz\u2009>\u20090), the T\u22a5 has a component parallel to z/dt which is proportional to the factor \u03be, as shown in T\u22a5, which can reduce the radius of precession, i.e. the oscillation amplitude of mz, being in agreement with the results shown in mz\u2009<\u20090), because the T\u22a5 has a component antiparallel to mz gets larger with increasing \u03be due to the partially canceled damping term. Consequently, in the presence of T\u22a5, the mz oscillation curves are shifted downwards, which eventually stabilizes at a negative value during the E-field pulse. Therefore, deterministic magnetization switching to the antiparallel state (mz\u2009=\u2009\u22121) can be achieved if the pulse duration is larger than \u03c4c.The effect of field-like torque on the stabilized E-field pulse durations at a field of Hy\u2009=\u20095\u2009mT (left panel) or 23\u2009mT (right panel), where \u03be is chosen as 0.02 and 0.15. Clearly, with the combined effects, the critical switching current is significantly reduced. The magnetization switching can be achieved by two different switching modes: toggle-like switching  at the case of shorter E-field pulse and weaker current density, and deterministic switching (the continuous blue area) for the E-field pulse longer than a critical value in \u201cS2\u201d switching region or current density higher than a critical value in \u201cS1\u201d switching region  although the E-field pulse duration can be reduced down to 2\u2009ns. In contrast, in the S2 region, the reliable switching can be achieved at a current density of 0.5\u00d71010\u2009A/m2 and an E-field pulse of 8\u2009ns [see \u03be can reduce the critical pulse duration \u03c4c, which has been observed in and 0.15 , while ag region . Obvious8\u2009ns see . AdditioE-field power is estimated byI is the current for STT, V is the voltage for generating E-field pulse, R is the resistance of MTJ, t is the function time of STT or E-field. We use the typical experimental parameters for MgO-based MTJE-pulse of \u03c4\u2009=\u20092\u2009ns and a switching current of E-field effect. In S2 region of E-field pulse as \u03c4\u2009=\u20098\u2009ns, a current density E-field pulse. The total energy consumption in both cases are much smaller than the switching driven by STT effect alone, which is around 312\u2009pJ for For practical applications, the power cost for driving the magnetization switching is a key factor to be considered. The required STT power is calculated according to E-field only is toggle-like, with final state either parallel or antiparallel with the reference layer, depending on the E-field pulse duration and external magnetic field. In contrast, reliable and deterministic switching can be realized by STT only under a quite strong current, which will limit the practical applications. By using a new switching scheme combining both the E-field pulse and STT current, the power cost for deterministic magnetization switching could be significantly reduced by two orders of magnitude if both the in-plane and field-like torques are considered. The deterministic switching can occur at a reduced current density of 109\u2009A/m2 as the E-field pulse duration is larger than a critical value, which is found to decrease with the increase of field-like STT term. The reliable and deterministic magnetization switching with low power consumption promises potential advantages for the future spintronic devices, especially for low power writing of the MRAMs.In summary, we have investigated magnetization switching properties in MgO-based magnetic tunnel junctions driven by the electric-field effect and spin-transfer torque effect. The magnetization switching of free layer driven by The roles of electric field and spin-polarized current acting on the free layer are modeled by including a change of perpendicular anisotropy and spin-transfer torque terms, respectively, into the Landau-Lifshitz-Gilbert (LLG) equation. In this study, macrospin simulations are carried out by solving the LLG equation, which is taken as:M\u2009=\u2009mMs is the magnetization vector of the free layer, m is the unit magnetization vector, Ms is the free layer saturation magnetization, Heff is the effective magnetic field that includes the external magnetic field, anisotropy field and demagnetization field. h\u2009T is an instantaneous thermal fluctuation field and in this study we set the temperature T\u2009=\u2009300 K. The third term is the in-plane spin torque, \u03b3 is the gyromagnetic constant, J is the electric current density, d is the free layer thickness, e is the electron charge, P is the spin polarization. The simulation code is developed in-house and has been used in our previous study38How to cite this article: Zhang, X. et al. Magnetization switching by combining electric field and spin-transfer torque effects in a perpendicular magnetic tunnel junction. Sci. Rep.6, 18719; doi: 10.1038/srep18719 (2016)."}
+{"text": "For decades, research in neuroscience has supported the hypothesis that brain dynamics exhibits recurrent metastable states connected by transients, which together encode fundamental neural information processing. To understand the system's dynamics it is important to detect such recurrence domains, but it is challenging to extract them from experimental neuroscience datasets due to the large trial-to-trial variability. The proposed methodology extracts recurrent metastable states in univariate time series by transforming datasets into their time-frequency representations and computing recurrence plots based on instantaneous spectral power values in various frequency bands. Additionally, a new statistical inference analysis compares different trial recurrence plots with corresponding surrogates to obtain statistically significant recurrent structures. This combination of methods is validated by applying it to two artificial datasets. In a final study of visually-evoked Local Field Potentials in partially anesthetized ferrets, the methodology is able to reveal recurrence structures of neural responses with trial-to-trial variability. Focusing on different frequency bands, the \u03b4-band activity is much less recurrent than \u03b1-band activity. Moreover, \u03b1-activity is susceptible to pre-stimuli, while \u03b4-activity is much less sensitive to pre-stimuli. This difference in recurrence structures in different frequency bands indicates diverse underlying information processing steps in the brain. Investigation of metastable states (MS) and transients of complex dynamical systems has become increasingly important over the last decades. In this context, dynamical systems spend longer time intervals in MSs than in transients between MSs. The large interest in studying such states comes from the belief that a complex temporal behavior of systems may be decomposed into a simple sequence of alternating MSs and transients between them. This reduced description is a model that captures the essential dynamic elements of rather complex underlying dynamics. Applications range from spin glasses  during a visual stimulus experiment allows to extract new insights into neural information processing. For instance, we show that temporal recurrence occurs in the \u03b1-frequency band but not in the \u03b4-frequency band. This result suggests that in the \u03b1-band the brain processes the information step-wise (state by state) while no step-wise process is performed in the \u03b4-band.In this work we propose a new method for the detection of metastable states in univariate neural signals. To obtain statistically significant evidence of recurrence structures in signals, we conduct a statistical test over the set of novel, frequency-selective recurrence plots (RP). Below we describe methodologies for building such frequency-selective RPs and performing statistical inference tests. These tests indicate how stable the recurrence plots are with respect to trial-to-trial variability. This novel statistical evaluation is necessary in the analysis of neurophysiological data, since trial-to-trial variability is a well-known experimental finding in such signals. In our work we analyse synthetic transient oscillations and one state variable of the Lorenz attractor involving acquisition noise to validate the methodology. Finally, the study of experimental Local Field Potentials obtained in partially anesthetized ferrets  \u2208 \u211dn, t \u2208 \u211d is sampled at times t = i\u0394t, i \u2208 {1, 2, \u2026, N}, where \u0394t is the sampling time interval and N is the total number of samples. For notation simplicity, in this paper we denote the signal sample x(i\u0394t) by x(i). Then, a recurrence plot (RP) is defined as the N \u00d7 N matrix R, whose elements ri, j take values ri, j = 1 when two trajectory samples lay within the open ball d is a distance function and i, j \u2208 {1, \u2026, N}. Hence, recurrence plots are two-dimensional binary matrices obtained by distance based thresholding and its elements take values ri, j \u2208 {0, 1}. In this work, pixels in RPs will be color-coded white for values ri, j = 0 and black otherwise.Deterministic dynamical systems are described by their trajectory. A trajectory * which maximizes the symbolic entropy for a given distance function, as proposed in beim Graben and Hutt  in EEG recordings. To take into account the distinct signatures of spectral bands present in neural signals, we propose a novel concept for building recurrence plots from time-frequency signal representations, instead of building them directly from univariate data or constructing them by employing delay-embedding techniques. Such representations, in general adapted for non-stationary signal analysis, give insights into frequency bands of importance and provide additional flexibility to recurrence plot analysis that is not present in time-domain, for e.g., the possibility to weight the importance of some frequency bands. In the literature there are several ways to choose values of the frequency bands. We use the following frequency interval definitions: the \u03b4-frequency band denotes the interval , the \u03b8-frequency band the interval , \u03b1-band , \u03b2-band , and the \u03b3-band denotes the interval .T univariate trials {x1, x2, \u2026, xT} to their corresponding time-frequency domains; (ii) we compute the mean power of the spectrum over certain sets of frequencies. These mean power time series may be called S is the number of frequency bands; (iii) we compute recurrence plots by computing distances between vectors y(i) and y(j), i, j \u2208 {1, \u2026, N} as in Equation (1). In the following paragraphs we describe these blocks in more detail.We build novel recurrence plots in three steps, as shown in Figure The first block in Figure The second block in Figure Finally, in the third processing block in the figure we compute recurrence plots from the obtained time-frequency dataset as in Equation (1). If we do not explicitly mention otherwise, we use features from all the frequency bands to compute recurrence plots. In the experimental ferret dataset, we additionally present cases when recurrence plots are calculated from the single frequency band features such as \u03b4- or \u03b1-frequency bands, since these bands play an important role in the loss of consciousness under anesthesia.To summarize, the proposed method for building recurrence plots from time-frequency representations grasps band-related features and allows flexibility in the analysis of particular frequency bands, which is not possible in the classical RP analysis. Our approach however requires additional computations of the synchrosqueezing transform and mean power of the spectrum.f(t) can be well approximated with K signal components, Ak(t) and e(t) represents a small error. We assume that the components fk have slowly time-varying amplitudes Ak(t) and sufficiently smooth IFs. These conditions assure that signal components are well separated in frequencies and the complete definition is available in Thakur et al.  be a square integrable and normalized function. Then, its scaled and time-shifted variants f at scale a and time shift b is defined by a. For example, for the first signal component with frequency \u03c91, the value of the wavelet coefficient Wf spreads around the scale factor \u03c8 is the central wavelet frequency. Therefore, the estimated IF in the neighborhood of this value of the scale is equal to the frequency \u03c91. The synchrosqueezing transform T uses estimates of the instantaneous frequency \u03c9f, computed for each scale-time pair  by ap (\u0394\u03c9) denote resolution steps in scale (frequency). Then, this transform, defined by q, b) in time-frequency plots, see Figures 5A,E, 6A,C.Let a wavelet \u03c8 is defined in Equation (3), \u03c9q are frequencies of one frequency band and t is time.For each frequency band with We study statistical properties of frequency-selective RPs obtained from time-frequency trial representations. By virtue of noise effects and an expected trial-to-trial variability, recurrence plot structures are expected to vary from trial to trial. To evaluate the recurrence plots statistically, we perform a statistical inference analysis based on a classical chi-squared test Yates, . To thisClassically, surrogate sets of univariate signals . To perform a chi-square test for categorical data, we build a two-by-two contingency table. For explanation, this tables first row takes values from the original RPs and the second row contains values from surrogate RP. The first table column marks the number of values ri, j = 1 and the second column the number of elements ri, j = 0. The elements of this table (two rows and two columns) have the coordinates , l, m \u2208 {1, 2}. Then, the chi-square statistics for the pixel , i, j \u2208 {1, \u2026, N} is computed byl, m) for the pixel  and nr(l) is the total number of elements in the row l, nc(m) is the number of elements in the column m and q is the total number of elements in the two-by-two table. The calculated chi-square value is compared with the result in the chi-square table for predefined values of the degree of freedom df = 1 and the significance level \u03b1s = 0.05. If the calculated chi-square value is larger than the value in the table, the hypothesis that signals share the same distribution is rejected, see Yates  \u2265 0, i \u2208 {1, 2, 3} is the activity rate of the element i, \u03c3n is the growth rate of the n-th population and \u03c1i define interactions between elements. In our setup, \u03c31 = 1, \u03c32 = 1.2 and \u03c33 = 1.6, \u03c1ii = 1, \u03c112 = 1.33, \u03c113 = 1.125, \u03c121 = 0.7, \u03c123 = 1.25, \u03c131 = 2.1, and \u03c132 = 0.83. The output signal s(t) is a linear superposition of transient oscillations with frequencies \u03bd1 = 170 Hz, \u03bd2 = 20 Hz, \u03bd3 = 75 Hz, where at one time instance, only one of these three components is dominant, see more details below. We point out that these frequencies are chosen rather arbitrarily for an optimal illustration. The activity rate xi defines the amplitude of the component ai with frequency \u03bdi and the output signal obeys1 = 0.5, \u03b72 = 0.33, \u03b73 = 0.4. By this construction, the amplitudes ai increase and decrease in a certain time window outside of which they almost vanish. These windows of the three oscillation modes i = 1, 2, 3 do not overlap and the transitions between them are rather rapid. The variable \u03be(t) represents measurement noise and its random values are i.i.d. Gaussian noise with zero mean and variance 0.5. The sampling rate is 450 Hz. We generate 10 trials which are time-jittered by shifting the trials by 1 sample to later instances, while each trial is subject to additive noise different in each trial. A single trial is given in Figure A modified Lotka-Volterra model with x(t), which is the solution of the above given system of equations. This time series may represent a macroscopic measured signal such as EEG recording  at 47 cm distance from the animal. Each trial was 30 s long and consisted of three parts: (i) recording interval . Hence the system remains close to the resting state (t < 0) during the first stimulus. Conversely, Figure t = 2 s resembles the activity just after t = 2.5 s. These different findings for two trials are surprising since the experimental presentation of the visual stimulus is well-controlled and the stimulus is simple enough to expect almost identical neural responses.Figure To reveal the recurrent structure that is common in all trials, we now study the trial-to-trial variability of recurrence plots and aim to reveal whether the signal trials preserve the same dynamical behavior, cf. Figure t-test results). The figure reveals that there is no statistically significant recurrent structure in the \u03b4 frequency band in signals under study. Conversely, the \u03b1-frequency band exhibits significant recurrent structures in the single granular electrode in both datasets, cf. Figures session one the first response to the stimulus at t = 0 s returns at t = 1 s. Results for all frequency bands differ to results obtained in the \u03b1 frequency band. The differences are dependent on the experimental sessions suggesting the presence of strong recurrences in bands different to \u03b1 and \u03b4 or strong noise artifacts. To gain further insights into the dependence on frequency bands, we consider single trials which represent spatial averages of time series from adjacent granular layers. This average denoises the time series. Figures t = 0.5 s indicates a MS common to all data with t \u2265 0.5 s. Additional recurrences occur in the time intervals , , and  ms. These results are consistent in the chi-square significance tests and the t-test involving corrections for multiple comparison. At last, we mention the prominent lack of recurrence in the baseline time interval observed in a single electrode in session one, cf. Figure session one nor in the spatially averaged data shown in Figures Figure subset one and the subset of \u201cstrongly spatially filtered version of foxes\u201d denoted by subset two. Subset one includes the trials {4, 6, 9}, while subset two is composed of the trials {1, 5, 10} of datasets session one and session two. The comparison of various pre-stimuli data is done by the chi-squared difference measure based on recurrence plots of both subsets. Figure t = 0 s) and during the stimuli, for t \u2208  s. In \u03b1-band, the figure shows more prominent recurrences, such as the patterns around t = 1.5 and 2.7 s. We point out that recurrences within \u03b4- and \u03b1-bands do not overlap, except in the pre-stimuli period, for t \u2208 {\u22120.5, 0} s. Finally, considering all the frequency bands together does not reveal significant similarities of two pre-stimuli. Results from the chi-square test and the t-test involving multiple comparison correction are similar. However, it is interesting to note that the t-test reveals more significant common recurrences than obtained with the naive chi-square test.The experimental paradigm includes visual presentations of stimulus types in a randomized order. The previous paragraphs show neurophysiological responses to the sine-wave stimulus only. To gain further insight into the trial-to-trial variability subject to various pre-stimuli, we have selected two subsets of sine-wave trials that have two different preceding stimuli, namely the \u201cblack screen\u201d subset denoted by The present work introduces a new recurrence analysis methodology for univariate time series. The first new element is the transformation to a time-frequency representation leading to a multivariate time series of spectral power. This new technique generates a new high-dimensional phase space in which the instantaneous power of the signal evolves. This high-dimensional phase space is mandatory to apply recurrence analysis. In addition, it permits to compute recurrence plots for specific frequency bands. The second new element is the statistical analysis of recurrence plots that takes into account spurious recurrence structures and allows to suppress them. The combination of the two methods permits to extract temporal recurrence structures in data which may reflect underlying transient dynamics in a certain range of frequencies that would have been hidden in conventional methods. To our best knowledge these two techniques have not been considered before.The first results for two artificial datasets illustrate the methodology and indicate that method detects recurrences in a variable dataset  by the statistical analysis as seen in Figure The subsequent analysis of single Local Field Potentials measured experimentally in ferret visual cortex reveals a high trial-to-trial variability, cf. Figure The effects of pre-stimuli have been hypothesized . It turns out that this conventional method does not provide high-quality extraction of transient recurrent structures, given by the reassignment method. This may result from the worse time-frequency resolution of conventional Morlet wavelets. Future work will further investigate the best choice of multi-resolution time-frequency methods. Moreover, the methodology considers surrogate data generated by a temporal random shuffling of data and hence destructing all temporal structure. Future work may include the destruction of the recurrence structure by phase randomization in certain frequency bands .We provide the time-series of the transient oscillation dataset and Lorenz dataset on the webpage of the corresponding author (The majority of the analysis steps and the implementations have been performed by TT. KS and FF have provided the experimental data and neurophysiological insights. MF has contributed additional time-frequency analysis results and PB and AH have conceived the study. All authors wrote the manuscript together.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Reserving time slots for urgent data, such as life-critical information, seems to be very attractive to guarantee their deadline requirements in wireless body area sensor networks (WBASNs). On the other hand, this reservation imposes a negative impact on performance for the utilization of a channel. This paper proposes a new channel access scheme referred to as the contention over reservation MAC (CoR-MAC) protocol for time-critical services in wireless body area sensor networks. CoR-MAC uses the dual reservation; if the reserved time slots are known to be vacant, other nodes can access the time slots by contention-based reservation to maximize the utilization of a channel and decrease the delay of the data. To measure the effectiveness of the proposed scheme against IEEE 802.15.4 and IEEE 802.15.6, we evaluated their performances with various performance indexes. The CoR-MAC showed 50% to 850% performance improvement in terms of the delay of urgent and time-critical data according to the number of nodes. To display human physiological status, these biosensors continuously monitor and transmit health conditions to a coordinating device wirelessly, forming a WBASN.Spurred by the rapid convergence of key technologies, such as physiological sensors, wireless communication and low power micro-electro-mechanical systems (MEMS), a new generation of wireless body area sensor networks (WBASNs) is emerging. These WBASNs exploit special-purpose implantable biosensors that aim to provide a large variety of applications, including computer-assisted rehabilitation, early detection of medical conditions, priority. There have been a large number of studies on priority-based mechanisms [Although the applications of these WBASNs are attractive, there are still a large number of challenges to be tackled for providing reliable and efficient WBASN systems. One of the important challenges is to provide urgent data transmissions for life-critical applications. Techniques for urgent data transmissions have traditionally been based on chanisms ,3,4,5,6 In addition to the above schemes, a number of studies related to WBASN are based on the IEEE 802.15.4 technology ,10,11. Tparametric [channelization-based [hybrid [For WBASNs, the few proposals for urgent data transmission in terms of priority-based MAC can be classified into three categories: rametric ,14,15, con-based ,17,18,19 [hybrid ,21 appro [hybrid . The chaIn this paper, we propose a hybrid priority-based MAC protocol for WBASN, referred to as contention over reservation MAC (CoR-MAC). In the CoR-MAC, each time slot is dedicated to a node that might transmit urgent data. However, dedicated time slots waste wireless resources. When the dedicated time slots are not used, the other nodes cannot use those time slots. To solve this problem, in the CoR-MAC, data can be transmitted over the time slot, which is dedicated to another node and not in use.The rest of this paper is organized as follows. We survey the existing related work in et al. [i.e., the AC traffic has the highest priority). To differentiate AC and CD traffic, a unique backoff exponent (BE) is configured for each. In other words, the AC has more transmission to opportunities than the CD, since the AC has a smaller BE. Nevertheless, there is no way that the AC can preempt the CD when the CD has already decreased its backoff counter to be smaller than that of the AC. Zhang et al. [et al. [According to the taxonomy mentioned in et al.  proposedg et al.  proposed [et al.  suggesteet al. [et al. [et al. [et al. [Zhang et al.  proposed [et al.  proposed [et al.  proposed [et al.  proposed [et al. , the priet al. [opportunistically. In other words, non-urgent data perform clear channel assessment (CCA) in the ETS and check for any urgent data transmission with shorter inter-frame space (IFS) and, thus, higher priority than the non-urgent data. Although an emergency alarm can occur during the DTSs, priority is given to non-urgent data in the PNP-MAC. Zhou et al. [As mentioned in et al.  suggesteu et al.  proposedu et al. . Since Iu et al. ,20,22,24u et al. . IEEE 80As we can conclude from the above data, research for WBASNs concentrates on urgent data transmission with a guaranteed time slot for urgent data. However, these research works are not considered to be wasting network utilization caused by the non-transmission of urgent data on the slot. The CoR-MAC, as we mentioned, can resolve this problem with the dual reservation scheme that allows transmitting within unused slots for urgent data.N sensor nodes  consisting of one coordinator , electroencephalogram (EEG), electromyographic (EMG) and medical video data. The non-time-critical data include messaging and traffic service, as in . SimilarNo non-emergency traffic can be transmitted during an inactive phase that is designed for energy reduction. Although transmission is not allowed, this phase can be utilized for emergency data transmission, as in . TransmiThe beacon phase is the time in which only the coordinator is allowed to transmit a beacon frame, and it is used for network synchronization and advertising information, such as time slot allocation. The beacon frame includes superframe length, subsequent superframe start time, beacon length, CFP length, CAP length, length of the CFP time slot, network ID, the number of time slots in the CFP and the CFP allocation map, including slot number and node ID. The size of the beacon is varied according to the size of the CFP allocation map. If the number of nodes is 10\u223c15, the size of the beacon will be around 228\u223c278 bits when the size of the CFP allocation information per node is 10 bits (five bits for the number of slots and five bits for the node\u2019s ID).Urgent data can be transmitted during either the CFP or CAP. A detailed description of urgent data transmission is described below.The time-critical data can be transmitted during CAP or the reserved time slot in CFP, as long as urgent data are not being transmitted.Non-time-critical data can be transmitted during either CFP or CAP, as long as urgent, time-critical or other non-time-critical data are not being transmitted.To accommodate all three traffic types in \u2026, M is the maximum allowable number of time slots in the CFP and is selected based on the number of nodes that generate urgent data. We call this phase the self CFP (SCFP). Further, to increase the transmission opportunities, urgent data of opportunistic CFP (OCFP). To prioritize Generally, transmitting urgent data over a CAP is not desirable, since timely transmission is not guaranteed due to contentions. Therefore, it would be better to transmit urgent data over a CFP by reserving a dedicated slot. However, the dedicated time slot might not be frequently utilized since urgent traffic is generated sporadically in general, resulting in degraded throughput. Therefore, in the CoR-MAC, the CFP is divided into time slots i.e., i.e., a reservation request command for time-critical data is transmitted over the CAP. To prioritize urgent data against time-critical data, time-critical data wait for the medium inter-frame space (MIFS) before transmitting a frame, where MIFS > SIFS. In other words, even if time-critical data are reserved at Moreover, in the CoR-MAC, In addition to the CFP, the CAP is used for the transmission of urgent data and non-time-critical data. In this way, urgent data have ample opportunity to access a channel. Using this mechanism, our scheme can transmit the urgent data significantly faster than the method in .Initially, there is no CFP, and the CAP is extended to the end of the beacon phase, as shown in  network c. S2, S3M, the coordinator allocates The CoR-MAC algorithm for the coordinator is shown in Algorithm 1. When Algorithm 1 The CoR-MAC algorithm for the coordinator.\u00a01:\u00a02:\u00a03:M\u2190 The maximum allowable number of time slots in CFP;\u00a04:i\u2019-th position;\u00a05:i;\u00a06:loop\u00a07:if Current time = start of beacon phase then\u2003\u00a08:\u2003\u2003Send beacon with CFP allocation map\u00a09:end if\u200310:ifthen\u200311:if # of time slots in the CFP < Mthen\u2003\u200312:\u2003\u2003\u2003Allocate 13:\u2003\u2003\u2003Update CFP allocation map14:else\u2003\u200315:\u2003\u2003\u2003Reject the join request16:end if\u2003\u200317:end if\u200318:if DATA is received from then\u200319:\u2003\u2003Send ACK to 20:elseif RTS is received from then\u200321:\u2003\u2003Send CTS to 22:end if\u200323:end loopAlgorithm 2 The CoR-MAC algorithm for the node.\u00a01:i\u2019-th position;\u00a02:\u03a6 \u2190 The current time;\u00a03:\u00a04:\u00a05:\u00a06:loop\u00a07:if BEACON is received from the coordinator then\u2003\u00a08:\u2003\u2003Synchronize itself to the coordinator;\u00a09:\u2003\u2003Record this 10:elseif The node has urgent data to transmit then\u200311:if \u03a6 \u2282 then\u2003\u200312:\u2003\u2003\u2003Send urgent DATA immediately;13:elseif \u03a6 \u2282 then\u2003\u200314:\u2003\u2003\u2003Send DATA with CSMA/CA after SIFS;15:elseif \u03a6 \u2282 then\u2003\u200316:\u2003\u2003\u2003Send DATA with CSMA/CA;17:end if\u2003\u200318:elseif The node has time-critical data to transmit then\u200319:if \u03a6 \u2282 then\u2003\u200320:\u2003\u2003\u2003Send DATA after MIFS;21:elseif \u03a6 \u2282 then\u2003\u200322:\u2003\u2003\u2003Send DATA with CSMA/CA;23:end if\u2003\u200324:elseif The node has non-time-critical data to transmit then\u200325:if \u03a6 \u2282 then\u2003\u200326:\u2003\u2003\u2003Send DATA with CSMA/CA after LIFS;27:elseif \u03a6 \u2282 then\u2003\u200328:\u2003\u2003\u2003Send DATA with CSMA/CA;29:end if\u2003\u200330:end if\u200331:end loopThe CoR-MAC algorithm for the sensor node is shown in Algorithm 2. When a beacon is received from the coordinator, nodes synchronize themselves to the coordinator and record this In this section, we analyze an urgent data delay of the proposed scheme with a theoretical approach. We show that our scheme guarantees the delay requirement of the urgent data. In the following, we describe our assumption and system model to obtain the expected delay in M) is less than or equal to the number of nodes N. In the CoR-MAC protocol, non-urgent data can be transmitted when no node has urgent data in CFP. Therefore, we do not consider non-urgent data in CFP. Denoting We assume that each node generates both urgent data and non-urgent data. Note that the arrival rates of urgent data follow exponential distributions with L as the number of G as the rate of attempted transmissions, including retransmission, new arrivals, urgent data and non-urgent data. Although G depends on time in reality, we assume that G is a constant value in our analysis.We assume that CAP consists of a number of system time slots . Therefore, each node has an opportunity to transmit if the slot owner does not have urgent data. If the slot owner has urgent data, the other nodes wait N\u2019-th slot in If the slot owner of the slot does not have urgent data, each node with urgent data vies with other nodes. If a node wins contention and transmissions are successful in the slot, then the delay is Equation , where PL is the number of CAP consists of a number of Equation .(6)D, res, resD; and the energy consumption.versus the arrival rate of the number of nodes. The delay of IEEE 802.15.6 increases from 11\u201312 nodes since IEEE 802.15.6 has an exclusive access phase (EAP) for the processing of urgent data and time-critical data. The EAP is efficient for processing urgent data and time-critical data, but cannot process non-time-critical data. In addition, the CoR-MAC and IEEE 802.15.4 can process non-time-critical data during the entire superframe. With a high arrival rate, the non-time-critical data delay of all schemes increases extremely, since those schemes have lower priority of non-time-critical data, and those MACs are unable to process non-time-critical data.versus the number of nodes, respectively. The delay of IEEE 802.15.4 is higher than that of the other schemes because IEEE 802.15.6 has EAP. Furthermore, CoR-MAC has a dual reservation scheme for urgent data and time-critical data. In any environment, CoR-MAC has a shorter delay than the other schemes, since the dual reservation scheme allows use of a slot even if the slot is owned by another node. IEEE 802.15.6 and IEEE 802.15.4 also have reserved slots; however, in these schemes, a slot cannot be used if it is owned by another node.For urgent data, the goal is to guarantee a delay that is below a given deadline (20 ms), not that the delay is the minimum possible value. Therefore, we measure the percentage of packets that exceeds the required deadline. The throughput is measured by the sensor nodes. When a node receives an ACK message from a data frame, it records the throughput with the size of the data frame. The utilization of a phase is measured by a node. When the node successfully transmits a data frame, the node records a utilization in that phase. Remark 1.\u00a0As previously mentioned, the contention window of CoR-MAC is divided into SIFS, MIFS and LIFS. This will lead to overhead, such as the increasing of each time slot\u2019s size and extra energy consumption. As shown in i.e., the slots are dually reserved) in order to increase the overall throughput.In this paper, we addressed the problem of the delay of urgent data and time-critical data. We also addressed the utilization of dedicated slots. Existing WBASN schemes cannot properly resolve the above problems and do not address heavy traffic load situations, since they do not consider urgent data transmission. To reduce the delay of urgent data transmission, we proposed a contention over reservation MAC protocol for WBASNs. Our protocol exploits CFP reservation among nodes. For the reservation, traffic is divided into urgent, time-critical and non-time critical data, in descending order of priority. Each time slot in the CFP is dedicated to a node that might transmit urgent data. To increase transmission opportunities, urgent data can be transmitted over the unused CFP time slots. Since the urgent data are sporadically generated, the slots of CFP can be further reserved for time-critical data (The simulation results show that our protocol is very effective and provides significantly shorter delay by providing opportunistic transmission chances. In the simulation, CoR-MAC shows an approximate 50%\u2013850% better performance in the delay of urgent and time-critical data. Furthermore, our protocol provides flexible power consumption compared to the existing protocols."}
+{"text": "A common problem in phylogenetic analysis is to identify frequent patterns in a collection of phylogenetic trees. The goal is, roughly, to find a subset of the species (taxa) on which all or some significant subset of the trees agree. One popular method to do so is through maximum agreement subtrees (MASTs). MASTs are also used, among other things, as a metric for comparing phylogenetic trees, computing congruence indices and to identify horizontal gene transfer events.https://code.google.com/p/mfst-miner/.We give algorithms and experimental results for two approaches to identify common patterns in a collection of phylogenetic trees, one based on agreement subtrees, called maximal agreement subtrees, the other on frequent subtrees, called maximal frequent subtrees. These approaches can return subtrees on larger sets of taxa than MASTs, and can reveal new common phylogenetic relationships not present in either MASTs or the majority rule tree (a popular consensus method). Our current implementation is available on the web at Our computational results confirm that maximal agreement subtrees and all maximal frequent subtrees can reveal a more complete phylogenetic picture of the common patterns in collections of phylogenetic trees than maximum agreement subtrees; they are also often more resolved than the majority rule tree. Further, our experiments show that enumerating maximal frequent subtrees is considerably more practical than enumerating ordinary  frequent subtrees. A phylogenetic tree is an unordered rooted tree whose leaves are in one-to-one correspondence with a set of species ; its topology represents the hypothetical evolutionary relationships among these species.agreement subtree (AST) for a collection of phylogenetic trees on a common leaf set is a minimal subtree connecting a fixed set of leaves that is homeomorphically included in all of the input trees. A maximal agreement subtree (MXST) is an agreement subtree that is not a subtree of any other agreement subtree. An MXST is a maximum agreement subtree (MAST) if it has the largest number of leaves  is an agreement triplet if all the input trees display the same topology over the leaf set {i,j,k}. For an ordered pair of trees  in an equivalence class, having a and b as their respective rightmost leaves, we say tree Tabexists if  join as Tab across all the input trees. Let I, J and K be three trees belonging to a common equivalence class; let i, j and k be their respective rightmost leaves. Suppose that Tij and Tik exist. If the ordered pair  exhibits a common join across all the input trees, we denote the join as Ti\u2212jk. Theorem 2 characterizes pruning among \u201csiblings\u201d and \u201cfirst cousins\u201d in the enumeration tree.For the next set of results, let X prunes Y if either of the following holds: 1. Txy exists and is not of join type 2.(a) Txy exists as a join of type 2 and for every child Z of E such that Tyz exists,  is an agreement triplet.(b) Txy and Tyz exist, and Txy is of join type 2, then Tyz is not of join type 2.2. If Part 1 of Theorem 2 deals with pruning among siblings; part 2 deals with pruning among first cousins. The proof of Theorem 2 relies on Lemmas 1, 2, 3 and 4, which we present next.Lemma 1. Suppose that Txy and Tyzexist. Then, the following holds:1. If Txyis not a result of a type-2 join:(a) Txzexists and is not a result of a type-2 join.(b) There exists an AST T on leaf setandis a descendant of X.2. If both Txy and Tyzare results of join type 2, and  is an agreement triplet:Txzexists.(a) (b) There exists an AST T on leaf setandis a descendant of X.3. If Txyis a result of a type-2 join and Tyzis not a result of a type-2 join:(a) Txzexists and is not a result of a type-2 join.(b) There exists an AST T on leaf setandis a descendant ofTxy\u2212z exists.Y, X has a descendant  whose core tree displays Tyx. Intuitively, this is an intermediate step in proving conditions under which X either prunes Y or Y or Txy and Tyz can be a result of one of the four types of join. Thus, considering Txy and Tyz together, there are 16 possibilities. Out of these, the case where each Txy and Tyz is result of a type-2 join is the only case where there can be multiple topologies that display both Txy and Tyz. That is why type-2 joins have a special significance in Lemma 1. The remaining 15 cases guarantee the existence of a single topology that displays both Txy and Tyz.Lemma 1 gives conditions under which for a given child Lemma 2. If Txyand Txzexist, and  is an agreement triplet, either Tx\u2212yz or Tx\u2212zy exists.X with y and z as the rightmost leaves of their respective core trees, the existence of agreement triplet  is a sufficient condition for the children to join in one of the two possible ways. That is, there exists only one topology that displays both the children; further, the topology must be a descendant of X.Lemma 2 states that for any two children of Lemma 3. Suppose A and B are two ASTs with a and b as their respective rightmost leaves such thatThen,is a descendant ofif and only if for everyTa\u2113exists.Lemma 4. Suppose Txyexists as a result of a type-2 join and D is descendant of Y. Then, for anyx,a,b] is an agreement triplet if  and  are agreement triplets.Txy. Intuitively, it states that for any two children of Y with a and b as the rightmost leaves of their respective core trees, agreement triplets  and  together form a sufficient condition for the existence of a descendant of X whose core tree displays the core trees of both children of Y. This is a stepping stone in proving that for every descendant D of Y, there exists a descendant of X whose core tree displays the core tree of D, thus, X prunes Y.Lemma 4 deals with the special case of type-2 joins for http://evolution.genetics.washington.edu/phylip/newicktree.html). E.g., ) represents the tree with leaf set {a,b,c} where the LCA of b and c is a proper descendant of the LCA of a, b and c, and  represents unresolved (star) tree on {a,b,c}.The proofs of the above Lemmas are given in Appendix: Proofs. We present next the proof of Theorem 2. In the proof, and in the rest of the paper, we represent trees in parenthesized Newick format  Txa\u2208X and Txb\u2208X exist, and each is also not a result of a type 2-join, and (ii) there exists ASTs on leaf sets x,y,a] and  are agreement triplets. Let A and B denote the children of E with a and b as their respective rightmost leaves. Since AST S exists, there exists an AST on leaf set Tab\u2208A or Tba\u2208B exists. Without loss of generality, let Tab exist. Since, Txa exists and is not a result of a type-2 join, and Tab exists, as per Lemma 1.1, there exists an AST on leaf set 1. (a) Consider any descendant Tx\u2113 exists,\u2022 for every leaf x1,x2} in\u2022 thus, for every pair of leaves {Xc,  is an agreement triplet.\u2022 \u2022 for every pair of leaves\u2022\u2022 on leaf set \u2113 in Xc,  is an agreement triplet.\u2022 leaf T on leaf set T displays Sc. Further, for every Tx\u2113 exists. Thus, by Lemma 3, T is descendant of X. Hence, X prunes Y, as claimed.Thus, there exists an AST S of Y. Consider any S is a descendant of Y, by Lemma 3, Tya and Tyb exists. Thus, as per the if condition of the claim to be proved,  and  are agreement triplets. Since Txy exists as a result of type-2 join and,  and  are agreement triplets, by Lemma 4,  is an agreement triplet, and, by Lemma 1 (part 2 and 3), Txa and Txb exist. Thus, as per Lemma 2, there exists an AST on leaf set (b) Consider any descendant Tx\u2113 exists,\u2022 for every leaf x1,x2} in\u2022 thus, for every pair of leaves {Xc,  is an agreement triplet.\u2022 \u2022 for every pair of leaves\u2113 in Xc, there exists and AST on leaf set \u2113,a,b] is an agreement triplet.\u2022T on leaf set T displays Sc. Further, for every Tx\u2113 exists, thus, by Lemma 3, T is descendant of X. Hence, X prunes Y, as claimed.Thus, there exists an AST Tyz is not a result of a type-2 join, by Lemma 1.3, Txz exists and is not a result of a type-2 join, and Txy\u2212z exists. Consider any descendant S of S is a descendant of Y, by Lemma 3, Ty\u2113 exists. We show that Ty\u2113 is not a result of a type-2 join by contradiction. Let Ty\u2113 be a result of a type-2 join with triplet  of type ). Since S is a descendant of Tyz,Ty\u2113) exists. Let Tyz be of type 1 join with triplet  of type . Since Ty\u2212z\u2113 displays both ) and , it must also display ,z). However, ,z) cannot exist in Ty\u2212z\u2113 because \u2113 and z cannot be the last and second-to-last leaves respectively in the IDFT. Similarly, for Tyz of join type 3 or type 4, we can show that \u2113 cannot be the rightmost leaf in Ty\u2212z\u2113. Thus, Ty\u2113 is not of join type 2. Thus, by Lemma 1.3, Tx\u2113 exists and is not a result of type 2 join, and Txy\u2212\u2113 exists. Consider any Txa and Txb exist and each is not a result of join type 2. Let A and B denote the ASTs in E with a and b as their rightmost leaves. Without loss of generality, let the AST on leaf set Ac,Bc), i.e., Tab exists. Thus, by Lemma 1.1, there exists an AST on leaf set 2. Since Txy\u2212\u2113 exists, thus, for every pair of leaves {x1,x2} in Txy,  is an agreement triplet.\u2022 for every \u2113 in Txy, there exists an AST on leaf set \u2113,a,b] is an agreement triplet.\u2022 for every T on leaf set T displays Sc. Further, since for every Txy\u2212\u2113 exists, by Lemma 3, T is descendant of Thus, there exists an AST \u25a1Y. However, there are cases when Y or a descendant of Y is pruned by X but it cannot be identified using Theorem 2. In this case, the branch at Y must be enumerated and potential pruning by X verified. For this, we maintain a \u201cpruner-list\u201d for every child of Y. We explain this idea next.Note that conditions in part (1a) and part (2) of Theorem 2 can be evaluated in constant time while testing the condition in part (1b) of Theorem 2 takes time linear in the size of the tree being pruned. Neither of these require enumerating the pruned branch at X,Y,Z be children of an equivalence class E in the enumeration tree. Let x,y,z be the rightmost leaves of Xc,Yc,Zc respectively. Let joins Txy,Tyz exist such that none of the cases of Theorem 2 hold. Then the pruner-list of Let Now, using arguments similar to the proof of Theorem 2, we can show that:Y is pruned by an equivalence class A with a as the rightmost leaf of Ac if either of the following holds: Y has no children and has a in its pruner-list.1. Y have a in their pruner-list.2. All children of MFSTMINER for the special case of enumerating all MXSTs for a collection C of input trees. MFSTMINER first invokes ENUMERATEAST_TRIPLETS (whose details are omitted) to enumerate all AST triplets and to partition them into equivalence classes. The set of all such classes is denoted by EC3. Note that each equivalence class in EC3 is a child of the root of the enumeration tree. After this, MFSTMINER invokes subroutine ENUMERATENODE, explained next, to enumerate the elements of the branch at each equivalence class in EC3. Algorithm 1 is a high-level description of ENUMERATENODE, which accepts an equivalence class E as input and enumerates the branch at E in the enumeration tree. In the pseudocode, Tx denotes an AST that has x as its rightmost leaf. Lines 3-5 perform pair-wise joining among members of an equivalence class in the enumeration tree. Comments in braces indicate where the algorithm performs assignment to pruner-lists, as per conditions (2) and (3), and pruning, according to the different cases of Theorems 2 and 3. In line 12, the core tree of an empty equivalence class \u2014 representing a leaf node \u2014 is produced as output if it is found to be not pruned. Algorithm 2 shows the details of ENUMERATENODE calls itself recursively to enumerate the children of a non-empty equivalence class In line 17, MFSTMINER handles the general case of mining MFSTs. The main difference between mining for MXSTs and mining for MFSTs is that the former is (as we have seen) based on enumerating ASTs, while the latter is based on enumerating FSTs. While an ASTs must be supported by all the input trees , an FSTs need only be supported by some fraction We now explain how Tx and Ty in an equivalence class, a join Txy on ordered pair  is an FST if it is supported by at least a fraction f of the input trees . Note that any such Txy is supported only by those trees that support both Tx and Ty as well. Motivated by this, for each FST Tx we maintain a support list, denoted by Tx.supList, that contains all trees in the input collection that support Tx. To estimate if the join on  results in an FST, we apply Theorem 1 only on trees in Tx.supList\u2229Ty.supList. We store the support list as a bitmap  is a frequent triplet if at least fraction f of the input trees display the same triplet over the leaf set {x,y,z}. Let .supList denote the support list of such a frequent triplet. Based on this, we can restate Theorem 2 for the case of enumerating MFSTs as follows.To verify whether an equivalence class X prunes Y if either 1. Txy exists, Yc.supList\u2286Xc.supList and Txy is not of join type 2, or(a) Txy exists as a type-2 join, Yc.supList\u2286Xc.supList and for every Z\u2208E such that Tyz exists,  is a frequent triplet with Yc.supList\u2286.supList.(b) Txy and Tyz, exist and Txy is of join type 2, then Tyz is not of join type 2 and Tyz.supList\u2286Txy.supList.2. If Tx,Ty,Tz be FSTs in an equivalence class E with x,y,z as their respective rightmost leaves, such that joins Txy and Tyz exist, and none of the cases of Theorem 4 hold. For an equivalence class A, let A.prunerList denote its pruner-list. Then, the next set of conditions describe pruner-lists for enumerating MFSTs. Pruning cases not identified by Theorem 4 require the use of pruner-list. In the case of MFSTs, along with leaf label the pruner-list also contains the support list of the core tree of the equivalence class that is claiming to prune. To explain further, let x,Txy.supList) if Txy is not of join type 2 and |Txy.supList\u2229Tyz.supList|\u2265f.1.x,S\u2229=Txy.supList\u2229.supList) if Txy is of join type 2,  is a frequent triplet and |S\u2229\u2229Tyz.supList|\u2265f.2.w such that S\u2229\u2229Tyz.supList|\u2265f.3. For every leaf label Condition 1 and 2 describe addition of new labels to the pruner-list of A with a as the rightmost leaf of Ac, Given an equivalence class A if (i) for every a,Sb(a)), and (ii) for 1.A if (i) a in its pruner list, or (ii) every child A as per part 1 of this Theorem.2.MFSTMINER for the general case of mining MFSTs. The overall framework is the same as the special case of mining all MXSTs. The difference lies in the finer details of incorporating support lists in the support estimation and the pruning step. These details were discussed in this section and are easy to incorporate in Algorithms 1 and 2.This completes the description of MFSTMINER algorithm. In the following discussion, let the input collection consist of n trees on a common leaf set f denote the input fraction for computing f-frequent subtrees.Here we discuss the runtime complexity of the preprocessing step, the data structures used in the algorithm implementation and the memory requirements in each step of T in the input collection, and every pair {u,v} of leaves of T, step (1) computes LCAT and stores it in a three-dimensional array indexed by triplet , thus, requires f=1. We should point out that it is well-known that one can pre-process a tree in linear time and space to produce a data structure that can answer any LCA query on that tree in constant time  is of type . We have four possibilities to consider. 1. Suppose Tyz is a result of a type-1 join <\u03c8(z) and agreement triplet  is of type . Potential AST T must be obtained by grafting z in Txy. Since T must display , there is only one possibility of grafting z in Txy: z should be grafted on the common parent of x and y. Thus, AST T exists. Further, since, \u03c8(x)<\u03c8(y)<\u03c8(z), there is only one possible canonical topology for potential AST T: see Figure T has x, y, z, as the third-to-last, second-to-last and last leaf respectively in the IDFT, pruning y will result in a tree that is (a) canonical, (b) has z as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txz  Tyz is a result of a type-2 join <\u03c8(z) and agreement triplet  is of type ). Potential AST T must be obtained by grafting z in Txy. Since T must display ), there is only one possibility of grafting z in Txy: z should be grafted on the edge . Thus, AST T exists. Further, since, \u03c8(x)<\u03c8(y)<\u03c8(z), there is only one possible canonical topology for potential AST T; see Figure T has x, y, z as the third-to-last, second-to-last and last leaf respectively in the IDFT, pruning y will result in a tree that is (a) canonical, (b) has z as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txz  Tyz is a result of a type-3 join , there is only one possibility of grafting x in Tyz: x should be grafted on the parent of y. Thus, AST T exists. Further, since, \u03c8(x)<\u03c8(y), there is only one possible canonical topology for potential AST T; see Figure T has x, y, z as the third-to-last, second-to-last and last leaf respectively in the IDFT, pruning y will result in a tree that is (a) canonical, (b) has z as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txz  Tyz is a result of a type-4 join , there is only one possibility of grafting x in Tyz: x should be grafted on the parent of y. Thus, AST T exists. Further, since, \u03c8(x)<\u03c8(y), there is only one possible canonical topology for potential AST T; see Figure T has x, y, z as the third-to-last, second-to-last and last leaf respectively in the IDFT, pruning y will result in a tree that is (a) canonical, (b) has z as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txz  in T will result in Txy. Thus, X.(d) Txy is a result of a join of type 3 or 4, irrespective of the type of join Tyz is a result of, ASTs T and Txz exist, Txz is not a result of a type-2 join, and X.Similarly, one can show that if Txy and Tyz is a result of a type-2 join ) and \u03c8(y)<\u03c8(z). Potential AST T must be obtained by grafting z in Txy. Since T must display ) and \u03c8(x)<\u03c8(y)<\u03c8(z), there are four possible canonical topologies for potential AST T: see Figures x,y,z] is an agreement triplet, only one of the four topologies exists across all input trees. Thus, AST T exists.2. Suppose each of T are y and z (either y comes before z or vice-versa), while x is the third-to-last leaf. Thus, pruning y in T will result in a canonical tree where x and z are the second-to-last and last leaves in the IDFT. By definition, the resulting tree is Txz. Thus, Txz exists. Further, pruning the last leaf in T will result in either Txy (if z is the last leaf in T) or Txz (if y is the last leaf in T). In either case, X, as claimed.Further, in all the cases discussed above, the last two leaves in the IDFT of Txy is a result of a type-2 join. Thus, \u03c8(x)<\u03c8(y). Consider the following possibilities: 3. Suppose Tyz is a result of a type-1 join <\u03c8(z). Potential AST T must be obtained by grafting x in Tyz. Since T must display ), there is only one possibility of grafting x in Tyz: x should be grafted on the edge . Thus, AST T exists. Further, since, \u03c8(x)<\u03c8(y)<\u03c8(z), there is only one possible canonical topology for potential AST T: see Figure T has x, y, z as the third-to-last, second-to-last and last leaf respectively in the IDFT, pruning y will result in a tree that is (a) canonical, (b) has z as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txz  Tyz is a result of a type-3 join ), there is only one possibility of grafting x in Tyz: x should be grafted on the edge . Thus, AST T exists. Further, since, \u03c8(x)<\u03c8(y), there is only one possible canonical topology for potential AST T: see Figure T has x, y, z as the third-to-last, second-to-last and last leaf respectively in the IDFT, pruning y will result in a tree that is (a) canonical, (b) has z as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txz  Tyz is a result of a type-4 join ), there is only one possibility of grafting x in Tyz: x should be grafted on the edge . Thus, AST T exists. Further, since, \u03c8(x)<\u03c8(y), there is only one possible canonical topology for potential AST T: see Figure T has x, y, z as the third-to-last, second-to-last and last leaf respectively in the IDFT, pruning y will result in a tree that is (a) canonical, (b) has z as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txz  y and z are the second-to-last and the last leaves in T. Thus, pruning z \u2014 the rightmost leaf \u2014 in T will result in a tree that is (a) canonical, (b) has y as the last leaf in the IDFT, and (c) has x as the second-to-last leaf in the IDFT. By definition, the resulting tree is Txy. Hence, Further, in all the above cases, \u25a1\u03c8(y)<\u03c8(z). Let px, py and pz denote the parent of x, y and z respectively. Consider the following cases: Without loss of generality, let Tx\u2212yz exists as a result of a type-4 join.1.Tx\u2212zy exists as a result of a type-4 join.2.3.x,y,z] is of type . Thus, depth)=depth)=depth) across all input trees. Thus, as per Theorem 1, Tx\u2212yz exists as a result of a type-1 join.(a) Agreement triplet  is of type ). Thus, depth)=depth) and depth)<depth) across all input trees. Thus, as per Theorem 1, Tx\u2212yz exist as a result of a type-2 join.(b) Agreement triplet  is of type ,z). Thus, depth)>depth) across all input trees. Thus, as per Theorem 1, Tx\u2212yz exists as a result of a type-3 join.(c) Agreement triplet  is of type ,y). Thus, depth)>depth) across all input trees. Thus, as per Theorem 1, Tx\u2212zy exists as a result of a type-3 join.(d) Agreement triplet  is an agreement triplet , where T1=A, such that B. Thus, Txy is a result of a type-2 join, agreement triplet  is of type ) and \u03c8(x)<\u03c8(y). Consider any x,y,\u2113] is an agreement triplet. Since D is a descendant of Y, by Lemma 3, Ty\u2113 exists. Since,  is an agreement triplet, by Lemma 1, there exists an AST T on the leaf set Txy and Ty\u2113, and X. Consider the possible topologies for T.  Since Txy is a result of a type-2 join, the topology of T depends on the type of join Ty\u2113 is a result of. Consider the following cases. Since Ty\u2113 is a result of a type-1 join. There exists only one possible canonical topology for T: the one corresponding to Figure z with \u2113 in tree T).1. Ty\u2113 is a result of a type-2 join. There exists four possible canonical topologies for T: the ones corresponding to Figure z with \u2113 in tree T).2. Ty\u2113 is a result of a type-3 join. There exists only one possible canonical topology for T: the one corresponding to Figure z with \u2113 in tree T).3. Ty\u2113 is a result of a type-4 join. There exists only one possible canonical topology for T: the one corresponding to Figure z with \u2113 in tree T).4. T, only one has \u2113 as the second-to-last leaf in the IDFT: the one corresponding to Figure z with \u2113 in tree T). Thus, this topology belongs to belongs to y as the second-to-last leaf in the IDFT, thus belong to x,y,a] and  are agreement triplets. Thus, by our earlier discussion in this proof, there exist ASTs Ta on leaf set Tb on leaf set X. Consider the following cases: Note that out of the possible topologies for Ta and Tb belong to y,a,b] is an agreement triplet, by Lemma 2, there exists an AST on leaf set x,a,b] is an agreement triplet.1. Both Ta and Tb do not belong to Ta belong to z with a in tree T). Thus, agreement triplet  is of type ,y) and \u03c8(x)<\u03c8(a). Consider potential AST T\u2019 on leaf set Ta and Tb. Since, the topology Ta is known, the topology of T\u2019 depends on the topology of Tb. Consider the following cases. In the subsequent discussion, let px, py, pa and pb denote the parent of x, y, a and b respectively. 2. Both Tb corresponds to the topology in Figure z with b in tree T). Potential AST T\u2019 must be obtained by grafting a in Tb. Since T\u2019 must display ,y), there is only one possibility of grafting a in Tb: a should be grafted on the edge . Thus, T\u2019 exists. Considering \u03c8(x)<\u03c8(a), the canonical topology for AST T\u2019 is shown in Figure (a) Tb corresponds to the topology in Figure z with b in tree T). Potential AST T\u2019 must be obtained by grafting a in Tb. Since T\u2019 must display ,y), there is only one possibility of grafting a in Tb: a should be grafted on the edge . Thus, T\u2019 exists. Considering \u03c8(x)<\u03c8(a), the canonical topology for AST T\u2019 is shown in Figure (b) Tb corresponds to the topology in Figure z with b in tree T). Potential AST T\u2019 must be obtained by grafting a in Tb. Since T\u2019 must display ,y), there is only one possibility of grafting a in Tb: a should be grafted on the edge . Thus, T\u2019 exists. Considering \u03c8(x)<\u03c8(a), the canonical topology for AST T\u2019 is shown in Figure (c) Tb corresponds to the topology in Figure z with b in tree T). Potential AST T\u2019 must be obtained by grafting a in Tb. Since T\u2019 must display ,y), there is only one possibility of grafting a in Tb: a should be grafted on the edge . Thus, T\u2019 exists. Considering \u03c8(x)<\u03c8(a), the canonical topology for AST T\u2019 is shown in Figure (d) Tb corresponds to the topology in Figure z with b in tree T). Thus, \u03c8(x)<\u03c8(b). Since, both Ta and Tb correspond to the topology in Figure \u03c8(a)<\u03c8(b). Potential AST T\u2019 must be obtained by grafting a in Tb and must display ,y). Since \u03c8(x)<\u03c8(a)<\u03c8(b), there are four possible canonical topologies for T\u2019; see Figure y,a,b] is an agreement triplet, thus, only one of the four possible topologies exits across all input trees Thus, T\u2019 exists.(e) Tb corresponds to the topology in Figure z with b in tree T). Potential AST T\u2019 must be obtained by grafting a in Tb. Since T\u2019 must display ,y), there is only one possibility of grafting a in Tb: a should be grafted on the edge . Thus, T\u2019 exists. Considering \u03c8(x)<\u03c8(a), the canonical topology for AST T\u2019 is shown in Figure (f) Tb corresponds to the topology in Figure z with b in tree T). Potential AST T\u2019 must be obtained by grafting a in Tb. Since T\u2019 must display ,y), there is only one possibility of grafting a in Tb: a should be grafted on the edge . Thus, T\u2019 exists. Considering \u03c8(x)<\u03c8(x), the canonical topology for AST T\u2019 is shown in Figure (g) T\u2019 exists. Thus,  is an agreement triplet.Thus, in each of the above cases This completes the proof. \u25a1The authors declare that they have no competing interests.AD and DFB conceived the problem, designed the experiments and drafted the manuscript. AD designed and implemented the algorithms, and implemented the experiments. DFB coordinated the project. All authors read and approved the final manuscript."}
+{"text": "While tree-oriented methods for inferring orthology and paralogy relations between genes are based on reconciling a gene tree with a species tree, many tree-free methods are also available . Recently, the link between orthology relations and gene trees has been formally considered from the perspective of reconstructing phylogenies from orthology relations. In this paper, we consider this link from a correction point of view. Indeed, a gene tree induces a set of relations, but the converse is not always true: a set of relations is not necessarily in agreement with any gene tree. A natural question is thus how to minimally correct an infeasible set of relations. Another natural question, given a gene tree and a set of relations, is how to minimally correct a gene tree so that the resulting gene tree fits the set of relations.We consider four variants of relation and gene tree correction problems, and provide hardness results for all of them. More specifically, we show that it is NP-Hard to edit a minimum of set of relations to make them consistent with a given species tree. We also show that the problem of finding a maximum subset of genes that share consistent relations is hard to approximate. We then demonstrate that editing a gene tree to satisfy a given set of relations in a minimum way is NP-Hard, where \u201cminimum\u201d refers either to the number of modified relations depicted by the gene tree or the number of clades that are lost. We also discuss some of the algorithmic perspectives given these hardness results. Homologous gene are grouped into gene families, usually via sequence similarity methods. Moreover, homologous genes can be orthologous, if their parental origin is a speciation, or paralogous, if it is a duplication. Orthologous gene are considered to be more similar in function than paralogs, a conjecture known as the orthology conjecture\u00a0S-consistgiven in\u00a0. The S-cR of relations: minimize the number of modified relations, and maximize the number of genes inducing an S-consistent set of relations. The first problem is shown to be NP-complete, while the second problem is shown to be not approximable within factor In this paper, two criteria are considered for correcting a set X, a tree T for X is a tree whose leafset X. We denote by V(T) the set of nodes and by r(T) the root of T. Given an internal node u of T, the subtree rooted at u is denoted clade ofu. A node u is an ancestor of v if u is on the (inclusive) path between v and the root, and we then call v a descendant of u. If v is a strict descendant of u, and if u and v are connected by an edge of T, then v is a child of u. The lowest common ancestor (lca) of u and v, denoted u and v are separated if and only if U of nodes. Let T to T rooted as T displays All trees considered in this paper are assumed to be rooted. They are not necessarily binary, but we assume that all nodes are of degree at least three, except possibly the root that can be of degree two. Given a set speciation, which is the separation of one species into distinct ones. A species tree S for a species set gene family is a set of genes mapping functiongene tree for Spec) or duplication (Dup) accordingly.Species evolve through DS-tree for G is a tree with G as a duplication or a speciation node  of G with children v can be made to be binary while preserving Let DS-tree v, adding a child v and adding S-consistent. It is readily seen that If v, v has a child v is a speciation, v, adding two children v, then adding S-consistent. As for v, by the definition of v is S-consistent. The species for every other node remaining unchanged, we conclude that S-consistency and does not modify If instead DS-trees in Fig.\u00a0S-consistent. For example, the speciation node z in v,\u00a0c,\u00a0d and w, which are pairwise separated in S. Notice that, from Definition\u00a0G is a DS-tree, then the lca of two leaves of G belonging to the same species must be a duplication node. The converse is not true. For example, in the S-consistent gene tree G of Fig.\u00a0We can verify that both mentclass2pt{minimmentclass2pt{minimfull if DS-tree G induces a full set A set of orthology/paralogy relations on relation graphR on a gene family uv of the edge set E(R) of R as an orthology relation between u and v, and each missing edge (non-edge) DS-tree G, denoted by R(G), is the graph with vertex set R in Fig.\u00a0We adopt the graph representation considered in\u00a0 for fullmentclass2pt{minimDS-tree for a gene family R is satisfiable if there exists a DS-tree G such that A essed in\u00a0. The fol A relation graph R is satisfiable if and only if Ris-free, meaning that no four vertices of Rinduce a path of length three. A relatR and DS-tree does not necessarily represent a true history for R should be consistent with the species tree, according to the following definition.For example, in Fig.\u00a0mentclass2pt{minimS, a relation graph R for S-consistent if and only if R is satisfiable by a DS-tree G which is itself S-consistent.Given a species tree R in Fig.\u00a0S-consistent. Notice that S-consistency implies satisfiability. Results from\u00a0[S-consistent graphs through Theorem\u00a0L of size three. For xy|z the unique triplet T on L for which S-consistency of a relation graph in terms of For example the graph lts from\u00a0 completeentclass1pt{minimaentclass1pt{minimaentclass1pt{minimaLet G be a DS-tree and S be a species tree. Then for any internal node v of G, there exist leaves x,\u00a0y of  such that both the following hold: (1)  and (2)x and y of s(x) and s(y), then (1) holds. Thus if we suppose that (1) does not hold, then We first show that (1) must hold for some x and y satisfying (1). Suppose that (2) does not hold for x and y, i.e. z is separated from v (i.e. x and z satisfy both (1) and (2). Otherwise, s(x) from s(y). In this last case, y and z are the leaves of interest, ending the proof. Now, take Let be a satisfiable relation graph and let S be a species tree. Then R is S-consistent if and only if S displays all the triplets of G be an S-consistent gene tree satisfying R, and let S must display the s(x)s(y)|s(z) triplet. Let xy|z must be a triplet of G. Moreover, since s(z) must be separated in S, implying that s(x)s(y)|s(z) is a triplet of S.R is satisfiable by some DS-tree DS-tree G satisfying R, in terms of speciation. That is, if v that has a speciation child w, we obtain v and w (delete w and give its children to v). Note that we have R. We obtain the DS-tree G by repeating this operation until we cannot find such a v and w. We claim that if S displays the triplets of G is S-consistent.v be a speciation node of G, and let v. By the construction of G, v is a speciation while R, which implies that S displays the S displays the S. We deduce that all child pairs of v are from separated species, and hence that G is S-consistent. Let entclass1pt{minimaS-consistent as the path of length 2 containing ac|b, while the triplet displayed by S is ab|c.As an example, the graph entclass1pt{minimasubgraphH is a graph with H and some subgraph ofHinduced byH with vertex-set induced subgraph of H if there is a subset I is another graph, we say H is I-free if there is no I. Finally, for some edge set We end this section with additional notations that will be of use later. A R in order to reach satisfiability and S-consistency. Two optimality criteria are considered: (1) the minimum number of edges that need to be removed; (2) the maximum number of genes that can be kept.We raise the issue of leaving out a minimum of information from a relation graph S does not make the problem of removing the minimum number of edges leading to a Based on the same construction used in paper\u00a0, we showsertion)\u00a0, here weMinimum edge-removal consistency problem:Input: A relation graph R for a gene family S and an integer k;Output: \u201cYes\u201d if and only if there exists an S-consistent subgraph R with The Minimum Edge-Removal Consistency Problem is NP-Complete, even if for any distinctS-consistent. It is also clear that verifying if W, does there exists W ? We assume that Given entclass1pt{minima problem\u00a0: given aW and Z, we construct R and S by first defining the species set X and Y. Then the species set is S is obtained by first connecting S has exactly g and its species s(g). We then define R with R, where R has Given arbitrary R described above can clearly be done in polynomial time. We now show that W and Z admit an exact 3-cover if and only if R admits an S-consistent DS-tree after the deletion of at most Notice that the construction of W, R in which all edges between W-clique are those belonging to a R missing from S-consistent, we use Theorem\u00a0i, inducing the S. Therefore there exists an S-consistent gene tree  and we consider the approximation complexity of the corresponding optimization version.Maximum Node Consistency problem:Input: A relation graph R for a gene family S and an integer k;Output: \u201cYes\u201d if and only if there exists an S-consistent induced subgraph R with n is the number of nodes of R). We refer the reader to\u00a0[We show that Maximum Node Consistency\u00a0is hard to approximate within a factor eader to\u00a0 for a deR. Denote m genes: First, we define the set of genes S. First consider S as any binary tree over m leaves m leaves (thus S has R. We make no distinction between s(g).Now, we define the species tree R. Moreover, for each t with Now, define the relation graph R,\u00a0S). Denote by Let Let  be two subsets of nodes of a solution of Maximum Node Consistency\u00a0over instance  such that  and . Then there is no edge with one endpoint in and the other in q such that S contains the triplet Assume on the contrary that there is some Now, we are ready to prove the main result of this section.Let a graph H be an instance Maximum Independet Set\u00a0with m nodes, and let  be the corresponding instance of Maximum Node Consistencywith  nodes. ThenGiven an independent set  of H, we can compute in polynomial time a solution of Maximum Node Consistency\u00a0of size at least Given a solution of Maximum Node Consistency\u00a0on instance  of size at least k m, we can compute in polynomial time an independent set of H such thatH and define a solution of Maximum Node Consistency\u00a0on instance  of size at least S-consistent.Consider an independent set R,\u00a0S) of size at least km, and consider the subsets k such sets, otherwise The case j, consider the set j that belong to some subset k nodes, since otherwise k, thus concluding the proof. Given an index AP such that OPT is the optimal value of a solution to the problem  be the corresponding instance of Maximum Node Consistency\u00a0with H, runs R,\u00a0S) and returns the independent set resulting from Lemma\u00a0H on which R. Let We get the following as an immediate corollary, which will be of use later:The decision version of Maximum Node Consistency\u00a0is NP-Hard, even on instances in which for any distinct S, an S-consistent DS-tree G for G according to C in a minimal way. The goal is thus to find a DS-tree C such that the difference between G and G, S are all binary trees.In this section, we are given a gene family Maximum Homology Correction problem:Input: A species tree S, an S-consistent DS-tree G for a gene family k, a set O of orthology and a set P of paralogy relations;Output: \u201cYes\u201d if there exists an S-consistent DS-tree The Maximum Homology Correctionproblem is NP-Complete, even if S, G and  are required to be binary.S-consistency can be done in polynomial time, as well as counting the common orthologs/paralogs relations (the set of relations is quadratic in size). For our reduction, we use the Minimum Edge-Removal Consistency problem for the case of a gene family with at most one gene per genome, which is NP-Hard by Theorem\u00a0S, a relation graph R with V(R) in bijection with k, we construct an instance of the Maximum Homology Correction Problem, i.e. a species tree DS-tree G, an orthologous set O and paralogous set P.The problem is clearly in NP, as verifying G by mimicking S - that is by first copying S and its leaf labels, then replacing each leaf G by the gene S is binary, then so is G. All internal nodes of G are labeled as speciations, so all genes of R(G) is a clique. Finally, let G in order to satisfy P.Let S-consistent subgraph R obtained by removing at most k edges if and only if there is an DS-tree O and P with at most G.We show that that there is an R and S. Then there exists a S-consistent DS-tree k edges from R. By Lemma\u00a0S is binary, then so is R(G).mentclass2pt{minimP and breaks at most P as non-edges, plus at most k other non-edges. Thus k edges from Maximum clade correction problem:Input: A gene tree G, a species tree S, a set O of orthology and a set P of paralogy relations and an integer k;Output: \u201cYes\u201d if there exists an S-consistent DS-tree O and P such that G and k clades in common.S, G and G and grafting operations to add leaves to G and satisfy a prescribed relation without breaking other relations.Notice that if connectingx and giving it Grafting a new leaf x to a tree T corresponds to adding x to x as a new child of some node u of T; (2) connecting T with x; (3) subdividing an edge uv and adding x as a child of the newly created vertex.Given two trees Let G be an S-consistent gene tree, for some species tree S. Let x be a gene not in G and y be some gene in G with  Then there exists a gene tree obtained by grafting x to G such that the following conditions are satisfied:x and y are orthologs in  andis S-consistent;x to r(G) under a common parent yields the desired result. So we assume u of G such that adding x as a child of u satisfies the three conditions of the Lemma, then we are done. So assume that there is no node u to which we can add x as a child.If uv be an edge of G, and suppose that we graft\u00a0 x on uv to obtain p the parent of x on u is the parent of p (i.e. p has children x and v). Note that if S-consistency. We will find such a uv that guarantees this S-consistent), and that S-consistent. This will prove the Lemma.Let g be the lowest ancestor of y in G such that g does not exist was handled in the beginning of the proof. Now suppose that g that is also an ancestor of y. Note that x to p being the parent of x and g the parent of p. Then, S by our choice of S-consistency. Also, Let x as a child of g to obtain a new tree S-consistent. By the choice of g, only the latter is possible, implying that all children of g are from separated species in G, but not in g such that s(x). Note that x to p being the parent of x. We have g remain unchanged in S-consistent, again satisfying all required conditions. So instead suppose that The Maximum Clade Correction Problem is NP-Complete, even if S, G and  are required to be binary.S-consistency and comparing the set of clades from G and R,\u00a0S and k be the Maximum Node Consistency\u00a0instance, letting R be the relation graph with S the species tree and k an integer. Let S. Construct G as follows: first consider G as any binary tree with n leaves R. Then, replace each leaf G has exactly Verifying mentclass2pt{minimR admits an S-consistent induced subgraph with at least k nodes if and only if G, O and P admit an S-consistent DS-tree O and P such that G and We show that H be a DS-tree satisfying S-consistent. By Lemma\u00a0S is binary, then so is H. Now, since H corresponds a subtree G. Then build a DS-tree H by replacing each leaf H by Dup . It is not hard to imagine a branch-and-bound algorithm that solves the problem. Call an induced subgraph H of a relation graph Rbad if it is a S. Each As the problems considered in this paper are all computationally hard, only non-polynomial exact algorithms or approximation algorithms avenues can realistically be explored. Let us generalize the Minimum Edge-Removal Consistency problem to the minimum ear time\u00a0, and cleplied in\u00a0 to desigR. The idea is simple: as long as R has a bad subgraph H, remove every edge incident to a vertex of H and continue. Even though this is the best known approximation algorithm so far, it has the undesirable effect of isolating many vertices, motivating the exploration of alternative algorithms. One direction would be to consider existing ideas on the problem of satisfiability, i.e. finding the minimum number of editings required to make a graph As for approximations, an algorithm proposed in\u00a0 can be dposed in\u00a0.S and partial sets of relations O and P, verifies if there exists an S-consistent gene tree O and P and if so, constructs one among the set of all possible solutions. In ordre to correct a gene tree G, we can envisage an extension of this algorithm allowing to provide G as input, and pick, among the solutions of the algorithm the one which is the closest to G (either in terms of common homology relations or clades).As for gene tree correction, we have developed in\u00a0 a polynoA gene tree induces a set of orthology and paralogy relations between members of a gene family, but the converse is not always true. In this paper we have shown that attempting to modify a set of relations as least as possible in order to ensure consistency with a species tree leads to the formulation of NP-Complete problems. Moreover, even assuming that the given relations are error-free, it remains computationally difficult to correct a gene tree in order to fit the given set of relations. As various model-free methods are available to infer orthology and paralogy, these correction problems are of practical biological interest. A future direction would be to explore the exact branch-and-bound algorithms and heuristics mentioned in the last section, and design fast approximation algorithms for the relation graph and gene tree editing problems."}
+{"text": "It grows optimally at 88\u00a0\u00b0C by coupling the reduction of Fe(III) oxides to the oxidation of a wide range of compounds, including long-chain fatty acids, and also grows autotrophically with hydrogen and Fe(III). It is the first archaeon reported to use a direct contact mechanism for Fe(III) oxide reduction, relying on a single archaellum for locomotion, numerous curled extracellular appendages for attachment, and outer-surface heme-containing proteins for electron transfer to the insoluble Fe(III) oxides. Here we describe the annotation of the genome of \u201cG. ahangari\u201d strain 234T and identify components critical to its versatility in electron donor utilization and obligate Fe(III) respiratory metabolism at high temperatures. The genome comprises a single, circular chromosome of 1,770,093 base pairs containing 2034 protein-coding genes and 52 RNA genes. In addition, emended descriptions of the genus \u201cGeoglobus\u201d and species \u201cG. ahangari\u201d are described.The online version of this article (doi:10.1186/s40793-015-0035-8) contains supplementary material, which is available to authorized users. It is an obligate Fe(III)-reducing archaeon isolated from the Guaymas Basin hydrothermal system and grows at temperatures ranging from 65\u201390\u00a0\u00b0C, with an optimum at about 88\u00a0\u00b0C , which have pyruvate kinase and alpha/beta domains and are homologous to an A. fulgidus enzyme with pyruvate kinase activity in vitro CC but lack the LRCXXC motif characteristic of most CcmH proteins. However, they all flank a duplicate CcmF-encoding gene found only in \u201cG. ahangari\u201d (GAH_01093), G. acetivorans [F. placidus [.) oxides . The mosochromes . Archaeas absent . Similarain CcmH , we identivorans , and F. placidus .c biogenesis pathway, the iron-reducing Archaeoglobales, Geoglobus and Ferroglobus species, also have more c-type cytochromes than any other archaeon, and many of these c-type cytochromes have multiple heme groups [\u201cG. ahangari\u201d contains 21 genes ; and G. acetivorans has 16 c-type cytochromes (8 with more than 5 heme groups). By contrast, Archaeoglobus species, which do not use Fe(III) electron acceptors . Other species such as A. profundus and A. sulfaticallidus have only 1 monoheme c-type cytochrome and A. fulgidus has 3 c-type cytochromes (none of which have more than 5 heme groups).In addition to having a distinct cytochrome e groups , 18, 26.c-type cytochromes of \u201cG. ahangari\u201d was also investigated. The ExPASy TMPred program [c-type cytochromes have at least 1 transmembrane helix, consistent with their association to the cytoplasmic membrane. One of these c-type cytochrome proteins (GAH_00504) was predicted to be extracellular. We also identified several c-type cytochromes  with predicted sizes once in mature form  matching those reported for outer-surface heme-containing proteins required for the reduction of insoluble Fe(III) oxides, but not soluble Fe(III) citrate, by \u201cG. ahangari\u201d [c-type cytochromes likely function as the terminal electron carriers between the cells and the oxides.The subcellular localization of the putative  program  revealedhangari\u201d  . We identified a number of ub iquinone/menaquinone biosynthesis proteins in the genome of \u201cG. ahangari\u201d  respiration as their primary metabolism. Fe-S proteins and ferredoxins are regarded as some of the most ancient of electron transfer carriers [c-type cytochromes, some of them localized to the outer surface, is consistent with a mechanism evolved for efficient extracellular electron transfer in hot environments.In addition to carriers  and alsocarriers , which i\u201cG. ahangari\u201d strain 234T is only one of three members of the Archaeoglobales capable of dissimilatory Fe(III) respiration. Furthermore, it is an obligate Fe(III) reducer that grows better with insoluble than soluble Fe(III) species. Consistent with this, the genome contains a large number of c-type cytochromes within and on the cell surface, as well as other redox-active proteins such as thermostable ferredoxin and Fe-S proteins. The paucity of c-type cytochromes within non-Fe(III) respiring members of the Archaeoglobales (Archaeoglobus species) is consistent with the physiological separation between these archaea and F. placidus,G. acetivorans, and \u201cG. ahangari\u201d, which can gain energy for growth from the reduction of Fe(III) electron acceptors. Additionally, some genes required for both dissimilatory sulfate and nitrate metabolisms are absent in \u201cG. ahangari\u201d and G. acetivorans. This supports the physiological separation of Geoglobusspp. from F. placidus, which is capable of Fe(III)-, thiosulfate-, and nitrate respiration, and from Archaeoglobus species which are primarily sulfur-respiring organisms. Genomic data also support the reported physiological similarities between \u201cG. ahangari\u201d and other Archaeoglobales such as autotrophic growth with H2 via the reductive acetyl-CoA/Wood-Ljungdahl pathway and the use of similar electron donors, including short- and long-chain fatty acids. Noteworthy is the fact that genomic evidence supports the synthesis of the methanogenic coenzyme-F420 in \u201cG. ahangari\u201d, which is responsible for the characteristic fluorescence detected in all Archaeoglobusspp. except for \u201cG. ahangari\u201d or F. placidus. Hence, the genome sequence of \u201cG. ahangari\u201d provides valuable insights into its physiology and ecology as well as into the evolution of respiration within the Archaeoglobales.Geoglobus\u201d genus and \u201cGeoglobus ahangari\u201d species was accepted for publication with extenuating circumstances at several culture-collection agencies. Thus, upon the original publication \u201cG. ahangari\u201d strain 234T was accepted only at a single agency. In addition, the G\u2009+\u2009C mol% determined from the complete genome sequence (53.1\u00a0mol%) differs from that originally published (58.7\u00a0mol%), representing a discrepancy of over 5\u00a0mol%. This publication thus warrants an emended description of the genus Geoglobus and the type species, \u201cGeoglobus ahangari\u201d.The initial publication  of the \u201cGeoglobus\u201d is the one provided by Kashefi et al. [The description of the genus \u201ci et al. , with thi et al. . The G\u2009+Geoglobus ahangari\u201d is the one provided by Kashefi et al. [T and has been deposited at three culture collection agencies, which include the Deutsche Sammlung von Mikroorganismen und Zellkulturen (DSM-27542), the Japan Collection of Microorganisms (JCM 12378), and the American Type Culture Collection (BAA-425).The description of the species \u201ci et al. , 2, with"}
+{"text": "Given a graph G = , the problem is to partition the vertex set V into {V1, V2,\u2026, Vh}, where each Vi is maximized, such that for any two vertices x and y in Vi, there are k edge-disjoint paths connecting them. In this paper, we present an algorithm to solve this problem for all k. The algorithm preprocesses the input graph to construct an Auxiliary Graph to store information concerning edge-connectivity among every vertex pair in O(Fn) time, where F is the time complexity to find the maximum flow between two vertices in graph G and n = \u2223V\u2223. For any value of k, the k-edge-connected components can then be determined by traversing the auxiliary graph in O(n) time. The input graph can be a directed or undirected, simple graph or multigraph. Previous works on this problem mainly focus on fixed value of k.The problem of finding  Graph connectivity is a fundamental problem in computer science, which has many background applications in the real world. For example, reliability is one of the major concerns in communications networks: if a network is reliable, the network would still work when some nodes or edges fail. Reliability in communication networks can be represented by the connectivity between each pair of nodes. In social networks, computing the closeness among people is a very important problem, which also relates to the connectivity of the networks. There are many other applications which are related to the connectivity of networks, e.g., finding web pages of high commonality in internet searching; finding protein complexes and gene clusters in computational biology, etc.In theoretical computer science, graph connectivity has been well studied for more than forty years. It has a strong relationship with the problems of maximal network flow and minimal cut.undirected graph G = , where V is the vertex set and E is the edge set, an edge set Ec, which is a subset of E, is an edge-cut of nodes x, y \u2208 V, if removing all edges in Ec disconnects x and y in G. We say that x and y are k-edge-connected in G if there is no edge-cut disconnecting x and y with cardinality strictly less than k. In other words, there are at least k edge disjoint paths connecting x and y. From the definition, if two vertices x and y are i-edge-connected, they must be j-edge-connected for any integer j < i. If any vertex pair is at least k-edge-connected in G, we say that graph G is k-edge-connected. For example, in Given an G is k-edge-connected, we are interested in finding subsets of vertices which are k-edge-connected in G. Note that each vertex is k-edge-connected to itself. For example, in social networks, finding a group of people who are strongly connected is more important than computing the connectivity of the entire social network. In an undirected graph G = , a vertex set V\u2032 \u2286 V is a k-edge-connected component if it is a maximal subset of V such that for any two vertices x, y \u2208 V\u2032, x and y are at least k-edge-connected in G. For example, in a, b, c, f, g} is a 3-edge-connected component. It is easy to see that k-edge-connectivity is an equivalence relation in V. Thus, the set of the k-edge-connected components forms a partition of V. The 2-edge-connected and 3-edge-connected components for the example in a, b, c, d, e, f, g} and {a, b, c, f, g}, {d}, {e} respectively. The collection of k-edge-connected components is a partition of V immediately implies that every k-edge-connected component is unique and maximal.Instead of just determining whether the entire graph G = , let u, v \u2208 V. Let kuv be the maximum number of edge-disjoint directed paths from u to v, and kvu be the maximum number of edge-disjoint directed paths from v to u. Then, u and v are k-edge-connected, where k = min{kuv, kvu}. Notice that the directed paths from u to v and the directed paths from v to u may not be edge-disjoint. Moreover, kuv and kvu may be different. A k-edge-connected component of G is a maximal subset V\u2032 of V such that \u2200u, v \u2208 V\u2032, u and v are at least k-edge-connected.For a directed graph edge-cut of u and v is an edge set whose removal destroys either all the directed paths from u to v or all the directed paths from v to u. A min-cut of u and v is an edge-cut of u and v with minimum cardinality. If u and v are k-edge-connected, the cardinality of their min-cut is k. In b, c, f, g} are 2-edge-connected.An Problem Statement: Given a graph G = , find the k-edge-connected components of G for every k \u2265 1.k-edge-connected components of undirected graphs has been extensively investigated, especially for some small k.Finding k = 1, this problem is equivalent to finding the connected components of G, which can be done in linear time by a single breadth first search or depth first search.For k = 2, based on depth-first search, Tarjan presented an algorithm for finding all 2-edge-connected components in linear time in [For  time in .k = 3, the first linear time algorithm was given by Galil and Italiano [G into tree edges and back edges. The tree edges form the DFS-tree while each back edge forms a cycle with a path in the DFS tree. Thus, back edges may be considered one by one to increase the connectivity between vertices.For Italiano . Their mItaliano  were givk, Matula [G =  in O(\u2223V\u2223\u2223E\u2223) time. He also showed that given k in advance, testing whether a graph is k-edge-connected can be done in O(k\u2223V\u22232) time. Nagamochi and Watanabe [k-edge-connected components in a direct or undirected graph G =  given k in advance. Using the reduction in [k-edge-connected undirected graph G =  has a k-edge-connected spanning subgraph G\u2032 =  with \u2223E\u2032\u2223 = O(k\u2223V\u2223). They showed that the time complexity can be reduced to O(\u2223E\u2223 + k2\u2223V\u22232) for undirected graphs. This result is also based on an interesting observation: if the cardinality of a cut  is strictly less than k, then the edge connectivity of any two vertices x and y such that x \u2208 X and y \u2208 V \u2212 X is also strictly less than k. In this case, there is no need to consider such vertex pair  since x and y must be in different k-edge-connected components. Thus, O(\u2223V\u2223) time for finding min-cut of vertex pairs is sufficient. In database community, k-edge-connectivity problem is also a well studied research topic [O(hl\u2223E\u2223) time algorithm, where h is the height of the decomposition tree of the graph, and l is a small number which is less than \u2223V\u2223.For general , Matula  gave an Watanabe  gave an ction in , i.e., ach topic , 10. Basu, v \u2208 V can be represented by the cardinality of the minimum -cut in G, if the minimum -cut can be computed efficiently for all pairs of vertices, the edge connectivity problem could be solved efficiently. The cut tree (a.k.a. Gomory-Hu tree) [u, v)-cut for all pairs of vertices. A cut tree is a tree T = , where each edge  \u2208 ET has a weight which represents the cardinality of the minimum -cut in G, and the cardinality of the minimum -cut for any two vertices s and t \u2208 V is the minimum edge weight on the path connecting s and t in the cut tree T. To construct the cut tree, there are mainly two methods from Gomory and Hu [\u03b2 cut-tree to show the edge connectivity between vertices in directed graphs. From the \u03b2 cut-tree, the minimal of the maximal number of edge disjoint paths for any pair of vertices can be found easily. Schnorr [\u03b2 cut-tree by calculating the maximal flow O(\u2223V\u2223 log \u2223V\u2223) times, which was improved to 3\u2223V\u2223 \u2212 3 times by Gusfield and Naor [Since the edge connectivity of two vertices Hu tree)  is a gooy and Hu  and Gusfy and Hu , respecty and Hu  introduc Schnorr  construcand Naor .k-edge-connected components when k is given in advance, especially for some small k, e.g., k = 2, k = 3, or the input graph is an undirected graph. Our algorithm can give answers for all possible values of k, and for both directed and undirected, simple graph or multiple graph.Previous works focused on finding the k-edge-connected component can be solved by executing an algorithm for max-flow  time algorithm proposed by Goldberg and Tarjan [O(n5) time algorithm to get the min-cut of any two vertices. The other method is to use the global min-cut algorithm proposed by Stoer and Wagner [O(mn + n2 log n) time. If the min-cut capacity is more than k, the graph is a k-edge-connected component; otherwise, any two vertices separated by the cut cannot be in the same k-edge-connected component. In the worst case, the global min-cut algorithm can be executed n \u2212 1 rounds, leading to an O(n2m + n3 log n) time algorithm.If the capacity of each edge is regarded as one, computing  theorem ). Since d Tarjan , we can d Wagner , which fk-edge-connected components for all k in a directed or undirected, simple or multiple graph. We use an s-t max-flow algorithm as the basic procedure which is executed 2n \u2212 2 rounds to construct an auxiliary graph to store information concerning the edge-connectivity between all vertex pairs of the input graph. The time complexity to construct the auxiliary graph is O(Fn), where F is the time required to compute the maximal flow between two vertices in graph G, e.g., for the maximal flow algorithm of Ford and Fulkerson [F = O(fm), where f is the maximal value of all pairs of maximal flows, and for the algorithm by Goldberg and Tarjan [F = O(n3). Furthermore, any improvement made on F automatically implies improvement on the time complexity of our algorithm.In this paper, we give a simple algorithm to find the ulkerson , F = O time by a simple scan over the auxiliary graph.After the auxiliary graph is constructed, for any value of auxiliary graph, which could be used to efficiently find all k-edge-connected components for all k is introduced. In Section 3, the procedure Construction for constructing the auxiliary graph is presented. The correctness proof and the complexity analysis are given in Section 4 and Section 5, respectively. Finally, we give the concluding remark in Section 6.In Section 2, a data structure, called k-edge-connected components (k \u2265 1) is a partition of V. Moreover, each k-edge-connected component is the union of a collection of (k + 1)-edge-connected components. k-edge-connected components of the graph in k \u2208 {1, 2, 3} . Consider k = 2. The 2-edge-connected component {b, c, f, g} is the union of the collection of 3-edge-connected components {b}, {c}, {f}, {g}. For the remaining three 2-edge-connected components, each of them is the union of the collection consisting of the component itself. For k = 1. There is only one 1-edge-connected component {a, b, c, d, e, f, g} which is the union of the collection of 2-edge-connected components {a}, {d}, {e}, {b, c, f, g}.It is well-known that the set of k-edge-connected components, it is possible to store the k-edge-connected components, for all k \u2265 1, in a compact form in a data structure which we call auxiliary graph. The auxiliary graph, henceforth denoted by A, is a weighted undirected tree with vertex set V. Let h be the smallest integers such that the h-connected components are singletons. Let Ah be the edgeless spanning forest of A. Then the collection of all h-edge-connected components of G is the collection of vertex sets of the connected components of Ah (each of which consists of a single vertex). Let Ah\u22121 be a spanning forest of A obtained from adding the edges of weight h \u2212 1 of A to Ah. Then the collection of all (h \u2212 1)-edge-connected components of G is the collection of vertex sets of the connected components of Ah\u22121. In general, for k < h, let Ak+1 be a spanning forest of A such that the collection of all (k + 1)-edge-connected components of G is the collection of vertex sets of the connected components of Ak+1. Let Ak be a spanning forest of A obtained from adding the edges of weight k of A to Ak+1. Then the collection of all k-edge-connected components of G is the collection of vertex sets of the connected components of Ak.Owing to this hierarchical structure of a}, {b}, {c}, {d}, {e}, {f}, {g}). The collection of all 2-edge-connected components is represented by the spanning forest induced by the edge set consisting of edges of weight two. The collection of all 1-edge-connected components is represented by the spanning forest induced by the edge set consisting of edges of weight one or two which is the auxiliary graph itself. Notice that in this subgraph, the edges of weight one connect subtrees that represent 2-edge-connected components.Auxiliary Graph:A =  is a weighted undirected tree, which represents the edge connectivity among vertices in G. Two vertices u, v \u2208 V is k-edge-connected in G if k is the minimum edge weight on the path connecting u and v in A (see Lemma 4). A is constructed by procedure Construction.k-edge-connected components, for any value of k.In the next section, we shall explain how to construct the auxiliary graph and how to generate the collection of all s-t max-flow algorithm, e.g., Ford and Fulkerson algorithm [To determine the weights of the edges in the auxiliary graph, we can use any lgorithm .G is undirected, then each of its edges will be replaced by two directed edges with opposite orientations.Since the max-flow algorithms run on directed graphs only, if the input graph onstruction (see Algorithm 1), on receiving a graph G = , a vertex s (the source) and a set of available vertices N (vertices that can be chosen as the sink), the algorithm randomly picks a vertex t \u2208 N \u2212 {s}, and runs the max-flow algorithm to determine the max-flow from s to t. If G is a directed graph, it would also run the max-flow algorithm to determine the max-flow from t to s because the two max-flow values can be different. After this step, if G is directed, we will obtain two min-cuts,  and . Since the connectivity of s, t in a directed graph is the minimum of the s \u2212 t max-flow and t \u2212 s max-flow, the smaller of these two max-flows, say x, is assigned to edge  as the connectivity between s and t. We also set  to the corresponding min-cut  is already the desired min-cut). Then, an edge  with weight x is added to the auxiliary graph A. The procedure then calls itself recursively, first with S as the set of available vertices and s as the source, and then with T as the set of available vertices and t as the source. The recursive calls terminate when S or T is reduced to a single vertex.In procedure CAlgorithm 1: Construction, s, N)IfN = {s}\u2003Return.\u2003\u2003t from N \u2212 {s}.\u2003Randomly pick a vertex x, S, T) \u2254 s-t max-flow.\u2003 \u2254 s-t max-flow.\u2003 with weight x to A\u2003Add edge \u2003Construction\u2003CA is constructed, for each query k, the k-edge-connected components can be easily determined as follows: traverse the auxiliary graph A and delete all edges with weights less than k. Then, each connected component in the resulting graph represents a k-edge-connected component in G. Since the number of edges in the auxiliary graph A is n \u2212 1 (see Lemma 5), a search on A can be done in O(n) time, e.g., running the depth-first-search.After the auxiliary graph Lemma 1. The connectivity of vertices is transitive. Let C denote the connectivity between p and q. Let C = x, C = y, C = z, thenProof. Suppose to the contrary that z < min. Let C be a min-cut for a and c. Then \u2223C\u2223 = z < min \u21d2 \u2223C\u2223 < x and \u2223C\u2223 < y. Since \u2223C\u2223 < x, C is not an edge-cut of a and b. Therefore, there is a directed path from a to b and a directed path from b to a after C is removed. Similarly, \u2223C\u2223 < y implies that there is a directed path from b to c and a directed path from c to b after C is removed. It follows that there is a directed path from a to c and a directed path from c to a after C is removed. This contradicts the assumption that C is a min-cut for a and c.onstruction, the vertex set of G is partitioned into subsets S and T such that s \u2208 S and t \u2208 T.After executing Procedure CLemma 2. For any s\u2032 \u2208 S and t\u2032 \u2208 T, C \u2264 C.Proof. Let C(x \u2192 y) to be the value of the minimal cut between x and y in graph G. Let x1 = C(s \u2192 t) and x2 = C(t \u2192 s). W.l.o.g., x1 \u2264 x2, thus, the connectivity between s and t is x1 and from Procedure Construction, the partition S and T are computed according to the cut from s to t such that s \u2208 S and t \u2208 T. For any s\u2032 \u2208 S and t\u2032 \u2208 T, we have C(s\u2032 \u2192 t\u2032) \u2264 C(s \u2192 t), thus, the connectivity between s\u2032 and t\u2032 satisfies C = min{C(s\u2032 \u2192 t\u2032), C(t\u2032 \u2192 s\u2032)} \u2264 C(s\u2032 \u2192 t\u2032) \u2264 C(s \u2192 t) = C.Lemma 3. A). ThenLet w denote the weight of an edge  in the auxiliary graph A = C, for every edge . As shown in C = x, C = y, C = z.x first. Since y has not yet been determined, we must have s \u2208 S; t, u \u2208 T . From Lemma 2, we have z = C \u2264 C = x. After y is determined, two cases are to be considered.Without loss of generality, assume we determine the value of y \u2265 x: Since z \u2264 x, then min = x \u21d2 z \u2264 min. But from Lemma 1, we have z \u2265 min. We thus have z = min \u21d2 C = min{C, C} = min, w).If y < x and we need to prove that y \u2265 z. By Lemma 1, C \u2265 min{C, C} \u21d2 y \u2265 min{x, z} \u21d2 y \u2265 z as z \u2264 x. It follows that z \u2264 y < x which implies that z \u2264 min{x, y} = min{C, C} = min{w, w}.Otherwise, Lemma 4. The auxiliary graph A is a tree and the connectivity between any two vertices in G is given by the minimum weight on the path connecting them in A.Proof. First, we shall prove that A is a tree by induction on \u2223N\u2223 .N\u2223 = 1 or 2, A is clearly a tree. Suppose A is a tree for \u2223N\u2223 < h(\u2265 3).When \u2223N\u2223 = h. Procedure Construction is invoked first, resulting in the edge  and the min-cut . Then Construction and Construction are invoked. Since \u2223S\u2223,\u2223T\u2223 < h, by the induction hypothesis, the auxiliary graph with vertex set S and that with vertex set T are trees. The two trees and the edge  forms a tree which is the auxiliary graph with the vertex set N(= S\u222aT).Consider \u2223G is given by the minimum weight on the path connecting them in A, we apply induction on the length of the path.Next, to prove that the connectivity between any two vertices in x, y be any two distinct vertices. Since A is a tree, there is a distinct path P connecting them in A. Suppose P consists of h edges and h+1 vertices, such that the length of P is h, and P = (x =)v0v1v2\u2026vh(= y). If h = 1, the lemma clearly holds true. If h = 2, the lemma follows from Lemma 3.Let h < k(\u2265 3). Consider h = k. Whenever an edge is added to the auxiliary graph A, it always connects a node with an isolated vertex in the current configuration of A, making the isolated vertex a leaf node of the updated A. Thus, when the path P = (x =)v0v1v2\u2026vh(= y) is constructed, either v0 or vh is the newly added vertex. W.l.o.g., let vh be the newly added vertex. From the induction hypothesis, C = min{w\u22231 \u2264 i < h \u2212 1}. Consider the three vertices x, vh\u22121 and vh, similar to the proof of Lemma 3, it is easily verified that C = min{C, C}. It follows that C = min{min{w\u22231 \u2264 i < h \u2212 1}, C} = min{min{w\u22231 \u2264 i < h \u2212 1}, w} = min{w\u22231 \u2264 i < h}.Suppose the lemma holds true for Theorem 1. The algorithm returns the correct auxiliary graph.Proof. Immediate from Lemma 4.onstruction is used to construct the auxiliary graph A. Then, in the query phase, A is used to compute the k-edge-connected components for any query k.Our algorithm works in a preprocessing-query manner. In the preprocessing phase, Procedure CLemma 5. There are n \u2212 1 calls of procedure Construction.Proof. Since each call of procedure Construction adds an edge to A, and there are n \u2212 1 edges in the finished A , there are n \u2212 1 calls of procedure Construction.Theorem 2. The preprocessing phase takes O(Fn) time and the query phase takes O(n) time per query, where F is the time to compute the maximal flow for two vertices in graph G.Proof. By Lemma 5, procedure Construction is called n \u2212 1 times. In procedure Construction, the basic algorithm for finding the maximal flow and runs in O(F) time is executed for n \u2212 1 times. Therefore, the preprocessing phase takes O(Fn) time. , where f is the maximal value of all pair of maximal flows).lgorithm  to compuA, the query time is thus O(m + n). Since the vertex set of A is V and \u2223V\u2223 = n, and m = \u2223EA\u2223 = n \u2212 1 , the query time is O(n).Since each query initiates a DFS traversal over k-edge-connected components of a graph, for all k, is presented. The algorithm performs a preprocessing over the input graph to construct an auxiliary graph which is a tree in O(Fn) time, where F is the time complexity to find the maximum flow in the graph. Clearly, any improvement made on F automatically implies improvement to the time complexity of our algorithm. Every subsequent query asking for the k-edge-connected components for any k(\u2265 1) can be answered in O(n) time by traversing the auxiliary graph A. The input graph can be a directed or undirected, simple or multiple graph.In this paper, an algorithm for finding all k-edge-connected problem has been studied by the database community [X is k-edge-connected in G if for any two vertices in X, there are at least k-edge disjoint paths within the subgraph G(X) of G induced by X. This variant was motivated by finding cores (or cliques) in large scale networks, which is a fundamental database problem. Note that k-edge-connectivity remains an equivalence relation under this new definition of k-edge-connectivity on induced subgraph, and the vertex partition is always a refinement of the vertex partition of the k-edge-connected components.There are other interesting problems concerning edge-connectivity that are worthwhile to study. For example, a variant of ommunity . In this"}
+{"text": "Owing to technical challenges, extant SV discovery algorithms either use one signal in isolation, or at best use two sequentially. We present LUMPY, a novel SV discovery framework that naturally integrates multiple SV signals jointly across multiple samples. We show that LUMPY yields improved sensitivity, especially when SV signal is reduced owing to either low coverage data or low intra-sample variant allele frequency. We also report a set of 4,564 validated breakpoints from the NA12878 human genome.  Differences in chromosome structure are a prominent source of human genetic variation. These differences are collectively known as structural variation (SV), a term that encompasses diverse genomic alterations including deletion, duplication, insertion, inversion, translocation or complex rearrangement of relatively large  segments. While SVs are considerably less common than smaller-scale forms of genetic variation such as single nucleotide polymorphisms (SNPs), they have greater functional potential due to their larger size, and they are more likely to alter gene structure or dosage.Our current understanding of the prevalence and impact of SV has been driven by recent advances in genome sequencing. However, the discovery and genotyping of SV from DNA sequence data have lagged far behind SNP discovery and genotyping because they are fundamentally more complex. SVs vary considerably in size, architecture and genomic context, and read alignment accuracy is compromised near SVs by the presence of novel junctions  between the \u2018sample\u2019 and reference genomes. Moreover, SVs generate multiple alignment signals, including altered sequence coverage within duplications or deletions (read-depth), breakpoint-spanning paired-end reads that align discordantly relative to each other (read-pair), and breakpoint-containing single reads that align in split fashion to discontiguous loci in the reference genome (split-read) ,2. TheseAn approach that integrates multiple signals allows for more sensitive SV discovery than methods that examine merely one signal, especially when considering heterogeneous samples and/or low coverage data, because each individual read generally produces only one signal type . The impact of improved sensitivity is particularly acute in low coverage datasets or in studies of heterogeneous cancer samples where any given variant may only be present in a subset of cells. However, even with high coverage data, integration of multiple signals can increase specificity by allowing for more stringent criteria for reporting a variant call.Here, we present a novel and general probabilistic SV discovery framework that naturally integrates multiple SV detection signals, including those generated from read alignments or prior evidence, and that can readily adapt to any additional source of evidence that may become available with future technological advances.Our framework is based upon a general probabilistic representation of an SV breakpoint that allows any number of alignment signals to be integrated into a single discovery process . We define a breakpoint as a pair of bases that are adjacent in an experimentally sequenced \u2018sample\u2019 genome but not in the reference genome. To account for the varying level of genomic resolution inherent to different types of alignment evidence, we represent a breakpoint with a pair of probability distributions spanning the predicted breakpoint regions  of the mapped reads Figure\u00a0A. The siOnce the evidence from the different alignment signals is mapped to breakpoint intervals, overlapping intervals are clustered and the probabilities are integrated . Any clustered breakpoint region that contains sufficient evidence (based on user-defined arguments) is returned as a predicted SV. The resolution of the predicted breakpoint regions can be improved by trimming the positions with probabilities in the lower percentile of the distribution .It is well established that variant calling is improved by integrating data from multiple samples ,6,14,15.We implemented LUMPY in an open source C++ software package (available at ) that isWe compared LUMPY\u2019s performance to three other popular and actively maintained SV discovery packages: GASVPro , DELLY  and PindDetection performance was measured using both simulated data and previously published Illumina sequencing data from the widely studied NA12878 CEPH individual. The first simulation measured each tool\u2019s basic detection capabilities in a prototypical scenario by simulating 2,500 homozygous variants from various SV classes at random genomic locations. The second simulation assessed the power of each tool to detect 5,516 known deletion variants present at varying allele frequencies within a mixed sample, as often occurs in heterogeneous tumors. Lastly, the analysis of SVs in the NA12878 genome assessed the performance of each tool on real data containing sequencing errors and other detection confounders that are difficult to simulate. In addition, the analysis of NA12878 (and her parents) measured the effect of considering multiple samples, prior SV knowledge, and third-party CNV predictions on LUMPY\u2019s performance. In each case, we measured performance in terms of sensitivity and false discovery rate (FDR) by comparing the predicted SV breakpoints to either known breakpoints or split-read alignments from long-reads (Pacific Biosciences (PacBio) and Illumina Moleculo) that span the breakpoint. Predictions that either overlapped known variants or had sufficient long-read support were considered true positives, and all other predictions were considered false positives .The simulated results were base on alignments generated by NOVOALIGN, and the NA12878 results were based on BWA alignments. In both cases, YAHA was used to generate split-read alignments. LUMPY was also tested using alternative read alignment pipelines using either BWA-backtrack or BWA-MEM for paired-end alignment, and BWA-MEM for split-read alignment . In this experiment we compared SV detection performance in the NA12878 individual by analyzing the Illumina Platinum Genomes dataset, which represents approximately 50X coverage of the NA12878 genome . We additionally subsampled this dataset to approximately 5X coverage to assess SV detection in low coverage scenarios.et al.  is the relative probability that position b.l.s\u2009+\u2009i is one end of the breakpoint (similar for b.r); and b.v is the breakpoint variety. Within the context of this method, breakpoint variety determinations are based on the orientation of the evidence. It is important to note that while a breakpoint may be labeled as a deletion when it contains evidence from a paired-end sequence alignment with a +/-orientation, the breakpoint may in fact be the result of some other event or series of complex events.A breakpoint is a pair of genomic coordinates that are adjacent in a sample genome but not in a reference genome. Breakpoints can be detected, and their locations predicted by various evidence classes such as paired-end sequence alignments or split-read mappings. To support the inclusion of different evidence classes into a single analysis, we define a high-level breakpoint type as a collection of the evidence that corroborates the location and variety  of a particular breakpoint. Since many evidence classes provide a range of possible breakpoint locations, we represent the breakpoint\u2019s location with a pair of breakpoint intervals where each interval has a start position, an end position, and a probability vector that represents the relative probability that a given position in the interval is one end of the breakpoint. More formally, a breakpoint is a tuple b and c in the set of all breakpoints B where b and c intersect , then b and c are merged into interval m, b and c are removed from B, and m is placed into B. The evidence set m.E is the union of the evidence sets b.E and c.E.If there exist two breakpoints m.l and m.r would be to let m.l.s\u2009=\u2009max and m.l.e\u2009=\u2009min, similar for m.r. However, if a spurious alignment is merged into a set of genuine breakpoints, the resulting breakpoint interval can be \u2018pulled\u2019 away from the actual breakpoint. The impact of an outlier can be minimized or eliminated once the full set of corroborating alignments is collected for a given breakpoint, but collecting the full set is complicated by the fact that alignments are considered in order and outliers typically occur first. To account for this, we define a liberal merge process where m.l.s is the mean start position for the left intervals in m.E, and m.l.e is the mean end position for the left intervals in m.E, similar for m.r.A straightforward method to define breakpoint intervals s  is made for each breakpoint b \u2208 B that meets a user-defined minimum evidence threshold . The boundaries of the breakpoint intervals s.l and s.r are the trimmed product of the distributions of the left and right intervals in b.E. Let s.l.s\u2009=\u2009max({e.l.s | e \u2208 b.E}), s.l.e\u2009=\u2009min({e.l.e | e \u2208 b.E}), and s.l.p[i]\u2009=\u2009\u220fe\u2208b.Ee.l.p[i-o] where o is the offset value e.l.s - s.l.s (similar for s.r). The intervals s.l and s.r can then trimmed to include only those positions that are in the top percentile  based on a user-provided value. Given the liberal merge process, it is possible for b.E to contain non-overlapping distributions that would result in a zero-length product. In this case, we identify the maximum point among the sum of the distributions in b.E, any distribution not intersecting this point is removed, and the resulting subset processed normally. Regardless of the trimming value, LUMPY reports both the intervals that contain 95% of the resulting probability distribution and the maximum position of s.l.p and s.r.p. Summation is another option for calculating the combined distribution boundaries and values. In that case s.l and s.r are the trimmed mixture distributions of the left and right intervals in b.E. Let s.l.s\u2009=\u2009min({e.l.s | e \u2208 b.E}), s.l.e\u2009=\u2009max({e.l.e | e \u2208 b.E}), and s.l.p[i]\u2009=\u2009\u2211e\u2208b.Ee.l.p[i-o]. The value at s.l.p[i] (or s.r.p[i]) represents the level of agreement among the evidence in b.E that position i is one end of the breakpoint. While summation will give less precise breakpoint predictions, it can be a useful option when considering low-quality data.Once all the evidence has been considered, an SV call To combine distinct SV alignment signals such as read-pair and split-read alignments with the general breakpoint type defined above, we define an abstract breakpoint evidence type. This abstract type defines an interface that allows for the inclusion of any data that can provide the following functions: is_bp determines if a particular instance of the data contains evidence of a breakpoint; get_v determines the breakpoint variety ; and get_bpi maps the data to a pair of breakpoint intervals.To demonstrate the applicability of this abstraction, we defined three breakpoint evidence instances: paired-end sequencing alignments, split-read alignments, and a general breakpoint interface. Read-pair and split-read are the most frequently used evidence types for breakpoint detection, and the general interface provides a mechanism to include any other sources of information such as known variant positions or output from other analysis pipelines . As technologies evolve and our understanding of structural variation improves, other instances can be easily added.x, y\u27e9, which we will refer to as \u2018read-pairs\u2019. Each read is aligned to a reference genome R(x)\u2009=\u2009\u27e8c, o, s, e\u27e9, where R(x).c is the chromosome that x aligned to in the reference genome, R(x).o\u2009=\u2009+|\u2009-\u2009indicates the alignment orientation, and R(x).s and R(x).e delineate the start and end positions of the matching sequence within the chromosome. We assume that both x and y align uniquely to the reference and that R(x).s\u2009<\u2009R(x).e\u2009<\u2009R(y).s\u2009<\u2009R(y).e. While in practice it is not possible to know the position of read x in the sample genome (in the absence of whole-genome assembly), it is useful to refer to S(x)\u2009=\u2009\u27e8o, s, e\u27e9 as the alignment of x with respect to the originating sample\u2019s genome.Paired-end sequencing involves fragmenting genomic DNA into roughly uniformly sized fragments, and sequencing both ends of each fragment to produce paired-end reads \u27e8R(x).o\u2009=\u2009+, R(y).o\u2009=\u2009- orientation, and at distance R(y).e - R(x).s roughly equivalent to the fragment size from the sample preparation step. Any read-pair that aligns with an unexpected configuration can be evidence of a breakpoint. These unexpected configurations include matching orientation R(x).o\u2009=\u2009R(y).o, alignments with switched orientation R(x).o\u2009=\u2009-, R(y).o\u2009=\u2009+, and an apparent fragment length (R(y).e - R(x).s) that is either shorter or longer than expected. We estimated the expected fragment length to be the sample mean fragment length l, and the fragment length standard deviation to be the sample standard deviation s from the set of properly mapped read-pairs (as defined by the SAM specification) in the sample data set. Considering the variability in the sequencing process, we extend the expected fragment length to include sizes l\u2009+\u2009vls, where vl is a tuning parameter that reflects spread in the data.Assuming that genome sequencing was performed with the Illumina platform, read-pairs are expected to align to the reference genome with a x and y align to the same chromosome (R(x).c\u2009=\u2009R(y).c), the breakpoint variety can be inferred from the orientation of R(x) and R(y). If the orientations match, then the breakpoint is labeled as an inversion, and if R(x).o\u2009=\u2009- and R(y).o\u2009=\u2009+ then the breakpoint is labeled as a tandem duplication. Any breakpoint with the orientation R(x).o\u2009=\u2009+ and R(y).o\u2009=\u2009- is labeled as a deletion. When x and y align to different chromosomes (R(x).c\u2009\u2260\u2009R(y).c), the variety is labeled inter-chromosomal. At present, LUMPY does not explicitly support identification of insertions that are spanned by paired-end reads; however, if desired these can be identified in a post-processing step through assessment of \u2018deletion\u2019 calls.When x, y\u27e9 to breakpoint intervals l and r, the ranges of possible breakpoint locations must be determined and probabilities assigned to each position in those ranges. By convention, x maps to l and y to r, and for the sake of brevity we will focus on x and l since the same process applies to y and r. Assuming that a single breakpoint exists between x and y, then the orientation of x determines if l will be upstream or downstream of x. If the R(x).s\u2009=\u2009+, then the breakpoint interval begins after R(x).e (downstream), otherwise the interval ends before R(x).s (upstream).To map \u27e8L and standard deviation s. Since we assume that only one breakpoint exists between x and y, and that it is unlikely that the distance between the ends of a pair in the sample genome (S(y).e - S(x).s) is greater than L, then it is also unlikely that one end of the breakpoint is at a position greater than R(x).s\u2009+\u2009L, assuming that R(x).o\u2009=\u2009+. If R(x).o\u2009=\u2009-, then it is unlikely that a breakpoint is at a position less than R(x).e - L. To account for variability in the fragmentation process, we extend the breakpoint to R(x).e\u2009+\u2009(L\u2009+\u2009vfs) when R(x).o\u2009=\u2009+, and R(x).s - (L\u2009+\u2009vfs) when R(x).o\u2009=\u2009-, where vf is a tuning parameter that, like vl, reflects the spread in the data.The length of each breakpoint interval is proportional to the expected fragment length i in the breakpoint interval l is part of the actual breakpoint can be estimated by the probability that x and y span that position in the sample. For x and y to span i, the fragment that produced \u27e8x, y\u27e9 must be longer than the distance from the start of x to i, otherwise y would occur before i and x and y would not span i (contradiction). The resulting probability is P(S(y).e - S(x).s\u2009>\u2009i - R(x).s) if R(x).o\u2009=\u2009+, and P(S(y).e - S(x).s\u2009>\u2009R(x).e - i) if R(x).o\u2009=\u2009-. While we cannot directly measure the sample fragment length (S(y).e - S(x).s), we can estimate its distribution by constructing a frequency-based cumulative distribution D of fragment lengths from the same sample that was used to find L and s, where D(j) gives the proportion of the sample with fragment length greater than j.The probability that a particular position X that does not contiguously align to the reference genome. Instead, X contains a set of two or more substrings xi\u2026xj (X\u2009=\u2009x1x2\u2026xn), where each substring aligns to the reference R(xi)\u2009=\u2009\u27e8c, o, s, e\u27e9, and adjacent substrings align to non-adjacent locations in the reference genome R(xi).e\u2009\u2260\u2009R(xi\u2009+\u20091).s\u2009+\u20091 or R(xi).c\u2009\u2260\u2009R(xi\u2009+\u20091).c for 1\u2009\u2264\u2009i\u2009\u2264\u2009n \u2013 1. A single split-read alignment maps to a set of adjacent split-read sequence pairs , and each pair \u27e8xi,xi\u2009+\u20091\u27e9 is considered individually.A split-read alignment is a single DNA fragment By definition, a split-read mapping is evidence of a breakpoint and therefore the function is_bp trivially returns true.xi, xi\u2009+\u20091\u27e9. When the orientations match R(xi).o\u2009=\u2009R(xi\u2009+\u20091).o, the event is marked as either a deletion or a tandem duplication. Assuming that R(xi).o\u2009=\u2009R(xi\u2009+\u20091).o\u2009=\u2009+, R(xi).s\u2009<\u2009R(xi\u2009+\u20091).s indicates a gap caused by a deletion and R(xi).s\u2009>\u2009R(xi\u2009+\u20091).s indicates a tandem duplication. These observations are flipped when orientations R(xi).o\u2009=\u2009R(xi\u2009+\u20091).o\u2009=\u2009-. When the orientations do not match R(xi).o\u2009\u2260\u2009R(xi\u2009+\u20091).o, the event is marked as an inversion and the mapping locations do not need to be considered. When x and y align to different chromosomes, the variety is marked as inter-chromosomal. LUMPY does not currently attempt to identify insertions that are completely contained within a long read, but this will be supported in future versions. We note that this capability requires long-read aligners to report the number and order of alignments within a read .Both orientation and mapping location must be considered to infer the breakpoint variety for \u27e8xi, xi\u2009+\u20091\u27e9 maps to two breakpoint intervals l and r centered at the split. The probability vectors l.p and r.p are highest at the midpoint and decrease exponentially toward their edges. The size of this interval is a configurable parameter vs and is based on the quality of the sample under consideration and the specificity of the alignment algorithm used to map the sequences to the reference genome.The possibility of errors in the sequencing and alignment processes creates some ambiguity in the exact location of the breakpoint associated with a split-read alignment. To account for this, each alignment pair \u27e8l and r are centered on either the start or the end of R(xi) and R(xi\u2009+\u20091). When the breakpoint is a deletion l is centered at R(xi).e and r at R(xi\u2009+\u20091).s, and when the breakpoint is a tandem duplication l is centered at R(xi).s and r at R(xi\u2009+\u20091).e. If the breakpoint is an inversion, l and r are both centered either at the start positions or end positions of R(xi) and R(xi\u2009+\u20091), respectively. Assuming that R(xi).s\u2009<\u2009R(xi\u2009+\u20091).s, if R(xi).o\u2009=\u2009+ then l and r are centered at R(xi).e and R(xi\u2009+\u20091).e, otherwise they are centered at R(xi).s and R(xi\u2009+\u20091).s. If R(xi).s\u2009>\u2009R(xi\u2009+\u20091).s, then the conditions are swapped.Depending on the breakpoint variety, the intervals The generic evidence subclass provides a mechanism to directly encode breakpoint intervals using the BEDPE format . BEDPE iBoth simulated and real datasets were used to compare the sensitivity and FDR of LUMPY to other SV detection algorithms . Two types of simulations were performed: one in which homozygous variants of diverse varieties were introduced at random positions throughout the reference genome, and another in which a heterogeneous tumor sample was simulated by mixing reads from a modified \u2018abnormal\u2019 human reference genome (containing 1000 Genomes deletions) and an unmodified \u2018normal\u2019 human reference genome in varying proportions. We also used publicly available Illumina sequencing data of the NA12878, NA12891, and NA12892 individuals. Two scenarios were considered: the original 50X coverage files, and 5X subsamples of the original data sets.In the case of the homozygous simulation, we used SVsim to create new versions of the human reference genome (build 37) containing 2,500 simulated variants of each variety. For deletions, tandem duplications and inversions we randomly placed 2,500 non-overlapping variants ranging from 100\u00a0bp to 10,000\u00a0bp in size. To simulate translocations, we randomly inserted 2,500 non-overlapping inter-chromosomal regions of 1,000\u00a0bp, derived from random donor sites in the reference genome. Although we note that the true variant variety in this case is actually an insertion, the inserted segment exceeds the insert size of the sequencing library as well as the read length, and thus the breakpoints formed by such insertions accurately simulate a translocation. Each simulated genome was sampled to 40X, 20X, 10X, 5X, and 2X coverage.To simulate a heterogeneous tumor sample, we combined simulated reads from both a modified and unmodified version of the human reference genome (build 37). The modified genome was created using SVsim, and included 5,516 non-overlapping deletions identified by the 1000 Genomes Project. Each simulation combined reads from both the modified and unmodified genomes in varying proportions. We refer to the proportion of reads that were derived from the modified genome as the SV allele frequency. The simulated SV allele frequencies were 5%, 10%, 20% and 50%, and the simulated coverages were 10X, 20X, 40X, and 80X. For example, in the simulation with 5% SV allele frequency and 10X coverage, the modified genome was sampled at 0.5X coverage and the unmodified genome was sampled at 9.5X coverage. The two sets of reads are then pooled into a single 10X coverage sample.For all simulations, WGSIM was used to sample paired-end reads with a 150\u00a0bp read length, a 500\u00a0bp mean outer distance with a 50\u00a0bp standard deviation, and default error rate settings. Paired-end reads were mapped to the reference genome with NOVOALIGN version V2.07.08, using the random repeat reporting and allowing only one alignment per read. From the NOVOALIGN output, all soft-clipped (\u226520\u00a0bp clipped length) and unmapped reads were realigned with the split-read aligner YAHA using a word length of 11 and a minimum match of 15. The NOVOALIGN output was used as input to DELLY, GASVPro, and Pindel, and both NOVOALIGN and YAHA output were used as input to LUMPY. In all algorithms, the minimum evidence threshold was four. For LUMPY, the tuning parameters min_non_overlap was set to 150, discordant_z was set to 4, back_distance was set to 20, weight was set to 1, and min_mapping_threshold was set to 1. For GASVPro, LIBRARY_SEPARATED was set to all, CUTOFF_LMINLMAX was set to SD\u2009=\u20094, WRITE_CONCORDANT was set to true, and WRITE_LOWQ was set to true. For DELLY, map-qual was set to 1, and the inc-map flag was set. DELLY paired-end (pe) and split-read (sr) calls were combined into a single paired-end and split-read (pe\u2009+\u2009sr) callset by taking the union of the two sets where the split-read call was retained when a call was common to both sets. For Pindel, minimum_support_for_event was set to 4, all chromosomes were considered, and report_interchromosomal_events was set to true. Since the output of DELLY and Pindel are single-base-resolution intervals, we increased the size of those intervals to match the mean interval size of a similar LUMPY call. Any call that had split-read support  was expanded to a 28\u00a0bp interval, and any call that had only paired-end support  was expanded to a 282\u00a0bp interval. The intervals for GASVPro were not modified since, like LUMPY, it reports an interval whose size is based on the supporting evidence.For the real data, LUMPY, GASVPro, DELLY, and Pindel considered Illumina sequencing of the NA12878 individual. The original sequencing files were at 50X coverage and were used in the 50X experiments. The 5X experiments considered sequencing files that were created by subsamples 10% of the original paired-end alignments. For all the tools, only deletion predictions on chromosomes 1 though X were considered. All sequencing samples were retrieved from the European Nucleotide Archives (submission ERA172924), and were previously aligned using BWA. Soft-clipped (\u226520\u00a0bp clipped length) and unmapped reads were realigned with the split-read aligner YAHA using a word length of 11 and a minimum match of 15. In addition to the NA12878 data, the LUMPY trio results also considered sequencing data from that individual\u2019s parents, NA12891 and NA12892. The LUMPY prior result considered all 1000 Genomes variant calls using the generic evidence module. The LUMPY read-depth results considered all deletion calls made by CNVnator  for the et al. study [For the identification of the first truth sets, the Mills l. study  validateThe second truth set consisted of the 4,095 deletions called by at least one tool in the 50X dataset or by the 1000 Genomes Project , and thaDeletion calls were considered to be validated if supported by at least two non-duplicate PacBio split reads or at least one Moleculo split read. A supporting long-read is defined by the following criteria: 1) the long-read is split by the aligner such that at least 20\u00a0bp aligned to the flanking sequence on either side of the reported breakpoint; 2) the left and right intervals of the split long-read both intersect with the respective left and right intervals of reported breakpoint, allowing 5\u00a0bp of slop space on either side of the long-read breakpoint to account for microhomology or inserted sequence at the novel adjacency; 3) the strand orientation of the split long-read is consistent with the strand orientation at the reported breakpoint; 4) in the case of PacBio, where at least two non-duplicate long-reads are required to validate a call, the two long-reads must not only fill criteria 1 to 3, but must also overlap with each other within 5\u00a0bp of slop on either side.We performed Monte Carlo shuffling of the callsets to estimate the number of spurious long-read validations due to random chance. We shuffled each callset 100 times using BEDTools shuffle while retaining identical interval sizes, variant spans, and number of variants for each iteration . RegionsFor structural variation detection with LUMPY and other tools, we excluded regions of the reference genome with consistently high sequencing depth over multiple individuals, since high depth is indicative of artifacts in the reference assembly. To define these regions, we first aligned the 17-member CEPH 1463 pedigree to the GRCh37 human reference genome using BWA-MEM 0.7.5a-r405 (bwa mem -t 32 -M -p) . Each mebp: base pair; CNV: copy number variation; FDR: false discovery rate; PacBio: Pacific Biosciences; PCR: polymerase chain reaction; SNP: single nucleotide polymorphism; SV: structural variation.The authors declare that they have no competing interests.RL developed the algorithms, wrote the source code, performed the experiments and prepared the figures. CC performed the long-read SV validation experiments. AQ and IH conceived the framework, devised the experiments and co-advised the project. RL, AQ and IH contributed equally to the writing of the manuscript. All authors read and approved the final manuscript.This file contains the breakpoints used for the homozygous variant simulation. The format is BEDPE. Each line has a \u2018TYPE:\u2019 field that indicates DELETION, DUPLICATION, INVERSION, or TRANSLOCATION.Click here for fileThis file contains the breakpoints used for the heterogeneous tumor simulation. The format is BEDPE. These deletions are based on the variants released by the 1000 Genomes Project in [oject in . We seleClick here for fileThis file contains the breakpoints used for the Mills et al. truth set. The format is BEDPE, which is described by [ribed by . The breribed by .Click here for fileThis file contains the breakpoint intervals for the deletion predictions that were made by LUMPY , GASVPro, DELLY, Pindel, or the 1000 Genomes Project [ and that were validated by long read alignments from PacBio and/or Illumina Moleculo sequencing. The format is BEDPE, and the score field indicates the number of overlapping predictions. Note: in some cases one algorithm made two predictions that contributed to a single call. For example, there are two calls with a score of 8. In both cases Pindel contributed two very similar calls. Project  and thatClick here for fileThis file contains the calls made by LUMPY for NA12878 with paired-end and split-read evidence that were also validated with PacBio/Moleculo data. The format is BEDPE and the score field is the total amount of supporting evidence. This file contains extra fields that are described at [ribed at .Click here for file"}
+{"text": "Spin Hall effect (SHE) has been discussed in the context of Kubo formulation, geometric physics, spin orbit force, and numerous semi-classical treatments. It can be confusing if the different pictures have partial or overlapping claims of contribution to the SHE. In this article, we present a gauge-theoretic, time-momentum elucidation, which provides a general SHE equation of motion, that unifies under one theoretical framework, all contributions of SHE conductivity due to the kinetic, the spin orbit force (Yang-Mills), and the geometric (Murakami-Fujita) effects. Our work puts right an ambiguity surrounding previously partial treatments involving the Kubo, semiclassical, Berry curvatures, or the spin orbit force. Our full treatment shows the Rashba 2DEG SHE conductivity to be  The time-space gauge field can, in turn be linked to a t-geometric velocity which has the same form as13On the other hand, Sinova On the other hand, a separate body of work15161718We are therefore motivated to provide, in this paper, a gauge-theoretic energy framework that unifies SHE velocity of kinetic, Yang-Mills, k-geometric, and t-geometric origins for any SOC system under one equation of motion (EOM). One unified energy system that merges the two spaces of t and k is derived, debunking any previous suspicion of overlapping energy terms. The energy equation with a merged t-k identity is then used to derive the velocity equation-of-motion (EOM) for all SHE systems. Previous efforts13The main accomplishment in our renewed treatment is that we show that a form-invariant t-k Hamiltonian is a complete energy equation, and can be used to derive a complete EOM that describes spin Hall. The complete EOM reveals in clear-cut, and non-overlapping manner, the velocity components of kinetic, Yang-Mills, and geometric origins. The significance of this result is the prediction of a reversal of sign in the SHE conductivity, suggesting the need to revisit and recalculate previously derived SHE conductivity. The Methods section will describe in details the theoretical techniques used in the process of unification. Unification provides the theoretical basis for a form-invariant, t-k manifestation of the gauge potential, which is summarized in We will now use the t-k form-invariant energy to derive a complete spin Hall EOM for the spin carrier. In the energy physics of the SOC systems, we have shown in Methods and summarized in We would like to note that the velocity expression The kinetic SHE velocity can also be written asn\u03a3 and az having unity magnitude. The \u00b1 sign arising from the two eigenstates of implies that energy is low when spin is aligned with the effective B field. Thus in the (+) band of B fields in both East and West. In the (\u2212) band of B field projected to the az. Note that -gauged spin orbit field, and with both tn. The expression Ex producing an effective B field. For illustration in the 2D projected region surrounded by the equator, n\u03a3 points along axis \u2212z in the region of +py, and axis +z in the region of \u2212py  band  band  would shThe kinetic velocity has been identified in previous time-spaceThe One popular form of SHE exists in device or hetero-structure that exhibits the Rashba spin orbit coupling (RSOC). Examples are the GaAs/AlGaAs/GaAs semiconductor heterostructure, or the oxide/Metal/Pt metal multilayer, both with structural inversion asymmetry. Shown above in \u03b1 is the strength of the Rashba SOC effect.where We will first examine a two-dimensional system, where the SHE current density is obtained from the SHE kinetic velocity as followsg represents spin flux for g\u2009=g\u2009=\u2009e. It has been shown that, for g\u2009=\u2009g\u2009=\u2009e) and the spin . The Dirac relativistic quantum mechanics is needed to account for this SOC energy. In the absence of any retardation effect due to scattering, the carrier would accelerate due to the E field. As a result, the carrier will acquire an E-dependent energy where The approach that has been used to derive SHE velocity in refs where the gauge potential \u03c3\u03b3.B(k) would become \u03c3\u03b3.B(t), where HS\u2009=\u2009H0\u2009+\u2009VS, and note the following:The t-space approach has on the other hand, been adopted in refs HI(t)\u2009=\u2009H0\u2009+\u2009VI(t). In the \u201cInteraction\u201d picture, one has it\u03c8I(t)\u2009=\u2009VI(t)\u03c8I(t). Thus a transformation in time space is appropriate hereor k/\u2202t \u2260 0, a condition that would be fulfilled when E field is present in the device. We assign as follows: H0\u2009=\u2009E.r. On the RHS of Eq. itU\u2020) is also known as the time-space gauge with the dimension of energy. The unitary rotation operator U in local space iswhere and one can quickly obtain that Equation H0\u2009=\u2009Eea.r is important for the survival of the gauge H0\u2009=\u2009Eea.r. Inverse transformation of iU(\u2202tU\u2020). Dropping the higher order terms, the following is arrivedleads to one obtaining a gauge expression in the k-space. Note that iU\u2202kU\u2020, subscripts are subject to rk, subscripts are subject to Note that for expression iU\u2020\u2202tU)\u2009=\u2009\u2212\u03c3.At.Note that in the above the convention z), generating a gauge field. Still, the post-transformed Hamiltonian only reveals the stationary eigen-states, but one which is more intuitive now with spin aligned to a total field out of plane. Note however, that in both pre- and post-transformed Hamiltonian, expectation values of observables remain the same. But this is not important as we are not interested in the stationary expectation values. What we need from these Hamiltonians are clues to determining the actual propagation physics of electron. In previous works23z-projection of the total field taken along the two lateral sides of the device.We would, however, note that the Hamiltonian alone, pre- or post-transformed could not reflect the full physical reality of the 2D system in which electron propagates in time. As electron propagates in momentum and spin space, so does the spin-orbit magnetic field, and the actual physics related to such effect can only be reflected in the wave-function that is solved taking into account the path of evolution. This is a separate task that needs to take into account approximations therein. Simply stated, a stationary Hamiltonian cannot reveal how electron propagates in time, as it only reveals the stationary eigen-states, which has spin aligned parallel or anti-parallel. Local gauge transformation locks the spin orbit field to a specific axis ."}
+{"text": "They concluded there is a \u2018surge of p-values between 0.041\u20130.049 in recent decades\u2019 which \u2018suggests (but does not prove) questionable research practices have increased over the past 25 years.\u2019 I show the changes in the ratio of fractions of p-values between 0.041\u20130.049 over the years are better explained by assuming the average power has decreased over time. Furthermore, I propose that their observation that p-values just below 0.05 increase more strongly than p-values above 0.05 can be explained by an increase in publication bias (or the file drawer effect) over the years . I explain why researchers analyzing large numbers of p-values need to relate their assumptions to a model of p-value distributions that takes into account the average power of the performed studies, the ratio of true positives to false positives in the literature, the effects of publication bias, and the Type 1 error rate (and possible mechanisms through which it has inflated). Finally, I discuss why publication bias and underpowered studies might be a bigger problem for science than inflated Type 1 error rates, and explain the challenges when attempting to draw conclusions about inflated Type 1 error rates from a large heterogeneous set of p-values.In recent years, researchers have attempted to provide an indication of the prevalence of inflated Type 1 error rates by analyzing the distribution of  However, as Thus far, however, no solid data exist on the prevalence of such research practices.\u2019 Some researchers have attempted to provide an indication of the prevalence of inflated Type 1 error rates by analyzing the distribution of p-values in the published literature. The idea is that inflated Type 1 error rates lead to \u2018a peculiar prevalence of p-values just below 0.05\u2019 . Two observations in the data they collected could seduce researchers to draw conclusions about a rise of p-values just below a significance level of 0.05. The first observation the authors report is how from 1990 to 2013 p-values between 0.041 and 0.049 rose more strongly than the percentage of p-values between 0.051\u20130.059. The second observation is that the percentage of p-values that falls between 0.041\u20130.049 has increased more than the increase in the percentage of p-values between 0.001\u20130.009, 0.011\u20130.019, 0.021\u20130.029, and 0.031\u20130.039 from 1990 to 2013 1p-values with 2 digits , which reveal similar patterns, but here I focus on the three digit data, which focuses on p-values between (for example) 0.041\u20130.049 because trailing zeroes  are rarely reported.The authors also analyze . The authors  conclude that: \u201cThe fact that p-values just below 0.05 exhibited the fastest increase among all p-value ranges we searched for suggests (but does not prove) that questionable research practices have increased over the past 25 years.\u201dRecently, p-values just below p = 0.05 compared to p-values just above p = 0.05 is not caused by a change over time in the percentage of p-values just below 0.05, but by a change over time in the percentage of p-values above 0.05. Perhaps surprisingly, p-values just above 0.05 increase much less than all other p-values. This might be due to a stricter interpretation of p < 0.05 as support of a hypothesis, and less leniency for \u2018marginally significant\u2019 p-values just above this threshold. Second, I will explain why the relatively high increase in p-values between 0.041\u20130.049 over the years can easily be accounted for by a decrease in the average power of studies. At the same time, I will illustrate why this increase in p-values just below 0.05 is unlikely to emerge due to an inflation of the Type 1 error rate due to optional stopping or trying out multiple analyses until p < 0.05. I want to explicitly note that it was possible to provide these alternative interpretations of the data because p-values.I will explain why the data does not suggest an increase in \u2018questionable research practices\u2019. First, I will discuss how the relatively stronger increase in p-value distributions before drawing conclusions about the underlying reasons for specific distributions of p-values extracted from the scientific literature. A model of p-value distributions consists of four different factors. First, the p-value distribution depends on the number of studies where the null-hypothesis (H0) is true, and the number of studies where the alternative hypothesis (H1) is true. Second, the p-values for studies where H1 is true depend upon the power of the studies. Statistical power is the probability that a study yields a statistically significant effect, if there is a true effect to be found. Power is determined by the significance level, the sample size, and the effect size. Third, p-values for studies where H0 is true depend upon the Type 1 error rate chosen by the researcher , and any possible mechanisms through which the Type 1 error rate is inflated beyond the nominal Type 1 error rate set by the researcher. When I talk about inflated Type 1 error rates in this article, I explicitly mean flexibility in dependent tests that are performed on the data  that have the goal to lead to a statistically significant result. When these statistical tests are dependent  the Type 1 error rate inflation has a specific pattern where p-values between 0.041\u20130.049 become somewhat more likely than smaller p-values.As I have discussed before , it is ep-value distribution in the published literature is influenced by publication bias. Publication bias is the tendency to publish statistically significant results . The threshold at which p-values indicate a statistically significant result, as well as the leniency towards \u2018marginally significant\u2019 findings, both influence the frequency of observed p-values in the literature. It is important to look beyond simplistic comparisons between p-values just below 0.05 and p-values in other parts of the p-value distribution if the observed p-values are not explicitly related to a model consisting of the four factors that determine p-value distributions.And finally, the p-values between 0.041\u20130.049 than in p-values between 0.051\u20130.059 . The data is clear, but the reason for this difference is not, and it is not explored by the authors. Although all p-values are increasing over time, the real question is whether p-values below p = 0.05 are increasing more, or p-values above p = 0.05 are increasing less. A direct comparison is difficult, because a comparison across the p = 0.05 boundary is influenced by publication bias. If publication bias increases, and less non-significant results end up in the published literature due to the file-drawer problem, the percentage of papers reporting p-values smaller than 0.05 will also increase (even when there is no increase in p-hacking). Indeed, both p-values between 0.041\u20130.049 and 0.051\u20130.059 observed by p-values between 0.051\u20130.059.p-values between 0.031\u20130.039 and 0.041\u20130.049 over the years on the one hand, and 0.051\u20130.059 and 0.061\u20130.069 on the other hand, we can examine whether there is an increase in p-values between 0.041\u20130.049 (due to an increase in the Type 1 error rate), or an increase in publication bias (or the file-drawer problem), which leads to a lower percentage of p-values between 0.051\u20130.059. If there is an increase in the Type 1 error rate due to flexibility in the data analysis, the biggest differences over time should be observed just below p = 0.05 . However, there are reasons to assume the biggest difference will be observed in p-values just above p = 0.05. As p-values just above 0.05 to be published, as indicated by a higher prevalence of p-values between 0.051\u20130.059 than would be expected based on the power of statistical tests and an equal reduction of all p-values above 0.05 due to the file-drawer problem. If publication bias becomes more severe, we might expect a reduction in the tolerance for \u2018marginally significant\u2019 p-values just above 0.05, and the largest changes in ratios should be observed abovep = 0.05.By comparing the relative differences between p-values between 0.031\u20130.039 to p-values between 0.041\u20130.049 is pretty stable: 1.13, 1.09, and 1.11, respectively. The ratio of p-values between 0.051\u20130.059 to p-values between 0.061\u20130.069 shows a surprisingly large reduction over the years: 2.27, 1.94, and 1.79, respectively. It is important to note that flexibly analyzing data with the goal to be able to report a significant finding leads to a change in the p-value distribution both above as below p = 0.05. However, the ratio of p-values between 0.031\u20130.039 to p-values between 0.041\u20130.049 should change much more than the ratio of p-values between 0.051\u20130.059 to p-values between 0.061\u20130.069, because p-values are drawn from a relatively larger range above p = 0.05, to a relatively small range just below p = 0.05. This surprisingly large change in ratios over time for p-values 0.051\u20130.059 to 0.061\u20130.069 indicates that instead of an increase in the Type 1 error rate of p-values below 0.05, the real change over time happens in the p-values between 0.051\u20130.059.Across the three time periods  the ratio of p-values just above p = 0.05 might be explained by an increasingly strong effect of the file-drawer problem. Where p-values between 0.051\u20130.059  might have been more readily accepted as support for the alternative hypothesis in 1990\u20131997, p-values just above 0.05 might no longer deemed strong enough support for the alternative hypothesis in 2005-2013. This idea is speculative, but seems plausible given the increase in publication bias over the years , but the ratios do increase as you move from bins of low p-values between 0.001\u20130.009 to bins of high p-values between 0.041\u20130.049.The first part of the title of the article by p-values are reported over the years. As p-value between 0.051 and 0.059. This increased 3.6-fold to 0.067%  in 2013. Positive results increased 10.3-fold in the same period: from 0.030%  in 1990 to 0.314%  in 2013.\u201dIn 1990, 0.019% of papers  reported a p-values are finding their way into more and more abstracts, which points to a possible increase in the overreliance on null-hypothesis testing in empirical articles. This is an important contribution to the literature.The first thing to understand is why none of the observed ratios are close to 1. The reason is that there is a massive increase in the percentage of abstracts of papers in which p = 0.05 can be explained. p-value distribution . The three remaining possibilities are a change in the average power of studies over time, a change in the inflated Type 1 error rate over time, and a change in the ratio of studies where H0 or H1 is true. I will discuss each of these three possible explanations in turn.The main question is how these differences in the ratios across the 5 bins below p-values depends on the statistical power of the studies , which is itself a function of the true effect size, the significance level, and the sample size . It is not difficult to model the ratios observed by p-value distribution across the 5 bins as detailed in p-values falling between 0.001 and 0.009 in 1990, but only 19.93% of p-values falling between 0.001 and 0.009 in 2013. This is just the p-value distribution as a function of the power of the tests.We can relatively easily reconstruct the observed data purely based on differences in the average power across the years. Remember that the distribution of p-values reported in abstracts has increased by 10% over the years, and I chose 0.01% in 1990 and 0.1% in 2013 as the percentage of abstracts that report p-values  by the percentage of articles reporting p-values , multiplied by the percentage of p-values expected in each p-value bin based on the assumed power . The number of reconstructed p-values is presented in p-values observed by The total number of studies analyzed by p-values in each of the five p-value bins can now be calculated by dividing the number (N) of p-values in a specific bin for a specific year  by the total (T) number of p-values  to get the fractions for 1990 and 2015 . The reconstructed fractions  is smaller than the reconstructed ratio of fractions in the 0.031\u20130.039 bin (9.417), but the pattern is reversed in the observed data . However, if we calculate the same ratios of fractions for 2013 with all other preceding years  we find a smaller ratio of fractions in the 0.021\u20130.029 bin than in the 0.031\u20130.039 bin for p-values between 0.031\u20130.039 should be very similar to those between 0.041\u20130.049. The predicted 1990/2013 ratio of fractions in the 0.031\u20130.039 bin is 9.417, and the predicted ratio of fractions for the 0.041\u20130.049 bin is 9.740, while the difference in observed ratios of fractions is much larger . This can hardly be called a \u2018surge\u2019 of p-values between 0.041\u20130.049. This observation is not in line with the idea that the Type 1 error rate has increased, because an increase in Type 1 error rates due to flexibility in the data analysis typically assumes p-values between 0.041\u20130.049 increase more strongly than p-values between 0.031\u20130.039  is not likely to reflect the true state of affairs in the real world. Although we lack data about changes in the ratio of true to false effects examined over time (a worthwhile research question in itself), it seems reasonable to at least entertain the possibility of some changes over time for this factor of the model. For now, the most important conclusion is that a change in power over time can mathematically account for the observed changes in ratios of fractions in the different p-value bins. Moreover, the idea that power decreases over time is theoretically plausible, since such a decrease in power over time has been observed in some disciplines, such as psychology  5% of the studies will observe p-values smaller than 0.05. De Winter and Dodou focus on p-values between 0.041\u20130.049 in the analysis of p-values with three digits , which means 0.8% of the time (0.049 minus 0.041) a p-value within each of the five p-value bins will be observed2p-values between 0.041\u20130.049 when the null hypothesis is true, p-values between 0.0405\u20130.0495, which would mean 0.9% of the time a p-value within a single p-value bin will be observed. Using 0.8% or 0.9% Type 1 error rates in each bin does not influence the reconstruction purely based on changes in power over time, and does not have consequences for any of the conclusions based on the reconstructions.Because researchers round numbers to the nearest 3 digits, one might argue that instead of 0.8% of . By increasing the Type 1 error rate above 0.8%, and doing so more strongly for higher p-value bins, we can attempt to reconstruct the consequences of an increase in false positives in the literature on the observed ratios of p-values over time.Let\u2019s assume the average power has not changed over time, and instead try to reconstruct the observed data by ositives , p. 6. Ap-values between 0.001\u20130.009 , and substantially higher for p-values between 0.011 and 0.049 . Although this would be substantial , it is not impossible.One attempt to specify the parameters to model the ratios  is presented in p-value distribution for true effects (based on the power of the studies) leads to a lower frequency of p-values in the 0.041\u20130.049 bin than in the 0.031\u20130.039 bin. A uniform inflation of the Type 1 error rate  would add the same number of false positive p-values to each bin, but because the frequency of true p-values decreases from bins with low p-values to bins with high p-values, the relative increase is stronger in the 0.041\u20130.049 bin than in the 0.031\u20130.039 bin because the extra p-values from false positives constitute a relatively larger increase. As However, such a pattern of Type 1 error rates does not predict the ratio of fractions in the last 20 years, which were on average equal for the 0.031\u20130.039 and 0.041\u20130.049 bins. If we would change the Type 1 error rates to reconstruct the very similar ratios in the majority of the years in the 0.031\u20130.039 and 0.041\u20130.049 bins only based on a change in Type 1 error rates, the Type 1 error rates should be equal across these bins, or even slightly lower in the 0.041\u20130.049 bin compared to the 0.031\u20130.039 bin. This would be opposite to predictions based on flexibility during the data analysis . The p-vp-hack studies where H1 is true. If such behavior increases over time, we can expect the percentage of p-values from true effects in the 0.041\u20130.049 bin to increase in 2013 compared to 1990. If we would incorporate this effect in the model, the relative increase over time in the 0.041\u20130.049 bin would be even stronger compared to the 0.031\u20130.039 bin. Again, we do not see huge differences in the ratios between the 0.031\u20130.039 and 0.041\u20130.049 bins, which makes the explanation based on flexibility in the data analysis even less likely.Researchers can (and probably do) p-values smaller than 0.05). This means that p-values are either true positives (when H1 is true) or false positives (when H0 is true). The ratios calculated by The third factor that could influence the ratios is the percentage of studies where true effects are examined. A hypothesis is either true or not. The current analysis focuses on statistically significant findings in the published literature  constant over time, the observed ratios of fractions  can be reconstructed purely based on a change in the H0/H1 ratio over time if we assume it was 10 times more likely to examine a true hypothesis compared to a false hypothesis in 1990, and at the same time assume it is 10 times more likely to examine a false hypothesis compared to a true hypothesis in 2013 . On the other hand, while increases in Type 1 error rates can be used to reconstruct the observed ratios, the pattern of inflated Type 1 errors across the 5 bins of p-values just below 0.05 without providing substantial evidence for such a rise . A better approach seems to be to perform targeted analyses of small sets of similar studies, which might be able to yield support for p-hacking (e.g., p-value distribution across a large number of studies.Analyzing huge numbers of ng e.g., . I do nop-hacking, are the biggest problems in the scientific literature. Without publication bias, Type 1 errors would be quite easily identified as they lead to follow-up research that will not observe the hypothesized effect. Even with publication bias, meta-analyses can identify sets of studies that lack evidential value, indicating the studies are a result of selection and reporting biases (p-value distributions in 1990 and 2013 in the data by p-hacking have been very salient in recent years, but I believe it is worthwhile to point out that designing well-powered studies with high informational value (e.g., Although it is important to control Type 1 error rates when performing statistical tests e.g., , I belieg biases . As the ue e.g.,  and prevue e.g.,  are at l10.7717/peerj.1142/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj.1142/supp-2Supplemental Information 2Click here for additional data file."}
+{"text": "Here we show such interplays in a Ag55 nanocluster using real-time time-dependent density functional theory simulations. We find that the disappearance of the zero-frequency peak in the Fourier transform of the band-to-band transition coefficient is a hallmark of the plasmon. We show the importance of the d-states for hot-carrier generations. If the single-particle d-to-s excitations are resonant to the plasmon frequency, the majority of the plasmon energy will be converted into hot carriers, and the overall hot-carrier generation is enhanced by the plasmon; if such resonance does not exist, we observe an intriguing Rabi oscillation between the plasmon and hot carriers. Phonons play a minor role in plasmonic dynamics in such small systems. This study provides guidance on improving plasmonic applications.Plasmon-generated hot carriers are used in photovoltaic or photochemical applications. However, the interplays between the plasmon and single-particle excitations in nanosystems have not been theoretically addressed using  Plasmons can enhance hot-carrier generation for efficient photochemical reactions, but the interplay between plasmons and single-particle excitations are difficult to capture in models. Here, the authors use real-time time-dependent density functional theory to study these interactions in silver nanocrystals. Plasmons are collective oscillations of the electron density, which can convert light energies into electronic excitations1346189101112131415\u03c9 of the inverse dielectric function \u025b\u22121\u03bd satisfies \u222b\u025b\u03bddr2=0. Here the plasmon frequency \u03c9p is a complex number, with its imaginary part indicating the plasmon life time. Unfortunately \u025b\u22121 does not provide a real-time picture of the interplays between the plasmon and hot carriers. There are several recent theoretical studies on the plasmon-induced hot-carriers generations, showing that hot carriers can be effectively excited by plasmons24Plasmon modes can be simulated classically using the Drude model and Maxwell equations. Such calculations can yield accurate plasmon modes for systems down to tens of nanometres. However, when the system sizes shrink to the order of nanometres, the classical method could fail1717192021The real-time (rt) time-dependent density functional theory (TDDFT) is a powerful tool to study the plasmonic processes. The rt-TDDFT describes directly the Coulomb interactions between electrons, and its ability to describe plasmons has been demonstrated in many previous publications262728292627282855 nanocluster. The Ag55 nanocluster has been experimentally synthesized and its atomic structure is well determined32d-to-s excitations resonant to the plasmon frequency exist, most plasmon energy will be converted into hot carriers, enhancing hot-carrier generations. However, if the resonances do not exist, the plasmon decays slowly and may exhibit Rabi oscillations. We propose that by modifying the electronic structures of nanoclusters , the plasmon decay and hot-carrier generations can be tuned. The electron\u2013phonon interactions play a minor role during the plasmon decay in Ag55.In this work, we will use rt-TDDFT to study the plasmon dynamics in a Ag55 are shown in 55 has 605 electrons and is an open-shell system. The 301st\u2013303rd states are almost degenerated and partially occupied, and the 304th state is the lowest unoccupied state (LUMO). To study the excitations, we apply an external electric field \u03c9l with a Gaussian envelope. The optical absorption spectrum can be obtained from the time-dependent dipole response (the imaginary part of \u03b1(\u03c9) described in Methods section), and is shown in \u03c9p\u22483.6\u2009eV, which is in good agreement with the recent experimental result of 3.8\u2009eV =\u03c1\u2212\u03c10(r) (where \u03c10(r) is the ground-state charge density) at t=19.2 and 19.8\u2009fs are shown in \u03c1 is localized on the surface, and sloshes from one side of the nanocluster to the other, fitting well with the classical picture of the surface plasmon. From 20 to 27\u2009fs, the dipole oscillation amplitude decays to relatively small values. Two of the charge density differences \u0394\u03c1 at t=38.0 and 38.6\u2009fs are shown in \u03c1 is not localized on the surface and does not slosh, which may suggest the plasmon decay qualitatively. Such dipole oscillations can be observed experimentally as demonstrated in a recent experiment by Mittal et al.To exam the resonant excitation, we set the laser frequency \u03c9p overlaps with the single-particle excitation energies, which makes their interplays interesting but difficult to analyse. There are several previous publications on this topic using different approaches1123373839404142ith eigen state to the jth eigen state also produces a charge density oscillation. This can be seen from the expansion of the time-dependent wave function \u03c8i(t) on the eigen states in a perturbation theory:How to distinguish the collective plasmon excitation from the non-collective single-particle excitation quantum mechanically is a challenging issue. In particular, for small molecules and nanostructures, the plasmon frequency and the charge density change is\u03c9j,i=\u03c9j\u2212\u03c9i=\u03c9p, so \u0394\u03c1(t) also oscillates at the frequency \u03c9p. Thus, we cannot use the charge density (or dipole moment) oscillation alone to tell the difference. One can attempt to use the charge density plot, such as et al.Cj,i(t), especially the Fourier transform of Cj,i(t) , compared with Cj,i(t) of single-particle excitations. In the following we will take j=304 (LUMO) state as an example to discuss the behaviours of Cj,i(t). i\u2264303) to the LUMO state (the 304th state). We observe two clearly distinct types of transitions. One type of i=292), and the other shows smooth amplitude variations .\u03c9LUMO\u2212\u03c9i\u2248\u03c9p . The Fourier transform of CLUMO,253(t) =f(t), where f(t) is a slowly varying (compared with \u03c9p) function, and All the slowly varying transitions have nearly resonant energies O,253(t)  shows on\u03c9j,i\u2248\u03c9p can be effectively excited. The charge density oscillates at \u0394\u03c9j,i\u2248\u03c9p due to the phase factor exp. The single-particle excitations correspond to the so-called \u2018hot-carriers'.This is a typical independent single-particle excitation described by the single-particle time-dependent perturbation theory within the rotating-frame approximation. Only single-particle transitions with nearly resonant frequencies \u0394\u03c9LUMO\u2212\u03c9i<\u03c9p , and the Fourier transform of CLUMO,292(t) shows two peaks at \u0394\u03c9j,i\u00b1\u03c9p. Both the real and imaginary parts of CLUMO,292(t) =A exp[it]+B exp[it], and it can be written as A, B and f(t) are slowly varying (compared with \u03c9p) functions, and \u03b8 is a complex phase factor. Thus, In contrast, all the rapidly oscillating transitions have off-resonant energies O,292(t)  oscillat\u03c9j,i\u2248\u03c9p, as \u0394\u03c9j,i does not appear in \u03c9p. These synchronized off-resonant transitions constitute the plasmon mode. Since there is no resonant requirement for the plasmon-related transitions, many transitions with i to j transitions are reduced. In It cannot be described by the single-particle perturbation theory. It also does not require that the resonant condition \u0394Cj,i(t) comes from the plasmon, we have performed a time-dependent evolution on a non-interacting system with the same external electric field. In this simulation, we fix the potential in the Hamiltonian V=V  making it independent of the charge density. We would like to stress that this non-interacting system is an unrealistic system with no experimental counterpart. In this model, all the electrons are treated as independent single particles. Because the electron\u2013electron interaction is zero, the plasmon excitation is impossible. Thus, the plasmon-related transitions should behave differently, while the single-particle transitions should remain the same.To further prove that the rapidly oscillating i=253), both the i=292) are replaced by irregular oscillations. The irregularly oscillating transitions decay with time, and almost disappear after the laser fades off. Besides the two peaks at \u0394\u03c9i,j\u00b1\u03c9p in CLUMO,292(t) has a strong peak at \u03c9=0 in \u03c9pt) perturbation along the x axis:The dipole moment of the non-interacting system inset of  shows anoth the   and the oth the   are simi\u03c9p, there are extra oscillating terms at the frequencies \u0394\u03c9j,i. These off-resonant oscillations have different \u0394\u03c9j,i and thus cannot add up in sync, which results in the irregular oscillations shown in \u03c9=0 peak in the Fourier transform must disappear, which is a hallmark of the plasmon mode. The disappearance can only exist with interactions between different transitions.Apparently, the Fourier transform should have three peaks in agreement with those in \u03bb=0 in ref. \u03c7 equals to that of the non-interacting system \u03c70. Thus, their model system with no electron\u2013electron interactions is exactly the same as our non-interacting system. The absorption spectrum of the non-interacting system is exactly the DFT result shown in \u03bb increases. Similarly, we find that the main absorption peak of the real system (\u03bb=1) is \u223c1.9\u2009eV higher than that of the non-interacting system (\u03bb=0).In refs i=253 and 292 with j=LUMO to represent the two types of transitions, respectively. All other transitions can also be classified into the two distinct types. The In the discussion above, we have used Cj,i(t) due to the electron\u2013electron interaction is a hallmark of the plasmon. For single-particle excitations, the charge density oscillation comes from the phase factor interference between \u03c6i and \u03c6j  and Cj,i(t) does not oscillate; for plasmons the oscillation comes from the Cj,i(t) amplitude oscillations. Each transition  can either belong to plasmon (off-resonant) or single-particle (near-resonant), but cannot belong to both. This provides an unambiguous way to sort out the plasmon from single-particle excitations.Here we summarize the analysis above. Both the plasmon and single-particle excitations are described by band to band transitions  in TDDFTj and i denote unoccupied and occupied states, respectively), which represents the number of transitions at the energy \u03c9 for a given time t. For the real system, as shown in SC has peaks around 1.5\u20132.5\u2009eV at t=17\u2009fs. Those off-resonant transitions constitute the plasmon. At t=39\u2009fs, those off-resonant peaks disappear, and the resonant peak is strengthened, showing that the plasmon has been converted into resonant single-particle excitations (hot carriers). From t=17 to 39\u2009fs, the laser is off. Thus, the hot carriers are generated completely by the plasmon. For the non-interacting system  shows much smaller peaks around 1.5\u20132.5\u2009eV (no plasmons), while the main peak always appears at the resonant frequency (single-particle excitations). There is no change in SC from 17 to 39\u2009fs because there are no laser nor electron\u2013electron interactions.We have calculated the energy spectrum of g system , SC defined by jth eigen state. The numbers of excited electrons (positive \u0394Oj(t)) on all eigen states are shown in j can have both resonant and off-resonant transitions from different states i, \u0394Oj(t) is a combination of both slowly varying and rapidly oscillating components as shown in Cj,i(t) in d-states to the eigen states around the Fermi energy are the major plasmon decay (hot-carrier generation) channels.We have also calculated \u0394t=0, the light energy is absorbed by both the plasmon and resonant single-particle (hot-carrier) excitations, with almost equal rates. Compared with the non-interacting system, the single-particle energy of the real system is lower at first (the blue line is negative), indicating that less hot carriers are generated at first due to the plasmon. After 3\u2009fs, the blue line becomes positive, indicating more hot carriers are generated due to the plasmon. After the laser fades off at t=10\u2009fs, the energy in the plasmon mode does not decay immediately, and we even observe a small single-particle to plasmon energy transfer around t=17\u2009fs. From 20 to 30\u2009fs, the plasmon energy starts to decay and is almost completely transferred into single-particle excitations. The speed of the decay agrees with previous experiments that the plasmon decay timescale is 1\u2013100\u2009fs (refs \u03c9pt/Q), we obtain Q=13.3 , as shown in \u2009fs refs , 36. By t=8 and 30\u2009fs are shown in t=8\u2009fs, there are broad excitations around the Fermi energy, indicating the plasmon excitation. At t=30\u2009fs, as the plasmon is decayed to hot carriers, the excited electrons and holes are concentrated in a few sharp peaks. These peaks can be classified into two groups. The major hot holes are around \u22123.6\u2009eV with the corresponding electrons around the Fermi energy (d to s transitions). There are fewer hot holes at \u22121.1\u2009eV with the corresponding hot electrons at 2.5\u2009eV (s to p transitions). In a recent perturbation calculation of plasmon-induced hot-carriers in bulk Ag . It is interesting to see what would occur if these transitions are blocked. We first consider the negatively charged j\u2264303 are fully occupied, and thus cannot accept electrons from d-states. The only important channel is the d to 304th state excitation. The amplitude of the dipole oscillation of 55 (Oj(t)  channels are blocked in As mentioned above, the major hot-carrier generations in Agtion of   decays m of  (55 . The num5 (Oj(t)  confirm 5 (Oj(t) . After 15 (Oj(t) . The chaOj(t) . To change the system more dramatically, one may change the plasmon or single-particle frequencies. Experimentally, it can be realized by alloying with other metals, changing the nanocluster size/shape, or using some dielectric mediums. Theoretically, by further modifying the pseudopotential (see Methods section), we can artificially push down the d-state energies, making the d to s transition energies much greater than the plasmon frequency. Thus, all the single-particle d to s excitations become impossible. First, we observe an intriguing oscillation of the dipole amplitude (Oj(t) (s to p excitations). However, their transition energies are slightly off-resonant from the plasmon frequency by \u223c0.2\u2009eV, and \u0394Oj exhibits Rabi oscillations at the frequency \u0394\u03c9j,i\u2212\u03c9p. We also observe a cyclic energy transfer between the plasmon and single-particle excitations at the Rabi frequency (\u03c1 (t=19.2 and 19.8\u2009fs (more energy is stored in the plasmon) show stronger charge localization on the surface than those at t=41.4 and 42.0\u2009fs (more energy is stored in the hot carriers). Around 40\u2009fs, there is still charge localized on surface, because the plasmon is not fully decayed. Although Rabi oscillations in two-level systems are well known, it is interesting to observe Rabi oscillations between a collective plasmon mode and individual hot carriers. In the original Ag55  e (Oj(t)  still shrequency . Differeences \u0394\u03c1  at t=19.nal Ag55 , we alsoet al.ab initio forces in the rt-TDDFT, and are able to describe the electron\u2013phonon effects explicitly. The results for neutral Ag55 and Ag55 without resonant hot-carrier generation channels are shown in The simulations above have only included plasmon dampings through hot-carrier generations within TDDFT. We have not included the electromagnetic radiation. 55 nanocluster. Our rt-TDDFT simulations include the electron\u2013electron interactions and electron\u2013phonon interactions (using the Ehrenfest dynamics). The plane-wave basis set allows accurate descriptions of excited states. We do not include the electromagnetic radiations because they are extremely small in Ag nanoclusters. The simulations are under DFT and Kohn-Sham orbital framework, and do not explicitly use many-body wave functions. We propose an approach to distinguish the plasmon from single-particle excitations based on band to band transition coefficients Cj,i(t). We find that the collective plasmon consists of off-resonant transitions with Cj,i(t) oscillating in their amplitudes at the plasmon frequency, whereas the single-particle excitation is characterized by a slowly varying Cj,i(t). The disappearance of the \u03c9=0 peak in the Fourier transform of Cj,i(t) makes the plasmon-related transitions different from the conventional independent off-resonant transitions described by the single-particle time-dependent perturbation theory, and is a hallmark of the plasmon. In Ag55, the single-particle d to s excitations resonant to the plasmon frequency exist. The plasmon will decay and generate hot carriers, and significantly enhance the hot-carrier generation rates. The main hot-carrier generations are from the low-energy d-states to the s-states around the Fermi energy. When applying a high-intensity laser, we also observe some nonlinear high-energy excitations. When most hot-carrier generation channels are blocked in d to s excitations have been completely blocked. Our rt-TDDFT Ehrenfest dynamic simulations show that the electron\u2013phonon interactions do not play important roles in the plasmon decay in nanoclusters.We have performed rt-TDDFT simulations on the Agd10 and 5s) are expanded using plane-waves with an energy cutoff of 40 Ry. Although the plane-wave basis set significantly increases the computational cost compared with the local orbital basis set, it can describe the high-energy excited states and charge responses more accurately, which is critical for the plasmon study. The Brillouin zone integration is sampled with the \u0393 point only for the isolated Ag55 cluster. DFT cannot correctly predict the energies of the Ag d-states, which may affect the accuracy of the plasmon calculations28d-states, we add a Gaussian term to the d-channel of the Ag pseudopotential. We have fitted the pseudopotential so that the calculated density of states of the Ag d-bands agrees well with the experimental X-ray photoemission spectroscopy dataOur fast rt-TDDFT algorithm55 adopts the icosahedral structure3255, and the simulated time-dependent results have similar features to those of the icosahedral structure, as shown in 55, which is shown in In experiments, the Ag55 nanocluster, and treat the Ag 4d electrons as valence electrons. Thus, our simulations give more accurate descriptions of the system than the studies based on jellium models.In our simulations, we explicitly consider the atomic structure of the AgSC, we broaden the Dirac \u03b4 function using a Gaussian function with a s.d. of 0.1\u2009eV.When calculating the density of states, the DFT absorption spectrum, and 55 in experiments due to the high mobility of the nanoclusterThe rt-TDDFT simulation explicitly includes the electron\u2013electron interaction, which is critical for the plasmon excitation and plasmon-induced hot-carrier generations. The rt-TDDFT does not include the radiative damping. Previous study shows that the radiative effect is very weak for small Ag nanoclusters, so it is safe to ignore it\u03c8i(t) at t=0 is occupied according to the ground-state Fermi-Dirac occupation number \u03c8i(t) are always orthogonal to each other. To evolve \u03c8i(t) with time, we expand it onto the adiabatic eigen states \u03c6j(t) (which satisfies H\u03c6j(t)=\u03c9j(t)\u03c6j(t) for the time-dependent Hamiltonian H):In our rt-TDDFT simulations, the time-dependent electronic state Cj,i is the expansion coefficient which can be calculated using our rt-TDDFT algorithmCj,i (i\u2260j) represents the transition from the ith adiabatic eigen state to the jth adiabatic eigen state. We note that Cj,i might depend on an arbitrary phase factor due to the non-unique definition from \u03c6j(t) to \u03c6j(t+dt). We have removed this arbitrary phase factor by requiring \u03c6j(t) can be taken as a real function (without magnetic fields), there will be no Berry phase. The simulation is under DFT and Kohn-Sham orbital framework, and thus it does not explicitly use many-body wave functions. By using our new algorithm, we can set the simulation time step to 0.1\u2009fs \u03c9j for the purpose of analysis, as the variations of \u03c9j(t) are rather small.The The charge density is calculated byCj,i, we define the occupation change \u0394Oj(t) on the jth adiabatic eigen state as:Using the coefficients Oj(t) represents the occupation change on the jth adiabatic eigen state at time t with respect to its ground-state occupation Oj(t) can be either positive or negative. Positive \u0394Oj(t) indicates increasing occupations (excited electrons) and negative \u0394Oj(t) indicates decreasing occupations (excited holes).The \u0394To simulate the laser excitations, we apply an external electric field to the Hamiltonian to mimic the laser pulseE is along the x axis. \u03c3, \u03c9l and \u03c9l=\u03c9p=3.6\u2009eV, \u03c3=6\u2009fs and The electric field The polarizability can be obtained from the time-dependent dipole moment of the nanocluster51D(\u03c9) and E(\u03c9) are the Fourier transforms of the dipole moment and the electric field, respectively. The absorption spectrum is obtained from the imaginary part of \u03b1(\u03c9).where The energies stored in the plasmon and the single-particle (hot-carrier) modes are estimated asj, i)\u2208plasmon' and \u2018\u2208single' indicate the Cj,i(t) belongs to the rapidly oscillating transitions and the slowly varying transitions, respectively. For a given  pair, the Cj,i(t) either belongs to the plasmon or single particle, and there is no mixture between the two types. Thus the energies in where \u2018.Supplementary Figures 1-6, Supplementary Notes 1-5 and Supplementary References"}
+{"text": "Much empirical evidence shows that individuals usually exhibit significant homophily in social networks. We demonstrate, however, skill complementarity enhances heterophily in the formation of collaboration networks, where people prefer to forge social ties with people who have professions different from their own. We construct a model to quantify the heterophily by assuming that individuals choose collaborators to maximize utility. Using a huge database of online societies, we find evidence of heterophily in collaboration networks. The results of model calibration confirm the presence of heterophily. Both empirical analysis and model calibration show that the heterophilous feature is persistent along the evolution of online societies. Furthermore, the degree of skill complementarity is positively correlated with their production output. Our work sheds new light on the scientific research utility of virtual worlds for studying human behaviors in complex socioeconomic systems. Complexity emerges in the evolving and self-organizing processes of many natural, social, technological, and biological systems. The constituents of a complex system interact with each other and form complex evolving networks, where the constituents are nodes and their interaction relationships are links123457In the sociological literature the local principle of similarity, i.e., the phenomenon that \u201cbirds of a feather flock together,\u201d is known as homophily11121310111214151617In general, it has long been accepted that one of the most significant factors in increasing productivity in modern human societies has been the division of labor2425262728293031In this work, we study the collaboration formation process of individuals with different professional skills. A mathematical model is proposed by assuming that individuals in socioeconomic systems choose collaborators that are of maximum utility. Based on the evolving collaboration networks of 124 virtual worlds in which the agents  belong to three different professions possessing different skills, empirical analysis and model calibration unveil that the agents prefer to collaborate with others of different professions. We further construct two measures to quantify the degree of complementarity of virtual societies. We find that social complementarity positively correlates with economic output.s on day t, whose size Ns is the number of s-agents. The number of -agents is denoted by Ns,i, where i\u2009=\u20091, 2, and 3 stand for the three professions. Hence i-agents in society s isConsider a society or a community j-collaborators of an -agent is fs,ij. Hence, the average number of collaborators that an -agent has is j-collaborators in all collaborators of an i-agent isThe average number of qs,ii is the homophily index15i-agents have zero preference for collaborating with j-agents, we have qs,ij\u2009=\u2009ws,j. If i-agents prefer to collaborate with j-agents, we have qs,ij\u2009>\u2009ws,j. In this case the i-agents are homophilous when j\u2009=\u2009i and the i-agents are heterophilous when j\u2009\u2260\u2009i.Note that s,\u2009j)-collaborators that an -agent has is identical to the proportion of j-agents in the group, that is qs,ij\u2009=\u2009ws,j. Hence the number of -collaborators of an -agent is s,\u2009i)-agent, there is an optimal configuration of collaborators with different skills, \u03b3ij are independent of society s. If the skill configuration in the collaborator list of an agent is optimal, her utility reaches its maximum. If the skill configuration deviates from that optimal value, her utility is reduced. In other words, the utility of an -agent increases when her/his real number fs,ij of -collaborators approaches the optimal value \u03b2\u2009<\u20091. Therefore, the utility function of an -agent isAn agent seeks collaborators when she/he finds it difficult to complete a task alone. If there is no collaboration preference, the proportion of -agents for -agents and \u03b1\u2009>\u20090 since the second term in i-agents do not have any preference on j-agents such that qs,ij\u2009=\u2009ws,j for all societies, we have \u03b3ij\u2009=\u20091. If i-agents prefer j-agents, we have \u03b3ij\u2009>\u20091. If i-agents prefer not to collaborate with j-agents, we have \u03b3ij\u2009<\u20091. For {i,\u2009j,\u2009k}\u2009=\u2009{1,\u20092,\u20093}, if \u03b3ij\u2009>\u2009\u03b3ik, then i-agents prefer j-agents over k-agents. To maintain a collaboration network of size fs,i, the -agent suffers a cost proportional to fs,i\u2009in which According to the above model, the overall utility in the decision-making process isDs,i, we can estimate the parameters \u03b3ij .By maximizing t\u2009=\u200915 of a group of 27 agents randomly chosen from a virtual society filtered by three intimacy thresholds Ic\u2009=\u20090, 100, and 2000. There are 12 warriors, 5 priests, and 10 mages. If i-agents are homophilous  in their collaboration-forging process, the proportion of links between i-agents is greater than  the square of the proportion of i-agents . For Ic\u2009=\u20090, there are 77 links including 15 intra-warrior links, 4 intra-priest links, and 4 intra-mage links. The proportions of intra-profession links are 0.1948 for warriors, 0.0519 for priests, and 0.0519 for mages. For Ic\u2009=\u2009100, there are 48 links including 8 intra-warrior links, 1 intra-priest link, and 1 intra-mage link. The proportions of intra-profession links are 0.1667 for warriors, 0.0208 for priests, and 0.0208 for mages. For Ic\u2009=\u20092000, there are 15 links including only one intra-warrior link and no intra-priest and intra-mage links. The proportions of intra-profession links are 0.0667 for warriors and 0 for priests and mages. Hence, the agents in Ic\u2009=\u20090. We will show below that heterophily is not a specific characteristic for these 27 agents but a universal feature presents in all the virtual societies.t\u2009=\u200915 and Ic\u2009=\u2009100 most virtual societies have qs,ij\u2009>\u2009ws,j when i\u2009\u2260\u2009j, but qs,ij\u2009<\u2009ws,j when i\u2009=\u2009j. Such heterophilous patterns are observed for other values of t and Ic as well . We obtain the values of \u03b3ij for each intimacy threshold Ic on each day t. \u03b3ij for socioeconomic networks using the intimacy threshold Ic\u2009=\u2009100, and Ic\u2009=\u20090, 1, 10, 500, 1000, and 2000. The F-tests presented in Materials and Methods show that all the results are significant at the 0.1% level (see SI Tables).To calibrate the model, we follow and further develop the econometric method presented in ref. \u03b3ii coefficients are less than 1, while all the \u03b3ij values for i\u2009\u2260\u2009j are greater than 1. This indicates that the agents are not seeking same-profession agents but different-profession agents and are thus heterophilous. In most cases, especially when the intimacy threshold Ic is not large, the \u03b3ij values do not have a trend along the evolution of virtual worlds. When Ic is large, however, we observe an increasing trend in \u03b313 for Ic\u2009=\u20091000 and 2000, in \u03b323 for Ic\u2009=\u20091000 and 2000, and in \u03b332 for Ic\u2009=\u2009500, 1000 and 2000 . For each member agent a in t\u2009\u2212\u20096 to t, denoted as Ys,a(t). The economic performance of the agents in To measure the economic implications of heterophilous preference in socioeconomic networks, we investigate the relationship between complementarity of professions and economic performance. Consider the socioeconomic network One measure of profession complementarity can be defined as the sum of preference measures between the three types of agents,qs,ij deviates from the optimal collaborator configuration \u03b3ijws,j . The lower the deviation, the higher the degree of complementarity. Thus, we haveAlternatively, we can measure complementarity by determining how much the real collaborator configuration Pk\u221212/Pk2), lg(Ck\u221212/Ck2) and lg(Yk\u221212/Yk2), rather than focusing on each society separately. Both measures of complementarity correlate strongly with the relative economic output when t and I are not large (t), most agents strive to achieve higher levels by implementing specific tasks with small economic outputs. Other agents attempt to obtain high intimacy levels by killing monsters in locations unrelated to economic outputs. In both cases the agents intend to form complementary collaboration networks, but their activities are not focused on economic outputs. With the development of a virtual world, the number of active agents increases and reaches a maximum at time tmax and then decays . And so on so forth. These tasks are usually not easy for the associated agents. However, they can ask their collaborators for help to form a team and fulfill the tasks together. Agents can also form teams to kill monsters and make productions. All these collaborations will increase the intimacy of the collaborating agents in the same team.s-agent is an agent belonging to society s. An i-agent is an agent having profession i. Similarly, an i-collaborator is a collaborator having profession i. An -agent or -collaborator is an i-agent or i-collaborator in society s.In each society there are three professions . We use subscripts 1, 2, and 3 to stand respectively for the three professions: warrior, priest and mage. For simplicity, we define several notations as follows. An s,\u2009i)-agent solves the following decision-making problem of how many collaborators to haveAn  denotes the average behavior (decision) of all agents having the same profession in a given society. If we consider an arbitrary agent  denotes a has is the sum of a universal (or systemic) term and an idiosyncratic error term. The error term is assumed to have mean 0 and variance \u03c32. Note that this assumption states that the variance of any agent of any profession is the same.which means that the \u201crealized\u201d number of collaborators agent Ns as the size of society s and ws,i as the fraction of i-agents in society s. Hence the number of i-agents in society s is Nsws,i, and the expectation of the aggregated number of collaborators that i-agents have in society s is Nsws,ifs,i. According to We denote Es,i has mean 0 and variance 2\u2009=\u20092\u03c32.where i\u2009\u2260\u2009j,It follows that, for s:Following ref. s,i,j is 0 and the variance is \u03d5s,ij\u03c32, whereAccording to \u03c32 for any society s. The sum of squared errors Thus the normalized variable Ns as expected. However, ws,i, which is consistent with the setup of our model but different from the model in ref. which is independent of as, bs and cs could be society-specific and are not included in the final objective function of model calibration.One can see that Ic and t, a society is excluded in model calibration if the number of agents having at least one collaborator is less than 500 to ensure that \u03f5a has enough realizations. Changing this threshold around 500 results in same results. In addition, if the number of societies included in a model is less than 50, we do not calibrate the model because the model has 10 parameters.For each pair of Q2, the taboo search algorithm is adopted\u03b3ij\u2009\u2264\u20092 for 9 with the constraint that 0\u2009\u2264\u2009\u03b3ij\u2009\u2264\u20091 or 1\u2009\u2264\u2009\u03b3ij\u2009\u2264\u20092. The parameters in certain cell corresponding to the minimum of Q2 in all cells are obtained as the solution. The normality assumption of fitting errors has been verified by QQ-plots  for each i are not well separated around \u03b3ij\u2009=\u20091  and a limited amount of the virtual currency How to cite this article: Xie, W.-J. et al. Skill complementarity enhances heterophily in collaboration networks. Sci. Rep. 6, 18727; doi: 10.1038/srep18727 (2016)."}
+{"text": "Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts. Hierarchical materials and structures are a class of systems which are composed of structural elements which themselves have structure1An equally interesting class of materials and structures are those designed to exhibit auxetic behaviour, i.e. exhibit a negative Poisson's ratio, which means they get wider rather than thinner when uniaxially stretched9101112Despite the advantages of auxetic and hierarchical materials, the concept of an auxetic hierarchical system has been poorly studied171820222325In this study, we propose and discuss a number of hierarchical auxetics based on rotating rigid units , were assigned stiffnesses of \u03d51) were given stiffnesses of \u03d51, which is related to \u03b81, the angle between through \u03d5 = \u03b81 + \u03b80. Three different cases were considered here, namely: Case I, where the \u03d51-hinges were set to be much stiffer than the \u03b80-hinges; Case II, where the stiffnesses were set to the exact opposite of those in Case I, and finally Case III, where all the \u03b80- and \u03d51-hinges were given low stiffness constants, i.e. both hinges were soft.To illustrate some of the properties and versatility of the proposed hierarchical structures, simulations were performed on the simple two-level system illustrated in \u03bdyz and \u03bdzy obtained from these systems are shown in \u03b80- and \u03d51- hinges. The change in angles that occur upon the application of on-axis uniaxial stress help us understand the deformations taking place upon loading . It was observed that the level 1 deformations associated with the \u03d51-hinges were much more significant than those of the \u03b80-hinges at level 0 , as planar ball and spring systems described by a harmonic potential as discussed in Grima y and z-directions.In all three cases, the squares were kept as rigid as possible by using the highest values for the stiffness constants to define the internal 90\u00b0 intra-square angles and side lengths. Full details of the simulations are provided within the The concept of hierarchical rotating systems was developed by J.N.G. The simulations were performed by L.M., J.I.A. and K.M.A. J.N.G., R.G. and D.A. wrote the main manuscript text while the figures were prepared by L.M. and K.M.A. A.C. and J.B. contributed to the discussion of the manuscript mainly on the medical aspects of the work involved. The work was supervised by J.N.G. and R.G. All authors reviewed the manuscript before submission.ANIM01.gifSupplementary Information"}
+{"text": "In the cloud, uploading encrypted data is the most effective way to ensure that the data are not leaked. However, data access control is still an open problem in cloud storage systems. To provide an authorization mechanism to limit the comparison of a user\u2019s ciphertexts with those of another, public key encryption supporting the equality test with four flexible authorizations (PKEET-FA) is presented. Subsequently, more functional identity-based encryption supporting the equality test (IBEET-FA) further combines identity-based encryption with flexible authorization. The bilinear pairing has always been intended to be replaced due to the high computational cost. Hence, in this paper, we use general trapdoor discrete log groups to construct a new and secure IBEET-FA scheme, which is more efficient. The computational cost for the encryption algorithm in our scheme was reduced to 43% of that of the scheme of Li et al. In Type 2 and 3 authorization algorithms, the computational cost of both was reduced to 40% of that of the scheme of Li et al. Furthermore, we give proof that our scheme is secure against one-wayness under the chosen identity and chosen ciphertext attacks (OW-ID-CCA), and indistinguishable against chosen identity and chosen ciphertext attacks (IND-ID-CCA). With the application of the Internet increasingly spreading, people have more extensive storage and computing requirements for cloud servers. Users make full use of cloud servers, allowing cloud servers to help them in storing and processing data, reducing the user\u2019s storage burden and computing overhead. Users in different regions can upload data onto and download data from a server, which provides convenience for users to share data. However, servers are also vulnerable to some attacks. If users store their data unencrypted in the cloud server, attackers or malicious internal administrators may access the data stored by users. The solution is for every user to upload encrypted data onto the cloud server. Previous classical encryption schemes cannot realize direct searches or calculations in the ciphertext.In a searchable encryption scheme , the cipA novel PKEET scheme  was firsBilinear pairing is computationally expensive, and to reduce the computational cost, we have attempted to replace pairing with discrete logarithms. We reconstructed an existing concept with a different tool, namely, reconstructing the IBEET-FA scheme with discrete logarithms. This can achieve more efficient searches in ciphertexts encrypted by different public keys, and maintain the nature of flexible authorization in which different authorizations correspond to different permissions. A public key infrastructure is not required.We first defined the scheme and its correctness. Subsequently, a specific scheme IBEET-FA without paring was constructed, and the scheme was proven to be correct. Our scheme is communicationally efficient, and it has a small public key and ciphertext. The scheme is computationally efficient, as the Aut-1, Aut-2, and Aut-3 authorization algorithms and testing algorithms in it all have a small computational overhead.We then define two security models for the scheme, and two types of adversaries, Adv-I and Adv-II. Our IBEET-FA without a pairing scheme achieved OW-ID-CCA security for Aut-A new concept of public key encryption with keyword search (PEKS) was proposed by Boneh et al.  in 2004 A new scheme of PKE with a delegated equality test (PKE-DET) was proposed by Ma et al. in ; in a muA new authorization mechanism for efficient PKEET-FA was proposed by Ma et al. , which cDuong et al.  proposedWe organize the remainder of the paper as follows. The definitions of Trapdoor Discrete Log Groups and Decision Diffie\u2013Hellman Problem are given in Definition\u00a01.A TDL group generator consists of algorithms TDLGen and SolveDL:Definition\u00a02.Let q be the prime order of group G, generator g is gotten from the running result of algorithm Definition\u00a03.Let q be the prime order of group G, generator g is gotten from the running result of algorithm In i and j. The trusted third party generates system parameters for users and cloud service. User i and user j encrypt their data with their public key, and store ciphertext in the cloud server, and the cloud server is authorized to do equality tests on stored ciphertext, but the server does not have the ability to decrypt them. We present the IBEET-FA system model in In our defined IBEET-FA scheme, we give four entities: a cloud server, a trusted third party, and two users labeled as Definition\u00a04.Our IBEET-FA scheme consists of four algorithms: \u22a5.i has the public-secret key pair j has the public-secret key pair User i and i\u2019s secret key i\u2019ciphertext i\u2019trapdoor j\u2019ciphertext j\u2019trapdoor Aut-1:i\u2019private key i\u2019ciphertext i\u2019trapdoor j\u2019ciphertext j\u2019trapdoor Aut-2:i\u2019private key i\u2019ciphertext j\u2019ciphertext i\u2019ciphertext i\u2019trapdoor j\u2019ciphertext j\u2019trapdoor Aut-3:i\u2019private key j and j\u2019s secret key i\u2019ciphertext i\u2019trapdoor j\u2019ciphertext j\u2019trapdoor Aut-4:Definition\u00a05.(Correctness): If for any M in the plaintext space, For any possible plaintext i and any possible ciphertext j, if DecryptFor any possible ciphertext Aut-1: For two trapdoors of Aut-2: For two trapdoors of Aut-3: For two trapdoors of Aut-4: For two trapdoors of i and any possible ciphertext j, if Decryptk:For any possible ciphertext Aut-1: For two trapdoors of Aut-2: For two trapdoors of Aut-3: For two trapdoors of Aut-4: For two trapdoors of Adv-I: For Aut-Adv-II: For Aut-According to the nature of our scheme, we use the IBEET-FA security models defined in . Since AUnder chosen ciphertext and chosen identity attacks, We now define the one-wayness security (OW-ID-CCA) against Adv-I for Aut-t  to Decryption queries: Authorization queries: For three types of authorization Aut-(a)i as input, (b)(c)t which has not been queried in extract queries, and sends it to t can not be queried in this phase and We give the advantage definition of Definition\u00a06.If the advantage t  authorization.Proof\u00a0of\u00a0Theorem\u00a02.i, where Game1:\u00a0\u00a01.Hash queries: Suppose (a)i, the oracle picks (b)(c)(d)2.i, challenger Key retrieve queries: For an identity 3.i, ciphertext Decryption queries: For an identity 4.Authorization queries: For Aut-(a)i as the input, (b)(c)t, and t has not been queried in previous extract query, t can not be allowed to query; and in the decryption queries, Game2:\u00a0It is almost equivalent to Game 1, the modified parts are as follows:R. We can see that E. If Game3:\u00a0Game2, the modified parts are as follows:It is almost equivalent to R is a random string, we can konw that We design several related games to prove OW-ID-CCA security against Adv-I From all the formulas obtained above, we derive the following formulaTheorem\u00a03.Based on DDH assumption, in the random oracle model our presented IBEET-FA scheme is IND-ID-CCA secure against Adv-II for Aut-\u03b3  authorization.Proof\u00a0(Proof of Theorem 3). If such an adversary For n key pairs 1.Hash queries:(a)(b)(c)(d)2.i, Key retrieve queries: Given an identity 3.i and a query ciphertext R, making equation M to Decryption queries: For identity 4.Authorization queries: For Aut-(a)i as the input, challenger (b)(c)t, there is a contraint that t can not be queried in extract queriy phase or Aut-1 authorization query phase. 1.i could not be allowed to query;In the key retrieve query phase or Aut-1 authorizations query phase, 2.In the decryption query phase or the authorization query phase, \u25a1G, In ize than ,23,24 inize than  in the cIn From the comparison results in In this paper, we propose a new IBE scheme without pairing, which supports the ciphertext equality test. Our scheme introduces the authorization mechanism proposed in the scheme , four tyOur proposed approach can be applied to equality tests over ciphertexts encrypted with different public keys, which increases the application range of cloud computing. Furthermore, our scheme is in IBE settings, avoiding complex key management issues. However, there are security channel key distribution and private key escrow issues in IBE. In the future, we will try to combine the advantages of IBE and PKE to propose more secure and efficient equality test schemes."}
+{"text": "The\u00a0investigation of the link between reduced forced vital capacity (FVC) and risk factors and health variables in\u00a0women aged \u2265 40 years is encouraged since a reduced FVC was related to all-cause mortality. The high frequency\u00a0of women with a reduced FVC, observed in some studies, could be related to the impacts of parity on lung. In the\u00a0literature, the association between parity and health consequences is discussed in terms of \u201cselection pressure\u201d,\u00a0and the trade-off between longevity and fertility described by scientists is termed the \u201clongevity determination\u201d or\u00a0\u201cbiological warranty period\u201d. The respiratory system could be influenced by parity. Above all, it is the respiratory\u00a0system, who endures the repercussions of the numerous physio-pathological experiences of the woman life. The\u00a0probable effects of parity on lung function data, including FVC, make parity a key predictor to be stressed and\u00a0evaluated. Parity is a promising original direction for physiological and pathophysiological research, particularly for\u00a0low- and lower-middle- income countries. Thus, upcoming epidemiological and clinical studies of lung function data\u00a0in women would need to include information about their parity status. Dear editor,ie; the number of offspring a woman has borne) on lung  or a mixed population of healthy/unhealthy women also reported opposing outcomes  initial mean FEV1, ii) rate of FEV1 decline; and iii) COPD incidence between the different groups of parity [1 or FEV1/FVC in never-smokers or in those with low smoking exposure [eg; multiparous women have a tendency to an obstructive impairment; lower flows; lower post-bronchodilator FEV1, and increased Pi levels) [The four studies \u201315 examies Table\u00a0. On the f parity , or that levels) \u201315.Tableeg, telomere length), oxidative stress, coronary heart conditions, stroke, heart-failure, arterial-hypertension, type 2 mellitus-diabetes, renal cancer, and bad health related quality-of-life [To conclude, parity is a promising original direction for physiological and pathophysiological research, particularly for low- and lower-middle- income countries . In the -of-life , 19. In"}
+{"text": "Nature Communications 10.1038/s41467-022-32795-y, published online 29 August 2022Correction to: The original version of this Article contained an error in Table 1. The correct version of the 11th row of the 2nd column states \u20180.635\u2019 instead of the original, incorrect \u2018\u22120.635\u2019. The correct version of the 12th row of the 2nd column states \u20180.881\u2019 instead of the original, incorrect \u2018\u22120.881\u2019. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Solving structural ensembles of flexible biomolecules is a challenging research area. Here, we propose a method to obtain possible structural ensembles of a biomolecule based on small-angle X-ray scattering (SAXS) and molecular dynamics simulations. Our idea is to clip a time series that matches a SAXS profile from a simulation trajectory. To examine its practicability, we applied our idea to a multi-domain protein ER-60 and successfully extracted time series longer than 1 micro second from trajectories of coarse-grained molecular dynamics simulations. In the extracted time series, the domain conformation was distributed continuously and smoothly in a conformational space. Preferred domain conformations were also observed. Diversity among scattering curves calculated from each ER-60 structure was interpreted to reflect an open-close motion of the protein. Although our approach did not provide a unique solution for the structural ensemble of the biomolecule, each extracted time series can be an element of the real behavior of ER-60. Considering its low computational cost, our approach will play a key role to identify biomolecular dynamics by integrating SAXS, simulations, and other experiments. However, revealing their dynamic processes in solution remains challenging.Many proteins are composed of multiple domains that realize complex and sophisticated functions by rearranging their domains flexibly. For example, each domain works together to introduce DNA supercoiling in DNA topoisomerases and each domain cooperates to refold substrate proteins in some foldases9. The SAXS profiles include structural information in the range of approximately 1\u2013100\u00a0nm, which is usually wide enough to study structural range of multi-domain proteins or their complexes. SAXS intensity I(Q) is calculated as a function of scattering vector (Q):Small-angle X-ray scattering (SAXS) is a representative experimental technique to study such behavior of biomolecules9: N is the number of atoms in a system, rij is the distance between the i-th and j-th atoms, and fi (Q) is an atomic form factor of i-th atom, which is regarded as a constant in the measured small-angle range.In Eq.\u00a0, the \u03b8 aSince all molecules in a sample solution contribute an experimental SAXS profile, the profile includes information on their structural ensemble. There could be two different types of structural sets of which ensembles reproduce the same SAXS profile. One is a \u201chomogeneous structural set\u201d in which all molecules have a similar structure. The other is a \u201cheterogeneous structural set\u201d. The latter includes the diverse structures, but their averaged SAXS profile reproduces the experimental one. It is difficult to determine which set should be adopted as the state of the molecule in solution. In other words, we cannot judge whether all molecules have similar or diverse structures only from an experimental SAXS profile.10. In the \u201cmaximum parsimony\u201d approach, a structural set composed of a small number of models is selected among possible structural sets matching an experimental SAXS profile. For example, the Akaike information criterion or Bayesian information criterion is calculated for possible structural sets, and a structural set minimizing the criteria is chosen12. Many algorithms, such as ensemble optimization, minimal ensemble search, sparse ensemble selection, and maximum occurrence, have been proposed and utilized17.To address this issue, two main criteria are considered in the context of structural modeling; they are reviewed as \u201cmaximum parsimony\u201d and \u201cmaximum entropy\u201d22. The other approach is to perform parallel simulations with additional potential to reproduce an experimental SAXS profile27.In the \u201cmaximum entropy\u201d approach, a free energy landscape derived from a simulation force field is adopted as the prior distribution. The resultant ensemble should match an experimental SAXS profile and be least inconsistent with the force field. A force field does not always reproduce a real structural ensemble of a molecule. Therefore, correction of a free energy landscape to match an experimental SAXS profiles is often effective. There are two ways to correct a free energy landscape while satisfying entropy maximization. One direct approach is reweighting the free energy landscape to match an experimental SAXS profile after structural sampling by molecular dynamics (MD) simulations or Monte Carlo simulationsAlthough both methods are effective, they are not necessarily sufficient to model any biomolecular systems. The structural set composed of a small number of models implies that the resulting structures discretely distribute in a structural space. In a largely fluctuating system, such as a multi-domain protein with intrinsic disordered regions, it is more reasonable to model a structural set which continuously distributes in a structure space.26. In many CG models, each CG bead reproduces net charge and hydrophilicity of their corresponding atom set, resulting in roughly reasonable inter- and intra-molecular interfaces in the simulations30. However, parameter adjustment using experimental data is often required32. A general-purpose CGMD potential does not necessarily guarantee accurate dissociation constant for the interfaces of a biomolecule. Therefore, it may not always be suitable to perform entropy maximization using a free energy landscape from a given CGMD potential as the prior distribution.Maximum entropy approaches are useful in that they can construct a physically reasonable structural set. It is necessary to sufficiently explore possible molecular structures in these approaches. However, sufficient stuructural sampling is often difficult for atomistic MD simulations. Coarse-grained (CG) MD simulation is a useful alternative to overcome this difficultyHere, we propose another approach to enumerate possible behaviors of a biomolecule using an experimental SAXS profile and CGMD simulations. In this method, CGMD simulations are first performed to obtain trajectories that efficiently cover their conformational space. Then, time series that match the SAXS profile are extracted from the trajectories. If the resulting time series are long enough, they reflect information on possible preferred states of the biomolecule; the molecule stays in the stable states for a longer time than unstable ones.3. ER-60 is composed a, b, b\u2032, a\u2032 domains and possesses reaction Cys-Gly-His-Cys (CGHC) motifs in both the a and a\u2032 domains  at each Q value. Therefore, diversity in scattering curves among structures was explained by open-close motion of ER-60. In addition, this linear relationship was indicated as two isosbestic points in Q-I(Q) plot. The actual structural ensemble of ER-60 in solution can be a mixture of these possible domain dynamics. Our method provides \"elements of biomolecular motion\u201d, which should be useful in the context of an integrated structural biology including SAXS, MD simulations, and other experiments.We tested our method on a multi-domain protein ER-60, which is a member of protein disulfide isomerase familyins Fig.\u00a0. The a aWhen stable inter- or intra- protein interfaces appear in CGMD simulations, they are regarded as candidates of actual interfaces, andSince atomistic-scale interactions, such as hydrogen bonds and hydrophobic interactions, cannot be expressed precisely in CGMD simulations, the accurate affinity of the interfaces is not guaranteed.Based on these assumptions, we devised a method to collect a series of structural models that include possible stable states. This is composed of two steps. In step 1, CGMD simulations changing a possible parameter are performed. In step 2, from each of the trajectories, the longest continuous time series that reproduces the SAXS profile is extracted. In summary, we clip a part of a CGMD trajectory that matches a SAXS profile and approximates the actual behavior of the biomolecule as a repetition of the clipped time series. We designate this method \u201cSAS-CLIP\u201d. Although only a single region is clipped from each trajectory, we can expect that possible structural ensembles can be enumerated by applying the SAS-CLIP to multiple trajectories. This point is studied in the \u201cTo compose a series of structural models that reproduces a SAXS profile, we made the following two assumptions about CGMD:35. Before CGMD simulations, it was necessary to clarify the structural stability of three folded regions, from Ser25 to Pro134 (system a), that from Ala132 to Lys366 (system b-b\u2032), and from Tyr364 to Glu493 (system a\u2032). For this purpose, single atomistic simulations for the three systems were first performed.All simulations were performed using GROMACS 2020.420. The Lennard\u2013Jones potential between i-th and j-th particles is described as:CGMD simulations were performed using the Martini 3 open-beta version. In the CGMD simulations, the Lennard\u2013Jones potential between water and ER-60 was scaled, as in previous reportsij as a parameter. When i-th and j-th bead pair is water-protein bead pair, the \u03b5ij is treated as \u03bbWP \u03b5ij,default. Here, the \u03b5ij,default is the default value in the Martini 3 open-beta version, and \u03bbWP is the scaling factor for water-protein interactions. The \u03c3ijs are constants depending on bead type, and rij is distance between i-th and j-th particles. First, we performed three 5000-ns production runs with \u03bbWP values of 1.0, 1.01, 1.02, 1.03, 1.04, 1.05, and 1.06. According to the results  and Isim,j (qi) are the scattering intensities of experimental SAXS profile and calculated scattering intensity of j th model, respectively. The theoretical profiles are normalized by Isim,j(0). c and offs are adjustment parameters. The latter parameter explains possible mismatch between buffer solution and sample solution in the experimental SAXS profile. The parameters are determined by the condition: The \u03c7The distance distribution function p (r) was calculated using the reverse-mapped atomistic model. For the calculation, all electrons were considered to be in the center of an atom, and hydrogen atoms were ignored.t was calculated by multiplying the number of snapshots in the time series by 2\u00a0ns/frame.Since snapshots were acquired every 2\u00a0ns for analysis, the duration time of the time series L38, where ER-60 consists of three domains: from Ser26 to Lys130 (a domain), from Phe160 to Asp355 (b-b\u2032 domains), and from Pro377 to Arg482 (a\u2032 domain). In previous reports, ER-60 was treated as four domain protein4, where the b-b\u2032 domain was further divided into b and b\u2032 domains. The \u03b8a-b-b\u2032, \u03b8b-b\u2032-a\u2032, and \u03c6a-b-b\u2032-a\u2032 are angles formed by centers of mass (COMs) of the three domains or dihedral angle formed by COMs of the four domains  and \u03c6b-b\u2032-a\u2032-CGHC(a\u2032) are angles formed by COMs of the three domains and the COM of the CGHC motif of either the a or a\u2032 domain. The Da-a\u2032 is distance between COMs of a and a\u2032 domains. The COM of each domain or CGHC motif is defined as the averaged coordinates of backbone beads of the corresponding residues  probability map between a clipped time series with the SAS-CLIP and its original trajectory  was evaluated using the following Kullback\u2013Leibler divergence:The difference in the shape of the  is the probability at  of a clipped time series, and Poriginal  is the probability of the original trajectory. KLSAS-CLIP only considers the region where PSAS-CLIP \u2009>\u20090 and their vicinity. In other words, the sum was calculated only for C1 and C2 are defined as follows  | PSAS-CLIP \u2009>\u20090}C2. { | Adjacent to C1}These conditions allow KLSAS-CLIP to be small when ER-60 stays only in a few (or one) of several stable states. Considering that the KLSAS-CLIP ignores outside the original  is normalized to meet the following relationship:39.Graphs and figures were created using gnuplot and inkscape. Images of protein structures were created using PyMOL4 because the SAXS profile calculated from crystal structure did not reproduce the experimental structure. To clarify the origin of this discrepancy, we first examined the dynamics of each folded structure. We performed atomistic MD simulations of three parts of ER-60, including the a, b-b\u2032, and a\u2032 domains. In any of the three simulations, root mean square deviation (RMSD) of the folded region between a simulation snapshot and the crystal structure distributed at approximately 1.5\u00a0\u00c5  of #A-1, #A-2, and #A-3 were 2690, 2208, and 1462\u00a0ns, respectively  probability distribution between a clipped time series and its original trajectory  of this Q contains information on domain conformation. That is, the SAS-CLIP could extract structural series with incorrect domain conformation even with small \u03c72. According to the observations, we improved the criteria: satisfying both \u201c\u03c72\u2009<\u20093.0\u201d and \u201cthe \u22121\u201d.Second, the criterion for reproducing the experimental SAXS profile, which was initially \u03c7\u00c5\u22121 Fig.\u00a0a. This Qt. We focused on the relationship between \u03bbWP and Lt. When \u03bbWP was small, Lt of the clipped time series tended to be small . In the second group, \u03b8a-b-b\u2032 was distributed at\u2009<\u200990\u00b0 . While the structural trends were common, the detailed distributions differed from each other. Additionally, we examined the dihedral angle \u03c6a-b-b\u2032-a\u2032. \u03c6a-b-b\u2032-a\u2032 distributed between\u2009\u2212\u200915\u00b0 and 75\u00b0  and \u03c6b-b\u2032-a\u2032-CGHC(a\u2032) for the six time series. In terms of the domain orientations, one or two preferred ones were observed for each time series. The preferred orientations also differed between the time series. In other words, the SAS-CLIP enumerated the possible distributions of the orientations of the a- and a\u2032-domains.Subsequently, we examined whether the a-b-b\u2032 and \u03b8b-b\u2032-a\u2032 with high appearance probability are shown in Fig.\u00a0483-Leu505) bridged a and a\u2032 domain. These were temporary bridging in the #B-2. Similar bridging was observed in #B-1, #B-3, #B-4, and #B-5, with lifetimes varying in the range 40\u2013160\u00a0ns. The C-terminal loop might contribute to the functional motion of ER-60 via the domain bridging.Finally, the tertiary structures of ER-60 in the clipped ensembles were overviewed. Several structures featuring \u03b8a- and a\u2032-domains were more diverse among the clipped ensembles.In summary, we confirmed that SAS-CLIP can enumerate a variety of ensembles of ER-60. The four-domain architecture could be roughly classified into two classes, whereas the detailed conformational distribution differed among the clipped ensembles. The orientations of the 40, an isosbestic point suggests existence of a variable having a approximate linear relationship with the scattering intensity as follows;Reflecting the structural diversity in each clipped ensemble, their calculated scattering profiles were also diverse Fig.\u00a0. We next0 is a parameter. The difference in I(Q) between molecular structures corresponds to difference in the X. Therefore, the X is a conformational coordinate.Here, X is the variable and X\u22121 and Q\u2009=\u20090.2 \u212b\u22121. In addition, intersections of the curves were concentrated at two regions around Q\u2009=\u20090.12 \u212b\u22121  distribution, p(r) showed sharp distribution between 50 and 60 \u212b  plot. We verified this linear relationship for the ensembles of ER-60 obtained with SAS-CLIP. In Fig.\u00a00 \u212b Fig.\u00a0. The two0 \u212b Fig.\u00a0. Based oa and a\u2032 domain (Da-a\u2032) approximately linearly correlated with I(Q) , the relationship was common to the six ensembles  Fig.\u00a0. Here, ta and a\u2032 domains.In summary, our result supports that a single molecular motion can explain diversity of I(Q)s in a structural ensemble when an isosbestic point is found in Q-I(Q) plot. In ER-60, that was open-close motion of the SAS-CLIP does not provide a unique solution of the structural ensemble of a biomolecule. The structural ensemble obtained by this method differ from each other, but they all reproduce the same SAXS profile. This also means that any combination of these time series also reproduce the experimental SAXS profile. Additionally, the structural distribution of each clipped time series approximates that of a long-term MD simulation. Therefore, each time series obtained by SAS-CLIP can be an element of motion of a biomolecule, and any combination of these are candidates for the real structural ensemble.X as a quantity obtained in an experiment other than SAXS, X will be expressed as follows:XSAS-CLIP,i is the quantity for i-th structure series of the SAS-CLIP, which is averaged over all structures in the i-th series. ci is a weight factor. A reasonable structural ensemble that is consistent with any of SAXS, CGMD, and another experiment can be obtained by simply determining the cis. We can assume a variety of data are the quantity X. In fact, many experimental data represent the average quantity over all molecules in solution. In addition, many kinds of experimental data can be calculated from a given atomistic structures. For example, the profile of small-angle neutron scattering (SANS)44, chemical shift for nuclear magnetic resonance (NMR)46, and efficiency of fluorescence resonance energy transfer (FRET)47 can be calculated from tertiary structures. The proposed method has at least two advantages. First, the method is advantageous for constructing realistic ensembles of highly flexible biomolecules; Combination of clipped ensembles with SAS-CLIP results in an ensemble with a very large number of structures. Second, resultant ensembles are consistent with a force field of MD simulation regardless of ci values. The linear combination approach can also avoid the possible effect of artificial free energy minimum derived from an incorrect simulation force field, which is often a problem in the entropy maximization approach. Sufficient ensembles should be clipped to perform such an analysis.Here, we propose a method to identify a structural ensemble of a biomolecule using clipped time series and another experimental data. With SAS-CLIP can be applied to atomistic MD simulations. It is easier for the atomistic simulations to compare a simulation step with real time. When the SAS-CLIP is applied to atomistic simulations, extracted time series will be useful to analyze experimental data including temporal information, such as neutron spin echo.t is large, KLSAS-CLIP is sufficiently small (Table When Lll Table . If we rIn practice, there are three major advantages of SAS-CLIP. First, time series can be extracted from relatively short MD simulations with low computational cost. We can obtain many time series at the same time when multiple simulations are performed in parallel. Second, obtained structural sets reflect a force field of MD simulations, and thus they are candidates of \u201celement of motions\u201d. Third, this method makes it easy to obtain a structural ensemble which matches SAXS, MD, and another experiment with simple linear model. This method will provide a new way to study biomolecules by integrating various type of experiments.Supplementary Information."}
+{"text": "Dear Editor,We would like to address the manuscript entitled \u201cTranscanal endoscopic myringoplasty: A case series in a university center\u201d by Garcia et al.The authors write, in the Materials and Methods: \u201cAll patients older than 12\u00a0years with a diagnosis of non-suppurative, non-cholesteatomatous COM sequela, or with traumatic perforations without spontaneous resolution for more than three months, were included in the study. The diagnosis was based on anamnesis, physical examination, audiometry, and impedance audiometry\u201d.n\u00a0=\u00a019) of patients three months after intervention.\u201dThe authors write, in the Materials and Methods: \u201cThe technique and the surgical instruments used were the same as in routine surgeries with microscope, except for the non-use of the microscope andotologic speculum, and the use of the Storz rigid endo-scopes, 4\u00a0mm diameter and 18\u00a0cm long, at 0\u00b0 angulation \u201d.In brief, the transcanal endoscopic approach is excellent for performing cartilage myringoplasty, reducing both the surgical time and complications. However, both the surgical indications, and careful consideration of the outer diameter of the endoscope, are very important, and long-term follow-up is required.The author declares no conflicts of interest."}
+{"text": "Since the beginning of the coronavirus disease 2019 pandemic, there has been an explosion of sequencing of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus, making it the most widely sequenced virus in the history. Several databases and tools have been created to keep track of genome sequences and variants of the virus; most notably, the GISAID platform hosts millions of complete genome sequences, and it is continuously expanding every day. A challenging task is the development of fast and accurate tools that are able to distinguish between the different SARS-CoV-2 variants and assign them to a clade.k-mers that match SARS-CoV-2 marker variants.In this article, we leverage the frequency chaos game representation (FCGR) and convolutional neural networks (CNNs) to develop an original method that learns how to classify genome sequences that we implement into CouGaR-g, a tool for the clade assignment problem on SARS-CoV-2 sequences. On a testing subset of the GISAID, CouGaR-g achieved an k-mers that capture relevant biological information that distinguishes the clades, known as marker variants.By combining FCGR and CNNs, we develop a method that achieves a better accuracy than Covidex (which is based on random forest) for clade assignment of SARS-CoV-2 genome sequences, also thanks to our training on a much larger dataset, with comparable running times. Our method implemented in CouGaR-g is able to detect https://huggingface.co/spaces/BIASLab/sars-cov-2-classification-fcgr. CouGaR-g is also available at https://github.com/AlgoLab/CouGaR-g under the GPL.The trained models can be tested online providing a FASTA file (with 1 or multiple sequences) at  All these data are stored in publicly available archives, such as the European Nucleotide Archive (ENA) and GISAID\u00a0 is a square matrix where each entry i, jc is the number of elements that belong to the true class i and were classified in the class j, and the sum of the entries in C is exactly S.Given a classification problem on accuracy of the model is defined as the proportion of the corrected classified samples over the total number of samples; this value ranges between 0 and 1, where 0 means that all samples were erroneously classified, while a value of 1 means a perfect classification. It can be defined in terms of the entries of the confusion matrix as follows:The Matthews correlation coefficient (MCC), proposed in , where 1 is perfect classification, \u22121 is the opposite, and 0 means that the confusion matrix is all zeros but for one single column, or when all entries are equal, The posed in  as a binposed in , and it posed in  for detaocument} .In order to assess the quality of the class separability given by the CNN, we evaluate the embeddings of the last layer (the one used to perform the classification) in the network with 3 clustering evaluation measures. These embeddings are the output from the final layer of the network for each FCGR.Silhouette coefficient\u00a0[v belonging to a cluster A, the silhouette coefficient s(v) of v compares the mean intracluster distance in A (a) with the mean nearest-cluster distance for v (b), that is, the closest cluster to v different from A.fficient\u00a0. Given as(v) ranges between \u22121 (wrongly assigned) and 1 (perfect separability). For a cluster A, the mean silhouette coefficient of A is computed as the average of s(v) over all embeddings v \u2208 A.The value of Calinski\u2013Harabasz score\u00a0[E of size En that has been clustered into k clusters, the Calinski\u2013Harabasz score s, also known as the variance ratio criterion, is defined as the ratio of the between-clusters dispersion and the intercluster dispersion for all clusters (the dispersion of a group of n points is measured by the sum of the squared distances of the points from their centroid).tr(kB) is the trace of the between-cluster dispersion matrix and tr(kW) is the trace  of the within-cluster dispersion matrix, defined as follows:qC is the set of embeddings in the cluster qq, c is the centroid of the cluster q, and Ec is the centroid of E and qn = |qC|.sz score\u00a0. Given as means that the clusters are dense and well separated.The higher the score GDV\u00a0[GDV\u00a0N D-dimensional embeddings {x1, \u2026, Nx}, with nx =  and a set of L classes {C1, \u2026, LC}, where each nx is assigned to one of the L distinct classes. Consider their z-scored points , with is = , where d. Using the rescaled data points ns = , the GDV \u0394 is calculated from the mean intraclass and interclass distances as follows:Given a set of lC is defined aslC and mC is defined as follows:kN correspond to the number of points in class k, and ith point of class k. The quantity d is the distance between a and b; for our case, we considered the Euclidean distance. The value \u0394 range is between \u22121 (perfect separability) and 0 (wrongly assigned).where the mean intraclass for each class k-mers for the classification of each clade.After the model is trained, we can perform feature importance methods  to analyze the impact of each element of the FCGR in our prediction. We selected saliency maps\u00a0 and SHAPk-mers for the classification of each clade in the trained models.Using these methods, we aim to analyze the most relevant Project name: Classification of SARS-CoV-2 genome sequence with CGR and CNNRRID:SCR_022952)Project home page: CouGaR-g (Operating system(s): e.g.,\u00a0Platform independentProgramming language: Python 3.10.5Other requirements: Python 3.10+, tensorflow 2.10.0, scikit-learn 1.1.2, tqdm 4.63.0, pandas 1.5.0, biopython 1.79, Pillow 9.0.1, matplotlib 3.5.1, shap 0.41.0, opencv-python 4.6.0.66License: GNU GPLThe list of FASTA sequences and metadata can be downloaded from\u00a0 after crA web app version of CouGaR-g with all the trained models is available online at\u00a0.GigaScience GigaDB database\u00a0[All supporting data and materials are available in the database\u00a0.CGR: chaos game representation; CNN: convolutional neural network; ENA: European Nucleotide Archive; FCGR: frequency matrix of chaos game representation; GDV: generalized discrimination value; SVM: support vector machine.The authors declare that they have no competing interests.This project has received funding from the European Union\u2019s Horizon 2020 Innovative Training Networks program under the Marie Sk\u0142odowska-Curie grant agreement No. 956229.This project has received funding from the European Union\u2019s Horizon 2020 Research and Innovation Staff Exchange program under the Marie Sk\u0142odowska-Curie grant agreement No. 872539.J.A.C. and S.A. wrote the code, prepared the data, and performed the experiments. J.A.C., S.A., S.C., P.B., and G.D.V. devised the methods and analyzed the results. J.A.C., S.C., and G.D.V. designed the experiments. All authors contributed to finalizing of the manuscript.giac119_GIGA-D-22-00106_Original_SubmissionClick here for additional data file.giac119_GIGA-D-22-00106_Revision_1Click here for additional data file.giac119_GIGA-D-22-00106_Revision_2Click here for additional data file.giac119_Response_to_Reviewer_Comments_Original_SubmissionClick here for additional data file.giac119_Response_to_Reviewer_Comments_Revision_1Click here for additional data file.giac119_Reviewer_1_Report_Original_SubmissionDominik Heider -- 6/1/2022 ReviewedClick here for additional data file.giac119_Reviewer_1_Report_Revision_1Dominik Heider -- 10/26/2022 ReviewedClick here for additional data file.giac119_Reviewer_2_Report_Original_SubmissionRiccardo Rizzo -- 7/19/2022 ReviewedClick here for additional data file.giac119_Reviewer_2_Report_Revision_1Riccardo Rizzo -- 10/25/2022 ReviewedClick here for additional data file."}
+{"text": "Most environments favor defection over cooperation due to natural selection. Nonetheless, the emergence of cooperation is omnipresent in many biological, social, and economic systems, quite contrary to the well-celebrated Darwinian theory of evolution. Much research has been devoted to better understanding how and why cooperation persists among self-interested individuals despite their competition for limited resources. Here we go beyond a single social dilemma since individuals usually encounter various social challenges. In particular, we propose and study a mathematical model incorporating both the prisoner\u2019s dilemma and the snowdrift game. We further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. The nonlinear evolutionary dynamics that results from these upgrades offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. With the help of analytical and numerical calculations, our theoretical model sheds light on the mechanisms that maintain biodiversity, and it helps to explain the evolution of social order in human societies. Numerous interdisciplinary researchers have long sought a way to understand how the tremendous biodiversity among species persists in nature despite the significant differences between them in terms of competitive capability. Darwinian evolution  always cWe construct a mathematical model on evolutionary multigames \u201327 by adWhile defection is the ultimate profitable strategy in the classical PD game, irrespective of the co-player\u2019s decision, a player\u2019s best strategy in the SD game depends on the co-player\u2019s decision. Thus, we select two different games with two contrasting outcomes. The stable coexistence of both cooperators and defectors is the expected consequence in the SD game, resulting in the persistence of cooperative behavior. In comparison, cheaters are always encouraged to exploit the cooperative individuals in the set-up of the PD game. In our constructed model, unrelated individuals have their probabilistic selection to choose which game they want to play. We also consider the mutation \u201342 as anApart from that, to reveal the interplay between ecological and evolutionary dynamics, we inspect the influence of free space in our mathematical model. In the context of complex systems, free space \u201349 proveThe concurrence of ecological changes and rational players\u2019 evolution, depicted in the present article, prevails through the same time scale, rather than the typical assumption that ecological processes are much faster than evolutionary processes . Our theC) and (ii) defection (D). Even they can play any of the two possible games (a) PD game and (b) SD game. They can adopt the PD game with probability p, and alternatively, they interact with other individuals by playing the SD game with the complimentary probability (1 \u2212 p). Both of these two-person games can be given by the following two payoff matrices A and B respectively, whereTo start with, we consider a simplistic assumption that each individual has two distinct choices, viz. (i) cooperation , and SPD = 0. Similarly, we choose TSD = \u03b2 > 1, RSD = 1, SSD = 0, and PSD = \u2212\u03b7 \u2208 , maintaining the relative ordering TSD > RSD > SSD > PSD for the standard SD game  is the probability of playing the PD game. Moreover, we consider free space F as an ecological variable, which contributes altruistically by helping others. Nevertheless, free space does not get any benefits by giving them reproductive opportunities. We incorporate this charitable role of free space by extending the 2 \u00d7 2 payoff matrix E to the 3 \u00d7 3 payoff matrix G as followsHere, G clearly reveals that the free space never earns any payoff for their selfless charitable act; however, it contributes a positive payoff \u03c31 and \u03c32 to the cooperators and the defectors, respectively. Since most of the game parameters  lies within the closed interval , we assume, for the sake of feasible comparison, \u03c31 and \u03c32 both lies within the interval . When \u03c31 and \u03c32 are equal to zero, free space will not contribute anything to anyone. However, whenever \u03c31 and \u03c32 attain positive values, individuals gain an additional payoff from free space.The matrix tInspired by the Malthusianism, we consider the following set of differential equations governing the changes in frequencies of cooperators and defectors as a function of time x and y are the normalized densities of cooperators and defectors, respectively. Let z be the available free space. Thus, we haveHere, x and y alone, one can easily capture the dynamics of the two strategies. We assume the birth rates of each individual depends crucially on the available free space as well as on their respective average fitness. Thus, we considerfC and fD are average fitness of the cooperators and the defectors, respectively. The average payoff of cooperators and defectors can be determined using the payoff matrix G of the multigames, and the relation Relation Note that the average fitness of free space is\u03be \u2208  must lie within the domain  \u00d7  maintaining the inequality 0 \u2264 x0 + y0 \u2264 1, as they represent the frequencies of the two strategies. To determine the positivity of the proposed model c1 and c2 are the integrating constants depending on the initial densities x0 and y0. This proves that both x and y are non-negative. Now, to calculate the upper bound of x + y, we proceed as follows. The dynamical Before investigating the model x + y \u2265 0 and the mortality rate \u03be is always positive, we have \u03be(x + y)\u22650. Thus, Since as per our previous analysis, c3 is the initial density dependent constant. Hence, we find thatx + y eventually remains bounded within the region . This boundedness within the closed interval  allows us to relate the possible emerging dynamics of the system x + y) is precisely one, the available free space is zero, as z = 1 \u2212 (x + y). i.e., there is no reproductive opportunity accessible to any individual in that situation with z = 0. When (x + y) = 0, then individually x = 0 and y = 0. Hence, all individuals die, and z is equal to one. Thus despite the presence of ample free space, all the individuals are extinct under that circumstances.Integrating both sides, we get\u03be = 0.38, \u03b2 = 1.1, \u03b7 = 0.85, p = 0.30, \u03c31 = 0.36, \u03c32 = 0.25 and \u03bc = 0 in x0, y0) within the interval  \u00d7  maintaining the inequality (x0 + y0)\u2208. We find that the dynamics switching between two stationary points, viz. E0 =  and E1 = . We analytically calculate the stationary points of the system \u03bc = 0. We trace out four different stationary points,Next, we point out the multistable dynamics of our model E0 =  reveals all individuals die. This point is locally stable whenE1 =  exhibits a society free from any defectors. Here,x* \u2208  represents that we have only left with defectors. Here, y* \u2208  indicates the coexistence equilibrium offering the survival of cooperation and defection simultaneously. Here, x** satisfies the equation, x** and y** both should lie within the interval . The local stability yields the conditions for the stability of  areE0 and E1. Note that E1 leads to two different values for the selected values of the parameters, out of which  always remains locally stable, and  is unstable. Thus, we see the appearance of two different stationary points E0 (shown by red points) and E1 (displayed by violet points) in the basin of attraction portrayed in x0, y0) =  always helps the system E0. The system is never able to give rise to the survival of any cooperators and defectors without the presence of any individual at the beginning. Since the chosen initial point  itself is the stationary state, the system always stabilizes in the  stationary point irrespective of the parameter values. \u03be = 0.15, \u03b2 = 1.06, \u03b7 = 0.85, p = 0.69, \u03c31 = 0.75, \u03c32 = 0.25, and \u03bc = 0. Similarly, we find the system \u03bc = 0) converges to E0 for the single initial condition  = . It is anticipated that the choice of x0 = 0 always leads to the cooperator-free steady state. The initial absence of cooperators in the mutation-free model will not entertain any exposure for the cooperators in the long run. The line of initial conditions x0 = 0 and y0 \u2260 0 produces the stationary state E2 (sea blue points in E1 (violet points) and E3 (yellow points) depending on the suitable choice of initial conditions  to   as follows,c4 is the integrating constant.Clearly, the chosen parameters satisfy the local stability criteria of both stationary points ions See . Thus, f\u03c31 = \u03c32 = \u03bc = 0 in the absence of cooperators  as followsc5 is the integrating constant.Similarly, the system \u03b4x0 = \u03b4y0 = 0.01 and maintaining 0 \u2264 x0 + y0 \u2264 1. To solve our proposed system 5 iterations with fixed integration step length \u03b4t = 0.01. The final point  is stored to decide the asymptotic dynamics of the system. Other initial conditions with y0 = 0 stabilize the dynamics in the defector-free state E1 (violet points). We also track a fair portion of the basin in \u03bc = 0 converges to either E2 (sea blue points) or E3 (yellow points) depending on the choice of initial conditions.\u03bc in \u03be = 0.30, p = 0.30, \u03b2 = 1.1, \u03b7 = 0.85, \u03bc = 0.02, \u03c31 = 0.30, and \u03c32 = 0.20. This non-zero \u03bc leads to the disappearance of two stationary points, (i) the defector-free steady state E1, and (ii) the cooperator-free steady state E2. The symmetric mutation from one species to another species always gives them two feasible opportunities. Either both strategies survive or all the individuals perish for \u03bc \u2260 0. We also mathematically derive two possible stationary points as follows,Although we choose the mutation-free model for the E0 = , which is stable under the conditions,The extinction equilibrium E3 =  becomes stable, ifThe interior equilibrium The compelling evidence of bistability under the same choice of parameters\u2019 values is recognized in p, \u03b2, \u03b7, and \u03be on the system \u03bc = 0 in \u03c31 = \u03c32 = 0 in subfigures (a), (c) and (e). Also, we set \u03c31 \u2260 0 and \u03c32 \u2260 0 for the subfigures (b), (d) and (f). In the absence of mutation (\u03bc = 0) and free space induced benefits (\u03c31 = \u03c32 = 0), the defector-free E1 exists for We examine the impact of the parameters \u03b2 > 1 and \u03be > 0, \u03bb2 is always positive. Consequently, E1 is always unstable. This result is physically meaningful, as both the chosen games (PD and SD) do not encourage a defection-free society without any supporting mechanism. However, we find three different steady states in Since E0 =  (red points in subfigures (a), (c) and (e) of The extinction equilibrium E2 =  is the cooperator-free stationary point (sea blue points in subfigures (a), (c) and (e) of \u03be\u03b7(2p \u2212 1)\u2264\u03b72(2p \u2212 1)2, and becomes stable if \u03be > \u03b7(2p \u2212 1)(2y** \u2212 3y**2).E3 =  allows the coexistence of both cooperators and defectors (yellow points in subfigures (a), (c) and (e) of p, players are prone to play the PD game. Hence, we can not anticipate the survival of cooperators for large p. Thus, for large p, either the extinction equilibrium E0 or the cooperator-free stationary point E2 stabilizes in E3. Even, p \u2212 \u03be parameter space, where the defector-free stationary point E1 stabilizes. The comparative study between the left and right column of With increasing \u03b2, the defectors are getting extra aid, and thus, we get the stabilization of the extinction equilibrium E0 (red zone) in p in both subfigures (a-b) permits only the existence of defectors, as people are playing mostly the PD game in such circumstances. Defectors are getting a favorable atmosphere in the PD game for our chosen PD game parameters\u2019 values. A similar sort of stabilization of cooperator-free steady state (sea blue area) is observed in subfigures (c-d) for larger values of p. However, lower values of p provide the opportunity for playing the SD game. Hence, coexistence equilibrium (yellow region) stabilizes in p. Nevertheless, the inclusion of free space induced benefits helps to broaden the region of coexistence in the p \u2212 \u03b7 parameter plane, as shown in \u03c31 and \u03c32 entertain the stabilization of a defector-free steady state (violet region). Hence, we can trace a fair portion of violet points in the p \u2212 \u03be parameter space of the subfigure (f). However, too large a mortality rate reduces the opportunity of survivability of any individual, resulting in the stabilization of the extinction equilibrium E0. We focus on the effect of mortality rate \u03be more elaborately in With increasing \u03be constantly enlarge the chances of extinction. Thus, we observe a fair portion of the red region in \u03c31 and \u03c32 in the right column of this figure. These free space induced benefits encourage maintaining a defector-free society, as shown in \u03c31 = 0.75 > 0.25 = \u03c32 for p = 0.3 in \u03be provide an opportunity to coexist for all strategies, which is observed in x0, y0) = . We plot the stability curve of all stationary points in Figs As expected, higher values of E2,(i) The brown dotted line for the cooperator-free steady state E1,(ii) the blue dashed line for the defector-free steady state E3, and(iii) the solid blue line for the interior equilibrium E0.(iv) the solid white line for the extinction equilibrium \u03c32 at 0.25 and examine the role of \u03c31. Since \u03c31 represents the free space induced benefits towards the cooperators, thus enhancement of its (\u03c31) value will help in promoting cooperation in the society. \u03b2\u2019s value challenges the prevalence of cooperation. Thus, for a small \u03c31, we find a defector dominated society  stabilizes. For the intermediate choice of \u03c31, the stationary point E3 (yellow) yields the stable coexistence of both strategies. However, cooperators strive to keep in existence for the lower values of \u03c31, and we find the sea blue region of cooperator-free steady state. The parameter p indicates the probability of playing the PD game. Thus, p \u2192 1\u2212 always gives defectors a more favorable environment to survive. That\u2019s why we spot a sea blue portion in p and \u03c31. When p is small, people are prone to play the SD game; and thus, we get the coexistence of both strategies  in \u03be always results in the extinction of both cooperators and defectors, and we locate a huge red region in the \u03c31 \u2212 \u03be parameter plane of \u03c31 always promotes the cooperation strategy, and we obtain a violet zone of defector-free stationary point and a yellow region of interior equilibrium E3 in In \u03c32 \u2212 \u03b2 parameter space produces the coexistence of both cooperators and defectors depending on other parameters\u2019 values. Despite the increment of \u03c32 and \u03b2, the cooperators are able to survive along with the defectors due to our choice of other parameters\u2019 values. The \u03c32 \u2212 \u03b7 parameter space portrays that smaller values of \u03c32 can not provide any benefit to the defectors, and stabilize the defector-free stationary point E1 (violet region) irrespective of \u03b7\u2019s value. However, if \u03c32 increases, it will yield a window of opportunity for the defectors to thrive. We observe a wide coexistence region (yellow region) and a small area of cooperator-free stationary point (sea blue region)in \u03c32 indicates the free-space induced benefits towards the defectors. So, it is expected that larger values of \u03c32 always enhance the chances of defectors\u2019 survivability. Thus, we notice a cooperator-free region (sea blue zone) in both p enhance the chances of playing the PD game, where defectors get a favorable environment to survive. Thus, the cooperator-free sea blue region is found in \u03c32 \u2212 p parameter space. However, we trace a healthy portion of coexistence (yellow) too in \u03bc \u2208  in \u03c31 increases, the cooperators are getting a better environment for survival. We find a portion of stable coexistence equilibrium in each two-dimensional parameter space for large \u03c31 in x0, y0) = . There are a few places where the stability analysis fails to predict the stabilization of the extinction stationary point . This is mainly due to the multistable behavior of the proposed model Now we investigate the influence of bidirectional mutation on the long-term behavior of the nonlinear differential \u03b2, \u03b7, and p always provide the defectors a favorable environment to dominate the cooperators. However, beyond a critical value of \u03c31, both the cooperators and defectors can coexist, as shown in \u03be always hinder the evolution of cooperators as well as of defectors. However, an intermediate choice of \u03c31 \u2212 \u03be favors the successful evolution of both strategies, as portrayed through \u03c32, the defectors are not getting enough advantages to survive, and thus the extinction equilibrium  stabilizes in the red region of all subfigures of \u03c32 benefits the defectors; hence the defectors can survive beyond a certain threshold of \u03c32. The employed 50% mutation rate helps to flow a certain fraction of defectors into cooperators, and we have a moderate portion of coexistence state (yellow region) in 5 times with fixed integrating step length \u03b4t = 0.01. The last point is gathered to finalize the asymptotic state. All the codes to generate these figures are publicly available at Ref. . In fact, the cooperators\u2019 density x is slightly better than that of y for the higher values of \u03c31 in \u03c32 in our proposed model \u03c32, the defectors will be benefited from free space, and hence, y (blue line) dominates x (red line) for larger values of \u03c32. But since \u03c31 is taken sufficiently large in this \u03c32 where x > y. Since the mutation rate Our mutation-induced model provides widespread coexistence of both strategies under suitable choices of parameters\u2019 values. Such stable persistence of ecological communities strengthens the theory of concurrency. Our thorough analysis with several numerical simulations enhances our understanding of the mechanisms that drive the survival of cooperative behavior in the multigames consisting of both the Prisoner\u2019s Dilemma and the Snowdrift games. The inclusion of altruistic behavior of free space along with the mutation in our proposed evolutionary model seems to be a natural course of action as observed in many realistic settings. Our findings clearly demonstrate that there exists an optimal probability of playing each game so that people are more likely to cooperate in such circumstances. Throughout the study, we have pointed out the positive impact of diverse factors (parameters) on significant improvement of cooperation. We have shown that the selfless contribution of free space promotes the coexistence of all strategies efficiently, even in the absence of mutation.In summary, our research indicates the proposed model Lastly, we discuss challenges related to our work that merits further investigation. Even though it is almost impossible to incorporate all complex, realistic relationships among social creatures using minimal modeling, it is nevertheless absolutely essential to investigate such models using elementary mathematical principles. In fact, the literature already provides a number of excellent models that offer a stimulating starting point for exploring many practical situations. Chen et al.  proposedOne should observe that our approach works absolutely fine with other social dilemmas. For any two two-person games of the form ony game , 76 . You should upload this letter as a separate file labeled 'Response to Reviewers'.A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.An unmarked version of your revised paper without tracked changes. 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They both agree that the paper is well written and highly appropriate for PloS One audience, and recommend acceptance with very minor amendments. Please carefully take them into account when preparing the revised version.[Note: HTML markup is below. Please do not edit.]Reviewers' comments:Reviewer's Responses to Questions <font color=\"black\"> Comments to the Author1. Is the manuscript technically sound, and do the data support the conclusions? </font> The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 2. Has the statistical analysis been performed appropriately and rigorously?  </font> Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 3. Have the authors made all data underlying the findings in their manuscript fully available?PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data\u2014e.g. participant privacy or use of data from a third party\u2014those must be specified. </font> The Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 4. Is the manuscript presented in an intelligible fashion and written in standard English? </font> PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.Reviewer #1:\u00a0YesReviewer #2:\u00a0Yes********** <font color=\"black\"> 5. Review Comments to the Author </font> Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. Reviewer #1:\u00a0In their paper titled \"Eco-evolutionary dynamics of multigames with mutations\" the authors study an interesting problem, namely what are the options for multigames to yield favorable conditions for cooperation subject to mutations and selfless one-sided contribution of altruist free space. Research reveals a broader range of equilibrium outcomes, which often favor cooperation over defection. With the help of analytical and numerical calculations, the theoretical model the authors are proposing and studying sheds light on the mechanisms that maintain biodiversity, and also explain the evolution of social order in human societies.Understanding cooperation in social dilemmas is a long standing problem of universal interest across social and natural sciences, and new results in this research field are always well received. In this way, the current manuscript is well-suited for PLOS ONE, and I am sure it will attract citations and readers when published.I find the manuscript is clear and written with love to detail and care for presentation. The figures are also high quality and should be accessible to the wider audience, as are the results and the research in general. For these reasons I recommend publication in PLOS ONE subject only to minor revision.The following comments can be considered:1. Would the approach also work on other social dilemmas games, such that for example the snowdrift and the harmony game would be considered as multigames? And perhaps even more interestingly, would it work in group interactions. The authors can discuss this in the final section if they find of interest.2. Can the caption to Table 1 be made more comprehensive to say what is the meaning of physical significance and domains.3. More relevant works, such as  and [Physica A 591 (2022) 126804], can be cited to make the introduction more comprehensive.4. The writing is occasional burdened with somewhat awkward grammar and could be polished further before resubmission.5. Finally, perhaps the authors can make source available to allow others to reproduce the results.Reviewer #2:\u00a0The manuscript is generally well written and easy to understand. The authors have proposed a math model that incorporates both prisoner\u2019s dilemma and the snowdrift game. In my opinion, this is quite interesting to see the combination of these two theories. THe authors further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. Their conclusion is that all of these offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. Their conclusion is well supported by their analytical derviations and numerical calculations. I have some minor queries:1) How is the steady state in fig 1 being determined?2) the manuscript is well written, and it will benefit the readers more if there is a section on the limitations and how these limitations can be overcome.3) I am happy to see that the code has been archived and made available. Can the readers include a section on future work to make the study more comprehensive?The manuscript can be readily accepted after the above minor queries are addressed.********** <font color=\"black\"> 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.If you choose \u201cno\u201d, your identity will remain anonymous but your review may still be made public.Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. </font> Reviewer #1:\u00a0NoReviewer #2:\u00a0No**********https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at\u00a0figures@plos.org. Please note that Supporting Information files do not need this step. </div> While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool,\u00a0 22 Jul 2022------------------------------------------------------------------------------------Reply to First Reviewer\u2019s commentsPONE-D-22-17613------------------------------------------------------------------------------------.Reviewer #1 (Remarks to the Author): In their paper titled \"Eco-evolutionary dynamics of multigames with mutations\" the authors study an interesting problem, namely what are the options for multigames to yield favorable conditions for cooperation subject to mutations and selfless one-sided contribution of altruist free space. Research reveals a broader range of equilibrium outcomes, which often favor cooperation over defection. With the help of analytical and numerical calculations, the theoretical model the authors are proposing and studying sheds light on the mechanisms that maintain biodiversity, and also explain the evolution of social order in human societies.Understanding cooperation in social dilemmas is a long standing problem of universal interest across social and natural sciences, and new results in this research field are always well received. In this way, the current manuscript is well-suited for PLOS ONE, and I am sure it will attract citations and readers when published.I find the manuscript is clear and written with love to detail and care for presentation. The figures are also high quality and should be accessible to the wider audience, as are the results and the research in general. For these reasons I recommend publication in PLOS ONE subject only to minor revision.Response: We greatly acknowledge the referees for appreciating our work and gratefully acknowledge their insightful suggestions that helped considerably improve the manuscript. As far as the clarifications part is concerned, we have gone through every effort to improve the same in the revised version of the manuscript.Q.1. Would the approach also work on other social dilemmas games, such that for example the snowdrift and the harmony game would be considered as multigames? And perhaps even more interestingly, would it work in group interactions. The authors can discuss this in the final section if they find of interest.Response: We acknowledge the referee not only for appreciating our work but also for careful reading and thoughtful comments, which help to improve the manuscript in a significant way. The model formed in the manuscript with the help of two different two-person games can be formulated using any two-person games, not necessarily with the prisoner's dilemma and the snowdrift game only. The solution's existence, uniqueness, and boundedness can be similarly guaranteed using the calculations shown in the manuscript for any two different two-person games. We have checked it with two other two-person games, and if the reviewer advises, we will include the generic calculations in the manuscript. However, one should note that the stationary points alter in those cases as different games create a mathematical model with other functions. We strongly believe the role of mutation and the generous free space remain almost similar even for multigame with other two-person games. Incorporating group interaction leads to a potentially exciting problem that is out of scope for the present manuscript. We discuss how one can include group interaction by considering interdependent networks and games like the public goods game in the final section of the revised manuscript, as suggested by the anonymous reviewer.Q.2. Can the caption to Table 1 be made more comprehensive to say what is the meaning of physical significance and domains.Response: We have enhanced the caption of table 1 by briefly describing the meaning of physical significances and domains.Q.3 More relevant works, such as  and [PhysicaA 591 (2022) 126804], can be cited to make the introduction more comprehensive.Response: The references suggested by the referee concerning the evolution of cooperation in the presence of eco-evolutionary dynamics are indeed noteworthy in the context of our study. We have cited these articles in the discussion section, where a series of relevant publications are introduced.Q.4. The writing is occasional burdened with somewhat awkward grammar and could be polished further before resubmission.Response: In the revised manuscript, we have tried our best to improve the grammatical errors throughout our work.Q.5. Finally, perhaps the authors can make source available to allow others to reproduce the results.https://github.com/SayantanNagChowdhury/The-evolutionary-dynamics-in-ecological-multi-games-involving-mutations.Response: The data that support the findings of this study are openly available online on GitHubat-----------------------------------------------------------------------------------Reply to Second Reviewer\u2019s comments -PONE-D-22-17613------------------------------------------------------------------------------------Reviewer #2 (Remarks to the Author):The manuscript is generally well written and easy to understand. The authors have proposed a math model that incorporates both prisoner\u2019s dilemma and the snowdrift game. In my opinion, this is quite interesting to see the combination of these two theories. THe authors further extend this model by considering ecological signatures like mutation and selfless one-sided contribution of altruist free space. Their conclusion is that all of these offer a broader range of equilibrium outcomes, and it also often favors cooperation over defection. Their conclusion is well supported by their analytical derviations and numerical calculations. I have some minor queries:Response: We are thankful to the reviewer for appreciating our work and also for valuable suggestions.Q.1 How is the steady state in fig 1 being determined?Response: To determine the steady states of Figure 1, we have iterated the constructed model numerically with 2\u00d7\u301610\u3017^6 iterations and a fixed integrating step length of 0.01. We used the 4th order Runge\u2013Kutta method (RK4) for the numerical simulation. If the values of x and y remain greater than 0.0001, then we store those values as non-zero values. Otherwise, whenever x and y remain below 0.0001, we consider those values zero. Although we prove the values of x and y remain analytically within the closed interval , we still maintain that constraint in the numerical code too and store the values only when they stay bounded within this interval .Q.2. the manuscript is well written, and it will benefit the readers more if there is a section on the limitations and how these limitations can be overcome.Response: We greatly acknowledge the referee for appreciating our work. As per your valuable suggestion, we have added a section discussing the limitations and future perspectives. We also try to emphasize how one can overcome those limitations.Q.3. I am happy to see that the code has been archived and made available. Can the readers include a section on future work to make the study more comprehensive?Response: We acknowledge the referee not only for appreciating our work but also for careful reading and thoughtful comments, which help to improve the manuscript in a significant way.We have added a small section in the revised manuscript emphasizing the future works worth studying and need to be addressed in the future.AttachmentResponse to Reviewers.pdfSubmitted filename: Click here for additional data file. 26 Jul 2022Eco-evolutionary dynamics of multigames with mutationsPONE-D-22-17613R1Dear Dr. Ghosh,We\u2019re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.Within one week, you\u2019ll receive an e-mail detailing the required amendments. When these have been addressed, you\u2019ll receive a formal acceptance letter and your manuscript will be scheduled for publication.http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at onepress@plos.org.If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they\u2019ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact Kind regards,The Anh Han, Ph.D.Academic EditorPLOS ONEAdditional Editor Comments :The authors have addressed all the comments from the reviewers very well, and I am happy to recommend its acceptance in the present form.\u00a0 30 Jul 2022PONE-D-22-17613R1 Eco-evolutionary dynamics of multigames with mutations Dear Dr. Ghosh:I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. onepress@plos.org.If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact plosone@plos.org. If we can help with anything else, please email us at Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staffon behalf ofDr. The Anh Han Academic EditorPLOS ONE"}
+{"text": "Nature Communications 10.1038/s41467-022-30079-z, published online 09 May 2022Correction to: The PDF version of this article contained an error in equation 12. The M matrix in equation 12 was incorrectly formatted as a row vector where they should form a square matrix.This has to be corrected only in the PDF version of the article, the HTML version is Ok.How it appears now:How it should appear:"}
+{"text": "G acts. Applications to the linearisation problem. A parametric Oka principle for sections of a bundle E of homogeneous spaces for a group bundle X with compatible actions of a reductive complex group on E, X. Application to the classification of generalised principal bundles with a group action. Finally, an equivariant version of Gromov\u2019s Oka principle based on a notion of a G-manifold being G-Oka.We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group  This is a survey of recent work, published since 2015, on equivariant Oka theory, mainly from our papers . Oka theOka theory has its roots in the pioneering work of Kiyoshi Oka. The Oka principle first appeared in his 1939 result that a holomorphic line bundle on a Stein manifold is trivial if it is topologically trivial. Oka theory was developed much further in the late 1950s to early 1970s, starting with Grauert\u2019s foundational papers \u201310. OtheG on an affine variety X and proved his famous slice theorem. A consequence is that the quotient variety X is smooth, the map of X to G-fibre bundle over each stratum.A very brief review of the geometric invariant theory relevant here starts with the foundational 1973 paper of Luna . He studThe holomorphic version of the theory, for a reductive complex Lie group acting on a Stein space, was developed by Snow  and HeinMost of the work surveyed here can be summarised in seven main results, Theorems A\u2013G. The following sections provide further details, relevant definitions, brief sketches of proofs, and other related results. In the final section, we list some open problems.G act holomorphically on a Stein manifold X. The categorical quotient G-orbits in X. Let G-finite holomorphic functions .Let a complex reductive group entclass1pt{minimaX and Y be Stein G-manifolds. If X and Y are G-biholomorphic, then X and Y have a common stratified quotient Q and G-biholomorphisms X and Y are locally G-biholomorphic over Q. Now our equivariant Oka problem is to see what kind of continuous or smooth G-isomorphism of X and Y implies that there is a G-biholomorphism.In Sects.\u00a0G-diffeomorphism Q is called strict if it induces a biholomorphism between strongG-homeomorphism is somewhat involved and will be given in Sect. G-homeomorphism restricts to a G-biholomorphism q. A strict G-diffeomorphism is not necessarily a strong G-homeomorphism 18]). It  Schwarz  for \\docchebauch . They shG be a reductive complex Lie group. Let X be a Stein G-manifold and V a G-module with common quotient Q. Suppose that V  is large or that X and V are locally G-biholomorphic over Q. Then X and V are G-biholomorphic.Let Note that this result does more than give a solution to the linearisation problem: it provides a sufficient condition for a Stein manifold to be biholomorphic to affine space.X be a reduced Stein space, G a complex Lie group, and A a complex Lie subgroup of the automorphism group of G. Then given a cocycle on X with values in A, we can produce a holomorphic group bundle X whose fibres are  isomorphic to G. As usual, trivial if it is isomorphic to E be a homogeneous holomorphic X, so E over X such that the action of each fibre of E is transitive. Ramspott proved that  Assume that X, E, and X and action of E. Then we say that X and that E is a holomorphic X. The next main theorem is an equivariant version of Ramspott\u2019s theorem, with the stronger conclusion that the inclusion is a weak homotopy equivalence.If E be a homogeneous holomorphic X,\u00a0 where K is a compact real Lie group whose complexification X,\u00a0 and X. Then the inclusion of the space of E over X into the space of K-equivariant continuous sections is a weak homotopy equivalence.Let K-equivariance and K-equivariance is an appropriate condition on continuous sections; Note that for holomorphic sections, E is a holomorphic principal E). The other special case is the \u201cuncoupled\u201d case. It is a parametric Oka principle for equivariant maps from a Stein G/H, where the G/H can be quite general . NamelyTheorem\u00a0X be a reduced Stein space and Y be a compact complex homogeneous space. Let K be a compact real Lie group whose complexification X and Y. Then the inclusion of the space of X to Y into the space of K-equivariant continuous maps from X to Y is a weak homotopy equivalence.Let For the basic theory of compact complex homogeneous spaces, we refer the reader to , Chap. 3Theorem\u00a0K be a compact Lie group. Suppose that X and on a holomorphic group bundle X.Let K-X is topologically K-isomorphic to a holomorphic principal X.(a) Every topological principal X. Every continuous K-isomorphism K-isomorphism. In fact, the inclusion of the space of holomorphic K-isomorphisms K-isomorphisms is a weak homotopy equivalence.(b) Let X to an Oka manifold Y can be deformed to a holomorphic map. To adapt this result to actions of a reductive group G on X and Y, we need to find the right notion of Y being G-Oka. We define Y to be G-Oka if, for every reductive closed subgroup H of G, the submanifold H is Oka in the usual sense. E is a topological principal G-bundle over Q, then it has a holomorphic structure.If (G3)E and G-bundles which are continuously isomorphic, then they are holomorphically isomorphic.If In fact, more is true. (G4)G-bundles over Q, then there is a homotopy G-bundles with If Returning to our more general case where X and Y are not necessarily principal G-bundles, we want to find some analogue of the sheaf of groups Now suppose that G-fibre bundles over the strata of Q and, moreover, the fibre of each stratum S is not usually a group or even a homogeneous space.Our problem here is more complicated than in Grauert\u2019s case since U be open in Q. Then we have the G-finite functions f of G-module. On a fibre G-finite functions G-submodule G-biholomorphism Q, induces algebraic G-isomorphisms of the fibres G-bundles are G-diffeomorphisms or G-homeomorphisms which behave reasonably on G-finite functions or on fibres.Let For G-diffeomorphism inducing the identity on Q. We say that strict if for all Let The definition is from ; in 20]20] we reX and Y be Stein G-manifolds locally G-biholomorphic over Q. Let G-diffeomorphism. Then there is a continuous deformation of G-diffeomorphisms, to a G-biholomorphism.K-invariaK-invariant strictly plurisubharmonic exhaustion function on X,\u00a0 whose Kempf\u2013Ness set R is a K-equivariant continuous strong deformation retract of X,\u00a0 such that the deformation preserves the closure of each , p.\u00a0341 The following equivariant version of the covering homotopy theorem is used to prove an important fact about the Kempf\u2013Ness set  By (a), we may take P is isomorphic to a constant bundle. Hence, once we identify the bundles K-bundle X,\u00a0 the topological principal K-Let [As a consequence we have the following result.K acts real analytically on a Stein space X by biholomorphisms. Let G be a complex Lie group and X with fibre G,\u00a0 whose structure group A is a Lie subgroup of the Lie automorphism group of G. Let K act continuously on A-bundle maps.[E be a topological K-X (not necessarily homogeneous). The restriction map from the space of continuous K-sections of E over X to the space of continuous K-sections of E over R is a homotopy equivalence.Let R to be a Kempf\u2013Ness set as defined above. Next comes the central notion of an NHC-section.In the following, we take C be a compact Hausdorff space and C, such that N is a strong deformation retract of C. We define a sheaf V of K-equivariant NHC-sections of NHC-section of W, we mean a continuous map for every for every for every The topology on Let th\u00e9or\u00e8me principal [Now we formulate the relevant results from , first trincipal , p.\u00a0105.The topological group U is Runge in If , p.\u00a0324 K-K-bundles in [Next we state Heinzner and Kutzschebauch\u2019s main result on the classification of principal ndles in ).K-X is topologically K-isomorphic to a holomorphic principal X.Every topological principal X. Let c be a continuous K-equivariant section of R. Then there is a homotopy of continuous K-equivariant sections R,\u00a0 such that K-equivariant isomorphism from Let [P be the holomorphic principal E. Take a continuous K-section s of E over X. The preimage in P of its image in E is a topological principal K-Q of P. We have a topological K-isomorphism Q is topologically K-isomorphic to a holomorphic principal K-isomorphism First we prove that the inclusion K-isomorphism K-isomorphism over X. Applying the deformation to Q through topological principal K-P to a holomorphic principal E yields a deformation of s through continuous K-sections of E to a holomorphic section.By Theorem\u00a0B be the closed unit ball in Now let P. We seek a global K-equivariant NHC-section E, maps X if R if Consider the holomorphic group Claim. On a sufficiently small saturated neighbourhood of each point of X, that is, locally over NHC-section exists.The proof of the claim is quite involved. It requires a detailed analysis of the equivariant local structure of the bundles involved. We will not attempt a summary, but refer the reader to .NHC-sections differ by a K-equivariant NHC-section of the holomorphic group P that fix NHC-sections together to produce On the intersection of two such saturated neighbourhoods, two such K-equivariant NHC-sections E obtained by letting R. Thus, we have a deformation B to By Theorem\u00a0X. The problem is that the extension of continuous sections using the strong deformation retraction of X onto R does not give back the holomorphic sections for parameters in At this stage the continuous sections are defined over the Kempf\u2013Ness set only, whereas the holomorphic sections are defined over all of  In fact, it suffices to show that The proof would now be done if we could show that the following commuting square has a continuous lifting. G-Oka manifold. Here G is a reductive complex Lie group. Let K be a maximal compact subgroup of G. It is natural to say that a G-manifold Y has the basic G-Oka property (G-BOP) if every continuous K-map from a Stein G-manifold X to Y can be deformed through such maps to a holomorphic map.We begin by motivating the definition of a Y satisfying G-BOP. First, if the G-action on X is trivial, then a K-map X to the submanifold Consider the following consequences of L be a closed subgroup of K. The complexification of L is a reductive closed subgroup H of G. Let X be a Stein H-manifold and consider the adjunctionY viewed as an H-manifold, G-manifold H-action X and Y. We conclude that if Y satisfies G-BOP, then Y also satisfies H-BOP, so by the above, Second, let Approximation and interpolation can easily be included in the above and we are led to the following definition.G act holomorphically on a manifold Y. We say that Y is G-Oka if the fixed-point manifold H of G.Let a reductive complex Lie group H to be the trivial subgroup, we see that a G-Oka manifold is Oka. On the other hand, the following example shows that an Oka G-manifold need not be G-Oka, even for Taking W of the involution X is smooth, given by the formula f such that W is Oka, then our promised example is f for which we have determined whether W is Oka or not.)[ore, Oka . The fixThe expected basic properties of the equivariant Oka property are easily established straight from the definition or from basic properties of Oka manifolds.G act holomorphically on a complex manifold Y. G acts trivially on Y,\u00a0 then Y is G-Oka if and only if Y is Oka.If Y is G-Oka and H is a reductive closed subgroup of G,\u00a0 then Y is H-Oka with respect to the restriction of the action to H.If If G-Oka, then G-Oka with respect to the diagonal action.If G-retract of a G-Oka manifold is G-Oka.A holomorphic Y is the increasing union of G-Oka G-invariant domains, then Y is G-Oka.If [Here are three ways to construct new equivariantly Oka manifolds from old. The first two are from . The locG be a complex reductive group and let H be a reductive closed subgroup of G. Y is an H-manifold, then G-action is G-Oka if and only if Y is H-Oka.If F. Assume that Y,\u00a0 Z,\u00a0 and F are G-manifolds and G-equivariant. Further assume that Z is Stein and F is G-Oka. Then Y is G-Oka if and only if Z is G-Oka.Let Y is covered by G-Oka G-invariant Zariski-open subsets, then Y is G-Oka. If Let The first main theorem of  is TheorG is finite, the Luna strata in Q, where the subvariety k. Each difference G-maps from a given map Since Step 1. Suppose that we have a homotopy of G-maps, to a holomorphic G-map G-invariant neighbourhood of X.G-module. The holomorphic map extends by Cartan\u2019s extension theorem followed by averaging. Finally, the homotopy extends since Y is an absolute neighbourhood retract in the category of metrisable G-spaces.For Step 2. There is a homotopy of G-maps, to a holomorphic G-map This step may be reduced to an application of Forstneri\u010d\u2019s Oka principle for sections of branched holomorphic maps ([G-Oka property. It is the property ascribed to the G-Oka manifold Y in part (a) of Theorem\u00a0Y in part (b) is called the basic G-Oka property with interpolation (G-BOPI), and the property ascribed to Y in part (c) is called the basic G-Oka property with approximation and jet interpolation (G-BOPAJI). The definition of the basic G-Oka property with approximation (G-BOPA) should be obvious. The following result combines [G-The remarkable fact that Oka manifolds can be defined in many nontrivially equivalent ways points to the concept being natural and important. The same has been proved to some extent in the equivariant setting. Above we defined the basic G,\u00a0 the following properties are equivalent: G-BOPA, G-BOPI, G-BOPAJI, G-G-Oka property.For a complex manifold with an action of a finite group We believe that generalising Theorem\u00a0G be a complex reductive group and K a maximal compact subgroup of G. Let X be a Stein G-manifold and Y be a G-Oka manifold. Assume that X has a single slice type, that is, the quotient map G-fibre bundle. Then every K-equivariant continuous map G-equivariant holomorphic map.Let Y is said to be elliptic\u2014Gromov\u2019s definition [E on Y, such that G acts on Y, then we say that s is a G-spray if the action on Y lifts to an action on E by vector bundle isomorphisms such that both s and the projection Y is G-elliptic if it carries a dominating G-spray.We now turn to the equivariant versions of two fundamental properties in Oka theory. A manifold finition  marked tG-ellipticity, also known as G-Y satisfies G-G-map f from a Stein G-manifold X to Y, there is a holomorphic G-vector bundle E over X and a dominating G-spray f. This means that E over x, and The weaker notion of relative Y is G-Runge if for every Stein G-manifold X and every G-invariant Runge domain X, the closure of the image of the restriction map G-maps G-maps G is the trivial group, the G-Runge property of Y is one of the equivalent formulations of the Oka property. When G is reductive, the property of a domain X being G-invariant and Runge can be described in several equivalent ways [We say that ent ways , Sect. 6G-Oka property hold for both G-ellipticity and the G-Runge property [G-homogeneous space is G-Runge. This is what we know about the relationships between the three properties.Analogues of the basic results about the G be a reductive complex group and Y a G-manifold. Y is G-elliptic, then Y is G-Runge.If Y is G-Runge, then Y is G-Oka.If G is finite and Y is Stein and G-Oka, then Y is G-elliptic.If Let The proof of (a) is somewhat involved: it is an equivariant version of Gromov\u2019s linearisation method, sketched in . The proY be a G-homogeneous space and take the trivial G-vector bundle G acts on its Lie algebra G-spray, so Y is G-elliptic. By Theorem Y is G-Runge.Now let G-biholomorphisms G-diffeomorphisms a weak homotopy equivalence with respect to the appropriate topology? The same question for strong G-homeomorphisms.Does the parametric version of Theorem\u00a0X does not have the infinitesimal lifting property?Is there a counterexample to Theorem\u00a0Does Theorem\u00a0Build approximation and interpolation into Theorem\u00a0Show that the weak homotopy equivalence in Theorem\u00a0G? Does it hold for actions for which all the G-orbits are closed?Does Theorem\u00a0Does the parametric version of Theorem\u00a0G be a reductive group and Y be a G-Oka manifold. Is YG-Runge?Let"}
+{"text": "Communications Medicine 10.1038/s43856-022-00209-1, published online 06 December 2022.Correction to: There was a mistake in Table 5 of this article. The specificity (%) value in the final row of Table 5 (the \u2018Spheroid\u2019 row) read \u2018100\u2019, but should have read \u201867\u2019. There was also a typographical error in the Background section of the Abstract. \u2018Organ-on-a-Chip technology has the potential improve success in drug development pipelines, as it can recapitulate organ-level pathophysiology and clinical responses\u2019 should have read \u2018Organ-on-a-Chip technology has the potential to improve success in drug development pipelines, as it can recapitulate organ-level pathophysiology and clinical responses\u2019. Both mistakes have been corrected in the HTML and PDF versions of the article."}
+{"text": "In wireless networks, MAC scheduling methods can be divided into two types according to the implementation model: centralized and distributed scheduling. By reasonably designing MAC scheduling policies, both centralized and distributed schedulers can ensure a reliable throughput capacity region, i.e., realizing throughput-guaranteed. However, it can be found that some existing throughput-guaranteed scheduling schemes cannot further ensure bounded end-to-end average delay, and the reason for this phenomenon has not been deeply analyzed. In practical communication networks, throughput and delay are equally important. Based on this idea, the existing MAC scheduling strategies are investigated systematically in this paper from two aspects of throughput and delay, and their performances are evaluated and compared through both theoretical analysis and simulation experiments. The work of this paper provides a theoretical basis for the improvement of MAC scheduling technology in the next-generation wireless networks. Depending on the way of obtaining the permission to use wireless channels, MAC layer protocols for wireless networks can be divided into two categories: competitive protocol and scheduling policy. The characteristic of the competitive protocol is that the node participates in the channel competition to win the permission to use the wireless channel. CSMA/CA protocol in IEEE 802.11 standard is a typical competitive protocol. Differently, the access permission of the wireless channel under the scheduling policy is pre-assigned in order to avoid the competition and conflict in transmission. The essence of MAC scheduling technology is to use STDMA (Space Time Division Multiple Access) to determine the scheduled time-slot for each link and allocate conflicting links into different time-slots . Let lq(n) denote the queue length of link l in time-slot n. Assume that the capacity of link l is fixed and denoted by lc. Indicator variable \ud835\udf11l(n) is used to indicate whether link l is scheduled in time-slot n. If l is scheduled and lq(n) > 0, \ud835\udf11l(n) = 1; otherwise, \ud835\udf11l(n) = 0. Thus, the queue update process of any link l is shown in Packets sent from the source node must be queued and forwarded to the destination node. The MAC scheduling method divides the time axis into time-slots and completes the input and output of the queue in each time-slot. Nodes are required to maintain data queues in both single-channel and multi-channel networks. The queue update action includes the arriving and sending of packets. According to the scheduling algorithm, when a queue is scheduled in this time-slot, data will leave the queue and be sent to the destination or to the next-hop node. Let + is the projection on  < \u221e, for any l \u2208 {1, ..., L}.In network queue analysis, it is usually assumed that the queue length at the initial time is finite, that is, After the Lyapunov function is constructed, Foster\u2019s Criterion is needed to determine the weak stability of the system . The criCriterion\u00a01.For positive integer H and constantif there exists a nonnegative Lyapunov function V(n) > 0 and a set0 with finite states such that\u0393holds for any time-slot n, then the aperiodic countable Markov chain (n) is positive recurrent and ergodic where E[V(n + H)q V(n) \u2502(n)] is defined as Lyapunov drift.q(n) is positive recurrent  < \u221e; otherwise, if q(n) \u2209 \u03930, E[V(n + H)V(n)\u2502q(n)] \u03b4. Based on Criterion 1, weak stability can be deduced. Therefore, strong stability can lead to weak stability, not vice versa.For the proof of Criterion 2, one can refer to . Accordi\u03bb \u2208 \u03b3 \u03a9 (0 < \u03b3 < 1), the scheduling policy is then considered to be throughput-guaranteed and its efficiency ratio is \u03b3. In fact, the efficiency ratio \u03b3 determines the throughput performance of a MAC scheduling policy.In this paper, we use \u03a9 to represent the maximum throughput capacity region that can be ensured by any scheduling strategy. Under a particular MAC scheduling mechanism, if the network system remains weakly stable when the input load This section uses Criterion 1 and Criterion 2 to evaluate the throughput and delay performances of several typical scheduling policies.For centralized scheduling in single-channel networks, the performance of the MWS  algorithAlgorithm implementation: In each time-slot n, the central control node in the network determines the schedule S represents the set of all possible schedules under a particular interference model and the schedule vector \u03c6 = . Obviously, the realization of MWS requires a central node to execute the scheduling process on the premise of knowing all the queue length information in the network and to determine the schedule in each time-slot through Equation (10). Hence, the implementation complexity of MWS is high.Performance evaluation of MWS: Assume that the input load vector \u03bb locates strictly inside the maximum capacity region. That is, there exists an L-dimensional vector \u03b5 with all elements equal to \u03b5 such that \u03bb + \u03b5 \u2208 \u03a9 holds. For time-slot n, the following Lyapunov function is constructed aseference  and obta\u03b5.It can be seen from the analysis above that MWS can achieve the maximum capacity region and can ensure the strong stability of the network when the input load locates inside the capacity region. The upper bound of average end-to-end delay is given by (15), which depends on the arrival rates and the parameter Algorithm implementation: MS is a typical distributed scheduling strategy. Under MS, any queue that meets lq(n) > lc is scheduled in time-slot n unless another queue in its interference set I(l) has already been scheduled. Hence, employing MS can ensurel. MS does not require the centralized control node and each link decides whether to participate in the data transmission at the current time-slot. The implementation complexity of MS is much lower than that of the MWS policy.Performance evaluation of MS: Assume that l, we use the following Lyapunov function:\u03c9 and B are positive numbers and K, where K is the interference degree [function:V(n)=\u2211l=1Algorithm implementation: Different from MS, the distributed Q-SCHED strategy divides each time-slot into scheduling-slot and transmission-slot, and further divides the scheduling-slot into M mini-slots, as shown in l picks the backoff time from the set {1, 2, \u2026, M + 1} according to the following probability:I represents the backoff time selected by l and the parameter lp is calculated byM + 1 means that the link is not scheduled in this time-slot. Once the backoff time expires, the link starts transmitting unless there have been other links in its interference set that are sending data.In each time-slot, link Performance evaluation of Q-SCHED: We introduce the following Lyapunov function:\u03bc > 0, if the input load of the network satisfiesH such that [V(n) \u2265 \u03a6. Since {q(n): V(n) < \u03a6} is a set with finite states, we can obtain that the Markov chain {q(n)} is positive recurrent using Criterion 1. Hence, the network is weakly stable. It should be noted that ensuring weak stability under the condition (23) implies that the Q-SCHED policy is throughput-guaranteed. However, strong stability is not achieved, and Q-SCHED cannot provide a bounded end-to-end average delay. On the other hand, based on the random access technology as shown in O(logL) number of iterations [uch that EV(n+H)\u2212erations .For scheduling in multi-channel networks, performances of the straightforward extension of MWS , distribAlgorithm implementation: MWS in single-channel networks can be directly extended to multi-channel networks. Similar to MWS, the scheduling indicator vector n according tol operating on channel c and l is scheduled on channel c, and 0 otherwise.Performance evaluation: Literature [q(n)} can be achieved. That is, the network system remains weakly stable when \u03bb \u2208 \u03a9. In fact, if we construct the following Lyapunov functionterature  has provrring to  that MWSAlgorithm implementation: Authors of [thors of  proposedI(\u03b6), \u03b6q(n) and \u03b6c represent the interference set, queue length and capacity of Tuple link \u03b6 respectively. According to MS, we have\u03b6.After the Tuple-based model is established, the MS algorithm is implemented based on Tuple links. Suppose Performance evaluation: To evaluate the performance of Tuple-based MS, the following Lyapunov function is constructed:\u03b6, one can achieve the one-step Lyapunov drift \u03ba and B1 are positive numbers and Y, where Y denotes the interference degree under the Tuple-based model.H such thatV(n) \u2265 \u03a6. Hence, the network should be weakly stable by using Criterion 1 under DA-LC. The efficiency ratio of DA-LC can be arbitrarily close to that of Tuple-based MS. Therefore, compared with Tuple-based MS strategy, DA-LC cannot guarantee a bounded end-to-end average delay. However, the implementation complexity of DA-LC is much lower and does not increase with the number of Tuple links since it adopts the random access technology.DA-LC algorithm is a combination of the Tuple-based model and the Q-SCHED strategy in a single-channel network. Specifically, the multi-channel environment is first virtualized into a single-channel network using the transformation process shown in \u03bb. In a single-channel environment, all links share one available channel to transmit data. In a multi-channel environment, the interface (network card) of a node can switch between four different channels with the channel capacity of 1, 1, 2, 2 respectively. The simulation parameters adopted in our experiments are shown in In this section, we use NS-2.31 software to simulate actual network scenarios and compare the throughput and delay performances of several existing wireless scheduling strategies. We use the topology shown in For a multi-channel network environment, In the next-generation wireless networks, MAC scheduling is becoming the preferred technology of MAC layer. In order to better design the scheduling algorithms and verify their performances in different scenarios, this paper summarizes a complete set of methods, including the concepts of strong/weak stability and their judgment methods. By using these methods, this paper analyzes the performances of typical MAC scheduling policies, including throughput performance and delay performance. Through theoretical analysis and simulation experiments, we verify that strong stability can provide lower end-to-end delay than weak stability in both single-channel and multi-channel networks. The research work of this paper provides a theoretical basis for the design and evaluation of MAC scheduling policies."}
+{"text": "In hypothesis testing, we first set up a null hypothesis and an alternative hypothesis. For example, if we are interested in comparing proportions between two groups, then the null hypothesis would be stated as \u201cthe proportions are the same\u201d and the alternative hypothesis as \u201cthe proportions differ\u201d between the two groups. We then gather data to test the veracity of the null hypothesis. In particular, the data allow us to calculate the p-value, which is defined as \u201cthe probability under a specified statistical model that a statistical summary of the data would be equal to or more extreme than its observed value\u201d [p-value is lower than the 0.05 significance level, we reject the null hypothesis and accept the alternative hypothesis. At the beginning of our research training, we learned about hypothesis testing, d value\u201d , and prap-value has become the most frequently used statistic in the biomedical research field\u2014a sine qua non for determining if a study finding is real or due to chance, if a new drug is effective or not, or if a health technology should be approved or denied by regulatory authorities. However, in recent years, there is a growing discussion that p-values and \u201cstatistical significance\u201d , albeit useful, have often been misused and misinterpreted in the biomedical field [p-values in clinical research. This methodology, often referred to as \u201cnull hypothesis significance testing\u201d, originated in the early 20th century with the ideas of Fisher . Since tal field ,7,8,9,10al field  will furTo begin with, let us assume that a single-center, randomized, double-blind, placebo-controlled trial is performed to determine if a new drug reduces mortality in 400 patients hospitalized with severe COVID-19 pneumonia, who are otherwise receiving standard-of-care. The occurrence of death at 28 days following randomization is the trial\u2019s primary endpoint. The numbers of patients who died or survived at 28 days, in each of the two study groups, are given in p-value that is higher than the cut-off threshold of 0.05 . Equivalently, the Risk Ratio is 0.70 , and the 95% CI includes the null value of one , or because the null value falls within the confidence interval. A statistically non-significant result does not \u201cprove\u201d the null hypothesis [Assuming that the particular study suffers no systematic error (bias) or confounding, we can employ significance testing or confidence interval (CI) methods to examine whether there is statistical evidence against the null hypothesis . Using the data from pothesis . This ispothesis . Let us now assume that a subsequent multi-center, randomized, double-blind, placebo-controlled trial assessed the efficacy of the same experimental drug in 1700 patients hospitalized with severe COVID-19 pneumonia . The Risk Ratio is 0.70 , but the 95% CI now excludes the null value of one  while the first one did not? Again, the answer is \u201cno\u201d. We cannot make such a claim! This is another misunderstanding about p-values. Especially when the study is underpowered and/or of a small sample size , the p-value has a large variance across repeated samples  [p-value obtained in a study to be indicative of the likelihood of getting the same results in future studies, conducted on the same topic, is not correct.Using the data from ulation) . This isp-value is probably \u201cthe most misunderstood, misinterpreted, and occasionally miscalculated index in all of biomedical research\u201d [It is wrong to claim that a statistically non-significant result shows \u201cno association\u201d, when the confidence interval includes clinically important decreases (or increases) in risk. Similarly, it is wrong to claim that two such studies  are in contrast. Yet, such errors are very common in the biomedical literature. Despite its seeming simplicity, the esearch\u201d . p-values, and improve the conduct of quantitative science: (1)p-values can indicate how incompatible the data are with a specified statistical model.\u201d Based on the observed data, the researcher either rejects or \u201cfails to reject\u201d the null hypothesis.\u201c(2)p-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.\u201d They can only tell us how consistent the data are with the null hypothesis.\u201c(3)Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.\u201d Decision-making must not rest solely on a p-value. Researchers should also consider a broad range of other factors, e.g., study design, data quality, related prior evidence, plausibility of mechanism, real-world costs and benefits, etc.\u201c(4)Proper inference requires full reporting and transparency.\u201d Researchers should not conduct multiple, unplanned analyses of the data and (selectively) report only those with certain p-values . This is usually called cherry-picking, data-dredging, significance-chasing, significance-questing, selective-inference, or p-hacking, and leads to a spurious excess of statistically significant results in the biomedical literature.\u201c(5)A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.\u201d For example, smaller p-values do not necessarily imply the presence of larger or more important effects, and larger p-values do not imply a lack of effect or lack of importance.\u201c(6)By itself, a p-value does not provide a good measure of evidence regarding a model or hypothesis.\u201d Analysis of the data should not end with the calculation of a p-value. Depending on the context, p-values can be supplemented by other measures of evidence that can more directly address the effect size and its associated uncertainty .\u201cDriven by increasing concern, the American Statistical Association (ASA) has issued a statement  with sixp-values in applied research. Importantly, it also provides great references and supplementary material for anyone who would like to delve further into this topic. The ASA\u2019s statement  outlinedp-values [A comprehensive understanding of statistical concepts improves the quality of clinical research. We strongly encourage clinical researchers to involve biostatisticians and methodologists early on in their studies; to ensure a sound study design and a cohesive data collection strategy to minimize biases; to prespecify a data analysis plan that can address potential misuse and misinterpretation of p-values ; and to p-values ."}
+{"text": "Nature 10.1038/s41586-022-05197-9 Published online 19 October 2022Correction to: \u0127k values shown in Fig. 1a,b and Fig. 2c\u2013e, the modified constant \u0127 was omitted in error. In addition, the Peer review information mistakenly linked to an earlier version of the article manuscript and has since been removed. The changes are reflected in the HTML and PDF versions of the article.In the version of this article initially published, for the"}
+{"text": "Euterpe oleracea Mart.), a species belonging to the Arecaceae family, has been cultivated for thousands of years in tropical Central and South America as a multipurpose dietary plant. The recent introduction of a\u00e7a\u00ed fruit and its nutritional and healing qualities to regions outside its origin has rapidly expanded global demand for a\u00e7a\u00ed berry. The health-promoting and disease-preventing properties of this plant are attributed to numerous bioactive phenolic compounds present in the leaf, pulp, fruit, skin, and seeds. The purpose of this review is to present an up-to-date, comprehensive, and critical evaluation of the health benefits of a\u00e7a\u00ed and its phytochemicals with a special focus on cellular and molecular mechanisms of action. In vitro and in vivo studies showed that a\u00e7a\u00ed possesses antioxidant and anti-inflammatory properties and exerts cardioprotective, gastroprotective, hepatoprotective, neuroprotective, renoprotective, antilipidemic, antidiabetic, and antineoplastic activities. Moreover, clinical trials have suggested that a\u00e7a\u00ed can protect against metabolic stress induced by oxidation, inflammation, vascular abnormalities, and physical exertion. Due to its medicinal properties and the absence of undesirable effects, a\u00e7a\u00ed shows a promising future in health promotion and disease prevention, in addition to a vast economic potential in the food and cosmetic industries.The a\u00e7a\u00ed palm ( Euterpe oleracea Mart.), a species belonging to the palm tree (Arecaceae) family, is native to several countries in the Amazon region of tropical Central and South America, including Brazil, Ecuador, and Venezuela [The a\u00e7a\u00ed palm . Furthermore, a\u00e7a\u00ed has been shown to exhibit anticancer, antiatherogenic, antimicrobial, antinociceptive, anticonvulsant, antileishmanial, and antiaging activities. Moreover, research has indicated the tissue-protective effects of a\u00e7a\u00ed on several organs, such as the heart, liver, lungs, kidneys, and brain ,23,24,25A\u00e7a\u00ed, popularly known as a\u00e7a\u00ed-do-Par\u00e1, a\u00e7aizeiro, or a\u00e7a\u00ed-de-toceira, is a palm tree a native Notably, the disease-preventing effects of a\u00e7a\u00ed are related to its composition of bioactive phytochemicals. The major constitutive phytochemicals of a\u00e7a\u00ed are present throughout various parts of the plant.In the a\u00e7a\u00ed fruit, the polyphenols are the most significant constituent of the chemical profile. Major secondary polyphenol metabolites include anthocyanins (ACNs) and proanthocyanidins (PACs), in addition to other flavonoids. Several phenolic acids , flavonoids , lignans, and procyanidin oligomers have been reported in the phytochemical profile of a\u00e7a\u00ed fruit ,31,32. Tp-hydroxybenzoic acid, vanillic acid, syringic acid, ferulic acid) and a flavonoid, (+)-catechin, in a\u00e7a\u00ed oil , such as 3,4-dihydroxybenzoic acid; \u00e7a\u00ed pulp . It has \u00e7a\u00ed pulp . Assays \u00e7a\u00ed pulp . SimilarO-caffeoylquinic acid, 4-O-caffeoylquinic acid, and 5-O-caffeoylquinic acid [O-caffeoylshikimic acid, 4-O-caffeoylshikimic acid, and 5-O-caffeoylshikimic acid (C-glycosides (ACGs), a group of flavonoids, including: 6,8-di-C-hexosyl apigenin; 6,8-di-C-hexosyl apigenin sulfate; 6-C-hexosyl-8-C-pentosyl apigenin isomers; 6-C-glucosyl luteolin, or homoorientin; 6-C-pentosyl-8-C-hexosyl apigenin isomers; 8-C-glucosyl luteolin; and 6-C-glucosyl apigenin  guidelines was maintained throughout the process of data collection [This review was designed on the basis of the following focal question: \u201cWhat are the described health effects of a\u00e7a\u00ed?\u201d A literature search through PubMed, Cochrane, Embase, and Google Scholar databases was conducted to identify studies performed with a\u00e7a\u00ed in relation to its health benefits, implications in disease, or both. Keywords directing the investigation included llection ,44. The Eligible studies published from 2004 to 2022 were included in this review. Exclusion criteria were non-English language studies, unpublished data, poster presentations, and conference abstracts. For each clinical trial study, the detection, selection, and reporting of bias was utilized to carefully consider and evaluate risk of bias. Patient inclusion, intervention category, outcomes analyses, missing events, and data were also examined. Assessments of both bias and quality were performed in alignment with directives of the Cochrane Handbook for Systematic Reviews of Interventions . The desNumerous preclinical studies have revealed the effects of a\u00e7a\u00ed in vitro  and in vAmong the health implications of a\u00e7a\u00ed included in this discussion, antioxidant and anti-inflammatory faculties have been documented most frequently in the current literature. A large quantity of in vitro evidence exists in support of the antioxidant capacity of several compounds  present in a\u00e7a\u00ed ,142,143.In a similar manner, Earing et al.  evaluateCCD-18Co cells to investigate the inflammatory protein expression, ROS suppression, and anti-inflammatory activity of a\u00e7a\u00ed phenolic compounds. A\u00e7a\u00ed extract was noted to decrease COX-2, TNF-\u03b1, and NF-\u03ba\u03b2 expression induced by lipopolysaccharide (LPS) in human colon myofibroblasts. Because the downregulation of biomarkers, such as COX-2, TNF-\u03b1, and NF-\u03ba\u03b2, is vital to the reduction of inflammation, these results provide further evidence of anti-inflammatory activities of phenolic compounds in a\u00e7a\u00ed. Another in vitro study performed by Machado et al. [Injury, toxins, infection, genetic defects, and trauma can induce resident immune cell activation . Subsequo et al.  demonstro et al. ,57,148. Pain can have a negative impact on quality of life, as well as the performance of daily activities. Currently, nonsteroidal anti-inflammatory drugs (NSAIDs) and opioids are common pharmacological options of the treatment of pain. The anti-inflammatory, antihypertensive, antioxidant, and vasodilatory activities of a\u00e7a\u00ed has resulted in the exploration of its value as an antinociceptive and analgesic agent ,118,149.Escherichia coli, Pseudomonas aeruginosa, Streptomyces aureus, and Enterococcus faecalis [E. coli [Due to growing antimicrobial resistance, the pharmaceutical field is constantly seeking new alternatives to oppose relevant pathogens. The high polyphenol content of a\u00e7a\u00ed has been associated with antimicrobial activity . One stufaecalis . EOO com[E. coli . OverallS. aureus and found it to be effective against planktonic cells and biofilms of this microorganism. Furthermore, hydroalcoholic extracts produced from dried pulp, leaves, and seeds of a\u00e7a\u00ed demonstrated significant antimicrobial activity against Clostridium perfringens, S. aureus, and P. aeruginosa [Leishmania amazonensis and Leishmania infantum and found a reduction in the number of promastigotes, augmented synthesis of ROS, and the induction of cell death phenotypes in both species. The use of a\u00e7a\u00ed juice for 72 h not only engendered protective effects against L. amastigotes and strongly diminished IL-17 levels, but also reduced the number of intracellular amastigotes in macrophages infected with L. amastigotes and L. infantum [Dias-Souza et al.  studied ruginosa . Hence, ruginosa  evaluateinfantum . Of noteGastric ulcers are one of the most common conditions afflicting humans. Current treatments for gastric ulcers include H2-receptor antagonists, M1-receptor blockers, and proton pump inhibitors. However, these drugs can be costly, have health-associated side effects, and result in relapse. For this reason, more efficacious and inexpensive therapeutics for gastric ulcers are in high demand. Cury et al.  investigThere are limited investigations examining the impact of a\u00e7a\u00ed berry on cognitive function or brain health. The experiments available have established that a\u00e7a\u00ed largely confers its neuroprotection through antioxidant and anti-inflammatory mechanisms, restoration of mitochondrial function, and inhibition of toxic protein aggregation ,154,155.2O2). Analysis of ABTS and deoxyribose assays revealed no differences in antioxidant activity amongst the various a\u00e7a\u00ed genotypes. All hydroethanolic extracts were found to reduce ROS produced by H2O2 in SH-SY5Y cells, elucidating their neuroprotective effects [The anti-inflammatory potential of a\u00e7a\u00ed extract was evaluated via an in vitro microglial model that substantiated its modulation of nucleotide oligomerization domain (NOD)-like receptor pyrin domain-containing 3 (NLRP3) inflammasome proteins and antioxidant pathways, augmentation of anti-inflammatory cytokines, and reduction of pro-inflammatory cytokines . Microgl effects .The vulnerability of the brain to oxidative stress, in addition to its energy requirements for neurotransmission, greatly increases the risk of mitochondrial dysfunction in neural tissue . Data suNeurodegeneration in the setting of NDDs can cause significantly altered neuron viability. This can lead to the overproduction, inadequate clearance, and ultimately, aggregation of toxic proteins in or around brain tissue . The deaBrain injury from seizures can result in neuronal cell death . FactorsDrosophila melanogaster fed a high-fat diet. This study found that a\u00e7a\u00ed supplementation increased the transcription of genes related to a small heat-shock-related protein and two detoxification genes. A\u00e7a\u00ed also reduced transcription of phosphoenolpyruvate carboxykinase (PEPCK), a critical gene in the appropriate regulation of gluconeogenesis. Moreover, a\u00e7a\u00ed increased the lifespan of females subjected to oxidative stress, suggesting that a\u00e7a\u00ed improves survival [Many neurodegenerative diseases eventually lead to symptoms of depression. Because depression has been linked to oxidative stress, the antidepressant effects of a\u00e7a\u00ed berry have also been explored . A\u00e7a\u00ed jusurvival . A\u00e7a\u00ed masurvival ,158,159.Cocos nucifera L. saturated fat in rats. Although no alterations in triglycerides were noted, there were reductions in total cholesterol and low-density lipoprotein cholesterol (LDL). A treatment regimen of both a\u00e7a\u00ed oil and simvastatin, a common anticholesterolemic drug, also prevented the formation of atheromatous plaques in the vascular endothelium of rats [Dyslipidemia is precipitated by disruptions in lipid metabolism that result in chronically elevated serum lipids and, therefore, increased predisposition to CVDs, obesity, atherogenic processes, diabetes, and metabolic syndrome (MetS) ,160. Die of rats ,109. Com of rats  evaluate of rats . For thi of rats ,120.Souza et al.  proposedGlobally, the most prevalent liver condition is nonalcoholic fatty liver disease (NAFLD) . NAFLD iAnother study revealed that the use of a\u00e7a\u00ed seed flour could prevent obesity-induced hepatic steatosis in mice . In thisThe effects of filtered a\u00e7a\u00ed pulp on the expression of paraoxonase (PON) activity in rats with NAFLD have also been investigated ,167. RatAlcoholic liver disease (ALD) is the most prevalent cause of advanced liver disease and has been linked to high levels of global mortality and morphological consequences, including alcoholic hepatitis, steatosis, fibrosis, cirrhosis, and hepatocellular carcinoma . The resWorldwide, T2DM is a serious public health crisis reaching epidemic proportions . DiabeteCardiovascular risk factors such as hypertension, dyslipidemia, obesity, diabetes mellitus, and MetS promote endothelial injury due to oxidative stress . This enROS play an intricate role in oxidative stress and accompanying myocardial injury. Increased quantities of ROS during heart ischemia can elicit cell membrane destruction, lipid peroxidation, and dysfunction in the antioxidative defense system. For this reason, a\u00e7a\u00ed has been studied as a prospective vasodilatory, anti-inflammatory, and antifibrotic agent . It has CVDs are currently the leading cause of morbidity and mortality among adults. Although scientific progress has identified a spectrum of different risk factors for cardiovascular pathologies, the current state of prevention, and even treatment, of CVDs is suboptimal ,168,169.Figueiredo et al.  treated Pontes et al.  demonstrChronic kidney disease (CKD) is a general term for a group of heterogenous disorders that affect kidney structure and function. Over time, considerable research has been conducted to properly define, classify, and treat CKD. Ultimately, data has indicated that prevention is the most effective way to avoid the development and progression of renal disorders ,170. Becda Costa et al.  found thOver time, the global frequency of cancer, a group of diseases characterized by abnormal cell growth, has continued to increase. Therefore, cancer prevention has become a topic of paramount importance within the scientific field. The chemopreventive and anticarcinogenic potency of a\u00e7a\u00ed has been linked to its ability to decrease the viability of cancer cells, as well as reduce the incidence of tumors and tumor cell proliferation ,172,173.Sibuyi et al.  investigFurthermore, Monge-Fuentes et al.  studied O-glucoside, cyanidin 3-rutinoside) and carotenoids, especially \u03b2-carotene and lutein. Hence, lyophilized a\u00e7a\u00ed pulp was found to have the potential to exert antitumor activity. Additionally, Fragoso et al. [Helicobacter felis in mice.Fragoso et al.  evaluateo et al.  demonstro et al.  studied o et al.  studied o et al.  found tho et al.  concludeStoner et al.  investigIn addition to preclinical studies, numerous clinical trials have evaluated the effect of a\u00e7a\u00ed on different aspects of human health. These studies are summarized in Euterpe edulis Mart.) juices on biochemical and antioxidant parameters in humans. The participants were indicated to drink 200 mL/day of a\u00e7a\u00ed juice for four weeks. The authors observed posttreatment improvement in HDL levels and antioxidant enzyme activities  in their test subjects. However, there was a noteworthy limitation of this trial. Although this report indicated that the patients were asked about adverse events throughout the experimental process, no information was provided with regards to the results for this question.De Liz et al.  performeAnother trial showed that the consumption of 200 g of a\u00e7a\u00ed pulp/day over a four-week timeframe afforded no modifications in total cholesterol, LDL and HDL, triglycerides, or apolipoprotein B (ApoB) in healthy female patients, besides the demonstration of significant antioxidant actions. Nonetheless, increased ApoA-I was observed, suggesting an improvement in the metabolism of this lipoprotein. The favorable actions on plasma HDL metabolism and antioxidant defenses indicate a potential use of a\u00e7a\u00ed as an antilipidemic agent .Additionally, Alqurashi et al.  investigCarvalho-Peixoto et al.  considerGale et al.  performeA study performed by Oppitz et al.  revealedAranha et al.  conducteIn addition, Kim et al.  evaluateIn overweight subjects, Udani et al.  revealedFurther, Kesller et al.  investigOn the whole, current scientific literature is deficient in information regarding the toxicity of a\u00e7a\u00ed. Marques et al.  publisheAdditionally, Ribeiro et al.  tested aHowever, Marques et al.  used ratMoreover, Caiado et al.  exploredLactobacillus rhamnosus, the fruit can be easily used as a suitable matrix for products that use this microorganism as a probiotic agent [A\u00e7a\u00ed has enormous economic potential in many fields of industry. In the food industry, a\u00e7a\u00ed may be used in the production many goods, ranging from probiotic beverages to desserts to ice cream. Due to its potent effects in preventing morphological changes in principally ic agent ,189,190.ic agent . Of noteic agent .Moreover, in the cosmetic industry, a\u00e7a\u00ed has been used to create multicomplex emulsions that enhance the photoprotective effects of sunscreens formulas. Due to its antioxidant capacity, a\u00e7a\u00ed also has potential as an ingredient in various other skincare products, such as skin lotions ,193,194.In the biotechnological industry, a\u00e7a\u00ed-derived ultrafine fibers have been used to compose innovative pH sensors for the visual monitoring of food quality . AdditioOur results show that a\u00e7a\u00ed has medicinal properties and the economic potential for widespread use throughout the food and cosmetic industry. The fruit presents a rich phytochemical profile composed of phenolic compounds, quinones, terpenes, and norisoprenoids, all of which are related to its health-promoting and disease-preventing potential. In vitro and in vitro studies demonstrated that a\u00e7a\u00ed possesses antioxidant and anti-inflammatory effects; exerts cardioprotective, gastroprotective, hepatoprotective, neuroprotective, and renoprotective activities; improves hyperinsulinemia and dyslipidemia; and shows antineoplastic actions. Additionally, a\u00e7a\u00ed exerts antimicrobial and antiparasitic effects. Clinical trials have demonstrated that a\u00e7a\u00ed protects against prostate cancer, MetS risk factors, and auditory dysfunctions. Moreover, its derivatives, such as berry extracts, whole fruit extracts, seed extracts, and phytochemically enriched extracts, have no hepatotoxicity, cardiotoxicity, or nephrotoxicity, strengthening its safety and health potential.However, our work had some limitations. Firstly, numerous included studies did not specifically define the composition of the utilized a\u00e7a\u00ed. Secondly, a limited number of clinical studies have been conducted on this fruit, especially concerning direct human consumption. In addition, the studies included in this paper are heterogeneous due to the variety of forms of a\u00e7a\u00ed administration used  and in different doses. In short, the accumulated scientific evidence on the properties of a\u00e7a\u00ed, in the absence of undesirable effects, awards this plant a promising future in health promotion and disease prevention. Moreover, there is a vast economic potential of a\u00e7a\u00ed in the pharmaceutical, food, and cosmetic industries."}
+{"text": "Correction to: Doc Ophthalmolhttps://doi.org/10.1007/s10633-022-09904-9xIn the original article, the formatting of \u201c<<\u201d and \u201c>>\u201d was indicated with different symbols.For example,and,Unified symbols are used to indicate greater than and less than.The original article has been corrected."}
+{"text": "Asher L, Birhane R, Weiss HA, et al. Community-based rehabilitation intervention for people with schizophrenia in Ethiopia (RISE): results of a 12-month cluster-randomised controlled trial. Lancet Glob Health 10: e530\u2013422022; \u2014In this Article the acknowledgments have been corrected to add \u201cMDS was not employed by the Wellcome Trust at the time of the study.\u201d This correction has been made as of May 10, 2022."}
+{"text": "ASTRA calculated values of power coupled to the ion species, at the dithering H-mode transition, exhibit a similar nonlinear dependence on density. This analysis points to the important contribution of the ion thermal channel to the L-H phase transition. The low-frequency plasma density and D-alpha dithers appear to be accompanied by sudden bursts of magnetohydrodynamic (MHD) activity. A simple model is tested to demonstrate a possible scenario of self-regulation among turbulence, zonal flows, pressure (density) gradient and MHD activities.The dithering H-mode phase, characterized by oscillations, is generally observed at input power values close to the L-H transition power threshold and low plasma collisionalities (low electron density and/or high plasma temperature). Measurements to characterize the dithering phase are presented for the low aspect ratio, high magnetic field tokamak, ST40. The dithering phase oscillation frequency is observed between 400 and 800\u2009Hz and demonstrates an inverse relationship with core plasma density. Dithering phase H-modes are documented across a nonlinear, low-density power threshold operational space, with signature low- and high-density branches. The minimum power threshold for dithering H-mode access is measured at a core, line average electron density of 4.7(\u00b10.5)\u2009\u00d7\u200910This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'. Various tokamaks have documented a dithering phase following the initial transition from L-mode, in which there is a sequence of L-H-L transitions or transitional edge localized modes (ELMs) at values of heating power close to Pth [et al. [The transition from a low confinement mode (L-mode) to a high confinement phase (H-mode) has been documented in tokamak plasmas since 1982 [e to Pth \u20137. UnderP, which eventually becomes dominant and suppresses the plasma turbulence. This hypothesis is consistent with experimental observations of a modulation of the edge rE profile and turbulence level in typical limit cycle oscillations, also frequently named as an intermediate phase, I-phase or dithering H-mode phase on a range of different tokamaks [et al. [Fundamental to the creation of plasma transport barriers and the transition to improved plasma confinement phases is the reduction of electrostatic turbulence by sheared flow. Both larger scale, mean E\u2009x\u2009B flows  and fine-scale zonal flows  are thought to play active, but different roles in turbulence suppression. Zonal flow models, such as Kim & Diamond's  predatortokamaks ,11,12. I [et al. , who speen, min [en,min have been reported to cover a wide range in different-sized conventional tokamaks in [19\u2009m\u22123 and 1.5\u2009\u00d7\u20091020\u2009m\u22123. The larger tokamaks such as JET and JT60-U populate the lower en, min range, medium size tokamaks DIII-D and ASDEX-U lie somewhat higher and the highest values have been measured for the high-field, compact machine, Alcator C-Mod [en,min for spherical tokamaks in the literature.The density dependence of the L-H power threshold has been known for a long time to be non-monotonic on conventional tokamaks, with a minimum power threshold at a given density, ne, min ,15. The amaks in , betweenor C-Mod . The autIt is also important to note that the fundamental dynamics of the H-L transition may also be quite different from that of the L-H, as the plasma conditions that precede the phase change, such as plasma profiles and turbulence are significantly different in the H-mode phase. There have been relatively few H-L transition and power hysteresis studies ,14,17, eIn this paper, the experimental conditions and analysis methods used to study the access to the dithering phase H-mode in the low-density region on ST40 are described in \u00a72. Section 3 describes the experimental characteristics observed for the dithering H-mode phase of the plasmas. The power threshold and temperature analysis are included in \u00a74, along with the power balance calculations for the different plasma species and an extended zonal flow model. The last section comprises a summary of the main results from the study along with planned futurework.. 2a, with plasma major radius, R\u2009=\u20090.46\u20130.48 m, and minor radius, a\u2009=\u20090.26\u2009m. A representative magnetic configuration at the start of the H-mode, is shown in figure 1b for shot number 9780, at t\u2009=\u200979.7\u2009ms prior to the L-H transition. The general plasma parameters for two shots, #9780, which transitioned to a dithering H-mode, and #9784, which remained in L-mode, are compared in The dithering H-mode phase results presented in this paper are from the compact, high-field, spherical tokamak, ST40  shown infigure 1c for the shots #9780 and #9784.Neutral beam injection (NBI) was the only auxiliary heating method used; one of the injectors provided a series of 0.1\u20130.2\u2009MW incremental power steps over 11\u201312\u2009ms. All shots included in this study were fuelled with the deuterium NBI in the quasi-stationary plasma current phase and example NBI power time traces are shown in figure 2a. A plasma density scan was performed for the series of shots in this study at pI/tB\u2009=\u20090.52\u2009MA/2.0\u2009T over a range of, \u03ba\u2009=\u20091.34\u20131.44, at the L-H transition.The plasma current typically increased from 0.52\u2009MA to a maximum of 0.56\u2009MA over the window of NBI injection, as shown for the example plasmas figure 2e and f. This instrument views along a radial line-of-sight through the mid-plane. The e and f are averaged values over the emission region of He- and Li-like ions and therefore a lowest estimate of the central plasma temperatures. The last L-mode and H-mode In the core plasma, electron and ion temperatures, und 4\u2009nm  with a td. The plasma-stored energy, pW, is evaluated from the reconstructed EFIT [The line averaged core plasma electron density, ted EFIT  magnetohted EFIT .. 3\u03b1D emission and \u03b1D intensity and rise in The L-H transition for these plasmas is characterized by a transition from L-mode to a dithering H-mode phase. The ng phase ,22,23. TpI, tB and core plasma L-mode t\u2009=\u200961.6\u2009ms for 8\u2009ms. The short reduction in power was sufficient to prevent the plasma from transitioning to the H-mode and provides a very useful L-mode reference shot under very similar vessel and plasma conditions. The L-H transition for shot #9780 occurs at t\u2009=\u200979.8\u2009ms, at which time a difference in plasma energy of \u0394pW\u2009=\u20097.3\u2009kJ, pW\u2009=\u20099.9\u2009kJ and b,d, displaying the enhanced energy and particle confinement characteristic of H-mode development. From figure 2f, the corresponding maximum difference in The temporal evolution of two shots with comparable a, in which the average number of cycles over the dithering time window has been considered. The cycle frequency is observed to vary between 400 and 800\u2009Hz over the pW\u2009=\u200935\u201339.5\u2009MJ and \u03b2N\u2009=\u20091.9\u20132.1 at the L-H transition, compared with peak values in dithering H-mode of pW\u2009=\u200935\u201345.6\u2009MJ and \u03b2N\u2009=\u20091.9\u20132.54. The data presented in figure 3b clearly show the L- and H-mode segments of the shots to be differentiated by the associated values of stored pW and N\u03b2.The frequency of the H-mode cycles of the dithering phase are found to decrease with core density, as shown in figure 3. 4LP, is defined at:PIN is the sum of the input power, which in these plasmas are ohmic and NBI, and dpW/dt is the rate of change of stored plasma energy. The value of Pth, have been taken as the values of LP, at the time of the forward and back transitions, defined as the first and final transition into and from the dithering phase, as described above.Following conventional analysis of experimental values in the field, the loss power, Pth for seven plasmas  are plotted in figure 4a as a function of Pth data. These results demonstrate a nonlinear dependence of Pth on Pth from the fit to the data lies in the region of core The values of the L-H and H-L a indicates the predicted value of et al. [19\u2009m\u22123, where pI in in MA, tB is in T, a and R, are in m. Ryter et al. [eT, iT thermal fluxes, even in the relatively cooler edge plasma region.The vertical shaded area in figure 4r et al.  for a mur et al.  suggest pI and tB accessible in ST40, along with the hot-ion mode plasma intrinsic separation of the ion and electron heating channels.The experimental value of NBI_iP, and electron, NBI_eP, plasma species have been analysed using a time-dependent power balance calculation with the ASTRA code [NBI_iP and NBI_eP are compared with the values of Pth in figure 4a. The behaviour of NBI_iP exhibits a similar trend to Pth, varying nonlinearly with NBI_eP decrease linearly with increasing Pth dependence on The heating power coupled to the ion, TRA code ,25 in MWb. The values of line averaged ion temperature measured using the He-like argon emission, Pth curve.The corresponding values of core Pth, also plotted in figure 4a. These H-L transitions appear to be triggered by the elevated values of dithering phase H-mode plasma density at the limited input power. The H-L Pth is measured to be up to 10% lower than the corresponding L-H Pth. For the observed H-L transitions, the values of b are observed to be comparable with the forward transition values, for the lower plasma density, iT is measured to be 1.2 times higher than for the L-H transition. The transition from H-mode to L-mode is less well controlled and therefore more difficult to access than the forward transition. While this limited dataset of two points indicates a small amount of hysteresis in power and differences in ion temperature observations over the density scan, more data are required over the The H-L transition for two of the plasmas (#9781 and #9831) occurred within the NBI heating phase and were used to determine the H-L a), dpB/dt (b) and D-alpha (c) for shot #9780. The dominant frequency of the MHD activity can be seen f\u2009<\u20091 kHz. The observed abrupt occurrences of large fluctuations in dpB/dt are associated with a sudden rise in D-alpha and a sudden collapse of The physical origin of the observed dithering is not entirely clear given no experimental measurements of edge plasma turbulence, rotation, radial electric field, etc. Although the dithering cycles may be due to self-regulation between self-generated zonal flows and turbulence , it seemet al. [V are generated by turbulence through the first term \u03b1EV on the right-hand side of equation (a3) while damped directly by mE as well as collisional damping. The example time evolutions of the mean ion pressure gradient, p , MHD activity, mE, and turbulence amplitude, E, together with input power, P, are shown in P is taken to increase up to P\u2009=\u20090.075 at =\u20092500 and then ramped twice down to P\u2009=\u20090.015 at t\u2009=\u20092600, as shown in figure 6a. Model parameters (see appendix A) are chosen to ensure the appearance of dithering shortly after the L-H transition.Assuming electrostatic turbulence in the L-mode, including MHD pressure gradient-driven instabilities in  would leet al. . As notea,b shows that as turbulence amplitude E grows, zonal flows V are amplified starting around t\u2009\u2248\u20091800, marking the L-H transition at crP\u2009\u2248\u20090.7. However, when V grows to a sufficiently large amplitude, it damps E, causing a certain phase shift between the oscillations of E and V. That is, V and E do not share a similar phase. At the same time, turbulence regulation by V leads to steeping of the edge pressure gradient p, causing MHD activity mE in figure 6f, which damps not only p but also V (through the damping term m VE in equation (a3)). MHD activity is also manifested as a sudden spike in c and powerloss d. The maximum power at P\u2009=\u20090.075 at t\u2009=\u20092500 is about 7% above crP\u2009\u2248\u20090.7. Self-regulation among E, V, mE and p (mean shear flow \u221d\u2009p2) can be seen more clearly in zoomed-in views in figure 6e,f. Note that because of the damping of V by magnetic activity, the self-regulation between turbulence E and zonal flows V is less evident than what was observed in [mE\u2009=\u20090 were used for the parameter values used in Figure 6erved in . If Em\u2009=. 5Pth for access to a dithering H-mode phase. All the plasmas remain in the dithering H-mode phase before transition back to L-mode due to the available power margin remaining close to the L-H Pth and in the absence of plasma density feedback control.A plasma density scan has been performed on the ST40 that shows a minimum Pth is measured has been observed at pI and tB in governing the Pth on ne in the nonlinear, low-density region. The calculated values of NBI_iP show a similar nonlinear dependence on core NBI_eP is observed to have a weak negative linear dependence over the density range scanned. These results indicate the ion thermal channel plays a key role in accessing the H-mode.The core electron density at which the minimum The line averaged core ion temperature just prior to the L-H transition has a peak value of Data for the power threshold for H-L transition have been included for two plasmas in this study and indicate a maximum of 10% hysteresis in the power threshold. Experiments are planned in forthcoming campaigns to carefully study and evaluate hysteresis in the ST40 H-mode.An extended self-regulatory limit cycle model has been developed to include turbulence amplitude, zonal flows, pressure gradient and MHD activity. This model reproduces the qualitative features of the dithering H-mode cycles well and points to the possible contribution of low-frequency MHD, due to a steep density or pressure profile, to the L-H-L cycle in the dithering phase of the plasmas.It will be interesting to include the effect of additional terms in forthcoming experimental H-mode and L-H/H-L transition investigations and power balance calculations; factors such as NBI shine through losses, fast ion losses due to charge exchange and ion orbit processes and radiated power. In addition, experiments to study the role of the edge, pedestal and SOL plasma parameters are foreseen on ST40 with an upgraded set of Charge Exchange Recombination Spectroscopy and Thomson Scattering diagnostics. Dedicated experiments are also planned with the updgraded diagnostic suite to build and expand the H-mode and L-H/H-L transition database with different plasma configurations."}
+{"text": "For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most Directed Additive Spanner asks whether G has an additive t-spanner with at most Directed Multiplicative Spanner admits a polynomial kernel of size Directed Multiplicative Spanner can be solved in Directed Additive Spanner is k for every fixed t and k.We initiate the parameterized complexity study of minimum  G, a spanner is a spanning subgraph of G that approximately preserves distances between the vertices of G. Graph spanners were formally introduced by Peleg and Sch\u00e4ffer in\u00a0 to denote the subgraph of G induced by X. For a set of vertices S, S, that is, v, we write S , S . A subgraph H of a (directed) graph G is a spanning subgraph of G if G has a topological ordering of its vertex set, that is there exists path with the vertices end-vertices of P and we say that P is a -path. A single vertex path is trivial, and for a trivial P is a -path. All considered paths are assumed to be simple, that is, length of a path is the number of edges  in the path. Also A(P) denotes the arc set of the path P. For a -path v,\u00a0w)-path concatenation of distance between u and v in G, that is, the length of a shortest -path; we assume that u,\u00a0v)-path in G. Clearly, We write t be a positive integer. It is said that a spanning subgraph H of G is a multiplicative t-spanner if H of G is called an additive t-spanner if Let G be an arc wighted directed graph, that is, we a given a weight (or length) function length of an arc e. The length of a weighted path weighted distanceG, it is said that a spanning subgraph H a weighted multiplicative t-spanner if t is not required to be an integer.We also consider the weighted variant of spanners for directed graph. Let Directed Multiplicative Spanner. We show that the problem admits a polynomial kernel and then complement this result by obtaining an Directed Multiplicative Spanner is Weighted Directed Multiplicative Spanner is k only. These results are based on locality of multiplicative spanners in the sense of the following observation made by Peleg and Sch\u00e4ffer\u00a0[In this section, we consider Sch\u00e4ffer\u00a0.t be a positive integer (or H of a directed graph G is a (weighted) multiplicative t-spanner if and only if for every arc u,\u00a0v)-path in H of length at most t  in the weighted case).. Let t t be a positive integer  and let G be a directed graph. For an arc G, we say that a -path P is a t-detour for a if the length of P is at most t (t times the length of a in the weighted case) and P does not contain a. By Observation\u00a0Directed Multiplicative Spanner for , it is necessary and sufficient to identify k arcs that have t-detours that do not contain selected arcs. Then H can be constructed by deleting these arcs. Notice that this observation holds for both unweighted and weighted spanners. However, for the weighted case, the number of arcs in a t-detour may be arbitrary and depends on the length of a.Let mentclass2pt{minimDirected Multiplicative Spanner admits a polynomial kernel.In this subsection, we show that Directed Multiplicative Spanner has a kernel of size G,\u00a0t,\u00a0k) be an instance of Directed Multiplicative Spanner. Clearly, if G,\u00a0t,\u00a0k) is a yes-instance, and our algorithm returns a trivial yes-instance in this case. We assume from now that Let  is a yes-instance of Directed Multiplicative Spanner.We say that obayashi\u00a0 for consG,\u00a0t,\u00a0k) is a yes-instance of Directed Multiplicative Spanner.If t-detour for a.Let select an arbitrary set set We show by induction, that the sets Let mentclass2pt{minimNow we select arcs t-detours t-spanner. Therefore,  is a yes-instance of Directed Multiplicative Spanner. Let mentclass2pt{minimBy Claim\u00a0Directed Multiplicative Spanner and stop.If From now, we assume that t-detours for S contrary to the undirected case, where all the edges of t-detours are in cycles of length at most t-detours themselves. We use the following procedure to mark the crucial arcs of potential detours.The analog of Reduction Rule\u00a0Marking Procedure Let (i)u,\u00a0v)-path P in P is at most t, then mark the arcs of P.For every (ii)t, then mark the arcs of find a shortest t, then mark the arcs of find a shortest t, then mark the arcs of find a shortest For every ordered pair of two distinct arcs Observe that marking can be done in polynomial time by Dijkstra\u2019s algorithm. Denote by L the set of marked arcs. Our final rule constructs the output instance.H, and for the obtained Consider the graph We argue that the rule is safe.G,\u00a0t,\u00a0k) is a yes-instance of Directed Multiplicative Spanner if and only if  is a yes-instance of Directed Multiplicative Spanner. Then, by Observation\u00a0k distinct arcs t-detours Suppose that -path in t-detour t-detour for Suppose that S. Let u). Note that S are vertices of u,\u00a0v)-walk u,\u00a0v)-walk of length at most t in t-detour Assume that t-detour Directed Multiplicative Spanner.We obtain that for every mentclass2pt{minimDirected Multiplicative Spanner. By Observation\u00a0k distinct arcs t-detours G, t-detours in G. By Observation\u00a0G,\u00a0t,\u00a0k) is a yes-instance. For the opposite direction, assume that mentclass2pt{minimmentclass2pt{minimt arcs for each S|t arcs are marked in this step. In step (ii), we mark at most 3t arcs for each ordered pair of arcs of S. Hence, at most To upper bound the size of Since each of the reduction rules and Marking Procedure can be applied in polynomial time, we conclude that the total running time of our kernelization algorithm is polynomial. k arcs of G and verifies whether the deletion of these arcs gives a multiplicative t-spanner, we obtain the straightforward Directed Multiplicative Spanner. If we use the intermediate steps of the kernelization algorithm, then the running time may be improved (upto some constants in the exponent) to S of t-good arcs and execute Reduction Rule\u00a0S has size at most k, we check whether t-spanner by computing the distances between every pair of vertices. However, we can slightly improve the parameter dependence by making use of the random separation technique proposed by Cai, Chan, and Chan in\u00a0[Directed Multiplicative Spanner.Combining Theorem\u00a0mentclass2pt{minim Chan in\u00a0  be an instance of Directed Multiplicative Spanner. If G,\u00a0t,\u00a0k) is a yes-instance, and if G,\u00a0t,\u00a0k) is a no-instance. From now we assume that Let  is a yes-instance of Directed Multiplicative Spanner for  if and only if there are k arcs that have t-detours avoiding these arcs. We use random separation to distinguish the arcs that have t-detours and the arcs of the detours. We randomly color the arcs of G by two colors red and blue. An arc is colored red with probability k red arcs that have t-detours composed by blue arcs. Let R be the set of arcs colored red and let B the set of blue arcs. For u,\u00a0v) has a t-detour with blue arcs by finding the distance between u and v in S of all red arcs with blue t-detours. If G,\u00a0t,\u00a0k) is a yes-instance by Observation\u00a0By Observation\u00a0mentclass2pt{minimG,\u00a0t,\u00a0k) is a yes-instance of Directed Multiplicative Spanner. Then by Observation\u00a0k distinct arcs t-detours L are colored blue is at least t-detours are blue is at least t-detours blue is at most G,\u00a0t,\u00a0k) is a no-instance with the mistake probability at most Suppose that  be an instance of Independent Set and let G and denote For every construct a vertex construct for every For every Denote the obtained directed graph by D  is a yes-instance of Independent Set if and only if Directed Multiplicative Spanner.We claim that  be an instance of Independent Set and let Weighted Directed Multiplicative Spanner as follows. First, we construct D for G,\u00a0k) is a yes-instance of Independent Set if and only if Weighted Directed Multiplicative Spanner. For the second claim, we modify the above reduction. Let ..IndependG,\u00a0k) be an instance of Independent Set and let t be a positive integer. Denote by G.For every if if For every Denote the obtained directed graph by D  is a yes-instance of Independent Set if and only if  is a yes-instance of Directed Additive Spanner.Let -path in D contains at most one arc of S. The proof is by contradiction. Assume that there are u,\u00a0w)-path P such that P contains at least two arcs of S. Let P. Since the arcs of S correspond to vertices of the independent set I, G. Therefore, D contains the P is a shortest path containing P should have length at most We first claim that for every two vertices u and w be two vertices of D. Let P be a shortest -path in D. If P is a path in P is not a path in P contains a unique arc P and let P plus the length of t-spanner of D.Now let D,\u00a0t,\u00a0k) is a yes-instance of Directed Additive Spanner. Then there is a set of k arcs t-spanner. Observe that if D has an -path P that does not use the arc . Otherwise, G. Assume, for the sake of contradiction, that this is not the case and there are G. Let D. Since t-spanner. We conclude that I is an independent set of G and, therefore,  is a yes-instance of Independent Set. Now we assume that (Directed Multiplicative Spanner admits a kernel of size (Weighted) Directed Multiplicative Spanner is Multiplicative Spanner is FPT on general graphs when parameterized by k only for both undirected and directed cases. Also, is the weighted version of Multiplicative Spannerk and t on general graphs? Again, this question is open for both undirected and directed graphs.We proved that Directed Additive Spanner is Directed Additive Spanner is tractable on some special classes of directed graphs, like planar directed graphs. We believe that this problem may be interesting even if the distortion parameter t is assumed to be a constant.Further we proved that H of a directed graph G is a multiplicative t-roundtrip-spanner if for every two vertices u and v, H approximates the sum of the distances between any two vertices in both directions. Is the analog of Directed Multiplicative Spanner for roundtrip spanners G constructed as follows: construct two vertices u and v and an arc , and then add a -path v,\u00a0u)-path G. However, H has no short detour for . It is also possible to define additive t-roundtrip-spanners and consider the analog of Directed Additive Spanner. We conjecture that this problem is at least as hard as Directed Additive Spanner.Another possible direction of research is considering different types of directed graph spanners. For example, what can be said about the roundtrips spanners introduced by Roditty, Thorup, and Zwick\u00a0? A spannmentclass2pt{minim"}
+{"text": "Background: Low-rank approximation is used to interpret the features of a correlation matrix using visualization tools; however, a low-rank approximation may result in an estimation that is far from zero, even if the corresponding original value is zero. In such a case, the results lead to a misinterpretation. Methods: To overcome this, we propose a novel approach to estimate a sparse low-rank correlation matrix based on threshold values. We introduce a new cross-validation function to tune the corresponding threshold values. To calculate the value of a function, the MM algorithm is used to estimate the sparse low-rank correlation matrix, and a grid search was performed to select the threshold values. Results: Through numerical simulation, we found that the false positive rate (FPR), interpretability, and average relative error of the proposed method were superior to those of the tandem approach. For the application of microarray gene expression, the FPRs of the proposed approach with  It is essential in applications to compute the correlation matrix and present it with a heatmap  to underA low-rank approximation address problem (a) . VariousWhile the low-rank correlation matrix has the above advantages, (i) the number of correlation coefficients to be interpreted becomes problematic when the number of variables is large, making interpretation difficult, and (ii) according to the Eckart\u2013Young\u2013Mirsky theorem , the errTo overcome this, in this study, we proposed a new approach to estimate sparse low-rank correlation matrices. The proposed approach, combined with a heatmap, provides a visual interpretation of the relationships between the variables. There are two types of techniques available for the sparse methods of the correlation matrix and the covariance matrix ,10. The The proposed approach adopts an approach that uses hard thresholding based ,24 thereThe summary of the proposed method is as follows: for small sample sizes and noisy data, a sparse low-rank correlation matrix can be used to emphasize the correlation coefficients between related variables. In addition, the inclusion of sparse constraints eliminates the problem of misunderstanding and facilitates interpretation. Furthermore, the direct estimation of the correlation matrix instead of the covariance matrix reduces the computation time comparatively. We introduce a new cross-validation function to estimate sparse low-rank correlation matrices modifying those used in Refs. ,24. ThisThe rest of this paper is structured as follows. We explain the model and algorithm in In this section, we present the proposed approach for estimating a sparse low-rank correlation matrix. First, an estimation of a low-rank correlation matrix is described based on the MM algorithm ,4. Next,p is the number of variables. Here, d, \u2299 is the Hadamard product, Let rij)rij\u2208\u2212,1=f=iwijrijyj\u2264\u2212yi(t\u22121)quation (fi(yi|{yjiwijrijyj\u2264\u2212yi(t\u22121)Algorithm 1 Algorithm for estimating the low-rank correlation matrixInput:Output:Initialisation: Set j and set \u2003\u2003whiledo\u00a01:\u2003forp\u00a02:\u2003\u2003\u00a03:\u2003\u2003\u2003\u2003Calculate \u00a04:\u2003\u2003\u2003\u2003Calculate \u00a05:\u2003\u2003\u2003\u2003Update Equation .End for\u00a06:\u2003\u2003\u00a07:\u2003\u2003End while\u00a08:\u2003returnj\u00a09:\u2003Using the Lagrange multiplier method and Equation , the updWe adopt hard thresholding to estimate the sparse low-rank correlation matrix in the proposed approach. To determine threshold values, we introduce a cross-validation function based on Ref. . The purLet  science . Let Wh(fined asTh(\u03b1)(R)=p)wherer\u02dcij=rij\u00b7d, and the correlation matrix d, such as minimizing k represent the index of the number of iterations for cross-validation, and d, K times and the proposed cross-validation function is calculated as follows.K is the number of iterations for the cross-validation. Among the candidates for threshold values, Algorithm 2 Algorithm of Cross-validation for tuning proportional thresholdsInput: candidates of threshold values Output:Initialisation: Set \u2003\u2003Forto\u00a0\u00a01:\u2003ForK\u00a0\u00a02:\u2003\u2003\u00a0\u00a03:\u2003\u2003\u2003Split \u00a0\u00a04:\u2003\u2003\u2003Calculate both \u00a0\u00a05:\u2003\u2003\u2003Calculate Algorithm 1 is applied to estimate \u00a0\u00a06:\u2003\u2003\u2003Given End For\u00a0\u00a07:\u2003\u2003\u00a0\u00a08:\u2003\u2003calculate \u00a0\u00a09:\u2003\u2003End For10:\u200311:\u2003return12:\u2003To estimate a sparse low-rank correlation matrix, we introduce the modified proportional threshold operator based on Equation  because follows;Th(\u03b1),d. Then2, Ref.  determinfollows.CV(h(\u03b1),dFinally, Equation  among thEquation .This section presents a numerical simulation to evaluate the proposed approach. The numerical simulation was conducted based on Ref. , with soIn this subsection, the simulation design is presented. The framework of the numerical simulation consists of three steps. First, artificial data with a true correlation matrix are generated. Second, sparse low-rank correlation matrices are estimated using two methods, including the proposed method. In addition, a sample correlation matrix and sparse correlation matrix based on the threshold also apply. Third, using several evaluation indices, these estimated correlation matrices are evaluated and their performances are compared.I and J be a set of indices for the rows and columns of the correlation matrices, respectively. In addition, p. In this simulation, we set d, the result of the estimation In this simulation, three kinds of correlation models are used. Let e set asrij(1)=1\u2212,2,\u22ef,p),rij(2)=0.\u22ef,p)and,rij(3)=0.e set asrij(1)=1\u2212,2,\u22ef,p),rij(2)=0.al lasso ) = 18 paNext, the settings of the numerical simulation are presented. For the summary, see CVglasso package is used [R. The correlation matrix is then calculated from the estimated sparse inverse covariance matrix.Finally, in setting four, we selected five methods: the proposed approach, tandem approach, sample correlation matrix calculation, and the sparse correlation matrix estimation based on threshold value  with modst step. 1K\u2211k=1K\u2225W in Ref. . In the  on Ref. . In shorEquation  is used  in Ref. ). The se in Ref. . To sele is used  in R. ThLikewise, as in the approach pursued in Ref. , we adopEquation , EquatioEquation , and EquEquation , respectg index. Sparsity=g index. Sparsity=Here, we present the results of applying both the proposed approach and the tandem approach to the microarray gene expression dataset in Ref. . This reIn Ref. , the samG indicates the number of classes, such as NB, RMS, BL, and EWS, g, g for gene j, j, and g for gene j. Here, if j is considered as \u201cinformative\u201d because the corresponding j tends to include information such that each class is discriminated. From the calculated Next, to construct the \u201cinformative\u201d class and the \u201cnon-informative\u201d class, the F statistics are calculated for each gene, as follows:To compare the results of the proposed approach with those of the tandem approach, the FPR is calculated. For the tandem approach, see g index: withinclaThis section presents the results of the numerical simulation and real application.In this subsection, we present the simulation results by the true correlation models. For the relative error of the For the estimated correlation matrices, In this subsection, the results of the application of the microarray gene expression dataset are shown. For the estimated original correlation matrix, Jiang (2013) with modifications, the proposed approach tandem approach, and graphical lasso, see Next, This study proposed a novel estimation method for sparse low-rank correlations based on the MM algorithm. The approach overcomes the problem of estimating low-rank correlation matrices. The low-rank approximation is an a potent tool, and the approach provides us with a straightforward interpretation of the features because the contrast of the estimated coefficients becomes larger. However, these estimates sometimes lead to misinterpretations. Even if the true correlation coefficient is zero, the corresponding estimated coefficient of the low-rank approximation without sparse estimation may be greater than zero. To confirm the efficiency of the proposed method, we performed numerical simulations and experimented using a real example, which involved the use of a microarray gene expression dataset. In the case of the real example, the FPR of the proposed approach with Next, we refer to each method compared. The sample correlation matrix was used as a reference and for comparison. For Jiang (2013), concerning modifications, the numerical simulation results confirm that the F-norm and the S-norm are better than the proposed approach and the tandem approach because the low-rank approximation is not performed. Furthermore, Jiang (2013) with modifications is better than the sample correlation matrix without sparse constraints. Graphical lasso is a method for the sparse estimation of the inverse of the covariance, and the computed correlation matrix is not necessarily a sparse. Therefore, FPR, sparsity, and within-class sparsity were not good compared to the other methods through numerical simulations and examples of real-data applications. In other words, when a correlation matrix is estimated, it would be better to estimate a direct correlation matrix or a covariance matrix. The TPR, FPR, and sparsity of the tandem approach are almost identical to Jiang (2013) with modifications. The tandem method has a higher FPR than the proposed method and worse results for sparsity and within-class sparsity, which are indicators of interpretability. Furthermore, the proposed method performed better for the F-norm and the S-norm because the tandem method does not take threshold values into account. However, the numerical simulation results show that the TPR tends to be better than the proposed method.Here, we show the recommendations of the proposed approach. First, the proposed approach can provide the interpretable sparse low-rank correlation matrix from the result of both the sparsity of the numerical simulation and the within-class sparsity of the real example. Second, in a real example, the sparse low-rank correlation matrix estimated by the proposed approach was close to previous studies . HoweverAlthough the proposed approach showed promising results in both experiments, several limitations need further investigation. First, when the rank is set low, the TPRs of the proposed method were low compared to those of the tandem approach. The relationship between the determination of the rank and the corresponding TPR, F-norm, S-norm, sparsity, and within-class sparsity was a trade-off. Therefore, a method for a more effective determination of the rank should be developed. As one of the solutions to the problem, we can consider the introduction of a nuclear-norm regularization . Second,"}
+{"text": "Deep neural networks have been successfully applied to generate predictive patterns from medical and diagnostic data. This paper presents an approach for assessing persons with Alzheimer\u2019s disease (AD) mild cognitive impairment (MCI), compared with normal control (NC) persons, using the zoom-in neural network (ZNN) deep-learning algorithm. ZNN stacks a set of zoom-in learning units (ZLUs) in a feedforward hierarchy without backpropagation. The resting-state fMRI (rs-fMRI) dataset for AD assessments was obtained from the Alzheimer\u2019s Disease Neuroimaging Initiative (ADNI). The Automated Anatomical Labeling (AAL-90) atlas, which provides 90 neuroanatomical functional regions, was used to assess and detect the implicated regions in the course of AD. The features of the ZNN are extracted from the 140-time series rs-fMRI voxel values in a region of the brain. ZNN yields the three classification accuracies of AD versus MCI and NC, NC versus AD and MCI, and MCI versus AD and NC of 97.7%, 84.8%, and 72.7%, respectively, with the seven discriminative regions of interest (ROIs) in the AAL-90. Neuroscience has provided inspiration for and insight into artificial neural networks, including deep-learning networks. However, the field of artificial neural networks has been optimized through mathematics rather than neuroscientific findings . In addiDeep-learning algorithms with a hierarchical architecture are exploited as representative learning schemes, including restricted Boltzmann machines (RBMs), using local unsupervised pretraining layers from the bottom to top layers ,6,7. A dA simple feedback alignment mechanism that adjusts weights by multiplying errors with even random synaptic weights performs as effectively as backprop . The algAs one of the features of deep-learning algorithms used in unsupervised learning, the pretraining is determined by starting with random weights. Biological learning is more advantageous for the optimization of weight initialization due to large numbers of trials and errors. However, because backprop consumes considerable time to correct the weights after initialization, optimization using various weight initializations is difficult to achieve.An intuitive way to consider diverse brain learning paradigms is to find another sup-pattern that is different from the main pattern. For example, ambiguous forms for a particular pattern can be learned through a more detailed look using a magnifying glass. This allows us to make more accurate judgments by learning the causes from a misjudgment, prejudice, or misclassification. In other words, learning can come from mistakes that are to be discarded or ignored. At the same time, it is possible to learn more precisely only through the refined instances. This paradigm reinforces learning efficiency through rewards, from both mistakes and well-learned domains simultaneously.According to Wikipedia, the dictionary meaning of metacognition is an awareness of one\u2019s thought processes and an understanding of the patterns behind them. When metacognition is applied to a person, it means that the person understands his or her learning process or judgment process or thinking process. This concept was applied to the learning algorithm in this paper. We propose a feedforward zoom-in neural network (ZNN) deep-learning algorithm that implements a learning paradigm called metacognitive learning. A ZNN stacks layers, each of which consists of a set of zoom-in learning units (ZLUs) in a feedforward manner. In a ZLU, meta-cognitive information is accumulated through subpattern learning and fine-tuning learning according to the learning results after learning occurs. Through subpattern learning, another pattern is found as meta-cognitive information from errors in standard learning. Through fine-tuning learning, a more detailed pattern for standard learning is found as meta-cognitive information.The outputs of the ZLUs in a layer are forwarded to a higher layer to achieve a gradual improvement in the discrimination power. This brings about a dimensionality reduction with structural flexibility by decreasing the number of ZLUs as the learning of the ZNN moves to higher-level layers .In this paper, a deep-learning model based on a neural network with weighted fuzzy membership functions (NEWFMs)  is propoThe proposed ZNN is a supervised feedforward deep-learning system using ZLUs implemented by the NEWFMs. The structure of the ZNN, illustrated in The basic processes of the ZNN are executed by the neuronal ZLU module. Each ZLU generates two subpatterns and a refined defuzzified output for the next layer. The subpatterns and the refined defuzzified output include metacognitive information.A ZLU consists of two-part learning, as shown in The first advantage of a ZLU module is that the load of learning can be distributed to the ZLUs according to the divided input features. Second, a ZLU module can be assembled flexibly to find a pattern of functional connectivity of neural networks. As the third advantage, the cost function for each ZLU module could first be applied locally, which may follow the cognitive processes of the human brain learning inferences of a hierarchical principle by fusing or filtering out of the local decisions .As the main contribution of ZLU, it applies a zoom-in learning process. A neuroscience basis for the learning scheme in the human brain is provided by the metacognitive learning method that monitors uncertainty regarding a decision ,20, as iZLU is a basic unit module of the ZNN algorithm. Each ZLU module generates two types of subpatterns and refined outputs for the next ZLU layer. The layerwise supervised learnings in ZNN are executed to improve the learning ability by zooming in on the input patterns using the ZLUs. Feedforward learning of a ZNN without backpropagation in deep-learning algorithms provides an efficient learning method by eliminating the vanishing gradient problem.The ZNN algorithm is divided into training and testing parts, i.e., a training algorithm and test algorithm of the ZNN, respectively. Algorithms 1 and algorithm 2 show train and test algorithms. To describe the training and testing that takes place in a ZLU, once the standard training, instance grouping, and zoom-in training are completed in a ZLU, as indicated by the solid lines in Train Algorithm of ZNNAlgorithm 1: Input Layer\u20031.1 Split train input data with n features into the k subsets with\u2003\u2003\u2003n/k features such that {I0,1}, {I0,2}, \u2026, {Ik0,}2 i-th ZLU layer \u20032.1 Let ZLUi,j be j-th ZLU in i-th ZLU layer\u20032.2 For each {Ii\u22121,j}, where j = 1 to k\u2003\u20032.2.1 Assign {Ii\u22121,j} to ZLUi,j as input\u20032.3 For eachZLUi,j, where j = 1 to k\u2003\u20032.3.1 Standard training\u2003\u2003\u20032.3.1.1 Standard training using NEWFMi,j from {Ii\u22121,j}\u2003\u2003\u20032.3.1.2 Instance grouping: divide {Ii\u22121,j} instances into\u2003\u2003\u2003\u2003\u2003\u2003misclassified instances (MI) {Mi,j} and correctly\u2003\u2003\u2003\u2003\u2003\u2003classified instances (CCI) {Ci,j}\u2003\u20032.3.2 Zoom-in training\u2003\u2003\u20032.3.2.1 Subpattern training from {Mi,j} using\u2003\u2003\u2003\u2003\u2003\u2003NEWFMi,j,M\u2003\u2003\u20032.3.2.2 Refine training from {Ci,j} using NEWFMi,j,C\u2003\u20032.3.3 Zoom-in output\u20032.3.3.1 Output TSD {Ti,j,M} using NEWFMi,j,M from {Ii\u22121,j}\u20032.3.3.2 Output TSD {Ti,j,C} using NEWFMi,j,C from {Ii\u22121,j}\u20032.4 Split the TSDs {Ti,1,M, Ti,1,C, Ti,2,M, Ti,2,C, \u2026, Ti,n,M, Ti,n,C}\u2003\u2003\u2003into {Ii,1}, {Ii,2}, \u2026, {i,nI}, where n is the number of ZLUs\u2003\u2003\u2003in the (i + 1)-th ZLU layer\u20032.5 i = i + 1, k = n, and go to 2 until predefined i is reached3 Output Layer\u20033.1 Train by the NEWFMi using {Ii\u22121,1}, {Ii\u22121,2}, \u2026, {Ii\u22121,k}1 Test Algorithm of ZNNAlgorithm 2: Input Layer\u20031.1 Split test input data with n features into the k subsets with\u2003\u2003\u2003n/k features such that: {I0,1}, {I0,2}, \u2026, {Ik0,} as in 1.1 ofTrain Algorithm of ZNN\u2003\u2003\u20032 i-th ZLU Layer \u20032.1 For each {Ii\u22121,j}, where j = 1 to k\u2003\u20032.1.1 Assign {Ii\u22121,j} to ZLUi,j as input\u2003\u20032.1.2 Zoom-in test:\u2003\u2003\u20032.2.2.1 Output TSD {Ti,j,M} using NEWFMi,j,M from {Ii\u22121,j}\u2003\u2003\u20032.2.2.2 Output TSD {Ti,j,C} using NEWFMi,j,C from {Ii\u22121,j}\u20032.2 Split the TSDs {Ti,1,M, Ti,1,C, Ti,2,M, Ti,2,C, \u2026, Ti,n,M, Ti,n,C}\u2003\u2003\u2003into {Ii,1}, {Ii,2}, \u2026, {Ii,n}, where n is the number of ZLUs\u2003\u2003\u2003in the (i + 1)-th ZLU layer\u20032.3 i = i + 1, k = n, and go to 2 until the output layer is reached3 Output Layer\u20033.1 Output TSD {Ti} by the NEWFMi using {Ii\u22121,1}, {Ii\u22121,2}, \u2026,\u2003\u2003\u2003{Ii\u22121,k}1 In this section, the experimental results for assessing persons with Alzheimer\u2019s disease (AD) and mild cognitive impairment (MCI), compared with normal control (NC) persons, using the proposed ZNN deep-learning algorithm, are presented to evaluate the ZNN algorithm with the discriminative regions of interest in the Anatomical Automatic Labeling (AAL-90) model.The experimental dataset contains the resting-state functional magnetic resonance imaging (rs-fMRI) data concerning 34 AD patients, 89 MCI patients, and 45 NC persons. It was obtained from the Alzheimer\u2019s Disease Neuroimaging Initiative (ADNI) database . The rs-To obtain an overall change in each ROI with 2000 to 3000 voxels, the average of voxels (AOV) of each ROI was generated as a representative signal of the ROI. The features were extracted using the Haar wavelet transform (HWT) from the 140-time series of AOVs. In addition, the local and global graph measures  were useThe series of experimental structures led to a 140-time series of ROIs, AOVs, feature extraction, feature selection, region selection, and ZNN classification, as shown in From the 140-time series of AOVi of ROIi a,b, the Finally, the highly accurate ROIs that were candidates for discriminative ROIs for AD assessments were selected for input into the ZNN model e,f. In pAD assessments by the proposed ZNN model have three pairs of classifications: AD versus NC-MCI (A-NM), NC versus AD-MCI (N-AM), and MCI versus AD-NC (M-AN). The ZNN model was run with a hold-out verification method by setting 23 subjects in the dataset as training sets and the rest  as test sets.ZNN yielded the three classification accuracies of A-NM, N-AM, and M-AN as 97.7%, 84.8%, and 72.7%, respectively, as shown in The increases in accuracy with the stacking of ZLU layers are shown in Ref.  shows 96The 16 most prominent ROIs in the AAL-90 were selected in accordance with the accuracies of the ROIs in Some of the ROIs in a column in The most discriminating ROI in http://nitrc.org/projects/bnv accessed on January 2020) was used to create the images of the ROIs.In this paper, we proposed a deep neural network model, ZNN, to classify Alzheimer\u2019s diseases, which is a new feedforward deep-learning model using brain-inspired metacognitive learning. The ZNN, model without a gradient descending problem in backprop, simulates activity-dependent learning using ZLU units, such as the synaptic plasticity in the brain. A neuroscientific basis for the learning scheme of the metacognitive learning in the human brain  is impleIn addition, the ZLU units enhance the connectivity of the neural networks by connecting the block-type neural network units in a flexible manner. In the proposed model, by using 10 graphic features and h\\Haar wavelet coefficients together as classification features, we obtained the effect that the regional characteristics of the brain were more clearly reflected in the classification through the Haar wavelet. The proposed model can also be used to evaluate other diseases. The features used in this method are features that can be extracted from images and numerical data. As the data used for the classification of diseases are mostly image or numerical data, it is possible to apply this model.The proposed algorithm yields a 97.7% classification accuracy for AD versus SCI-MCI, 84.8% classification accuracy for SCI versus AD-MCI, and 72.7% classification accuracy for MCI versus AD-SCI, using the discriminative ROI specifications in the AAL-90. Thus, ZNN learns more efficiently through the zoom-in learning processes following a human-like approach in the way it acts. A further matter to be considered is that AD and SCI are classifications in which symptoms are clearly distinguished. However, as MCI is an intermediate state between AD and SCI, the accuracy of the classification of MCI and others is lower than that of AD and SCI. Another document that shows that the MCI classification results are relatively low is .The importance of classification of MCI is gradually increasing. Accurate classification of MCI enables early diagnosis or prevention of dementia. This can slow the progression of dementia, alleviate symptoms, or increase the probability of a cure. Therefore, improving the classification accuracy of MCI is a future research task.One limitation in this study was that the number of data used was not balanced. We need to balance the data with additional up-to-date data from ANDI. Recent data are continuously accumulating on the ANDI site, and it is necessary to experiment with the accumulated data. We have one more limitation: As the datasets collected from ANDI were not all from the same machine , they ma"}
+{"text": "Nature Communications 10.1038/s41467-022-32162-x, published online 30 July 2022Correction to: The original version of the\u00a0These errors have been corrected in the PDF and HTML version of the article, and the HTML has been updated to include a corrected version of the\u00a0Updated Supplementary Information"}
+{"text": "Although language-family specific traits which do not find direct counterparts outside a given language family are usually ignored in quantitative phylogenetic studies, scholars have made ample use of them in qualitative investigations, revealing their potential for identifying language relationships. An example of such a family specific trait are body-part expressions in Pano languages, which are often lexicalized forms, composed of bound roots  and non-productive derivative morphemes . We use various statistical methods to demonstrate that whereas body-part roots are generally conservative, body-part formatives exhibit diverse chronologies and are often the result of recent and parallel innovations. In line with this, the phylogenetic structure of body-part roots projects the major branches of the family, while formatives are highly non-tree-like. Beyond its contribution to the phylogenetic analysis of Pano languages, this study provides significative insights into the role of grammatical innovations for language classification, the origin of morphological complexity in the Amazon and the phylogenetic signal of specific grammatical traits in language families. It comprises approximately 33\u201334 (extant and dormant) languages from neighbouring territories in eastern Peru, western Brazil and northern Bolivia. There have been various internal classification proposals for the Pano language family in the literature, but there is no full agreement on the structure of the Pano phylogenetic tree, the classification of some languages, and the number of major branches \u20135. This figure 1Pano languages exhibit a significant list of shared grammatical features, which may be suggesting a shallow time-depth . Among tm\u0268k\u0268n, which is synchronically non-segmentable, but can be diachronically analysed as the combination of the root m\u0268- \u2018hand\u2019 and the formative -k\u0268n. The root m\u0268- \u2018hand\u2019 can also function as a prefix and as such it can be attached to nouns , and verbs (m\u0268-t\u00e1\u0283ka \u2018to slap on the hand\u2019 [< t\u00e1\u0283ka \u2018to slap\u2019]). Many expressions related to external body-parts exhibit a similar pattern: Iskonawa t\u0268hu \u2018neck\u2019 (t\u0268-hu), Kapanawa hana \u2018tongue\u2019 (han-a) and Poyanawa k\u0268ha \u2018mouth\u2019 (k\u0268-ha). The forms t\u0268- \u2018neck\u2019, han- \u2018tongue\u2019, k\u0268- \u2018mouth\u2019 are synchronic body-part prefixes in those languages and, thus, they can be combined with further nouns, verbs and adjectives .t\u0268-, but we find substantial variability regarding the formatives recruited for the formation of the lexicalized body-part expressions . In some other instances, the root itself exhibits variation across the languages . We also find full lexical innovations, for instance, piti \u2018food\u2019 is the word for \u2018tooth\u2019 in Chaninawa, Mastanawa, Sharanawa, Yaminawa and Nawa; while t\u0268tun \u2018neck\u2019 in Matis is \u2018Adam's apple\u2019 in Shipibo-Konibo. Finally, there are some cases of stable lexicalized forms in which both the root and the formative are shared by all or almost all the languages in our database . At least some of these stable forms might have originated as monomorphemic words (see the discussion in 4.1).Body-part roots and body-part formatives do not exhibit the same history and the same chronology. We often encounter that body-part roots are stable across languages while body-part formatives may exhibit significant cross-linguistic variation. For example, all the terms for \u2018neck\u2019 in the Pano languages in our database share the body-part root ma \u2018head\u2019, *\u03b2u \u2018hair\u2019 and *\u03b2\u0268 \u2018eyes, forehead\u2019. In addition, there are four formatives combined with them: -\u0282o, -pi, -pu and -\u0282ka. As an illustration of the intricacies of body-part terms for Pano classification, In this paper, we explore the history of body-part expressions in Pano aiming to quantify and understand their diachronic development. We tease apart the phylogenetic behaviour of the roots and the formatives, and we implement data analysis and clustering techniques to measure their stability. We then explore how tree-like these roots and formatives are, and investigate their potentiality for shedding light on the phylogeny of the Pano languages and for contributing to further topics in the linguistic history of Amazonia. Body-part concepts are often claimed to be basic vocabulary and therefore they are expected to be stable and conservative , p. 132.. 2. 2.1https://digling.org/edictor). The conversion procedure required, among others, to standardize phonetic transcriptions by segmenting distinct sounds from each other (by adding spaces) and by using the B(road)IPA transcription system proposed by the Cross-Linguistic Transcription Systems reference catalogue ([https://clts.clld.org). With the help of the EDICTOR tool, the data were then annotated for partial cognancy. EDICTOR simplifies not only the annotation of partial cognates but also allows to add information on individual morphemes in the form of so-called morpheme glosses\u2014short glosses, by which the basic meaning or function of individual morphemes can be characterized for the purpose of historical language comparison [We constructed a comparative database of a total of 26 Pano language varieties. This database contains lexical data based on concept list of 181 items (including 25 concepts related to the body). These data were automatically pre-processed by converting the tabular data that had been originally collected into long-table formats that are required by the LingPy software package ,10 and ttalogue  and M(formative), with 26 rows and 26 columns, in which each entry represents the aggregated Hamming distances between a pair of language varieties. With this, we compare both distributions of pairwise distances using a histogram. We used a t-test, implemented in SciPy [To serve as a first quantitative approach to the variability displayed by the morphological structure of body parts in the Pano family, using root and formative-based representations, we developed a simple exploratory analysis based on the Hamming distance . The feain SciPy , to quanSecond, to assess the relative prevalence of the cognate sets in each dataset, we calculated the number of languages contained in each cognate set. Cognate sets that connect many languages will likely derive from a deep branch in the tree, and are therefore useful for recovering the deeper structure in the phylogeny. By contrast, smaller cognate sets that connect fewer languages will tend to be more recent innovations that are therefore useful for refining the fine structure of the tree topology.sklearn library [Third, we applied a principal component analysis (PCA) to the distance matrix M, in order to visualize the overall similarity in the roots and formatives for the internal organization of the Pano family. This method allows us to represent languages in a two-dimensional space, in which location proximity indicates languages with a closer body-part morphological structure (in terms of roots and formatives). We used the PCA implementation of the  library .We finally calculate and plot \u03b4 scores ,38 for b. 3. 3.1U-test  confirms this observation. Thus, based on these results, we conclude that roots are more similar lexically and phonetically across languages 1To quantitatively measure the differences between root and formative-based representations of morphological structure of the Pano family, we look at the distribution of the (average) Hamming distance between any pair of languages. On average root-based distances are shorter than formative-based distances: mean root-based distances = 0.14 (s.d. = 0.089) versus mean formative-based distances = 0.17 (s.d. = 0.0829). A Mann\u2013Whitney U-test  and is plotted in Next, we quantify the size of cognate sets in the dataset (i.e. how many languages does each cognate set contain?). We find that, on average, roots connect more languages in a given cognate set: median root size = 2.5 (s.d. = 9.75) versus median formative size = 1 (s.d. = 6.84). This difference is significant under a two-tailed Mann\u2013Whitney . 3.2To gain deeper insight into the internal organization of the morphological structure of body-part terminology among Pano languages, we describe the low-dimensional representation of the root and formative-based distance matrices using PCA . The fig. 3.3At this stage, the radically different story of roots and formatives in body-part terms becomes clear. Roots are less internally variable (i.e. more stable) than formatives . Furthermore, we find significant differences in how languages cluster together when they are viewed as root-based and formative-based low-dimensional representations . Although these results are suggestive of some possible diachronic scenarios, it is necessary to further explore the phylogenetic behaviour of each set of forms in order to arrive at any definitive interpretation. Aiming to test the tree-likeness of body-part roots and body-part formatives we calculated \u03b4 scores ,38 for t. 4. 4.1hana \u2018tongue\u2019, for instance, which comes from the combination of a body-part root han- and the formative -a, is systematically attested (with predictable sound variation) in all the languages of the family. In cases like this, it is out of question that the protolanguage had already lexicalized the form *hana. At this stage, however, we cannot totally leave out the possibility that *hana \u2018tongue\u2019 was indeed originally a monomorphemic word Our quantitative experiments demonstrate that body-part roots are more conservative than body-part formatives, which are often innovative and can be attributed to specific language(s) within the family. The instability of formatives is likely behind their low tree-likeness. This, however, does not mean that the processes of body-part lexicalization postulated here happened at once. Although it is true that a good number formatives were recruited by independent languages in a relatively recent period , some lexicalized body-part terms can be traced up to the protolanguage. The form hana \u2018tongue\u2019 is not unique. Indeed, the form ta\u0268, which might be analysed as the combination of the body-part root ta- and the formative -\u0268, is also attested in all the Pano languages in our sample and therefore *ta\u0268 is also unequivocally a proto-form. A similar situation is found in association with other lexicalized forms, which are attested in several languages from various branches: \u03b2\u0268-ru \u2018eye\u2019 (attested in 23 languages), *\u0282\u0268-ta \u2018tooth\u2019 (attested in 22 languages), *r\u0268-kin \u2018nose\u2019 (attested in 19 languages), *in-a \u2018tail\u2019 (attested in 18 languages), *p\u0268-i \u2018feather\u2019 (attested in 18 languages) and *ki-\u0283i \u2018upper leg\u2019 (attested in 16 languages). Although some of these forms might have been originally monomorphemic (Cf. *hana \u2018tongue\u2019 and *ta\u0268 \u2018foot\u2019), other forms like *\u0282\u0268-ta \u2018tooth\u2019 or *r\u0268-kin \u2018nose\u2019 fully satisfy the definition of lexicalized form, and thus constitute evidence that the lexicalization process that gave rise to (some) body-part terms in Pano started relatively early.The form *m\u00ebk\u00ebn (Amawaka), m\u00ebdante (Matses), m\u00ebbi (Shanenawa); or \u2018nose\u2019 r\u00ebkin (Kapanawa), r\u00ebxan (Matis), r\u00ebchoko (Yaminawa)).At least some of the lexicalization processes that shape the evolution of body-part terminology in Pano happened in the protolanguage before it began to diverge. This necessarily implies that the construction in which a monosyllabic body-part root was combined with extra morphological material  was productive in a very early stage of the development of the Pano lineage. Therefore, it may have been inherited by modern Pano languages, thus providing the construction frame for future innovative lexicalizations based on conservative roots. Innovative lexicalizations seem to be abundant and this explains the non-tree-like nature of formatives, which are in constant renovation and change. This is why, as explained, while body-part roots are reflected by cognate sets that are largely invariant, body-part formatives may show a great degree of variation  eye, face\u2019 participates in lexicalized body-parts like: b\u0268-ru \u2018eye\u2019, b\u0268-un \u2018tear\u2019, b\u0268-s\u00b8ha \u2018rheum\u2019, b\u0268-mana \u2018face, forehead, front\u2019, b\u0268-bun \u2018in front of\u2019. The lexicalization processes described here have to do with the development of new terms as a strategy to denote more specific body parts and related concepts.A question that still remains open would be why body-part roots became combined with extra morphological material to produce new terms in the first place. This seemingly has to do with the need to refer to specific body parts. One of the challenges in the study of body-part terms has to do with the clear delimitation of their semantics . Pano bkin (< kini \u2018hole\u2019), -\u0282a\u223c-\u0282ka (< \u0282aka \u2018skin\u2019), \u0282u , puku (< puku \u2018belly\u2019), manan (< manan \u2018upper part\u2019) and probably -iwi . Note that in some cases the formative is a reduced version of the original form, but this is not surprising, since synchronic body-part prefixes (which come from body-part roots), may reduce the form of some roots when attached to them [A further question would then have to do with the origin of the formatives involved in these lexicalization processes. Most of these formatives are currently non-productive and exhibit an opaque semantic value. This, however, was not necessarily the case when the morphological process from which most body-part terms evolved was fully productive. Although most formatives remain semantically enigmatic, some of them can be attributed to nominal expressions, as is the case with - to them . Formati. 5. 5.1It is well-known that a relatively clear-cut criterion for distinguishing Western and Eastern Amazonian languages has to do with their overall morphological profile . More sp. 5.2Since early approaches to historical linguistics, shared innovations were considered the gold standard for language clustering and tree topologies. Shared innovations are innovations that occurred in a stage that precedes language splitting, so they are likely to be inherited by the resulting linguistic varieties. Not all innovations, however, are \u2018shared\u2019 in the sense just specified. The possibility of finding the same innovation in two or more related languages as the result of independent processes is also a possibility making the task of clustering languages based on innovations a non-trivial one.ma \u2018related to head/upper area\u2019 + puku \u2018belly\u2019 which seems to be the etymology of modern term mapu \u2018head\u2019, the motivation may be found in the round shape that heads and bellies share. On the other hand, if one uses the compound ma \u2018related to head/upper area\u2019 + xaka \u2018skin\u2019 which seems to be the etymology of modern maxka \u2018head\u2019, then the motivation comes from the fact that heads are covered by skin. Such motivated compounds that lexicalized into modern terms for \u2018head\u2019 in various Pano languages can easily have happened in two or more varieties independently. As Pano body-part terminology seems to demonstrate, motivated compounds like the ones associated with some of the body-part terms in Pano seem to be more amenable to parallel development. This fully coincides with one of the major findings of this paper: according to their \u03b4 scores, Pano body-part formatives are poorly tree-like. Pano body-part terminology may, thus, be a productive domain to test hypotheses regarding the nature of grammatical innovations and their role in language classification, but also proves that \u03b4 scores may be recruited to distinguish between shared and parallel innovations in comparative databases.This study demonstrates that in the process of coining body-part terms in Pano, so-called body-part formatives exhibit a complex and diverse chronology and that indeed a good number of them are innovative. Nevertheless, they are less tree-like in terms of their distribution and internal structure, thus suggesting that although they may be attested in two or more languages, they do not satisfy the expectations that one would have for shared innovations. Why, then, did the process of coining body-part terms through innovative morphological combinations trigger so many instances of \u2018false\u2019 shared innovations? One possible answer to this question that may provide interesting insights into the nature of linguistic innovations may relate to the origin of the formatives. As argued in \u00a75.2, at least some of these formatives clearly come from nouns, thus suggesting that the various instances of synchronic body-part terms were indeed nominal compounds. The crucial point here is that these compounds are not totally arbitrary. If one uses the compound . 5.3In this paper, we use various statistical methods to demonstrate that body-part roots are generally conservative traits that can be attributed to the protolanguage, while formatives exhibit diverse chronologies, being the case that a number of them are the result of recent and parallel innovations. Language-family-specific traits are usually ignored in quantitative phylogenetic studies. The independent analysis of body-part roots and body-part formatives led us to argue that they exhibit different levels of tree-likeness and therefore cope in different degrees to the understanding of Pano phylogeny. The use of family specific traits proves to be significant for phylogenetic studies. Our results suggest that body-part roots are expected to provide a better classification of Pano languages than body-part formatives, and crucially this is exactly the case as shown in . 6Here we have explored the complex diachronic story of body-part expressions in Pano languages using both quantitative methods and analytical tools from historical linguistics. Body-part expressions in Pano languages are often lexicalized forms, composed by monosyllabic bound roots and semantically opaque morphological formatives. We have demonstrated here that body-part roots and body-part formatives exhibit different diachronic trends: body-part roots are generally conservative forms that can be attributed to the protolanguage, while formatives exhibit a diverse historical signal in the sense that some are retentions from the protolanguage, but a good number of them are recent and parallel innovations in one or a few languages. The diachronic nature of the formatives is behind their highly non-tree-like nature. Based on these results, we provided a full diachronic account of body-part expressions, arguing that while body-part root are generally retentions from the protolanguage, lexicalized body-part terms, which combine roots and formatives, evolved throughout a large period of time. Lexicalized body-part expressions come from a body-part noun compounding process, which was already productive in the protolanguage (see ). Our re"}
+{"text": "Extracting detailed information from remote sensing images is an important direction in semantic segmentation. Not only the amounts of parameters and calculations of the network model in the learning process but also the prediction effect after learning must be considered. This paper designs a new module, the upsampling convolution-deconvolution module (CDeConv). On the basis of CDeConv, a convolutional neural network (CNN) with a channel attention mechanism for semantic segmentation is proposed as a channel upsampling network (SCU-Net). SCU-Net has been verified by experiments. The mean intersection-over-union (MIOU) of the SCU-Net-102-A model reaches 55.84%, the pixel accuracy is 91.53%, and the frequency weighted intersection-over-union (FWIU) is 85.83%. Compared with some of the state-of-the-art methods, SCU-Net can learn more detailed information in the channel and has better generalization capabilities. Remote sensing image processing technology has developed rapidly. The image semantic segmentation approach based on CNN has become a hot research direction in satellite remote sensing image semantic segmentation , and it Recently, the deep learning method has performed well in the computer vision recognition task, and CNN has achieved very good results in image classification \u20139, semanThere are many important methods of image processing, among which image semantic segmentation is one. Semantic segmentation is to divide the pixels in the image and predict the category of each pixel in the image using the neural network , which iInspired by these studies, this paper proposes a new method for semantic segmentation of satellite remote sensing images. In the task of semantic segmentation of satellite remote sensing images, the improved upsampling method proposed in this paper not only reduces the number of model parameters but also improves the recognition ability of the model. Based on the new upsampling module, a novel image semantic segmentation model and introduced attention mechanism are proposed. In addition, a new remote sensing image dataset is provided, which shows the remote sensing information of Chenzhou, China. These satellite remote sensing images come from China's GF-2 satellite with a spatial resolution of 0.8 meters, showing various spatial information of cultivated land, forest land, waters, buildings, etc. The original images in the dataset are labeled based on local geomorphological features. Finally, the method in this article was tested on this dataset. Compared with other semantic segmentation methods based on deep learning, SCU-Net has better segmentation performance and stronger generalization ability.This section will, firstly, introduce the structure of FCN. Secondly, the structure and principle of SCU-Net proposed in this paper are introduced. Finally, the network complexity of SCU-Net is analyzed through experiments.The main difference between the FCN network and the traditional deep learning convolutional network is that it does not use a full connection layer. The FCN network adds an upsampling method to the network structure. The output image has the same size as the original input image, which realizes pixel classification. FCN is mainly composed of the feature extraction module of the ordinary convolutional network, upsampling, and skip connection. H\u2009\u00d7\u2009W, the original image will be reduced to (H\u2009\u00d7\u2009W)/2 after the \u201cConv1\u201d and \u201cMaxPooling\u201d operations. Then, the feature map is reduced to (H\u2009\u00d7\u2009W)/4 through the operations of \u201cconv2\u201d and \u201cMaxPooling.\u201d By using the \u201cConv3\u201d and \u201cMaxPooling\u201d operations, the output feature map \u201cfeatureMap-3\u201d with reduced size (H\u2009\u00d7\u2009W)/8 can be obtained. Then, \u201cConv4\u201d and \u201cMaxPooling\u201d operations are performed to reduce the size of the feature map to (H\u2009\u00d7\u2009W)/16, and the output feature map is named \u201cfeatureMap-4.\u201d In the next step, the feature map goes through \u201cConv5\u201d and the last \u201cMaxPooling\u201d operation, and the feature map, namely \u201cfeatureMap-5,\u201d will be reduced to (H\u2009\u00d7\u2009W)/32.The first operation is feature extraction. If the input image size is H\u2009\u00d7\u2009W)/8. Next, \u201cfeatureMap-5\u201d performs the \u201cUpsampling-2\u201d operation to obtain the feature map \u201cfeatureMap-7\u201d whose size is (H\u2009\u00d7\u2009W)/8. Then, \u201cfeatureMap-6\u201d and \u201cfeatureMap-7\u201d are stitched together. Finally, the \u201cUpsampling-3\u201d operation is performed on the output result to output the feature map. The size of this feature map is the same as the original image, and the semantic segmentation is completed.After the feature extraction is completed, the upsampling operation is performed. First, the \u201cUpsampling-1\u201d operation is performed on \u201cfeatureMap-4\u201d to obtain a feature map \u201cfeatureMap-6\u201d with a size of  is introdThe CFWE module is a multilayer structure. The first is the short connections layer of the CFWE. It contains 3 convolutional layers, of which, there are two conv1 and one conv3. The two \u201cconv1\u201d in the module are used to increase and decrease the number of channels, respectively, with the purpose of reducing the amounts of parameters. The shortcut connections layer can alleviate the network degradation problem to a certain extent. Next comes the serial pool layer and full connection layer structure, which consists of two \u201cFC\u201d structures and a \u201cGAP\u201d structure. Firstly, the feature map of each channel is processed as a global feature using the \u201cGAP\u201d structure. Then, the feature dimension is reduced through the first \u201cFC\u201d layer, and the feature dimension is restored by the second \u201cFC\u201d layer. The weight coefficient model of each channel can be learned after passing through two \u201cFC\u201d layers. Finally, the final output feature map is to multiply the original feature and the extracted feature map channel weight coefficients by short connections. When extracting features, the weight coefficient is useful for the model to extract more important channel features and then enhance the feature extraction ability of the network.In the traditional semantic segmentation neural network, the upsampling step is divided into two steps. Firstly, the feature map size is up-sampled to the original image size, and then point convolution is performed to complete the semantic segmentation. The parameters and calculations of the network model using this method are relatively large. The \u201cCDeConv\u201d module proposed, firstly, performs point convolution to make the number of feature map channels consistent with the number of segmentation task categories, and then, it performs deconvolution to make the output feature map size consistent with the original image size. This module not only reduces the number of model calculations and parameters but also improves model performance. Its structure is shown in k equal to 7 and a stride equal to 2. \u201cConv1\u201d is a \u201cConv\u201d structure with k equal to 1 and a stride equal to 1. \u201cConv1-3-1\u201d is a structure consisting of \u201cConv1,\u201d \u201cConv3,\u201d and \u201cConv1\u201d in series. One of the two \u201cConv1\u201d structures is used to increase the dimensionality and the other can decrease the dimensionality. This operation can reduce the complexity of the model. \u201cConv3\u201d is used for feature extraction. \u201cMaxpooling\u201d means the maximum pooling layer with a step size of 2 and a window size of 3. Its main function is to upsample, reduce dimensionality, and reduce the amount of calculation. \u201cUpsampling\u201d represents an 8 times upsampling module, and its function is to upsample the feature map to the same size as the original image to achieve semantic segmentation.According to the CFWE module and the \u201cCDeConv\u201d module, a novel semantic segmentation network model SCU-Net is proposed, whose structure is shown in X and the size is H\u2009\u00d7\u2009W\u2009\u00d7\u20093, it, firstly, passes through the \u201cConv7\u201d module with 64 convolution kernels. The step size is 2, and the convolution kernel size is 7. Set the output feature map of the \u201cConv7\u201d module to X1. The size becomes H/2\u2009\u00d7\u2009W/2\u2009\u00d7\u200964, which is shown as follows:If the input image is X2 will become 0.25 times that of X1, as shown below.After a maxpool layer, the number of channels will not change, however, the size of the output feature map n  serially connected \u201cConv1_3_1,\u201d the output size of the feature map is H/4\u2009\u00d7\u2009W/4\u2009\u00d7\u2009256. Next, the output X3 can be obtained by using CFWE module. Its feature map size is H/4\u2009\u00d7\u2009W/4\u2009\u00d7\u2009256, which can be expressed as follows:Then, through X3 is input to the n series of \u201cConv1_3_1\u201d modules, and then through a layer of CFWE module, the output feature map X4 has a size of H/8\u2009\u00d7\u2009W/8\u2009\u00d7\u2009512, which can be expressed as follows:After that, the feature map X4 is input to the n series of \u201cConv1_3_1\u201d modules, and then through a layer of CFWE module, the output feature map X5 size is H/16\u2009\u00d7\u2009W/16\u2009\u00d7\u20091024, which can be expressed as follows:The feature map X5 is input to n serially connected \u201cConv1_3_1\u201d modules, and the output feature map X6 has a size of H/32\u2009\u00d7\u2009W/32\u2009\u00d7\u20092048, which can be expressed as follows:Then, the feature map X6 uses a CDeConv module to perform point convolution, firstly, to achieve the purpose of reducing the number of channels, reducing the number of channels to 7. Then, upsample 4 times, and get the output X7. Its feature map size is H/8\u2009\u00d7\u2009W/8\u00d77, which can be expressed as follows:The feature map X5 enters a CDeConv module through a skip connection. Firstly, point convolution is performed to reduce the number of channels to 7. Then, upsample 2 times. Get the output X7\u2032. Its feature map size is H/8\u2009\u00d7\u2009W/8\u2009\u00d7\u20097, which can be represented as follows:Feature map X4 reduces the number of channels to 7 through a point convolution, and the size of the output feature map X7\u2033 is H/8\u2009\u00d7\u2009W/8\u2009\u00d7\u20097, which can be represented as follows:The feature map X7, X7\u2032, and X7\u2033 bit-by-bit to get X8. Its feature map size is H/8\u2009\u00d7\u2009W/8\u2009\u00d7\u20097, which can be expressed as follows:Then, add X8 passes an 8 times upsampling module to output the final output feature map, whose size is H\u2009\u00d7\u2009W\u2009\u00d7\u20097, and can be expressed asThe final feature map Three different upsampling methods using different numbers of \u201cCDeConv\u201d modules and skip connections are designed. Based on SCU-Net, combined with data expansion technology for image preprocessing, an automatic remote sensing image segmentation method is proposed. Model complexity refers to the amount of calculation and parameters of the network. The parameters and calculations of different upsampling methods and depth models are compared through the experiments. Experiments were performed with one \u201cCDeConv,\u201d two \u201cCDeConv,\u201d and three \u201cCDeConv\u201d modules in the network model using three different upsampling methods. By combining three different upsampling methods and three different network depths, we can get 9 different network models. As shown in The floating point of operations refers to the number of multiplication and addition operations in the model. As shown in This experimental dataset comes from the fusion image of GF-2 in the Chenzhou area in 2016. As shown in Firstly, set the dataset image to the output image of the specified size as needed.Secondly, perform random window sampling with a window size of 256\u2009\u00d7\u2009256 on the image, i.e., randomly generate sampling coordinates, and then obtain an image with a size of 256\u2009\u00d7\u2009256 under the coordinates.Finally, data enhancement is performed on the segmented images, and image transformation operations are performed, such as rotation, vertical flipping, horizontal flipping, blurring, corrosion, random gamma transformation, bilinear filtering, and adding noise at random.In the deep learning network, it is easy to cause memory overflow when large remote sensing images to be classified are directly input into the network model. It is difficult for the model to identify the original data without preprocessing. Furthermore, training a deep learning network model needs lots of training data, however, labeling geographic information in satellite remote sensing images is a very complicated and time-consuming task, and labor costs are too high, making it difficult to produce large datasets. Additionally, for avoiding overfitting because of the small amount of data in the training data set in the process of deep learning neural network training, the existing training set needs to be enhanced and expanded. The image sizes of high-resolution remote sensing datasets are also inconsistent. Therefore, for a high-resolution remote sensing image, it needs to be cut into small images of uniform size as an experimental dataset. The pretreatment process is as follows:After the above data preprocessing and data expansion, the amount of data in the training set has become 6 times that of the original dataset, which reduces the risk of network overfitting in a way.To ensure the reliability of the performance comparison of different network models, the experiments in this paper are carried out under the same development platform and hardware environment. The experimental equipment system is Windows 10, CPU  is Intel i7 3.30\u2009GHz, GPU (graphics processing unit) is GeForce GTX 1080Ti (11G), GPU environment is CUDNN 10.0 and CUDA 10.0, the development platform is PyCharm, the programming language is Python, and the framework is Pytorch. The batch size of the test set is 4, and the batch size of the training set is also 4.K\u2009+\u20091. The formulas of PA, MIOU, and FWIU are as follows:There are a variety of evaluation criteria used in semantic segmentation models. The evaluation criteria adopted in this paper are those adopted by most semantic segmentation models, including frequency weighted intersection (FWIU), pixel accuracy (PA), and mean intersection (MIOU) as performance indicators . The evaPii represents the number of class i pixels that are correctly classified, and Pij represents the number of class i pixels classified as class j.Among them, i. TN is defined as the negative sample predicted correctly by the model. Defining FP as a negative sample is incorrectly predicted by the model to be a positive sample. Define FN as the class i is predicted to be other classes. Then, the precision is defined as follows:In addition, the precision, recall, and F1-score indicators in image classification are used in the experiment to evaluate the prediction effect of a single category. TP is defined as the model correctly predicted class Recall is defined as follows:F1-score is defined as the harmonic mean of precision and recall, which is as follows:In this paper, nine kinds of SCU-Nets are designed and tested on the dataset. The effect of depth and upsampling methods on the segmentation performance of SCU-Nets is studied. The experimental results are displayed in According to the above table, the performance of SCU-Net using the C structure as the upsampling method is lower than the model using the other two structures. SCU-Net-102-A has the best comprehensive performance in the dataset. PA and MIOU are the highest, i.e., 91.53% and 55.84%, respectively. The MIOU of SCU-Net-102-A is the highest, which is 55.84%. It is 0.95% and 1.43% higher than SCU-Net-51-A and SCU-Net-153-A individually.The results show that the depth of SCU-Net should be moderate, while scaling shallower or deeper may cause the performance of the network model to decrease. Meanwhile, SCU-Net-51-A is compared with other networks for studying the influence of parameters on network performance. Further comparisons are also conducted with the classic semantic segmentation neural networks DeepLab, U-Net, SegNet, FCN, Dilated, and the most recent networks FC-DenseNet and DFCN121. For the model obtained when the CFWE module in SCU-Net-102-A was deleted, a comparative experiment was carried out to verify the effectiveness of the CFWE module. The experimental comparison results are shown in As can be seen from the above table, SCU-Net-102-A without a CFWE module is significantly lower than that of SCU-Net-102-A with CFWE module, and the parameters of the three CFWE modules are only 10,000. Hence, it can be inferred that the CFWE module has very few parameters and can greatly improve the performance of SCU-Net. DeepLabV3 uses and improves the ASPP module, which has a good effect on the GF-2 dataset, however, the performance is still lower than SCU-Net, and DeepLabV3 has many more model parameters than SCU-Net-102-A. FCN-8s achieved pixel classification by abandoning the fully connected layer of the traditional neural network and made great success on the GF-2 dataset with very few parameters. SegNet is a semantic segmentation network that improves VggNet-16 and is based on the FCN network. At the same time, it introduces the encoder-decoder structure, which has achieved good results on the GF-2 dataset, and the number of parameters is more than SCU-Net-51-A. U-Net was put forward to settle the matter of semantic segmentation of medical images. A U-shaped network structure was proposed to obtain location information and context information simultaneously. Although the parameters of U-Net are very few, it performs poorly on the GF-2 dataset. FC-DenseNet and DFCN121 introduced DenseNet into the model of semantic segmentation. At the same time, regardless of the number of other network parameters, SCU-Net performance is better than theirs. SCU-Net-51-A has low parameters and high performance. It shows that SCU-Net has better performance and lower model complexity and can be more targeted to complete the task of semantic segmentation of satellite remote sensing images.To evaluate the application effect of the network in actual remote sensing images, use 2000 remote sensing images of 256\u2009\u00d7\u2009256 size as a test. It can be seen from The experimental results show that the PA and MIOU of SCU-Net-102-A are the highest, which are 91.53% and 55.84%, respectively. After comprehensive consideration, SCU-Net-102-A is chosen to compare with other typical semantic segmentation networks and the more recent semantic segmentation networks. It is found that the comprehensive performance of the network is better than other networks. Judging from the experimental results, the network depth should be kept appropriate in the task of semantic segmentation of satellite remote sensing images. Too few network layers make it difficult to extract sufficient features, and too many network layers will cause vanishing gradient problem or gradient explosion problem. The problems of gradient dispersion and gradient explosion can be solved to some extent by batch normalization, and the degradation problem can be alleviated by jumping connection. The CDeConv upsampling module uses a point convolutional layer, which improves the feature extraction capability of the network on the basis of reducing the number of network parameters. In addition, the attention mechanism module CFWE module, which uses skip connections to settle the matter of network degradation to some extent, is introduced. Simultaneously, the CFWE module learns the channel weight coefficients using the attention mechanism, which enhance the feature extraction capability of the network and achieves a better image segmentation effect. SCU-Net-102-A and DFCN121C networks are selected for experiments to compare and predict the effects of different categories. The precision of the SCU-Net-102-A model for forest land prediction is 97.10%, and the recall is 93.42%. The corresponding F1-scores reached 0.952, which is the best among the 7 classes, and these three values are higher than those of the DFCN121C model. At the same time, all kinds of F1 scores predicted by SCU-Net-102-A are higher than those predicted by DFCN121C, except for the \u201cothers\u201d class. Combined with the experimental results, it can be proved that SCU-Net-102-A is better than DFCN121C in predicting each.The visualization diagram of the SCU-Net-A test output is shown in On the whole, the prediction effect of SCU-Net-102-A is better than the image predicted by DFCN121C. In the first raw image, the waters are marked as bare ground because of human labeling errors. Both SCU-Net-A and DFCN121C can correctly predict waters, however, it is clear that SCU-Net-102-A understands the details better, as shown by the yellow boxes in the first column of This paper proposes a new semantic segmentation model for high-resolution remote sensing images based on CNNs. A new upsampling module CDeConv is proposed in this network model, and the attention module CFWE is used to improve the feature extraction ability of the network. In the experiment of this paper, the GF-2 satellite remote sensing image of Chenzhou in 2016 is used, and the ground truth was labeled manually. Finally, there were 7 categories of classified objects in the dataset. By analyzing the experimental results, it is concluded that SCU-Net-102-A has the highest value, and its PA and MIOU are 91.66% and 55.61%, respectively. The precision of SCU-Net-102-A for woodland prediction is 97.10%, and the corresponding F1-score is 0.952, which is the highest F1-score among the seven categories. It can achieve accurate segmentation of complex targets in GF-2 image classification tasks. The model designed in this paper is designed to detect the changes in forest land and water area in Chenzhou, China, and to provide help for the protection and development of forest and water environment. It is hoped that more satellite remote sensing images of the same kind can be obtained in the future, and higher-quality segmentation datasets can be generated to further train SCU-Net to improve its versatility and segmentation performance."}
+{"text": "Parkinson's disease is mainly characterized by clinical motor manifestations, with postural instability being a predominant symptom that leads to many falls. One way in which postural control is assessed is to measure the characteristics of postural sway during quiet standing. In this test, subjects standstill on a force platform, which records ground forces and reaction moments that can be used to calculate the center of pressure (CoP) . Inclusion criteria were the absence of neurological or physical dysfunctions other than those associated with PD and no diagnosed vestibular, visual, or somatosensory dysfunctions as self-declared.A convenience sample of 32 idiopathic PD patients  was recruited to participate in this study. The patients were recruited from local communities and included local neighborhoods and ambulatory movement disorders. The patients were interviewed to collect information about their demographic characteristics, socio-cultural characteristics, and overall health condition. Their ages varied from 44 to 81 years, body masses from 53.3 to 95.6 kg, heights from 151.5 to 184.0 cm, body-mass indexes (BMI) from 17.5 to 31.5 kg/mThe stabilography evaluation was based on the most common practices used in research laboratories . The patient's feet were positioned on the marks at the force platform or on the foam blocks. The researcher instructed the patient to maintain the position of his or her arms along his or her body and to stand as still as possible. During the trials, with the patient's eyes open, the patients were told to fix their gaze ahead on the round black target placed on the wall at the patient's eye level. During the trials with eyes closed, the patients were told to fix their gaze ahead at the same target, close their eyes when they felt ready, and only open them when the researcher indicated that the trial was over.The researcher started the data collection around 5 s later when the patient said he or she was ready.At the end of the trial, the subject was assisted to step from the force platform, and he or she could rest (and sit if desired) for about one minute before the subsequent trial.If the subject was unable to complete a 30 s trial, the test was stopped.The force platform data were smoothed with a 10 Hz fourth-order zero-lag low-pass Butterworth filter, and the center of pressure (CoP) was calculated according to the standard formula ; the data is stored in ASCII (text) format with tab-separated columns that can be downloaded as a single compressed file that is made available under the CC0 1.0 license (https://creativecommons.org/publicdomain/zero/1.0/). The data set comprises a file with metadata plus 767 files with the GRF for the 32 patients in each medication condition.All the data is available at Figshare ; XX identifies the patient and varies from 01 to 32.Gender: gender (F or M).Age: patient's age in years.Height (cm): height in meters .Weight (kg): weight in kilograms .2): body mass index in kg/m2.BMI (kg/mOrtho-Prosthesis: name of the orthosis or prosthesis the subject wears (\u201cNo\u201d if the patient did not wear any orthosis or prosthesis).Years of formal study: years of formal education.Disease duration (years): year from diagnosis.\u22121): total daily levodopa equivalent dose in mg\u2022day\u22121 according to Tomlinson et al.  or not (non-freezers) of freezing of gait.NFoG-Q (score): score of New Freezing of Gait Questionnaire.PIGD or TD: Postural Instability/Gait Difficulty (PIGD) or Tremor Dominant (TD) phenotypes of Parkinson's disease according to Stebbins et al. .Initial symptoms: self-reported initial symptoms.Is there a family history of PD? Who?Do you feel improvement after using the antiparkinsonian medicine?: Yes or No.Have you ever had any surgery? Which?Any rehabilitation or physical activity?: name of the rehabilitation or physical activity performed by the patient .Other diseases : name of the disability of the patient (\u201cNo\u201d if the patient did not present any disability).ON\u2014Hoehn & Yahr: Hoehn & Yahr score in the ON medication.ON\u2014MoCA: MoCA score in the ON medication.ON\u2014UPDRS-II: total score of the UPDRS-II in the ON medication.ON\u2014UPDRS-III: total score of the UPDRS-III in the ON medication.ON\u2014UPDRS-III\u2014Rigidity: score of item 5\u2014rigidity of UPDRS-III in the ON medication.ON\u2014UPDRS-III\u2014Gait: score of item 12\u2014rigidity of UPDRS-III in the ON medication.ON\u2014UPDRS-III\u2014Bradykinesia: score of item 14\u2014bradykinesia of UPDRS-III in the ON medication.ON\u2014UPDRS-III\u2014Dyskinesia: score of item 15\u2014dyskinesia of UPDRS-III in the ON medication.ON\u2014miniBESTest: miniBESTest score in the ON medication.ON\u2014FES-I: FES-I score in the ON medication.OFF\u2014Hoehn & Yahr: Hoehn & Yahr score in the OFF medication.OFF\u2014MoCA: MoCA score in the OFF medication.OFF\u2014UPDRS-II: total score of the UPDRS-II in the OFF medication.OFF\u2014UPDRS-III: total score of the UPDRS-III in the OFF medication.OFF\u2014UPDRS-III\u2014Rigidity: score of item 5\u2014rigidity of UPDRS-III in the OFF medication.OFF\u2014UPDRS-III\u2014Gait: score of item 12\u2014rigidity of UPDRS-III in the OFF medication.OFF\u2014UPDRS-III\u2014Bradykinesia: score of item 14\u2014bradykinesia of UPDRS-III in the OFF medication.OFF\u2014UPDRS-III\u2014Dyskinesia: score of item 15\u2014dyskinesia of UPDRS-III in the OFF medication.OFF\u2014miniBESTest: miniBESTest score in the OFF medication.OFF\u2014FES-I: FES-I score in the O OFF medication.Each text file with the GRF data is named by the corresponding condition and trial . The header refers to the signal at each column and are:Time: Time in s.GRFml [N]: mediolateral Ground Reaction Force (GRF) in N.GRFap [N]: anteroposterior GRF in N.GRFv [N]: vertical GRF in N.Mml [N.m]: mediolateral moment of force in N.m.Map [N.m]: anteroposterior moment of force in N.m.Mml [N.m]: vertical moment of force in N.m.Mfree [N.m]: Free Moment at the direction Y in Nm.CoPml [m]: mediolateral center of pressure in m.CoPap [m]: anteroposterior center of pressure in m.https://doi.org/10.6084/m9.figshare.13530587).This study provides a publicly available data set with qualitative and quantitative evaluations related to the balance of PD patients. All the data is available at Figshare  can be found in the article/supplementary material.The studies involving human participants were reviewed and approved by Federal University of ABC. The patients/participants provided their written informed consent to participate in this study.CO: conceptualization, methodology, data collect, writing\u2014original draft, and writing\u2014review and editing. CR: conceptualization, methodology, data collect, and writing\u2014original draft. RT, SH, EL, CB, TS, LS, TN, DC, and EG: methodology and data collect. MC: methodology, data collect, and writing\u2014review and editing. DBC: conceptualization, methodology, data collect, writing\u2014original draft, writing\u2014review and editing, and supervision. All authors contributed to the article and approved the submitted version.This study was supported by Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo (FAPESP/Brazil)\u2014grant #2019/06604-1, Universidade Federal do ABC (UFABC/Brazil), and by Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior (CAPES/Brazil).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher."}
+{"text": "As in the standard complex setting, states and observables of a p-adic quantum system are implemented by suitable linear operators in a p-adic Hilbert space. In particular, owing to the distinguishing features of p-adic probability theory, the states of an p-adic quantum system are implemented by p-adic statistical operators, i.e., trace-one selfadjoint operators in the carrier Hilbert space. Accordingly, we introduce the notion of selfadjoint-operator-valued measure (SOVM)\u2014a suitable p-adic counterpart of a POVM in a complex Hilbert space\u2014as a convenient mathematical tool describing the physical observables of a p-adic quantum system. Eventually, we focus on the special case where p-adic qubit states and 2-dimensional SOVMs. The analogies\u2014but also the non-trivial differences\u2014with respect to the qubit states of standard quantum mechanics are then analyzed.We propose a model of a quantum  It came as a complete surprise when, at the end of the past century, some concrete applications of p-adic numbers to physical theories began to appear. Indeed, in the late 1980s, Vladimirov, Volovich and Zelenov [non-Riemannian model, that is, a model in which the Archimedean property is no more valid at very small distances. In particular, they proposed a model of quantum mechanics based on the non-Archimedean field of p-adic numbers. Later on, different p-adic quantum mechanical models were studied [p-adic numbers and theoretical physics were revealed. e.g., it was argued that the natural fractal-like structure of this field makes it suitable for the description of the dynamics of chaotic and disordered systems. In particular, it was proved that the ground state of spin glasses exhibits a natural (non-Archimedean) ultrametric structure [The field of  Zelenov  argued t studied ,12, and  studied ,16,17,18tructure ,21.p-adic numbers, not necessarily related to foundational physics, have begun to appear. Indeed, p-adic numbers have found a fertile ground of application in the context of algebraic dynamical systems, also in connection with problems from computer science, image analysis, compression of information, image recognition and cryptography [pseudorandom numbers and uniform distribution of sequences [More recently, new and interesting applications of tography ,23,24,25equences ,27,28.p-adic quantum information theory is two-fold: On the one hand, the peculiarities of p-adic numbers may provide a new line of attack for notoriously hard problems in quantum information theory; e.g., it has been recently argued that p-adic numbers  can be profitably used in the construction of mutually unbiased bases (MUBs), in any given Hilbert space dimension [p-adic model of quantum information may provide useful tools for the study of fundamental physical theories.A very recent research trend involves applications to quantum information theory , as wellimension . On the p-adic numbers has been formulated. We believe that the main reason for this is the lack of a well established theory of quantum states in the p-adic setting. Recently, this issue has been addressed in [p-adic framework, by suitable p-adic (trace class) operators in a p-adic Hilbert space. In the present contribution, on the base of the ideas presented in the aforementioned reference, we propose a p-adic model of a quNit. In particular, in these finite dimensional systems, we will show that the set of p-adic linear operators has itself a structure of a p-adic Hilbert space. This turns out to be useful for describing observables and the measurement process. The case of p-adic qubit will be worked out explicitly.Until today, it seems, however, that no general model of quantum information based on essed in , where ip-adic numbers and its quadratic extensions. In p-adic Hilbert spaces and the associated linear operators. We devote p-adic states in a finite-dimensional quantum system. Finally, by focusing on the case of a two-dimensional p-adic Hilbert space, we obtain an explicit realization of a p-adic qubit. The structure of the paper is as follows. In p-adic numbers that are relevant for p-adic quantum mechanics [In this section, we remind the reader some basic notions and results concerning echanics ,6,7,9,15valuation  on By a (V1)(V2)(V3)(V3))In particular, in the case where (V4)non-Archimedean valuation; otherwise, the valuation is called Archimedean.we say that distance function (or metric) defined by: non-Archimedean, instead, we still have a metric on (V4)) entails that the distance ultrametricity and, accordingly, a metric function satisfying it is called an ultrametric.An Archimedean valuation ined by: d|\u00b7| namely,d|\u00b7|Example\u00a01\u00a0Recall that, according to the unique factorization theorem, every rational number ble by p ,35. The (V4). Therefore, if we consider the associated metric functionIt is easily shown that we obtain an ultrametric on . It is a metric space that, by means of a standard procedure, can be completed [p-adic numbersp-adic numbers. A more concrete characterization is given as follows. Let x admits a unique decomposition of the formp-adic number by means of a suitable converging series. In particular, this is reminiscent, to some extent, of the usual decimal expansion of a real number Consider the pair ompleted . The resnt of Qp . Therefothe formx=\u2211i=0\u221exip-adic valuation on p-adic numbers when describing physics on length scales comparable to Planck\u2019s length (P1)Every point in an open (closed) ball is a centre.(P2)Two open (closed) balls are either disjoint or one is contained in the other.(P3)Every ball in (P4)All triangles are isosceles in .As a topological space, completely regular (being a metric space) and totally disconnected; namely, the only connected subsets of The rametric  can be eength lP ,5,10,11.ength lP ,38, we lngletons .quadratic extensions of We devote the last part of this section to a brief discussion of the on on Qp ,33. Thisimaginary unit in conjugation, namely, the mappingp-adic absolute value (1)non-quadratic unit, i.e., If (2)if The definition of a quadratic extension of  we have :(1)If p\u2260Example\u00a02.\u00a0For p-adic Hilbert space and the associated p-adic linear operators [This section is devoted to introduce a suitable notion of a perators  iff;(N2);(N3),for all Remark\u00a01.\u00a0(N3) differs significantly w.r.t. the standard  case, where the usual triangle inequality holds.The explicit definition of a p-adic Banach space is motivated by the fact that the strong triangle inequality As is well known, complex Hilbert spaces are defined as (complex) Banach spaces endowed with a suitable inner product, namely, the one inducing the relevant norm. It turns out that this familiar picture keeps some of its main futures\u2014but also requires some essential modification\u2014when switching to the field of p-adic normed space. Our first concern is to provide a suitable notion of a basis for this space [p-adic normed space X are said to be  norm-orthogonal if, for any X is norm-orthogonal if any finite subset of X is normal, if it is norm-orthogonal and, additionally, p-adic Banach space, and let countable subset of X  basis, if dimension of X\u2014in symbols, X, i.e., we set p-adic Banach space X admitting a normal basis a normal p-adic Banach space.Let is space ,34,37,42Example\u00a03.\u00a0Let us consider the space (b)(c)We call the triple As in the standard complex case, also in the (a) and (b) of Definition 2, it is clear that the inner product sesquilinear form. Also note that, from the Hermitianity condition (b), and the sesquilinearity of non-degenerate if the condition From conditions Example\u00a04.\u00a0Let where Remark\u00a02.\u00a0The notion of non-Archimedean inner product naturally leads us to a notion of inner-product orthogonality, which is distinct from the\u2014previously introduced\u2014norm orthogonality. Explicitly, we say that two vectors The notion of inner-product orthogonality, introduced in Remark 2, entails the following natural extension of the notion of normal basis:Definition\u00a03.\u00a0\u03a8 is a normal basis in X, and its elements are mutually IP-orthogonal, namely, Let p-adic Banach space X is, in general, not guaranteed. On the other hand, when X is a normal p-adic Banach space\u2014where the existence of a normal basis is assumed\u2014it is always possible to turn any given normal basis into an orthonormal one by making a suitable choice of the inner product. Indeed, it suffices to consider the canonical inner product associated with this normal basis in X . Therefore, we have the following natural definition of Hilbert space in the p-adic setting:We stress that the existence of an orthonormal basis in an inner-product Definition\u00a04.\u00a0A p-adic Hilbert space is a triple p-adic Hilbert space may be thought of as a normal p-adic Banach space endowed with a distinguished normal basis and with the associated canonical inner product. It is then not difficult to check the following two properties of a p-adic Hilbert space:(H1)Every vector (H2)non-Archimedean Parseval identity holds true:The From the previous definition, it is clear that a Example\u00a05.\u00a0Let us consider the set rd basis . Then, iterature ,43, thisI)); see .p-adic case one can define a convenient notion of isomorphism of Hilbert spaces  [p-adic Hilbert space, where Hilbert space automorphism of two Hilbert spaces over different, but mutually isomorphic, p-adic Hilbert spaces. The p-adic Hilbert spaces stemming from the same p-adic Banach space As in the complex setting, also in the another) . Let us Remark\u00a03.\u00a0It is worth stressing that the analogies between complex and p-adic Hilbert spaces cannot be pursued too far. Indeed, quite generally, in a p-adic Hilbert space, p-adic Hilbert space p-adic quNit.Hereafter, borrowing the terminology from the standard (complex) quantum mechanics, we shall call a quantum system with associated p-adic framework as well, with some non-trivial differences w.r.t. the standard complex setting.In , it is dfinite-dimensional\u00a0p-adic Hilbert space. In this case, we only need to consider the space Since our main concern is to consider applications to quantum information theory, we will actually focus our attention to linear operators acting in a p-adic Hilbert space, with L and the fixed orthonormal basis operator norm\u2014which is given byp-adic Banach space.Then, let 6.2.1 in ), it is given byL\u2254sup0\u2260\u03d5\u2208Remark\u00a04.\u00a0Let us explicitly note that, by using the Dirac notation, the operator adjointL is given byinvolutive automorphism of p-adic Banach space p-adic Banach \u2217-algebra. In fact, in the next section, the set physical observables of a  p-adic quantum system.For every given byL*=\u2211i=1N\u2211Remark\u00a05.\u00a0As in the complex setting, also in the p-adic case it is possible to single out the subset is verified.p-adic Hilbert space. Indeed, let us first observe that given trace, linear functional\u2014namely, the trace functional\u2014on Hermitian, becausep-adic Hilbert-Schmidt product. Next, note that, for all non-Archimedean inner product, and inner-product p-adic Banach space.To conclude this section, we will now argue that Now, let Remark\u00a06.\u00a0Let From this fact, we deduce that the product orthonormal basis in We now prove that the set \u2014as (cf. )(36)L=\u2211Summarizing, we have the following result:Theorem\u00a01.\u00a0Given an algebraic formulation. This formulation essentially relies on two fundamental assumptions; namely, that every quantum system can be described by means of two main classes of objects\u2014i.e., states and observables\u2014mutually related by means of a natural pairing map. Specifically, the observables can be identified with the selfadjoint elements of an abstract non-commutative unital density or statistical operators [As is well known, the most general and abstract description of quantum mechanics is provided by the so-called perators ,47,48,49p-adic quantum mechanics, physical states should be defined as  involution-preserving bounded functionals on the unital Banach \u2217-algebra p-adic setting, by the class of the so-called p-adic statistical operators, defined as a suitable subclass of the selfadjoint trace class operators in a p-adic Hilbert space p-adic probability theory [Following the same route, it has been recently argued that, in perators . It has  space H . The proy theory ,7,50,51.Remark\u00a07.\u00a0Since p-adic probability theory is a rather non standard topic, for reader\u2019s convenience, we now briefly sketch its main features. Let us first observe that both p-adic and classical probability theory arise in a natural way from a common conceptual background. In fact, in both theories, one starts by considering the set ibutions ,7,50,51.Definition\u00a05.\u00a0Let the set of p-adic statistical operators in p-adic quantum mechanics. To begin with, we need to introduce a suitable notion of observable in the p-adic setting. In particular, as argued in [p-adic setting is provided by the so-called (discrete) selfadjoint operator valued measures (SOVMs) in p-adic counterpart of a POVM in a complex Hilbert space. In the finite-dimensional setting we are considering, a discrete SOVM can be defined as a family I is a finite index set\u2014of selfadjoint operators in It is convenient, at this point, to better clarify the statistical interpretation of rgued in , a conveRemark\u00a08.\u00a0We remark that, as for a discrete POVM, a discrete SOVM should actually be defined as an additive measure on the algebra of subsets of the index set I (the power set of I), by putting, e.g., for Remark\u00a09.\u00a0We stress that, in p-adic quantum mechanics, there is no straightforward counterpart of a POVM of standard (complex) quantum mechanics. In fact, the field of p-adic numbers pairing between states  and observables. To this end, similarly to the standard complex case, by means of the trace functional normalized involution-preserving linear functional on pairing between p-adic statistical operators and observables.The trace functional p-adic probability distribution.For every elations  guaranteAs a further step, we need to specify the We have then obtained a complete description of the statistical content of the theory.p-adic counterpart of the complex qubit. To this end, let us first note that, since trace-one p-adic Hermitian . Let us focus on the particular case where traceless p-adic Hermitian matrix. In particular, the conditions Q:p-adic Hermitian matrix, with zero trace, is given by:p-adic Pauli matricesQ in a more compact form:p-adic Hermitian matrix in p-adic quantum systems isp-adic Pauli matrices defined in  is not algebraically closed, namely, not every non-constant polynomial admits a root in formal eigenvaluesdoes not admit any root in the quadratic extension of not diagonalizable. Actually, it is not difficult to construct examples of non-diagonalizable qubit states also for all other quadratic extensions of p-adic qubit states that cannot be diagonalized, for every quadratic extension As a first point, note that ic qubit . As is eQ2,2 see . Now, coe matrix  does notExample\u00a06.\u00a0We now provide an explicit example of a SOVM for a two-dimensional p-adic quantum system. Let us consider the family of linear (matrix) operators It is clear that the matrices Therefore, it state , iswith p-adic numbers, we have proposed a model of QuNit on the field As a first step towards a quantum information theory based on a quadratic extension of the non-Archimedean field of p-adic Hilbert space and, restricting to the case where p-adic Banach \u2217-algebra. Then, we have proved that the linear space p-adic Hilbert space, once it is endowed with the p-adic Hilbert-Schmidt inner product.We started by introducing a notion of p-adic probability theory, we have argued that the states of an p-adic quantum system are implemented by p-adic statistical operators, i.e., trace-one selfadjoint operators in the carrier Hilbert space. In particular, it turns out that the set of p-adic statistical operators,  subset of p-adic probability theory\u2014hence, it is an unbounded subset of Owing to the distinguishing features of p-adic counterpart of a POVM in a complex Hilbert space\u2014as a convenient mathematical tool describing the physical observables of a p-adic quantum system.We have next introduced the notion of (discrete) selfadjoint-operator-valued measure (SOVM)\u2014a suitable p-adic qubit states and of two-dimensional SOVMs.Eventually, focusing on the special case where p-adic model of quantum information theory. Tensor products and entanglement play a central role in quantum information theory, and we expect that they will play a central role in the p-adic setting too. Therefore, as a first step, we plan to investigate tensor products of p-adic Hilbert spaces and the associated classes of entangled states. Our next concern is the description of dynamical maps and dynamical (semi-)groups in p-adic quantum mechanics. This will provide a suitable p-adic counterpart to quantum channels. Another interesting prospect concerns the possibility of defining typical entropic quantities, such as the von Neumann and the R\u00e9nyi entropies\u2014which are relevant in standard quantum information theory\u2014in the p-adic framework too.We close by outlining some potential extensions of this work, especially focusing on those ones that are relevant for our  program aimed at developing a"}
+{"text": "Correction to: Pharmaceutical Research10.1007/s11095-022-03249-3This article was updated to correct the phrase \u201cin vitro\u201d in the Abstract and in three instances in the text."}
+{"text": "Nature Communications 10.1038/s41467-022-33453-z, published online 30 September 2022Correction to: The original version of this Article contained an error in a sentence in the last paragraph of the Introduction, which incorrectly read \u2018The shuttling-mode exchange switching allows us to efficiently control exchange coupling with an on/off ratio above 1000,000.\u2019 The correct version states \u20181000\u2019 in place of \u20181000,000\u2019.This has been corrected in the PDF version of the Article."}
+{"text": "We prove that for antisymmetric vector field  GL(N)-gauge, namely a matrix-valued function GL(N)-gauges have the advantage that they can transform equations of the formH-surfaces, and more generally the Euler\u2013Lagrange equations of a large class of conformally invariant variational functionals. The GL(N)-gauge transform allows for regularity theory and the study of weak convergence [In the celebrated work  Rivi\u00e8re  gauges, , namely howed in , the GL-Coulomb gauge [Applying a gauge  the Eq. , we find the Eq. ,\\documenmb gauge , namely There exists a number If As an immediate corollary, we obtainA such that for (Conservation law) Assume Theorem\u00a0With the methods of Theorem\u00a0f in Assume Here, as usual, we denoteod\" stands for \u201coff diagonal\u201d.We follow the notation of  for the s-gradient For two vector fields s-divergence in the distributional wayLet With this notation we have Let Moreover, for any We haveombining . The proombining  is similWe also denoteLet For the proof see Appendix C.We will also need the following Wente\u2019s inequality from .p. Assume moreover that R be a linear operator such that for some ,,3.23), aly, from , 3.21),,3.25\\docproof of .In order to prove  we obserstimates  and R.For the last term of , we simixdy=0.By , 4.11),,\\documenxdy=0.By , and , , \\documeombining .Step \u00a02. We claim that (up to a subsequence)Indeed, we writeAs for the second term on the right-hand side of , we begiWe verify the convergence of the first term on the right-hand side of . First w term of  follows  term of .Now  follows Step \u00a03. We claim thatStep \u00a04. We claim that (up to a subsequence)R, whenever As for the second term of the right-hand side of ,,\\document}\u2113\u2192\u221e in , and (4.t}\u2113\u2192\u221e in , we obtaLet We follow in spirit the covering argument of Sacks\u2013Uhlenbeck [By assumptions there is a number Let In order to conclude we will need a removability of singularities lemma, compare with [Let For simplicity of presentation let us assume that Now let Thus, by  and by tSecondly,Thus, passing with t}\u2113\u2192\u221e in  we get fause, by , we haveThis finishes the proof. Combining Corollary"}
+{"text": "Scientific Reports 10.1038/s41598-022-22856-z, published online 28 October 2022.Correction to: The original HTML version of this Article contained an error in Figure\u00a0The original Figure\u00a0This error has now been corrected in the HTML version of the Article; the PDF version was correct from the time of publication."}
+{"text": "This paper proposed an image algorithm based on a cascaded chaotic system to improve the performance of the encryption algorithm. Firstly, this paper proposed an improved cascaded two-dimensional map 2D-Cosine-Logistic-Sine map (2D-CLSM). Cascade chaotic system offers good advantages in terms of key space, complexity and sensitivity to initial conditions. By using the control parameters and initial values associated with the plaintext, the system generates two chaotic sequences associated with the plaintext image. Then, an S-box construction method is proposed, and an encryption method is designed based on the S-box. Encryption is divided into bit-level encryption and pixel-level encryption, and a diffusion method was devised to improve security and efficiency in bit-level encryption. Performance analysis shows that the encryption algorithm has good security and is easily resistant to various attacks. After decades of development, digital information has grown extensively in capacity, and various electronic devices are changing gradually, accompanied by a large amount of data for transmission and communication , which bDue to chaotic sensitivity to initial state and control value, good pseudo-randomness, ergodicity and unpredictable trajectory , the comTwo types of cryptosystems can be classified: stream ciphers, which are converted bit-by-bit, and packet ciphers, which convert n-bit inputs into m-bit outputs. At the core of this conversion is the static S-box, which gives the cryptosystem the obfuscation properties described by Shannon . An S-boAs the security strength of the entire encryption algorithm is determined by the cryptographic strength of the S-box, the researcher has proposed many methods to enhance the S-box\u2019s performance, such as using the high-dimensional chaotic system, and multiple chaotic systems to generate S-boxes have become solutions. Liu et al.  used a hBased on the above analysis, a cascade chaotic map 2D-Cosine-Logistic-Sine map (2D-CLSM) is proposed in this paper. The initial values and parameters of the chaotic map are combined with the original image to resist known plaintext attacks. Then, an S-box construction method is proposed, and an S-box-based encryption method is designed. The encryption method is divided into four stages: key generation, S-box generation, bit-level encryption and pixel-level encryption. In bit-level encryption, a bit-level operation is performed on the plaintext pixel values, converting the original decimal plaintext image pixels to eight-bit binary, then permuting the lower four bits and using a proposed new diagonal diffusion method for the higher four bits. In the pixel-level encryption part, one diffusion is completed by a three-number XOR , and the resulting value calculates the row and column index of the S-box for pixel value replacement. Through experimental analysis, the encryption algorithm in this paper has good security performance.The remainder of this essay is structured as follows: In nonlinear dynamic systems, chaos is a stochastic process that is frequently employed in cryptography research . One-dimThe chaotic behavior of a chaotic system can be measured by the bifurcation diagram and the Lyapunov exponent. A cascade map is a form of a chaotic map; the use of cascades can effectively improve the performance of chaotic systems. In order to solve the problem of small chaotic intervals and uneven distribution, we designed a two-dimensional cascade chaotic map, which has a more complex chaotic behavior than one-dimensional chaos and a faster iteration speed than two-dimensional chaos. The cascade system is shown in The essence of cascading is that the output of a certain initial value after the iteration of system 1 is taken as the iterative output of system 2, and the iterative output of system 2 is taken as the iterative output of system 1, thus forming a circular iteration between two subsystems. Chaotic systems are generated by the cascade method, where the Lyapunov value of the system is the sum of the Lyapunov exponents of the cascaded subsystems, and the sequential trajectory of the system output deviates sharply as the number of iterations increases .Using cosine functions is proposed and demonstrated in , where eIn Equation (3), to increase the chaotic complexity of the cosine function-based system, a new control parameter Further, controlling the value of the parameter k2=1\u221219\u03b8 , and wheIn order to analyze the 2D-CLSM\u2019s performance, we compared it with another existing 2D chaotic map for image encryption, i.e., the 2D Logistic-Sine-Coupling Map (2D-LSCM) .(8)xi+1The trajectory of a 2D-CLSM shows how motion increases over time from a specific initial state. In the case of periodic motion, the trajectory would be a closed curve, whereas the trajectory of chaotic behavior would theoretically never close or repeat. Therefore, chaotic trajectories usually occupy a part of the phase space and can reflect the randomness of the chaotic system output. If a chaotic trajectory can occupy a larger portion of the phase space, the chaotic system has a better stochastic output.From We set initial value as The LE (Lyapunov exponent) describes the sensitivity of a chaotic mapping to initial values. In general, a chaotic map is in a chaotic state when Its Jacobian matrix at the point Let The larger the value of p-values to show the test result. The sequence is considered random when the p-value is over 0.01. In this paper, 15 NIST tests were used to test the randomness of the generated sequences, and 15 correspond to In information theory, information entropy is used to quantify the uncertainty of the information content. It can be used to evaluate how random a set of data is. We transformed the chaotic sequence obtained by iteration into values between 0 and 255 and obtain the information entropy according to Equation (12):Better randomness is correlated with larger information entropy values, and There are four main stages in our encryption algorithm: key generation, S-box generation, bit-level encryption and pixel-level encryption. The size of the plaintext image Two different chaotic maps are used in our algorithm: Logistic and 2D-CLSM, which are used in different stages of encryption. In the S-box generation stage, a Logistic map is used to generate the chaotic sequence needed to generate the S-box; a 2D-CLSM map is used in the bit-level operation and pixel-level operation phases. By using the different chaotic maps in different stages to expand the key space, a more complex encryption algorithm is generated.If the key stream used for encryption is only related to the key and not related to the plaintext image, the designed algorithm is not safe for chosen/known plaintext attack. In order to ensure the security of encryption, the encryption key is generated from the initial key and the plaintext image.Algorithm 1 Generation of the encryption keysOutput: The encryption keys\u2003\u2003\u20031: Read the size:\u2003\u2003\u20032: Obtain the sum of all pixels and add scramble number \u2003\u2003\u2003\u2009\u2003\u2003\u20033: Calculate the mean of the all pixels\u2003\u2003\u20034:\u2003\u2003\u20035:\u2003\u2003\u20036:\u2003\u2003\u20037:\u2003\u2003\u20038:\u2003\u2003\u20039:Input: Plain image Initial encryption keys contain six decimal numbers, In the construction method of a chaotic S-box, there is the problem of generating useless chaotic sequences that affect efficiency. Wang et al. proposed in  to use aStep 1: Obtain the length Step 2: Generate a random number Step 3: Shuffle the values of the two positions according to Step 4: Subtract 1 from Step 5: Repeat step1~step4 until The Fisher\u2013Yates shuffling algorithm is an algorithm proposed by R. Fisher and F. Yates for generating random permutations of finite linear arrays . The mosAlgorithm 2 Generation of S-boxOutput: S-box\u2003\u2003\u20031: for\u2003\u2003\u2003\u2003\u2003\u2009\u2009Substituting\u2003\u2003\u2003\u2003\u2003\u2009\u2009if\u2003\u2003\u2003\u2003\u2003\u2009\u2009\u2009\u2009\u2009obtain the 512-length chaotic sequences\u2003\u2003\u20032: Divide\u2003\u2003\u2003\u2003sort index of the \u2003\u2003\u20033: Read the size:\u2003\u2003\u20034: while\u2003\u2003\u2003\u2003\u2003\u2009\u2009Obtain a random number\u2003\u2003\u2003\u2003\u2003\u2009\u2009Swap the value of\u2003\u2003\u2003\u2003\u2003\u2009\u2009Set\u2003\u2003\u20035: If\u2003\u2003\u20036: Obtain S-boxInput: encryption keysAlgorithm 2 describes the generation process of the S-box. In order to verify the performance and strength of the generated S-boxes, we used the general criteria for S-box performance evaluation to be able to test them . In this(I) Nonlinearity In the process of encryption, if the given S-box makes a linear mapping between the input (plaintext) and the output (ciphertext) [NLf is the 8-bit Boolean function, hertext) , then a (II) Strict Avalanche Criterion (SAC) Webster and Tavares used the strict avalanche criterion as an important feature of the performance of an S-box [an S-box . The str(III) Output Bits Independence Criterion (BIC) This criterion was introduced by Webster et al. as one of the important properties of S-box evaluation, a property that ensures that there is no dependence on the change of any two output bits when a single input bit is changed, a property that makes any Boolean function must be independent and highly nonlinear. For two output bit Boolean functions Through experimental tests, the average BIC nonlinearity value of the proposed S-box is 104.5, and the BIC-SAC test result is 0.5009, which satisfies the BIC criterion.(IV) Difference Approximation Probability (DP) differential cryptanalysis, introduced by Biham and Shamir [d Shamir , is ableIn comparison with the other four methods, the results show in Traditional image encryption generally falls into one of three categories: permutation-only, diffusion-only, or combined forms. Due to its simpler computational complexity, the permutation-only type of these is more efficient, but the security is not very strong. Due to the substantial computational load required for real arithmetic operations, the diffusion type is a time-consuming process. The pixel values and random numbers are used to perform an XOR operation, and the calculated numbers are used to determine the ranks of the S-boxes and substitute the original pixels with the values in the S-boxes, but the overall encryption efficiency is low due to the lack of permutation and diffusion operations on the plaintext image and the low efficiency of S-box generation .In this stage, by separating the eight-bit pixel values into upper four bits and lower four bits, different operations are performed on the two parts, respectively, and a new diagonal diffusion method for irregular matrices is proposed to be applied to the high four-bit matrix. The bit-level encryption process is shown in We converted the original pixel value of the plaintext image into a binary representation and extracted it into two parts for different operations. The upper four bits P1 of the pixel value and the lower four bits P2 of the pixel value are shown in In order to make the information of pixel points have a good diffusion effect, many diffusion methods, such as V-diffusion, zigzag diffusion and chunk diffusion, were proposed. A zigzag algorithm was used in  and imprHowever, the security of the zigzag is not guaranteed due to the fact that it is extremely easy to be broken by a single variation.In order to obtain faster diffusion speed and diffusion effect, this paper proposes a new diagonal diffusion method by randomly and irregularly rearranging the image matrix through a chaotic sequence. The number of pixel values in each row is controlled by the random sequence, there may be no pixel values at some positions of the diagonal, and the matrix presents an irregular arrangement. Through the proposed new diagonal diffusion, it can complete the diagonal of diffusion. Through the comparative analysis of the relevant experiments in Algorithm 3 Matrix rearrangeOutput: irregular matrices\u2003\u2003\u20031: Obtain the size of\u2003\u2003\u20032: Set an empty list\u2003\u2003\u20033: While\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u20034:Input: upper 4-bits sequenceIn this paper, after obtaining the upper four-bit matrix, we changed its alignment through a random sequence to generate different irregular matrices, performed diagonal diffusion on the matrix according to the changed alignment and changed its alignment, as shown in Where Based on the rearranged matrices, we proposed a diagonal diffusion to perform diffusion operations on upper 4-bit matrices capable of new diagonal diffusion operations based on different irregular matrices, as shown in Algorithm 4 Diagonal diffusion orderOutput: order sequence\u2003\u2003\u20031: Obtain the size of\u2003\u2003\u20032: Set tow empty list\u2003\u2003\u20033: for\u2003\u2003\u2003\u2003\u2003\u2003\u00a0Obtain the size of\u2003\u2003\u2003\u2003\u2003\u2003\u00a0for\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u20034: Obtain the size of\u2003\u2003\u20035: for\u2003\u2003\u2003\u2003\u2003\u2003\u2003Obtain the size of\u2003\u2003\u2003\u2003\u2003\u2003\u2003for \u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003Input: irregular matricesAccording to the irregular matrix obtained by Algorithm 3, we need to diffuse according to the diagonal, but the shape of the matrix is irregular, so given Algorithm 4 used to obtain the order of the pixel values of the diagonal of the irregular matrix, sequentially traversing the diagonal to obtain its diffusion order matrix for diffusion, according to different irregular matrices for the order of diagonal diffusions, such as the first: (1- > 3- > 2- > 7- > 4- > 8- > 5- > 9- > 6), the second: (1- > 2- > 4- > 3- > 5- > 6- > 7- > 8- > 9) and the third: (1- > 5- > 2- > 6- > 3- > 9- > 7- > 4- > 8), if we use the normal zigzag, then the order of each diffusion is fixed in a 3 \u00d7 3 matrix, and the result is (1- > 2- > 4- > 7- > 5- > 3- > 6- > 8- > 9) each time, which is not guaranteed in terms of security.Where Step 1: Generate S-boxes Step 2: Generate the encryption key Step 3: Iterate over Step 4: Process the chaotic sequence to obtain the random numbers for array rearrangement;Step 5: Based on the resulting upper 4-bit matrix Step 6: Perform a diffusion operation on the irregular matrix Step 7: Diffusion operation based on the 1D matrix Step 8: Process the chaotic sequence to obtain chaotic values for the lower four positions;Step 9: Based on the resulting At the end of the bit-level encryption, pixel-level encryption is performed by the resulting pixel values using the S-box. It mainly includes pixel value diffusion and substitution. The main process is shown in Generate an empty matrix Finally, The simulation results of the proposed method are presented in this section by running PyCharm software under Windows 10 64-bit system. By using the method in this paper, 10 images were both encrypted and decrypted. The results of encrypting and decrypting several grey-scale images such as Baboon.png, House.png, Cameraman.png and Peppers.png pixels are shown here, respectively. The initial keys used for encryption/decryption are shown in From Assuming that the accuracy of the computer is In a secure encryption system, a mirror change in the key can cause a complete change in the ciphertext obtained from the encryption. Through testing, the encryption key As shown in The distribution of the image\u2019s pixel values can be directly described by the histogram. A secure encryption system should ensure that pixel values of the obtained ciphertext image are uniformly distributed in order to reduce readability, improve security and provide effective protection against statistical attacks.The variance of the histogram can be used to specifically describe the distribution of pixel values. The calculation equation is shown in (21), and the result shows in Where A differential attack is a common form of attack in cryptography, in which an attacker usually selects to encrypt the plaintext and a slightly altered plaintext and analyses them to find a specific relationship. In order to be effective against differential attacks, the encryption algorithm should be sensitive enough to the plaintext that a diffusion operation during encryption can cause small changes in the plaintext to affect all pixels, and we usually evaluate the sensitivity of the algorithm using the pixel change rate NPCR and the normalized pixel average change intensity UACI, their ideal expectations are 99.6094% and 33.4635%, respectively. We obtained NPCR and UACI values by randomly modifying two pixel points of the plaintext image. In this paper, we choose to modify pixel points  and . In When the image is not encrypted, there is a strong correlation between the pixel values of the images; the encryption operation on the plaintext allows us to break this correlation. We calculated the correlation coefficient by randomly selecting The closer the calculated correlation coefficient is to 1, the stronger the correlation is, and the closer it is to 0, the weaker the correlation is. As shown in In addition, from Information entropy is another metric for evaluating the security of a ciphertext and represents the strength of the uncertainty of the image information, which is expressed in Equation (12).For a grey-scale image with 256 states, it has a maximum expectation value of 8, During the transmission of information, information may be lost due to humans or some uncontrollable factors. If the encryption algorithm is able to restore the plaintext image in this case, then the encryption algorithm is valid. In Running speed is an important index to evaluate the encryption algorithm; we simulated it in Python 3.7 environment on a PC with a 2.2 GHz CPU and 8 G RAM. As can be seen from In this paper, we propose an improved cascaded chaotic map 2D-CLSM and design a novel encryption scheme based on it and S-box. By generating a key associated with the plaintext, the whole encryption process is associated with the plaintext, effectively resisting the chosen/known plaintext attack. An S-box encryption scheme is designed and applied to our encryption, increasing the overall security of the algorithm. Dividing the encryption into bit-level encryption and pixel-level encryption improves the complexity and security of the encryption to a certain extent but reduces its efficiency. The encryption method in this paper can be applied to different image types, such as grey-scale images, grey-scale medical images, etc., while the algorithm is able to meet everyday encryption requirements, both in terms of efficiency and security. The experimental results show that the algorithm has sufficient key space, is resistant to brute force attacks and performs well against statistical analysis attacks, clipping attacks and differential attacks. However, although we improved the efficiency of S-box generation, we used two rounds of encryption, one at the bit level and one at the pixel level, which makes us less efficient overall, so the next step is to improve the efficiency of encryption in both rounds."}
+{"text": "Nature Communications 10.1038/s41467-022-30773-y, published online 27 July 2022Correction to: The original version of this Article contained an error in Fig. 3, in which the case and control colors were swapped in panels c and f. The correct version of Fig. 3 is:which replaces the previous incorrect version:b, e, h, j) Bar plot of multiple P-value thresholds (PT) for PRS prediction of Sj\u00f6gren\u2019s\u201d. The correct version replaces this sentence with \u201c Bar plot of multiple P-value thresholds (PT) for PRS prediction of Sj\u00f6gren\u2019s\u201d. This has been corrected in both the PDF and HTML versions of the Article.In addition, the original version of this Article contained an error in the legend for Fig. 3, which incorrectly read \u201c("}
+{"text": "Nature Materials 10.1038/s43588-01431-x. Published online 29 December 2022.Correction to: In the version of this article initially published, the first name of Flora Ascione was listed as \u201cFloriana\u201d; the error has been corrected in the HTML and PDF versions of the article."}
+{"text": "Although the continuous-variable position-momentum entanglement of photon pairs produced by parametric down-conversion has applicability in several quantum information applications, it is not suitable for applications involving long-distance propagation. This is because entanglement in the position-momentum bases, as seen through Einstein-Podolsky-Rosen (EPR)\u2013correlation measurements, decays very rapidly with photons propagating away from the source. In contrast, in this article, we show that in the continuous-variable bases of angle\u2013orbital angular momentum (OAM), the entanglement, as seen through EPR-correlation measurements, exhibits a remarkably different behavior. As with the position-momentum bases, initially, the entanglement in the angle-OAM bases also decays with propagation, and after a few centimeters of propagation, there is no angle-OAM entanglement left. However, as the photons continue to travel further away from the source, the entanglement in the angle-OAM bases revives. We theoretically and experimentally demonstrate this behavior and show that angle-OAM entanglement revives even in the presence of strong turbulence. Entanglement in the angle\u2013orbital angular momentum bases survives at large distances even in the presence of a turbulent medium. Quantum entanglement  and \u03c1i \u2261  are the transverse positions of the signal and idler photons, respectively at z, and where k = \u03c0/\u03bbp. In addition, w0 is the pump beam waist at z = 0, L is the length of the crystal, \u03bbp is the wavelength of the pump field, and P = \u2223\u03c82\u2223 at z is therefore given byWe present a quantitative analysis of the propagation of conditional position and angle uncertainties of the signal photon in SPDC. For a Gaussian pump with beam waist at the crystal plane y direction, the two-photon position probability distribution is referred to as the conditional position probability distribution of the signal photon at z and is denoted by P. The standard deviation of P is referred to as the conditional position uncertainty \u0394 of the signal photon  in the transverse momentum basis, one can calculate conditional momentum uncertainty \u0394 of the signal photon at z. According to the EPR criterion of entanglement, if the product \u0394\u0394 < 0.5 \u0127, then the two photons are entangled in the position-momentum bases  and \u03c1i = , we can write the two-photon angle probability distribution function P asrs, \u03b8s) and  are the polar coordinates of the signal and idler photons. Using P, one can obtain the conditional angle probability distribution function P and thereby the conditional angle uncertainty \u0394 of the signal photon , we write the EPR criterion for entanglement in the angle-OAM bases as \u0394\u0394 < 0.5 \u0127[1 \u2212 2\u03c0P]  represents the conditional probability of detecting the signal photon at the boundary \u03b8s = \u03b80.In addition to the position-momentum bases, the down-converted photons are rendered entangled in the angle-OAM bases as well. Using w0 = 507 \u03bcm, L = 5 mm, and \u03bbp = 355 nm, we numerically evaluate P and P at different propagation distances z and plot them in P and P, we scale them to make their maximum values equal to one. Next, by fixing yi = 0 in P and \u03b8i = 0 in P, we calculate P and P and thereby the conditional position uncertainty \u0394 and the conditional angle uncertainty \u0394, and we plot them in Now, using z, we derive expressions for how the conditional uncertainties scale with z in the near- and far-field regions. The two dotted lines in ys\u2223yi; z) scales with z in the near and far fields. We find that \u0394 increases as \u03c3(z) in the near field, while it increases as w(z) in the far field. The two dotted lines in s\u2223\u03b8i; z) scales with z. We find that while \u0394 increases as z in the near-field regions, it decreases as 1/z in the far-field regions. .Although it is very difficult to derive the general analytical expressions for the conditional position and angle uncertainties as a function of ys\u2223yi; z) and conditional angle uncertainty \u0394 change as a function of z. We note that the conditional momentum and OAM uncertainties \u0394 and \u0394 remain constant as a function of z because of the conservations of momentum and OAM, respectively, in SPDC. As a result, the functional dependence of \u0394\u0394 and \u0394\u0394 on z is same as that of \u0394 and \u0394, respectively. Therefore, the entanglement in the position-momentum bases as seen through EPR correlation product was found to decay very rapidly as a function of z, and after a few centimeters of propagation, there is no entanglement left in the position-momentum bases. On the other hand, although there is no entanglement left in the angle-OAM bases after a few centimeters of propagation just as in the case of position-momentum bases, the entanglement in the angle-OAM bases comes back after further propagation. We refer to this as the propagation-induced revival of entanglement in the angle-OAM bases. Although in our analysis, so far, we have used EPR uncertainty product as an entanglement witness, we observe qualitatively the same features in the propagation of angle-OAM entanglement with another witness, entanglement of formation , which is the conditional position uncertainty of the signal photon at z. Therefore, if we have a line of idler positions, shown by green line, the signal photon has the appreciable probability of being found in the blue shaded region. This green line represents the angular position \u03b8i = 0 of the idler. The corresponding conditional angle uncertainty \u0394 of the signal photon can be estimated by averaging the angle over the radial extent of the down-converted field from the center up to beam width ws(z) of the field. However, to a very good approximation, we can take the conditional angle uncertainty \u0394 to be of the order of \u0394/ws. ys\u2223yi; z) changes as a function of z, and fig. S3 in the Supplementary Materials shows how ws(z) changes as a function of z. We find that in the near field, \u0394 increases much faster compared to ws(z), while in the far field, it increases much slower compared to ws(z). Because of this, as a function of z, the conditional angle uncertainty \u0394 increases in the near field, while it decreases in the far field , P, P, and P through coincidence measurements of the two photons. An ultraviolet (UV) continuous wave (CW) Gaussian pump (Coherent Genesis STM UV laser) of wavelength \u03bbp = 355 nm, beam waist w0 = 507 \u03bcm is incident on a 5 mm\u2013by\u20135 mm\u2013by\u20135 mm \u03b2-barium borate (BBO) crystal. The crystal is cut in a manner that it produces signal and idler photons with collinear type I phase-matching condition. A long-pass filter is placed after the crystal to block the UV pump. We use an Andor iXon Ultra-897 electron-multiplied charge-coupled device (EMCCD) camera that has a 512 \u00d7 512 pixel grid with each pixel being 16 \u03bcm by 16 \u03bcm in size. A 10-nm bandpass filter centered at 710 nm is used to detect the down-converted photons. The blower heater (BH) produces turbulence by blowing hot air, and it is switched on during our experiments involving turbulence.P, P, and P, we use an EMCCD camera  and P and thereby the corresponding uncertainties \u0394 and \u0394, we image the transverse plane at z onto the EMCCD camera plane using a 4f-imaging system, as depicted in P at z, we use a 2f imaging system and keep the EMCCD camera plane at the Fourier plane of the transverse plane at z, as depicted in P at z. The conditional momentum uncertainty \u0394 is obtained by multiplying the conditional position uncertainty at the EMCCD plane by k\u0127/f, where f is the focal length of the lens. . For the coincidence measurements of the two-photon OAM probability distribution P, we make use of two electronically gated single-photon avalanche diode (SPAD) detectors  kept in the signal and idler arms. Specific holograms are displayed onto both the SLMs, and then, the signal and idler SLM planes are imaged onto the input facets of single-mode fibers (SMFs) kept in the signal and idler arms. The combination of the hologram and SMF in each arm projects the input field into a particular OAM mode, which then gets detected by the SPAD detector through the SMF. An electronic coincidence circuit then yields the coincidence counts. By displaying different holograms on the SLMs, we measure the two-photon OAM probability distribution. Next, we report our measurements of the condition uncertainty products \u0394\u0394 and \u0394\u0394 at various z values in the absence of turbulence. In our experiments, we measure \u0394 to be 2.13\u0127 \u00b1 0.1\u0127 mm\u22121, which is in good agreement with the value 1.97 \u0127 mm\u22121 calculated using ls\u2223li; z) should be zero. However, because of the imperfection in the spatial profile of the beam and other background issues, \u0394 is always finite in realistic experimental situations. We measure \u0394 to be 0.72 \u00b1 0.04 \u0127 radian\u22121 and use this in our experiments . Last, we measure \u0394 and \u0394 at various z values and plot the conditional uncertainty products \u0394\u0394 and \u0394\u0394 as a function of z in For the coincidence measurements of z = 15 cm to introduce turbulence \u0394 at different propagation distances ranging from z = 15 cm to z = 60 cm and plot them in s\u2223\u03b8i; z)\u0394 in the presence of turbulence, see sections S6 and S7 of the Supplementary Materials. Our numerical simulations show that in the presence of turbulence, the angle-OAM entanglement revives at z = 35 cm; experimentally, we find this distance to be about 45 cm. Therefore, we find that although turbulence does affect entanglement in the angle-OAM bases in an adverse manner, its effect can be completely undone by just propagating the photons further away by some distance.We next investigate whether the propagation-induced entanglement revival takes place in turbulent environments, which is quite often the limiting factor in the practical implementations of many entanglement-based applications. For this, we repeat our experiments depicted in ys\u2223yi; z)\u0394 and \u0394\u0394 close to the crystal (z < 3 cm) or in the far field (z > 10 cm). However, because of the signal-to-noise limitations of the EMCCD camera, it is not possible to make measurements in the intermediate regions. We find a very good qualitative agreement between our experiment results and numerical simulations reported inz = 0 plane of the down-conversion crystal onto a suitable z plane in the far field (In conclusion, using the two-photon field produced by SPDC, we have reported experimental observations of propagation-induced revival of entanglement in the angle-OAM bases. We have demonstrated this entanglement revival even in the presence of turbulence, the only effect of which is to increase the propagation distance for revival. Once revived, the two photons remain entangled up to an arbitrary propagation distance in the angle-OAM bases. We note that the entanglement revival strategies in turbulence or random media are usually based on adaptive optics techniques ("}
+{"text": "Lyapunov's first method, and Matlab 2020b is used for simulation analysis to verify the influence of each decision variable on different players' strategic choices. The results show that, firstly, new media's true reporting can make up for the lack of supervision of drug enterprises by local government, and the greater the impact of new media reporting, the more active drug enterprises will be to produce high-quality drugs. Secondly, non-collusion of third-party testing agencies can improve the self-discipline ability of drug enterprises, encourage new media to report truthfully, and play the role of co-regulation supervision. Furthermore, the greater the probability of new media's true reporting, the more local government tend to be stricter, and the probability of strict supervision is positively related to the central government's accountability. Finally, increasing penalty for producing low-quality drugs and collusion will help standardize the behavior of drug enterprises and third-party testing agencies. This article enriches and expands the theoretical basis of the drug quality co-regulation supervision and proposes corresponding countermeasures and suggestions.The efficiency and level of drug quality supervision are highly related to the distorted or true reporting of new media, and the collusion or non-collusion of third-party testing agencies. Therefore, based on the co-regulation information platform, considering the strategic choices of local government, drug enterprises, third-party testing agencies and new media, this article constructs a four-party evolutionary game model of co-regulation supervision. The stable equilibrium points of each participant's strategic choices are solved. The stability of the strategic combination is analyzed by  Drug quality supervision is an important part of ensuring the safety of public using drug and the national medical level. The development of the internet and the rise of new media have brought new opportunities and challenges to countries in drug quality supervision. In order to effectively reduce the uncertainty of regulatory decision-making, the US Food and Drug Administration utilizes new media platform, through social supervision and industry self-discipline, and after considerable development, has formed a set of effective regulatory model. The European Directorate for the Quality of Medicines is responsible for the drafting of policies on drug quality and risk prevention management of counterfeit drug, and incorporates drug safety supervision into daily management. The Pharmaceuticals and Medical Devices Agency uses non-governmental organizations, such as societies, industry associations, and the media, to supervise the self-discipline of the pharmaceutical industry, which has been an effective monitoring method for drug safety in Japan in recent years. In order to promote scientific drug supervision, the Chinese government is establishing a sound scientific and reasonable drug quality co-regulation supervision system .With the development of economic globalization, drug supervision is facing more problems. The development of regulatory science in the field of drug is not only between regulatory agencies and the industry, but also between patients, third-party testing agencies and society. Therefore, countries need to establish and improve drug supervision technology and information platforms, and make full use of emerging information technologies such as big data and artificial intelligence to establish drug information collection and tracking platform based on the concept of drug life cycle risk management. At the same time, there must be a standardized and authoritative new media platform to screen and release information to accelerate the development of scientific supervision and ensure the quality and safety of drug.Therefore, this article considers new media reporting and third-party testing agency behavior, based on the co-regulation information platform, constructs an evolutionary game model involving the participation of local government, drug enterprises, third-party testing agencies and new media. The stable equilibrium point of each game player's strategic choice is solved. The stability of the strategy combination and the influence of the changes of decision variables on the strategic choice are analyzed. The following three problems are solved, firstly, how does the co-regulation system affect the strategic choices of local government, drug enterprises, third-party testing agencies and new media? Secondly, how to play the role of the co-regulation information platform to promote the drug quality co-regulation supervision? Thirdly, how does the participation of local government and new media affect the strategic choices of drug enterprises and third-party testing agencies?Lyapunov's first method; The sixth part is the simulation analysis with Matlab 2020b; The seventh part discusses and outlines related suggestions; The last part suggests the conclusions.The remaining parts of this article are arranged as follows. The second part combs and reviews the relevant literatures; The third part makes hypotheses and constructs an evolutionary game model which involves local government, drug enterprises, third-party testing agencies and new media; The fourth part analyzes the stability of the strategic choices of the four participants; The fifth part analyzes the stability of strategy combination according to The problems and potential hidden dangers of drug quality shouldn't be underestimated. Once a drug quality accident occurs, a strong data drive is needed to support and enhance supervision decision-making . The outWith the increasingly wide range of supervision channels , the sinThe emergence of new media has made the transmission of information fast and extensive . When neFeedback from participants outside the government can strengthen the role of a national supervision system . Third-pIn summary, there is still a lack of consideration of four participants from the perspective of co-regulation supervision. In addition, the influence of new media reporting on the different strategic choices of each participant in the co-regulation supervision is not taken into account.Matlab 2020b simulation analysis, the validity of the model is verified, and countermeasures and suggestions are put forward for co-regulation supervision.Therefore, the research contributions of this article have the following three points. Firstly, considering new media participation and collusion behavior, based on the co-regulation information platform, this article builds a game model of quartet participation involving local government, drug enterprises, third-party testing agencies and new media. Secondly, considering the influence of true or distorted reports by new media, collusion or non-collusion of third-party testing agencies on the strategic choices of other participants, the evolutionary stable strategic combination under different conditions is solved. Finally, the influence of each decision variable on the strategic choices of four participants is solved and analyzed. And through This article chooses evolutionary game as the research method because it can explain the dynamic process of the evolution of each stakeholder's strategic choice and explain why this state has been reached and how to reach. The analysis paradigm of evolutionary game has a wide range of applications in social governance. Using the evolutionary perspective can more clearly see the final optimal decision of all parties in the game. Of course, when building a game model, the assumptions made for various relationships often deviate slightly from the reality, and need to be considered repeatedly, not only to meet the actual situation, but also to ensure the feasibility of the model. Therefore, considering new media participation and third-party testing agencies' collusion behavior, this article constructs the drug quality supervision structure relationship involving local government, drug enterprises, third-party testing agencies, and new media, as shown in H1 the local government chooses strict supervision with probability x, and loose supervision with probability 1 \u2212 x; drug enterprise chooses to produce high-quality drug with probability y, and low-quality drug with probability 1 \u2212 y; third-party testing agency chooses non-collusion with probability z, and collusion with probability 1 \u2212 z; new media chooses true reporting with probability p, and distorted reporting with probability 1 \u2212 p;x, y, z, p \u2208 . The four players are bounded rational participants.H2 the income from the operation of drug enterprises is Re, the cost of producing high-quality drugs is Ch, and the cost of producing low-quality drugs is Cl(Cl < Ch). The cost of seeking collusion is B.H3 the cost of strict supervision is Gh, and the cost of loose supervision is Gl (Gl < Gh). When local government strictly supervises, the drug enterprises that produce low-quality drugs will be fined as Fe; the third-party testing agencies that participate in collusion will also be fined as Fp.H4 the income of third-party testing agencies is V, and their detection cost is Cp. If third-party testing agencies choose collusion, they need to forge test records and issue false test reports. Let the speculative cost of collusion be Ct (Ct < B).H5 the cost of new media reporting is Cm, and the revenue from the true reporting is Rml. In reality, new media will distort reports in order to pursue economic benefits and obtain additional page views. Distorted reports will obtain a profit of Rmh. According to the \u201cspiral effect\u201d of media communication, negative news has a magnifying effect. The news that drug enterprises produce low-quality drug will get more clicks and benefits than news that produce high-quality drug, so there are Rml < Rmh. When drug enterprises produce low-quality drug, local government loosely supervises but third-party testing agencies are not colluding, the true reports of new media will cause local government to be held accountable by the central government, setting the accountability as Fg.H6 new media reports will affect the reputation of drug enterprises, which will bring economic gains or losses to them. Set the influence effect of new media reports as \u03b4, \u03b4 \u2208 . When drug enterprises produce high-quality drug, new media true reporting will bring a reputation value to them \u03b4I, and distorted reports will cause negative impacts and economic losses \u03b4L. At this time, drug enterprises can sue new media for rights protection and receive compensation Fm. When drug enterprises produce low-quality drug, new media reporting will damage the reputation of drug enterprises and cause loss of reputation value \u03b4N.The parameters and descriptions of this article are shown in Based on the above hypotheses, this article constructs a four-party mixed strategy game matrix for local government, drug enterprises, third-party testing agencies and new media, as shown in The expected benefit of local government choosing the \u201cstrict supervision\u201d strategy is:The expected benefit of local government choosing the \u201cloose supervision\u201d strategy is:The replicated dynamic equation and the first derivative of the local government's strategic choice are:F(x) < 0 and F\u2032(x) < 0.According to the stability theorem of differential equations, if the probability of local government choosing the \u201cstrict supervision\u201d strategy is to be in a stable state, the following conditions must be met: Proposition 1 When y < y0, z < z0 or p > p0, the local government's stabilization strategy is \u201cstrict supervision.\u201d When y > y0, z > z0 or p < p0, its stabilization strategy is \u201cloose supervision.\u201d When y = y0,z = z0 or p = p0, we are unable to determine its stabilization strategy. The thresholds areProof Make G = Gl \u2212 Gh + Fg \u2212 yFg + (1 \u2212 y)(1 \u2212 z)p(Fe + Fp \u2212 Fg), when G = 0,G/\u2202y < 0, \u2202G/\u2202z < 0 and \u2202G/\u2202p > 0, G is a decreasing function of y and z, and an increasing function of p. When, z < z0 or p > p0,G > 0,F(x)|x = 1 = 0 can be calculated, so x = 1 is stable. When y > y0, or p < p0 \u201e F(x)|x = 0 = 0 can be calculated, so x = 0 is stable. When, z = z0 or p = p0,G = 0 and F\u2032(x) = 0 can be calculated, we are unable to determine a stable strategy.y or z increases, the local government's stabilization strategy will change from strict supervision to loose supervision. If increases, the local government's stabilization strategy will change from loose supervision to strict supervision. Therefore, in drug quality co-regulation supervision, true reporting from new media can urge local government to perform strict supervision duty. When drug enterprises consciously produce high-quality drugs, local government will choose loose supervision in order to maximize social benefits and save supervision cost.Proposition 1 shows that if x isIn summary, the response function of According to Proposition 1, the phase diagram of local government strategic choice is shown in Vg1 is the probability that local government chooses the \u201cstrict supervision\u201d strategy, and the volume of Vg0 is the probability that local government chooses the \u201cloose supervision\u201d strategy. And,It can be seen from Corollary 1.1 when local government imposes more fines on drug enterprises and third-party testing agencies, it tends more to choose the \u201cstrict supervision\u201d strategy.Proof According to the probability Vg1, the first-order partial derivatives of Fe and Fp can be calculated:Fe and Fp. With the increase of Fe and, local government will conduct \u201cstrict supervision\u201d in order to obtain more revenue.Corollary 1.1 shows that the probability of local government choosing \u201cstrict supervision\u201d strategy is an increasing function of Corollary 1.2 When local government pays more additional cost for strict supervision, it tends more to choose the \u201cloose supervision\u201d strategy.Proof According to the probability Vg0, the first-order partial derivatives of Gh \u2212 Gl can be calculated:Gh \u2212 Gl. The higher the additional cost of strict supervision, local government will tend to choose loose supervision in order to save cost.Corollary 1.2 shows that the probability of local government choosing the \u201cloose supervision\u201d strategy is an increasing function of The expected benefit of drug enterprises choosing the \u201cproducing high-quality drug\u201d strategy is:The expected benefit of drug enterprises choosing the \u201cproducing low-quality drug\u201d strategy is:The replicated dynamic equation and the first derivative of drug enterprises' strategic choice are:F(y) = 0 and F\u2032(y) = 0.According to the stability theorem of differential equations, if the probability of drug enterprises choosing the \u201cproducing high-quality drug\u201d strategy is to be in a stable state, the following conditions must be met: Proposition 2 When x < X1, z > z1 or p > p1, drug enterprises' stabilization strategy is \u201cproducing high-quality drug.\u201d When x < x1,z < z1 or p < p1, their stabilization strategy is \u201cproducing low-quality drug.\u201d When x = x1,z = z1 or p = p1, we are unable to determine their stabilization strategy. The thresholds areProof Make, when K = 0, K/\u2202x > 0,\u2202K/\u2202z > 0 and \u2202K/\u2202p > 0, K is an increasing function of x, z and p. When x > x1, z > z1 or p > p1, K > 0, F(y)|y = 1 = 0 can be calculated, so y = 1 is stable. When x < x1,z < z1 or p < p1,K < 0,F(y)|y = 0 = 0 can be calculated, so y = 0 is stable. When x = x1,z = z1 or p = p1,K = 0 and can be calculated, we are unable to determine a stable strategy.x, or p increases, drug enterprises' stabilization strategy will change from producing low-quality drug to producing high-quality drug. Therefore, strict supervision by local government, urging third-party testing agencies to perform non-collusive social responsibility, and encouraging true reporting by new media can all prompt drug enterprises to proactively produce high-quality drug.Proposition 2 shows that if In summary, the response function of y is:According to Proposition 2, the phase diagram of drug enterprises strategic choice is shown in Ve1 is the probability that drug enterprises choose the \u201cproducing high-quality drug\u201d strategy, and the volume of Ve0 is the probability that drug enterprises choose the \u201cproducing low-quality drug\u201d strategy. And,It can be seen from Corollary 2.1 The higher the reputation value of high-quality drugs produced by drug enterprises and the greater the reputation loss of low-quality drugs, the greater the probability of producing high-quality drugs.Proof Make A = Ch \u2212 Cl \u2212 Fm \u2212 Fe\u2212\u03b4(N \u2212 L)\u2212(1 \u2212 z)B, T = \u03b4I + \u03b4N + Fe. According to the probability Ve1, the first-order partial derivatives of N and I can be calculated:Corollary 2.1 shows that increasing the price that drug enterprises need to pay for producing low-quality drugs or increasing the reputation benefits they earn from producing high-quality drugs can increase the probability that drug enterprises choose the strategy of \u201cproducing high-quality drug.\u201dCorollary 2.2 The higher the additional cost of producing high-quality drug by drug enterprises, the higher the probability of producing low-quality drug; the greater the influence effect of new media reporting, the lower the probability of drug enterprises producing low-quality drug.Proof Make A = Ch \u2212 Cl \u2212 Fm \u2212 Fe \u2212 \u03b4(N \u2212 L)\u2212(1 \u2212 z)B, T = \u03b4I + \u03b4N + Fe, U = \u03b4I+\u03b4L \u2212 Fm. According to the probability, the first-order partial derivatives of (Ch \u2212 Cl) and \u03b4 can be calculated:Ve0 is an increasing function of (Ch \u2212 Cl), and a decreasing function of \u03b4. When the additional cost of producing high-quality drug increases, drug enterprises tend to produce low-quality drug for economic benefits; when the influence effect of new media reporting is greater, in order to reduce reputation loss and ensure economic benefits, they are less likely to choose the strategy of \u201cproducing low-quality drug.\u201dCorollary 2.2 shows that the probability The expected benefit of third-party testing agencies choosing the \u201cnon-collusion\u201d strategy is:The expected benefit of third-party testing agencies choosing the \u201ccollusion\u201d strategy is:The replicated dynamic equation and the first derivative of third-party testing agencies' strategic choice are:F(z) = 0 and F\u2032(z) = 0.According to the stability theorem of differential equations, if the probability of third-party testing agencies choosing the \u201cnon-collusion\u201d strategy is to be in a stable state, the following conditions must be met: Proposition 3 When x > x2, or p < p2, third-party testing agencies' stabilization strategy is \u201cnon-collusion.\u201d When x < x2,y < y2 or p > p2, their stabilization strategy is \u201ccollusion.\u201d When x = x2, y = y2 or p = p2 we are unable to determine their stabilization strategy. The thresholds are Proof Make J = y(V \u2212 Cp) + (1 \u2212 y)(Fp + Ct \u2212 B) \u2212 (1 \u2212 y)(1 \u2212 x)pFp, when J = 0,J/\u2202x > 0,\u2202J/\u2202y > 0 and, J is an increasing function of x and y, and a decreasing function of p. When x > x2, y > y2 or p < p2,J > 0,F(z)|z = 1 = 0 can be calculated, so z = 1 is stable. When x < x2,y < y2 or p > p2,J < 0,F(z)|z = 0 = 0 can be calculated, so is stable. When x = x2, y = y2 or p = p2, J = 0 and F\u2032(z) = 0 can be calculated, we are unable to determine a stable strategy.x, yincreases, or p decreases, the stability strategy of third-party testing agencies changes from collusion to non-collusion. Therefore, in the drug quality co-regulation supervision, the government should strictly restrict the behavior of third-party testing agencies and promote the work pattern of co-regulation supervision.Proposition 3 shows that when z isIn summary, the response function of According to Proposition 3, the phase diagram of third-party testing agencies strategic choice is shown in Vp1 is the probability that the third-party testing agencies choose the \u201cnon-collusion\u201d strategy, and the volume of Vp0 is the probability that the third-party testing agencies choose the \u201ccollusion\u201d strategy. And,It can be seen from Corollary 3.1 The probability of non-collusion by third-party testing agencies is positively related to the speculative cost of participating in collusion.Proof According to the probability, the first-order partial derivatives of can be calculated:Corollary 3.1 shows that when the speculative cost of collusion by third-party testing agencies is higher, their motivation for collusion is weakened and the probability of choosing \u201cnon-collusion\u201d is higher.Corollary 3.2 The probability of collusion by third-party testing agencies is positively related to the cost of drug enterprises seeking to collude.Proof According to the probability, the first-order partial derivatives of B can be calculated:Corollary 3.2 shows that when the cost of seeking collusion increases, in order to obtain economic benefits, the higher the probability that third-party testing agencies choose to \u201ccollusion.\u201dThe expected benefit of new media choosing the \u201ctrue reporting\u201d strategy is:The expected benefit of new media choosing the \u201cdistorted reporting\u201d strategy is:The replicated dynamic equation and the first derivative of new media's strategic choice are:F(p) = 0 and F\u2032(p) < 0.According to the stability theorem of differential equations, if the probability of new media choosing the \u201ctrue reporting\u201d strategy is to be in a stable state, the following conditions must be met: Proposition 3 When x > x3, y < y3 or z > z3, new media's stabilization strategy is \u201ctrue reporting.\u201d When, y > y3 or z < z3, its stabilization strategy is \u201cdistorted reporting.\u201d When, y = y3 or z = z3, we are unable to determine its stabilization strategy. The thresholds areProof Make H = y(Rml \u2212 Rmh + Fm) + (1 \u2212 y)(1 \u2212 x)(1 \u2212 z)(Rml \u2212 Rmh), when H = 0\u201e,H/\u2202x > 0, \u2202H/\u2202y < 0 and \u2202H/\u2202z > 0, H is an increasing function of x and z, and a decreasing function of y. When x > x3, y < y3 or z > z3H > 0,p = 1 is stable. When x < x3, y > y3 or, H < 0,F(p)|p=0 = 0 can be calculated, so is stable. When x = x3, y = y3 or z = z3, H = 0 and F\u2032(p) = 0 can be calculated, we are unable to determine a stable strategy.x, z increases, or y decreases, the stability strategy of new media changes from distorted reporting to true reporting. Therefore, in drug quality supervision, new media can urge local government to strictly supervise, drug enterprises' integrity production, and third-party testing agencies to fulfill their social responsibility by reporting on drug quality information.Proposition 4 shows that whenIn summary, the response function of is:According to Proposition 4, the phase diagram of new media strategic choice is shown in Vm1 is the probability that new media chooses the \u201ctrue reporting\u201d strategy, and the volume of Vm0is the probability that new media chooses the \u201cdistorted reporting\u201d strategy. And,It can be seen from Corollary 4.1 The probability of true reporting by new media is positively correlated with the compensation to drug enterprises.Proof According to the probability Vm1, the first-order partial derivatives of can be calculated:Corollary 4.1 shows that as the cost of distorted reports increases, new media tend to report truthfully, which will help promote the social pattern of co-regulation supervision.Corollary 4.2 The probability of new media \u201cdistorted reporting\u201d is positively correlated with the additional revenue gained from distorted reporting.Proof According to the probability Vm0, the first-order partial derivatives of Rmh \u2212 Rml can be calculated:Corollary 4.2 shows that when the additional revenue of distorted reporting increases, new media will be more inclined to choose \u201cdistorted reporting.\u201d Therefore, local government should pay attention to the construction of new media platform, strengthen the management and regulation of it, and build new media into a healthy and upward platform.Corollary 4.3 When Fm > Fm0, new media will choose the \u201ctrue reporting\u201d strategy. When Fm < Fm0, it will choose the \u201cdistorted reporting\u201d strategy. The threshold is Proof According to Proposition 4, when H = 0, can be calculated. Because \u2202H/\u2202Fm > 0, H is an increasing function of Fm. When Fm > Fm0, H > 0, F(p)|p = 1 = 0 can be calculated. When Fm < Fm0, H < 0, F(p)|p = 0 = 0 can be calculated.Corollary 4.3 shows that when new media chooses to report distortedly, it needs to pay compensation to drug enterprises. If, it is possible to ensure that it will choose the \u201ctrue reporting\u201d strategy. Therefore, increasing compensation for distorted reporting can prompt new media to report truthfully, while at the same time making up for the losses caused by distorted reporting to drug enterprises, so as to avoid damaging the enthusiasm of them to produce high-quality drugs.Lyapunov's first method. If all the eigenvalues of the Jacobian matrix are negative, the equilibrium point is an evolutionary stable strategy (ESS). If at least one eigenvalue is positive, the equilibrium point is an unstable point. If the eigenvalues are all negative except for zero, the equilibrium point is in a critical state and the stability is uncertain. This article analyzes the stability of the 16 pure strategy Nash equilibrium points, the Jacobian matrix of the replication dynamic system isThe stability of each strategic combination can be judged according to When the stability strategy of new media is \u201ctrue reporting,\u201d that is, when condition is satisfied, the asymptotic stability analysis of the equilibrium point of the replicated dynamic system is shown in Cp < V, the equilibrium point  of the replicated dynamic system is ESS.It can be seen from The production of high-quality drugs by drug enterprises, non-collusion by third-party testing agencies, and true reporting by new media are the most ideal situation for local government. Therefore, when drug enterprises produce low-quality drug, local government must actively perform its supervision responsibility and impose severe penalty on them; encourage new media to report truthfully in a timely manner, so as to urge drug enterprises consciously produce high-quality drug.Rmh \u2212 Rml > Fm is satisfied, the asymptotic stability analysis of the equilibrium point of the replicated dynamic system is shown in When the stability strategy of new media is \u201cdistorted reporting,\u201d that is, when condition Cp < V, the equilibrium point  of the replicated dynamic system is ESS. When Gh \u2212 Gl < Fg and Cp < V, the equilibrium point  of the replicated dynamic system is ESS. When Cp > V, the equilibrium point  of the replicated dynamic system is ESS.It can be seen from When drug enterprises produce high-quality drug, in order to obtain economic benefits, new media will have distorted reporting, which will undermine the enthusiasm of drug enterprises to produce high-quality drug. Therefore, it is necessary to encourage all parties to perform their social responsibilities and play their respective roles. Standardize the behavior of new media and impose legal sanctions on distortions, rumors and so on. In addition, it is necessary to guide it to build a positive platform to better reflect the authority of the co-regulation information platform.Matlab 2020b for numerical simulation to verify the validity of the evolutionary stability analysis. Based on the actual conditions and the research of other scholars, this article makes assumptions about the numerical values in This article uses I = {0.0, 2.0, 4.0}, N = {0.0, 3.0, 6.0}, and the evolution process and results of players' strategy of the quartet game are shown in Set I and N are zero, the stable strategy of drug enterprises is to produce low-quality drugs. At this time, local government chooses loose supervision, new media chooses distorted reporting, and the probability of third-party testing agencies choosing non-collusion is stable at a relatively high level. With the increase of and, local government's stable strategy is loose supervision, the strategic choices of others continue to fluctuate. When I and N further increase, drug enterprises produce high-quality drug, new media reports truthfully, and third-party testing agencies are not colluding. At this time, local government doesn't need to conduct strict supervision. New media must actively play a supervisory and reporting role, urge drug enterprises to produce high-quality drugs, and establish a good image. Therefore, local government should improve drug quality public opinion supervision mechanism, use the co-regulation information platform to share information with new media, and give full play to the advantages of new media in drug quality supervision.Rmh \u2212 Rml = {0.0, 2.0, 4.0}, and the evolution process and results of players' strategy of the quartet game are shown in Set \u03b4 = {0.0, 0.4, 0.8}, Rmh \u2212 Rml are zero, the stability strategy of third-party testing agencies is collusion, the stability strategy of drug enterprises is the producing low-quality drugs, and the stability strategy of local government is loose supervision. The probability of new media choosing true reporting strategy is stable at a higher probability. When \u03b4 and Rmh \u2212 Rml increase, local government loosely supervises, and the strategic choices of drug enterprises, third-party testing agencies and new media are in a state of fluctuation. With the further increase in \u03b4 and, the strategic choices of drug enterprises and third-party testing agencies are in a state of fluctuation, local government loosely supervises, and new media distortedly reports. Therefore, we must pay attention to the construction of new media platforms, standardize the dissemination of drug quality information, and realize the active governance function of new media.p = 0.5. Suppose Gh \u2212 Gl = {0.0, 7.0, 11} and Ch \u2212 Cl = {0.0, 7.0, 11}. The tripartite game evolutionary process and results of local government, drug enterprises, and third-party testing agencies are shown in Let the probability that new media chooses true reporting is It can be seen from p = 0.5. Let Fg = {0.0, 4.5, 6.0}, Fe = {0.0, 4.5, 6.0}, and Fp = {0.0, 4.5, 6.0}. The tripartite game evolutionary process and results of local government, drug enterprises, and third-party testing agencies are shown in Suppose the probability of new media true reporting is It can be seen from Considering new media participation and third-party testing agencies' collusion behavior, this article constructs a quartet evolutionary game model. This article analyzes the influence of the change of each decision variable on the strategy evolution and puts forward the following suggestions.First of all, complete a co-regulation information platform, promote the establishment of a good co-regulation supervision system, and emphasize the joint participation of local government, drug enterprises, new media, and third-party testing agencies. It is necessary to mobilize the forces of all sectors of society to promote the formation of a drug quality supervision pattern involving government supervision, drug enterprises operation, new media reporting, and third-party testing agencies participation.Secondly, fully implement the main responsibility of drug enterprises, establish a \u201cblacklist\u201d system for them, notify and criticize enterprises that produce low-quality drugs, increase the scale and frequency of drug sampling, and give play to their self-discipline capability. In addition, drug enterprises should actively use new media platform to release authoritative information, track drug quality events and provide scientific professional knowledge explanations. Improve the public's ability to discriminate, and increase interactive communication through platforms such as Facebook, Twitter, and WeChat. Guide the public to use drug safely, and avoid losses caused by negative effects.Besides, we must attach importance to the construction of new media platforms, strengthen the management of new media, and impose legal sanctions on unscrupulous media that distortedly reports. Standardize the dissemination of drug quality information, improve the quality of new media practitioners, and build it into a healthy and upward platform. Give full play to the assisting role of media supervision to government supervision, further win the trust of the public, and realize the positive governance function of new media.Eventually, standardize the behavior of third-party testing agencies. Encourage them to fulfill their social responsibilities, feedback real drug quality test reports to the co-regulation information platform, and promote a good situation in drug quality co-regulation supervision.The sharing and interactive nature of new media makes it play an important role in drug quality supervision. Promoting the modernization of drug quality supervision requires the joint participation of multiple parties. Improve the social responsibility awareness of drug enterprises, increase policy support, reduce their production costs, and encourage them to consciously produce high-quality drugs. Restrict the behavior of third-party testing agencies, urge them not to participate in collusion, and assist local government to strictly supervise drug enterprises. Give full play to the advantages and functions of new media and encourage it to actively participate in co-regulation. According to the information provided by the co-regulation information platform, true reporting by new media are of great significance to enhancing the dissemination, guidance, and credibility of local government news releases.Considering the strategic choices of local government, drug enterprises, third-party testing agencies, and new media, this article constructs a four-party evolutionary game model. However, the constructed game model is fully informative and single-stage under bounded rationality, and the game sequence is not considered. Therefore, considering the condition of incomplete information, constructing a multi-stage, repetitive and dynamic game model with multi-agent participation is the next research direction.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.SZ wrote the manuscript and analyzed the data. LZ revised the manuscript and solved the model. All authors contributed to the article and approved the submitted version.This work was supported by the National Social Science Fund of China under grant Nos. 20BGL272 and 21ZDA024.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher."}
+{"text": "Nature Communications 10.1038/s41467-022-32852-6, published online 31 August 2022Correction to: The original version of this article contained errors in Eq. (1) and in Fig. 6b.T2. The equation incorrectly read:In Eq. (1), the values of the constant and coefficients were incorrectly given and the third term within the parentheses was missing the quadratic variable The correct form of Eq. (1) is:Furthermore, the original version of this article contained an error in Fig. 6b, in which the \u2018x\u2019 and \u2018y\u2019 axes were incorrectly labelled as \u2018Time (min)\u2019 and \u2018Resonant frequency (GHz)\u2019, respectively. The correct version of Fig. 6b is:These have been corrected in both the PDF and HTML versions of the article."}
+{"text": "Recently, deep learning methods have allowed the community to address both problems simultaneously, especially in the non-Cartesian acquisition setting. This work aims to contribute to this field by tackling some major concerns in existing approaches. Particularly, current state-of-the-art learning methods seek hardware compliant k-space sampling trajectories by enforcing the hardware constraints through additional penalty terms in the training loss. Through ablation studies, we rather show the benefit of using a projection step to enforce these constraints and demonstrate that the resulting k-space trajectories are more flexible under a projection-based scheme, which results in superior performance in reconstructed image quality. In 2D studies, our novel PROjection for Jointly lEarning non-Cartesian Trajectories while Optimizing Reconstructor (PROJeCTOR) trajectories present an improved image reconstruction quality at a 20-fold acceleration factor on the fastMRI data set with SSIM scores of nearly 0.92\u20130.95 in our retrospective studies as compared to the corresponding Cartesian reference and also see a 3\u20134 dB gain in PSNR as compared to earlier state-of-the-art methods. Finally, we extend the algorithm to 3D and by comparing optimization as learning-based projection schemes, we show that data-driven joint learning-based PROJeCTOR trajectories outperform model-based methods such as SPARKLING through a 2 dB gain in PSNR and 0.02 gain in SSIM.Compressed sensing in magnetic resonance imaging essentially involves the optimization of (1) the sampling pattern in  Using Compressed Sensing (CS) theories\u00a0[k-space according to Variable Density Sampling (VDS)\u00a0[k-space, as this type of sampling, which relies on curves, is more flexible and efficient compared to straight lines used in traditional Cartesian acquisitions. While conventional non-Cartesian sampling patterns such as spiral, radial, rosette, etc. [k-space according to VDS, they do not sample at a well-defined user specified Target Sampling Density (TSD). Tailoring such non-Cartesian trajectories according to a MR imaging protocol and a given TSD is hard, as these k-space sampling curves or trajectories are constrained by the MR hardware limits, notably on the maximum gradient magnitude A major challenge limiting the use of Magnetic Resonance Imaging (MRI) is long acquisition times, arising due to short decay of the MR signal, which is used to sample multi-dimensional theories\u00a0, signifing (VDS)\u00a0,3,4,5,6,te, etc. ,10,11,12k-space sampling pattern according to a prescribed TSD. Such patterns are typically segmented into multiple shots or k-space trajectories, each of them being compliant with the above-mentioned MR hardware constraints. Further, the algorithm results in locally uniform sampling patterns, and thus avoids holes and clusters in k-space. However, the SPARKLING is a model-driven framework, which is characterized by a TSD that needs to be known in advance to feed the optimization process. Previously, in\u00a0[To meet these constraints in a safe manner, the Spreading Projection Algorithm for Rapid K-space sampLING (SPARKLING) was introduced in ,14, and usly, in\u00a0, to addrusly, in\u00a0 as an acusly, in\u00a0, griddedk-space sampling trajectories and MR image reconstruction in a data-driven manner on the fastMRI dataset\u00a0[Recently, new methods\u00a0,19,20 ha dataset\u00a0. In\u00a0[18, dataset\u00a0, resultik-space. Finally, both methods do not make use of Density Compensators (DCp), which plays a key role in obtaining clearer MR images in the non-Cartesian deep learning setting\u00a0[In B-spline parameterized Joint Optimization of Reconstruction and K-space trajectories (BJORK)\u00a0, the aut setting\u00a0.k-space trajectories in a data-driven manner while embedding a projected gradient descent algorithm\u00a0[k-space sampling trajectories and use multi-resolution\u00a0[k-space trajectories and demonstrate its superiority over penalty-based methods like PILOT and BJORK to enforce hardware constraints. Finally, we compare and show the superiority of data-driven PROJeCTOR trajectories compared to model-based non-Cartesian SPARKLING trajectories.In this work, we first develop a generic model for PROJeCTOR. More precisely, we introduce a method that learns the lgorithm\u00a0 to fulfisolution\u00a0 similar solution\u00a0 and BJORsolution\u00a0 in 2D MRk-space trajectories and deep neural networks for MR image reconstruction. Particularly, we discuss 2 sub-models; namely, (1) an acquisition model parameterized by k-space trajectory, and (2) a reconstruction model parameterized by a deep neural network. Later, we discuss in detail how to handle the MR hardware constraints and which approach seems the most efficient within the sampling pattern optimization process to end up with hardware compliant k-space trajectories.In this section, we present a generic and modular framework  for leark-space data as input in the pipeline shown in In order to reduce the memory footprint and the training time, we did not process multicoil N. This assumption is purely for notational convenience and does not limit the applicability of our framework to isotropic data. If D is the imaging dimension, we denote a MR image or volume as k-space of this acquisition is defined in k-space to TObs) = 5.12 ms\u00a0(readout time), giving us Overall, we rely on notations developed in\u00a0, and we For our experiments in 2D imaging, we used the fastMRI brain MR data set\u00a0, which cdata set\u00a0, which c 20\u00a0(see ), resultk-space sampling pattern The acquisition model is parameterized by a k-space trajectories are constrained in speed and acceleration by the maximum gradient strength k-space is sampled at Echo Time (TE) in every shot, resulting in a stable and required target contrast of reconstructed MR images. From [The es. From ,24, we m \u03a9 (from ):(2a)\u03b1=A and v in  at every dwell time k-space data k-space trajectory to have With the  (NUFFT)\u00a0 operatork-space trajectories are non-Cartesian, this creates a variable density sampling in k-space, due to which a simple adjoint of NUFFT operator k-space samples associated with the low and high frequencies during the iterative reconstruction process. Following this principle, we obtained DS(K) for the linearly interpolated k-space trajectory As the 20 years\u00a0. It alloribed in . As noteribed in , DCp is k-space data k-space trajectory The reconstruction network k-space and convolutional neural network (CNN) based denoising in the image domain with kernel size A simple parameter-free reconstruction would be the density compensated adjoint, i.e., NC-PDNet\u00a0) as the re as in  except tx and its reconstruction S) [k-space trajectory K as follows: The reconstruction error used as loss function pired by\u00a0 and is dndex\u00a0(S) :LrK, we derived the gradient of the loss function K: For optimizing the trajectory For ease of mathematical derivation, here we take the case of a parameter-free reconstruction as described in k-space trajectory K, we used [k-space region\u00a0(as noted in [In order to compute the gradient of NUFFT operators  we used  to obtainoted in ), we usek-space trajectory were extremely noisy for this low batch size in 3D, we relied on a smaller learning rate of During training, the gradient descent was carried out stochastically with a batch size of 64 in 2D, while due to memory limitations, it was limited to 1 in 3D. However, as the gradients with respect to k-space sampling trajectories was performed using a multi-resolution strategy\u00a0[K at the maximal Inspired by SPARKLING\u00a0, the leastrategy\u00a0 which stk-space trajectory over a reduced number of locations\u00a0LNeed for hyper-parameter tuning: Under the penalty based formulation, the hyper-parameters Equation\u00a0 as an auEquation\u00a0, the corInfluence of gradients and convergence: With the addition of penalty terms k-space trajectories. Gradient updates with these additional gradient terms can no longer guarantee optimal image reconstruction by minimizing the reconstruction loss Guarantee of admissibility: Finally, the optimization of the augmented Lagrangian form does not guarantee that the final optimized k-space trajectory K satisfies the constraints Equation\u00a0 generatPractical implementations involved 50 iterations of the projection algorithm from , which wtensorflow-nufft\u00a0[cuFINUFFT\u00a0[All our implementations in 2D were carried out on a V100 GPU with 32GB memory, while our 3D implementations needed the next generation A100 GPUs with 80 GB of memory. Most of the memory in 3D was occupied by the activations from the 3D convolutional neural networks used in the image denoising step in NC-PDNet. Memory efficient implementations of NUFFT was carried out by using ow-nufft\u00a0, which iuFINUFFT\u00a0.k-space sampling pattern and reconstruction network in 3D by comparing it to SPARKLING trajectories with a learned neural network for image reconstruction.In this section, we first compare our results with state-of-the-art methods, particularly BJORK\u00a0 and PILOk-space trajectories with We learned ng LOUPE\u00a0 as obtaing LOUPE\u00a0 as a recWe compared our results with PILOT and BJORK trajectories\u00a0, which wk-space is under-sampled with respect to the fully sampled Cartesian k-space, while AF reflects on how fast the scan is with respect to the Cartesian reference scan.As the BJORK trajectory was learned for mparison  was donek-space trajectories as compared to those yielded by BJORK and PILOT. Then, we compare the reconstruction results of the learned trajectories with BJORK and PILOT.We first proceed to analyze the k-space (cf. the white spot shown in the bottom inset), while BJORK samples the k-space densely slightly off the center (cf. bottom inset), which is suboptimal. In contrast, PROJeCTOR and SPARKLING methods sample the central region of k-space more densely, which could help obtain improved image quality, notably the contrast.When looking at the zoomed portions of optimized trajectories in We also observe at the bottom of each panel in k-space data using PILOT /Peak Signal-to-Noise Ratio (PSNR) scores between PILOT and PROJeCTOR on one hand and BJORK and PROJeCTOR on the other hand and obtained p-values Next, we compared the results of image reconstruction from retrospectively under-sampled ng PILOT  and BJORng PILOT  trajectok-space sampling trajectories through joint optimization with a reconstruction network using a penalty term instead of a projector.In the above section, we showed how our method outperforms PILOT and BJORK in terms of reconstructed image quality. We assume that these results are due to the different manners that the hardware constraints on the gradients are enforced in the learning process (projector vs. regularizer). To validate this hypothesis, we learned 3D hardware compliant k-space sampling trajectories using the projection and penalty-based methods, and then in In k-space trajectories get more constrained. Interestingly, as k-space trajectories are getting hardware compliant  and (A.c)). This type of imperfection is not present in the learned PROJeCTOR k-space sampling pattern ((B.b) and (B.c)). Further, as the trajectories and reconstruction network were learned on partial Fourier k-space data, PROJeCTOR trajectories also learned to exploit this by not sampling these regions (see the dark areas pointed out by green arrows in (B.b) and (B.d)).From the mid-slice cuts of gridded sampling patterns in Finally, comparing the actual reconstructed MR images in In this work, we present a generic framework for jointly learning the trajectory and image reconstruction neural network. We embedded the projection step from  and learAlthough the learned neural networks in PILOT  and BJORThis improvement over state-of-the-art methods can be attributed to the embedded projection step as compared to penalty to ensure hardware compliance. We carried out an ablation study and showed that the projection step is crucial for having significantly improved performance of the learned trajectories, as compared to penalty-based approaches.Finally, in 3D, we compared the model-driven method SPARKLING with the data-driven method PROJeCTOR and showed a gain of 2 dB in PSNR and 0.02 gain in SSIM in favor of the latter.Future prospects of this work include prospective implementations through modifications of A limitation of current work is that our training paradigm was set-up in an emulated single coil setting as we were limited by memory constraints on GPU. A more realistic implementation would involve a multi-coil imaging setting, which is mandatory to efficiently utilize parallel imaging and become closer to the real data acquisition context, allowing us to reach higher AF. However, this memory bottleneck can be alleviated through efficient transfers between CPU and GPU or multi-GPU implementations. Further, the network can be improved by extending the currently implemented simple forward acquisition model NUFFT to a more realistic and complex model, which takes off-resonance effects due to eneities  and grad"}
+{"text": "Originally, the information in row Availability of work and column Comparison category/base category appeared as 0: Working, 1: Not working. This has been corrected to 0: Not Working, 1: Working.In the article, \u201cFactors related to preparedness for emergency hemodialysis in the event of a natural disaster\u201d,"}
+{"text": "This protocol provides instructions on how to run a linear optimization model that determines the cost-optimal supply of coal, from Chinese and foreign mines, to satisfy a given demand for coal in Chinese power and steel plants. We describe how to download the code and required software and detail steps to insert third-party data. We further provide instructions to adjust and define the scenario settings, build and solve the optimization problem file, and visualize the model outcomes.For complete details on the use and execution of this protocol, please refer to Gosens et\u00a0al. (2022).  \u2022Protocol describes a model to determine the least cost supply of coal to China\u2022Describes how to download all required code and software and insert coal mine data\u2022Provides instructions to adjust scenario settings and run the optimization model\u2022Has instructions to expand node-and-link model and scripts to visualize outcomes Publisher\u2019s note: Undertaking any experimental protocol requires adherence to local institutional guidelines for laboratory safety and ethics. This protocol provides instructions on how to run a linear optimization model that determines the cost-optimal supply of coal, from Chinese and foreign mines, to satisfy a given demand for coal in Chinese power and steel plants. We describe how to download the code and required software and detail steps to insert third-party data. We further provide instructions to adjust and define the scenario settings, build and solve the optimization problem file, and visualize the model outcomes. This protocol provides instructions on how to run the \u201cInstallation-Level China Coal Model (IL-CCM)\u201d,,,Understanding the Chinese market is of key relevance to understanding international trade in coal. China is the largest importer of both thermal coal (used for power generation) and coking coal (used for steelmaking), being responsible for roughly a quarter of total global imports of both types of coal.,,,,,,,,,,Determining the likely volumes of coal shipped from any mine, or from any country, to the Chinese market, requires understanding the relative competitiveness between these suppliers. A common approach to modelling such relative competitiveness is with so-called \u201cmultiregional coal supply models\u201d, with previous applications to global coal markets,The regions, or nodes, in such models can either produce or consume coal (or both), and are connected with other nodes through links, which represent transport infrastructure, and allow one node to supply coal demand in another node. These models include information on coal production capacity and cost for each producing node , transport capacity and cost for each link , and coal demand levels in consuming nodes.In comparison to these previous models, the IL-CCM stands out because of its very high geo-spatial resolution. The most detailed previous analysis with this modelling method represented China\u2019s coal production and demand conflated into provincial-level nodes, and the transport system conflated into inter-provincial links, for a total of 31 nodes and about 150 links.The IL-CCM model uses input data stored in spreadsheet files. Data preparation, processing of the solution file created by the optimization software, and visualization of results is done in R. The file with the linear problem written out as a set of mathematical expressions (a .lp file), for use in linear optimization, is created in Jupyter on a cloud computing instance, whilst solving the problem file is done locally with the CPLEX solver.,We provide all code and data used in this protocol in a public repository, whereas earlier work with similar methods, at best, provided only mathematical descriptions of the optimization model,Timing: 10\u00a0min1.https://doi.org/10.5281/zenodo.7222764.Download the repository with fully functional code, data, and folder structure from Zenodo: 2.Extract the repository to any location on your computer.Note: Most of the scripts used below use relative file paths. Any absolute file reference in the below will use \u201c\u223c/China-coal-model-star-protocol/\u201d to indicate the location of the extracted repository on your machine.The IL-CCM repository includes all the required code and data to run the model. When editing files in this model, only change the values of input data, and do not change the names of files, or sheet or column names in spreadsheet files.Timing: 1\u20132 h3.a.https://www.woodmac.com/).Option 1: Purchase the \u201cChina and Mongolia coal supply\u201d and the \u201cSeaborne Export Thermal Curve\u201d and \u201cSeaborne Export Metallurgical Curve\u201d from Wood Mackenzie  is in for Chinese mines, or what country a mine (cluster) is in for foreign mines.iii.A technical production capacity and total cash cost in US$/t.iv.Coal quality data, specifically: whether it is thermal, hard coking, semi-soft coking, or pulverized coal for injection, as well as calorific value  for thermal coals.Option 2: Use any other data supplier or own assumptions. Data requirements are:Purchase or prepare mine-level coal-mine data.Note: the repository described in the step \u201cDownload IL-CCM data and code repository\u201d still includes the coal mine data sheets with the required layout. These files have been censored by replacing data with arbitrarily picked numbers for key technical and economic indicators. That means the model will run fine, but will produce unrealistic results until these coal mine data sheets have been updated with real data.The repository described in the previous step does not include mine-level production costs, production capacity, and coal qualities, as this is proprietary third party data. The user can either use the same third-party data as was originally used in creating this model, or alternatively they may use their own coal mine data, or from any other commercial supplier, although it is substantially more work to insert such data into the model.Timing: 1\u20133 h4.Note: the versions mentioned in the steps below are the versions as used during the creation of this protocol. Older or newer versions may work as well.a.Download and install R version 4.0.5.b.Download and install R Tools version 4.0.c.i.Open the file \u201cChina-coal-model-star-protocol.Rproj\u201d in the data and code repository.ii.>install.packages('renv')Install renv by typing:iii.>renv::restoreInstall all required packages by typing:iv.Type \u201cy\u201d when prompted \u201cDo you want to proceed?\u201dOption 1 (Recommended): Install required packages using the environment file provided with the data and code repository.d.i.>install.packages('devtools')Install devtools by typing:ii.> require(devtools)> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_version> install_versionInstall all required packages by typing:Option 2 (Alternatively): Install required packages manually.Install R and associated software.5.a.Download and install Anaconda 3 v2022.05.b.https://docs.anaconda.com/anaconda/install/verify-install/).Open a Anaconda prompt : Install required software using the environment file provided with the data and code repository, by typing:d.> conda create -n china-coal-imports python=3.6.10 pandas=1.1.1 numpy=1.19.1 xlrd=1.2.0 spyder=4.1.5> conda activate china-coal-imports> conda install -c conda-forge pulp=2.3Option 2 (Alternatively): Install required software manually, by typing:Install Python and associated software.6.a.https://www.ibm.com/products/ilog-cplex-optimization-studio) and click \u201cget the no-cost academic edition\u201d.Browse to the CPLEX website .Timing: 1\u20132 h7.a.https://azure.microsoft.com/ and click \u201cget started\u201d.Browse to b.Note: A free account will be sufficient for several model runs.Sign up with your details and pick a subscription plan.c.https://portal.azure.com/#home and click \u201ccreate a resource\u201d.Browse to d.Search for \u201cAzure Machine Learning\u201d in the resources search box, click \u201ccreate\u201d.e.Choose configuration options , and click \u201creview and create\u201d.Option 1: sign up with MS Azure.8.a.https://aws.amazon.com/sagemaker/ and click \u201cGet started with SageMaker\u201d.Browse to b.Sign up with your details and login.c.Click on \u201cget started\u201d and then \u201cset up sagemaker domain\u201d.d.Choose configuration options , and click \u201ccreate\u201d.e.Click on \u201cServices\u201d, then \u201cSupport\u201d, then \u201ccreate a case\u201d, \u201cLooking for service limit increases\u201d.f.https://docs.aws.amazon.com/sagemaker/latest/dg/notebooks-available-instance-types.html).Select limit type \u201cSagemaker studio\u201d form the dropdown, pick a region, and ask for a service limit increase to 1 for an instance  or as gross as received (SE gar), or both. For metallurgical coals define their coking strength after reduction (CSR) number.In the file \u201cselected coal quality data by mine and type -- CENSORED.xlsx\u201d: for every mine, define its name. Define whether its product type is thermal or metallurgical coal.ii.Note: For metallurgical, also define product sub-type  has to list the node that connects these foreign mines to the rest of the node-and-link network. There is one such node for each country, with values provided in the \u2018possible values\u2019 sheet. Do the same for all Russian thermal coal mine connected to the Chinese market via rail or road connections, in the sheet \u201cworksheet ovld mines connectors\u201d.In the file \u201cSeaborne Export Thermal - non energy adjusted Worksheet -- CENSORED.xlsx\u201d, in the sheet \u201cworksheet navo mines connectors\u201d: for every thermal coal mine supplying the seaborne market, define its name, and the country and 3 letter iso country code it is located in. Also define its production capacity, production cost, and the calorific value of its output.v.In the file \u201cSeaborne Export Met Worksheet -- CENSORED.xlsx\u201d, do the same as in last step, but for metallurgical coal mines. Define their coal subtype , and not their calorific value. Exclude Australian mines in this sheet.vi.In the file \u201cAustralia met coal worksheet -- CENSORED.xlsx\u201d, do the same as in last step, but for Australian metallurgical coal mines.vii.Copy all files in the folder \u201c\u223c/China-coal-model-star-protocol/1 input/alternative coal data - template\u201d into the folder \u201c\u223c/China-coal-model-star-protocol/1 input/WoodMac data\u201d, overwriting the files there in the process.Insert coal mine data as follows:b.Note: For this step, we have provided template files with a small set of example entries. Each of these template files contains a sheet named \u2018possible values\u2019 to explain restrictions on the values in each column. Adjust as follows:i.Note: the above mentioned file in the code and data repo contains exactly such a list for the node names as used in all of the files described in step a above.From each of the files created in step a above, collect all values in the column \u2018orig_node_name\u2019, and create a list with unique values of node names  in the file \u201c\u223c/China-coal-model-star-protocol/1 input/helper files/mine node list helper.xlsx\u201d.ii.Copy the list of mine node names from step i into the file \u201c\u223c/China-coal-model-star-protocol/1 input/alternative coal data - template/helper files/node location helper.xlsx\u201d, sheet \u201cloclist\u201d, pasting the list in column A, row 11438 onwards (highlighted in green in the spreadsheet).iii.For each mine node in step ii, add latitude and longitude.iv.Copy the list of mine node names from step i into the file \u201c\u223c/China-coal-model-star-protocol/1 input/alternative coal data - template/helper files/mine name to location.xlsx\u201d, sheet \u201cSheet1\u201d, pasting the list in column B, row 2 onwards (highlighted in green in the spreadsheet).v.Note: A list of self-explanatory basin names is provided in the sheet \u201cpossible values\u201d.For each mine node in step iv, add the location, which is either the country name, or for mines in China, the name of the province. For mines in China and Mongolia, also select the corresponding basin name.vi.For those mine nodes located in China, copy the list of node names and basins from step iii into the file \u201c\u223c/China-coal-model-star-protocol/1 input/alternative coal data - template/helper files/basin and mine names.xlsx\u201d, sheet \u201cchina mines\u201d, pasting the node name list into column B, row 2 onwards and the corresponding basin names into column C, row 2 onwards (highlighted in green in the spreadsheet). The rest of sheet automatically updates.vii.For those mine nodes located in Mongolia, copy the list of node names from step i into the file \u201c\u223c/China-coal-model-star-protocol/1 input/alternative coal data - template/network connector files/ international mongolia russia interconnectors cities.xlsx\u201d, sheet \u201cinternational\u201d, pasting the node name list into column B, row 44 onwards (highlighted in green in the spreadsheet).viii.Note: These destination nodes are all cities or railway stops along the border with Mongolia. More precise information on each is provided in the sheet \u201cdest node description\u201d.For each mine node in step vii, indicate to which node it should be connected (column dest_node_name), picking from the list of nodes provided in the sheet \u201cpossible values\u201d.ix.For each mine node in step vii, Also define whether the connection type between the mine and destination nodes is via rail or road, and what distance the link represents.x.Copy the contents of the folder \u201c\u223c/China-coal-model-star-protocol/1 input/alternative coal data - template\u201d into the folder \u201c\u223c/China-coal-model-star-protocol/1 input/\u201d, overwriting the files there in the process.Connect the mines defined in the above step to the rest of the node-and-link network.Option 2: when using mine-level data from other sources.The user can also use their own coal mine data, or from any other commercial supplier, but inserting such data into the model will require additional steps, as described below.Timing: 1\u20132 h3.Open the file \u201c\u223c/China-coal-model-star-protocol/1 input/input file details.xlsx\u201d.Note: This file contains explanations on the calculations made in each of the spreadsheets in the folder \u201c\u223c/China-coal-model-star-protocol/1 input\u201d, including on the values to be adjusted for scenario settings.4.Adjust demand for coal through 2030 for different industries using the files in \u201c\u223c/China-coal-model-star-protocol/1 input/energy demand files\u201d.Note: Demand levels can either be set at national levels, with an automatic distribution to provincial-level demand calculated by these sheets, or the user can adjust provincial-level demand directly.5.Adjust production capacity of coal-fired power plants and steel plants through 2030 using the files in \u201c\u223c/China-coal-model-star-protocol/1 input/Global Energy Monitor data\u201d.6.Adjust transport capacity of the railway network through 2030 using the file \u201c\u223c/China-coal-model-star-protocol/1 input/rail network/rail line capacities.xlsx\u201d.7.Adjust annual throughput capacity of coal ports through 2030 using the file \u201c\u223c/China-coal-model-star-protocol/1 input/port data/port loc and capa consolidated sources.xlsx\u201d.8.Adjust transmission capacity of the UHV network through 2030 using the file \u201c\u223c/China-coal-model-star-protocol/1 input/network connector files/UHV overview.xlsx\u201d.9.Run the script \u201c\u223c/China-coal-model-star-protocol/1 Build preparation script.R\u201d; this will take adjusted input files in \u201c\u223c/China-coal-model-star-protocol/1 input\u201d and summarize these into model build files, which are saved into \u201c\u223c/China-coal-model-star-protocol/2 build\u201d.These are instructions on how the user may define their own scenario settings for coal production, consumption and transport infrastructure capacity. Running the build preparation script (step 9 below) gathers the scenario settings from their respective spreadsheet files and processes these into model build files which are in the correct format to be read by the optimization script used in the next step.Timing: 10 hhttps://pypi.org/project/PuLP/). You can do this on a desktop machine, but it is recommended to be done using an online cloud computing service. These steps will create a problem file (extension \u201c.lp\u201d) to be used in a solver in the next step.10.a.https://portal.azure.com/#home and click on the Azure Machine Learning instance created under \u201cBrowse to b.Click \u201claunch studio\u201d.c.Click \u201cstart now\u201d under \u201cNotebooks\u201d.d.In the file folder structure, click on whatever folder you want to run the code in.e.In that folder, create two subfolders called \u201cbuilds\u201d and \u201cproblemfiles\u201d.f.In that same folder, upload the file \u201c\u223c /China-coal-model-star-protocol/2c Create problem file on MS Azure ML.ipynb\".g.In the folder \u201cbuilds\u201d, upload all the .csv files from the folder \u201c\u223c /China-coal-model-star-protocol/2 build\".h.>selected_year\u00a0= 2025Open the file \u201c2c Create problem file on MS Azure ML.ipynb\u201d on Azure, select the year you want to run the model for and fill that in line 32, i.e.:i.Note: We\u2019d recommend a \u201ccompute optimized\u201d instance with at least 16 virtual CPU and 32 GB of memory, i.e., an instance of type \u201cStandard_F16s_v2\u201d or better.Click on \u201cCompute\u201d under \u201cManage\u201d in the sidebar and click \u201cnew\u201d. Choose your options.j.Click on \u201cNotebooks\u201d under \u201cAuthor\u201d in the sidebar to go back to the optimization model script.k.> pip install pulpClick on \u201c+ Code\u201d under the code cell and type:l.Click \u201cRun cell\u201d next to the cell created in step k.m.Click \u201cRun cell\u201d next to the first cell.n.The problemfile created by these steps will appear in the folder \u201cproblemfiles\u201d after about 10 h; download it and copy it to \u201c\u223c /China-coal-model-star-protocol/4 solutionfiles\".Option 1: Create the problemfile with MS Azure.11.a.https://aws.amazon.com/sagemaker/ and login.Browse to b.Click \u201cServices\u201d, and then \u201cS3\u201d.c.Click \u201ccreate bucket\u201d, use a bucket name \u201csagemaker-studio-SOMETHING\u201d, i.e., anything starting with \u201csagemaker-studio\u201d; this allows easier access to the bucket from sagemaker studio.d.In this bucket, create two subfolders called \u201cbuilds\u201d and \u201cproblemfiles\u201d.e.In the folder \u201cbuilds\u201d, upload all the .csv files from the folder \u201c\u223c /China-coal-model-star-protocol/2 build\".f.Click \u201cServices\u201d, \u201cAmazon Sagemaker\u201d, then \u201cSagemaker dashboard\u201d in the sidebar, then \u201cOpen Sagemaker Domain\u201d, then \u201claunch app\u201d, then \u201cStudio\u201d from the dropdown.g.In the Sagemaker studio, click \u201cupload files\u201d, and upload the file \u201c\u223c /China-coal-model-star-protocol/2b Create problem file on AWS Sagemaker.ipynb\".h.Double click the uploaded file, choose image \u201cData Science\u201d, Kernel \u201cPython 3\u201d, Start-up script \u201cNo script\u201d when promoted, and click select.i.CRITICAL: You must have previously requested access to this type of instance. How to get that access is explained in step 8 under \u201cClick \u201cSelect instance\u201d at the top and select your preferred type of instance.j.> pip install pulpClick on the\u00a0+ icon to insert a cell below, and type:k.Click on this cell and click \u201cRun cell\u201d from the menu at the top.l.> bucket\u00a0='sagemaker-studio-SOMETHING'Click on the first cell and fill in the bucketname from step c where it reads:m.> selected_year\u00a0= 2025Select the year you want to run the model for and fill that in where it reads:n.Click \u201cRun cell\u201d in the menu at the top.o.The problemfile created by these steps will appear in the folder \u201cproblemfiles\u201d after about 10 h; download it and copy it to \u201c\u223c /China-coal-model-star-protocol/4 solutionfiles\".Option 2: Create the problemfile with AWS Sagemaker.12.a.> conda activate china-coal-importsLaunch an anaconda prompt and type.b.> spyderLaunch spyder by typing.c.Click open file and browse to \u201c\u223c /China-coal-model-star-protocol/2a Create problem file locally.py\".d.> currentDirectory\u00a0= \"\u223c/China-coal-model-star-protocol/\"Fill in the correct file location of the code and data repository in line 15, e.g.:e.> selected_year\u00a0= 2025Select the year you want to run the model for and fill that in line 12, e.g.:f.Press F5 to run the file.g.The problemfile created by these steps will appear in the folder \u201c\u223c/China-coal-model-star-protocol/3 problemfiles\" after a given period of time, depending on the computing power of your desktop machine, between circa 10\u00a0h to many days.Option 3: (Not recommended): Create the problemfile on your desktop machine.This step will take your scenario build files, and process it these with the Linear Programming modeler Package \u201cPuLP\u201d  solver, and can be 10\u2013100 faster when compared with other open source solvers. IBM offers a free license for the CPLEX Optimization Studio, but only for academic users, however. The CBC solver is an open source and completely free alternative.13.a.Open CPLEX Optimization Studio.b.> read \"\u223c\\China-coal-model-star-protocol\\3 problemfiles\\prob v13 baseline 2019.lp\"> opt> set logfile \"\u223c\\China-coal-model-star-protocol\\4 solutionfiles\\solution v13 baseline 2019.txt\"> display solution variables -Type below code, adjusting for the file name for the problem file you created in the previous step:Option 1: with CPLEX Studio.14.https://github.com/coin-or) included in PuLP.a.> conda activate china-coal-importsLaunch an anaconda prompt and type.b.> spyderLaunch spyder by typing.c.Click open file and browse to \u201c\u223c/China-coal-model-star-protocol/3a Solve with python.py\".d.Adjust the problem file and solution file name and location in lines 10 and 12.e.Run the script.Option 2: with python and the Coin-or branch and cut solver Open script \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/geocode locations.R\u201d and copy your Google Maps api credentials into line 19:c.Run this script; this saves location names with latitude and longitude data into the file\u00a0\u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/locations geocoded.xlsx\u201d.Geocode your nodes.19.Note: This step takes the geocoded locations from step 18, and creates a matrix with a combination of each location with all other locations in list of nodes from step 18. This is used to calculate distances from each node to every other node, using the latitude and longitude data of each point determined in step 18, as geodesic or \u201cas the crow flies\u201d distances. For each node, it retains links with the 12 nearest other nodes. For nodes even further away, we consider that these can be reached via other nodes. This ensures that each node is connected, whilst reducing the total number of links.a.Note: The example files currently included with the data and code repository contain a list of Chinese cities and their latitude and longitude.Copy the data (location names with latitude and longitude) in the file \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/locations geocoded.xlsx\u201d, created in step 18, into the files for origins \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/origins.xlsx\u201d and the file for destinations \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/destinations.xlsx\u201d.b.Run the script \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/calculate geodesic distances.R\u201d; this calculates \u201cas the crow flies\u201d distances between all node pairs and saves this info in \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/geodesic distances all.csv\u201d.Determine geodesic distances.20.Note: This step takes the pairs of nodes that are relatively close to each other, as determined with \u201cas the crow flies\u201d distances in step 19, and finds the real world driving distance between these node pairs.a.>register_googleOpen script \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions/geocode distances.R\u201d and copy your Google Maps api credentials into line 21:b.Run this script; this saves location names with geodesic as well as driving distances into the file \u201c\u223c/distances 12 nearest geodesic and geocoded.csv\u201d.Find driving distances.21.Insert these new connections in the appropriate file in the folder \u201c\u223c/China-coal-model-star-protocol/1 input/network connector files\u201d.As an example, we have included the exact data and code that we used to identify driving distances between each city and its nearest neighboring cities, in the folder \u201c\u223c/China-coal-model-star-protocol/9 geocoding network additions\u201d.The expected outcome with each run is 1) a problem file; 2) a solution file; 3) a set of spreadsheets with coal suppliers and coal flows; and 4) a set of visualizations of these model outcomes. The IL-CMM was built specifically to determine levels and origin of coal imports, at given levels of Chinese demand for coal, and with constraints on mine-level production capacity and transport capacity of different types of transport infrastructure. Model outputs are therefore focused on visualizing the origin of supply, the networks used to get to the final source of consumption, and changes in flows of coal under different scenario settings.The code and data repository includes 9 problem files; for each of the years 2015\u20132019, and a low and high demand scenario for 2025 and 2030. These demand scenarios correspond with the \u201cstated policies\u201d and \u201csustainable development\u201d scenarios from the IEA\u2019s World Energy Outlook.The current model is a highly detailed model of China\u2019s coal market. The demand and supply conditions in the rest of the world are included in very simplified form only, and cannot be adjusted. The model is also purely focused on coal consumption; it does not include cost-optimization between different sources of electricity and instead uses exogenous input from user defined demand scenarios to determine cost-optimal supply of that demand.A package throws a certain error in R or Python.It is recommended to use the environment files for both R and python provided with the code and data repository. These have been tested to run as a self-contained package. Instructions on how to use either of these environment files are provided under step \u201cThe solver reports that the problem is infeasible.\u2022You\u2019ve set demand levels for a certain type of coal at level exceeding the production capacity of all the mines in the model. This is an issue especially with PCI, which has the least supply slack in the model.\u2022You\u2019ve set provincial level demand for coal-fired power or steel at levels exceeding the provincial-level production capacity of coal-fired power plants or steel plants.\u2022You\u2019ve set a reduction in transport network capacities that disconnects different parts of the network from each other. This is unlikely as almost all nodes can also be reached by trucking networks.\u2022A special case is that the provincial-level city of Beijing has no operational power plants in the dataset after 2029; any coal-fired power demand must be delivered via UHV networks. Removing the UHV network whilst simultaneously setting a non-zero coal-fired power demand in Beijing will cause infeasibility.This is a generic issue that could happen when defining problem files. It indicates an incompatibility between different constraints in the model. Investigate by opening the problem text file and finding the definition of the constraint that the CPLEX Optimization Studio reports as causing the infeasibility. A number of likely causes are:The solution is to investigate whether and which demand, supply, and transport constraint cause the infeasibility and adjust scenario settings.When running the script in AWS Sagemaker it reports an error loading the files from the S3 bucket. This is likely due to a version of boto3 , as installed on AWS Sagemaker by default, that is incompatible with the provided script.> pip uninstall -y boto3> pip uninstall -y botocore> pip uninstall -y aiobotocore> pip install boto3==1.17.106 s3fs pulp mipreadUninstall the incompatible version of boto3 and its dependencies, and install a version that does work. To do so, run below code in a new cell in your jupyter notebook:jorrit.gosens@anu.edu.au).Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Jorrit Gosens (This study did not generate new unique reagents."}
+{"text": "T\u201d. It should be \u201cVKM Ac-2882T\u201d.In the original publication of the article, the number of the strain in VKM was incorrectly published as \u201cVKM 2882And the missing funding information \u201cThis research was funded by Sirius University (project BTH-RND-2127) for YVZ and by Ministry of Science and Higher Education of the Russian Federation (Agreement \u2116 075-15-2021-1085) for IAO, MVB\u201d are included.The original article has been corrected."}
+{"text": "Hearing a groove rhythm (GR), which creates the sensation of wanting to move to the music, can also create feelings of pleasure and arousal in people, and it may enhance cognitive performance, as does exercise, by stimulating the prefrontal cortex. Here, we examined the hypothesis that GR enhances executive function (EF) by acting on the left dorsolateral prefrontal cortex (l-DLPFC) while also considering individual differences in psychological responses. Fifty-one participants underwent two conditions: 3 min of listening to GR or a white-noise metronome. Before and after listening, participants performed the Stroop task and were monitored for l-DLPFC activity with functional near-infrared spectroscopy. Our results show that GR enhanced EF and l-DLPFC activity in participants who felt a greater groove sensation and a more feeling clear-headed after listening to GR. Further, these psychological responses predict the impact of GR on l-DLPFC activity and EF, suggesting that GR enhances EF via l-DLPFC activity when the psychological response to GR is enhanced. Our recent study using acute exercise with music showed that the key factor of exercise\u2019s effect on prefrontal executive function is a positive affective response3 expressed the two-dimensional axis of pleasure and arousal.A growing amount of evidence shows that physical exercise has beneficial effects on cognitive functions5. GR can be defined by the subjective score of \u201cWanting to move to the music\u201d and \u201cGood nori\u201d6. The groove sensation can be modulated by syncopation. Syncopation is a method of shifting rhythmic emphasis by manipulating the complexity of a rhythm. Rhythm with low to medium syncopation induces a higher groove sensation than does rhythm with high syncopation as evidenced by averages of mass groups in previous studies9. Low-frequency components, such as the bass drum, induce entrainment of body movement and musical beat10. In several previous studies, drum breaks consisting of hi-hat, snare-drum, and bass-drum sounds were used because they made it easy to control rhythmic factors, syncopation, bass sound, and tempo12.Another potential stimulus which can improve EF through a positive affective response is groove rhythm (GR). GR is a musical rhythm that induces the sensation of \u201cWanting to move to the music\u201d (groove sensation) accompanied by positive affective responses while listening to music13. Music with groove-inducing characteristics increasing in recent music popularity charts may be indicative of this14. That groove music improves gait performance in Parkinson\u2019s disease (PD) by reducing the cognitive demands of synchronizing to the beat and promoting vigorous movement17 shows that groove music affects the interaction between body movement and brain function. More interestingly, listening to groove music induces entrainment of body movement and musical rhythm together with positive affective responses18 and activates neural networks associated with motor and reward systems20. Since the dopaminergic reward system projects not only to emotion-related brain areas but also to cognition-related areas such as the PFC23, GR could increase PFC activity and lead to improved EF. However, no research has explored the effect of groove music on EF and prefrontal activity to date. The reason for this could be that the effect of GR on EF may have large individual differences because both groove sensation and concurrent positive affective responses to groove music would have many individual differences24 and both responses are associated with reward system activity11. Therefore, we should examine the single effects of GR on EF and its relationship with PFC activity. To examine this, consideration of the psychological responses to listening to GR as influential factors that explain individual differences and creation of an experimental model which can evaluate the effect of GR on EF and how it is related to PFC activity are necessary.Moving the body to music is a universal phenomenon  and one of the main powers of music26, which evaluates inhibitory EF, in order to clarify the effects of an acute bout (10\u00a0min) of exercise31. fNIRS is a non-invasive neuroimaging method which can monitor hemodynamic response to neural activation (neurovascular coupling)32 by using near-infrared light passing through tissue. Since fNIRS allows for the least restrictive measuring environment among neuroimaging modalities, it can measure regional cortical activation boosted by listening to music while minimizing possible negative environmental influences on psychological response and cognition. The CWST has been adopted in numerous neuroimaging studies including fNIRS studies35, and the brain regions related with the task are well known. The DLPFC is a key region for inhibitory control of EF36 and responsible for CWST performance38. In addition, the left hemisphere plays a key role in the processing of verbal information42. Therefore, we focused on the left dorsolateral prefrontal cortex (l-DLPFC) as the region of interest (ROI). A previous study indicated that l-DLPFC activity correlated with a positive affective response and that EF changed with a single bout of exercise with music3. Therefore, in the current study, the CWST was performed before and after listening to GR while monitoring l-DLPFC activity using fNIRS. In addition to this acute model, cluster analysis using the subjective senses of both groove sensation and psychological state when listening to GR was introduced, and we tried to reveal the individual differences in the effect of listening to GR on EF and task-related l-DLPFC activity.To that end, in the current study we introduce the combination of an acute experimental model that was used for the detection of exercise\u2019s effect on cognition and prefrontal activity and a grouping analysis to explore the psychological response to GR. In our previous research, we used functional near-infrared spectroscopy (fNIRS) with the color-word-matching Stroop task (CWST)GR elicits groove sensation and concurrent positive affective response, but it is not known whether it enhances inhibitory EF with l-DLPFC activity as a result. The purpose of this study is to determine whether GR enhances EF and l-DLPFC activity, focusing on individual differences in psychological responses to GR. Our working hypothesis is that GR presented as drum breaks with low to medium syncopation enhances CWST performance with task-related l-DLPFC activation. Furthermore, the effects can be remarkable in participants who experience a higher groove sensation and positive psychological state. This study will allow us to look ahead to new aspects of the effect of GR, for example a potential cumulative effect with exercise.t tests were conducted over condition . We confirmed that there were no differences in HR between conditions (t(48)\u2009=\u2009\u2212\u20090.983, P\u2009=\u20090.33). GR elicited significantly higher scores compared to WM in these items: \u201cGood nori\u201d (t(50)\u2009=\u2009\u2212\u200911.99, P\u2009<\u20090.001), \u201cWanting to move to the music\u201d (t(50)\u2009=\u2009\u2212\u20099.17, P\u2009<\u20090.001), \u201cFeeling like my body is resonating with the rhythm\u201d (t(50)\u2009=\u2009\u2212\u20095.62, P\u2009<\u20090.001), \u201cHaving fun\u201d (t(50)\u2009=\u2009\u2212\u200911.62, P\u2009<\u20090.001), \u201cExcited\u201d (t(50)\u2009=\u2009\u2212\u20099.00, P\u2009<\u20090.001), and \u201cFeeling clear-headed\u201d (t(50)\u2009=\u2009\u2212\u20094.16, P\u2009<\u20090.001). WM elicited significantly higher scores compared to GR in these items: \u201cStruggling to synchronize with the beat\u201d (t(50)\u2009=\u20094.35, P\u2009<\u20090.001), \u201cBored\u201d (t(50)\u2009=\u200910.73, P\u2009<\u20090.001), \u201cWanting to stop listening\u201d (t(50)\u2009=\u20096.48, P\u2009<\u20090.001), and \u201cFeeling discomfort\u201d (t(50)\u2009=\u20095.18, P\u2009<\u20090.001).Physical load and psychological measures for each experimental condition for all participants are shown in Table P\u2009<\u20090.001, Fig.\u00a0P\u2009<\u20090.001, Fig.\u00a0We confirmed whether the Stroop interference could be observed in this experiment Fig.\u00a0A-C. Reacneutral, RTincongruent, RTinterference, l-DLPFC oxy-Hbneutral, l-DLPFC oxy-Hbincongruent, and l-DLPFC oxy-Hbinterference were subjected to repeated measures two-way ANOVA with condition  and time  as within-subject factors \u2009=\u200925.02, P\u2009<\u20090.001 and F\u2009=\u200915.18, P\u2009<\u20090.001, respectively). There was no significant change of RTinterference \u2009=\u20091.33, P\u2009=\u20090.25), l-DLPFC oxy-Hbneutral \u2009=\u20090.89, P\u2009=\u20090.34), l-DLPFC oxy-Hbincongruent \u2009=\u20090.78, P\u2009=\u20090.37), or l-DLPFC oxy-Hbinterference \u2009=\u20090, P\u2009=\u20090.99) before or after listening for either of the GR or WM conditions.Stroop RTors Fig.\u00a0D,\u00a0E. Fornori\u201d  and \u201cFeeling clear-headed\u201d , respectively. In subsequent analyses,\u201cGood nori\u201d and \u201cFeeling clear-headed\u201d were used as representative items for psychological responses to listening to GR.To account for individual differences, we objectively classified the participants into groups using cluster analysis based on their psychological responses to listening to GR and compared the effects between inter/intra clusters. Pearson correlation coefficient between Stroop performance and all psychological variables are shown in Table In the two-cluster solutions, the ratio [inter-cluster variance/total variance] was 0.41 and there was overlapping of two clusters in the plot  was characterized by high groove and high feeling clear-headed and named the \u201cGroove-familiar\u201d cluster. The second cluster (n\u2009=\u200914) was characterized by high groove and low feeling clear-headed and named the \u201cLow feeling clear-headed\u201d cluster. The third cluster (n\u2009=\u200921) was characterized by low groove and low feeling clear-headed and named the \u201cGroove-unfamiliar\u201d cluster.nori\u201d (GR-WM) than the \u201cGroove-unfamiliar\u201d cluster \u2009=\u200946.15, P\u2009<\u20090.001). The \u201cGroove-familiar\u201d cluster had higher \u201cFeeling clear-headed\u201d (GR-WM) than the \u201cLow feeling clear-headed\u201d and the \u201cGroove-unfamiliar\u201d clusters \u2009=\u200936.44, P\u2009<\u20090.001). The \u201cGroove-unfamiliar\u201d cluster had higher \u201cFeeling clear-headed\u201d (GR-WM) than the \u201cLow feeling clear-headed\u201d cluster (P\u2009<\u20090.05). In the comparison of basic individual specifications of music/dance between the clusters with a repeated measures one-way ANOVA, no significant differences were revealed (Supplementary Table In the comparison of condition differences (GR-WM) between clusters, a repeated measures one-way ANOVA with cluster  was conducted Fig.\u00a0. The \u201cGrt test \u2009=\u20092.22, P\u2009<\u20090.05). \u0394l-DLPFC oxy-Hbinterference in the GR condition was significantly increased compared to the WM condition (t(15)\u2009=\u2009\u2212\u20092.16, P\u2009<\u20090.05). In the \u201cLow feeling clear-headed\u201d cluster, there were no significant differences between conditions for both CWST performance and l-DLPFC activity. In the \u201cGroove-unfamiliar\u201d cluster, \u0394Stroop RTinterference in the WM condition was significantly shorter than in the GR condition (t (20)\u2009=\u2009\u2212\u20093.52, P\u2009<\u20090.01). There were no significant differences between conditions for l-DLPFC activity.Next, comparisons between condition  within each cluster were conducted using the paired est Fig.\u00a0. In the nori\u201d, \u201cFeeling clear-headed\u201d), \u0394l-DLPFC oxy-Hbinterference, and \u0394Stroop RTinterference were used. The first model, \u03c72\u2009=\u20090.01, CFI\u2009=\u20090.69, and RMSEA\u2009=\u20090.22, yielded a very poor fit to the data. The relative effects were as follows ; \u201cFeeling clear-headed\u201d to \u0394l-DLPFC oxy-Hbinterference ; and \u0394l-DLPFC oxy-Hbinterference to \u0394Stroop RTinterference . The second model, \u03c72\u2009=\u20090.12, CFI\u2009=\u20090.91, and RMSEA\u2009=\u20090.14, yielded a poor fit to the data. The relative effects were as follows ; \u201cFeeling clear-headed\u201d to\u00a0\u0394l-DLPFC oxy-Hbinterference ; \u201cFeeling clear-headed\u201d to\u00a0\u0394Stroop RTinterference ; and \u0394l-DLPFC oxy-Hbinterference to \u0394Stroop RTinterference . The third model, \u03c72\u2009=\u20090.24, CFI\u2009=\u20090.98, and RMSEA\u2009=\u20090.08, yielded a satisfactory fit to the data. The relative effects were as follows ; \u201cGood nori\u201d to \u0394l-DLPFC oxy-Hbinterference ; \u201cFeeling clear-headed\u201d to \u0394l-DLPFC oxy-Hbinterference ; \u201cFeeling clear-headed\u201d to \u0394Stroop RTinterference ; and \u0394l-DLPFC oxy-Hbinterference to \u0394Stroop RTinterference . The final model showed both \u201cGood nori\u201d inducing \u201cFeeling clear-headed\u201d and \u0394l-DLPFC oxy-Hbinterference as starting factors and that \u201cFeeling clear-headed\u201d affected both \u0394l-DLPFC oxy-Hbinterference and \u0394Stroop RTinterference.In all models, the variables which were employed in cluster analysis  and positive affective response  compared with the WM by comparing average values. This agreed with previous studies showing that drum breaks with a low to medium degree of syncopation induce higher groove sensation9. To make the rhythm more interesting\u00a0to listeners and to thus induce\u00a0groove sensation and the related\u00a0positive affective responses,\u00a0a balance between expectation and\u00a0violation\u00a0of\u00a0the\u00a0rhythm is thought to be important12. This is supported by the hypothesis that prediction error (deviation from predicted rhythm) is a requisite for music to activate the reward system in the brain45. Since the validity of our experimental design was confirmed, we proceeded to the detection of the effect of GR on cognitive function.First, as a precondition of the experiment, we confirmed that drum breaks with a low to medium degree of syncopation (GR) induced groove sensation , listening to GR significantly enhanced EF and l-DLPFC activity compared to the WM condition  could be among the important factors for promoting the positive effects of GR. Generally, music induces positive affective responses and concurrently increases dopamine release and brain activation related to the reward system including the basal ganglia (BG), midbrain, and orbitofrontal cortex54. In the current experiment, the average scores for the beat-processing ability test among participants in both the \u201cLow feeling clear-headed\u201d and \"Groove-unfamiliar\" clusters were relatively low compared to the participants in the \"Groove-familiar\" cluster, but not significantly so (Supplementary Table 55) are needed to detect the influence of inhibiting factors.Conversely, the participants grouped in the \u201cLow feeling clear-headed\u201d and \u201cGroove-unfamiliar\u201d clusters experienced no or negative effects of GR on EF and l-DLPFC activity. One potential inhibiting factor is low beat-processing ability in those individuals. It is possible that participants who have a low beat-processing ability were forced to pay extra attention to the beat while listening to the GR. This may have resulted not only in inducing failure to become entrained, but also in reduced mental resources, which limited attention, motivation, and cognitive performance58. Though more than 50 students participated in the current experiment, the sample size was insufficient for conducting sub-analyses to seek the effects of these potential influential factors. Future studies should plan to compare the effects between participants grouped by these potential influential factors. Second, in the auditory stimulus, we used rhythm with a low to medium degree of syncopation as the GR stimulus and a white-noise metronome as the control stimulus. We could control tempo, but could not control the type and number of sounds. Further studies are needed to try to detect the influence of other acoustic specifications by using different patterns for the GR and control stimuli. Third, in the measurement of the brain\u2019s neural activation, the current study focused on only cortical, specifically the l-DLPFC, activity. We should use fMRI and PET to examine brain activity in broader and deeper regions that are involved with motor, reward, and cognitive systems, their networks, and released neurotransmitters.This study has several limitations. First, widespread individual differences in psychological responses to the rhythm were demonstrated in the current results. Various potential factors such as musical training experience, music reward sensitivity, beat processing ability, familiarity with groove music/dance, body morphology and cultural background could influence psychological responses to the rhythmIn conclusion, listening to a rhythm with low to medium syncopation enhanced EF and l-DLPFC activity in only groove-familiar participants, which supports our hypothesis. These results suggest that individual differences in psychological responses to GR are one of the key factors in predicting the effects of listening to GR on prefrontal EF. This study raises the potential that GR can enhance human cognitive performance like exercise.28 showed that the effect sizes of exercise were Cohen's d\u2009=\u20090.5\u2009~\u20090.7. In the current study, we estimated a slightly lower effect of GR than of exercise and conducted a Power Analysis with Cohen's d\u2009=\u20090.4. A Power Analysis using the sample size determination software G-power showed that 52 subjects would be considered sufficient to detect a significant difference (dz\u2009=\u20090.9) between groups on a two-sided, 0.05 test of proportions (difference between two dependent means [matched pairs]) with\u2009>\u200980% power. All participants were recruited from the student population of the University of Tsukuba through ethics board approved flyers that were displayed across the campus. No subject reported a history of neurological or psychiatric disorders or had a disease requiring medical care. All participants were Japanese native speakers and right-handed. All experimental protocols were approved by the Institutional Ethics Committee of the University of Tsukuba. The experiment protocols were in accordance with the guidelines of the latest version of the Helsinki Declaration. Written informed consent was obtained from all participants after being given complete information about this study. Before all statistical processes, seven participants were excluded from the analysis for the following reasons: reported short sleep duration the night before the experiment (N\u2009=\u20091), had a pre-session CWST correct-answer rate equal to 80% or less (N\u2009=\u20091), had a pre-session Stroop RTinterference with a negative value or 2SD greater than the average (N\u2009=\u20093), or had missing fNIRS data (N\u2009=\u20092). As a result, we analyzed the data of fifty-one participants. Demographics of the participants are presented in Supplementary Table Fifty-eight healthy young adults  took part in this study. Our previous fNIRS studies examining the effect of very light to moderate intensity exercise on CWST performance59, and they rated their dance familiarity by responding to the phrase, \u201cI often start to dance when music plays\u201d on an eleven-point scale ranging from 0\u2009=\u2009\u201cNot at all\u201d, 5\u2009=\u2009\u201cNeutral\u201d and 10\u2009=\u2009\u201cExtremely\u201d. On the third and fourth days, they underwent two experimental conditions: listening to groove rhythm (GR condition) or listening to a white-noise metronome (WM condition). The participants listened to auditory stimuli played through studio speakers  for 3\u00a0min in a standing position. To increase the groove sensation18, participants were instructed to \u201cplease beat the rhythm freely in your upper body, for example, tapping, nodding, and swaying\u201d. However, dynamic physical movement such as stepping was discouraged. In order to confirm the physiological load during listening, heart rate (HR) was measured using a wireless sports heart rate meter . Before and after listening, the CWST was conducted while hemodynamic changes in the l-DLPFC were monitored using fNIRS. After listening, participants answered a questionnaire about their psychological responses to the stimuli   by referencing a previous studynori\u201d, \u201cWanting to move to the music\u201d, \u201cFeeling like my body is resonating with the rhythm\u201d, \u201cEasy to synchronize with the beat\u201d, and \u201cStruggling to synchronize with the beat\u201d. We employed several terms closely related to groove as suggested in previous studies61. \u201cGood nori\u201d is a Japanese term similar to the concept of groove6. These items were also shown to be highly correlated with groove. The second category was about psychological state and included descriptors such as \u201cHaving fun\u201d, \u201cExcited\u201d, \u201cBored\u201d, \u201cWanting to stop listening\u201d, \u201cFeeling clear-headed\u201d, and \u201cFeeling discomfort\u201d. \u201cHaving fun\u201d and \u201cExcited\u201d have been shown to correlate with groove in previous studies62. \u201cBored\u201d, \u201cWanting to stop listening\u201d, and \u201cFeeling discomfort\u201d were the reverse. \u201cFeeling clear-headed\u201d was set as an item which expresses cognitive alertness64 to detect responses to GR based on the preliminary study. The eleven-point (0\u201310) scale ranged from 0\u2009=\u2009\u201cNot at all\u201d, 5\u2009=\u2009\u201cNeutral\u201d to 10\u2009=\u2009\u201cExtremely\u201d.To evaluate the potential for a psychological response to listening to the rhythm to mediate the effects on EF, we created two categories each consisting of eleven questions. The first category was about the sensation of groove including \u201cGood 28. The CWST is a task in which participants are presented with two rows of letters and they must determine whether the top row\u2019s color corresponds to the bottom row\u2019s color name. Subjects answered by pressing the \"yes\" or \"no\" buttons on a keyboard  with the index finger of their right and left hands.The Japanese version of the CWST, which has been validated in previous studies, was used to assess inhibitory control of a core component of executive function Fig.\u00a0B3,27,28.This task consists of three conditions: neutral, congruent, and incongruent. In the lower part of the screen, one of the four color-name words \"RED\", \"BLUE\", \"GREEN\", and \"YELLOW\" were displayed, in Japanese, for all trials. However, the characters displayed in the upper row of the screen were different for each condition: the symbol \"xxxx\" was presented in the neutral condition, a color word written in an ink color matching its meaning  was presented in the congruent condition, and a color word displayed in a color that did not match its meaning  was presented in the incongruent condition. The incongruent condition causes a cognitive conflict between the meaning and color of the upper row\u2019s word and induces a delay in reaction time (RT). We randomly displayed 30 trials including 10 neutral, 10 congruent, and 10 incongruent.interference), which represents inhibitory executive function. Every participant practiced the CWST at least three times before starting the first CWST session.To force the subjects to look from the upper row to the lower row, the upper row was displayed 100\u00a0ms earlier than the lower row. After 2\u00a0s of the upper characters being displayed, the screen returned to the fixation screen, which was centered on a \"+\" mark (gazing point). The inter-stimulus interval was randomized (10\u201312\u00a0s) for each subject to prevent them from predicting the timing. We evaluated RT for the incongruent task minus that for the neutral task to determine Stroop interference time  was placed over FT7, with the medial edge of the probe column parallel to the medial line , which is equipped with two wavelengths of near-infrared light (785 and 830\u00a0nm), was used. To cover the l-DLPFC using an fNIRS probe holder, the composition and placement of the fNIRS probe holder followed the same procedure as described in our previous studiesine Fig.\u00a0A. Likewi65. The oxy-Hb changes in the l-DLPFC were preprocessed with a band pass filter . The differences of the oxy-Hb signal between peak  periods and baseline  periods were calculated as the oxy-Hb change  space67. In brief, this method allows us to place a virtual probe holder on the scalp using a simulation of the holder\u2019s deformation and to register the probes and channels on reference brains in the MRI database71. ROIs are created by combining four neighboring channels, and anatomically labeled using LBPA40, which is a widely used method . The l-DLPFC as a ROI accounts for channels 13, 14, 16, and 17.The oxygenated hemoglobin (oxy-Hb) was analyzed and calculated in units of millimolar-millimeter (mM\u22c5mm)interference in the categories of \u201cSensation of groove\u201d and \u201cPsychological state\u201d . Regarding HR data, two datasets were missing because of slippage of the sensor band. For Stroop task performance, RT and ER were subjected to repeated-measures three-way ANOVA with condition , time , and task condition  as within-subject factors to examine whether the general tendencies for the Stroop task could be reproduced in all conditions. This analysis was limited to the main effect of the task condition because the purpose of the ANOVA was to examine the occurrence of Stroop interference. Subsequently, Stroop RTneutral, RTincongruent, and RTinterference [Incongruent\u2014Neutral] were calculated, and repeated-measures two-way ANOVA were performed with condition  and time  as within-subject factors. When there were significant interaction or main effects in the two-way ANOVA, post-hoc tests using the Bonferroni method were carried out. For l-DLPFC activity, in order to confirm whether there was a Stroop effect (l-DLPFC oxy-Hbinterference), l-DLPFC oxy-Hb changes were subjected to repeated-measures three-way ANOVA with condition , time , and task condition  as within-subject factors as for the Stroop task performance analysis. Subsequently, l-DLPFC oxy-Hbinterference [Incongruent \u2212 Neutral] was calculated, and a two-way ANOVA was performed with condition  and time  as within-subject factors. When there were significant interactions or main effects in the two-way ANOVA, post-hoc tests using the Bonferroni method were carried out.For HR and each psychological measure, paired interference and interference were calculated for the following contrast: [post \u2212 pre]. Condition differences of psychological measures, interference, and interference were calculated for the following contrast: [GR-WM]. Pearson correlation analysis between all psychological measures as independent variables and interference as a dependent variable was carried out.Subsequently, 72, representative variables which had the highest correlation with \u0394Stroop RTinterference in each category of \u201cSensation of groove\u201d and \u201cPsychological state\u201d were used for cluster analysis. As a result, \u201cGood nori\u201d and \u201cFeeling clear-headed\u201d were used. Regarding determination of the optimal number of clusters, we used the ratio of inter-cluster variance and total variance (R script: km$betweenss/km$totss)73 and visual inspection of the scatterplots. The ratio shows aggregability of intra-cluster and separation of inter-cluster. We determined the cluster number which showed a greater ratio of inter-cluster variance and total variance not exceeding three cluster numbers to avoid the difficulty of defining the clusters.The K-means method was used to identify relatively homogenous participant groups on R software. As with a previous study using the k-means methodinterference and interference between clusters, and the comparison of basic individual features of music/dance between clusters were conducted using a repeated measures one-way ANOVA with clusters. When there were significant main effects in the one-way ANOVA, a post-hoc test using the Gabriel method was carried out. Then, to detect the effect of listening to GR by cluster, the comparison of psychological measures, interference, and interference between conditions within each cluster were conducted using the paired t test over condition .After clustering, to reveal the specification of clusters, the comparison of condition differences [GR-WM] in psychological measures, 2 goodness of fit, the root mean square error of approximation (RMSEA), and the Comparative Fit Index (CFI). The criteria were as follows: CFI\u2009\u2265\u20090.90, RMSEA\u2009<\u20090.10, and \u03c72\u2009\u2265\u20090.05. Regarding RMSEA values, 0.05 is often used as the cutoff; however, this rejects too many valid models with small sample sizes (n\u2009\u2264\u2009100)74. Conversely, RMSEA values greater than or equal to 0.10 suggest a poor fit75. Thus, we set the criteria as RMSEA\u2009<\u20090.10. The variables were \u201cFeeling clear-headed\u201d, \"Good nori\", interference, and interference, and they were reflected in differences between conditions [GR \u2013 WM].To address a possible causal relationship, path analysis was conducted using the \u201clavaan\u201d package in R software. Model fit was evaluated with the \u03c7interference as an indirect effect on EF and to interference as a direct effect on EF. The third model was a modified version of the second model which included the influence of \u201cGood nori\u201d on\u00a0\u0394l-DLPFC oxy-Hbinterference.Three models were tested to examine the causal relationship between the variables depending on the hypothesis. The first model assumed that all variables have only a direct effect. The second model allowed that \u201cFeeling clear-headed\u201d has two paths: to\u00a0\u0394l-DLPFC oxy-HbSupplementary Information."}
+{"text": "It perturbs data nonlinearly while accommodating the requirement of strict privacy protection, for instance, differential privacy. We highlight multiple facets of data flush through examples.Data perturbation is a technique for generating synthetic data by adding \u201cnoise\u201d to raw data, which has an array of applications in science and engineering, primarily in data security and privacy. One challenge for data perturbation is that it usually produces synthetic data resulting in information loss at the expense of privacy protection. The information loss, in turn, renders the accuracy loss for any statistical or machine learning method based on the synthetic data, weakening downstream analysis and deteriorating in machine learning. In this article, we introduce and advocate a fundamental principle of data perturbation, which requires the preservation of the distribution of raw data. To achieve this, we propose a new scheme, named  The explosive growth of large volumes of data with complex structures demands the wide usage of data in applied sciences. In privacy protection, data perturbation is an effective technique. For instance, it privatizes the U.S. Decennial Census Data to protect the confidentiality of individuals by the standard of differential privacy  In the \u03b5-differential privacy  from a cumulative distribution function (CDF) F, we perturb the raw sample to follow a prespecified target distribution R. For example, R can be a standard normal distribution or a uniform distribution. But more commonly, R = F if F is known and Given an independent sample  from Uniform and relabel them so that the rank of Ui in  remains the same as that of Zi in . This transformation from Zi to Ui encodes a positive (Spearman\u2019s rank) correlation between the perturbed and the original samples, c.f., m perturbed samples. We add independent continuous noise eij, j = 1, . . .,m, to Ui independently. Then, we map Ui + eij to yield a perturbed sample following the target distribution R:G is the CDF of Ui + eij.First, we sample  following a p-dimensional continuous distribution F, we apply Rl)-differential privacy  distribution to guarantee \u03b5-differential privacy  for a Gaussian sample . Data flush provides a means of evaluating the model sensitivity for various data.To quantify the impact of model selection on estimation, Data-flush in 3.\u03b8.This section develops a data perturbation tool for pivotal inference based on raw data without privacy concerns. We apply the data-flush scheme Z = , with each Zi following a probability distribution F(\u03b8), and F is known but \u03b8 is unknown. The distribution of T is independent of \u03b8, which requires a Monte-Carlo resampling method such as bootstrap to estimate, as its analytic form is often unavailable. However, such a resampling method may suffer the difficulty of inference after model selection. As pointed out in T.Let Z =  according to Zi follows a target distribution Z\u2217 by applying the same statistical procedure for Data flush generates a pseudo sample T\u2217 given Z, which can substitute an unknown distribution of T for pivotal inference. Note that the former can be computed but not the latter.(Distribution preservation) The conditional distribution of T\u2217givenZremains the same as the distribution of T for anyZ. Hence, any test or a confidence interval on the conditional distribution of T\u2217givenZis exactly as if the distribution of T would have been used.The proof is given in the T\u2217 given Z via a Monte-Carlo approximation while correcting bias through data perturbation to improve the finite-sample performance. Data perturbation permits estimation of the bias of a statistical procedure through repeated experiments as in simulations, as illustrated in a subsequent data example. The following data-flush Monte-Carlo method summarizes this proposal.For an exact or asymptotic pivotal, we may compute the conditional distribution of D independent perturbed samples d = 1, . . .,D, m = D. Note that we may choose any continuous unbounded distribution of eij in \u03b5-differential privacy). In what follows, D refers to as a Monte-Carlo size. Compute the perturbed pivotal d = 1, . . .,D. Compute the empirical distribution of T as D \u2192 \u221e.Generate Compute the bias estimate Use Next, we illustrate this data-flush inference method by two examples.\u03b8 of a normal distribution with unknown \u03c32. The pivotal is of the form S is the sample standard deviation. Here, we apply the data-flush inference scheme to simulate the distribution of perturbed pivotal T\u2217 and compare it with the bootstrapped pivotal  distribution with \u03b5 = 0.01 and R being the CDF of Z.The first example concerns the distribution of a pivotal quantity for construction of a confidence interval of the population mean  pivotal  and the T, whereas nonparametric bootstrap differs substantially for a small sample size n = 5. In other words, nonparametric bootstrap\u2019s approximation accuracy depends highly on the sample size n. Indeed, data flush yields an exact distribution of a pivotal as the Monte-Carlo size D \u2192 \u221e. This observation agrees with the result of p predictors:p could be substantially larger than the sample size n, \u03b2 =  is a vector of regression coefficients, Xi =  ~ N is a vector of predictors that are independent of the error \u03b5i, and the -th element of the covariance matrix \u03a3 is \u03c1j\u2212k||, and \u03c32 is an unknown error variance. Our goal is to construct a confidence interval for an individual coefficient \u03b2l with other covariates involving model selection.Our second example focuses on the construction of a confidence interval in linear regression on a vector of L1-penalty  constraint approximates the L0-constraint for computation. Towards this end, we apply the data-flush Monte-Carlo inference method based on L0-norm regression (CTLP) estimate To construct a confidence interval for parameter gression  to selec/SE(\u03b2^l) , where Seij is independently sampled from the Laplace distribution and \u03b5 = 0.01, Then, \u03b5-differential privacy for any j, where \u03c32 based on a holdout sample that is independent of the inference sample, R is the CDF of G is the CDF of Ui +eij with Ui following the Uniform distribution.To replicates \u03b21 = \u03b22 = \u03b23 = 1 and \u03b2j = 0 otherwise, with \u03c3 = 0.5 and \u03c1 = 0.5. Then, we apply m = D/n and D = 10p to construct a 95% confidence interval for each \u03b2j based on CTLP. The results for \u03b21 and \u03b24 are representative and are presented. Specifically, we use the glmtlp package in R to compute the CTLP estimate We perform simulations with the true parameters \u03b21 and \u03b24 are close to the nominal level 95% in each scenario. The discrepancy between the empirical converge and its target 95% is because the asymptotic pivotal may suffer from the bias in the finite-sample situation. Overall, the data-flush Monte-Carlo inference scheme yields a credible confidence interval for a non-smooth problem involving model selection.4.This section applies the data-flush scheme The American Community Survey collects demographic data from 3.24 million persons nation-wide, roughly 1% of the population in the Year 2019 . StatistAlternatively, an investigator can apply data flush to privatize survey data like ACS data without incurring information loss when the data-flush scheme preserves the distribution of raw data. For the ACS dataset, we use In particular, we investigate the impact of privatization by \u03b5-differential privacy, we apply eij following a Laplace distribution to preserve the joint distribution of 16 covariates and 1 response variable across common data types. In this fashion, privatization protects each individual\u2019s information. To illustrate this point, we scrutinize the histogram of the variable AGE before and after privatization in To satisfy We apply the data-flush Monte-Carlo method to construct confidence intervals for raw and privatized data. In particular, for each replication, we only perturb the linear regression residuals and follow the high-dimensional regression example in \u03b5, is 1 for \u03b5-differential privacy, which requires a stricter level of privacy protection 1/17 for each of the 17 variables. It is equivalent to that each variable requires independent Laplace, where the noise variance greatly exceeds the ranges of many variables in the ACS data, especially for binary dummy variables.Privacy loss usually occurs for high-dimensional data, which is an inherent challenge for any method in differential privacy. In particular, to maintain the same accuracy level, the overall level of privacy protection for each variable tends to decay as the number of variables increases. In our situation, the overall level of privacy protection, defined by the privacy factor 5.Data perturbation has its great potential as an effective tool for replicating a sample, which can apply to data security, statistical inference, data integration, among others. The fundamental principle, distribution preservation for data perturbation, that we described in this article allows users to design data perturbation schemes, such as data flush, to satisfy task-specific requirements, as we showcase for statistical inference with differential private data in Several future directions of research include a more flexible model-based estimation  for high-dimensional target distributions and a compatible data perturbation scheme, as well as generalizations to independent but non-identically distributed data, time-series data, and unstructured data."}
+{"text": "Light Science & ApplicationsCorrection to: 10.1038/s41377-022-00864-y published online 10 June 20221, it was brought to our attention that the Supplementary Information was attached by mistake, the article is a review article and it doesn\u2019t have Supplementary Information. The original publication has been corrected.After publication of this article"}
+{"text": "The Vaccine Ontology (VO) is a biomedical ontology that standardizes vaccine annotation. Errors in VO will affect a multitude of applications that it is being used in. Quality assurance of VO is imperative to ensure that it provides accurate domain knowledge to these downstream tasks. Manual review to identify and fix quality issues  is challenging given the complexity of the ontology. Automated approaches are highly desirable to facilitate the quality assurance of VO.is-a relations in VO. First, we construct two types of VO concept-pairs: (1) linked; and (2) unlinked. Each concept-pair further derives an Acquired Term Pair (ATP) based on their lexical features. If the same ATP is obtained by a linked concept-pair and an unlinked concept-pair, this is considered to indicate a potentially missing is-a relation between the unlinked pair of concepts.We developed an automated lexical approach that identifies potentially missing is-a relations. A manual review by a VO domain expert on a random sample of 70 potentially missing is-a relations revealed that 65 of the cases were valid missing is-a relations in VO (a precision of 92.86%).Applying this approach on the 1.1.192 version of VO, we were able to identify 232 potentially missing is-a relation in VO.The results indicate that our approach is highly effective in identifying missing  A vaccine as defined by the Centers for Disease Control and Prevention (CDC) is a preparation that is used to stimulate the body\u2019s immune response against diseases and is usually administered via needles while oral and nasal sprays are also available . VaccineDue to the clinical usage and extensive research regarding vaccines, it has become necessary to standardize vaccine annotation, combine vaccine information from disparate sources, and support machine-readability. To address such challenges, the Vaccine Ontology (VO) has been developed , 4. VO finfectious bursal disease virus vaccine\u201d (with VO concept identifier VO:0001497) is claimed as a subconcept of \u201cviral vaccine\u201d (VO:0000609), but \u201clive attenuated infectious bursal disease virus vaccine\u201d (VO:0000961) is not claimed as a subconcept of \u201clive attenuated viral vaccine\u201d (VO:0001220). It is imperative that VO is audited so that quality issues can be identified and addressed especially because it has been used in a multitude of applications including vaccine data integration [Being a community-based ontology in the domain of rapidly evolving biomedical knowledge, VO may suffer from incomplete knowledge and inconsistent modelling. For example, \u201ce\u201d VO:00020. It isegration , 14. SucOntology development tools such as Prot\u00e9g\u00e9 , 16 ensuis-a relations and missing concepts in SNOMED CT, NCIt, and GO [is-a relations [is-a relations in VO.The principal objective of automated and semi-automated methods for quality analysis of biomedical ontologies is to uncover concepts with high likelihood of being problematic, which can then be reviewed by a subject domain expert for verification. Various approaches have been investigated for identifying different quality issues of biomedical ontologies , 23. For, and GO \u201333. Non-, and GO . Additioelations , 36. To is-a relation.To demonstrate our approach, we used the 1.1.192 version (released on 03/19/2022) of VO in Web Ontology Language (OWL). Utilizing the OWLReady2 python library , we obtaHepatitis B Surface Antigen Vaccine 0.01 MG/ML\u201d (VO:0003423). This concept would be represented as {hepatitis, b, surface, antigen, vaccine, 0.01, mg/ml}.Our approach requires a concept to be represented as a set of its features. In this work, we obtain the features from concept names as follows. We first convert the name of a concept to lowercase. Then we tokenize the concept name to words and remove duplicate words. The result would be a set of words which can be considered as the lexical features corresponding to the name of the concept. For example, consider the concept \u201cC and A would form a linked concept-pair L if the following constraints are satisfied: A is an ancestor of C; andif C and A have at least a single common lexical feature.if We leverage the ancestor information for each concept obtained through OWLReady2 to construct a set of linked concept-pairs as follows. A given concept-pair L indicate that C is the descendant and A is the ancestor. This means that L and L are different pairs. However, usually L and L would not both exist in an ontology as they would form a cycle.Note that linked concept-pairs are ordered pairs. That is, infectious bursal disease virus vaccine\u201d (VO:0001497) and \u201cviral vaccine\u201d (VO:0000609) in Fig.\u00a0vaccine}. Similarly, considering Fig.\u00a0Bovine rotavirus\u201d (NCBITaxon:10927) and \u201cRotavirus\u201d (NCBITaxon:10912) form a linked concept-pair.For example, the concepts \u201ce\u201d VO:000497 and \u201cWe iterate through ancestors of all the concepts and construct a set of all linked concept-pairs.C and D would form an unlinked concept-pair U only if the following conditions are satisfied: C\u2260D;if D is not an ancestor of C and C is not an ancestor of D;if C and D have at least a single common lexical feature;if C and D both belong to the same ontology ; andif C and D fall within the same subhierarchy out of the 19 different subhierarchies under concept \u201cmaterial entity\u201d (BFO:0000040) of VO.if We leverage the hierarchical information of VO to construct a set of unlinked concept-pairs. A given concept-pair material entity\u201d for the following reasons: (1) the vast majority of VO concepts (including vaccines) are under \u201cmaterial entity\u201d; and (2) the subhierarchies under \u201cmaterial entity\u201d model different domains of VO.Here the fifth condition requires the unlinked concept-pair to be in the same subhierarchy of \u201cU is considered to be different from U. However, in certain situations, one of them could form a linked concept-pair. For instance, if U is an unlinked concept-pair but L is a linked concept-pair, then we do not include U in the unlinked concept-pair set. Otherwise, both are included.Note that unlinked concept-pairs are ordered as well. That is, live attenuated infectious bursal disease virus vaccine\u201d (VO:0000961) and \u201clive attenuated viral vaccine\u201d (VO:0001220) in Fig.\u00a0processed material\u201d (OBI:0000047) which is a subhierarchy under \u201cmaterial entity\u201d (BFO:0000040) and both the concepts have common lexical features {live, attenuated, vaccine}. Similarly, in Fig.\u00a0Bovine Respiratory Syncytial Virus vaccine\u201d (VO:0001507) and \u201cRespiratory syncytial virus vaccine\u201d (VO:0000753) form an unlinked-pair.As an example, the concepts \u201cVO:000096 and \u201cliv\u201d VO:000120 in Figmaterial entity\u201d (BFO:0000040), we iterate through all combinations of concept-pairs and construct a set of all unlinked concept-pairs.For each subhierarchy under \u201cC1 and C2 be F(C1) and F(C2) respectively. Then the ATP generated by the concepts is defined as: infectious bursal disease virus vaccine\u201d (VO:0001497) and \u201cviral vaccine\u201d (VO:0000609) in Fig.\u00a0Bovine Respiratory Syncytial Virus vaccine\u201d (VO:0001507) and \u201cRespiratory syncytial virus vaccine\u201d (VO:0000753) in Fig.\u00a0A linked or unlinked concept-pair derives an ATP which emphasises the unique lexical features of each concept. Let the lexical features of a concept-pair C1,C2) would generate an ATP that is different from an ATP generated by concept-pair .Note that a concept-pair  and an unlinked concept-pair U, if ATP=ATP, then we suggest a potentially missing is-a relation: C3is-aC4. In other words, if an ATP derived by a linked concept-pair can also be derived by an unlinked concept-pair, this is considered to indicate a potentially missing is-a relation among the unlinked concept-pair.Given a linked concept-pair infectious bursal disease virus vaccine\u201d (VO:0001497) and \u201cviral vaccine\u201d (VO:0000609) derive the ATP , which can also be derived by the unlinked concept-pair \u201clive attenuated infectious bursal disease virus vaccine\u201d (VO:0000961) and \u201clive attenuated viral vaccine\u201d (VO:0001220). Hence, this denotes a potentially missing is-a relation: VO:0000961 is-a VO:0001220.For example, in Fig.\u00a0Bovine rotavirus\u201d (NCBITaxon:10927) and \u201cRotavirus\u201d (NCBITaxon:10912) as well as the unlinked concept-pair \u201cBovine Respiratory Syncytial Virus vaccine\u201d (VO:0001507) and \u201cRespiratory syncytial virus vaccine\u201d (VO:0000753), derive the same ATP , and thus indicate a potentially missing is-a relation: VO:0001507 is-a VO:0000753. Note that as in this example, the linked or unlinked concept-pairs may originate from external ontologies as VO reuses concepts from external ontologies.Similarly, in Fig.\u00a0is-a relations.Given the unlinked-pairs and linked-pairs, Algorithm 1 shows the procedure that was used to extract such potentially missing is-a relation C3is-aC4 may be obtained leveraging multiple linked concept-pairs L and L if they derive the same ATP. We remove such duplicate cases from our final set of potentially missing is-a relations.Note that the same potentially missing is-a relations as described below. For an unlinked concept-pair U and a linked concept-pair L generating the same ATP, if the name of the concept C3 is the same as the concept C1 or the name of the concept C4 is the same as the concept C2, then we do not suggest a potentially missing is-a relation between C3 and C4. This is because two concepts with the same name but different identifiers may reveal a different type of quality issues  rather than a missing is-a relation. For example, the linked concept-pair \u201cF fusion protein\u201d (VO:0011167) and \u201cMeasles virus protein\u201d (VO:0010784) and the unlinked concept-pair \u201cF fusion protein\u201d (VO:0011208) and \u201cMeasles virus protein\u201d (VO:0010784) generate the same ATP: . However, VO:0011167 and VO:0011208 have the same name: \u201cF fusion protein\u201d. Hence, we do not suggest a missing is-a relation between VO:0011208 and VO:0010784.We further perform a filtration step on the set of potentially missing is-a relations identified by this method need to be manually reviewed for validation and confirmation before their adoption to VO. We randomly selected a subset of suggested potentially missing is-a relations for domain expert evaluation. For each missing is-a relation in the subset, the names of the two concepts together with their identifiers were provided to a domain expert . The domain expert examined whether the suggested relation is valid; not only theoretically, but also in terms of its suitability to current modeling practices of VO.Potentially missing is-a relations in VO. Table\u00a0is-a relations identified by our approach, as well as their ATPs and corresponding linked concept-pairs. As an example, our method suggested that \u201cinactivated acellular pertussis vaccine\u201d (VO:0003196) is a descendant of \u201cinactivated vaccine\u201d (VO:0000315). The 232 potentially missing relations were based on 120 distinct ATPs. Table\u00a0is-a relations. For instance, the ATP  accounted for 12.07% (28/232) potentially missing is-a relations.Table\u00a0e\u201d VO:000196 is a is-a relations, we constructed a random sample of 70 potentially missing is-a relations for manual evaluation by the VO domain expert. The 70 cases were selected so that no two cases correspond to the same ATP to avoid reviewing similar cases. The evaluation revealed that 65 of our suggestions represent valid missing is-a relations in VO. Therefore, the overall precision of the method is 92.86% (65/70).To assess the effectiveness of our approach in discovering valid missing is-a relation inconsistencies from the Vaccine Ontology. We constructed two types of concept-pairs: linked and unlinked. For the unlinked concept-pairs, we focused on the different subhierarchies under the \u201cmaterial entity\u201d (BFO:0000040) concept. This is because we needed to pair unrelated but relevant concepts as unlinked concept-pairs. Each subhierarchy under \u201cmaterial entity\u201d (BFO:0000040) models different domains such as \u201canatomical entity\u201d, \u201cantigen\u201d, \u201cchemical entity\u201d, \u201cgene\u201d, etc. Therefore, concepts under each of these subhierarchies have a certain degree of relevance with each other. This is important as pairing irrelevant concepts may not only lead to the extraction of invalid missing is-a relations, but would also increase the running time of the method. In fact, VO currently does not have any is-a relations across these subhierarchies. It should also be noted that out of the 6,883 concepts in the 1.1.192 version of VO used in this work, 5,672 concepts (82.4%) were in these subhierarchies.In this work, we investigated a lexical approach to extract is-a relations uncovered in this work. For example, 80 missing is-a relation suggestions had ATPs of size , while only 16 had size . The analysis of the ATP sizes as displayed in Fig.\u00a0is-a relations (74.57%) correlate with situations where the second set in the ATP is an empty set. This happens when the lexical features of the potential ancestor form a subset of the lexical features of the potential descendant. In fact, the most number of is-a relations were suggested by the following ATP size: , , , and .We denote the size of an ATP by a pair of integers corresponding to the sizes of the two sets the ATP contains. For instance, the size of the ATP  is 3, 1). Figure\u00a0, 1. Figuis-a relations decreases. For instance,  was observed in 80 potentially missing is-a relations, while  was observed in 16, and  was observed in 5. Since the ATP contains unique words in each concept, this shows that in a majority of missing is-a relations, more unique words can be found on the descendant concept than the ancestor concept. This is expected as descendant concepts are supposed to be more specific concepts than ancestors.In addition, it can be seen that for a certain size of the first set of the ATP, when the size of the second set increases, the number of suggested missing is-a suggestions were invalid. For example, as displayed in Fig.\u00a0is-a relation between concepts \u201csmallpox vaccine\u201d (VO:0004613) and \u201cSmallpox virus vaccine\u201d (VO:0000651). However, these concepts were found to be synonyms that need to be merged into one concept. Therefore, in this instance, while our suggestion is invalid, it has lead into the identification of a different inconsistency in VO.Based on the evaluation by the VO domain expert, it was seen that 5 of our missing is-a relation between concepts \u201cBrucella canis\u201d (NCBITaxon:36855) and \u201cCanis\u201d (NCBITaxon:9611), which was found to be invalid. This is because brucella canis is a bacterium, while canis is a mammal. Our method also suggested an invalid missing is-a relation between concepts \u201cCorynebacterium pseudotuberculosis\u201d (NCBITaxon:1719) and \u201cCorynebacterium diphtheriae\u201d (NCBITaxon:1717). These terms are actually siblings under the parent concept \u201cCorynebacterium\u201d (NCBITaxon:144193) and do not form a valid is-a relation. Note that these two false positives were missing is-a suggestions among concept-pairs in the NCBI Taxonomy [is-a suggestion for an external ontology was valid, the actual fix would need to be handled by the external ontology so that VO could re-import and re-use the corrected version.In another example, our method suggested a potentially missing Taxonomy , an exteis-a suggestions. Regarding the suggested is-a relation between \u201cVaricella-Zoster Virus Vaccine Live (Oka-Merck) strain 29800 UNT/ML\u201d (VO:0003279) and \u201cVaricella-Zoster Virus Vaccine Live (Oka-Merck) strain Injection\u201d (VO:0003274), the expert was uncertain whether the former concept always corresponds to an injection. For the suggested is-a relation between concepts \u201ctoxoid vaccine\u201d (VO:0000561) and \u201ctoxoid\u201d (VO:0001252), the expert was uncertain about the validity as the latter concept corresponds to a component of the former. We categorized both these cases as false positives.The expert was indecisive about two of the missing A major distinction between our approach and most other ontology quality assurance approaches is its capability of identifying the exact quality issues, as a result of which less manual review effort is needed by domain experts. For example, abstraction networks based approaches , 25 onlyNote that due to the discovery nature of the ontology quality assurance task , differen different words . In this work, we generalized the approach without such limitations, and applied it to the Vaccine Ontology, for which according to our knowledge, systematic automated approaches have not being developed for auditing purposes. Additional improvement of the approach in this work is requiring the unlinked concept-pair to be within the same subhierarchy, which was not leveraged in the prior work and without which invalid cross-hierarchical missing is-a relations would be more likely to be suggested.In prior work, we introduced a similar approach leveraging word differences between concepts to audit the Gene Ontology , 36. Howis-a discovered and the precision of the method. The features may also be imported from mapped concepts in external ontologies. Additionally, the only normalization that was performed in this work was to convert the lexical features to lowercase. Leveraging other strategies like lemmatization and synonym identification may help identify additional potentially missing is-a relations.One limitation of this work is that our concepts were represented by lexical features obtained from concept names. An interesting future direction is to investigate whether incorporating additional attributes of concepts such as other lexical metadata , ancestor lexical features, attribute relations, etc. would improve the overall results in terms of the number of potentially missing is-a relations identified by this method are only between concept-pairs with common words. In the future, we will explore other strategies that can also handle cases between concepts without any common words. A particularly interesting direction is to investigate whether machine learning could be of help. To train a machine learning model, the lexical features of concepts will need to be represented numerically using techniques such as word embedding. These representations would embed the meaning of the lexical features and therefore, through machine learning it might be possible to learn complex relationships between lexical features of the concept-pairs. Hence, such an approach may have the potential to predict a missing is-a relation between any concept-pair, not restricting to concept-pairs with common words.Another limitation of the method is that the missing is-a suggestions were evaluated by one expert. The precision of the method may be different if the size of the evaluation samples varies or multiple experts were involved. However, it should be noted that our expert (YH) is currently leading the development of VO. Since only 70 out of 232 missing is-a suggestions were evaluated (30.17%), a future work would be getting the entire set of 232 evaluated and incorporated into a future release of VO.A limitation of our evaluation is that only a subset of the missing is-a relations in the Vaccine Ontology, by leveraging term differences between concept-pairs. A total of 232 potentially missing is-a relations were suggested by our approach applied on the 1.1.192 version of the ontology. A random sample of 70 potentially missing is-a relations was evaluated by a Vaccine Ontology domain expert and 65 of them were confirmed as valid cases. The results revealed that our lexical approach is highly effective in identifying missing is-a relations in the Vaccine Ontology.In this paper, we presented an automated lexical approach to discover potentially missing"}
+{"text": "Cell Research 10.1038/s41422-022-00646-6, published online 29 March 2022Correction to: In the initial published version of this article, there is an error in the\u00a0These corrections do not affect the major findings and conclusions of this work. We deeply apologize for this oversight.Supplementary information"}
+{"text": "Unitary t-designs mimic the Haar-measure up to t-th moments. It is known that Clifford operations can implement at most 3-designs. In this work, we quantify the non-Clifford resources required to break this barrier. We find that it suffices to inject t-design. Strikingly, the number of non-Clifford gates required is independent of the system size \u2013 asymptotically, the density of non-Clifford gates is allowed to tend to zero. We also derive novel bounds on the convergence time of random Clifford circuits to the t-th moment of the uniform distribution on the Clifford group. Our proofs exploit a recently developed variant of Schur-Weyl duality for the Clifford group, as well as bounds on restricted spectral gaps of averaging operators.Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full  The notion of a unitaryt-design captures an efficiently realizable version of uniform randomness [t-design if it matches the uniform Haar measure up to t-th moments.Random vectors and unitaries are ubiquitous in protocols and arguments of quantum information and many-body physics. In quantum information, a paradigmatic example is the protocol \u20133, whichprotocol . In thesndomness \u20137. More decoupling procedures, a primitive in quantum Shannon theory [Applications abound. The randomness provided by designs is used to foil attackers in quantum cryptography protocols \u201310. It gn theory . In quann theory , 20. Unin theory , 21\u201323.t-designs [n qubits with t-design. In practice, it is often desirable to find more structured implementations. Designs consisting of Clifford operations would be particular attractive from various points of view: (i) Because the Clifford unitaries form a finite group, elements can be represented exactly using a small number (fault-tolerant architectures [magic-state distillation) carries a significant overhead. The difference is so stark that in this context, Clifford operations are often considered to be a free resource, and the complexity of a circuit is measured solely in terms of the number of non-Clifford gates [The multitude of applications motivates the search for efficient constructions of unitary -designs \u201328. In p-designs  show thatectures , 30, Clird gates , 32.t-design for any local gate set that generates an exact unitary design of order The Clifford group is known to form a unitary ment}t=3 \u201335, but ment}t>3 \u201337. In fment}t>3 . Moreovement}t>3 , 39 togeHow many non-Clifford gates are required to generate an approximate unitaryt-design? A direct application of the random circuit model of Ref. [system size-independent number of This leads us to the central question underlying this work:  of Ref.  yields aWe establish this main result for two different circuit models Fig.\u00a0. In Sectt-th tensor power of the Clifford group, described by a variant of Schur-Weyl duality developed in a sequence of recent works [t-design from a representation theoretical perspective \u2013 is independent of the system size. Refs. [sphericalt-designs that consist of a system size-independent number of Clifford orbits. It has been left as an open problem whether these ideas can be generalized from spherical designs to the more complex notion of unitary designs, and whether the construction can be made efficient [The key to this scaling lies in the structure of the commutant of the nt works , 41\u201343. e. Refs. , 42 haveT gate to a random Clifford circuit has dramatic effects on the entanglement spectrum. A relation to t-designs was suspected. Our result provides a rigorous understanding of this observation.Finally, we note that in Ref. , it has U(d). The measure U chosen according to t-th moment operator associated with t-design by the diamond norm distance of its moment operator to the moment operator of the Haar measure U(d).To state our results precisely, we need to formalize the relevant notion of approximation, as well as the circuit model used. Let ing Ref. , we quanApproximate unitary design). Let t-design if. Let K-interleaved Clifford circuit of depthk is the random circuit acting on n qubits described by the probability distribution. Let t and n. In this sense, our construction can be seen as a classical-quantum hybrid construction of unitary designs: The scaling is significantly improved by outsourcing as many tasks as possible to a classical computer. A construction in which all parts of the random unitary are local random circuits is considered in Corollary\u00a0We give the proofs of this theorem in Sect.\u00a0dom bits  and then)) gates . Combinementclass2pt{minim to Ref.  in the dK-interleaved Clifford circuits are sufficient to approximate t-designs. This intuition is supported by the numerical results of Ref. [T-gate has dramatic effects on the entanglement spectrum of a quantum circuit.For designs generated from general random local circuits, numerical results suggest that convergence is much faster in practice than indicated by the proven bounds . We expe of Ref. , which sT-gates can be efficiently simulated [T-gates. Combined with our result, this implies that for fixed additive errors O(nt) suffices to approximate t-designs [It is moreover noteworthy that circuits with few imulated \u201351. The -designs , 52. If t-th moment operator of the Haar measure and the commutant of the diagonal action of the Clifford group. The latter was proven to be spanned by representations of so-called stochastic Lagrangian sub-spaces in Ref. [t-design in diamond norm.For the proof of Theorem\u00a0 in Ref. . In part in Ref.  on restrrelative approximate designs:Moreover, the bound for Theorem\u00a0Relativeapproximatet-design). We call a probability t-design if(K-interleaved Clifford circuits as relative t-designs). There are constants K-interleaved Clifford circuit is a relative t-design in depth (O(nt) at least until Hence, if we drop the system-size independence, we can achieve a scaling of K-interleaved Clifford circuits to be the more relevant case, the same method of proof works for Haar-interleaved Clifford circuits. Here, we draw not from the gate set U(2). The advantage is that we obtain explicit constants for the depth, while the depth in the K-interleaved setting has to depend on a constant (as K might be arbitrarily close to the identity).While we believe the setting of t-designs). For k form an additive t-design for all . Let n qubits. A local random Clifford circuit of depth m is the random circuits described by the probability measure . Let relativeapproximate Cliffordt-design if. Let The proof of the theorem is given in Sect.\u00a0k-times alternatingly applies a local random Clifford circuit of depth m, and a unitary drawn from the probability measure We can combine this result with the bounds obtained in Sect.\u00a0t-design for all . Let t-groups and a criterion for the universality of finite gate sets [The complete argument for the corollary is given at the end of Sect.\u00a0ate sets , 39, 55.Hilbert-Schmidt inner productadjoint action of an invertible operator Given a  Hilbert space p-normsA. In particular, we use the trace normFrobenius or Hilbert-Schmidt normspectral normdiamond normWe consistently reserve the notation e useful 12\\documen-qubit Clifford groupU(1) yielding a finite group with minimal center H and the phase gate S.In this section, we review some of the machinery developed in Ref. . Recall t-th diagonal representation of the Clifford group, defined ast copies of an n-qubit system. However, it will turn out that the operators commuting with this representation naturally factorize with respect to a different tensor structure on this Hilbert space, namely stochastic Lagrangian sub-spaces [For this work, the b-spaces :Stochastic Lagrangian sub-spaces). Consider the quadratic form T is totally t .T has dimension stochastic: T is  developed in Ref. [Since the representation in question is fixed throughout this paper, we will simplify the notation from now on and write Stochastic orthogonal group). Consider the quadratic form stochastic orthogonal groupO with entries in . A defect subspace is a subspace q, that is, that  to keep with the notation of that reference.The quadratic form g., Ref. , App.\u00a0A guage of , all q-iference,  works siN, it holds that Calderbank-Shor-Sloane (CSS) codesFor any defect subspace  of Ref. , Sect.\u00a04. Considr(T) operators with right defect subspace given by N, i.e., with N we obtain the full set Recall from Ref.  that ther(T)). Suppose  operators which we define asIn the following, we will often work with a normalized version of the t-design. This is made precise by the following two theorems which rely on two distinct proof strategies and come with different trade-offs.In this section, we give a bound on the number of non-Clifford gates needed to leverage the Clifford group to an approximate unitary K-interleaved Clifford circuit with depth k acting on n qubits is an additive t-design for all (Unitary designs with few non-Clifford gates). Let K-interleaved Clifford circuit has an associated probability measure A. Thus, we can rewrite the difference of moment operators asRecall from Def.\u00a0Non-vanishing probability of applying the identity). We apply K, R(K) is Hermitian. The non-vanishing probability of applying K and T-gate.. Let The second lemma is of a more technical nature.(Diamond norm bound). Consider non-orthogonal. Thus, the projectors do not possess a natural expansion in this basis and we can not directly use the above bounds. However, we can write it explicitly in a suitable orthonormal basis of the commutant obtained by the Gram-Schmidt procedure from the basis The difficulty of using these results to bound the differencet! spaces (Properties of the constructed basis). Let t by their leading order term in the following. Specifically, the bounds in Lemma\u00a0t.We believe that the explicit bounds in Lemma\u00a0i and j do not correspond to permutations and hence n.Notice that from\u00a0, we haveing Eqs.\u00a0 and\u00a033)37\\documeentclass1pt{minimar,\u00a0i. Moreover, we have used the triangle inequality,We provide two bounds for l changes. Moreover, we will treat differently the cases The second bound follows from Eqs.\u00a0 and\u00a033)33), and =i using\u00a0. Moreoveain from\u00a0 and\u00a027)\\documentto bound\u00a0. Eqs.\u00a0. Let t-th moment operator was defined asspectral norm asThe proof of Theorem\u00a0t-designs). Suppose that t-design.. Let We will prove Proposition\u00a0k-step random walk t-design, if we choose First, note that entclass1pt{minimaG and write G is closed under taking inverses, the moment operator r-th largest eigenvalue of a normal operator X. Hence, we findFor the sake of readibility, let us from now on drop the dependence on entclass1pt{minimanerators . Equivalt-designs in depth To this end, consider the linear operator  By Ref. , Lem.\u00a01,entclass1pt{minimalocal Hamiltonians with vanishing ground state energy:Therefore, we consider the more relevant case when . Let from Eq.\u00a0. It hold(Ground spaces). The Hamiltonians frustration-free  Let the Hamiltonian s in Eq.\u00a0 and assut. To this end, we make again use of the averaging operator G|n) and d is the diameter of the associated Cayley graph (given in Ref. [We can now combine the bound in\u00a0 with any in Ref.  as \\docuc(G). We note that the applicability of Ref. [Since the representation  of Ref. , Cor.\u00a01 We can combine Theorem\u00a0t-design for all . Let m local random walk on the Clifford group (i)q prime and orIf (ii)eitherorIf (iii)If Then, one of the following cases apply: t-design.Note that a finitely generated infinite subgroup of a. Finite case. In the classification in Ref. [t-groups was shown for  in Ref. , the nonH is either one of finitely many exceptional cases or H is isomorphic to the Clifford group ii), the This establishes the finite version of .The former, the Lie-type cases, happen in dimensions cument}$$^n\\pm 1/2b. Infinite case. Define the commutant for a set rom Ref.  applied . Consider r(T) is described by a stochastic orthogonal and a defect space First, recall that ral norm . Given smentclass2pt{minimframe operator associated to the basis Next, we define a Clifford frame operator). We define the Clifford frame operator of the basis . To der(Overlap of stochastic Lagrangian sub-spaces). We have n qubits. Since the operators r(T) are entry-wise non-negative, we have Denote by cp.\u00a0Thm.\u00a0. We obtaLet synthesis operator of the frame as the mapDefine the K be a single qubit gate which is not contained in the Clifford group. Then, there is a constant (Overlap bound). Let r(T) of the commutant of tensor powers of the Clifford group either belong to the commutant of the powers of the unitary group, or else are far away from it.The proof of Lemma\u00a0t and for all t-th moment operator of the single-qubit unitary group (Haar symmetrization). For all s in Eq.\u00a0 and \\docT that attains this bound.The proof is given in Sect.\u00a0The second ingredient to Lemma\u00a0 that the representation .g. Ref. ). Hence,s in Eq.\u00a0. CombiniQuantum gates with algebraic entries). If we restrict to gates K that have only algebraic entries, we can apply the result from Ref. [T-gate and for essentially all gates that might be used in practical implementations. Here, we have chosen the more general approach.(rom Ref.  and saveImplications for quantum information processing). Theorem\u00a0( in Ref. . Extendit! spaces (Properties of the constructed basis). Let n elements with no fixed points is known from Ref. [D stands for \u201cderangement\u201d as permutations without fixed points are sometimes called. Then, the number of permutations having exactly k fixed points is k points times the number p will shortly become useful. Note that we have for any The form of\u00a0 is up torom Ref.  to be113k fixed points. For any such permutation, the product of overlaps collapses to only We start by bounding the diagonal coefficients sing Eq.\u00a0 with \\doused Eq.\u00a0 in the l use Eq.\u00a0 as beforNote that we can alternatively bound ith Eqs.\u00a0 and\u00a0. For all s in Eq.\u00a0 and \\docr(T), we can turn the statement  of T has components of equal Hamming weight.For an analysis of the tightness of the bound, see \u201cAppendix\u00a0C\u201d. Recall thattatement  from oneT with trivial  and non-trivial defect spaces.We will bound the probability in slightly different ways for spaces a. Case I: trivial defect sub-spaces In this case, O. The next proposition treats a slightly more general situation.O has a column of Hamming weight r. Then the probability that O preserves the Hamming weight of a vector y chosen uniformly at random from (Hamming bound). Let r. Orthogonal stochastic matrices O satisfy r that can appear is The bound in Eq.\u00a0 decreaseO does not preserve weights for bothy and O changes the Hamming weight.The proof idea is as follows: For each r entries of Assume without loss of generality that the first y be a uniformly distributed random vector on Oy, and O(y) by flipping the first r components. This operation changes the Hamming weight by r components of O(y) equals r, this condition cannot be met, and correspondingly Let r, this probability becomesIn case of odd b. Case II: non-trivial defect sub-spaces We now turn to Lagrangians T with a non-trivial defect subspace.x is chosen uniformly at random from T be a stochastic Lagrangian with non-trivial defect sub-spaces. Then, for an element  drawn uniformly from T, we have(Defect Hamming bound). Let N. Permuting coordinates of x is drawn uniformly from G has a column, say the first, with G have Hamming weight 1.  is distributed uniformly in T. By the first cited fact, x is distributed uniformly in x,\u00a0y), for each We have proven the first advertised claim. It implies the second one, as argued next. Let t-designs). Suppose that t-design.. This implies thatThis follows similar to Ref. [ition in\u00a0 is equivsymmetric subspaceSince  in Ref. , Lem.\u00a04,r(T).In order to prove Lemma\u00a0There is a constant There are Denote the ground state projector of Then, it holds thatWhile conditions 1) and 2) are merely translation-invariance with finit range of interactions and frustration-freeness in disguise, the third condition is highly non-trivial and involves knowledge of the ground-space structure. Usually, finding the ground space in a basis can be just as hard as computing the spectral gap in the first place. Fortunately, the ground space structure of the Hamiltonians . Let the Hamiltonian s in Eq.\u00a0 and assuThe first condition immediately follows from the fact that we consider a translation-invariant 2-local Hamiltonian. It is fulfilled for any choice of q due to translation-invariance. Thus, we can set The second condition follows again for all l. We have to bound the quantity k is large enough. Concretely, we have by Lem.\u00a0The third condition requires a calculation and a non-trivial choice of mentclasspt{minimamentclasspt{minimaHence, for the choices We make use of the Nachtergaele lemma. We have to verify the three conditions of Lemma\u00a0t-designs. This is surprising, conceptually interesting and practically relevant: After all, it is the main objective in quantum gate synthesis to minimize the number of non-Clifford gates in a circuit implementation of a given unitary. There are multiple open questions and ways to continue this work:n is near to optimal, the scaling in t can probably be improved.Similar to the result in Ref. , the scaAnother natural open question is whether the condition mentclasspt{minimaOur result holds for additive errors in the diamond norm. For relative errors, our bounds can be used to obtain a quadratic advantage in the number of non-Clifford gates in Corollary\u00a0dits for arbitrary d, giving rise to analogous conclusions concerning an independence of the system size for additive errors in the diamond norm.We strongly expect that the results can be generalized to quWe hope the present work stimulates such endeavors.We have found that a number of non-Clifford gates independent of the system size suffices to generate"}
+{"text": "As phylogenetic networks become more widely studied and the networks grow larger, it may be useful to \u201csimplify\u201d such networks into especially tractable networks. Recent results have found methods to simplify networks into normal networks. By definition, normal networks contain no redundant arcs. Nevertheless, there may be redundant arcs in networks where speciation events involving allopolyploidy occur. It is therefore desirable to find a different tractable class of networks that may contain redundant arcs. This paper proposes distinct-cluster tree-child networks as such a class, here abbreviated as DCTC networks. They are shown to have a number of useful properties, such as quadratic growth of the number of vertices with the number of leaves. A DCTC network is shown to be essentially a normal network to which some redundant arcs may have been added without losing the tree-child property. Every phylogenetic network can be simplified into a DCTC network depending only on the structure of the original network. There is always a CSD map from the original network to the resulting DCTC network. As a result, the simplified network can readily be interpreted via a \u201cwired lift\u201d in which the original network is redrawn with each arc represented in one of two ways. A (rooted) phylogenetic tree is a tree in which the vertices correspond to biological species, the leaves are extant species, and the branchings correspond to speciation events, usually by mutation. Recently there has been increased interest in speciation events such as hybridization and lateral gene transfer which are not modeled well using trees  such that there is another directed path from u to v that does not include . More details are given in Sect.\u00a0There are various interesting classes of networks that have been investigated. Tree-child networks  so they have \u201cdistinct clusters,\u201d abbreviated DC.The network is tree-child, abbreviated TC.Since they have both properties, they are called distinct-cluster tree-child networks, or, more briefly, DCTC networks.Roughly, DCTC networks are defined by two properties: N has additional interesting properties which in many ways resemble those of normal networks. In particular, a DCTC network satisfies the following: (3)N has n leaves. Then the number of vertices of N is at most Suppose (4)Every vertex is visible.(5)The number of hybrid vertices is at most (6)v with out-degree at least 2, there exist two distinct leaves x,\u00a0y such that v is the most recent common ancestor of x and y.For every vertex Property (4) is true of all tree-child networks . This w Willson . , if N has n leaves, then N. The construction resembles that in Willson . An X-network V,\u00a0A) where V is a finite set of vertices and A is a finite set of arcs. There are no directed cycles, there are no loops , and there is at most one arc  for in-degree of a vertex v in N, denoted indeg(v) or indeg , is the number of arcs , i.e., the number of parents of v. The out-degree of a vertex v, denoted outdeg(v) , is the number of arcs  , i.e., the number of children of v. Here root; it is the only vertex with in-degree 0. A leaf is a vertex Briefly, suppose X-networks except that cycles are possible. If that occurs we will explicitly specify that the network is not necessarily acyclic.Occasionally we may have to deal with p or p(x). The arc of form x-arc. If x is not specified, any such arc will be called an X-arc.Except where specified otherwise, we assume that each leaf Note that we make no assumption about the network being binary. A vertex may have in-degree greater than 2 or out-degree greater than 2 or both.path in N from a to b is a sequence N are thus directed. If there is a path from u to v, then we write V. For every vertex v, it is true that A x and y are distinct vertices. A vertex u is a common ancestor of x and y if v is a most recent common ancestor of x and y, denoted v is a common ancestor of x and y and, in addition, for every common ancestor u of x and y, x and y exists, it is unique.Suppose v is hybrid or reticulate if u of v is a tree-child if v,\u00a0u) is the only arc coming into u. A vertex v is trivial if A vertex a,\u00a0b) is redundant or a short-cut if there exists a path a,\u00a0b).An arc . We call it the cluster of v. Note that cl(v) is nonempty. It is immediate that if N.For each X-networks which will be of interest:There are several types of X-network is successively cluster-distinct (SCD)  satisfies that either (i)(ii)Thus, successive vertices have different clusters except possibly for the arc An  Willson  if each  Willson  because X-network N is tree-child  is the power set of X;the cluster map N has no redundant arcs; andNote that because of (3), any regular network is SCD.An X-network N is normal  and X-networks, X, it is a metric on the collection of regular X-networks  map (Willson digraph map).For each arc For each u,\u00a0v in V such that For each N. Thus, in the undirected graph Und(N) of N, if W and edge set For each Note that if N and Let  Willson  \\documenX-networks. A CSD-map leaf-preserving if for each (7)V such that (8)x-arc x-arc the If Let  Willson  that theV. A wired lift of f (or of N) is a pair For each arc u,\u00a0v) representspre-arc of For every arc Call the members of representative arcs since each represents an arc of Let V. Thus for all Note that the collection of all N and X-networks and Willson  Suppose N. An example is shown in Fig.\u00a0N except that each arc may be solid or dashed. Suppose u,\u00a0v) a solid arrow if N and each vertex of The wired lift mentclass2pt{minim Willson , the wir Willson , while tX-networks, with f. If u and v are in V, we say there is an allowed step from u to v if either Let generalized path or g-path in N from a to b is a sequence A N denote the initial X-network and N. Because of the dashed arcs, we see that N, there is clearly no path from 12 to 1. Note also that all children of 12 in N are hybrid. But In Fig.\u00a0mentclass2pt{minimmentclass2pt{minimX-networks, with g-path in N from a to b.Willson  Let \\docX-network. A subset strongly closed if it satisfies the following: Suppose there are vertices V with k such that K.Let X-network and (i)(ii)K is strongly closed, and(iii)for every strongly closed Thus, K is the unique minimal strongly closed subset of A containing D.Willson  Let \\docK of the theorem is denoted K(D) and called the strong closure of D.The subset The following theorem summarizes the fundamental construction  Willson . While ( Willson .X-network and X-arc. There is a uniquely determined X-network There is a projection map For each arc K(D) is the strong closure of D, then If X-network, Suppose Willson  Suppose D consists of a list of arcs in N. For each arc N to a point. If these contractions result in any directed cycles, we contract the arcs in any such cycle. The result is N, it is a kind of quotient graph of N.The idea of  Willson  to be a Parts (1), (2), and (3) are directly from Willson . We provA that starts with K(D). An easy inductive argument shows that each Let Now we may complete the proof of Part (4). Suppose D and X-network, then all the identifications in X-network that contracts the members of D.Note that (4) shows that if As an application, there is the following result:N be an acyclic X-network. There is an X-network There is a leaf-preserving CSD map Willson  Let N bea,\u00a0b) such that b is a leaf to ensure that no leaf becomes hybrid.Essentially, the computation of X-network N is distinct-cluster or DC if, whenever u and u and v is a leaf p(x) where p(x) is hybrid with out-degree 1. Thus the only way to have p(x) is hybrid with out-degree 1. More briefly, the only way to have x-arc p(x) is hybrid with out-degree 1. It is immediate that if p(x) is hybrid with out-degree 1, then An tree-child path if, for A path The following theorem restates some results in Cardona et\u00a0al. .X-network that is tree-child. v to some leaf Given any vertex Assume there is a tree-child path Suppose X-network that is both SCD and tree-child. Then N is distinct-cluster (DC).Suppose u and u is a leaf, say v is a leaf. So we may assume that neither u nor v is a leaf. There is a tree-child path u to a leaf N is tree-child, and hence v to v is a vertex of P or else N is SCD. Thus Suppose X-network N a DCTCX-network if it is acyclic, distinct-cluster (DC), and tree-child (TC).We will call an X-network that is SCD and tree-child is a DCTC X-network.An M is DC but not TC since 9 has no tree-child. N is TC but not DC since In Fig.\u00a0n leaves has at most Any tree-child network with a et\u00a0al. . The folee Steel .X-network with n leaves. Then the number of hybrid vertices is at most Suppose N is TC, the root N is DC, c of c is a tree-child. We cannot have c and Since c to the leaf c to c. Hence, c to c lies on the path from c lies on a cycle, contradicting that N is acyclic.Choose a tree-path from Suppose the hybrid vertices are X-network. A vertex v is visible  if therentclass1pt{minimav is not visible, then the evolutionary history of gene flow in the corresponding phylogenetic network may have bypassed v and the presence of v could have no genetic impact on any of the leaves. Hence, visibility of all vertices is a desirable property in a phylogenetic X-network.As is pointed out in Francis et\u00a0al.  if a verX-network. Then every vertex v is visible.Suppose u is visible since it is on every path from the root to x is a strict descendant of u.\u201d This result is shown in Cardona et\u00a0al. , where iX-network or a normal X-network. Every Let X-network and every normal X-network is tree-child. Every DCTC X-network. Suppose u is a leaf u is hybrid with out-degree 1; oru has out-degree at least 2, and for each child c of u, Suppose c be the unique child of u. Then N is DC by Theorem c is a child of u, since N is DC it follows If m be the maximal in-degree of a hybrid vertex and n be the number of leaves. Then Let X there is a metric  on the class of tree-child phylogenetic X-networks.For each The following facts about tree-child networks, proved in Cardona et\u00a0al. , necessaX-network. u and v satisfy v is hybrid with out-degree 1, so Suppose w distinct from u and v such that u,\u00a0v) is redundant.Suppose Let v to u to N is CD this means that (1) By Theorem\u00a0u to w and a path from w to v. Hence,  is redundant. (2) By Part (1) there is a path from N is a DCTC X-network and If M that is DCTC but not normal, because  is redundant. On the right N is normal but not DCTC because X-network there is a closely related normal X-network.The property of being DCTC is closely related to being normal, but not the same. Figure\u00a0The operator S If X-network, let S(N) denote the result of contracting every arc  such that w is a leaf. The operator S was briefly introduced in Willson ( Willson . Some baX-network. X-network except that a leaf may be hybrid.S(N) contains no vertices with out-degree one.N is normal, then S(N) is both regular and normal.If Let (4)(5)For all (6)Suppose D may contain X-arcs. (2) is immediate by the construction. (3) follows from Willson ((1) follows naturally, with leaves possibly being hybrid because  Willson , and (4)u,\u00a0w), and every nontrivial path starting at u must pass through w since For (5), if X-network, let R(N) denote the result of removing all redundant arcs from N. More explicitly, let A that are not redundant in N; then X-network. For more details, see Willson (If  Willson .S will be to compute S(R(N)) where N is an acyclic X-network. Note that R(N) then has no redundant arcs, and often the result can be simplified. The simplification might be performed by the operator S. If N is DCTC, we show below that S(R(N)) is normal.An important use of S(R(N)). Start with the DCTC X-network N. Remove the two redundant arcs from A to form S(R(N)) the leaf  is hybrid. In S(R(N)) the map Figure\u00a0N is a DCTC X-network, then S(R(N)) is a normal network. This relationship shows a close relationship between DCTC networks and normal networks. It will be the basis for an expanded analysis in Sect.\u00a0The following theorem shows that if X-network. Then R(N) is a normal X-network.u, For each vertex u,\u00a0w) in R(N) either satisfies p(x) is hybrid with out-degree one.Any arc (S(R(N)) is a normal X-network, possibly having some leaves that are hybrid, and containing no vertex with out-degree one. No two vertices have the same cluster.Suppose R(N) contains no redundant arcs, so we must only show R(N) is TC. Since N is tree-child, each vertex u that is not a leaf has a tree-child w. The arc  cannot be redundant. Otherwise, if  is redundant in N, then by redundancy there is a lengthening path starting at u and ending at w but not including the arc . Hence, u,\u00a0w) remains an arc in R(N), so w is a tree-child of u in R(N).(1) It is immediate that N from u to u to R(N). Hence, u to R(N) is also such a path in N, proving Part (2).(2) Note that u,\u00a0w) is an arc of R(N) then N is DC, (3) If (R(N) is normal, Part (4) follows from Theorem\u00a0Since X-network with n leaves is quadratic in n. We also study when a vertex is the In this section, we prove that the number of vertices in a DCTC post-hybrid if p(x) is hybrid with out-degree one. Equivalently, x is post-hybrid iff N is a DCTC X-network, let N is understood) denote the number of Call X-network N with Figure\u00a0X-network and N. Then Suppose N is CD, there is exactly one vertex for each member of Cl(N) except for the vertices p(x) for p(x) is hybrid with out-degree one. For such x, there are two vertices p(x) and (1) Since N to obtain R(N). By definition, R(N) contains no redundant arcs. Clearly R(N) is tree-child since no arc w of u is redundant; otherwise there would be a lengthening path from u to w which does not contain , hence another parent of w. It follows that R(N) is normal.(2) Remove all redundant arcs of cl(u) for any vertex u. Hence, R(N) remains CD. For every arc  such that cl(w) is not u,\u00a0w) with S(R(N)) which will have exactly c(N) vertices, one for each cluster. But S(R(N)) is normal and has no vertices of out-degree one. By a result in Willson (X includes the root as well as the leaves.)Moreover, the removal of redundant arcs does not change  Willson , it has  Willson  differs (3) follows immediately.n leaves. Suppose p(x) is hybrid with out-degree 1. Yet N is tree-child and there must be a tree-path from the root p(x) is hybrid, this is not possible. Hence, (4) Clearly (5) N with N. On the other hand, Part (5) will be improved in Theorem\u00a0Figure\u00a0N is tree-child, then it is immediate that for any vertex u there is a tree-child path from u to a leaf.If most recent common ancestorx and y may sometimes be traced back to The notion of the entclass1pt{minimaX-network that every vertex with out-degree at least two has the form The following theorem shows in a DCTC X-network. Suppose There exists j such that For every Assume u. Assume u to (3)(4)If (5)Suppose i that u is hybrid with out-degree one. But the latter contradicts that u has out-degree at least 2. Hence Part (1) is true.(1) Assume for each Part (2) follows since in the proof of Part (1) the choice of u.The second half of (3) is immediate since i and s such that i is minimal satisfying this condition. If u to u and i, contradicting that u. If i, contradicting that u, which is not possible since Next I claim that there are no i, i, s satisfying For (4) suppose w has the parents Consider the case where x cannot be post-hybrid, but it is possible that y is post-hybrid.Note in the proof that x,\u00a0y, it does not say that for all u is a common ancestor of 2 and 3 and v of 2 and 3 we must have N, but neither is an ancestor of the other.While Theorem\u00a0entclass1pt{minimaA related observation in Fig.\u00a0For Fig.\u00a0X-network. x and y is not post-hybrid.If u is hybrid.If p(x) that are hybrid with out-degree one, both having cluster The only vertices which do not have the form Suppose u has out-degree one, let c be its unique child. Then N is DC, there exists u is hybrid, proving Part (2). Then Part (3) is immediate. (1) follows from the theorem. If N is DCTC, we also have the following result involving u satisfies If X-network. For each If Let u is a common ancestor of cl(u). Conversely, if For (1), it is immediate that for u is hybrid. Thus, For (2), if In Fig.\u00a0The next result makes use of most recent common ancestors to find an upper bound on X-network, Suppose P denote the set of post-hybrid members of X, so Let p(x). It follows that there is no tree-child path from p(x) to If u to u :We now obtain our best upper bound for X-network and Suppose n the function v(N) is an integer, For fixed X-network in Fig.\u00a0For the DCTC We show in Theorem\u00a0X-networks Several different DCTC L, M, M allows the redundant arc . The redundant arc  in N did not require a new vertex. In general, adding a redundant arc between two existing vertices in a DCTC X-network N to create M does not change the set of clusters and hence yields Their differences will involve redundant arcs. For example, consider Fig.\u00a0X is a nonempty set. Let X such that for each X-network which we shall denote X, and the map Suppose i et\u00a0al.  construcX-network (possibly having hybrid leaves).X-network N (possibly having hybrid leaves) with cluster set Cl(N) is regular iff N is isomorphic with Reg(Cl(N)).An Figure\u00a0Following are some properties of i et\u00a0al. : \\documeX-network. Then S(R(N)) is X-isomorphic with Reg(Cl(N)).X-networks and X-isomorphic.Suppose Suppose S(R(N)) is normal and contains no vertices with out-degree one. By results in Willson (S(R(N)) is X-isomorphic with Reg(Cl(S(R(N)))). But Cl(S(R(N))) (1) By Theorem\u00a04.11 Willson , this ne Willson  we know  Willson , provingX-isomorphic with (2) From Part (1), for X-network N, all DCTC X-networks M such that u of M that is hybrid, then there exists a unique X-network. Next recursively adjoin redundant arcs to a,\u00a0b) where a and b are vertices of a,\u00a0b) where a is a vertex of b is a new vertex in the middle of what was the arc Theorem\u00a0N, we compute Cl(N) and then Reg(Cl(N)). Suppose we want to reconstruct N. Let N. We could continue to get another DCTC X-network with the same clusters as N by adjoining new redundant arcs For example, consider Fig.\u00a0N is a DCTC X-network with n leaves, then the number of vertices is at most n leaves and Theorem\u00a0 Bickner  of interr3 and the child r3m1 is the child of r3 that is an ancestor of 3.We start with r4 with a tree-child path of new vertices r4,\u00a0r4m1,\u00a0r4m2,\u00a04. Note r4 also has tree-child r3; r4m1 also has child r3m1, and r4m2 also has child p2. Note that r3m1 has become hybrid with tree-child 3, while r3 still has the tree child p1. Since p2 was already hybrid in r3m1 is the only new hybrid. Every non-leaf vertex of v of To obtain rnm1 but rn still has the tree-child rn. All non-leaf vertices of Given v of For each vertex We have proved the following:n leaves which is both DCTC and normal and which has For X-network with n leaves has at most 3 vertices, where n is needed.If N is an acyclic X-network there is an X-network N, it follows that Recall from Theorem\u00a0X-network. Then X-network containing no redundant arcs.Let v is not a leafFrom Willson , the firu,\u00a0v) is contracted in the formation of If w be another child of u beside v. Since N is normal, we may assume at least one of u. Choose a tree-path from v to the leaf x and from w to the leaf y. Note that If  Willson , \\documep(x) for some p(x) be denoted u(x).By Theorem 4.3 of Willson  \\documenu(x),\u00a0p(x)) to suppress the trivial vertex p(x). Thus, Now Theorem\u00a0u,\u00a0v] the tree-child of v becomes a tree-child for . And whenever we contracted (u(x),\u00a0p(x)) into , u(x),\u00a0p(x)]. Hence N contained no redundant arcs, the same is true about But it is clearly tree-child as well since whenever we contracted The operatorS is described in Sect.\u00a0X-network N, let v is not a leafu(x),\u00a0p(x)) where, for p(x) is a trivial vertex with unique parent u(x) having out-degree at least 2.N is normal, then The proof of Theorem\u00a0X-network. Then X-network, but contains no redundant arcs.Let We will illustrate the use of Corollary\u00a0X-network N, this section shows how to produce a uniquely determined X-network which is DCTC and which we denote Given an  Willson  used to  Willson  involvesX-network. A vertex v of N is a tree-child obstacle or (in this section) an obstacle if v is not a leaf; andv is hybrid. Hence, whenever  is an arc, u has a parent other than v.every child of An X-network N is tree-child obstacle-free if it contains no tree-child obstacle.Let N is an X-network that is tree-child obstacle-free. Then N is a tree-child X-network.Suppose v that is not a leaf, there is an arc  with c is a tree-child of v. Hence, N is tree-child. By hypothesis, for every vertex X-network N, suppose we seek a related DCTC X-network. Our strategy will be to compute Given an Just as for pre-normal obstacles in Willson , there aN be an X-network. Suppose c is a tree-child obstacle. An allowable 1-fold parent chain of c is a path c, c is of type 1 if c has an allowable 1-fold parent chain. If c has type 1, and Let c is a tree-child obstacle. An allowable k-fold parent chain for c is a path c is of typek if c is not of type c has an allowable k-fold parent chain.In this situation, for each such allowable k-fold parent chain writeSuppose X-network every tree-child obstacle has a type. Figure\u00a0X-network N in which 6 is a tree-child obstacle that has no type. Nevertheless, in an SCD X-network, the next result shows that every tree-child obstacle has a type.It is false that in every N be an SCD X-network. Then every tree-child obstacle c has a unique type.Let N is SCD, every child c of d of d with maximal cl(d), then d has no parent other than d is a tree-child of N is SCD and no child of X, It is clear that the type, if it exists, is unique. The root c which has maximal length k. Write it as k-fold parent chain of c since c has type Consider a path from  Willson , every aThe next result shows a way to remove a single obstacle of type 1.N is an X-network and c is a type 1 tree-child obstacle with allowable 1-fold parent chain p,\u00a0c such that p has tree-child d and is not an obstacle.Suppose p,\u00a0c) is not redundant, D is strongly closed and from Willson  into a vertex . In p,\u00a0c],\u00a0d). If q is any parent of d in p,\u00a0c], then q was a parent of d in N as well, contradicting that d was a tree-child of p. Since  is a non-redundant arc in the X-network N and p and c. Let a,\u00a0b) is a non-redundant arc in N and b is a tree-child of a. Assume Suppose (X-network N: The procedure is similar to that in Willson (These results lead to a procedure for finding a DCTC network closely related to a given  Willson  for findProcedure DCTC.Input An X-network N.Output An X-network and an integer.1. Let 2. If 3. Let 4. If c in 5. For each tree-child obstacle k.(5a). Compute the type (5b). Initialize k-fold parent chain c, let (5c). For each allowable k-fold parent chains for c.(5d). Let c.6. Let 7. Let 8. If i.9. Output X-network N will be denoted height of N is itself DCTC, and the height is 1 only if The network which is output from procedure DCTC applied to the X-network r and an X-network The procedure terminates and outputs an integer N and not any arbitrary choices.There is a leaf-preserving CSD map N.Let Suppose we apply the procedure DCTC to an c, then by Theorem 7.2 c has a type, so step (5a) can be carried out. Hence, the procedure is well-defined. Every time, the procedure enters step 5, the network has at least one obstacle, so the set D in step 6 is nonempty. Then at least one arc of N is finite, it follows that the procedure terminates.(1) By construction, for (2) It is immediate that the output (3) is immediate since no choices are made between different obstacles or allowable parent chains for an obstacle.N to (4) is immediate if (5) Just as in Willson , one cank-fold parent chain c and let (5c\u2019). Select one allowable C indicates the choice of each parent chain when there are more than one possible. As in Willson  for vi is the number of visible vertices. In a tree tc is the number of non-leaf vertices with no tree-child. In a tree, tc.0N, for the specified network M, When several networks are being analyzed related to the network For example, in Fig.\u00a0Let N, two of them using real data.This section contains three detailed examples of the calculation of N as described in  in u and v provided there is a path in N from u to v and in addition there is no visible vertex w distinct from u and v such that there are paths from u to w and from w to v. It is proved in Francis et\u00a0al. =\\psi =\\psi , and noN had none. It also contains the most hybrid vertices among the three DCTC networks, just one more than Of the three DCTC networks, N, From the mentclass2pt{minimN in the sense of N was simplified. Moreover, We see that Viola and present a phylogenetic network N with 16 leaves and with 21 proposed polyploid speciations in their Fig.\u00a0Marcussen et al. in Marcussen et\u00a0al.  study thn et\u00a0al. . Here weN has been published in Francis et\u00a0al.  for It is interesting that N have been reduced to 10 reticulations in N but some of the hybrids of N have been merged. Hybrids 6, 13, 14, 57, 59 in N disappeared since they were merged with their parental line. For any DCTC X-network M, From the table, the 21 hybrids of x,\u00a0y); for example, In x,\u00a0y) of distinct leaves, Moreover . In their Additional File 4, Figure S7\u20139a is the cluster network for their dataset 9, constructed using all fragments passing the SH test against 100 random trees by support at least 15%. Let N be the network of their Figure S7\u20139a. The wired lift of N.Here is another example with real data. Kamneva et\u00a0al.  study alThere are 13 leaves with Drymocallis being the outgroup that roots the network. X-networks. There is, however, no CSD map from N to It is clear that N, while N. The other hybrid 25 of N was merged with its parental line and descendant 28 into .From Table\u00a0N in terms of the distance Note that N, we have seen that Given a general network D consists of the arcs of some allowable parent chains. We here consider these two operations separately.The construction of N on the left with N, there is a \u201cladder\u201d structure involving 4, 5, 6, 7, and 8. Note that N may be correct in the sense that there might have been several stages of contribution to the genome of 9, nothing really identifies the relevant species. The result would be indistinguishable from the result if the species 5, 6, 7, and 8 were permuted. It can be argued that the data do not really support a network with distinct vertices 5, 6, 7, and 8; the simplification of N into To study the first operation, consider Fig.\u00a0M of Fig.\u00a0M, M is DCTC, so The fact that these identifications occur in N on the left, there is another \u201cladder\u201d N. As for Fig.\u00a0N.Similar considerations apply to a more complicated situation as in Fig.\u00a0N is the Viola dataset for Example\u00a0Less extreme \u201cladders\u201d can occur. Figure\u00a0entclass1pt{minimaa in N with a unique child b which is not a leaf, so a and b are not distinguishable from the data; these include N, such arcs  may merely indicate the distinction between a hybrid vertex a and the next descendant b where another speciation event occurs. If b is a tree-child, as in the case p(x)) and these can be mentally retained. When b is hybrid, as for example in the case a and b are parts of another ambiguous ladder, justifying the identification of 47 and 48.Figure\u00a0N in the formation of We see that in general the merging of arcs from D consists of the arcs of some allowable parent chains to make the network tree-child) is different. Figure\u00a0N on the left and also N, N and N is assumed to describe the genetic history, a mutation from 5 which is absent in 1 and 4 but present in 2 and 3 should be more common than if instead The interpretation of the second operation  Fig.\u00a0 which ar(N) Fig.\u00a0 5 has beFragaria dataset N of Kamneva et\u00a0al. (For the a et\u00a0al.  and ExamN so that every vertex becomes visible. As a result, every vertex has at least one leaf on which its genetic influence is important. Changes from In general,"}
+{"text": "Prioritization of self-related information (e.g. self-face) may be driven by its extreme familiarity. Nevertheless, the findings of numerous behavioral studies reported a self-preference for initially unfamiliar information, arbitrarily associated with the self. In the current study, we investigated the neural underpinnings of extremely familiar stimuli  and stimuli newly assigned to one\u2019s own person and to a close-other (abstract shapes). Control conditions consisted of unknown faces and unknown abstract shapes. Reaction times (RTs) to the self-face were shorter than to close-other\u2019s and unknown faces, whereas no RTs differences were observed for shapes. P3 amplitude to the self-face was larger than to close-other\u2019s and unknown faces. Nonparametric cluster-based permutation tests showed significant clusters for the self-face vs. other  faces. However, in the case of shapes P3 amplitudes to the self-assigned shape and to the shape assigned to a close-other were similar, and both were larger than P3 to unknown shapes. No cluster was detected for the self-assigned shape when compared with the shape assigned to the close-other. Thus, our findings revealed preferential attentional processing of the self-face and the similar allocation of attentional resources to shapes assigned to the self and a close-other. In order to ensure our adaptive functioning in complex social environments, only some pieces of incoming information are selected for further processing. Such selection is often guided by the self-relevance of the information . To starImportantly, in the cited studies self-related stimuli were represented by highly familiar items like one\u2019s own name or face. The daily exposure to one\u2019s own face and name across the whole lifespan determines their extreme familiarity in comparison with all other faces and names. Hence, it cannot be clearly differentiated whether the observed effects were caused by the self-relevance or familiarity of those stimuli .To control for the confounding effects of familiarity, Sui and colleagues  introducAll in all, a brief association of a neutral shape with the self seems to increase the salience of those stimuli and is sufficient to elicit the self-prioritization effect . Self-prHowever, it is worth noting that in trials with matching pairs of self-associated shape and self-label, participants were processing both self-associated arbitrary stimuli and familiar verbal labels with an established meaning. Therefore, the self-advantage may be caused by the high familiarity of the self-label and not by the self-association of the shape. This fact led some studies to test self-prioritization effects in experimental paradigms with new self- vs. other-associated stimuli only. For example, Most studies investigating the self-prioritization of information that was newly assigned to one\u2019s self vs. another person were based on behavioral measures . In contrast, studies investigating the neural correlates of such information processing are rather rare . One of In yet another fMRI study , particiFurther, in an event-related potential (ERP) study three unfamiliar faces were identified with the verbal labels \u201cYou,\u201d \u201cFriend,\u201d and \u201cStranger\u201d instead of shapes . AfterwaIn the current ERP study, we investigated the neural underpinnings of highly familiar and new information that was arbitrarily assigned to the self and to a close-other. We were interested in whether previously irrelevant, abstract information that was newly associated with the self would benefit from preferential processing as is the case for well-known self-referential information, and whether self-prioritization effects would be comparable in both cases. Therefore, we directly compared the processing of two types of stimuli: extremely familiar  stimuli, and stimuli that were newly assigned to one\u2019s own person and to a close-other (an abstract shape). The control conditions consisted of unknown faces and unknown abstract shapes. We decided to present participants with abstract shapes alone, without labels. The reason for doing so was twofold. First, this approach avoids the aforementioned controversies regarding familiar labels. Second, as there was no need to use any labels in the case of faces, this approach (i.e. avoiding labels) guaranteed similar visual stimulation in both cases.Participants were tasked with indicating whether presented stimuli  were familiar or unknown. Prior to the EEG recording session, arbitrarily selected shapes were associated with the self and a close-other (i.e. one shape for each person). The close-other was freely chosen by each participant as representative of the most significant person in their life at the time of experimentation. This operationalization of a close-other was used in several previous studies on the topic of self-prioritization . It is wIn this study, the P3 results obtained for faces served as a kind of reference for ERP results for shapes. We expected to observe enhanced P3 associated with self-face processing when compared to close-other and unknown face processing. We aimed at testing whether information newly assigned to the self and a close-other would lead to an analogous pattern of findings. As far as behavioral indices of self-prioritization are also concerned, we were interested in whether behavioral findings would be comparable for faces and shapes.Moreover, the distinct spatial patterns of activity elicited by faces and shapes were also tested with nonparametric cluster-based permutation tests . This meM\u2009=\u200927.594; SD\u2009=\u20093.131). The Edinburgh Handedness Inventory  were tested in the study, ranging in age between 21 and 34\u00a0years old (nventory  indicatenventory .www.nencki.edu.pl) developed at the Nencki Institute in cooperation with the University of Warsaw. SONAR-II is dedicated to the asymptomatic population of people who do not meet the criteria for SARS-CoV-2 testing but who may come into contact with infected people.An additional present-day restriction was a negative test for the SARS-CoV-2 virus. As all participants were PhD students and employees at the Nencki Institute, they took part in the SONAR-II project . All participants provided written informed consent prior to the study and received financial compensation for their participation.We used two different types of stimuli in this study: (1) faces and (2) shapes. The set of stimuli was individually tailored to each participant. Faces belonged to three categories: self-face, close-other\u2019s face, and unknown faces. Participants freely chose the close-other according to their subjective high level of closeness and importance. We did not predefine the type of relationship between the participant and their close-other in order to avoid a spuriously close relation. The only restriction placed on the selection of the close-other was that they had to be of the same gender as the participant. Twenty-two participants chose their friend, eight their sibling, and two their partner. The face of each participant and their close-other was photographed  prior to the study. The photographs of eight unknown neutral faces were taken from the Chicago Face Database , gender 2. Shape assignment to each experimental \u201ccondition\u201d  was pseudo-random on the group level; e.g. a self-assigned shape in a given set of stimuli was assigned to a close-other or unknown condition in some other set of stimuli. Faces and shapes were presented against a black background. The second type of stimuli consisted of abstract shapes. In previous studies on the processing of new information assigned to the self and others, simple geometric figures  were typically used. As the number of shapes was supposed to be equal to the total number of faces  we generated 10 different abstract shapes. We aimed at equalizing low-level physical features of faces and shapes. Thus, each shape\u2019s area was equal to face oval\u2019s area, i.e. 43.12\u00a0cmParticipants were seated in a comfortable chair in a dimly lit and sound-attenuated room, 57\u00a0cm from the computer monitor . Subsequently, during the electrode cap placement and adjustment of EEG electrode impedances, they were primed for the task: two different shapes, one assigned to the participant and the second to their close-other, were presented on the monitor and participants were required to associate those geometric shapes with the self and chosen close-other. The learning phase lasted on average 23.53\u00a0min (SD\u2009=\u20095.900). Just before the beginning of the task, participants were asked to draw the assigned shapes. This was done to check the efficiency of learning.After electrode cap placement , the participants used an adjustable chinrest to maintain a stable head position. Presentation software  was used for stimuli presentation. Participants performed a recognition task\u2014if they recognized a presented face or shape (i.e. representing the participant or their close-other), they were asked to push the response button assigned to \u201cYES.\u201d If that was not the case, they were asked to press the button defined as \u201cNO.\u201d The assignment of \u201cYES\u201d and \u201cNO\u201d buttons was counterbalanced across the participants.After reading the instructions displayed on the screen, the subjects confirmed they understood the task and initiated the experiment by pressing a response button. Trials with faces and shapes were inter-mixed (in one session) and their order was pseudo-random with respect to the type of stimulus  and the experimental condition . Each trial started with a blank screen, presented for 1500\u00a0ms. Next, a white fixation cross  was centrally displayed for 100\u00a0ms and followed by a blank screen which lasted either (randomly) 100, 200, 300, or 400\u00a0ms. Afterwards, a face or a shape was presented for 500\u00a0ms. Regardless of which stimulus was shown, participants were asked to push the appropriate response button as quickly as possible. Next, a blank screen was shown and lasted until a response was made. The procedure structure is presented in To account for possible fatigue during the experiment, a break was planned in the middle of experimental session. It was terminated after one minute, unless the participant ended it earlier. Participants needed 24\u00a0min on average to complete the whole experiment.The electroencephalogram (EEG) was continuously recorded with 62 Ag-AgCl electrically shielded electrodes mounted on an elastic cap  and positioned according to the extended 10\u201320 system, with two additional electrodes placed on the left and right earlobes. The EEG signal was recorded using the BrainAmp MR plus amplifier  and digitized at a 500-Hz sampling rate, using BrainVision Recorder software . EEG electrode impedances were kept below 10 k\u03a9. The EEG signal was recorded against an average of all channels calculated by the amplifier hardware.Responses were scored as correct if the appropriate button was pressed within 100\u20131000\u00a0ms of stimulus onset. In order to conduct statistical analyses of behavioral and ERP data in a consistent manner, similarly to our analyses of ERP components, only every other trial with an unfamiliar stimulus was included in the analyses. This was done because the number of trials with unfamiliar faces (80) and shapes (80) was doubled in comparison to the number of trials with familiar faces and shapes in each familiar  condition (40). Statistical analyses were performed using JASP software . Mean ac10 between 1 and 3 implies anecdotal evidence in favor of H1, between 3 and 10\u2014moderate evidence, between 10 and 30\u2014strong evidence, between 30 and 100\u2014very strong, and higher than 100\u2014extreme evidence. As far as low values of BF10 are concerned, a BF10 between 0.33 and 1 indicates anecdotal evidence in favor of H0, between 0.1 and 0.33\u2014moderate evidence, and between 0.03 and 0.1\u2014strong evidence of the absence of an effect. Finally, a BF10 between 0.01 and 0.03 and lower than 0.01 indicates very strong and extreme evidence for the absence of an effect, respectively.The traditional null-hypothesis significance-testing approach was complemented with Bayesian analysis methods and Bayes factors (BFs) were computed using JASP software . BFs werOff-line analysis of the EEG was performed using BrainVisionAnalyzer software . The 62 channels were re-referenced off-line to the algebraic average of the left and right earlobes, notch filtered at 50\u00a0Hz, and band-pass- filtered from 0.1 to 30\u00a0Hz using a Butterworth filter. The next step in data pre-processing was the correction of ocular artifacts using Independent Component Analysis (ICA) . After eAfterward, the EEG signal was segmented into 1200\u00a0ms epochs, from \u2212200\u00a0ms before to 1000\u00a0ms after stimulus onset. The subsequent automatic artifact rejection procedure allowed only trials, which fulfilled the following requirements: the maximum permitted voltage step per sampling point was 50\u00a0\u03bcV, the maximum permitted absolute difference between two values in the 200-ms-long segment was 100\u00a0\u03bcV, the minimal and maximal allowed amplitudes were\u2009\u2212150\u00a0\u03bcV and 150\u00a0\u03bcV, and the lowest permitted activity in the 100\u00a0ms interval was 0.5\u00a0\u03bcV.Trials with correct responses were subsequently analyzed. In the case of unfamiliar stimuli, only every other trial was included in the analyses. This was done in order to keep a similar signal-to-noise ratio (SNR) for each experimental condition (defined by the type of stimulus and type of face). It should be reminded that the total number of trials with unfamiliar faces and shapes (80 for each of them) was twice as large as the total number of trials with familiar faces and shapes in the single \u201cself\u201d and \u201cclose-other\u201d conditions (40 for each type of stimulus). The mean number of segments averaged afterwards for each experimental condition was as follows: self-face\u201437.031 (SD\u2009=\u20092.800), shape assigned to self\u201435.250 (SD\u2009=\u20093.298), close-other\u2019s face\u201436.938 (SD\u2009=\u20092.449), shape assigned to close-other \u221235.031 (SD\u2009=\u20093.441), unknown other face\u201436.344 (SD\u2009=\u20092.868), and unknown shape\u201435.938 (SD\u2009=\u20093.816). In the final stage of pre-processing, the epochs were baseline-corrected by subtracting the mean of the pre-stimulus period.Selection of electrodes for ERP analysis was orthogonal to potential differences between experimental conditions . Therefohttp://statcheck.io/index.php). A two-way repeated measure ANOVA was performed with \u201ctype of stimulus\u201d  and \u201ccondition\u201d  as within-subject factors. All effects with more than one degree of freedom in the numerator were adjusted for violations of sphericity . The reported results were cross-checked with Statcheck  was used in all Bayesian tests. BF10 were interpreted according to The traditional null hypothesis significance testing approach was complemented with Bayesian analysis methods. To test whether the self-face and other faces, as well as the self-assigned shape and other shapes, were characterized by similar levels of neural activity, BFs were computed using JASP software . The maiCluster-based permutation tests were used here as an exploratory analysis procedure, as they efficiently handle the multiple comparisons problem in high-dimensional magnetoencephalographic and EEG data . In geneWe directly compared: self-face vs. close-other\u2019s face, self-face vs. unknown faces, close-other\u2019s face vs. unknown faces, self-shape vs. close-other\u2019s shape, self-shape vs. unknown shapes and close-other\u2019s shape vs. unknown shapes. As clustering in both space and time was used, such an analysis procedure revealed differences in the spatial distributions of activity as a function of time between the tested conditions.F\u2009=\u200928.758, P\u2009<\u20090.001, \u03b72\u2009=\u20090.141) and \u201ccondition\u201d \u2009=\u20094.022, P\u2009=\u20090.023, \u03b72\u2009=\u20090.028), as well as a significant two-way interaction: \u201ccondition\u201d \u00d7 \u201ctype of stimulus\u201d \u2009=\u200910.689, P\u2009<\u20090.001, \u03b72\u2009=\u20090.119). The significance of the \u201ctype of stimulus\u201d factor indicated a significantly higher accuracy score in the case of faces in comparison with shapes (see P\u2009=\u20090.020), whereas other differences were non-significant .A repeated-measures ANOVA conducted on the mean number of correct responses revealed the significant main effects of \u201ctype of stimulus\u201d , the self-face and unknown faces , and the close-other\u2019s face vs. unknown faces . Significant differences in accuracy rates were present between the self-assigned shape and unknown shapes  and between the close-other assigned shape and unknown shapes , whereas the self-assigned shape and the close-other assigned shape did not differ .Post-hoc tests of the \u201ccondition\u201d \u00d7 \u201ctype of stimulus\u201d interaction revealed non-significant differences in accuracy scores between the self-face and the close-other\u2019s face , but it was similar for faces and shapes in the case of the \u201cunknown\u201d condition .Moreover, post hoc tests of the \u201ccondition\u201d \u00d7 \u201ctype of stimulus\u201d interaction also showed that the number of correct responses to faces was significantly higher than to shapes in the \u201cself\u201d and \u201cclose-other\u201d conditions \u2009=\u200925.374, P\u2009<\u20090.001, \u03b72\u2009=\u20090.159) and a significant two-way interaction: \u201ccondition\u201d \u00d7 \u201ctype of stimulus\u201d \u2009=\u200936.036, P\u2009<\u20090.001, \u03b72\u2009=\u20090.230). Post hoc tests of the \u201ccondition\u201d factor showed that RTs in the \u201cself\u201d condition were substantially shorter than in the \u201cclose-other\u201d (P\u2009<\u20090.001) and \u201cunknown\u201d conditions (P\u2009<\u20090.001). However, this pattern of findings was driven mainly by RTs to faces. Post hoc tests of the \u201ccondition\u201d \u00d7 \u201ctype of stimulus\u201d interaction revealed significantly shorter RTs to the self-face than to the close-other\u2019s face  and unknown faces , as well as shorter RTs to the close-other\u2019s face than to unknown faces . In contrast, in the case of shapes, all differences between conditions were non-significant .A repeated-measures ANOVA conducted on mean RTs revealed the significant main effect of \u201ccondition\u201d . The opposite effect, i.e. longer RTs, was observed for unknown faces when compared to unknown shapes , but no significant differences were found in the case of the \u201cclose-other\u201d condition .Post hoc tests of the \u201ccondition\u201d \u00d7 \u201ctype of stimulus\u201d interaction also showed that RTs to the self-face were significantly shorter than to the self-assigned shape \u2009=\u200927.004, P\u2009<\u20090.001, \u03b72\u2009=\u20090.466), \u201ccondition\u201d \u2009=\u200932.288, P\u2009<\u20090.001, \u03b72\u2009 =\u20090.510), and a significant 2-way \u201ccondition\u201d\u2009\u00d7\u2009\u201ctype of stimulus\u201d interaction \u2009=\u200915.514, P\u2009<\u20090.001. \u03b72\u2009=\u20090.334). The significance of the \u201ctype of stimulus\u201d factor indicated that the P300 amplitude for faces was significantly higher than for shapes  as well as for stimuli associated with the close-other (P\u2009<\u20090.001). The difference between stimuli associated with self and close-other was non-significant (P\u2009=\u20090.221).Post-hoc analyses for the \u201ccondition\u201d factor showed that the unknown stimuli evoked significantly lower P3 than stimuli associated with the self . This was also the case for the close-other condition: P3 to the close-other\u2019s face was larger than P3 to the shape assigned to a close-other . Such an effect was not observed for unknown stimuli, as the difference between unknown faces and unknown shapes was not significant . Moreover, P3 amplitude was significantly increased for self-face in comparison to close-other\u2019s face  as well as in comparison to unknown faces , and for close-other\u2019s face compared to unknown faces . P3 amplitudes to the self-assigned shape and the close-other assigned shape did not differ . However, unknown shapes were associated with lower P3 amplitude than the shape assigned to the self  and to the close-other .Post hoc tests performed for the two-way \u201ccondition\u201d \u00d7 \u201ctype of stimulus\u201d interaction revealed that the self-face was associated with significantly higher P3 than the shape assigned to the self  are processed preferentially . RTs analyses revealed that all self-related stimuli were characterized by shorter RTs in comparison to the other stimuli (i.e. referring to the close-other and unknown people). Additionally, it should be highlighted that this result was primarily driven by the RTs to faces\u2014significant differences were observed between self-face and other faces, but not between shapes. Moreover, RTs to the self-face were significantly shorter than to the self-assigned shape. Such faster reactions to faces than to shapes were not observed in the case of the \u201cclose-other\u201d and \u201cunknown\u201d conditions.Based on numerous studies showing behavioral indices of the self-prioritization effect for new information that is arbitrarily associated with the self , one migTo start with, one of the differences refers to the presence vs. absence of labels. Specifically, in the matching trials of the self-prioritization task used in previous studies, participants were processing not only self-associated arbitrary stimuli but also familiar verbal labels with a pre-experimentally established meaning. Therefore, the self-advantage may be caused by the familiarity of the labels, rather than the self-association of the shape. In contrast, the present study did not present labels with shapes. However, it should be noted that the self-prioritization effect in RTs was also observed in the absence of any pre-experimentally familiar stimuli related to the self . Thus, tCrucially, the behavioral tasks performed by participants were different. While in previous studies, it was the perceptual matching task, in the current study it was the discrimination of familiar vs. unfamiliar stimuli. Thus a question may arise whether participants ignored self- and close-other associations when responding to the shapes and simply re-conceptualized those shapes as simply representing the category \u201cfamiliar.\u201d Such strategy was fully efficient in successfully accomplishing the task and accuracy rates seemed to support this view as they did not differ for self- and close-other assigned shapes.It is worth noting that the self-relevance facilitated stimulus processing only when task sets drew attention to previously formed shape-label associations . CompareEven so, we found faster reactions to one\u2019s own face than to other faces. Our RTs results are in line with the findings reported in numerous studies, typically reporting shorter RTs to the self vs. other faces . In a reOn the neural level, the ERP findings differed for faces and shapes. First of all, amplitudes of P3 to faces were\u2014in general\u2014higher than amplitudes of P3 to shapes. As the P3 component is linked to the cognitive evaluation of stimulus significance , this fiHowever, the pattern of findings was different in the case of shapes. P3 to the self-assigned shape and P3 to the close-other assigned shape were similar, and both were larger than P3 to unknown shapes. Moreover, nonparametric cluster-based permutation tests showed significant clusters for comparisons of \u201cself vs. \u2018unknown\u2019 and \u2018close-other\u201d vs. \u201cunknown\u201d conditions, but no significant cluster was detected for the self-assigned shape when compared to the close-other assigned shape. The latter is in line with the lack of differences in P3 amplitude between the self- and close-other conditions.Due to methodological differences, it is rather difficult to directly compare our P3 findings for the self-assigned shape to previous ERP findings on the processing of newly acquired self-related information . In Wo\u017anHowever, our P3 results to faces corroborate the findings of previous studies reporting enhanced P3 to the self-face in comparison with other (either familiar or unfamiliar) faces . Such anIn the present study, one of the main differences between the processing of faces and shapes referred to the relation between the \u201cself\u201d and \u201cclose-other\u201d conditions. While those two conditions differed in the case of faces, they did not differ in the case of shapes, as indicated by significant differences found both in the neural underpinnings and in RTs for faces and lack of such differences for shapes. The most obvious explanation of this dissociation refers to the familiarity of processed information. Specifically, the self-advantage found for the self-face vs. close-other\u2019s face comparison was not observed if levels of familiarity of information referring to the self and the close-other were strictly equalized, as it was done for shapes. Thus, our P3 findings for the \u201cself\u201d and \u201cclose-other\u201d conditions may be driven by the higher pre-experimental familiarity of one\u2019s own face than the close-other\u2019s face.Moreover, this pattern of P3 findings may also be interpreted in reference to the attentional processing of information related to the self and close-other. Specifically, it has been proposed that the mechanisms boosting the prioritized processing of self-relevant information could be driven by automatic capture of attention and prioritized allocation of attention to self-related stimuli review . Indeed,In general, interpretations of P3 findings referring to attentional processes are in line with the notion that P3 reflects stimulus processing only, i.e. with the view that P3 is a signature of a comprehensive evaluation of incoming stimuli . This evMoreover, one may view P3 findings reported in the current study in the light of the locus coeruleus-noradrenergic (LC-NE) system activity. The pivotal role of the LC-NE system in regulating task engagement is well documented . ThroughSo far, we viewed our P3 findings in the light of attentional mechanisms. However, this view may be complemented by the interpretation of P3 as reflecting processing of stimuli that are highly arousing in nature . These tAs the P3 component reflects the cognitive evaluation of stimulus significance , differeThe limitations of the current study are as follows. Shapes were arbitrarily assigned to one\u2019s own person and to the chosen close-other, and their processing was compared to unknown shapes. As those familiar conditions (the self and the close-other) are personally relevant, it is a matter of debate whether similar\u2014or rather dissimilar\u2014patterns of behavioral and electrophysiological findings would be observed for shapes assigned to famous people. Therefore, the inclusion of such an additional experimental condition would provide a more global view on the processing of newly acquired information referring to the self and others. Moreover, our study did not provide an answer to the question of whether the self-relevance of newly acquired information triggers the self-representation in the brain, similarly to highly familiar self-referential information (self-face). In order to adequately relate to this issue, some source analyses  should be done. However, due to rather a low number of experimental trials, such analyses\u2014in the case of our present study\u2014would be not very reliable. Future EEG studies may investigate whether newly learned and long-term established self-related information are represented in the same (or overlapping) neural network in the brain.In conclusion, P3 and permutation test results revealed a clear self-advantage in the case of faces, i.e. significant differences between the processing of the self-face and other faces . These findings may be viewed in the light of preferential attention allocation to highly familiar and well-established self-referential information. However, the processing of new information arbitrarily assigned to one\u2019s own person and the close-other did not differ. We propose that this effect is mainly driven by similar attentional biases to self- and close-other assigned shapes."}
+{"text": "From the assumption that the residual seismic data (the difference between the modeled and observed data) obeys the R\u00e9nyi \u03b1-Gaussian probability distribution, we introduce an outlier-resistant criterion to deal with erratic measures in the FWI context, in which the classical FWI based on l2-norm is a particular case. The new misfit function arises from the probabilistic maximum-likelihood method associated with the \u03b1-Gaussian distribution. The PGF technique works on the forward modeling process by dividing the computational domain into outside target area and target area, where the wave equation is solved only once on the outside target (before FWI). During the FWI processing, Green\u2019s functions related only to the target area are computed instead of the entire computational domain, saving computational efforts. We show the effectiveness of our proposed approach by considering two distinct realistic P-wave velocity models, in which the first one is inspired in the Kwanza Basin in Angola and the second in a region of great economic interest in the Brazilian pre-salt field. We call our proposal by the abbreviation \u03b1-PGF-FWI. The results reveal that the \u03b1-PGF-FWI is robust against additive Gaussian noise and non-Gaussian noise with outliers in the limit \u03b1 \u2192 2/3, being \u03b1 the R\u00e9nyi entropic index.The estimation of physical parameters from data analyses is a crucial process for the description and modeling of many complex systems. Based on R\u00e9nyi  Full-waveform inversion (FWI) is a powerful methodology to estimate subsurface physical parameters by exploring the complete waveforms recorded in a seismic survey , 2. FromDespite the FWI potentials, it is inherently an ill-posed problem in the sense of Hadamard, which means that at least one of the following features is violated: the solution (i) exists, (ii) is unique; and (iii) depends continuously on the observed data. The characteristic (ii) is commonly violated in FWI because in a typical geophysical survey there is information only on the positions associated with the seismic receivers that cover a small area of the region of interest, which leads the FWI to solve an inconsistent and overdetermined system of equations. Regarding the characteristic (iii), the FWI solution may be unstable, as a small variation in the noise level of the observed data can lead to discontinuous changes in the reconstructed subsurface model . Furtherl1-norm of the error. Such criterion is based on the assumption that the errors obey the Laplace distribution. Its success is associated with the long tails of the Laplace distribution ,\u201366,\u03b1-entgiven by :Z\u03b1=1-\u03b1\u03c0x are independent and identically distributed by the \u03b1-Gaussian distribution  is formulated as the following minimization task:A\u03c8s(\u03c9) = Ss(\u03c9). Thus, the solution of the optimization problem formulated in )]+subject \u03b1-adjoint equation,\u03b1 \u2192 1.Computing the stationary point of )\u2020\u039bs(\u03c9),\u2202L\u03b1).We noticSs(\u03c9)).2We noticthat Eqs , respectthat Eqs . In thisgrangian , we obta\u03b1-misfit function is given by:\u03b1-misfit function is computed by solving the wave equation and correlating it with the solution \u039b of the wave equation in \u03b1 \u2192 1.Thus, the function  is a par\u03b1-misfit function mitigates the effects of non-Gaussian errors, specially the outliers. It is possible to see such behavior through the analysis of the \u03b1-adjoint-source , we notice that the adjoint wavefield tends to zero (\u039bs \u2192 0), and therefore \u2207m\u03d5\u03b1(m)\u21920 in that case. Indeed, the \u03b1-misfit function magnifies small errors and suppresses large ones, since the \u03b1-adjoint-source \u2212ds,r for small errors and inverse of the errors \u0394ds,r, \u039bs \u221d 1/\u0394ds,r for large ones. The classical approach (\u03b1 \u2192 1), on the other hand, linearly suppresses small errors and magnifies large errors , which explain the sensitivity of this approach to non-Gaussian errors [In contrast to the classical approach, the t-source  is propon errors .A is given by the inverse of the Green\u2019s function G\u22121, \u03c8s is the discretized pressure wavefield, and h is the grid spacing (in meters), F\u03c9 is the amplitude of the Fourier coefficients of the seismic source and Us is a column vector with zero elements everywhere except on the source position xs representing \u03b4(x\u2212xs).As discussed earlier, solving the wave equation is a critical issue of the FWI technique. In this way, the patched Green\u2019s function (PGF) technique appears as a powerful alternative to reduce the computational cost of imaging problems based on wave equation. In the PGF framework, the solution of the frequency-domain wave equation  and at the position of sources (s) and receivers (r). The subscripts e and i refer, respectively, to the elements of the outer edge and the inner edge of the target region, connected through the employment of the potential Vi,e. Eqs -1ges,Gts=gtiViVieGes.where tht and the blue squares represent the area outside the target region t\u2032, in which h is the grid spacing. The PGF method is performed in two steps: First, we find the element that connects the edges of the target area e and i  algorithm [l-BFGS optimizer fetches an informative  minimum of the misfit function using its gradient \u2207m\u03d5(m). In this way, the l-BFGS computes an approximation of the inverse Hessian matrix H\u22121 from previous gradients by imposing a secant condition [\u03b2 along the descent-direction search of the gradient, which satisfies the Wolfe conditions [\u03bcp is the peak frequency.To illustrate how the lgorithm  to solvelgorithm . The l-Bondition . Moreovenditions . In addinditions , which ind and 8th order approximations for time and space, respectively, in a regular grid with 5m spacing with a convolution-perfectly matched layer (C-PML) [nd and 4th order approximations for time and space, respectively, in a regular grid with 10m spacing with perfectly matched layer (PML) absorbing layers [m spacing with C-PML absorbing boundaries [To avoid the inversion crime in all numerical experiments, we generated the observed dataset in the time domain by employing the finite difference method with 2 (C-PML) , 75. In g layers  for the undaries .\u03b1-FWI regarding erratic data (outliers), we consider a 2D acoustic velocity model which is widely used in geophysical imaging tests, named the Marmousi model. Such a model presents a complex velocity geometry, as depicted in m in-depth with 183 equally spaced seismic sources spaced 48m apart, from 216m to 8952m, in which we employ a Ricker wavelet with \u03bcp = 5Hz as the seismic source. Furthermore, we consider 23 equally spaced receivers located every 408m, from 96m to 9072m, deployed at the ocean floor (240m in-depth) to simulate an ocean bottom nodes (OBN) acquisition, which is a marine type seismic acquisition often used in the last years. The recording time was 5s. To analyze the robustness of the dB and 60dB, respectively, as depicted in SNR = 70dB and that only one of the seismic traces from each receiver is contaminated by outliers  and Gaussian noise to simulate a realistic circumstance like to Ref. . In the \u03b1 \u2192 1), and the last seven ones are based on the \u03b1-misfit function with \u03b1 = 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, and 0.95. In all numerical experiments, we inverted for 200 l-BFGS iterations from the above-described geometry seismic acquisition and the initial model depicted in For each noisy-scenario, we carried out eight data inversions, in which the first one refers to the classical approach  the Pearson product-moment correlation coefficient ; and (ii) the normalized root-mean-square (NRMS). The Pearson\u2019s R measures the linear correlation between the reconstructed model and the true model, in which it varies between \u22121 and 1, inclusive. In this regard, R = 1 means a strong correlation between the two models and, in our case, R-values far from 1 mean low correlation. The NRMS varies from 0 (perfect model) to \u221e (bad model) and is defined as:ctrue is true model and cFWI corresponds to the FWI result. The statistical measures for the noiseless data case (first scenario) are summarized in R \u2265 0.8, according to the strength-scale suggested by Ref. [\u03b1 = 0.55 and \u03b1 = 0.65 have the highest Pearson\u2019s R and the lowest NRMS value. by Ref. ), althou\u03b1-FWI results are very satisfactory as the resulting models are close to the true model. In fact, regardless of the \u03b1-value, the reconstructed P-wave models present the main structures of the Marmousi model despite the imprint of the noise. Again, case \u03b1 = 0.55 has a higher correlation and lower NRMS error compared to the true model, as summarized in Figs \u03b1 \u2192 1) completely fails to reconstruct a P-wave velocity model, as depicted in \u03b1-value decreases, which means a greater deviation from the Gaussian statistics, the resulting model is more suitable , the misfit function decay is more accentuated  and \u03b1 = 0.35 cases to compare our proposal with the classical approach. We notice that the water layer in all P-wave velocity models are assumed to be known and, therefore, are kept constant during the inversion process.In this section, we explore the potential of the \u03b1-PGF-FWI. In the first one, we consider the noiseless data set generated by the acquisition geometry described previously. In the second one, we consider the same data set, but polluted by non-Gaussian noise. The non-Gaussian perturbations were generated through a Student\u2019s t-distribution with three degrees of freedom. We solve the forward problem by solving the 2-D frequency-domain acoustic wave equation using the finite-difference method, in which we consider a 9-point stencil with a C-PML boundary condition [The first two experiments consist of imaging the pre-salt region, which remains a great challenge, using the ondition , 75 in okm/s), and a linear velocity increasing, from 5.4km in-depth, rang the second frequencies group. Again, the resulting model is used as the initial model for the third group. For each frequency group, we compute 20 l-BFGS iterations.We discretize the Helmholtz operator on a regular grid with a spacing of 25 m. In the inversion process, we consider a multiscale approach , 84 in wkm to 8.5km in-depth and horizontally from 2.5km to 17.5km, as well-demarcated in Figs \u03b1-PGF-FWI results for the noiseless and non-Gaussian noise cases, respectively, in which the left column refers to the classical approach (\u03b1 \u2192 1) and the right column refers to our proposal with \u03b1 = 0.35. We notice in The target region consists of a rectangular area, mostly composed of the Brazilian pre-salt, which comprises a region from 4.5\u03b1-PGF-FWI with \u03b1 = 0.35 decays more accentuated . It is worth mentioning that if the observed data does not contain noise or is polluted by Gaussian noise, \u03b1-PGF-FWI and classical PGF-FWI have similar performances. However, the \u03b1-PGF-FWI is robust to non-Gaussian noise, while the classical PGF-FWI estimates biased models in these circumstances. The reason is that large errors are better attenuated in the adjoint-source of our proposal compared to the classical approach, leading to a better weighting of waveforms crossing the less illuminated regions of the model. Indeed, the classical misfit function treats all residuals equally, while the proposed misfit function weights residual data according to their amplitude, giving less importance to large errors in the dataset.We notice that the \u03b1-PGF-FWI is a powerful methodology to deal with non-Gaussian errors, which may become a valuable tool in geophysical imaging problems, especially when the data is polluted by large errors. It is also worth noting that our proposal can be applied to any problem of estimating physical parameters linked to partial differential equations similar to the Helmholtz equation, such as in biomedical imaging issues [The numerical results show that the g issues .Plots and numerical simulations were done, respectively, with MATLAB R2016b and Julia Language, on a computer hosting a quad-core (Intel Xeon E5-1620 v3) processor at 3.50GHz and 256GB RAM memories."}
+{"text": "The Eating Disorder Examination Questionnaire (EDE-Q) is a frequently used scale to evaluate eating behaviors and attitudes. In recent years, its use has increased due to the fact that the use of short forms is more practical. The aim of this study was to validate the short Turkish form of the Eating Disorder Examination Questionnaire (EDE-Q) including 13 items.The study included 924 adults at a mean age of 30.3\u2009\u00b1\u200910.93\u00a0years. EDEQ-13 was translated and adapted to Turkish according to the Beaton Guidelines. The Eating Attitudes Test-26 (EAT-26), the Satisfaction with Life Scale (SWLS), and the Body Appreciation Scale (BAS) were used to analyze their relationships to EDE-Q-13.In this study, the rate of the total variance explained by the factors of EDE-Q-13 according to the Explanatory Factor Analysis (EFA) results of the scale was 83.54%. The Cronbach's alpha value of the scale was 0.89, and the Cronbach's alpha values of the 5 subscales were calculated in the range of 0.75\u20130.94. The criterion validity analysis showed an acceptable correlation between EDE-Q-13 and EAT-26, SWLS, and BAS. The confirmatory factor analysis (CFA) revealed that the model had fit values that were acceptable or good.Both EFA and CFA results showed that it is appropriate to use the Turkish EDE-Q-13. EDE-Q-13 was significantly correlated with eating disturbances, body appreciation, and life satisfaction. In conclusion, the Turkish version of EDE-Q-13 possesses high levels of validity and reliability. The rate of eating disorders has been increasing in recent years. Although there are many scales in the evaluation of eating disorders, one of the most frequently used scales is the Eating Disorder Examination Questionnaire (EDE-Q). In recent years, its use has increased due to the fact that the use of short forms is more practical. The aim of this study was to validate the short Turkish form of EDE-Q. The study included 924 adults. Our results showed that it is appropriate to use the Turkish EDE-Q-13. EDE-Q-13 was significantly correlated with eating disturbances, body appreciation, and life satisfaction. In conclusion, the Turkish version of EDE-Q-13 possesses high levels of validity and reliability. Eating disorders are a group of chronic psychiatric diseases characterized by severe disturbances in eating behaviors originating from the interactions of genetic, biological, psychological, and socio-cultural factors . AlthougVarious scales are used in the evaluation of the variety and severity of eating disorder symptoms, and the most widely used instrument among these scales is the Eating Disorder Examination Questionnaire (EDE-Q), which is a 28-item self-report instrument developed by Fairburn and Beglin . EDE-Q hShorter versions of EDE-Q have been developed because the 4-factor structure of the original questionnaire was not confirmed. It was also not economical in terms of time due to the large number of items , 21. TheConsidering that there is an alarming increase in eating disorders in Turkey, especially in young people , it is iAll participants were Turkish-speaking and Turkish national adults living in Turkey. Non-Turkish individuals, non-adult individuals, and those who did not agree to participate were not included in the study. Simple random sampling was used to select participants. Before the study, a power analysis was performed using the G*Power software to determine the number of individuals to be included in the sample. Based on alpha (\u03b1)\u2009=\u20090.05, power (1\u2009\u2212\u2009\u03b2)\u2009=\u20090.80, and the considered effect size, the minimum required sample size was calculated as 560 participants, and it was decided that at least 616 individuals should be recruited with the possibility of 10% data loss. A questionnaire was used as the data collection tool. The questionnaire was disseminated via e-mail or WhatsApp to the individuals who agreed to participate in the study. The participants were able to fill out the online questionnaire after they agreed to participate in the study.2 , and 52.5% had a normal body weight according to the BMI classification. The test\u2013retest reliability coefficient of the scale was found to be 0.93.The study included 924 participants  between the ages of 18 and 64. Their mean age was 30.3\u2009\u00b1\u200910.93\u00a0years, 42.0% of the participants were students, and 20.3% worked in the private sector. The mean BMI of the participants was 24.3\u2009\u00b1\u20094.51\u00a0kg/mEDE-Q was developed by Fairburn and Beglin  to evaluEDE-Q-13 consists of 13 items and 5 subscales, namely Eating Restraint (ER), Shape and Weight Over-Evaluation (SWO), Body Dissatisfaction (BD), Bingeing, and Purging . Its valThe Eating Attitudes Test\u2014Short Form (EAT-26) was developed by Garner et al. . Erg\u00fcneyIn 1985, Diener et al.  developeThe Body Appreciation Scale (BAS) was developed by Avalos et al.  to measuThe validity and reliability study of the scale in Turkish was performed by Bakal\u0131m et al. . The Tur2. According to the World Health Organization (WHO) [2 (underweight), 18.50\u201324.99\u00a0kg/m2 , 25.00\u201329.99\u00a0kg/m2 (pre-obese), and\u2009\u2265\u200930.00\u00a0kg/m2 (obese).The height and body weight values of the participants were recorded based on self-report. Body Mass Index (BMI) values were calculated with the following equation: 'BMI\u2009=\u2009Body weight (kg)/(height (m))on (WHO) , BMI is The demographic characteristics of the participants, their age, height, and body weight were recorded based on self-report. Several scales with established validity and reliability in Turkish were used to determine the criterion validity of the scale, including the Eating Attitudes Test-Short Form (EAT-26) , 28, theFor the validity and reliability study of the Turkish EDE-Q-13, permission was obtained from Lev-Ari  via e-map-value smaller than 0.05 was considered statistically significant.The data obtained in this study were analyzed using the SPSS  for Windows 25.0 program. Descriptive statistical methods were used for data analysis. To determine the normality of the distribution of the data, Skewness and Kurtosis Tests and Z-values were used. The Cronbach\u2019s alpha value was calculated using the SPSS program to determine internal consistency indicating reliability. A value of Cronbach's alpha should be at least 0.60 to be acceptable, and a good value is considered to be 0.70 or above . A p-val2/df\u2009\u2264\u20093.0, RMSEA\u2009\u2264\u20090.05, 0.90\u2009\u2264\u2009GFI, 0.95\u2009\u2264\u2009AGFI, 0.95\u2009\u2264\u2009CFI, 0.95\u2009\u2264\u2009NFI and 0.95\u2009\u2264\u2009TLI indicate good fit, and 3\u2009\u2264\u2009\u03c72/df\u2009\u2264\u20095, 0.05\u2009\u2264\u2009RMSEA\u2009\u2264\u20090.08, 0.80\u2009\u2264\u2009GFI\u2009\u2264\u20090.90, 0.85\u2009\u2264\u2009AGFI\u2009\u2264\u20090.95, 0.85\u2009\u2264\u2009CFI\u2009\u2264\u20090.95, 0.80\u2009\u2264\u2009NFI\u2009\u2264\u20090.95, and 0.80\u2009\u2264\u2009TLI\u2009\u2264\u20090.95 indicate acceptable fit according to conventions for Model Confirmatory Factor Analysis Fit Indices [Explanatory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) were performed to assess the reliability and construct validity of the adapted scale. The CFA in this study was performed using the AMOS-24 software. The following parameters were examined within the scope of CFA: Kaiser\u2013Meyer\u2013Olkin (KMO) value and multiple fit indices including Root Mean Square Error of Approximation (RMSEA), Goodness-of-Fit Index (GFI), Adjusted Goodness-of-Fit Index (AGFI), Comparative Fit Index (CFI), Normed Fit Index (NFI), Tucker\u2013Lewis Index (TLI). In CFA, \u03c7 Indices .2(78)\u2009=\u20098694.05; KMO\u2009=\u20090.84 p\u2009<\u20090.01). Accordingly, it was assumed that the data had multivariate normal distribution. The total variance explained by the factors was 83.54%.The results of the EFA and Cronbach\u2019s alpha internal consistency coefficient of EDE-Q-13 are presented in Table A Cronbach\u2019s alpha coefficient above 0.70 is considered sufficient for reliability. In this study, as seen in Table 2/df\u2009=\u20094.90, and AGFI\u2009=\u20090.93.The model goodness-of-fit statistics of the scale were found as follows: GFI\u2009=\u20090.95, CFI\u2009=\u20090.97, NFI\u2009=\u20090.96, and TLI\u2009=\u20090.96. These statistics were found to show good fit based on recommended thresholds. The other indices reached acceptable fit levels as: RMSEA\u2009=\u20090.06, \u03c7The t-statistics for the items showed that all items were significant. The accepted limit for factor loading values was determined as 0.40. In the analyses, no item with a score below 0.40 was identified, and the factor loadings were within acceptable limits. The CFA results of EDE-Q-13 are shown in Fig.\u00a0Correlations between the EDE-Q-13 subscales and EAT-26, BAS, SWLS, and BMI are given in Table This study was conducted to establish the validity and reliability of the Turkish version of EDE-Q-13, which was originally developed by Lev-Ari . The relThe results of the present study support the original 13-item and 5-factor structure  of EDE-QCFA values and construct validity of short versions of EDE-Q are very important. In this study, according to recommended thresholds in the literature, the goodness-of-fit index values of the scale were determined to indicate a good or acceptable fit. In contrast, for EDE-Q-8  and EDE-This study examined the properties of EDE-Q-13 in terms of its evaluations of eating disorder pathologies as measured by EAT-26. There was a significant positive correlation between the EDE-Q-13 scores of the participants and their EAT-26  scores, and this result was in line with the results of previous studies , 40. TheThis study had some limitations. First, the assessment of all scales was based on self-report. Second, the body weights and heights of the individuals were also recorded based on their self-reports. Third, the sample was limited to some demographic characteristics. Although the aim was to include equal numbers of male and female participants, the majority of the individuals who agreed to participate in the study consisted of female individuals. Additionally, EDE-Q was validated in clinical and non-clinical samples . Due to Despite some limitations, the validity and reliability of a short form of EDE-Q were demonstrated for the first time in a Turkish sample with this study. In the present study, it was determined that the Turkish version of EDE-Q-13 possesses high levels of validity and reliability. Both EFA and CFA results showed that it is appropriate to use the Turkish version of EDE-Q-13. EDE-Q-13 takes less time because it is approximately 50% shorter than the original EDE-Q, thereby reducing the burden on both the researcher and the participants. Therefore, it may also prevent the participants from withdrawing due to the time burden. It was also thought that EDE-Q-13 has an advantage because it includes Bingeing and Purging items as a Likert-type scale, which are not available in other short versions, but they were asked in an open-ended form in the original scale .Scales that are used in the identification of eating disorders, whose prevalence has increased in recent years, are important in preventing the risk of eating disorders. In this study, it was determined that the Turkish version of EDE-Q-13 showed high levels of validity and reliability. The Turkish version of EDE-Q-13 is considered particularly useful for epidemiological studies and large-scale surveys, as it is short, user-friendly, and reliable for assessing eating disorder symptoms, investigating risk factors, and examining the psychological and physical consequences of eating disorders in the Turkish population."}
+{"text": "Ideomotor theory is an influential approach to understand goal-directed behavior. In this framework, response-effect (R-E) learning is assumed as a prerequisite for voluntary action: Once associations between motor actions and their effects in the environment have been formed, the anticipation of these effects will automatically activate the associated motor pattern. R-E learning is typically investigated with (induction) experiments that comprise an acquisition phase, where R-E associations are presumably learned, and a subsequent test phase, where the previous effects serve as stimuli for a response. While most studies used stimuli in the test phase that were identical to the effects in the acquisition phase, one study reported generalization from exemplars to their superordinate category . However, studies on so-called R-E compatibility did not report such generalization. We aimed to conceptually replicate Experiment 1 of Hommel et al.  with a free-choice test phase. While we did observe effects consistent with R-E learning when the effects in the acquisition phase were identical to the stimuli in the test phase, we did not observe evidence for generalization. We discuss this with regard to recent studies suggesting that individual response biases might rather reflect rapidly inferred propositional knowledge instead of learned R-E associations. Human actions aim to attain goals and to change the environment in desired ways. The resultant changes and consequences are often referred to as action effects. Goal-driven behavior thus requires an actor to know what (motor) behavior leads to which consequence(s) in the environment. The present study investigates one particular question on learning associations between actions and their effects, namely whether the effects\u2019 representations generalize to a higher hierarchy level.Ideomotor theory is a general framework of action control  has been addressed with an experimental approach that has sometimes been termed induction experiments  was presented. Randomly intermixing these trials aimed to prevent participants from pre-planning their response prior to the onset of each stimulus . Similar to Experiment 1 of Hommel et al. , the cathttps://aspredicted.org/g8gu4.pdf. Data are\u00a0available publicly at\u00a0https://osf.io/z3qc4/.This study was preregistered on AsPredicted.org before data collection. The pre-registration is available at N\u2009=\u2009100 participants  to be included in the analysis. In total, 99 students from the University of Bremen participated for course credit and 6 other people from the Bremen area participated without any reimbursement. Five participants were excluded from further analyses due to the exclusion criteria (see below). All participants were either native German speakers or had advanced written and spoken knowledge of German and had normal or corrected-to-normal vision. Eighty-eight participants were right-handed, 12 left-handed, and 0 ambidextrous. All participants were na\u00efve to the hypotheses of this experiment.The preregistered sequential sampling plan resulted in 10\u2009<\u20091/10 was calculated for the one-sample Bayesian t test of the category group. This result would mean that participants have reacted randomly during the test phase instead of showing a response bias, in turn suggesting that no learning of associations at all took place during the acquisition phase of the experiment even in the category group.A BF10\u2009\u2265\u20096 was calculated for the one-sample Bayesian t test of the category group (suggesting that learning took place for this group) and at the same time a BF10 of\u2009\u2265\u20096 or\u2009<\u20091/6 was calculated for the two-sample t test comparing the category and the exemplar group. The first result would mean that no, or at least no full, generalization occurred. The second result would mean that full generalization occurred, as the response biases would be of the same size in both groups. In the first case, a one-sample Bayesian t test would also be calculated for the exemplar group to assess whether some signs of generalization can be observed, as would be indicated by a response bias in this group (and a corresponding BF10\u2009\u2265\u20091).A BFn\u2009=\u200950 participants per group has been reached.A maximum number of The following, pre-registered exclusion criteria were applied: Participants who did not press the left and the right key at least 80 times each (out of a maximum of 100) during the acquisition phase were excluded from further analyses  counterbalanced across participants. All participants took part in the experiment in a single session of approximately 35\u00a0min.BFs were monitored after data from an initial sample of 20 participants per group have been collected. Then, they were monitored after four additional participants . More precisely, the participants were each assigned to one of four conditions resulting from the combination of the group (category group vs. exemplar group) and R-E mapping during the acquisition phase within each group  and omissions (RT\u2009>\u20091000\u00a0ms) were excluded. Thus, each participant contributed 200 valid acquisition trials and 200 valid test trials. As described in our pre-registration, we used Bayesian sequential sampling  were recorded in 2.59, 4.70, and in 0.88% of all trials, respectively, and these trials were excluded from analyses. Both response keys were used about equally often . Biases during the acquisition phase were calculated by dividing the number of left responses by the number of right responses for each participant, and they ranged from 0.71 to 1.33.t tests indicate that those values are not reliably different, BF10\u2009=\u20090.54, t(98)\u2009=\u2009\u2212\u00a01.46, p\u2009=\u20090.148, d\u2009=\u2009\u2212\u00a00.29.Mean RTs were 380\u00a0ms for the category group and 403\u00a0ms for the exemplar group. Bayesian as well as frequentist two-sample 10\u2009=\u20090.85, t(98)\u2009=\u20091.78, p\u2009=\u20090.078, d\u2009=\u20090.36. The percentage of congruent choices was then calculated for each participant and used as the dependent variable in the following analyses. Figure\u00a0Anticipations, omissions, and false alarms in no-go trials were recorded in 0.01, 0.47, and 2.35% of all trials, and these trials were excluded from analyses. Mean RTs in go trials were 433\u00a0ms in the category group and 413\u00a0ms in the exemplar group, and were not reliably different, BF10\u2009=\u200948.01, t(49)\u2009=\u20093.69, p\u2009=\u20090.001, d\u2009=\u20090.52.For the category group, inspection of Fig.\u00a010\u2009=\u20091.95, with the frequentist t test indicating a significant difference, t(98)\u2009=\u20092.25, p\u2009=\u20090.027, d\u2009=\u20090.45. Indeed, the percentage of congruent choices in the exemplar group is around chance-level, and the statistical tests favor the null hypothesis of chance-level performance, BF10\u2009=\u20090.32, t(49)\u2009=\u20091.26, p\u2009=\u20090.212, d\u2009=\u20090.18. These results suggest the absence of a response bias in the exemplar group.For the exemplar group, however, an inspection of Fig.\u00a0Taken together, evidence for (a full) generalization in the exemplar group seems weak at best. If at all, the evidence seems to favor the null hypothesis of chance-level performance in the exemplar group.The present study set out to re-assess generalization (from exemplars to categories) in R-E learning. Evidence for generalization was reported by Hommel et al.  in a sert tests do not contradict the BFs, but rather are well in line with this conclusion.A limitation of the present results is the strength of evidence as indicated by the respective BFs. According to the suggestions of Jeffreys ,2 we havWhat could be the reasons for the diverging results in the literature? Of course, either our results or those reported by Hommel et al.  could reIn sum, we aimed at demonstrating evidence for generalization in the exemplar group, but rather failed to do so. In light of this, in the following, we will discuss our results against the background of a recent study. Specifically, Sun et al. , Exp. 1 That response strategies indeed play a role in free-choice tasks was also investigated by Vogel et al.  who focucrit\u2009=\u20090.55. Higher values point towards a bimodal distribution, whereas lower values point towards a unimodal distribution. Using the procedures of Kieslich et al. (Against this background, we also explored the distribution of the percentages of congruent choices separately for our category and exemplar groups see Fig.\u00a0. Indeed,h et al. , the BCsThus, in our category group, the observed response bias seems to be driven by few participants (as in Exp. 1 of Sun et al. This interpretation would also point to a lack of generalization in the exemplar group, although it is fair to ask, what exactly is learned and expressed by participants in experiments like ours, that is, when using a free-choice test phase? According to Sun et al. , the resIn sum, the results from our experiment as well as results from R-E compatibility experiments (F\u00f6ldes et al."}
+{"text": "Nature 10.1038/s41586-022-4696-z,published online 11 May 2022.Correction to: In the version of this article initially published, the surname of author Chaitanya Bandlamudi was misspelt\u00a0as\u00a0Bandlamundi. The error has been corrected in the HTML and PDF versions of the article"}
+{"text": "By using trapezoidal QWs, the quantum-confined Stark effect (QCSE) can be reduced, leading to an enhanced electron-hole wave function overlap, thereby increasing the recombination rate and reducing the differential carrier lifetime. In addition, the improved hole transport also creates favorable conditions for shortening the differential carrier lifetime. Furthermore, by comparing with traditional \u03bc-LEDs with different thicknesses of QW, the modulation bandwidth of \u03bc-LEDs with trapezoidal QWs exhibits a large advantage at lower current densities of below 2 kA/cm Light-emitting diode (LED) has undergone great developments since its birth, penetrating every corner of our lives. Recently, great opportunities for LEDs are beginning to emerge in visible light communications (VLC) ,2. HowevThe modulation bandwidth of LEDs is inversely related to the Resistance\u2013Capacitance (RC) time constant and the carrier lifetime ,6, and gThrough the great efforts of researchers, the modulation bandwidth of \u03bc-LEDs measured in the laboratory has been significantly improved ,27,28,29Simulation provides a device design method without relying on the epitaxial process, saving development costs. In this article, APSYS  has been used to study the modulation bandwidth of GaN-based blue \u03bc-LEDs with different QW structures for VLC applications . In addiR) is defined as the number of carriers recombined per unit time and unit volume. Based on the ABC efficiency model [R is mainly composed of Shockley\u2013Read\u2013Hall (SRH) recombination, radiative recombination, and Auger recombination, which are proportional to the first, second, and third power of the carrier concentration, respectively [G) is defined as the number of carriers generated per unit time and unit volume. Under equilibrium conditions, the carrier generation rate in the active region of a \u03bc-LED is approximately equal to the recombination rate in it, expressed by the following formula [A, B, and C represent SRH recombination coefficient, radiative recombination coefficient, and Auger recombination coefficient, respectively, n represents electron concentration, and p represents hole concentration.The carrier recombination rate G=R=AG) and the increment of the carrier concentration is (\u0394n) as follows:Under high current density, the excess carriers dominate, while the excess electron concentration balances with the excess hole concentration ,39,40,41\u03c4) can be obtained from the derivative of the carrier generation rate with respect to the carrier concentration, expressed by the following formula [The differential carrier lifetime 1\u03c4\u22123dBf) is defined as the corresponding frequency when the normalized power drops to half of the maximum value. Generally, the differential carrier lifetime has a relationship with the 3 dB modulation bandwidth of the LED as follows [In the frequency response of \u03bc-LEDs, the \u22123 dB modulation bandwidth f\u2212\u22121, and 200 ns [\u221231 cm\u22126/s [In the physical model of simulation, band offset, internal loss, and the SRH recombination lifetimes are set to 70:30, 2000 md 200 ns ,43,44, r1 cm\u22126/s ,45,46. O1 cm\u22126/s .18 cm\u22123 and a three-period GaN/InGaN multiple quantum well (MQW) layer. The thickness of QBs is 10 nm, where the n-type doping concentration is 3 \u00d7 1017 cm\u22123. The indium content in QWs is set to 20% to ensure an emission at a wavelength of around 450 nm. On the top of the active area, there is a 20 nm thick Al0.23Ga0.77N as an electron blocking layer (EBL) with a p-type doping concentration of 1.2 \u00d7 1018 cm\u22123 and a 50 nm thick GaN as a cladding layer with a p-type doping concentration of 1.2 \u00d7 1018 cm\u22123. The ohmic contact on the cladding layer is defined as the p-electrode of the \u03bc-LED and that on the n-type GaN layer is defined as the n-electrode of the \u03bc-LED.The structures of the \u03bc-LEDs in this work are shown in To study the effect of QWs on the modulation bandwidth, \u03bc-LEDs with two different QW structures have been designed, represented by \u03bc-LED A and \u03bc-LED B in 2. It can be seen that the electron concentration reaches a maximum near the p-side in \u03bc-LED A, but that reaches a maximum near the n-side in \u03bc-LED B. Besides, the hole concentration reaches a maximum at the middle in \u03bc-LED A, but that reaches a maximum near the n-side in \u03bc-LED B. In To understand the internal differences between the two devices, 2. The \u03a6 is used to represent the energy gap between QB and QW, calculated by the difference between the peak energy of the next QB and the energy valley of the QW, reflecting the transport capacity of carriers. The larger the \u03a6, the higher the barrier of the QB, the harder the carriers escape, and the weaker the carrier transport. In In order to study the variation rules of carrier concentration, 2. In Equation (3), the concentrations of electrons and holes used to calculate 1/\u03c4 are taken from the data at the corresponding locations in Based on Equations (3) and (4), it can be concluded that the \u22123 dB modulation bandwidth is positive relative to 1/\u03c4, which is positive relative to carrier concentration. 2, we calculated the carrier distribution and carrier wave function of \u03bc-LED C  of \u03bc-LED A, \u03bc-LED B, and \u03bc-LED C, as shown in The modulation bandwidths of \u03bc-LEDs with different QW structures were compared, and the physical mechanisms involved were discussed in detail. Compared with \u03bc-LEDs with 3 nm and 2.5 nm thick QWs, \u03bc-LEDs with trapezoidal QWs are superior in both carrier distribution and electron-hole wave function overlap, exhibiting a higher modulation bandwidth. It is desired that the modulation bandwidth will continue to increase as the QW thickness continues to decrease, but the trapezoidal QW structure we designed is still excellent at lower current densities, where the \u03bc-LED can operate more efficiently. Although it is natural to use thinner QWs, our research provides an alternative design for developing high-efficiency and high-speed \u03bc-LEDs for VLC application."}
+{"text": "This difference in island sensitivity between argument and adjunct wh\u2019s-in-situ is known as argument\u2013adjunct asymmetry in the theoretical literature. Recently, this long-established asymmetry is challenged by a formal judgment study. It was claimed in the study that this asymmetry is an illusion and both argument and adjunct wh\u2019s-in-situ are subject to island constraints. The present study demonstrates that such a claim is not convincing because it is based on problematic experimental design. We designed two experiments to test the island effects on Chinese wh\u2019s-in-situ. The results reaffirm that the argument\u2013adjunct asymmetry in Chinese wh\u2019s-in-situ is indeed present, contrary to the findings of previous formal judgment study, and they also corroborate our assumption that when object wh\u2019s-in-situ like sh\u00e9nme \u2018what\u2019 are located inside a relative clause, they are subject to a pragmatic constraint, suggesting that the VP (formed by a verb and its wh-object) in the relative clause tends to describe the prominent/salient feature of the relativized nominal head.Unlike adjunct  The same is true of (1b).In English and many other languages of Indo-European origin, a wh-phrase generally moves overtly to a clause-initial position in wh-interrogative sentences. As is well known, such a movement cannot cross islands, namely, the structures out of which a constituent cannot be extracted. One of the famous islands is the complex NP island, where the complex NP refers to the NP modified by a clause . The comwh\u2019s-in-situ, argument wh\u2019s-in-situ do not seem to be subject to island constraints, as (2) shows.However, in Mandarin Chinese (hereafter \u2018Chinese\u2019) and other East Asian languages, wh-elements stay in situ. Furthermore, different from adjunct wh\u2019s-in-situ is known as argument\u2013adjunct asymmetry in the literature.1 This phenomenon has drawn the interest of many scholars, and many influential hypotheses have been advanced to account for it  in the relative clause tends to describe the prominent/salient feature of the relativized nominal head. Improving on the design in experimental materials, we conducted two experiments on Chinese wh\u2019s-in-situ. The results of the experiments show that unlike adjunct wh\u2019s-in-situ, argument wh\u2019s-in-situ are not sensitive to island constraints, which is in line with the long-established findings on the issue at stake.Inspired by the studies of wh-in-situ, namely Let us first expound the logic of the factorial design for isolating island effects, on which the previous formal judgment study into 2 In other words, if the island effect is present, the total effect will be greater than the sum of the dependency length effect and the structure effect , and the island effect is reflected by the super-additive effect. The island/super-additive effect can be identified statistically. If the island effect is present, there will be a significant interaction effect between the two factors: Dependency Length and Structure.The island effect can be isolated with the logic of subtraction. First, the total effect is quantified by calculating the difference between (3a) and (3d) , and then the effect of dependency length can be captured by calculating the difference between (3a) and (3b) , and the effect of structure can be isolated by calculating the difference between (3a) and (3c) . The island effect can now be obtained by subtracting the effect of dependency length and that of structure from the total effect. Put differently, the island effect can be quantified with the following formula: island effect = [3a \u2212 3d] \u2212 [3a \u2212 3b] \u2212 [3a \u2212 3c]. If there is no island effect, the score for the island effect will be zero . By contrast, if there is an island effect, the score for the island effect will be larger than zero.The formula for the island effect also has an equivalence like \u2018island effect = [3d \u2212 3c] \u2212 [3b \u2212 3a].\u2019 The formula can be interpreted as follows. [3b \u2212 3a] can capture the effect of dependency length. If there is an island/super-additive effect, the difference between (3c) and (3d) should be greater than the difference between (3a) and (3b) though (3c) and (3d) appear to be different only by dependency length .Dependency Length (short vs. long), Structure (non-island vs. island) and Wh-Category (argument vs. adjunct). This gave the following eight conditions: (i) short + non-island + argument, (ii) long + non-island + argument, (iii) short + island + argument, (iv) long + island + argument, (v) short + non-island + adjunct, (vi) long + non-island + adjunct, (vii) short + island + adjunct, (viii) long + island + adjunct.Inspired by the experimental paradigm in studying island effects, Consider the following sentences cited from their experiment, representing one set of their stimuli.xi\u01cengzh\u012bd\u00e0o \u2018wonder\u2019 takes an interrogative clause as its complement. For the sake of exposition, we will name the complement of xi\u01cengzh\u012bd\u00e0o \u2018wonder\u2019 as CP1. In the short condition, SpecCP1/C1 and the wh-phrase form mono-clausal dependency. If the wh-phrase is to move covertly to SpecCP1, such a movement in (4), (6), (8), and (10) will be a short-distance one. By contrast, in the long condition, SpecCP1/C1 and the wh-phrase form bi-clausal dependency. If the wh-phrase is to move covertly to SpecCP1, such a movement in (5), (7), (9), and (11) will be a long-distance one. The factor Structure controls for whether the complement of xi\u01cengzh\u012bd\u00e0o \u2018wonder\u2019 contains an island (the island condition) or not (the non-island condition). The factor Wh-Category controls for whether the wh-phrase at hand serves the role of an argument or an adjunct.In these sentences, the verb wh\u2019s-in-situ, there was a significant super-additive interaction effect of Dependency Length \u00d7 Structure. This is an intriguing result because if proved to be true, their findings pose a challenge to the long-standing generalization on argument\u2013adjunct asymmetry in wh\u2019s-in-situ. That is, argument wh\u2019s in Chinese are not subject to island constraints, whereas adjunct wh\u2019s are . With the Complex NP Island as a test case, they argued that both argument and adjunct wh\u2019s are subject to island constraints. This conclusion was too hastily drawn because the subject sh\u00e9i \u2018who\u2019 was placed outside an island in their design ,3 and there is no compelling evidence that object wh\u2019s-in-situ are a typical case for testing island sensitivity. Without a detailed study of island effects on subject wh\u2019s-in-situ, it would be particularly inappropriate to jump to the conclusion that both wh-argument and wh-adjunct elements are sensitive to island constraints. Second, when the object wh-in-situ in the relative clause is sh\u00e9nme \u2018what,\u2019 the interpretation of the construction is susceptible to factors not bearing on island constraints. One of the factors is that when object wh\u2019s-in-situ are in a relative clause, the construction is subject to a pragmatic constraint, suggesting that the VP (formed by a verb and its wh-object) in the relative clause tends to characterize the prominent feature of the relativized nominal head.4 To illustrate the point, consider (7). Its alleged low acceptability might be caused by pragmatic inappropriateness rather than by a violation of an island constraint. To be exact, (7) is taken to be unacceptable because\u2014without a proper context\u2014eating a certain thing is not the prominent feature of a girl. On the other hand, if we provide an appropriate context, (7) will become acceptable. Suppose that there are three girls in a street eating different kinds of things: One girl is eating a hamburger, another girl, an omelet, and the third girl, fried chicken. If both the speaker and the hearer share this common ground, (7) will be acceptable because, in this context, eating a certain thing is the characteristic feature of the girls at issue, and it is natural to ask what the girl that Bill met ate.There were 24 target items and 72 filler sentences for the experiment. The participants were instructed to rate the naturalness of sentences on a seven-point Likert scale, with 1 being completely unnatural and 7 being completely natural. Their findings show that for both argument and adjunct wh-in-situ is that when we replace the lexical item in (7) with other appropriate ones, the resulting sentences such as (12)\u2013(14) will become acceptable too.The argument to the effect of displaying the role of a pragmatic factor in the interpretation of an island-internal object For example, in the context of (12), the girl\u2019s eating habit is important because after she and Bill got married, this would affect their relationship. Perhaps it will also affect John if he knows Bill. On this condition, it is natural to ask what the girl likes eating. The same kind of construal applies to (13). The content is a prominent feature of a book because in most cases whether the book can attract a person or not is dependent on its content. Consequently, it is valid to ask what the book that Bill bought is about. Likewise, teaching is the prominent feature of a teacher as the primary duty of a teacher is to teach. Given this, it is natural to ask what he taught, as in (14). However, wh\u2019s-in-situ, and the other is that when studying the island effects of object wh\u2019s-in-situ, they fail to put the pragmatic confounding factor under control. These drawbacks undermine their conclusions that argument wh\u2019s-in-situ in Chinese are subject to an island constraint, and that there is no argument\u2013adjunct asymmetry in wh\u2019s-in-situ. In the next section, we will introduce our two experiments, in which the weaknesses of wh\u2019s-in-situ was tested, and in the other one, the island sensitivity of object wh\u2019s-in-situ was tested with the pragmatic confounding factor under control.To sum up, although Ninety-six participants were recruited from a university in China, and each of them was paid 15 Yuan for taking part in the experiment.wh\u2019s-in-situ. Just as in Dependency Length (short vs. long), Structure (non-island vs. island), and Wh-Category (argument vs. adjunct). Hence, this yielded eight conditions. The following examples are one set of the eight conditions constructed.Correcting the potential problems with In total, there were 24 target items in this experiment, and each item consisted of the eight conditions listed above. We thus had 192 target sentences. Using Latin Square, we assigned all of these sentences to eight lists. Consequently, each list had 24 test/target sentences and 72 filler sentences. With four practice sentences, each list had 100 sentences in total. Each list was pseudo-randomized, so that the sentences of the same experimental condition would not be adjacent. After that, each list was counterbalanced into four orders in order to remove the confounding factor of order.sh\u00e9i \u2018who\u2019 for the argument wh\u2019s-in-situ. In the condition of short dependency, sh\u00e9i \u2018who\u2019 served as the subject of the first embedded clause, and in the condition of long dependency, sh\u00e9i \u2018who\u2019 served either as the subject of the second embedded clause or as that of the relative clause/CNP. In other words, the grammatical roles of argument wh\u2019s-in-situ were held constant across conditions, which helped to exclude the confounding factors such as thematic role and word order. In addition, we carefully selected the words to ensure that in all the conditions, wh-phrases in long dependency were placed two words/four syllables further away from xi\u01cengzh\u012bd\u00e0o \u2018wonder\u2019 than those in short dependency, which ensured that the effect of Dependency Length could be subtracted from the results.Just like w\u00e8ish\u00e9nme \u2018why\u2019 is ambiguous, the participants were told at the very beginning of the experiment that w\u00e8ish\u00e9nme \u2018why\u2019 in all the experimental sentences was to question the reason of an action/event, which is similar to the English counterpart why rather than for what.5 This was intended to prevent an unnecessary processing load caused by ambiguity resolution. To check whether the participants correctly understood the instructions, we asked them to provide answers to the experiment items. To be exact, they were told that xi\u01cengzh\u012bd\u00e1o \u2018wonder\u2019 takes an interrogative clause as its complement. They were asked to provide an answer to the interrogative clause containing w\u00e8ish\u00e9nme. Their answers were supposed to be based on their interpretation of the wh-phrase in making the acceptability judgment\u2014that is, whether under such an interpretation the relevant interrogative clause is unacceptable or not. If the participant\u2019s answer to the question containing w\u00e8ish\u00e9nme is y\u012bnw\u00e8i\u2026 \u2018because\u2026\u2019 or y\u00f3uy\u00fa\u2026 \u2018since\u2026,\u2019 etc, it would indicate that he/she understood the instructions correctly. By contrast, if his/her answer to w\u00e8ish\u00e9nme is w\u00e8ile \u2026 \u2018for the purpose of \u2026,\u2019 all his/her scores would be excluded from the data because he/she would have failed to understand our instructions.Since w\u00e8ish\u00e9nme can only be used in front of the future modal hu\u00ec. If preceded by the future modal hu\u00ec as in (23a), it cannot be interpreted as \u2018why.\u2019 However, if in this context it is interpreted as \u2018for what,\u2019 as w\u00e8ile sh\u00e9nme is in (23b), then the sentence will be acceptable. Based on w\u00e8ish\u00e9nme is y\u012bnw\u00e8i\u2026 \u2018because\u2026\u2019 or y\u00f3uy\u00fa\u2026 \u2018since\u2026.\u2019 The reason is that giving such a high score might indicate that the participant unconsciously interpreted w\u00e8ish\u00e9nme as \u2018for what,\u2019 defiant of our instruction.As noted by wh\u2019s-in-situ in terms of island effects. Put differently, there should be a super-additive interaction, or a super-additive effect between Structure and Dependency Length factors for both argument and adjunct wh\u2019s-in-situ. If this is true, we should also expect no three-way interaction of Structure \u00d7 Wh-Category \u00d7 Length. On the contrary, provided that argument and adjunct wh\u2019s-in-situ are different in terms of island effects, we should expect to find a significant three-way interaction in Structure \u00d7 Wh-Category \u00d7 Length.If w\u00e8ish\u00e9nme was correctly interpreted by all the participants. Then, following 6 The results showed a significant main effect of Structure , of Length , and of Wh-Category . Contrary to the findings of Structure \u00d7 Length , Structure \u00d7 Wh-Category , and Length \u00d7 Wh-Category . Furthermore, we did find that there was a significant interaction in Structure \u00d7 Wh-Category \u00d7 Length . See also the We found that Structure \u00d7 Length under the levels of Wh-Category to examine the island sensitivity effect of each wh-category. The result showed that as for the wh-adjunct w\u00e8ish\u00e9nme, there was a significant super-additive interaction effect between Structure and Dependency Length . As for the wh-argument sh\u00e9i in subject position, however, no super-additive effect was observed . In other words, the wh-argument and the wh-adjunct exhibited a significant difference regarding island effects. This can be seen clearly in wh-in-situ and the right panel presents the interaction plot for adjunct wh-in-situ.On a par with The mean acceptability scores are presented in wh-in-situ is generally rated to be better than the adjunct wh-in-situ, contrary to the findings of wh\u2019s-in-situ exhibit no significant difference in acceptability. Notably, in the short + non-island condition, the adjunct wh-in-situ is better than the argument wh-in-situ. However, it is in the long + island condition that the adjunct wh-in-situ is significantly worse than the argument wh-in-situ, with their mean rating scores being 2.20 and 6.14, respectively.As can be seen from wh-in-situ\u201d that when the object wh-in-situ sh\u00e9nme \u2018what\u2019 is in a relative clause island, its interpretation is susceptible to factors not bearing on the Complex NP Constraint. Specifically, the object wh-in-situ in the relative clause is subject to a pragmatic constraint, such that the VP (formed by a verb and the following wh-object) in the relative clause is bound to characterize the prominent feature of the relativized nominal head. In this experiment, putting this pragmatic confounding factor under control, we intend to ascertain whether there is argument-adjunct asymmetry in island sensitivity of wh\u2019s-in-situ.It is pointed out in Section \u201cThe logic of factorial design for isolating the island effects and the previous formal judgment study into 7 and each of them was paid 15 Yuan for taking part in Experiment 2.Another group of 64 participants were recruited from a university in China,Dependency Length (short vs. long), Structure (non-island vs. island), and Wh-Category (argument vs. adjunct). Therefore, this yielded the eight conditions. Similar to wh-in-situ in the short condition is served by sh\u00e9i \u2018who,\u2019 and the one in the long condition is served by sh\u00e9nme \u2018what.\u2019 The following examples are one representative set of the eight conditions constructed.Just like Another set of three experimental sentences for the long + island + argument condition is shown below to demonstrate how the pragmatic confounding factor is controlled for.j\u01d0ngch\u00e1 \u2018policeman\u2019 has different kinds of features. He can engage in different kinds of actions. For example, a policeman can drink water, watch TV, read books, inspect something, etc. In the context of (32), the feature like \u2018inspect something\u2019 becomes prominent because after reading \u2018Y\u00e1nli\u00e0ng will bribe the policeman,\u2019 one expects to know something associated with this policeman\u2019s duty. Put differently, the use of the verb ji\u01cench\u00e1 \u2018inspect\u2019 can render the whole sentence coherent. By contrast, if we change this verb to ch\u012b \u2018eat\u2019 or h\u0113 \u2018drink,\u2019 the acceptability of the sentence such as (35) will decrease substantially because \u2018eat something\u2019 and \u2018drink something\u2019 are not prominent actions or features associated with j\u01d0ngch\u00e1 \u2018policeman.\u2019As can be seen in (32)\u2013(34), all the verbs in the relative clauses are related to the prominent features of the relativized nominal heads. To illustrate this point, consider (32). The relativized nominal head b\u00e0od\u00e0o \u2018report\u2019 are used to describe the prominent features of the corresponding relativized nominal heads. For more discussion about the notion of prominence adopted in this study, see Consider also (33). When one wants to recruit a salesperson, he will pay attention to the person\u2019s ability or specialty. Therefore, being good at something will be one of the prominent features of this person. The same is true of (27) and (34). The main activity associated with a hunter is to capture and kill something, and the main function of news is to report something. In other words, b\u01d4sh\u0101 \u2018capture and kill\u2019 and Other designs of this experiment are similar to those of Experiment 1. For example, just like Experiment 1, we also used four lexicalizations of the sentence type in (23a) (repeated as (36)) as part of our filler items. If a participant\u2019s mean acceptability score for sentences like (36) was more than 5, all his/her scores would be removed. For the sake of space and simplicity, we will not reiterate the introduction of the experiment design.wh\u2019s-in-situ in terms of island effects. In other words, there should be a super-additive interaction, or a super-additive effect between Structure and Dependency Length factors for both argument and adjunct wh\u2019s-in-situ. Along this line, we should also expect no three-way interaction of Structure \u00d7 Wh-Category \u00d7 Length. Unlike wh\u2019s-in-situ in relative clause islands, reported by wh\u2019s-in-situ. If our assessment of Structure \u00d7 Wh-Category \u00d7 Length.If w\u00e8ish\u00e9nme as \u2018for what\u2019 rather than \u2018why.\u20198 Then, the acceptability rating scores were analyzed with same method as that of Experiment 1. The results showed significant main effects of Structure , of Length , and of Wh-Category . Contrary to the findings of Structure \u00d7 Length , Structure \u00d7 Wh-Category , and Length \u00d7 Wh-Category . Furthermore, there was a significant interaction in Structure \u00d7 Wh-Category \u00d7 Length .The rating scores of two participants were removed from subsequent analysis because both rated all the sentences like (36) as 7, which indicates that they did not follow our instruction and interpreted Structure \u00d7 Length under the level of Wh-Category to examine the island sensitivity effects of each wh-category. The result showed that as for the wh-adjunct w\u00e8ish\u00e9nme \u2018why,\u2019 there was a significant super-additive interaction effect between Structure and Dependency Length . As for the wh-arguments, however, no super-additive effect was observed . Put differently, the wh-arguments and the wh-adjuncts exhibited a significant difference in island effects. This can be seen clearly in wh-in-situ and the right panel presents the interaction plot for adjunct wh-in-situ.On a par with The mean acceptability scores are presented in wh\u2019s-in-situ are generally rated to be better than the adjunct wh-in-situ. Notably, in the short + non-island condition the adjunct wh-in-situ is better than the argument wh-in-situ sh\u00e9i \u2018who.\u2019 Moreover, in the short + island condition the adjunct wh-in-situ is slightly better than the argument wh-in-situ sh\u00e9i \u2018who.\u2019 It is worth noting that in the long + island condition the adjunct wh-in-situ is significantly worse than the argument wh-in-situ sh\u00e9nme \u2018what,\u2019 with their mean rating scores being 2.10 and 6.15, respectively.As can be observed, just like those of Experiment 1, the mean acceptability scores in Structure \u00d7 Wh-Category \u00d7 Dependency Length was observed. In this regard, our study renders reinforcing support to the long-standing generalization concerning the argument\u2013adjunct asymmetry in wh\u2019s-in-situ in Chinese  rather than wh-adjuncts\u2019 sensitivity to island constraints. Our two experiments have demonstrated that the validity of their claim needs to be re-evaluated. Recall the results of Experiment 1 and Experiment 2. They reveal that the wh-arguments were not always rated to be better in acceptability than the wh-adjunct, which is different from the findings made in 10 Based on the findings in our study, we can conclude that even if wh\u2019s-in-situ in the island condition cannot be attributed to the effects of Wh-Category.Second, wh\u2019s-in-situ, without explicit reference to minimal pairs involving both adjunct wh\u2019s-in-situ and argument wh\u2019s-in-situ. It is, then, implausible to claim that the participants in these studies always implicitly construct a minimal pair, which\u2014as In addition, it is worth noting that previous studies often focus only on island effects that arise on adjunct wh\u2019s-in-situ and adjunct wh\u2019s-in-situ. As can be seen from the two interaction plots of our experiments, the dotted lines for argument wh\u2019s-in-situ in the left panels are almost flat, and the dotted ones for adjunct wh\u2019s-in-situ in the right panels slope downward visibly. The identical result is also found in wh\u2019s-in-situ are more sensitive to dependency length than argument wh\u2019s-in-situ. Therefore, it is highly likely that the mean acceptability rating score for wh-adjuncts is higher than or approximately equal to that of wh-arguments  in short dependency condition, and the rating score for wh-adjuncts is lower than that of wh-arguments in long dependency condition. Given this, it will be unsurprising that in the short + non-island condition, wh-adjuncts were judged to be more acceptable than wh-arguments.Perhaps, at this moment one may wonder why the wh-adjunct in the short + non-island condition was judged to be more acceptable than the wh-argument in our experiments and why there was a difference in this regard from If we continue to investigate why there is a difference in sensitivity to dependency length, we speculate that the reason might be that wh-adjuncts and wh-arguments establish dependency in different ways: wh-adjuncts establish dependency through LF movement and wh-arguments through unselective binding . It willwh\u2019s-in-situ are preferred over adjunct wh\u2019s-in-situ in the short + non-island condition in Lu et al.\u2019s experiment, a result different from ours, we speculate that one reason lies in the choice of an embedded subject. The embedded subject in the adjunct + short + non-island condition of their experiment is a proper noun, as in (8). It has been reported in the literature that a proper noun/definite phrase provokes a higher processing cost . The embedded subject may thus not have induced any additional processing cost. This may have resulted in the explicit short dependency effect of adjunct wh\u2019s-in-situ. Consequently, the mean rating score for adjunct wh\u2019s-in-situ is greater than that of argument wh\u2019s-in-situ.As to the question why argument ing cost , which wwh-in-situ is in a relative clause/an island, the processing of such a sentence is susceptible to an additional pragmatic constraint. This is confirmed by Experiment 2, in which the experiment items were carefully designed so that the pragmatic confounding factor could be removed. The results of this experiment have shown that once the pragmatic confounding factor is under control, the acceptability score for the object wh-in-situ in the long + island condition is very high.Third, we suspect, as pointed above, that the low acceptability score reported by wh-in-situ is in a relative clause/an island, it is subject to an additional pragmatic constraint, and the low acceptability score reported by wh-in-situ and the object wh-in-situ behave almost in the same way. For example, in the long + island condition, both the subject wh-in-situ and the object wh-in-situ are judged to be better than the adjunct wh-in-situ, and in the short + non-island condition, both the subject wh-in-situ and the object wh-in-situ are considered to be worse than the adjunct wh-in-situ. Their parallel behaviors are well expected because both subject and object wh\u2019s-in-situ serve as arguments. Unlike Experiment 2, wh-in-situ and the adjunct wh-in-situ in the long + island condition are rated to be very low in acceptability. If their findings are reasonable, then object wh\u2019s-in-situ and adjunct wh\u2019s-in-situ are distinguished in acceptability from the subject wh-in-situ in the long + island condition. Such a difference is surprising given that both subject wh-in-situ and object wh-in-situ are arguments. After fixing the experimental materials so that the pragmatic confounding effect is controlled for or eliminated, Experiment 2 has shown that the object wh-in-situ exhibits the same characteristics as the subject wh-in-situ does. This argues strongly in favor of our claim that it is the pragmatic confounding factor that prevents wh\u2019s-in-situ. Put differently, under the impact of the pragmatic confounding factor, their result shows that just like adjunct wh\u2019s-in-situ, there is also a significant Structure \u00d7 Dependency Length interaction for argument wh\u2019s-in-situ. Consequently, they fail to find a significant three-way interaction of Structure \u00d7 Wh-Category \u00d7 Length. Actually, the significant Structure \u00d7 Dependency Length interaction for argument wh\u2019s-in-situ in Moreover, a comparison of the results of Experiment 1 and Experiment 2 also suggests that we should be on the right track in assuming that when the object wh\u2019s-in-situ in this language are not sensitive to island constraints, they usually use subject wh\u2019s-in-situ as in (37) rather than object wh\u2019s-in-situ as a test case.11Our claim can also explain the practice that theoretical linguists in Chinese generally rely on: when intending to show that argument wh\u2019s-in-situ, when object wh\u2019s-in-situ occur in a relative clause, namely an island, they are more likely subject to an additional pragmatic constraint. Therefore, it is much easier to create sentences with appropriate subject wh\u2019s-in-situ than sentences with object wh\u2019s-in-situ to examine the island sensitivity of argument wh\u2019s-in-situ.According to the findings of our experiments, the reason lies in that unlike subject wh\u2019s-in-situ in Chinese are insensitive to island constraints, unlike adjunct wh\u2019s-in-situ. This has led to the celebrated generalization regarding the argument and adjunct asymmetry in wh\u2019s-in-situ in this language. With the acceptability judgment experiment, wh-in-situ and the argument wh\u2019s-in-situ are subject to island constraints. In this study, we point out that their results are not convincing because their experimental design has some drawbacks. We redesigned the experimental materials in question to examine island effects on wh-elements in situ in Chinese. The results of the two experiments in this study show that the argument versus adjunct asymmetry in wh\u2019s-in-situ is present. Furthermore, the argument\u2013adjunct asymmetry at issue cannot be attributed to the main effect of Wh-Category.Different from their counterparts in English, wh-elements in Chinese remain in situ in question sentences. Argument wh\u2019s-in-situ, this study also discovers that when object wh\u2019s-in-situ are located inside a relative clause, they are subject to a pragmatic constraint, suggesting that the verb phrase in the relative clause tends to describe the prominent/salient feature of the relativized nominal head. This contributes to the understanding of the processing of relative clauses and wh-in-situ sentences.On top of supporting the traditional theoretical generalization on Chinese Finally, it will be much fair to point out that although The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.QT conceived and designed the study, implemented the experiments, analyzed the data, drafted, and revised the manuscript. M-KP provided theoretical guidance when necessary and made revisions to the manuscript. XY participated in the conception of the study, statistical analysis, as well as the revision of part of the manuscript. All authors contributed to the article and approved the submitted version."}
+{"text": "Vol. 219, No. 4 | 10.1084/jem.20211498 | March 10, 2022The authors regret that in the original version of their article, the symbols and lines for the \u201cVeh; host-derived\u201d group were inadvertently swapped with those of the \u201cVeh; donor-derived\u201d group in The errors appear in print and in PDFs downloaded before June 1, 2022."}
+{"text": "Correction to: Nature Communications 10.1038/s41467-022-31202-w, published online 23 June 2022The original version of this Article contained an error in the legend for Fig. 3, in which all colour-coded findings were incorrectly attributed as \u2018Direct SDG influencers\u2019, rather than only \u2019Unique\u2019, \u2018Cross-sectoral\u2019, and \u2018Substitute\u2019. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Dear Editor,In a meta-analysis, Liao et al. . concludFirstly, in contrast with their stated inclusion criteria, the data from 2 trials  did not d) of \u22120.31 \u2009=\u2009\u22120.57 to \u22120.05) favoring n-3 PUFAs over placebo in the treatment of depression. Liao et al. report an SMD of \u22120.26 (95% CI\u2009=\u2009\u22120.47 to \u22120.09). Consequently, the errors do not invalidate the study conclusion, but note that the CI has widened.We carried out a random-effect meta-analysis on the corrected dataset, which yielded a Standardized Mean Difference . In the meta-analysis, the same RCT is presented as having a large and statistically significant effect (SMD\u2009=\u2009\u22120.82). This mismatch is due to the parameter for efficacy that Liao et al. .Notably, the results from Iranian studies put a stamp on the outcomes of the meta-analysis. When excluded from the analysis, the overall result of the meta-analysis  is a nuWe argue that the quality of the underlying data reported by Liao et al. . does no"}
+{"text": "P of soft magnetic laminations like SiFe sheets tends to be expressed through an integral over the power product H \u00b7 dB/dt. Already in earlier papers, we stressed that distinctions are needed for the quantities H and B. However, they are not considered in practically consistent ways, in the so far literature. Here, we discuss these distinctions in closer ways, comparing loss determination by calculation and measurement, respectively. A physically consistent procedure is described for the determination of loss and magnetization power functions through measurement of bi-located quantities HS and BC . On the other hand, it is concluded that corresponding quantitative calculations\u2014based on co-located quantities H and B\u2014are impeded by the high amount of technological parameters of modern steel products. For example, they result from chemical additions, and\u2014in particular\u2014also from specific technologies of rolling, annealing, coating or scribing.Magnetic energy loss  However, during the last years, higher frequencies, up to an order of several kHz, gained industrial relevance. This is due to widened applications for electric drives, in particular for electro-mobility.Soft magnetic laminations like silicon iron sheets represent the standard material for cores of electric machines. Since hundred years, intensive attempts are made to reduce the magnetic energy loss of core materials, supported by standards for their experimental testing , 2. TradP that usually is given in W/kg, i.e. related to the mass of material. For example, grain-oriented (GO) steels as applied for power transformers show very low values P\u2009<\u20091\u00a0W/kg for a peak induction value BPEAK\u2009=\u20091.7\u00a0T. This is significant with respect to long-term operation. On the other hand, in the case of electric drives, loss values up to the order of 100\u00a0W/kg are accepted, however, mainly for non-oriented (NO) steel that is loaded for a rather short duration of time with f\u2009>\u200950\u00a0Hz.Magnetic loss is expressed by a quantity P has been strongly extended, from less than 1\u00a0W/kg, up to 100\u00a0W/kg. As a consequence, accurate loss determination gains industrial significance. This is valid for both, the experimental measurement and the mathematical calculation. In both cases, it is a convention to express loss quantities in a time-averaged way by a function of the following type:\u03c1 is the density of sample. T\u2009=\u20091/f is the length of the period of sinusoidal magnetization with frequency f. B stands for induction, H for magnetic field strength.Historically, the above means that the practically relevant range of loss B and H, partly also replacing B through the\u2014practically identical\u2014polarization J. Different text books on magnetisms tend to use different definitions, partly lacking the corresponding physical conditions.As a reason of confusion, the literature uses different definitions for the two quantities B by the polarization J (in T), without any closer definition or comment. The quantity H is introduced as the \u201cmagnetic field strength\u201d, as well without further specification. For the first time, in 1978, Pf\u00fctzner [In a surprising way, this is even valid for international standards. In particular, IEC standards  for EpstPf\u00fctzner  proved tH, the induction B, the electric field strength E and the current density S\u2009=\u2009\u03b3E (with \u03b3 the conductivity). A further interdependency is given by the vacuum permeability (magnetic constant) \u00b5o, according to B\u2009=\u2009\u00b5oH\u2009+\u2009J. All above quantities are defined for a location of the soft magnetic matter, as a macroscopic continuum. The level below is described by the Lorentz-Maxwell equations [As it is well known, expressions of type (1) are derived from Maxwell Equations (MEs). For magnetic problems, the latter offer a link between the vector field quantities magnetic field strength quations , as a liB\u201d, we usually address the induction that results from an average over several grains and introduce this quantity into the system of MEs. Analytically or numerically, we finally can determine the \u201clocal\u201d distribution of induction, also as a global quantity, e.g. averaged over a given region of the magnetic object.As a characteristic of a heterogeneously built-up soft magnetic steel sample, it offers itself to define five levels Table , in rathB and H correspond to each other, for a given \u201cco-location\u201d and a given point of time. For example, they express induction and field in the inner centre of a sample\u2014or at any other location, i.e. volume element dV, respectively. On the other hand, comparable experimental measurements are not possible in co-local ways, due to the lack of sufficiently small sensors. Moreover, almost not any sensor types are given for interior measurements.As a specific problem for the here discussed case, calculated field quantities like B in an individual grain of GO-steel on Level L3 use smallest search coils in holes that are drilled into the tested lamination. In a\u2014usually much smaller\u2014grain of NO-steel, a corresponding measurement cannot be performed at all. A search coil tends to yield an average over several grains, corresponding to L5. The corresponding vectors of field H can hardly be measured at all. Smallest tangential field coils or Hall plates show dimensions of many mm for effective tests. Thus, they yield results on level L5, a priori.Apart from exceptional indirect methods, as described in , measureFor the here given task of comparing calculated loss determinations with experimental one, the above conditions cause problems of restricted comparability. Analytical or numerical calculations tend to yield local results on L4 that can be handled by Maxwell equations (MEs). Of course, they can be averaged for the determination of regional results. On the other hand, experiments are restricted to regional results, a priori. This means that their results cannot be handled through MEs in straightforward ways.V can be expressed asH is the magnetic field at the given location dV, B is the corresponding local induction. On the other hand, for the first time, it was proved in [A, total averaged losses can be expressed byHS is the magnetic field as measured at the surface, averaged over some distance that covers a sufficiently large amount of grains. BC is the induction averaged over the cross section A. p(t) is the magnetization power function.In clear ways, it follows from MEs that mere hysteresis losses at a given local volume element droved in  that forB(H) locally, for mere PH,Bozorth , p. 508 B(H) locally, for mere PE,Kneller , p. 612 B(Ha) locally, for loss portions, with Ha as the applied field,Bertotti , Ch. 12 B(H), for total P,Handley , p. 339 Ha) for cross section and surface, respectively, for measurement of total P,Fiorillo  p. 367\u00a0JB(H), for total P,Coey  (p. 442)B(H), for total P,Hilzinger  (p. 121)B(Ha) for cross section and surface, respectively, for measurement of total P.Moses  (p. 167)As already mentioned above, even standards , 2 do noNot any of the above references offers a distinction between Eqs.\u00a0(2) and (3). This causes errors of interpretation in scientific studies, but even more in industrial discussions.f, this loop is very weakly affected by varying f. A well-known mechanism is the nucleation of main Bloch walls with rising f, as being typical for highly GO steel [As a resulting problem, also the term \u201chysteresis loop\u201d is used in ambivalent ways. Per definition, it is applied for the quasi-static case where the loop area expresses mere hysteresis loss. But the literature uses also the term \u201cdynamic hysteresis loop\u201d. In fact, due to a very weak change of hysteresis with varying frequency GO steel , 15. Howf. For electric steel, the main reason for this widening is that a dynamic loop is not determined by a measurement at a single defined locality, i.e. in a co-local way, according to level L4. In all usual practice, it is measured in a bi-local way (on level L5), HS at the surface of sample and BC as an average over its cross section.On the other hand, in accordance with , we distHS at the surface (as location 1) as the driving source of progressing external and internal induction B through Bloch wall displacements. The initiated time-changes of B cause eddy currents that affect the inner magnetization (as location 2) in two ways: (i) reducing its intensity, and (ii) causing a lag of phase  would hardly be affected by increased frequency f. A thought experiment would result in a very similar loop BC(HC), from a co-local measurement that is taken as an average over the cross section. On the other hand, the practically usual, bi-local measurement of HS and BC reveals a widened dynamic loop, the area of which represents the sum of hysteresis loss and eddy current loss.We assume that performing a (fictive) co-local measurement of both P and instantaneous magnetization power functions p(t).For the practical design of loss testers, we addressed the needed distinctions in several publications like \u201318. HereP is measured either by the already mentioned Epstein Tester [According to international standards, loss n Tester  or by thn Tester . In the BC that is averaged over the samples cross section. Actually, it is not possible to measure the induction BS of the sample surface, approximate determinations being restricted to evaluations of surface positions of main domain Bloch walls.For loss measurements, the induction tends to be detected by a B-coil round the sample. As an alternative, it can be detected through the so-called needle method. In both cases, the result reflects the induction i. As a drawback, the result of measurement is affected by the yoke system, in particular also by the contact regions between sample ends and yoke. A more effective alternative is the arrangement of a tangential field coil (H-coil) on the sample surface . As . As i. Ace e.g. , 19). Al. Ali. AsP is performed by the well-known rise-of-temperate method. However, in cases of low P, it yields poor resolution. Thus, it tends to be replaced by the so-called electro-dynamic principle.The physically clearest measurement of loss BC and the surface field HS.Figure\u00a0BC and HS allow a determination of loss P in exact ways. However, a condition is that HS is a constant along the whole surface. Later, in 2018, we confirmed this in [d, as it is illustrated by Fig.\u00a0As already mentioned, in 1978, reference  proved iSPG,S [SPG,S represents the instantaneous power density that \u201cstreams\u201d into the material, related to a surface area element. The aim of our measurement is to determine the total loss P averaged over both the duration T of the period and the sheets cross section and also related to the materials density \u03c1. Due to both-sides power stream, the loss results asAs a basis, we apply the surfaces Poynting vector SPG,S , 17, 18.HS(t) by means of a tangential field coil (H-coil) of just 2\u00a0mm thickness. For good averaging, its length is close to 300\u00a0mm, the width is almost 500\u00a0mm. With an effective distance of little more than 1\u00a0mm from the sample surface, the first ME promises that the detected field equals the samples surface field HS in very good approximation. It follows from the coils voltage uH prop. dHS/dt, through numerical integration.As a very effective option, we measure ES(t). Easily, it can be determined from the voltage uB of a B-coil of 300\u00a0mm length around the sample. The second ME yields the simple relationuB.The second to be detected quantity is the surfaces electric field P, related to the materials density \u03c1, according to (3).Finally, the above procedure yields the total loss P. However, the above described procedure is characterized by a high degree of physical consistency, thus promising good absolute accuracy. Residual sources of systematic error result from the effective distance of H-coil from the sample surface and from the problem that the B-coil windings have some distance from the sample surfaces. Both mechanisms are considered by careful manufacturing of hardware, supported by some software correction . With these measures, the accuracy can be estimated as being close to about 2%, i.e. distinctly better than that of standardized measurements on the basis of Watt-metric measurement of total power consumption that includes also loss of the magnetization yoke system.Unfortunately, so far, no golden standard exists for the measurement of HS with cross section averaged induction BC. Further, we stressed that local measurements of surface BS or field H at an interior location are not possible in practice. Assuming that we produce very small sensors for co-local measurements of induction B and field H at any single point of sample, then the experiment would yield mere hysteresis loss PH, according to the further down Eq.\u00a0(9). Assuming that we also produce a very small sensor for the measurement of the current density S at this location, the equation would allow for the additional determination of the local eddy current loss PE. The sum would offer the local total loss P.At this point, we would like to add a thought experiment. According to the above, total losses are measurable in bi-local ways, i.e. linking surface field E, the dielectric polarization D, the current density S, the magnetic field strength H and the induction B. Let us now consider an electromagnetically excited volume element of solid matter. For it, the MEs yield in well-known ways the instantaneous, local electromagnetic power density asS being assumed to represent mere eddy currents, i.e. no galvanically impressed currents. The second term is the magnetization power density, the third one is the electric polarization power density that is neglected in the following.As it is well known, the Maxwell equations (MEs) describe vector interdependencies of the electric field strength Averaged over the sample thickness, we findd as sketched in Fig.\u00a0H and B are parallel to each other, without other components. The crucial task is to perform an effective analytical or numerical calculation of local quantities S, H and B that are needed in order to determine the instantaneous thickness-averaged (or volume-averaged) power density.Let us now consider a soft magnetic sheet of thickness P. Per definition, it is related to the density \u03c1 of material and averaged over the duration T of the period. With (3) and (8), this yieldsP:Theoretically, the latter promises a calculation of the total loss HS(t) and BC(t)\u2014a task that hardly is possible in practice.(1) Straightforward analytical or numerical calculation of the two key quantities H(t), B(t) and S(t), for all locations of the sheet, followed by averaging over the cross section. This would yield eddy current loss asS resolves the 3D structure as resulting from both the classical and the excess currents round moving Bloch walls, Eq.\u00a0(10) in vector expression would reflect the sum of classical and excess eddy current losses\u2014but this is not feasible, in practice due to technological conditions as discussed further down.(2) Analytical or numerical calculation of the quantities PE, the second term represents the mere hysteresis loss PH [In analogous ways, we find hysteresis loss as loss PH , contrarmentclasspt{minimaHa as the \u201capplied\u201d field which however may differ from the samples surface field HS in strong ways through effects of demagnetization. Further, dynamic \u201chysteresis\u201d loops are introduced as functions B(H) of strong frequency dependence. This is in contrast to the already mentioned fact that hysteresis loss PH depends on frequency in very weak ways. As already hint to in Sect.\u00a0Unfortunately, the textbooks define the field quantity in demanding ways. In particular, several authors introduce B(H) that describes for a given volume element dV the very weak dependence of mere hysteresis from frequency f,\u201cDynamic hysteresis loop\u201d\u2014as the local function BC(HS) that comprises both hysteresis and eddy currents, thus depending on f in strongest ways.\u201cDynamic magnetization loop\u201d\u2014as the global function P that represent the main demand for industrial applications\u2014irrespective of physically relevant portions.The literature reports many attempts to calculate individual portions of loss , conditions of rolling and annealing, as well as after-treatments like stress coating or laser scribing. Even best tools of calculation are not likely to consider the corresponding consequences on quantities like As a conclusion, we assume that mathematical loss predictions are not feasible, apart from rough predictions within a given class of steel, based on parameter fitting. As a benefit, loss separation favours discussions of frequency dependencies, as also stressed in , Ch. 12.P.According to (3), for the definition of instantaneous magnetization power functions, we relate to the density, according toP. Thus, we restrict the following to the experimental determination.First attempts for corresponding calculations by Petrun et al. , 23 werep(t) for grain-oriented steel, demonstrating that instantaneous values p may offer effective conclusions on the temporal \u201chistory\u201d of loss generation. For the measurement, we applied the Low Mass SST according to Fig.\u00a0uB yields dBC/dt in a direct way. The H-coil voltage uH(t) yields HS(t) after numerical integration.Recently, we reported in  our firsp(t) in [P\u2009=\u20092.43\u00a0W/kg for 50\u00a0Hz and BPEAK\u2009=\u20091.5\u00a0T. Figure\u00a0p(t) for sinusoidal induction. Close to the instant t\u2009=\u20092\u00a0ms, p exhibits a peak value pPEAK\u2009=\u20093\u00a0W/kg, that indicates that peak losses may exceed averaged ones in distinct ways. Round t\u2009=\u20095\u00a0ms and 15\u00a0ms, we see a pair of spikes that are due to turns of atomic moments, thus being of non-dissipative nature.While the just mentioned function p(t) in  concernef\u2009=\u2009100\u00a0Hz, where averaged loss results as P\u2009=\u20096.52\u00a0W/kg, corresponding to an increase of 170%. On the other hand, p(t) reveals an instantaneous peak loss, according to about pPEAK\u2009=\u200912\u00a0W/kg. Also, the intensity of non-dissipative spikes is strongly increased, the negative spike showing \u2212\u200913\u00a0W/kg, instead of \u2212\u20096\u00a0W/kg for 50\u00a0Hz.Figure\u00a0As a conclusion, instantaneous power functions can be measured in easy ways. They yield both practically and theoretically relevant information about the \u201chistory\u201d of temporal development, as arising during a period of magnetization.P uses different interpretations of terms of type o\u222b H \u00b7 dB(see Eq.\u00a0(1)). Reference [H and B as specific local values of field and induction, respectively, for the determination of mere hysteresis loss PH. On the other hand, for total loss P, bi-locally determined values HS and BC were suggested for the surface and for an average over the materials cross section, respectively. The regional difference is characterized by phase shifts through eddy currents, as a main reason for different results.As early as in 1978, the first author of the present paper pointed to the finding that the literature on magnetic power loss eference  expresseHS and BC, a priori.So far, the above distinction has not found common use. Thus, the present paper discusses practical aspects and consequences of lacking distinction. In particular, the latter is a possible explanation for too low values of calculated losses. On the other hand, measured losses are less problematic, since they tend to be based on bi-locally quantities p(t), the suggested relation to density shows the advantage that both P and p are given in W/kg, which favours interpretations. On the other hand, the distinction between dissipative and non-dissipative portions needs deeper theoretical knowledge. Unfortunately, a restricted distinction yields errors of interpretation that may be of high practical significance.For the here also addressed instantaneous power functions"}
+{"text": "This study aimed to optimize the trade-in pricing strategy. To leverage market share, many sellers adopt trade-in strategy for advance selling, Customers can return their old products at a discount price when they buy new products. This can help increase the market share and decrease natural resource consumption.We consider a seller who sells new-generation products over two periods: advance selling and regular selling. Based on the rational expectation equilibrium, we adopt dynamic programming to construct a two-period pricing model with three different trade-in strategies\u2013only in period 2, in both periods, and not at all\u2013explaining the trade-in strategy as a promotion tool used by a monopolist to discriminate for advance selling between new and old customers.The results suggest that the optimal price is determined by the proportion of old customers, discount factor and product innovation level. Whether and when to give a trade-in rebate to old customers depends on these parameters. The seller\u2019s choice of optimal trade-in strategy depends on the threshold value of the new customer demand and trade-in demand.Most existing literature focuses on advance selling strategies and trade-in strategies. To the best of our knowledge, this is a pioneering study that adopts trade-in as part of the advance selling strategy. Advance selling is a retail practice that a seller accepts customer orders before new products are launched. It has been widely adopted in various industries, such as electronics, fashion, travel and ticketing. For example, customers were encouraged to pre-order Apple smartphone XR before it was released, The advance selling period is also called the first period in this paper; after that, sales became a regular selling period where consumers could purchase in a usual manner, that is, the second period. The benefits of advance selling are threefold: period extension of product sales, more accurate demand forecasting, and improvement in cash flow because customers pay in advance .With the accelerating speed of product updates, an increasing number of customers would replace those \u201calmost new\u201d products with the latest generation products. According to a survey in China, it takes approximately 18 months for customers to switch to a new mobile phone. More than 80 million mobile phones are scrapped every year. Each mobile phone contains over 20 hazardous materials that threaten the environment  refers to the proportion of new high-type customers over all new customers; (d) the number of old customers is 1\u2212\u03bb. As explained earlier, all old customers are high-type customers; therefore, the total number of high-type customers is \u03b8\u03bb+(1\u2212\u03bb). We assume \u03bb follows the generation distribution F(\u22c5) and density f(\u22c5). The resulting distributions of the consumer segments are summarised in For the sake of simplicity, we consider the following scenario and make some necessary assumptions: (a) the market size is 1; (b) no second-hand market exists, no price competition exists between the rebates and other offers; (c) the proportion of new customers is a(0<a\u22641) be an exogenously given constant that captures the innovation level, so old customers\u2019 original valuation for the last generation product is \u03b2vH\u2264vL i.e. p1 and decides whether to introduce the trade-in strategy. Strategic high-type customers who observe p1 simultaneously decide to pre-order. In the second period, the seller sets the regular selling price p2, and all low type customers arrive to buy. We assume that the willingness-to-pay of all high-type customers remains constant in the second period. The seller produces a new generation product at a marginal cost c. The seller and customers are risk-neutral and forward-looking. The seller aims to optimize their total expected profit, and the customers maximize their expected net utility. It should be noted that capacity k(0<k\u22641) is a limited constraint.We assume that all high-type customers are strategic. There is a risk that this product will be out of stock if strategic consumers wait to buy in the second period. Let and Carr ). Customand Carr ). The seFollowing this sequence as shown in i to denote strategy \u201ci\u201d, where \u03b1 for future periods in different trade-in strategies and assume this to be common to both price and product valuation. Thus, the trade-in price for old customers is \u03b1 is the durable parameter or discount factor for customers\u2019 willingness to pay for old products. Then 1\u2212\u03b1 is a depreciation parameter. The old customers\u2019 valuation for the last-generation product is \u03b1\u03b2vH in two selling periods for the new generation product. Then, the old customers\u2019 willingness-to-pay for the new-generation product is vH\u2212\u03b1\u03b2vH as adopting a trade-in strategy. Let the trade-in rebate be rj (rj>c) in both periods, j = 1,2 denotes the selling period, that is, r1 = (1\u2212\u03b1)P1, r2 = (1\u2212\u03b1)P2. The old  customers maintain the original valuation for the new-generation product and the same level of willingness-to-pay as for the last-generation one in both periods. Therefore, whenever the old customers choose a trade-in for the new-generation product, the seller optimally maintains the same trade-in price that is no more than the old high-type customers\u2019 willingness to pay for the last-generation product  and s1>s2\u2265c. The unit salvage must be greater than the trade-in rebate (sj>rj), otherwise, trade-in products have no value to the monopolist.To examine the benefit of the trade-in strategy, we consider a benchmark strategy in this study. First, we consider the \u201cbase case\u201d in which the seller offers advance selling without a trade-in, i.e. strategy \u201cn\u201d. Second, in addition to the advance selling strategy, we examine the case when the seller offers a trade-in strategy in the second period, i.e. strategy \u201cs\u201d. Finally, the seller offers a trade-in strategy in both periods, i.e. strategy \u201cb\u201d. Throughout this paper, we reserve superscript n and Li ). HoweveThe decision variable for the seller is pricing strategy. The monopolist sets the pre-order price, regular selling price, and trade-in price.We adopt the rational expectation (RE) framework to characterize market outcomes. In the RE equilibrium, each player decides based on individual beliefs that are rationally formed and consistent with the actual outcomes. According to the backward induction, we first calculate the optimal regular price and the available probability in the second period when new low-type customers arrive in the second period.k\u2264\u03b8\u03bb, the probability of product availability in the second period k>\u03b8\u03bb in period 1, the available probability in period 2 isThe optimal regular price is The seller\u2019s expected revenue is For new high-type consumers, the utility function is All new high-type customers arrive to pre-order the new-generation product in the advance selling period. Because of limited capacity, the product availability probability is According to the RE equilibrium, all strategic high-type customers consistently believe in the reality of the available probabilities and prices in both periods. The utility function is Proposition 1. Under the no trade-in strategy for advance selling, there is a unique RE equilibrium in which all new high-type customers pre-order in the first period at the optimal price given by Eq  the optimal pre-order price has nothing to do with the innovation level. (\u2171) \u03b8.Proposition 2. The seller can set up the optimal pre-order price and trade-in price is \u03b1vL respectively, the optimal trade-in rebate is (1\u2212\u03b1)vL. The old high-type customers would like to use the trade-in rebate to buy the new-generation one in the second period when the trade-in discount factor satisfies the condition with a. The trade-in rebate strictly decreases with the innovation level a.In Proposition 2, we find that the ceiling of the trade-in discount factor is determined by the innovation parameter. When the innovation parameter is higher, the old high-type customers would rather buy the new-generation product at a higher trade-in price than hold the old one. Then, the seller can decide a higher trade-in price.With trade-in strategy just in the second period, the seller\u2019s expected total profit isIf the optimal release price is still k\u22641\u2212\u03bb+\u03b8\u03bb, the product availability probability is When the seller permits old customers to trade-in in either period, all old high-type customers would certainly choose to use the trade-in rebate to pre-order in the first period because they are strategic. When the seller\u2019s capacity is less than the demand for new and old high-type customers, that is, \u03bb+\u03b8\u03bb<k<1, that is. \u03b8 satisfies the condition 0\u2264\u03b8<k, which means the seller\u2019s capacity must be so large that the trade-in strategy is worth implementing, then the product availability probability in period 2 isWhen 1\u2212Then the expected revenue in period 2 is,For new low-type customers, the utility function in the second period isThe availability probability is The utility function is Then the trade-in price is The expected revenue is The seller\u2019s expected total profit isvH\u2212\u03b1\u22c5\u03b2vH, the old customer would trade-in. At least the seller should set up Only if the trade-in price \u03b8<k, the ceiling of the trade-in discount factor is less than When 0\u2264The purchasing utility of old customers is To induce the old customers to trade-in as early as possible rather than wait until the second period, according to \u03b8<kThen we can induce the optimal trade-in discount factor to be \u03b8<k or k\u2264\u03b8<1, the optimal trade-in discount factor is the same.Either 0\u2264Property 3. We find (\u2170) there is only one optimal pre-order price as 0\u2264\u03b8<k. And the optimal trade-in discount factor exists a. Recall \u03b8 as 0\u2264\u03b8<k.\u03b8<k, when all high-type customers including all old customers using the trade-in rebate pre-order in the first period, and all low-type customers buy in the second period, the seller\u2019s expected total profit isFor 0\u2264\u03bb<k) 0\u2264\u03b8<k.And we assume that the new consumers demand \u03bb is uniform distribution in the distance . Then, we can obtain the available probability in different strategies.It is obviously that Because of \u03b8<k, we can get property 4.According to Property 4. Comparing the Eqs (\u03b8<k. This implies that  the Eqs  with 7)Property  the Eqs , and \u03be2b\u03b8<k. This result is consistent with practice. The seller can use trade-in program in both periods to induce old and new high-type consumers to obtain a higher pre-order price.According to the Property 4, the seller can always set up highest pre-order price with the trade-in program in both periods as 0\u2264k\u2264\u03b8\u22641(ii) k\u2264\u03b8\u22641, it\u2019s useless for the seller to adopt the trade-in program in both periods for advance selling strategy. Therefore, we analyze only the two strategies ahead, i = n, b. We find that k\u2264\u03b8\u22641.When the proportion of new high-type customers is no less than the capacity number, Theorem 2. According to Eqs  and andTheorg to Eqs , the preAccording to Theorem 2, the seller can set up highest pre-order price \u03b8<k(i) 0\u2264\u03c0s\u2212\u03c0n\u22650This means that it is always beneficial for the seller only if the durable parameter or discount factor for the customers\u2019 willingness to pay for old products is no more than its threshold.The forehead five items delegate the first profit difference, the last three items delegate the second profit difference. The second profit difference is positive.To guarantee k\u2264\u03b8\u22641(ii) We then analyze the different profits in the three different strategies. According to Eqs  and 8),,8), we c\u03c0s\u2212\u03c0n\u22650, as\u03b1 increases with the new high-type customers\u2019 demands. When new high-type customers\u2019 demands are higher, the seller can control higher trade-in price, lower trade-in rebate.We find that \u03b8.Because the unit revenue from dealing with the old product is certainly more than that of the trade-in rebate, the profit difference is more than zero. This means that it is optimal for a seller to adopt trade-in program for any Property 5. For k<\u03b8\u22641, the seller can use trade-in for advance selling in both periods, but the trade-in price must be larger than k = 0.85, vH = 3.0, vL = 2.0, c = 0.1, s1 = 0.25, s2 = 0.15, \u03b2 = 0.667 (as a = 0.5), we can calculate \u03b1* = 0.5999.We set \u03b8-axis is the demand of all new high-type customers, and the price-axis is the seller\u2019s optimal prices under different trade-in strategies. \u03b8 under no trade-in strategy and trade-in strategy in period 2. \u03b8<k and remains constant and the same as the customer\u2019s high value for the new generation product for k<\u03b8\u22641.\u03b8 indicates the popularity of the new-generation products.\u03b8-axis is the demand of all new high-type customers, and the profit-axis is the seller\u2019s expected total profit under different trade-in strategies. The grey curve represents the seller\u2019s expected total profit \u03c0n with just advance selling no trade-in strategy, the orange curve represents the seller\u2019s expected total profit \u03c0s with advance selling and just trade-in strategy in second period, and the blue curve represents the seller\u2019s expected total profit \u03c0b with advance selling and trade-in strategy in both periods. \u03b8. The two trade-in strategies are much better than no trade-in strategy for any \u03b8, so either trade-in strategy is always optimal for the seller because the seller can set a higher pre-order price with a higher value demand. It is also noted that there exists a threshold value of \u03b8\u2032 which is the intersection of the two profit curves of strategy 2 and strategy 3, and the profit is the same as \u03b8 = \u03b8\u2032. The profit of strategy 3 is greater than strategy 2 as \u03b8<\u03b8\u2032, and the profit of strategy 2 is greater than that of strategy 3 as \u03b8>\u03b8\u2032. This means more new high-type customers do not always benefit the seller under strategy 3. Because more new high-type customers buy new generation products at the optimal pre-order price in the first period, the seller can earn more profit.We now examine the impact of the high-value customer proportion and new customer number on profit in different trade-in strategies. Although the trade-in strategy and advance selling strategy have been widely studied separately in extant literature. Our paper is one of few literature combined trade-in with advance selling strategy. And we adopt trade-in strategy as part of the advance selling strategy. In practice, many sellers including retailers and manufacturers have adopted the trade-in with advance selling strategies. However the trade-in rebate can hurt the seller\u2019s profit and the discarded old products can damage the living environment. So designing an appropriate trade-in strategy is crucial for sellers that frequently release the new generation products.\u03b8 and 03bb \u03bb. Moreover, how the seller chooses the optimal trade-in strategy depends on the threshold value of new customer demand and trade-in demand. We helped the seller find the threshold value \u03b8\u2032 of new high-value customers under strategy 3. More new customers can hurt the seller when the new high-type customers are less than the threshold value. So we find that the optimal price is determined by stochastic factors such as the proportion of old customers, discount factor and product innovation level, which can help the seller make an appropriate decision of whether or not, and when to provide a trade-in rebate to old customers also depends on these parameters.In this study, based on the rational expectation equilibrium, we adopt dynamic programming to construct a two-period pricing model with three different trade-in strategies between the seller and consumers. We developed an analytical model to study how the innovation level, discount factor, and trade-in customers\u2019 demand influence the choice of optimal trade-in strategy for advance selling. From the firm\u2019s perspective, we identified that the seller can always make the highest pre-order price under the third strategy, i.e. offering trade-in in both periods because of old high-value strategic consumers. Given the innovation level, the seller can obtain the optimal discount factor, and both trade-in strategies are always more profitable than the no trade-in strategy for advance selling for This study only focuses on the advance selling period and the regular selling period. The next avenue is to extend the period to a third phase when the product reaches the end-of-life cycle. We mainly take innovative products into account. In practice, many large e-commerce retailers such as Jindong, Suning, Taobao have adopted trade-in strategy with advance selling for durable products. Thus future related research can also pay attention to durable products such as washing machine, refrigerator, etc. The limitation of this study is that the trade-in rebate is constant and proportional to the pre-order or regular price. In future research, it can also be considered that the seller can adjust the trade-in rebate according to the characteristics of the old product. We just combined the trade-in strategy with advance selling between the seller and consumers. So how to choose supply chain contracts can be studied with trade-in and advance selling strategy between the supplier and retailer in the future. And how to stimulate product returns by designing return incentives and optimizing pricing strategies in this type of closed-loop supply chain would be interesting to explore."}
+{"text": "QuickXplain algorithm, which provides a divide-and-conquer computation strategy to find within a given set an irreducible subset with a particular (monotone) property. Beside its original application in the domain of constraint satisfaction problems, the algorithm has since then found widespread adoption in areas as different as model-based diagnosis, recommender systems, verification, or the Semantic Web. This popularity is due to the frequent occurrence of the problem of finding irreducible subsets on the one hand, and to QuickXplain\u2019s general applicability and favorable computational complexity on the other hand. However, although (we regularly experience) people are having a hard time understanding QuickXplain and seeing why it works correctly, a proof of correctness of the algorithm has never been published. This is what we account for in this work, by explaining QuickXplain in a novel tried and tested way and by presenting an intelligible formal proof of it. Apart from showing the correctness of the algorithm and excluding the later detection of errors (proof and trust effect), the added value of the availability of a formal proof is, e.g., (i) that the workings of the algorithm often become completely clear only after studying, verifying and comprehending the proof (didactic effect), (ii) that the shown proof methodology can be used as a guidance for proving other recursive algorithms (transfer effect), and (iii) the possibility of providing \u201cgapless\u201d correctness proofs of systems that rely on (results computed by) QuickXplain, such as numerous model-based debuggers (completeness effect).In his seminal paper of 2004, Ulrich Junker proposed the  MSMP  problem  of an unsatisfiable (satisfiable) clause set is unsatisfiable (satisfiable). In fact, there are two MUSes for S, i.e., manifestation of the MSMP problem.The task of finding within a given universe an irreducible subset with a specific monotone property is referred to as the minimal unsatisfiable subsets , prime Horridge ), prime  Marquis , and mosA for a specific manifestation of the MSMP problem can be used to solve arbitrary manifestations of the MSMP problem if (i)\u00a0the procedure used by A to decide the monotone predicate is used as a black-box , and (ii)\u00a0no assumptions or additional techniques are used in A which are specific to one particular manifestation of the MSMP problem.Numerous algorithms to solve manifestations of the MSMP problem have been suggested in literature, e.g., Marques-Silva et\u00a0al. , Rodler Not all algorithms meet these two criteria. For instance, there are algorithms that rely on additional outputs beyond the mere evaluation of the predicate \u00a0(re)used as is for suitable manifestations of MSMP \u00a0adapted in order to solve other manifestations of MSMP (Rodler (c)\u00a0modified or extended, respectively, e.g., to achieve a better performance for a particular MSMP manifestation  and (ii), n Junker  \u00a0explaining (2)\u00a0presenting a clear and intelligible proof of Proof Effect(a) It shows (b) It creates compliance with common scientific practice. That is, every proposal of an algorithm should be accompanied with a (full and public) formal proof of correctness. This demand is even more vital for a highly influential algorithm like Didactic Effect(a) It promotes (proper and full) understanding (Hanna and Jahnke (b) It provides the basis for understanding (hundreds of) other works or algorithms that use, rely on, adapt, modify or extend Completeness Effect It is necessary to establish and prove the full correctness of other algorithms that rely on (the correctness of) Trust and Sustainability Effect It excludes the possibility of the (later) detection of flaws in the algorithm, and is thus the only basis for placing full confidence in the proper-functioning of Transfer Effect It showcases a proof template for recursive algorithms and may thus provide guidance to researchers when approaching the  proof of other recursive algorithms.The rest of this paper is organized as follows. We discuss related work in Sect.\u00a0In this work, we account for this by entclass1pt{miniman Junker , i.e., wmin. As a side note in Bradley and Manna , min, although being similar to p. In this case, min would return First, d Junker , Fig.\u00a03,mentclass2pt{minimmin given in Bradley and Manna \u00a0segment our proof into small, intuitive, and easily digestible chunks, thus putting a special focus on its clarity, elucidation, and didactic value, (2)\u00a0provide visualizations of the interrelations between and of the sequence and meaning of the individual proof steps by means of diagrams \u00a0organize the proof in a way it is illustrative and amenable to a mental \u201ctracking\u201d in that it can be viewed as directly traversing the algorithm\u2019s call-recursion-tree while verifying the correctness of all transitions in the tree \u00a0explicate the proof template adopted in our proof in order to promote the reader\u2019s comprehension of the underlying general proof principle and to provide them with well-founded justifications for the individual proof steps  knowledge base  U for which we are interested in finding a minimal unsatisfiable subset (MUS) X.U be the universe (a set of elements) and p holds for p is a monotone property iff (Monotone Property) Let p is monotone iff, given that p holds for some set p also holds for any superset p does not hold for some set p does not hold for any subset So, (a)\u00a0some elements of the universe must not occur in the sought minimal subset, or (b)\u00a0the minimal subset of the universe should be found in the context of some reference set. Both cases (a) and (b) can be subsumed as searching for a minimal subset of the analyzed setbackgroundU  and U that are possibly faulty); in case (b), X of elements in In practical applications it is often a requirement that p-Problem-Instance) Let p be a monotone predicate. Then we call the tuple p-problem-instance (p-PI).(p-Set (given some Background)) Let p-PI. Then, we call X a p-set wrt.p-set X wrt. minimal iff there is no p-set  A p-set exists foriffis a\u2014and the only\u2014p-set wrt.iff(Existence of a p-PI p(X) for arbitrary p-set wrt. p-set\u2019 is output. Note, in order to not overload the discussion, we focus in this work on QX\u2019s property of computing a minimalp-set . That imentclass2pt{minimTrivial Cases: Before line\u00a07 is reached, the algorithm checks if trivial cases apply, i.e., if either no p-set exists  p-set is non-empty. (Line\u00a011): If the analyzed set mentclass2pt{minimRecursion: Subsequently, the recursion is started. The principle is to partition the analyzed set non-empty  subsets split and get functions; lines\u00a013\u201315), and to analyze these subsets recursively (divide-and-conquer). In this vein, a binary call-recursion-tree is built  returns the subset of those elements  returns the subset of those elements : The first question is: Are all elements of p-set, i.e., Right subtree : Here, we can distiguish between two possible cases, i.e., either the set (i)\u00a0empty or (ii)\u00a0non-empty.p-set (as verified in the left subtree before returning the empty set) and every p-set is non-empty . Hence, Given (i), we know that p-set, are all elements of p-set, i.e., p-set X found by For (ii), the question is: Given the subset Finally, the union of the outcomes of left .Fig. 1CNotation: Below, we show the workings of p in line\u00a09, the double-underlined elements are those that are already fixed elements of the returned minimal p-set, and the grayed out elements those that are definitely not in the returned minimal p-set. Finally, p-set (function p in line\u00a09 returns 1); p-set (function p in line\u00a09 returns 0).15HowProceeds: After verifying that there is a non-empty p-set wrt. Explanation: After splitting p-set in the left half p-set, the right subset p-set, and 8 is irrelevant. From now on, 7, as a fixed element of the p-set, takes part in all further executed predicate tests.p-set is included in p-set, i.e., the test for p-set. So, 4 is fixed. To check the relevance of 3, X, one of our minimal p-sets. In step (4), the goal is to figure out whether the left half p-set wrt. the p-PI it gets as an input, if a p-set exists, and \u2019no p-set\u2019 otherwise. While reading and thinking through the proof, the reader might consider it insightful to keep track of the meaning, implications, and interrelations of the various propositions in the proof by means of Fig.\u00a0In this section, we give a formal proofmentclass2pt{minimLetbe ap-PI. Thenterminates.17(Termination) p-PI First, observe that split and get functions.Now, assume an infinite sequence of nested recursive calls of entclass1pt{minimaFinally, there can only be a finite number of such nested recursive call sequences because no more than two recursive calls are made in any execution of The following proposition witnesses that returns \u2019nop-set\u2019 in line\u00a03 iff there is nop-set wrt.Ifreturnsin line\u00a05, is a minimalp-set wrt.If the execution ofreaches line\u00a07, holds.\u2013(3) in turn.Proof of (1): The fact follows directly from Proposition\u00a0Proof of : The facProof of (2): Because line\u00a05 is reached, p-set wrt. p-set wrt. p-set wrt. mentclass2pt{minimProof of (3): This statement follows directly from the test in line\u00a02 and the fact that line\u00a07 is reached. We now characterize an invariant which applies to every call of  when it returns in line\u00a010 or 12 p-set wrt.If the execution ofreaches line\u00a011, thenholds.Ifreturnsin line\u00a012, thenis a minimalp-set wrt.If the execution ofreaches line\u00a016, whereis called, then(Invariant Causes Sound Outputs and Propagates Downwards) We prove all statements (1)\u2013(4) in turn.Proof of (1): \u201cp-set wrt. Proof of : \u201c\\docump-set wrt. \u201cmentclass2pt{minimProof of (2): Proposition\u00a0p-set wrt. mentclass2pt{minimProof of (3): A return in line\u00a012 can only occur if the test in line\u00a011 is positive, i.e., if line\u00a011 is reached and p-set wrt. p-set wrt. p-set wrt. p-set wrt. First, mentclass2pt{minimProof of (4): Consider the call split and get functions  As per Definition\u00a0p-set wrt. We first prove It remains to be shown that Overall, we have demonstrated that At this point, we know that the invariant property of Definition\u00a0p-set wrt. its p-PI given as an argument, due to Proposition\u00a0Due to the fact that entclass1pt{minimap-set for the p-PI given as an input argument to the call of p-set wrt. their given p-PIs\u2014whether or not these calls directly return\u2014the combination of these p-sets is again a minimal p-set for the respective p-PI at the call that executed lines\u00a016 and 17.The next proposition evidences\u2014as a special case\u2014that the combination (set-union) of the two outputs Let the recursive callin line\u00a016 during the execution ofreturn a minimalp-set wrt.and let the recursive callin line\u00a017 during the execution ofreturn a minimalp-set wrt. Thenreturns a minimalp-set wrt.) The statement is a direct consequence of Lemma\u00a0Letbe a partition ofIf(a)\u00a0is a minimalp-set wrt.and(b)\u00a0is a minimalp-set wrt.thenis a minimalp-set wrt.p-set, and then we show its minimality.We first show that p-Set Property: First, by Definition\u00a0p-set wrt. p-set wrt. Minimality: To show that minimalp-set wrt. p-set wrt. X can be represented as X is a p-set wrt. p, it follows that p-set wrt. Let us first assume that X is a p-set wrt. p, and since p-set wrt. Second, assume that p-Set is Returned By Tree) Ifholds forthen it returns a minimalp-set wrt. k. Therefore, by the Induction Assumption, p-set wrt. p-set wrt. k. Consequently, p-set wrt. Induction Assumption.Because p-set wrt. their given p-PIs p-set wrt. As both recursive calls made throughout the execution of This completes the inductive proof. Letbe ap-PI. Then,terminates and returns a minimalp-set wrt.if ap-set exists forOtherwise,returns \u2019nop-set\u2019.20\u00a0holds when the loop is entered , (2)\u00a0remains true for the next loop iteration if it is true for the current iteration (L-maintenance), and (3)\u00a0yields a property at termination of the loop that is useful to prove the algorithm\u2019s correctness (L-termination).recursion invariant, i.e., a predicate that is true for every recursive call of a procedure, andrelies on a R-initialization),holds for the first call of the recursive procedure (remains true for any further (recursive) call of the procedureR-maintenance), and(R-termination).entails correctness of the procedure\u2019s output . Consequence: These combine-steps need to be addressed when proving R-termination.In case the recursion implements a divide-and-conquer approach, there can be As an illustration, the following table shows how the building blocks of our proof are assigned to the three different proof phases of R-INV:24(1)\u00a0The finding of a \u201cright\u201d invariant can be tricky and will often represent the key to success in proving a recursive algorithm by means of the R-INV template. However, once an appropriate invariant has been determined, the rest of the proof can be relatively straightforward provided that the systematic steps suggested by R-INV are followed. (2)\u00a0There can be multiple  invariants that allow to prove one and the same algorithm by means of the R-INV template. Indeed, also in the case of QX, a second possible invariant exists and is given by: The foundation for our used template is provided by the proof principle for (non-recursive) algorithms based on loop invariants detailed in Cormen et\u00a0al. . The ideQuickXplain , it fosters proper and full understanding of didactic effect), it is a necessary foundation for \u201cgapless\u201d correctness proofs of numerous algorithms, e.g., in model-based diagnosis, that rely on (results computed by) completeness effect), it makes the intuition of trust and sustainability effect), as well as it might be used as a template for devising proofs of other recursive algorithms (transfer effect). Since (i)\u00a0we exemplify the workings of (ii)\u00a0we put a special emphasis on the clarity and didactic value of the given proof (e.g., by segmenting the proof into small, intuitive, and easily-digestible chunks, by showing how our proof can be \u201cdirectly traced\u201d using the recursive call tree produced by"}
+{"text": "This grating encoder is composed of a stationary reading head and a movable grating reflector. A light beam from the reading head is projected onto the grating, and three diffracted beams  are generated, collimated, and received by three separate quadrant photodetectors (QPDs). The information of \u03b8x, \u03b8y, \u03b8z, and Z is coded into spot positions of these three diffracted beams on the QPDs. Thus, the modeling and decoupling algorithms were investigated, and an independent calculation of these four-DOF absolute positions was theoretically guaranteed. A prototype was then designed, constructed, and evaluated. Experimental results verified that the proposed grating encoder could achieve the absolute measurement of four-DOF \u03b8x, \u03b8y, \u03b8z, and Z with an accuracy of sub-arcseconds and sub-micrometers. To the best of our knowledge, the proposed encoder in this research is the first one to achieve absolute simultaneous measurements of four-DOF position and pose with a large measurement range. The success of this new grating encoder can benefit various multi-DOF positioning applications, especially for large-scale synthetic aperture optics (SAO), including stitching off-axis parabolic mirrors and pulse compression grating.An absolute-type four-degree-of-freedom (four-DOF) grating encoder that can simultaneously measure the three-axis pose ( Large-scale synthetic aperture optics (SAO) systems are highly important in several applications, such as deep space exploration , high-enCurrently, the multi-degree-of-freedom position and pose measurement schemes mainly include optical and electrical schemes. The electrical method can demonstrate a high accuracy but is limited in its applications ,7 becausX- and Y-directions. Furthermore, Shi et al. [X- and Y-direction absolute position measurement, the main research work of the six-DOF absolute measurement can focus on the out-of-plane, i.e., the 4-DOF absolute position and pose measurement of \u03b8x, \u03b8y, \u03b8z, and Z-direction. To address the same problems, some effective measurement schemes were proposed for in-plane position measurement by phase detection . Li et ai et al.  proposedi et al.  and an i\u03b8x, \u03b8y, \u03b8z,) autocollimator by using a grating reflector to replace the flat mirror in the conventional laser autocollimator [Z-direction position measurement. Then, Liu et al. modified the proposal in Ref. [Z-direction [Several related types of research have been proposed for out-of-plane measurement ,29. Gao llimator ,31. Alth in Ref.  and propirection , which wirection . These sIn order to meet the high accuracy and absolute measurement demand of the out-of-plane 4-DOFs of the sub-mirror, three improvement works based on the abovementioned multi-DOF out-of-plane research were carried out in this study. Firstly, an absolute zero-point of the QPD coordinate system was proposed to establish the absolute coordinate of the spot position, and the absolute position and pose of the grating reflector can be decoupled by the absolute coordinates of the three diffracted spots . Secondly, a homogeneous error compensation matrix involving installation posture error and installation distance error was proposed, which can significantly reduce the crosstalk error and improve the measurement accuracy. Finally, a compact prototype system was designed and built in this study. For the first time, a verification experiment of simultaneous input of multiple main motions was used to obtain the optimal homogeneous error compensation matrix, and high-precision independent decoupling of the absolute position and pose of the out-of-plane 4-DOF was realized, fully verifying the excellent performance of the proposed grating encoder.As shown in xA, yA, xB, yB, xC, yC) of the light spot are calculated according to the back-end photocurrent information, and the specific calculation formula can be expressed as formula (1). In this paper, the obtained coordinates are absolute coordinates; thus, the position coordinates on the QPD are all signed, and from the front of the QPD, right and up are positive directions.I\u03b1 are the four-way current signal outputs of the QPD, \u03b1 = A, B, or C.xA, yA) of the coordinate system of the QPD, and xA and yA are very close to 0. The point  is used as the origin of a new QPDA coordinate system in Taking QPDA as an example, due to different light intensity distributions, the coordinate value can be calculated from Formula (1). The coordinate origin of the two-dimensional coordinate system is the symmetric center of the four photodetectors. Due to the mechanical structure, it is difficult to adjust the light spot to be perfectly located at the symmetrical center of the QPD. Therefore, at the beginning of the test, the light spot is located at the position , , and  positions, respectively, which are unique coordinates for calculating the absolute position and pose. First, the initial positions of the spots are set as the zero-point positions, i.e., every spot position is at the origin of the new QPD coordinate system. When the grating moves simultaneously in four degrees of freedom, the three light spots in the QPDA, QPDB, and QPDC assume the  and (3). In addition, z and z also cause the movement of the other spots and can be solved using Formulas (4) and (5).zk, k\u03b8x, k\u03b8y, and k\u03b8z are the parameters measured in the pre-experiment. f is the focal length of the convex lens, and L is the equivalent distance between the photodetectors A and B (or C and B). \u03b8xzk1 and \u03b8xzk\u22121 are the impact factors of x on the +1st- and \u22121st-order spot positions during the movement, and so are \u03b8ydzk1 and \u03b8ydzk\u22121 of y.In these coordinates, the position of the 0th-order light change is only related to O ) and the true value T (shown in Formula (7)) due to the imperfection in grating encoder alignment. This posture error can be viewed as a system error and be predicted by using a compensation matrix. The error compensation matrix is a 4 \u00d7 4 matrix (M), which can be obtained using Formula (8) after the pre-experiment. With this error compensation matrix, the original value can be converted into the output of the grating encoder .M can be obtained in the pre-experiment with one main motion.However, in the simultaneous motions of 4-DOF absolute position and pose experiment, there is an unexpected posture error inevitably generated between the grating encoder measured value \u03b8x, \u03b8z, O composed of \u03b8x_Original, \u03b8y_Original, \u03b8z_Original, and z_Original can be collected, and M = T \u00d7 O1\u2212.Due to installation errors, the 4-DOF movement is output simultaneously. The three main motions move separately, i.e., \u03b8x and \u03b8z.The absolute 4-DOF grating encoder test bench was built, and the schematic figure of the experiment is shown in \u03b8x, \u03b8z) of the grating with a measurement accuracy of 0.1\u2032\u2032. The laser interferometer can measure the absolute displacement of the z-direction with a resolution and measurement accuracy of 0.1 nm and \u00b1160 nm, respectively. The movement element is shown in \u03b8x, \u03b8z, z, and error motion \u03b8y. The z-direction movement is controlled by the high-dynamic Z Nanopositioner (PI) (model: p-733. Z), with a resolution of 0.3 nm and a linearity of 0.03%, and the angles are controlled by a two-axis tilt table driver, with a resolution of 0.02\u201d and a linearity of 0.5%.The actual test bench is shown in \u03b8x_True, \u03b8z_True, and z_True. Owing to the limitation of the autocollimator, the true value of \u03b8y was obtained during another set of repeated experiments by changing the measurement surface. The following single motion, resolution, and multiple motion experiments were carried out in this study.The value measured by the laser interferometer and autocollimator is called the true value, as described below and shown in the following figure as \u03b8x(80\u2032\u2032), \u03b8z(80\u2032\u2032), and the z-direction (100 \u03bcm) as the main motions and obtained all the constant parameters and the error compensation matrix (M) in Formulas (2)\u2013(8). As is evident from I\u03b11, I\u03b12, I\u03b13, and I\u03b14 on QPDs A, B, and C are 0.1802, 0.2662, and 0.3135, respectively. Upon this, the resolutions of rotation around the x- and z-axes and the displacement along the z-axis are 0.02\u2032\u2032, 0.06\u2032\u2032, and 20 nm, respectively, as shown in The pre-experiment was performed in \u03b8x rotation, \u22120.81 to 0.85 arcsec in 40 arcsec \u03b8z rotation, and \u22120.55 to 0.49 \u03bcm in the 100 \u03bcm z-direction displacement. This indicates that in the continuous measurement of a single degree of freedom, the encoder has good linearity and stability without a large drift.In In multiple motion experiments, the square wave rotation motions with a frequency of 0.1 Hz and the amplitude of 40\u2032\u2032 and 80\u2032\u2032 around the x- and z-axes and a z-direction motion with 100 \u03bcm at a speed of 2 \u03bcm/s are simultaneously given by the movement element. Three main movements are input concurrently, and their comparison with the true value is shown in z-axis displacement is different from that of the grating encoder in periodic motion, a moving arm length linearly increases the displacement along the z-axis. Since the error matrix calculation includes the linear relationship based on this structure, the measured value of the laser interferometer represents the true value of the grating displacement herein.Because the measurement point of the \u03b8x = 40\u2032\u2032, \u03b8z = 40\u2032\u2032, z = 100 \u03bcm) shown in x-axis is about \u22123\u2032\u2032 to 7\u2032\u2032, while the angular measurement error around the z-axis is large, reaching the degree of about \u00b140\u2032\u2032. Additionally, the angular measurement error first decreases overall and then rises and returns, mainly because the rotation around the z-axis is affected by z-axis displacement. The error of the original value is far from the true value; therefore, the original signal requires compensation by the error matrix.During the period  is applied to the grating, the \u03b8z error range is  before compensation and  after compensation. The error range in z-direction position is  before compensation and  after compensation. When the motion period  is applied to the grating after compensation, the \u03b8z error range is , and the error range in the z-direction position is reduced to . \u03b8x remains a relatively low error range without obvious change in these two periods. During the period  shown in x-axis increased by 2.26%, mainly because the fluctuations of the other three degrees of freedom were superimposed on it after compensation by the error matrix. The RMS of the errors around the z-axis was reduced by 78.99%, and the RMS of the errors of the displacement of the z-axis was reduced by 88.14%, demonstrating the effectiveness of the error matrix compensation method. As shown in \u03b8x = 80\u2032\u2032, \u03b8z = 80\u2032\u2032, and z = 100 \u03bcm, the same compensation matrix is used, and the RMS of the errors of the encoder value is 3.02\u2032\u2032, 3.25\u2032\u2032, and 1.21 \u03bcm in \u03b8x, \u03b8z, and z-direction, respectively. When the measuring range is enlarged, the error does not increase obviously, which proves the effectiveness and reliability of the compensation method.\u03b8x and z-direction. Initially, the precision of sub-angular seconds can be reached in \u03b8z; however, after a movement of long duration, the average measurement residuals of \u22121.03\u2032\u2032 and 2.93\u2032\u2032 are generated, respectively. This is because in the calculation of the roll angle of the grating, the rotation movement of the light spot is simplified to a linear movement, and its initial position is not at the QPD center, resulting in the enhancement of nonlinearity and error during the measurement. y\u03b8 is not caused by crosstalk but by the motion of the movement element itself due to the installation, which could be detected in the repeated experiments. The data time length in y\u03b8 is more stable and shows a similar change of displacement of the z-axis, indicating that the compensation matrix method is correct. It proves that during the simultaneous operation of the four degrees of freedom, although the DOFs affect each other, they share a relatively linear relationship within a certain range. A larger measurement range and accuracy can be achieved by optimizing the nonlinear formula and the design of the optical path onto the QPD center. Since the autocollimator cannot measure 3-DOF angles simultaneously, only the compensation data are shown in \u03b8x, \u03b8y, \u03b8z, and Z) of the grating reflector in space can be decoupled. Secondly, the homogeneous error compensation matrix was proposed to greatly reduce the crosstalk error caused by installation posture error and installation distance error and improve the accuracy. Finally, a compact prototype system was designed, and the effectiveness of the proposed structure and compensation matrix was fully verified by experiments. Experiments demonstrate that this encoder can provide absolute 4-DOF position and pose monitoring with sub-arcsecond and sub-micron accuracy and high stability. This paper proposes an ultra-precision absolute-type multi-degree-of-freedom grating encoder. Three aspects are studied as follows: Firstly, the absolute position matrix was constructed by establishing the zero-points of the diffracted light spots on QPD coordinates, and the absolute 4-DOF position and pose (x and y can be realized at present [z-direction. The current commercial products, such as the TriAngle Products of Trioptics [In terms of absolute measurement, the measurement of  present ,26,27, b present ,31 do norioptics , can onl"}
+{"text": "We propose a stochastic generative model to represent a directed graph constructed by citations among academic papers, where nodes and directed edges represent papers with discrete publication time and citations respectively. The proposed model assumes that a citation between two papers occurs with a probability based on the type of the citing paper, the importance of cited paper, and the difference between their publication times, like the existing models. We consider the out-degrees of citing paper as its type, because, for example, survey paper cites many papers. We approximate the importance of a cited paper by its in-degrees. In our model, we adopt three functions: a logistic function for illustrating the numbers of papers published in discrete time, an inverse Gaussian probability distribution function to express the aging effect based on the difference between publication times, and an exponential distribution  for describing the out-degree distribution. We consider that our model is a more reasonable and appropriate stochastic model than other existing models and can perform complete simulations without using original data. In this paper, we first use the Web of Science database and see the features used in our model. By using the proposed model, we can generate simulated graphs and demonstrate that they are similar to the original data concerning the in- and out-degree distributions, and node triangle participation. In addition, we analyze two other citation networks derived from physics papers in the arXiv database and verify the effectiveness of the model. Scientific papers are major achievements in the academic field. Recently, the number of academic papers has increased rapidly; hence, it is necessary to evaluate their quality. Impact factor  and h-inSeveral studies have proposed network models to grow a network, which are categorized as random graph generators. The Barab\u00e1si\u2013Albert model  attempteKrapivsky and Redner  note theIn this study, we consider a stochastic generative model for citation networks generated on discrete time. The proposed model comprises several functions expressing the number of nodes at each time, the aging effects based on the difference in publication times between citing and cited papers, and the out-degree distribution for nodes. These functions are used to grow a network based on PA and TF mechanisms. In the next section, we discuss the data obtained from the Web of Science database. Subsequently, we define our stochastic model, estimate it using data, and demonstrate the performance of the proposed model by comparing the original data with simulated results based on our model and a few previously defined models. In addition, we similarly analyze other citation networks on the arXiv database. Finally, we conclude the paper with a few remarks.WoS-Stat, which is a citation network that comprises the citations between papers published in journals whose subject is associated with \u201cStatistics and Probability.\u201d We construct a citation network utilizing a paper identifier (ID), publication year, and reference list (list of paper IDs) for 36 years, from 1981 to 2016. WoS-Stat consists of 179483 papers and 1106622 citations. Although it includes 6411 books, we have checked that they have little effect on the following analysis. Note that the \u201cStatistics and Probability\u201d journals are also associated with subjects such as \u201cMathematics\u201d, \u201cComputer Science\u201d, etc. WoS-Stat. We used publication year because the time granularity of the papers varies annually, monthly, and daily. WoS-Stat. It has generally increased and saturated in recent years.Our research was started by analyzing the citation network generated from the Web of Science (WoS), which is a famous large-scale scientific bibliographic database . Each reG = , where a paper i corresponds to a node vi \u2208 V, and the citation relationship in which paper i cites paper j is represented by a directed edge \u2208E. Each node vi has a publication time \u03c4(vi). We usually assume that the time is normalized as 1, 2, \u2026, T.We denote the citation network using a directed graph vi, vj), \u03c4(vi)\u2265\u03c4(vj) should be satisfied. However, a few exceptions to this rule exist in the data. Possibly, these exceptions emerge when multiple papers are submitted in a short period of time and have citation relationships, and when there are different periods of reference processes.It is evident that a paper cannot cite future papers, i.e., for an edge (Ain(v) = {u |  \u2208 E} and Aout(v) = {u |  \u2208 E}, i.e., sets of the adjacent nodes of a node v that connects by in-coming and out-going edges. The in-degree of node v is defined by din(v) = |Ain(v)| and the out-degree of node v is defined by dout(v) = |Aout(v)|, where |\u22c5| denotes the number of elements. We note that the out-degree of a paper depends on the type of the paper, for example, a survey paper has many citations, and a paper that analyzes data mainly has few citations in WoS-Stat.It is known that the typical features of a paper include the number of papers that cite it (in-degree in graph terminology), the number of citing papers (out-degree in graph terminology). Let v \u2208 V is defined by\u03b4(v) is the number of triads  that consists of connected nodes  adjacent to v, ignoring the direction of edge. For example in v has 3 triangles. Although directions of edges have a clear meaning in bibliographic contexts as citing and cited papers, we consider the number of triads for simplicity of analysis. This is called node triangle participation in [We also consider triangle-type citation structures (node triangle participation in graph terminology) , 7, 10. In the citation network, it is known that more triangles are generated than those of the graph that uses only the preferential attachment , becausek. The node triangle participation is defined as k. pin and pout, and the node triangle participation ptri in WoS-Stat. Note that each plot adopts the log-scale axes, and the x-axis is shifted by + 1, i.e, x = 1 corresponds to k = 0. From these figures, we can infer that they follow heavy-tailed distributions. Note that 10.2% of papers have out-degree k = 0; this means that these papers have no citations in \u201cStatistics and Probability\u201d because WoS-Stat includes citations within this field. These papers must have citations to papers in other fields or older papers before 1981, but they are outside the scope of our data.The in- and out-degree distributions are defined as A citation network constructed from bibliographic data has clear characteristics: older papers have fewer out-degrees, while newer papers have fewer in-degrees. If features of the entire network are modeled by considering all nodes equally, biases will appear in the modeling of the generative process. We need some corrections for features depending on time.s by the time difference s = \u03c4(vi) \u2212 \u03c4(vj) between a citing paper vi \u2208 V and a cited paper vj \u2208 Aout(vi). Then the number of citations for age s at time t isc for citing age s and citing time t is c = m/n(t), where n(t) = |{v | v \u2208 V, \u03c4(v) = t}| [v to age s isWe define the citation age v) = t}| . Then, ws \u2264 \u03c4(v) \u2212 1, and dout(v) is given bys < 0). It is clear that dout(v) depends on \u03c4(v) heavily, for example, dout(v) is near 0 if \u03c4(v) = 1. Therefore, we correct dout(v) under the assumption that c is almost independent with respect to time t. We define k.Note that 0 \u2264 c for citing age s for each time t and the time-adjusted out-degree distribution t. They are plotted for citing time t \u2208 {10, 13, 16, 19, 22, 25, 28, 31}. It can be observed that both features c and t. The citing age distribution is discussed in [ussed in \u201314.n(t) published at time t is approximated by the logistic functionfn(t) + \u03f5n(t)\u23a3, where \u03f5n(t) is an independent x\u23a3 denotes a maximum integer that does not exceed the real number x. We note that [nf = a(1 \ud808\ude12 exp(\u2212bt)) for this purpose; however, we assume that it is not satisfactory, at least for WoS-Stat.The proposed model for a citation network comprises several components. We first assume that the expected value of the number of papers ote that  adopted c(s) for citing age (time difference) s is approximated byNext, we assume that the expected value of the citing age distribution \u03bac times the probability density function (PDF) of the inverse Gaussian distribution [WoS-Stat, the citing age distribution c(s) after publication is relatively low, rapidly increases toward the peak, and then gradually decreases. Such shapes are appropriately approximated by the PDF of the inverse Gaussian distribution.This function is ribution . Note thribution , the expSubsequently, we assume that the time-adjusted out-degree distribution ribution , whose P\u03b3o = 0 and \u03bco = 0. Since the estimation for WoS-Stat shows that these are almost zero, we will use the simpler exponential distribution, whose PDF was given byThe generalized Pareto distribution is equivalent to an exponential distribution when WoS-Stat: n(t) for t \u2208 {1, 2, \u2026, T} are used to estimate fn(t), c(s) for s \u2208 {0, 1, \u2026, T \u2212 1} are used for fc(s), and fo. For fn, We adopt the least squares method to estimate parameters and obtain estimates fc, it is also estimated by the least squares method; accordingly, we obtain estimates v as data, to estimate parameters using the maximum likelihood method, and obtain estimates fo. We estimated parameters of fc and fo using c and t \u2265 10, which are stable and can be seen in n(t), c(s), and WoS-Stat. We infer that these estimated functions fit well to the real network.We estimate these functions for fn, fc, and fo. Nodes at time t are generated according to \u23a5fn(t) + \u03f5n(t)\u23a6. Each node has out-degree generated from fo. We generate edges according to the combination of PA and TF, where PA and TF are performed with probability 1 \u2212 \u03b2 and \u03b2, respectively. Consider that a node vi is introduced to the network. In PA, vi selects vj \u2208 V with probabilityIm(vj) represents the importance of vj and fc(\u03c4(vi) \u2212 \u03c4(vj)) denotes the aging effect for the time difference \u03c4(vi) \u2212 \u03c4(vj). In TF, vi selects vk \u2208 A(vj) with probabilityvj is selected in the last PA and A(vj) denotes the adjacent nodes of vj. Subsequently, we repeat PA or TA specified times using the out-degree of vi. It is difficult to determine the importance of a paper. Hence, we decide to adopt the value din(v) + 1 as Im(v). The verification of the proposed model will be provided by simulations in the next section.The last component of the model is the generating mechanism of edges. We adopt the PA and TF mechanisms considering functions Our edge generation mechanism combines the PA proposed by   + \u03f5n(t)\u23a6 nodes to V\u2032 at each time t. For t \u2265 1, each node vi generates k edges using PA or TF. Here k = \u23a5x\u23a6 and x were generated from fo(x). PA was first executed, and then PA or TF was executed with probabilities 1 \u2212 \u03b2 and \u03b2, respectively. In our simulation based on s \u2208 {0, 1, \u2026, T \u2212 1} with a probability proportional to fc(s), then vj was selected from the subset of nodes {v | v \u2208 V\u2032, \u03c4(iv) \u2212 \u03c4(v) = s} with a probability proportional to din(vj) + 1. In TF based on W = { v | v \u2208 A(jv), \u03c4(iv) \u2212 \u03c4(v) = s} \\ {iv} of the node vj selected at the preceding PA, for each time difference s. Then, we selected a time difference s that has a nonempty W with a probability proportional to fc(s), and chose a node vk \u2208 W with a probability proportional to din(vk) + 1. When all W were empty, PA was executed instead of TF. We skipped the edge generation when t was in past, i.e., t \u2264 0. Finally, we deleted the out-of-range nodes and edges: V = {v | v \u2208 V\u2032, 1 \u2264 \u03c4(v) \u2264 T} and E = { | iv, jv \u2208 V,  \u2208 E\u2032}, respectively.We first set nodes \u03b2 parameter; hence, we adopted simulations to determine it. We executed simulations for values of \u03b2 from 0.85 to 0.99, with an increment of 0.01. Then we compared the Kullback\u2013Leibler (K\u2013L) divergence [WoS-Stat for the in- and out-degree distributions, and node triangle participation. More precisely, we compared appropriate histograms of given data to calculate K\u2013L divergence. \u03b2 values, and the node triangle participation takes its minimum around \u03b2 = 0.92. So we decided to adopt \u03b2 = 0.92. Note that \u03b2 = 0.92 does not necessarily imply that TF is executed with a probability of 0.92 in the simulations because PA is executed at the first edge generation process.It is difficult to estimate the value of the vergence  between n(t), c(s) and WoS-Stat. Each figure presents the mean with the approximately 95% confidence interval obtained via ten times simulations. It can be inferred that all features fit well together. Note that this simulation checks the total model appropriateness, and is different from WoS-Stat) for each node on Barab\u00e1si\u2013Albert and Holme\u2013Kim, which assume a constant out-degree. Holme\u2013Kim, Wu\u2013Holme and our models used \u03b2 = 0.92. The Wu\u2013Holme model requires the order of publication of papers. We adopted the sorted order by considering the paper ID and publication year in WoS-Stat. We applied the NetworkX implementations [We diagnosed the model fitting by visualizing network features suitable for elucidating a citation network: in- and out-degree distributions, node triangle participation, and scree plot. The scree plot shows the singular values of the graph adjacency matrix, versus their rank, using the logarithmic scale . These pntations  of the Bntations  and the ntations . We adopntations  to compuWoS-Stat. All models succeeded in imitating the in-degrees. This may indicate that PA works well for all models. Regarding the out-degree, there are severe problems in the data generated by the Barab\u00e1si\u2013Albert and Holme\u2013Kim models because these models assume the out-degree is a constant. The Wu\u2013Holme model seems to fit well; however, it is natural because it uses the out-degree of the original data directly in simulations. Compared with the Wu\u2013Holme model, the proposed model does not require the original out-degrees but adopts the estimated out-degree distribution. For the node triangle participation, the proposed model has similar results to those of the Wu\u2013Holme model and exhibits better results than the Holme\u2013Kim model, which does not consider the aging effect. Although scree-plot has a similar pattern among models, our model has larger differences from the data than other models.Note that our model can produce a legitimate simulation results for considered network features.arXiv-HepTh and arXiv-HepPh. These citation networks are generated from papers and citations of the high-energy physics fields, hep-ph and hep-th, in the bibliographic data of arXiv [arXiv-HepTh has publication dates. Because almost all papers did not have the publication date in arXiv-HepPh, we assumed their publication months from their paper IDs. Note that arXiv-HepTh was analyzed in [arXiv-HepPh in [arXiv-HepTh and arXiv-HepPh.This section shows that the proposed model also works well for two other citation networks: of arXiv . We usedof arXiv . The arXlyzed in , 10, 12 fc and fo with t \u2265 10 and compare fitted functions in arXiv-HepTh in arXiv-HepPh in arXiv-HepTh and arXiv-HepPh are presented in Figs \u03b2 = 0.99 in both arXiv-HepTh and arXiv-HepPh, which are obtained by performing simulations similar to WoS-Stat. This result for \u03b2 is consistent with the existing model [WoS-Stat case, the proposed model visually fits well for in- and out-degree distributions and node triangle participation. For the scree plot, the proposed model is confirmed to fit the same or more, compared with other models for arXiv-HepTh and arXiv-HepPh. The proposed model fits better than the Wu\u2013Holme model, especially from the scree plot for arXiv-HepPh.We estimated parameters of ng model . SimilarWoS-Stat generated from the statistics and probability field in the bibliographic data from the Web of Science. We obtained the models on this network for the number of papers on publication time, the citing age distribution, and the time-adjusted out-degree distribution. In other words, we assume that their structures do not change for all publication times in the data. These assumptions are supported by the data to some extent and are required to estimate parameters accurately. However, today, situations in the academic society are changing rapidly. So the citation structure may change in the future.We proposed a stochastic generative model for a graph representing a citation network. Our research motivation first came from the citation network We adopted three functions to define the model: a logistic function, an exponential distribution, and an inverse Gaussian probability density function. These functions were selected to approximate the data. However, it is difficult to interpret or theoretically verify their meaning. Our objective is to ensure that they are beneficial in generating similar data to the original data. Accordingly, we adopted PA and TF mechanisms. PA is employed to approximate the importance of the paper by the in-degree. We understand that the true importance of a paper is a latent variable and needs to be estimated by a significantly more complex model. We considered that the out-degree approximates the type of a paper; for example, a small out-degree indicates that the paper focuses on other fields. Because cited papers of old papers are not included in the data, they usually exhibit a small out-degree. Therefore, we considered papers focusing on other fields and old papers are in the same type. It may be problematic. In-degree and out-degree consider relationships between two nodes. Triangle considers relationships among three nodes. Hence, it is clear that our model explicitly considers the relationships among up to three nodes. We demonstrated that our model is a simple but satisfactory approximation of the graph generating process in this constraint. This constraint may explain that the scree plots of the simulated graphs tend to be relatively apart from that of original data because the scree-plot can exhibit the relationships among more than three nodes.arXiv-HepTh and arXiv-HepPh. Consequently, we can expect that the proposed model provides a good approximation of general citation networks.The important feature of the model is that the discrete-time is considered explicitly, and the discrete-time information is easy to interpret the graph structure. In addition, it enables the data generation outside of the data period, especially in past time. We can generate edges in the past and execute simulations similar to the real situation. The outside nodes and edges are discarded in the final phase of the generative algorithm, similar to the real data. This differs from other existing models , 6, and"}
+{"text": "N\u2009=\u2009130, 102 women, 28 men) read a gendered (feminine or masculine) text and a gender-neutral text with passive voice. Most gave a masculine name to the person in the neutral text, but addressed them in a gender-neutral way when asked to react to them in presented scenarios. The gender-neutral text was evaluated as being less comprehensible than the gendered texts, and the non-binary person was rated less competent and colder than a man or a woman and was less socially accepted. Furthermore, the negative evaluation of non-binary people seemed to be attributable to unfamiliarity with gender-neutral language and its lower comprehensibility. More research is needed to understand these perceptions better and to be able to prevent their potential negative consequences.People can express their identity in different ways, one of which is through language. Non-binary individuals often speak in a gender-neutral way and use specific language forms. Language use not only reveals their identity but also can shape how others perceive them. The present study\u2019s purpose was to analyze how non-binary people are perceived through the language they use. The research was conducted in Polish, a language that is especially challenging for non-binary individuals because it has many gender markers. To avoid using gendered forms, they often use a specific form of passive voice. In an experiment, participants (The online version contains supplementary material available at 10.1007/s10508-021-02234-y. One important way to express one\u2019s gender identity is through language. Within the LGBTQ+\u2009community: non-binary people. The term non-binary can be described as an umbrella term for individuals who do not identify as male or female Barker, , encompacoming out and are at risk of being misunderstood or rejected. An example of this can be found in what Respondent 89 said in a study by Hord  and an invented (onu) neutral version of on (he) and ona (she) that can be considered equivalents of the singular they , a non-binary person may say jestem osob\u0105 psychologa (I am a psychologist person) or jestem osob\u0105 profesji psychologicznej . To avoid this, one can use an adverb (jest mi weso\u0142o).When it comes to personal pronouns, some Polish non-binary people use or ask others to refer to them with ild B\u0105k, . Onu is \u0107 Dukaj, . It then\u0107 Dukaj, . Some no\u0107 Dukaj, . Generalem for masculine forms and \u2013am for feminine ones. Some non-binary people use \u2013um or \u2013om endings as an alternative  or czyta\u0142em ksi\u0105\u017ck\u0119 (I was readingmas a book), they say czyta\u0142o mi si\u0119 ksi\u0105\u017ck\u0119. This is not a standard passive voice, like the book was read by me (ksi\u0105\u017cka by\u0142a czytana przeze mnie), but rather reflects the English I\u2019ve got my hair cut, or in this case, I\u2019ve got my book read. In Polish, it emphasizes the activity, rather than the person, and is gender neutral. Another example is the sentence Sz\u0142am ulic\u0105  or Szed\u0142em ulic\u0105 . Instead of using the gendered forms, a non-binary person could say Sz\u0142o mi si\u0119 ulic\u0105, which is gender neutral.Past-tense verbs also are gendered and often end with \u2013 Helena, . An inteyou instead of the more common and polite, but gender marked, Sir/Madam by Pan/i co\u015b do picia? (Wouldmas/fem you Sir/Madam like something to drink?), one can say Czy chcesz co\u015b do picia? (Would you like something to drink?).Non-binary people choose the language that they, themselves, want to use, but how should others address them? In Polish, some non-binary individuals prefer that strangers address them directly using The present study\u2019s focus was on how others perceive non-binary individuals through the language they use. While gender-fair language focuses on personal pronouns and nouns, especially professional names, we focused on omnipresent verbs , and in the second version, they were in a store and answered a phone (Text B). Therefore, there were four possible versions of the questionnaire. If the participant was assigned randomly to a condition with a masculine/feminine Text A, they were automatically assigned to receive a gender-neutral Text B. In the case of being assigned to a masculine/feminine Text B, the second text was a gender-neutral Text A. After each of the texts, participants answered questions regarding the text and its narrator.N\u2009=\u2009130 .Mage\u2009=\u200926.80, SD\u2009=\u200910.03), with most studying at a university (41%) or holding a higher education degree (39%). Most lived in a city of more than 500,000 residents (37%), but there were also many from medium-size cities (18%), smaller cities (21%), towns (11%), or villages (13%).The sample was collected using a snowball method. The questionnaire was posted on a private social media profile with a request to share it with others. Altogether, 222 participants clicked the study link, and 133 filled out the entire questionnaire. We excluded one trans-man and two non-binary people from the analyses. Thus, the maximum final sample was Participants were informed that the questionnaire comprises three parts and takes approximately 10\u00a0min to complete.n\u2009=\u200961) after a masculine text and part of them (n\u2009=\u200975) after a feminine text. Thus, on the crucial comparison between gendered and neutral texts, the study had a within-participant design, and on a secondary comparison between male and female texts, a between-participants design.3There were three versions of the text, depending on the narrator\u2019s language: masculine, feminine, and gender neutral. Participants randomly received two texts: a masculine and a gender-neutral text or a feminine and a gender-neutral text. The two texts varied in content, and participants were assigned randomly to version A or B of the text. The texts described everyday activities and short interactions with others (family members or friends). We used everyday activities to ensure that the texts\u2019 protagonists would not be special in any way other than their gender identity, allowing the reader to relate to the texts easily. All participants evaluated gender-neutral texts, part of them (strongly disagree) to 5 (strongly agree). The Text Comprehensibility scale comprised the items understandable, sounds good, and is reliable . The Person Evaluation scale comprised a set of four questions asking whether the person from the text seems competent, credible, nice, and whether the participant would like to go out for coffee with this person . As a separate question, we included an item from the social distance scale that measures acceptance of a minority member in different spheres that are closer to or more distant from the participant. We chose the most intimate item, asking whether participants would accept a relationship between a person from their family and the person from the text  to 5 (I definitely would accept it).For each text, participants were asked whether they were familiar with this kind of language . The main dependent variables were then assessed with a few questions measuring text comprehensibility and person evaluation using Likert-type scales, from 1 .hard to say , 0 people\u2009=\u20092, 1\u20132 people\u2009=\u20093, a few\u2009=\u20094, many\u2009=\u20095, and very many\u2009=\u20096. As all six items showed high reliability of the scale (\u03b1\u2009=\u20090.83), the mean of all items  was taken. Finally, participants answered demographic questions about their gender identification with an open-ended question, age, education, and place of residence.After text and person evaluation, we measured contact with non-heteronormative individuals.The study\u2019s purpose then was explained to the participants, who were informed that the questionnaire measured reactions to gender-neutral language used by non-binary individuals. There was also a request to share the questionnaire with others but without revealing the study\u2019s purpose. The participants also were invited to leave comments about the study.Most participants (89%) declared that they were familiar with the language used in the gendered texts. However, the opposite was the case with the gender-neutral texts, in which 81% answered that they were not familiar with this kind of language.Alex).When asked to provide a name for the narrator of the text, for the masculine text, most participants gave a masculine name, and for the feminine text, most gave a feminine name Fig.\u00a0, left. Wyou or plural and passive forms that avoid gender , we explored the potential influence of the text version and the participants\u2019 gender, age, education, and place of residence on the dependent variables of text comprehensibility, person evaluation, and social acceptance.Fs\u2009<\u2009 .58, ps\u2009> .45, s\u2009<\u2009.004) nor were there any interactions . Therefore, we combined the data from both versions.Three 2 \u2009\u00d7\u20092 (Gendered Text: Masculine vs. Feminine)\u2009\u00d7\u20092 (Text Version: A vs. B) mixed ANOVAs showed that reading version A or B of the text did not exert significant influence on any of the dependent variables: text comprehensibility, person evaluation, or social acceptance. There were no significant main effects of the text version  than women did . There was no such effect on person evaluation . To sum up, in the current sample, there were very few gender effects that did not replicate on different variables and did not involve the study\u2019s main comparison between gendered and neutral texts.To explore gender differences, we conducted three 2 \u2009\u00d7\u20092 (Gendered Text: Masculine vs. Feminine)\u2009\u00d7\u20092 (Participant\u2019s Gender: Woman vs. Man) ANOVAs. The results showed that there was a weak main effect of gender on comprehensibility .Correlations showed no significant relationships concerning age, education, and place of residence with comprehensibility, person evaluation, and social acceptance \u2009=\u2009165.51, p\u2009<\u2009.001, d\u2009=\u20091.08, which showed that the participants rated gendered texts as being much more comprehensible  than the neutral texts \u2009=\u20090.003, p\u2009=\u2009.96, To compare the effect of a gendered (masculine/feminine) vs. neutral version of the text on text comprehensibility, we conducted a 2 \u2009\u00d7\u20092 (Gendered Text: Masculine vs. Feminine) ANOVA. There was a main effect of gendered vs. neutral text, F\u2009=\u2009121.28, p\u2009<\u2009.001, d\u2009=\u20090.95. The participants rated men and women more favorably on the person evaluation scale  than non-binary individuals from the neutral texts \u2009=\u20090.29, p\u2009=\u2009.59, A similar ANOVA for person evaluation showed, again, a large main effect of gendered vs. neutral text, F\u2009=\u200986.45, p\u2009<\u2009.001, d\u2009=\u20090.81.M\u2009=\u20093.88, SD\u2009=\u20090.85) than a non-binary individual as a new member of their family \u2009=\u20090.004, p\u2009=\u2009.95, The last ANOVA was for social acceptance, and it showed, yet again, a large main effect of gendered vs. neutral text, entclass1pt{minimaIn terms of contact with non-heteronormative people, our sample had more such contact than an average Pole. Most participants (69%) knew at least one non-heteronormative person, with relatively many knowing a few (36%), and also relatively many (21%) stating that it is hard to say. Most participants (94%) personally knew gays and/or lesbians, with almost half (46%) knowing a few and 4% indicating that it is hard to say.To explore relationships between the amount of contact with non-heteronormative people and the main dependent measures, correlations were computed \u2009=\u20090.15, p\u2009=\u2009.19, nor was the influence of the text on person evaluation, b\u2009=\u20090.04, SE(boot)\u2009=\u20090.10, p\u2009=\u2009.66.The mediation analysis showed that, as in the earlier ANOVA, people from gender-neutral texts were evaluated much less favorably than people from gendered texts. However, when including comprehensibility, the effect disappeared Fig.\u00a0. The modyou.The current research shows that non-binary language forms, such as passive voice, are unfamiliar to most listeners or readers and are perceived as less comprehensible than gendered and active language. Furthermore, non-binary people using such language are evaluated more negatively and are socially less accepted than women and men. The negative evaluation could be due to the lower comprehensibility of the language that some non-binary people use. When study participants were asked to give a name to a non-binary person on the basis of their speech, they more often chose a masculine over a feminine name, but when given more freedom on how to address a non-binary person, they often chose gender-neutral language forms, such as There may be different reasons for the negative evaluation of non-binary people and their language. First, gender-neutral language can indicate the speaker\u2019s non-normative gender identity. Second, it also may be that participants evaluated non-binary people negatively partly because passive voice is used more frequently to talk about negative emotions and events, so these people may expect more negativity from a person using it Ka\u0142kus, . Third, If negative evaluation of non-binary people was indeed largely due to the incomprehensibility of their language, familiarizing people with non-binary language could help the social perception of non-binary individuals. Extant research on gender-fair language shows that more exposure to, and preferably usage of, gender-fair language makes people more tolerant not only to such language, but also to the people it describes  and would, thus, choose a gendered form. It could also be that if the people in the scenarios were described as much older than an average participant, even younger participants might tend to use Sir/Madam.As expected, most people gave the non-binary person a masculine name, which is, regrettably, in line with the male-as-the-norm phenomenon and vast research showing that people assume that the protagonist or the narrator of a text is male even when described using gender-neutral language , a question about readiness to help would tell us something about the potential discrimination.As in all research with non-representative samples, the current results should not be generalized to all languages, cultures, or to the whole Polish population. Our participants were more likely than an average Pole to be female, live in bigger cities, and were relatively young. Most also had contact with non-heteronormative individuals, which does not reflect the low amount of contact in the whole Polish population Supplementary file2 (SAV 826 kb)Supplementary file3 (DOCX 29 kb)Below is the link to the electronic supplementary material."}
+{"text": "Modern Pathology 10.1038/s41379-022-01147-y, published online 10 September 2022Correction to: The \u201cCompeting interests\u201d section was erroneously not transferred from the manuscript to the originally published version of the article. The \u201cCompeting interests\u201d section should read: F.Z. is a shareholder of asgen GmbH. P.S. is a member of the supervisory board of asgen GmbH. All other authors declare that they have no conflict of interest. The original article has been corrected accordingly."}
+{"text": "Correction: Journal of NeuroEngineering and Rehabilitation (2020) 17:86 https://doi.org/10.1186/s12984-020-00713-2Following publication of the original article , there iThen the values under the Methods and Results has been changed. So, the Methods and Results will read as follows:Methods: We assessed participants twice within 15 days on all tasks presently available in KST. We determined the 5\u201395% confidence intervals for each task parameter, and derived thresholds for significant change. We tested for learning effects and corrected for the false discovery rate (FDR) to identify task parameters with significant learning effects. Finally, we calculated intraclass correlation of type ICC  (ICC-C) to quantify consistency across assessments.Results: We recruited an average of 56 participants per task. Confidence intervals for Z-Task Scores ranged between 0.84 and 1.41, and the threshold for significant change ranged between 1.19 and 2.00. We determined that 6/11 tasks displayed learning effects that were significant after FDR correction; these 6\u00a0tasks primarily tested cognition or cognitive-motor integration. ICC-C values for Z-Task Scores ranged from 0.29 to 0.70.Also, a text \u201crunning Dexterit-E version 3.7 software\u201d needs to be inserted under the section \u201cRobotic assessment\u201d. So, the line has been changed.from:Robotic assessment for the study was conducted on the Kinarm exoskeleton robotic platform .to:Robotic assessment for the study was conducted on the Kinarm exoskeleton robotic platform running Dexterit-E version 3.7 software .An equation number under the section \u201cIntraclass correlation\u201d has been changed.from:For the purpose of this study, the consistency ICC metric ) was used, which we refer to as ICC-C throughout. ICC-C is calculated as follows:to:For the purpose of this study, the consistency ICC metric ) was used, which we refer to as ICC-C throughout. ICC-C is calculated as follows:The values under the section \u201cSignificant change across assessments and assessment confidence interval\u201d has been changed. So, the paragraph will read as follows:diff.Significant change thresholds (SC) and confidence intervals (CI) were estimated by first computing the difference in performance between the first and second assessments and determining the variability of these difference scores. A parameter Z-score difference (i.e. the difference between first and second assessments) exceeding\u2009\u00b1\u20093.2 was considered an outlier, reflecting the fact that such a large difference should only be observed 1 in 1000 data samples. These outliers were not included in any further calculations; however, we quantified the number of difference scores removed in this way. We then computed the standard deviation (SD) of the remaining difference scores, referred to as SDdiff allowed the determination of both the CI and the SC. CIs were simply represented as CI\u2009=\u2009\u00b1\u20091.64\u00a0*\u00a0SDdiff. The choice of 1.64 as the width of the CI signifies that only 5% of healthy subjects should display such a large increase or a large decrease in performance across repeat testing. This can also be considered as approximately the 90% one-tailed confidence interval, to reflect that the most common question under consideration will be whether or not a participant had improved or deteriorated specifically . The CI then led to the threshold for significant change (SC) in the following ways [31\u201335]:Determination of the SDdiff may be replaced with sqrt(2)\u2009*\u2009SDpre\u2009*\u2009sqrt(1\u2009\u2212\u2009ICC) .Note that in situations in which only the pre- or posttest SD is known, and the SD of difference scores is not, the SDThere is a text change under the section \u201cSimulations: CI, SC, and effect of task score transform on CI\u201d. So, the text will change.from:We performed three simulations of (1) the probability that a participant is \u201ctruly impaired\u201d, (2) that their score had \u201csignificantly changed\u201d using the example of the Reaction Time (RT) parameter of VGR, and (3) of the effects on the CI of the conversion of the Task Score from a two-sided metric (the \u201cZ-Task Score\u201d) to a one-sided metric (the \u201cTask Score\u201d).to:We performed three simulations of (1) the probability that a participant is \u201ctruly impaired\u201d, (2) that their score had \u201csignificantly changed\u201d using a simulated parameter score with a CI of 0.95, and (3) of the effects on the CI of the conversion of the Task Score from a two-sided metric (the \u201cZ-Task Score\u201d) to a one-sided metric (the \u201cTask Score\u201d).Also, there is value change under the section \u201cAccounting for intra-individual variability\u201d. So, the text will change.from:diff, so we calculated the final IS error by multiplying SEM by \u221a2\u2009*\u20091.64 so that it would be comparable to the SC .The SEM is in the same units as SDto:diff, so we calculated the final IS error by multiplying SEM by 1.64 so that it would be comparable to the SC .The SEM is in the same units as SDThere is value and text change under the sections \u201cSignificant change and confidence intervals\u201d, \u201cLearning effects\u201d, \u201cICC\u201d, \u201cProbabilistic interpretation of impairment and change\u201d. So, the passage will read as follows:Significant change and confidence intervalsTable Significant change and confidence intervals for all task parameters are presented in Fig.\u00a0We additionally calculated IS error to understand the contribution of the variability across trials within the same assessment to the overall SC. We identified that IS values were typically on the order of 20\u201330% of the SC value , with the RVGR-D reaction time parameters being the highest and VGR-ND speed maxima count being the lowest. We report all of these values in the Additional file as an additional column for each of the tables for RVGR-D and RVGR-ND , and for VGR-D and VGR-ND .Learning effectsLearning effects ranged from 0.12 to \u2212\u20090.76 for Z-Task Scores and the average learning effect was \u2212\u20090.30 ; ICC-C); see Table , 1; ICC-The cumulative sum plots of ICC-C for all parameters are presented in Fig.\u00a0Probabilistic interpretation of impairment and changeWe performed simulations of parameter values to depict the probabilistic interpretation of our CI and SC results in terms of identifying impairments and quantifying significant change see Fig.\u00a0. There iThere is also, a value change under the section \u201cDiscussion\u201d. So, the value in the text will change.from:We determined that the confidence intervals averaged approximately 1.12 across Z-Task Scores and 1.07 across all parameters.to:We determined that the confidence intervals averaged approximately 1.08 across Z-Task Scores and 1.12 across all parameters.Also, there is a text change under the section \u201cDiscussion\u201d. So, the text will change.from:We observed the highest IS errors relative to SC in VGR reaction time at ~\u200920%.to:We observed the highest IS errors relative to SC in RVGR reaction time at ~\u200935%.Also, there is a the text change under the section \u201cDiscussion\u201d and the text will change.from:Importantly, we observed learning effects in some parameters and in some Z-Task Scores. In particular, RVGR had a preponderance of significant learning effects, with 18 parameters out of 24 (across both arms) demonstrating learning effects that were significant after correction for FDR.to:Importantly, we observed learning effects in some parameters and in some Z-Task Scores. In particular, RVGR had a preponderance of significant learning effects, with 22 parameters out of 28 (across both arms) demonstrating learning effects that were significant after correction for FDR.Also, there is a percentage change under the section \u201cLimitation\u201d, so the text needs to change.from:The IS error was typically <\u200910% of the absolute value of the SC, suggesting that the dominant source of variability is change over repeated assessments, and not change within a single session.to:The IS error was typically <\u200930% of the absolute value of the SC, suggesting that the dominant source of variability is change over repeated assessments, and not change within a single session.The values in Table There is a change in the x-axis for the Fig.\u00a0There is a small change in the label for Fig.\u00a0The original article has been corrected."}
+{"text": "Imbalanced outcome is one of common characteristics of oncology datasets. Current machine learning approaches have limitation in learning from such datasets. Here, we propose to resolve this problem by utilizing a human-in-the-loop (HITL) approach, which we hypothesize will also lead to more accurate and explainable outcome prediction models.A total of 119 HCC patients with 163 tumors were used in the study. 81 patients with 104 tumors from the University of Michigan Hospital treated with SBRT were considered as a discovery dataset for radiation outcomes model building. The external testing dataset included 59 tumors from 38 patients with SBRT from Princess Margaret Hospital. In the discovery dataset, 100 tumors from 77 patients had local control (LC) (96% of 104 tumors) and 23 patients had at least one grade increment of ALBI (I-ALBI) during six-month follow up (28% of 81 patients). Each patient had a total of 110 features, where 15 or 20 features were identified by physicians as expert knowledge features (EKFs) for LC or I-ALBI prediction. We proposed a HITL based Bayesian network (HITL-BN) approach to enhance the capability of selecting important features from imbalanced data in terms of accuracy and explainability through humans\u2019 participation by integrating feature importance ranking and Markov blanket algorithms. A pure data-driven Bayesian network (PD-BN) method was applied to the same discovery dataset of HCC patients as a benchmark.In the training and testing phases, the areas under receiver operating characteristic curves of the HITL-BN models for LC or I-ALBI prediction during SBRT are 0.85  or 0.89 (0.81-0.95) and 0.77 or 0.78, respectively. They significantly outperformed the during-treatment PD-BN model in predicting LC or I-ALBI based on the discovery cross-validation and testing datasets from the Delong tests.By allowing the human expert to be part of the model building process, the HITL-BN approach yielded significantly improved accuracy as well as better explainability when dealing with imbalanced outcomes in the prediction of post-SBRT treatment response of HCC patients when compared to the PD-BN method. Hepatocellular cancer (HCC) is the third leading cause of cancer death worldwide. In 2020, the American Society of Clinical Oncology (ASCO) estimated that 830,180 people around the world died from the disease. While radiotherapy is designed to achieve tumor local control (LC) in HCC patients, it may also lead to radiation-induced toxicities (RITs). As a relatively newer radiation treatment technique, stereotactic body radiation therapy (SBRT) uses focused beams of radiation aimed at the tumor from many different angles given in one to five treatment fractions. Thus, the aim of SBRT is to cure tumors in the meanwhile decreasing the radiation to nearby healthy tissues. While it is more effective for tumor LC and RITs reduction compared to conventional approaches, stringent dose volume constraints of SBRT require the treatment planning to be highly personalized to meet its intended goals  into ML frameworks to overcome issues related to model bias and uncertainty  approval from University of Michigan Hospital (Michigan Medicine). Since each patient may have one or more tumors, there are totally 104 tumors in our discovery dataset. In this study, two or more tumors in an HCC patient are assumed to be independent from each other for the sake of simplicity. There are 23 patients with I-ALBI during six-month follow up, and 100 tumors from 77 patients achieved LC. Each patient has 97 features, including dosimetric information, clinical factors, pre- and during-treatment labs and cytokines as summarized in LIVER_GTV_Mean_Dose\u201d, \u201cpre_ICGR15\u201d, \u201cD_ICGR15\u201d, \u201cChild_Pugh\u201d, \u201cCirrhosis\u201d, \u201cLiver_GTV_Volume\u201d, \u201cpre_HGF\u201d, \u201cD_HGF\u201d, \u201cAge\u201d, \u201cSex\u201d, \u201cpre_CD40_L\u201d, \u201cD_CD40_L\u201d. The EKFs for LC prediction include \u201cChild_Pugh\u201d, \u201cGTV\u201d, \u201cTotal_BED\u201d, \u201cLIVER_GTV_Mean_Dose\u201d, \u201cPrior_Liver_Occurrences\u201d, \u201cpre_MELD\u201d, \u201cpre_Bilirubin\u201d, \u201cpre_Albumin\u201d, \u201cTumor_Size\u201d, \u201cGTV_Mean_Dose_LQ\u201d, \u201cpre_ICGR15\u201d, \u201cpre_HGF\u201d, and \u201cpre_TGF_Beta\u201d. Except the above EKFs related to two different outcomes, the rest of features in Physicians\u2019 acquired knowledge and experience from treating HCC SBRT patients were collected and treated as expert knowledge (EK) for SBRT outcomes prediction in this study. The EK features (EKFs) related to I-ALBI prediction comprise \u201cGained from many years of experience, reading articles, training, peers\u2019 interaction, EK has a potential of bypassing otherwise complex systems and providing parsimonious solutions that focus on key aspects of a given situation. By incorporating EKFs into the feature selection of the PD-BN approach, we previously developed a situational awareness BN (SA-BN) method to predict the radiation outcomes of lung cancer patients . With thSelecting an ML approach for outcome prediction often involves a trade-off between prediction accuracy and explainability . While scomputational agent to improve the prediction model\u2019s explainability by exploring EKFs and non-EKFs that have strong relevance to an outcome, the integrated feature ranking list was treated as another computational agent to enhance the prediction model\u2019s accuracy by investigating each feature\u2019s importance in terms of outcome prediction. Then, the HITL-BN approach can improve its capability of learning from the imbalanced HCC SBRT data by allowing human agents to interact these two computational agents during the process of feature selection.The selected features from the EML and UML approaches are generally different, even though they are evaluated from one single dataset. The former and latter have the potential of improving an outcome prediction model\u2019s explainability and accuracy respectively. While the MB algorithm and network structure learning were considered as a K be the total kinds of these UML approaches, k be the index of these approaches , Lk be a feature ranking list obtained from UML approach k  with the most important feature for outcome prediction at the top of the list, and AUCk be the performance of an outcome prediction model developed from UML approach k based on cross validation in the discovery dataset . Let J be the total number of features in the discovery dataset, j be the index randomly assigned to them , Nj(Lk) be the rank of feature j in ranking list Lk . The rankings Nj(Lk) of the feature in different lists Lk may not be the same, and the performance AUCk of UML approaches for outcome prediction could be different. It is assumed that a robust feature ranking list can be developed by integrating all these ranking lists based on their corresponding UML approaches\u2019 prediction performance. Let L* be an integrated feature ranking list based on K UML approaches, be the weighted ranking score (WRS) of feature j to determine its ranking in list L* , and its value can be evaluated from the following equation by integrating its ranks Nj(Lk) in different ranking lists LkAs stated previously, the UML approaches include RF, SVM, GBM, DL, etc., and each of them can generate a feature ranking list in terms of importance in outcome prediction from all features including EKFs and non-EKFs in a dataset. Let L* in terms of features\u2019 importance in outcome prediction can be obtained from sorting all the features based on their WRSj , where the feature with the minimal score value is ranked at the top of the list.Then, the ranking list I be the total number of EKFs in list L* with I<J , i represent the order of an EKF within all EKFs . An initial HITL-BN is developed from the top n percent of features in the list. The value of n depends on the total number N of features in a dataset and appropriate feature dimension D to satisfy the MB algorithms\u2019 faithfulness assumption, and we assumed n = 100* n percent of features in list includes i EKFs (i\u2264D ), an initial HITL-BN based outcome prediction model can be denoted as HITL-BN(i). Since some EKFs in the top rank of list L* may be redundant or less relevance to an outcome compared to other ones, the most relevant EKFs can be identified from the outcome\u2019s MB. Given the selected EKFs, important non-EKFs in the top rank of the list to improve the outcome prediction should also be strongly related to these EKFs, which can be identified from each of their MBs. Thus, important EKFs and non-EKFs can be selected from the top rank of the list with balanced accuracy and explainability for HITL-BN(i) development. Note that the structure learning of HITL-BN(i) is the same as that of PD-BNs, where less important EKFs and non-EKFs are eliminated from the network to maximize its prediction performance. The rest of our HITL-BN approach is to repeatedly evaluate whether a next EKF and additional non-EKFs before it in list L* can improve the accuracy of previous outcome prediction models or not.Including feature selection and BN structure learning processes, HITL-BN based outcome prediction models are mainly developed based on the integrated ranking list. Let ri be the rank of i-th EKF in list L* . As the evaluation moves from i-th EKF to i+1-th EKF in the integrated feature ranking list, the set of additional indices between them is denoted as ri,\u00a0i+1 . Let S represents the set of non-EKFs associated with ri,\u00a0i+1 , and the number of non-EKFs in the set could be zero when two EKFs are consecutive in the list. If set S is not empty, the importance of these non-EKFs for the outcome prediction depends on whether they have strong relevance with selected EKFs, including the EKFs in HITL-BN(i) and i+1-th EKF. Let MBs  ) be these EKFs\u2019 MBs based on non-EKFs in S , and the set of selected non-EKFs from these MBs is indicated as i+1) can be developed based on i+1-th EKF, non-EKFs in i) by employing PD-BN\u2019s structure learning process. The process continues along list until the performance of prediction model cannot be improved or meet a target prediction performance. The details of the HITL-BN approach to generate an accurate and explainable outcome prediction model are described in Let pre_Bilirubin\u201d, \u201cpre_Cirrhosis\u201d, \u201cPortal_Vein_Thrombosis\u201d, \u201cpre_Creatinie\u201d, \u201cpre_CD40_L\u201d, \u201cpre_HGF\u201d, and \u201cLiver_GTV_DC_LQ_EQD2\u201d for pre-treatment I-ALBI prediction, additional variables \u201cD_Protime_INR\u201d, \u201cD_Bilirubin\u201d, and \u201cD_ICGR15\u201d were chosen for during-treatment I-ALBI prediction. The prediction performances of the former and the latter based on the discovery dataset are 0.78 (95%CI: 0.67-0.83) and 0.82 (95%CI: 0.74-0.88) as described in As a comparison of the HITL-BN approach, PD-BN models for I-ALBI or LC prediction were developed based on our HCC SBRT patients as shown in pre_Albumin\u201d, \u201cActive_Liver_Lesions\u201d, \u201cPortal_Vein_Thrombosis\u201d, \u201cpre_ECOG_PS\u201d, \u201cpre_TGF_Beta\u201d, \u201cpre_HGF\u201d, and \u201cGTV_gEUD_N20_LQL_10\u201d for pre-treatment LC prediction, additional variables \u201cpre_Cirrhosis\u201d, \u201cAdapted\u201d, \u201cD_CD40_L\u201d, and \u201cD_TGF_Beta\u201d were chosen for during-treatment LC prediction. The prediction performances of the former and the latter based on the discovery dataset are 0.75 (95%CI: 0.60-0.86) and 0.79 (95%CI: 0.69-0.89) as shown in K=2), were employed in this study to generate an integrated feature ranking list for a HITL-BN based outcome prediction model development before or during treatment. RF and GBM share similar tree/graph structure learning to BN. Packages \u2018randomForestSRC\u2019 and \u2018gbm\u2019 were used to identify feature ranking lists from the former and latter approaches based on the discovery dataset respectively. After evaluating the two UML approaches\u2019 prediction performances, each feature\u2019s WRS was computed based on its ranks in two different ranking lists and the corresponding UML approaches\u2019 prediction performances from Equation (1). Then, an integrated feature ranking list to rank all the features in the discovery dataset for I-ALBI or LC prediction before or during SBRT can be generated from their WRSs.We conducted numerical experiments to develop or test HITL-BN models for I-ALBI or LC prediction based on the discovery and testing datasets in the same R environment as that of developing or testing the PD-BN models. Two UML approaches, the RF and GBM  and 0.89 (95%CI: 0.81-0.95) as shown in Prior_Liver_Occurences\u201d, \u201cGTV\u201d, \u201cMELD_baseline\u201d, \u201cpre_TGF_Beta\u201d, \u201cpre_HGF\u201d, \u201cGTV_gEUD_LQ\u201d, and \u201cLIVER_GTV_Mean_Dose\u201d for pre-treatment LC prediction, additional variables \u201cMELD_Na_baseline\u201d, \u201cpre_Billirubin\u201d, \u201cpre_ICGR15\u201d, \u201cGTV_Mean_Dose_LQ\u201d, \u201cD_Protime_INR\u201d, and \u201cD_TGF_Beta\u201d were chosen for during-treatment LC prediction. italic font in these tables, and the features from the HITL-BNs are emphasized with bold font in them. Especially, the features marked with italic and bold fonts come from both the PD-BN and HITL-BN.p-value=0.0367. For the testing dataset, the performance of pre- or during-treatment HITL-BN for LC prediction is 0.71 or 0.77 as illustrated by p-value=0.0406. The results of our numerical experiments are summarized in The performances of pre- and during-treatment HITL-BNs for LC prediction based on the discovery dataset are 0.82 (95%CI: 0.67-0.93) and 0.85 (95%CI: 0.75-0.95) as shown in Developed from our previous PD-BN method, the HITL-BN approach also includes feature selection and BN structure learning. To handle imbalanced data, the HITL-BN approach allows human agents to integrate the EML-based and UML-based feature selections in identifying important EKFs and non-EKFs in terms of outcome prediction. The reasons for the improvement of accuracy and explainability of HITL-BN based outcome prediction models in handling the imbalanced proportion of tumors with and without LC or I-ALBI in our HCC SBRT patient dataset could be twofold. First, since traditional ML approaches for crowdsourcing labeled training examples are not effective at locating the scarce minority class examples , they haAs some EKFs may be missing or not available in clinical practice, the HITL-BN approach can skip these EKFs or investigate the EKFs that physicians are most interested in along the integrated ranking list for the outcome prediction model development. The purpose of this study is to verify whether the HITL-BN approach can significantly improve the performance of HCC SBRT patients\u2019 outcome prediction models or not based on imbalanced data compared to the PD-BN method. The HITL-BN approach based on two UML approaches with RF and GBM had been implemented in our numerical experiments to test the hypophysis. Our choices of these two because they resemble BN in terms of graph/tree structures. However, if the number of UML algorithms increases, whether the predictive power of the HITL-BN based outcome prediction models could be improved or not and how much it can be improved are interesting research topics that beyond our current scope and we would like to explore in the next step.via the HITL-BN approach to conduct prospective personalized SBRT trials for improving HCC patients\u2019 radiation treatment outcomes.Our numerical experiments on developing the HITL-BN based outcome prediction models for HCC SBRT patients have shown that human intelligence can positively augment machine intelligence, and the assistance of human agents involved in the learning phase can enhance the capability of learning from imbalanced data. However, our study still has limitations in terms of small sample size and the assumption of two or more independent lesions in an HCC patient. In the next steps, in addition to developing more robust HITL-BN approaches by removing the within patient tumor independence assumption and conducting further external independent validations, we plan to explore an interactive human-computer interface change in albumin\u2013bilirubin score (ALBI) score at three months after SBRT were used in many studies to capture acute toxicity occurring <90 days after SBRT  of at least 5-fold and/or that of bilirubin of at least 3-fold compared to either the upper normal limit or the pretreatment level corresponding to grade 3 or higher hepatic toxicity without disease progression within 3 months after SBRT is one of the conditions to define radiation-induced liver disease  in HCC patients complicating with liver cirrhosis, and lower serum sodium concentration is a useful predictor for these patients  is the most important score when determining the incidence of radiation-induced liver disease during SBRT in patients with CP-A score 6 (INR) is derived from Protime which is calculated as a ratio of the patient\u2019s Protime to a control Protime standardized for the potency of the thromboplastin reagent developed by the World Health Organization. The MELD is used to prioritize patients for liver transplantation and includes results for creatinine, bilirubin, and Protime expressed as international normalized ratio (Protime-INR) . La. Latreatof death . While iof death , study sn cancer  52). In. Intreatsurvival . Prolong score 6 . Internaime-INR) . Evidencime-INR) . While lime-INR) , a mathearcinoma . It turnIn this study, we have developed a new HITL-BN approach for HCC patients\u2019 I-ALBI or LC prediction before and during SBRT based on previous PD-BN method. In addition to incorporating EK into its feature selection process, the HITL-BN approach allows humans to participate in an outcome prediction model building process for better handling of imbalanced HCC SBRT data. Especially, we created a novel feature selection mechanism for the HITL-BN approach by integrating the prediction strength of multiple UML methods and the explainable capability of the theoretically sound MB algorithms. Numerical experiments show that the HITL-BN based outcome prediction models significantly outperform the PD-BN based models during SBRT in terms of accuracy and explainability. In addition to gaining physicians\u2019 trust in clinical decision making, the HITL-BN approach has the potential of becoming an important component of future human-computer interface to bridge physicians and advanced ML techniques in improving HCC patients\u2019 treatment outcomes. Our approach can be applied to the outcome prediction of treating other types of cancer, but it still needs to be validated in external further independent datasets.The raw data supporting the conclusions of this article will be made available upon request from authors and per institutional guidelines.KC, TL, MM, RT, IE, and YL conceived of the presented idea. YL developed the theory and performed the computations. IE and DN verified the analytical methods. LD provided the testing dataset. All authors discussed the results and contributed to the final manuscript."}
+{"text": "Motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations, this work develops a theory of space-time integral currents with bounded variation in time, which enables a natural variational approach to the analysis of rate-independent geometric evolutions. Based on this, we further introduce the notion of Lipschitz deformation distance between integral currents, which arises physically as a (simplified) dissipation distance. Several results are obtained: A Helly-type compactness theorem, a deformation theorem, an isoperimetric inequality, and the equivalence of the convergence in deformation distance with the classical notion of weak* (or flat) convergence. Finally, we prove that the Lipschitz deformation distance agrees with the  homogeneous Whitney flat metric for boundaryless currents. Physically, this means that two seemingly different ways to measure the dissipation actually coincide. The recent work  introducb  along the dislocation movement. Also, The 2-current in space given asently in .b) move from time s to time t, is derived in )\u2264C by\u00a0 and so tH was assumed to possess T into In this section we consider progressive-in-time deformations of (boundaryless) integral currents. To see how one could generalize currents deformed via Then, by\u00a0 we have\\S itself.Unfortunately, the class of We first consider the case of Lipschitz homotopies in more detail. The following lemma also provides a further motivation for our definitions\u00a0,\u00a03.2) o o3.2) ofLet k-rectifiable carrier set R such that k-dimensional Jacobian of t,\u00a0x) with respect to Z. It follows, see, e.g., [k-covector field k-covector field Let kby\u00a0 and the sumption\u00a0 now implThen, by\u00a0, there eis shows\u00a0; the bouis shows\u00a0 follows R being the carrier set of T), instead of\u00a0 t t\\documeo obtain\u00a0  Let P,\u00a0S satisfy the conclusion of the theorem for our P,\u00a0T and S(t)  also follows from the estimates of Lemmas\u00a0We have As a corollary, we obtain the following version of the isoperimetric inequality: Let P,\u00a0S as in the deformation theorem withThe proof is similar to the one for the classical isoperimetric inequality and follows immediately from the deformation theorem: Assuming that k-currents via progressive-in-time deformations, namely Lip-integral currents. In all of the following, We now define a metric measuring the distance between two boundaryless integral (Lipschitz) deformation distance between k-currents.For With regard to the notion of convergence induced by the (Lipschitz) deformation distance, we have the following result:j from a subsequence of the j\u2019s, there are  For every N depend only on the dimensions and the domain P that can possibly satisfy the conclusion of the deformation theorem for a For the first direction, assume T)\u21920. By\u00a0 we have its, cf.\u00a0. Thus,\\dN sufficiently large , we may find a diagonal subsequence, still denoted by m bounded by Returning to our sequence T. Hence, also We now pass to the limit ur claim\u00a0.Finally, taking the upper limit of the mass estimate,integral homogeneous Whitney flat norm in the bounded Lipschitz domain Finally, we investigate the relationship of the deformation distance to the (i)(ii)(iii)(iv)For every The equivalence of\u00a0(i) and (ii) was proved in Theorem\u00a0global Whitney flat norms For the We can now prove the main result of this section, namely that the integral homogeneous Whitney flat distance is equal to the deformation distance. For S yields the above inequality.First, the inequalityQ) as in\u00a0. Taking k-face For the other inequality, let Q exists, the result holds trivially since in this case Q.Next, take any Q. According to this result, there is a polyhedral chain We now apply the approximation result of Proposition\u00a0k-polytope V as required.We claim that there exists For Q with d-current in global boundary operator). Hence, by the constancy theorem (see, e.g., [R is a fixed multiple of Q with globally finite mass, which we denote as Note that in codimension 1, i.e.,"}
+{"text": "Scientific Reports 10.1038/srep28840, published online 29 June 2016Correction to: This Article contains errors in the Methods section, subheading \u2018Mathematical Backgrounds\u2019.Formulation of Lemma 1 is incorrect:n, if n\u201d.\u201cGiven a genome should read:\u201cGiven a genome The corresponding proof:k such that all k-mers are hapaxes of \u201cThe minimum value of should read:k-mers in k are hapaxes too. But, if \u201cFor The proof of Lemma 2 is incorrect for the lack of an explicit characterization of \u201crandom genomes\u201d. Here a correct proof is given:n is obtained by a random process of generation where, at each step, one of four possible genome symbols is generated with probability 1/4. Let k-mers in a circular sequence k-mer occurs exactly once. Of course, any contiguous portion long n of k-mers and corresponds to a random genome of length n . In fact, all symbols of k-mers, then, maximum statistical homogeneity (required by randomness) is reached when k-mer has of occurring in one of the disjoint n-genomes of k-mer positions of a n-genome . This condition is expressed by equation (14) of the paper, from which equation First at all, a random genome of length Consequently, proposition 3\u2019s opening sentence:\u201cIn the class of genomes of length n, for every should read:\u201cIn the class of genomes of length n, for every Finally, in Results, subheading \u2018Information genomics laws\u2019 Eq. 7 should be removed, because it follows from (8), being"}
+{"text": "Secondly, we define a new connectivity, which can be referred to as divided connectivity, which differs from traditional connectivity, and present an equivalence relationship between traditional connectivity and our divided connectivity. Afterwards, we explore the structures of graphs based on the vertex-divided connectivity. Then, as an application of our divided operations, we show some necessary and sufficient conditions for a graph to be an Euler\u2019s graph. Finally, we propose some valuable and meaningful problems for further research.The graph connectivity is a fundamental concept in graph theory. In particular, it plays a vital role in applications related to the modern interconnection graphs, e.g., it can be used to measure the vulnerability of the corresponding graph, and is an important metric for reliability and fault tolerance of the graph. Here, firstly, we introduce two types of divided operations, named  Graph connectivity is one of the most basic concepts used in the application of graph theory, both in the combinatorial sense and in the algorithmic sense. Especially, it plays an important role in applications related to graph embedding. The connectivity can serve to assess the vulnerability of the corresponding graph and measure the capability of connection for a set of vertices in the graph. To better understand the characteristics of graph connectivity, a wide range of technical methods were developed and then used to analyze various problems.v of degree s, say s of even degree in a graph G with n vertices and m edges, namely, This classical issue has attracted attention to understanding and utilizing various operations regarding graphs. By consulting the literature, we found that the splitting operations on graphs can be divided two classes: one is the vertex-splitting operation and another is the edge-splitting operation. id graph . Mertzioned an On algorith a graph , O graphs, graphs just organically combine them into a whole, which is also the most natural and reasonable technique.By splitting and refining the network, the minimal structural features are obtained. Similar to how matter is made up of molecules, ions and atoms, the minimal structural features of networks can help us to understand the structure and topological properties of graphs. Battaglia et al., in , points The remaining sections of our article are organized as follows. We present a preliminary introductionin x in a simple graph, and we call neighbor set, so the cardinality x. We present two types of divided operations ..X\u2282V(G) tX of a connected graph G below.Thus, we obtain the structure of a connected graph having the most components of a disconnected graph Theorem\u00a0\u00a04.A connected graph G holds G is 2-connected. In fact, H can produce two or more graphs Q such that Q is 2-connected. The inverse of Theorem 4 is shown below.We show an example in Theorem\u00a05.Let each connected graph G, if H has no two nonadjacent vertices H an overlapping kernel graph of G. Evidently, there are two or more such overlapping kernel graphs of G. What characteristics does H have? First of all, H is connected obviously. An Euler\u2019s graph is one without odd-degree vertex, and such graphs were obtained first by the famous mathematician Euler. We present new characters for Euler\u2019s graphs here.Coinciding two nonadjacent vertices Theorem\u00a06.A simple graph G of n edges is a connected Euler\u2019s graph if and only if(E-1)\u00a0It can be divided into a cycle (E-2)\u00a0Its overlapping kernel graph H holds diameter Proof.\u00a0We prove (E-1) first.Necessary. Let G be a connected Euler\u2019s graph, not being a cycle. A 2-degree 2-connected v-divided operation is defined as follows: Take a vertex x. We divide the vertex 2-degree 2-connected v-divided operation. Thereby, we can perform such operation on Sufficiency. We can coincide a pair of vertices, G by performing a series of v-coinciding operations, because each We come to show (E-2) in the following.The proof of \u201cif\u201d. We perform a so-called non-neighbor coincident operation on a connected graph overlapping kernel graph of the original graph The proof of \u201conly if\u201d. Suppose that the overlapping kernel graph H of the connected graph G has its own diameter H. If H is a complete graph, and has no vertex having two neighbors of odd degrees. Thereby, H is a connected Euler\u2019s graph. Performing a series of 2-degree 2-connected v-divided operations on H produces the original graph G. Clearly, G is a connected Euler\u2019s graph. If H holds H is a connected Euler\u2019s graph since H has no odd-degree vertex. Obviously, the original graph G is the result of v-dividing H after performing a series of 2-degree 2-connected v-divided operations.The proof of the theorem is complete. \u25a1t, where t.Notice that each Sierpinski model k-connectivity for each maximal planar graph of order k-connectivity of an Euler\u2019s graph are not easy.To investigate an open question proposed by Battaglia et al. in , we defitivity \u03ba . HoweverX of X controls the topological structure of scale-free deterministic network control the topological structure of the network?We consider that finding connected-perfect subsets of a connected graph (respective networks) may be interesting and important for investigating topological structures of GNs. As known, the Sierpinski model G with its k-connectivity, our v-divided graph (respective networks) G easily, but it is very difficult to rebuild G from the disconnected vertex-deleting graph (respective networks) X of the vertex set G, in which For a connected simple graph (respective networks) We emphasize that our v-divided operation can dilute a connected Euler\u2019s graph into a cycle; conversely, our e-coincident operation can concentrate a cycle to an Euler\u2019s graph. Moreover, each connected simple graph can be obtained by deleting some edges from some Euler\u2019s graph. We ask the following: How many different Euler\u2019s graphs made by a given cycle are there?"}
+{"text": "R(\u03b7). Recently, schemes based on single-photon interference have been proposed to improve the key rate to Quantum key distribution \u2014 the establishment of information-theoretically secure keys based on quantum physics \u2014 is mainly limited by its practical performance, which is characterised by the dependence of the key rate on the channel transmittance  Measurement-device-independent QKD schemes suffer from a trade-off between ease of implementation  and high rates (quadratic improvement in rate). Here, the authors propose a protocol which offers both simple implementation and strong performances. A core advantage of QKD compared to other quantum communication tasks is that it is ready to implement with current commercially available off-the-shelf optical devices. However, two major characteristics of QKD\u2014its practical security and key-rate performance\u2014limit its real-life implementation. The key generation speed suffers heavily from transmission loss in the optical channel. Fundamentally, the asymptotic key rate for point-to-point QKD schemes is upper bounded by the repeaterless rate-transmittance bounds5, which are approximately linear functions of the transmittance, R\u2009\u2264\u2009O(\u03b7). For example, when \u03b7 is small, the PLOB repeaterless rate-transmittance bound5 is about 1.44\u03b7. Quantum repeaters8 have been proposed as a radical solution to this problem. Unfortunately, none of the quantum repeater proposals is easy to implement in the near term.Quantum key distribution (QKD)9. A typical QKD system can be divided into three parts: source, channel, and measurement. The security of the channel has been well addressed in the security proofs for QKD12. The source is relatively simple and can be well characterised13. In contrast, the measurement device is complicated and difficult to calibrate. Moreover, an adversary could manipulate the measurement device by sending unexpected signals15. To solve this implementation security problem, measurement-device-independent quantum key distribution (MDI-QKD) schemes have been proposed to close the detection loopholes once and for all16. Various experimental systems have been successfully demonstrated20, with extension to a communication network21.In real-life use, the deviation of the realistic behaviour of physical devices from their ideal ones gives rise to critical issues in practical security. There are many quantum attacks that can take advantage of the loopholes introduced by device imperfections15.A generic MDI-QKD setup is shown in Fig.\u00a016, in which Alice and Bob both encode a \u2018dual-rail\u2019 qubit into a single-photon subspace on two polarization modes, unfortunately, cannot overcome this bound. Later, alternative schemes were proposed23 in which the qubit is encoded into two optical time bins. We refer to schemes of this type as two-mode MDI-QKD, in the sense that the single-side key information is encoded in the relative phase of the coherent states in the two orthogonal optical modes, i.e., second-quantized electromagnetic fields. To correlate Alice\u2019s and Bob\u2019s encoded information in a two-mode scheme, a successful two-photon interference measurement is required. If either Alice or Bob\u2019s emitted photon is lost in transmission, there will be no conclusive detection result. For example, in the time-bin encoding scheme23 shown in Fig.\u00a0A1 and A2 and Bob emitting B1 and B2. Only when both the interference between modes A1 and B1 and that between A2 and B2 yield successful detection can Alice restore Bob\u2019s raw key information. Thus, successful interference requires a coincidence detection. Due to this coincidence-detection requirement, rounds with only a single detection are discarded, resulting in a relatively low key generation rate\u2014one that is a linear function of the transmittance, O(\u03b7). From the perspective of practical implementation, however, coincidence detection also has certain merits. This approach can ensure stable optical interference, while Alice and Bob need only to stabilise the relative phases between the two modes.Strictly speaking, MDI-QKD is not a point-to-point scheme, as there is an interference site between Alice and Bob. Consequently, it is not necessarily limited by the repeaterless rate-transmittance bound. Nevertheless, the original MDI-QKD scheme24, illustrated in Fig.\u00a026 (known as phase-matching QKD) or the intensity27 (known as sending-or-not-sending TF-QKD) of coherent states. In this work, we refer to these twin-field-type schemes as one-mode MDI-QKD schemes for a conceptual comparison to the traditional two-mode MDI-QKD schemes, since the single-side information in these schemes is encoded into a single-optical mode in each round. We remark that the single-optical-mode encoding MDI-QKD scheme was first proposed in ref. 28 as \u201cMDI-B92\u201d scheme. Similar to the Duan-Lukin-Cirac-Zoller-type repeater design29, such one-mode schemes use single-photon interference instead of coincidence detection, hence yielding a quadratic improvement in key rate compared to two-mode schemes26. As a result, they can overcome the point-to-point linear key-rate bound5. Unfortunately, one-mode schemes are more challenging to implement due to the unstable optical interference resulting from the lack of global phase references. For example, in the phase-matching QKD (PM-QKD) scheme25, the key information is encoded into the global phase of Alice\u2019s and Bob\u2019s coherent states. The phases of the coherent states generated by two remote and independent lasers need to be matched at the measurement site. A small phase drift or fluctuation caused by the lasers and/or channels is hazardous for key generation.Coincidence detection is the essential factor that prevents MDI-QKD from overcoming the linear key-rate bound. To eliminate this requirement, a new type of MDI-QKD scheme called twin-field quantum key distribution (TF-QKD) based on encoding information into a single-optical mode have been proposed\u221215\u2009s), optical length (~200\u2009nm) and light frequency (~100\u2009kHz). Recently, experimentalists have made great efforts to demonstrate high-performance in one-mode schemes, utilising high-end technologies to perform a precise control operation to stabilise the global phase by locking the frequency and phase of the coherent states37. However, this increases the experimental difficulty and undermines the applicability of one-mode schemes in real life.At first glance, it seems that we cannot simultaneously enjoy the advantages of one-mode schemes  and two-mode schemes , due to an intrinsic trade-off between the information-encoding efficiency and robustness. On the one hand, the relative information among different optical modes is more difficult to retrieve when the channel loss is large. On the other hand, the global phase of a coherent state is not as stable as the relative phase between two coherent states travelling through the same quantum channel. In a typical 200-km fibre with a telecommunication frequency of 1550 nm, the phase of a coherent state is susceptible to small fluctuations in the optical transmission time  during data postprocessing to optimise the system performance.In this work, we propose a mode-pairing MDI-QKD scheme that aims to offer both\u2014simple implementation and high performance. Hereafter, we refer to this scheme as the mode-pairing scheme for simplicity. By observing that the majority of detection events are single-clicks and are discard in the two-mode MDI-QKD schemes, we try to recycle the discarded single-click in the mode-pairing scheme. To do that, the coherent states in the transmitted modes are initially prepared independently with randomly encoded information. Based on the fact that the two detection events used to read out the encoded information do not need to occur at two predetermined locations, the key is extracted from two paired detection events rather than coincidence detection, as shown in Fig.\u00a040 and discrete phase randomisation here. A complete description of the mode-pairing scheme is given in the Methods\u2019 subsection \u201cMode-pairing scheme with decoy states\u201d.In the mode-pairing scheme, Alice and Bob first prepare coherent states with independently and randomly chosen intensities and phases in each emitted optical mode. These coherent states are sent to the untrusted measurement site, Charlie. Based on Charlie\u2019s announced measurement results, Alice and Bob pair the optical modes with successful detection and determine the key bits and bases for each mode pair locally. They then sift the bases and generate secure key bits via postprocessing. The scheme is introduced in Box\u00a0Z-pair data, since they have a much lower quantum bit error rate X-pair data. The encoding of the mode-pairing scheme in Box\u00a023. If Alice\u2019s two paired optical modes {Ai,\u2009Aj} are assigned to the Z-basis, then the state of the two optical modes is either \u03baa is the encoded key information and \u03ba. In the other case, in which the two optical modes {Ai,\u2009Aj} are assigned to the X-basis, we can rewrite their two independent random phases In the mode-pairing scheme, we mainly consider the keys generated from the mentclass2pt{minim\u03d5a becomes a global random phase on the pulse pair, while \u03d5a and \u03c0). By definition, we have X-pair state can be written as,\u03bca\u2009\u2208\u2009{0,\u2009\u03bc}. When \u03b8\u2009=\u20090 or \u03c0/2, Alice emits X-basis or Y-basis states, respectively, as used in the time-bin encoding MDI-QKD scheme23.In this way, the phase Z-pair state in Eq.  phase randomisation, the emitted Z- and X-pair states can be regarded as a mixture of photon number states40. Then, Alice and Bob can estimate the detections caused by the pairs where they both emit single photons and use them to generate secure keys, in a manner similar to traditional two-mode schemes. Therefore, the security of the mode-pairing scheme is similar to that of two-mode schemes. Nevertheless, the mode-pairing scheme in Box\u00a0Ai} are independent and identically distributed (i.i.d.). Therefore, the information encoded in different optical modes is completely decoupled.The emitted states in different optical modes {Based on the postselection of clicked signals, different optical modes are paired afterwards. The relative information between the two modes is then converted into raw key data.We remark that in either the e in Eq.  or the Xe in Eq. , there i42. It is the untrusted measurement site that determines the location of successful detection and thereby affects the pairing setting. The \u2018dual-rail\u2019 qubits encoded on the single photons are \u2018postselected\u2019 on the basis of this detection. By virtual of the independence of the optical modes, the information encoded in the \u2018postselected\u2019 qubits cannot be revealed from other optical pulses.In the mode-pairing scheme, the key information is determined not in the state preparation step, but by the detection location, sharing some similarities with the differential-phase-shifting QKD scheme27 also uses a Z-basis time-bin encoding, whereby either Alice or Bob emits an optical mode to generate key bits. The state preparation of the mode-pairing scheme shares similarities with the SNS-TFQKD scheme. However, the information of the mode-pairing scheme is encoded into the relative information between the two optical modes. As a result, the basis-sifting and key mapping of the mode-pairing scheme follow different logic originated from the time-bin encoding MDI-QKD scheme23. Note that in the SNS scheme, bits 0 and 1 are highly biased in the Z basis, whereas in the mode-pairing scheme, they are evenly distributed.For another comparison, the sending-or-not-sending (SNS) TF-QKD schemeX-basis error rate fairly estimates the Z-basis phase error rate for the signals for which Alice and Bob both emit single photons.A critical issue in the security analysis of the mode-pairing scheme is to maintain the flexibility to determine in which two optical modes to perform the overall photon number measurement until Charlie announces the detection results. Note that, in the original two-mode QKD schemes, the encoders can always be assumed to perform an overall photon number measurement and post-select the single-photon components as good \u2018dual-rail\u2019 qubits before they emit their signals to Charlie. In the mode-pairing scheme, however, this is not viable because the optical pulse pair, for which the single-photon component is defined, is postselected based on Charlie\u2019s detection announcement. To solve this problem, we introduce source replacement for the random phases in the coherent states to purify them as ancillary qudits and define an indirect overall photon number measurement on them. The source-replacement procedure can be found in the Methods\u2019 subsection \u201cSource replacement of the encoding state\u201d. Conditioned on the indirect overall photon number measurement result to be single-photon states, the In Supplementary Note\u00a0Box 1 Mode-pairing schemeState preparation: In the i-th round , Alice prepares a coherent state Ai with an intensity \u03bc} and a phase \u03c0). Similarly, Bob randomly chooses Bi.Measurement: Alice and Bob send modes Ai and Bi to Charlie, who performs single-photon interference measurements. Charlie announces the click patterns for both detectors L and R.N rounds. Then, they postprocess the data as follows.Alice and Bob repeat the above two steps for Mode pairing: For all rounds with successful detection, in which one and only one of the two detectors clicks, Alice and Bob apply a strategy of grouping two clicked rounds as a pair. The encoded phases and intensities in these two rounds form a data pair. A simple pairing strategy is introduced in Box\u00a0Basis sifting: Based on the intensities of the two grouped rounds indexed by i and j, Alice labels the \u2018basis\u2019 of the data pair as Z if the intensities are  or , as X if the intensities are , or as \u20180\u2019 if the intensities are . Bob sets the basis using the same method. Alice and Bob announce the basis of each data pair; if they both announce the basis X or Z, they maintain the data pairs, whereas otherwise, the data pairs are discarded.Key mapping: For each Z-basis pair (Z-pair for simplicity) at locations i and j, Alice sets her key as \u03baa\u2009=\u20090 if \u03baa\u2009=\u20091 if X-basis pair (X-pair for simplicity) at locations i and j, the key is extracted from the relative phase \u03bab and determines \u03b8b. The difference in the key mapping for Z-pairs is that, Bob sets the raw key bit \u03bab as 0 if \u03bab\u2009=\u20091 if X-pairs, if Charlie\u2019s detection announcement is  or , Bob keeps the bit \u03bab; otherwise, if Charlie\u2019s announcement is  or , Bob flips \u03bab. For the X-pairs, Alice and Bob announce the alignment angles \u03b8a and \u03b8b. If \u03b8a\u2009=\u2009\u03b8b, then the data pairs are kept; otherwise, the data pairs are discarded.Parameter estimation: Alice and Bob estimate the fraction of clicked signals q and the corresponding phase error rate Z-pairs where Alice and Bob both emit a single photon at locations i and j, using the data of the Z-pairs and X-pairs. They also estimate the quantum bit error rate E\u03bc,\u2009\u03bc),Z, E\u03bc,\u2009\u03bc),Z. The details are shown in the simple pairing strategy in Box\u00a0i-th round is denoted by a Boolean variable Ci that indicates whether the detection is successful. That is, Ci\u2009=\u20091 implies that either the detector L or R clicks. Otherwise, there is no click or double clicks.Here, we consider a simple pairing strategy in which Alice pairs adjacent detection pulses together if the time interval between them is not too large (\u2264rp (i.e. the average number of pairs generated per pulse). We assume that Alice and Bob choose intensities 0 and \u03bc with equal probability, maximising the number of successful pairs in the Z basis. With a typical QKD channel model, the pairing rate rp is calculated as shown in the Methods\u2019 subsection \u201cMode-pairing-efficiency calculation\u201d,p is the probability that the emitted pulses result in a click event, given approximately by \u03b7s\u03bc. Here, \u03b7s and \u03b7 denote the channel transmittance from Alice to Charlie and the total transmittance from Alice to Bob, respectively. When the channel is symmetric for Alice and Bob, we have p in a pure-loss channel is given in Supplementary Note\u00a0rp and the detection probability p can be directly obtained by experimentation.To check the efficiency of this pairing strategy, let us calculate the pairing rate rp. Now, let us check the scaling of rp with the channel transmittance in the symmetric-channel case. If the local phase reference is sufficiently stable, then the maximal interval can be set to l\u2009\u2192\u2009+\u221e. In this case,\u03bc\u2009=\u2009O(1), as evaluated in Supplementary Note\u00a0l\u2009=\u20091; then,The raw key rate mainly depends on the pairing rate 23. Now, if we consider a finite value of l, the dependence of rp on \u03b7 will be decided by how the denominator of the first term in Eq. (p[1\u2009\u2212\u2009(1\u2212p)l], depends on p\u2009\u2248\u2009\u03b7s\u03bc. When pl \u226b 1, rp scales with p linearly, hence pl \u226a 1, it scales with p2, resulting in rp\u2009=\u2009O(\u03b7). Around pl\u2009=\u20091, there will be a performance transition from rp\u2009=\u2009O(\u03b7).In this case, the experimental requirements for the mode-pairing scheme are close to those of the existing time-bin MDI-QKD schemem in Eq. , p[1\u2009\u2212\u2009, q is the fraction of Z-pairs caused by single-photon-pair states \u03c1 in which both Alice and Bob send single-photon states in the two paired modes, \u03c1, f is the error-correction efficiency, and E\u03bc,\u2009\u03bc),Z and the phase error 44. A detailed estimation procedure for q and The key rate of the mode-pairing scheme, as rigorously analysed in the Supplementary Note\u00a0X-pair sifting condition \u03b8a\u2009=\u2009\u03b8b is impossible to fulfil exactly. This results in insufficient data for X-basis error rate estimation. To solve this problem, one can apply discrete phase randomisation45 such that \u03b8a and \u03b8b are chosen from a discrete set. We expect the discretisation effect to be negligible when the number of discrete phases is reasonably large, such as D\u2009=\u200916, similar to the situation in previous works on one-mode MDI-QKD46.During the key mapping step in Box\u00a0l of the mode-pairing scheme as a value between 1 and 1\u2009\u00d7\u2009106, aiming to illustrate the dependence of the key rate on l. We also compare the key rate of the mode-pairing scheme with those of a typical two-mode scheme, time-bin encoding MDI-QKD23, and two one-mode schemes \u2014 PM-QKD46 and SNS-TFQKD47. The simulation results are shown in Fig.\u00a0l\u2009=\u20092000. Here, we compare the asymptotic key-rate performance of all the schemes under the scenario of one-way local-operation and classical communication. The simulation formulas for these schemes are listed in Supplementary Note\u00a049 show that the key-rate performance of SNS-TFQKD can be further improved by introducing the two-way classical communication51. We will leave the advanced key distillation for future studies.Based on the above analysis, we simulate the asymptotic performance of the mode-pairing scheme under a typical symmetric quantum-channel model, using practical experimental parameter settings. We assign the maximal pairing interval l\u2009=\u20091, show a performance comparable to that of the original two-mode scheme. These two schemes have the same scaling property, i.e., R\u2009=\u2009O(\u03b7). The deviation is caused by an extra sifting factor in the mode-pairing scheme as a result of independent encoding. When the maximal pairing interval l is increased to 1\u2009\u00d7\u2009103, the key rate is significantly enhanced by 3 orders of magnitude compared to the l\u2009=\u20091 case, making it able to surpass the linear key-rate bound. If we further increase l above 1\u2009\u00d7\u2009105, then the mode-pairing scheme has a similar key rate to PM-QKD and SNS-TFQKD and a scaling property given by l. When l falls within the range of 1 to 1\u2009\u00d7\u2009106, the key rate of the mode-pairing scheme lies between the two extreme cases of O(\u03b7) and As shown in Fig.\u00a0n in Eq. .32). Hence, the coherence time of the laser is around 333\u2009\u03bcs. In practice, the frequency fluctuation of the lasers will affect the stabilization of the phase. To test the feasibility of the mode-pairing scheme, we perform an interference experiment using a commercial optical communication system with a repetition rate of 625 MHz. The experiment detail is shown in Supplementary Note\u00a0l\u2009=\u20093000\u2009~\u20094000. If we apply the state-of-the-art optical communication system with the repetition rate of 4\u2009GHz37, we can realize a pairing interval over l\u2009=\u200920000. As an extra remark, our current discussion on the implementation of the mode-pairing scheme is based on the multiplexing of optical time-bin modes. Nonetheless, the proposed mode-pairing design is generic for the multiplexing of other optical degrees of freedom. For example, we can introduce frequency multiplexing. The optical modes with different frequencies are first prepared and interfered independently, i.e., only the pulses with the same frequency will be interfered. After the announcement of detection results, Alice and Bob then pair the locations with different frequencies during the post-processing. This can be used to increase the effective maximal pairing interval to an even larger value without the global phase locking. From Fig.\u00a0l\u2009=\u20091\u2009\u00d7\u2009104 remains \u03b7 is smaller than 30 dB, corresponding to a communication distance of 300\u2009km. The asymptotic key rate of the mode-pairing scheme is 3 to 5 orders of magnitude higher than that of the two-mode scheme. We remark that the decoherence effect caused by the optical-fibre channel is negligible compared to the laser coherence time. When the fibre length is around 500 km, the velocity of phase drift in the fibre is <10\u2009rad/ms32, which can be calibrated using strong laser pulses without the need for real-time feedback control. As a result, the value of l depends only upon the local phase reference and not the communication distance.In typical optical experiments, the typical line width of a common commercial laser is 3\u2009kHz  to be  to simplify the notations.The main idea of the security proof for the mode-pairing scheme is to introduce an entanglement-based scheme and reduce the security of the scheme to that of a traditional two-mode MDI-QKD scheme. To realise this, we perform a systematic source-replacement procedureD phases, evenly distributed in [0,\u20092\u03c0). We expect the corresponding correction term in the security analysis due to the discretisation effect to be negligible46. Second, in the security proof, we modify the phase encoding and postprocessing procedures, as shown in Table\u00a0A1 and A2 based on two random phases X-basis processing, she calculates the relative phase difference \u03b8a in the range of [0,\u2009\u03c0) and a raw key bit \u03baa. We modify these procedures as follows: in addition to the two random phases A1 and A2, respectively. During the X-basis processing, she calculates the relative phase difference For convenience in the security proof, we slightly modify the scheme described in Box\u00a0d\u2009=\u2009D) j1 in the first round. Based on the values of With the modification above, Alice further generates a random bit In Fig.\u00a0A1. The controlled-phase gate is defined asa\u2020 and a are the creation and annihilation operators, respectively, of mode A1. Alice also applies a controlled-phase gate A1.Here Alice applies a controlled-phase gate Z-basis and X-basis postprocessing, respectively.In the entanglement-based mode-pairing scheme, Alice and Bob generate the composite encoding state M on A1 and A2. The construction of M is described in Supplementary Note\u00a0M, Alice (same for Bob) is able to determine at which two locations to perform the global photon number measurement after Charlie\u2019s announcement. With this measurement, Alice and Bob can further reduce the encoding state to a two-mode scheme. The detailed security proof is provided in Supplementary Note\u00a0A key point in our security proof is that we replace the random phases and register them into purified systems mentclass2pt{minim\u03bd to estimate the parameters q11 and State preparation: In the i-th round , Alice prepares a coherent state Ai with an intensity \u03bd,\u2009\u03bc} (0\u2009<\u2009\u03bd\u2009<\u2009\u03bc\u2009<\u20091) and a phase Bi.Measurement: , Alice and Bob establish a strategy for grouping two clicked rounds as a pair. A specific pairing strategy is introduced in Box\u00a0Basis sifting: Based on the intensities of two grouped rounds, Alice labels the \u2018basis\u2019 of the data pair as: Z if one of the intensities is 0 and the other is nonzero;X if both of the intensities are the same and nonzero; orZ and X bases; or\u20180\u2019 if the intensities are , which will be reserved for decoy estimation of both the \u2018discard\u2019 when both intensities are nonzero and not equal.X, Z, \u20180\u2019, or \u2018discard\u2019) and the sum of the intensities i,\u2009j. If the announced bases are the same and no \u2018discard\u2019 state occurs, they record the pair basis and maintain the data pairs; if one of the announced bases is \u20180\u2019 and the other one is X(Z), they record the pair basis as X(Z) and keep the data pairs; if both of the announced bases are \u20180\u2019, they record the pair basis as \u20180\u2019 and maintain the data pairs; and otherwise, they discard the data. See also Table\u00a0See also Table\u00a0Key mapping:  that corresponds to the simple mode-pairing strategy in Box\u00a0p during each round, and the maximal pairing interval l.We calculate the expected pairing number Fk,\u2009Rk) of the k-th pair, Alice and Bob also record the starting location Sk, which indicates the location at which the first successful detection signal occurs during the pairing procedure for the k-th pair. If the second successful detection signal Rk is found within the next l locations, then Fk\u2009=\u2009Sk; otherwise, Fk will be larger than Sk. Let Gk\u2009\u2254\u2009Sk+1\u2009\u2212\u2009Sk denote a random variable that reflects the location gap between the k-th and (k\u2009+\u20091)-th starting pulses. Then the expected pairing number per pulse is given byGk. First, we split it into two parts,Hk:\u2009=\u2009Rk\u2009\u2212\u2009Sk and For calculation convenience, we assume that in addition to the front and rear locations (It is easy to show that Hk is more complex. Suppose that we already know the expectation value The calculation of the pulse interval 59, who consider a similar MDI-QKD protocol that match the clicked data to generate key information. Under the assumption that the single-photon distributions in all the Charlie\u2019s successful detection events are independent and identically distributed, the authors simulate the performance of the protocol and show its ability to break the repeaterless rate-transmittance bound.After we submitted our work for reviewing, we became aware of a relevant work by Xie et al.Supplementary Information"}
+{"text": "We derive a variety of results on this problem. The problem is strongly NP-hard even on graphs of treewidth\u00a02, and it does not allow a polynomial time approximation scheme (unless P=NP). Furthermore, we discuss the performance of a simple greedy algorithm, and we construct and analyze a number of parameterized and exact algorithms.An instance of the non-preemptive tree packing problem consists of an undirected graph  The tree packing problem of Nash-Williams. For a given undirected connected graph w(e) of these spanning trees. For example, consider Fig.\u00a0G is a complete graph on three vertices, and Williams  considermentclass2pt{minimNash-Williams  derives w(e) time units. The objective now is to activate the edges in such a way that the graph remains connected for the longest possible overall time. Figure\u00a0The tree packing problem may also be interpreted as a scheduling problem: Every edge entclass1pt{minimaentclass1pt{minimaThe non-preemptive version of tree packing. We consider a non-preemptive variant of the above tree packing problem, where the execution of edges must not be preempted: Every edge e is activated at some time point non-preemptive tree packing (N-TreePack for short), and the optimal objective value for a graph In the example in Fig.\u00a0Related literature. The non-preemptive tree packing problem can be understood as a topic with connections to several different areas. First of all, it can be understood as a non-preemptive scheduling problem equipped with a structurally rich global constraint. In scheduling it is the conventional case to assume non-preemption of the scheduled tasks . This sf Pinedo\u00a0 the comptime-varying graphs (TVG). These are graphs over time, where every edge is equipped with the information at which time it is available. Time-varying graphs are used to model networks, where change in the network topology is an inherent part of the system. This includes for example delay-tolerant networks where information links often fail, like satellite networks, vehicular or passenger networks.Our model is also strongly related to the area of constant connected  TVGs anonnected , or to eonnected . Our proFinally, our problem is a modification of the classic tree packing problem  the greedy algorithm fails to find an optimal solution. We show by means of a gap-reduction that (unless P=NP) problem N-TreePack does not allow a polynomial time approximation algorithm with worst case ratio strictly better than 7/6; this of course excludes the existence of a PTAS.With respect to polynomial time approximation, we introduce a simple greedy algorithm which has a worst case guarantee of N-TreePack where both the treewidth and the maximum edge weight are bounded by a constant k allows an FPT-algorithm whose running time is linear in |E|.  Furthermore we design an exact algorithm for N-TreePack whose  running time is bounded by Finally, we derive a number of FPT-results in the area of parameterized complexity. The special case of Organization of the paper. Section\u00a0N-TreePack, and Sect.\u00a0a,\u00a0b] denotes the time slot starting at a and ending at b. For an integer t-th time slot or time slot t. Every graph edge cutinduced subgraph of G by v from G, we obtain the graph We write  by West .N-TreePack is a weighted graph , where schedule for instance  is a map e to its activation time e, the activity interval of e is t-th time slot, and we let V with all the edges that are active in the t-th time slot. Finally, we define the objective valueAn instance for problem G is connected does not necessarily have to be one continuous time interval. Formally, if t, where We clarify a few points in this definition: First, the time during which Throughout the paper, we investigate the (parameterized) complexity of non-preemptive tree packing with respect to different graph classes and structural graph parameters.treewidth of a graph is a popular parameter in the area of parameterized algorithms and measures in some sense how close the graph is to a tree. It can be defined as the minimum integer G is subgraph of a k-tree . For graph Q], , ..., Graph Since graph Graph Since The induction yields for Q], , ..., Q that start at an even multiple of Q) and fully-connected during the time intervals , , ..., Q that start at an odd multiple of Q).The graph Q,\u00a02Q], , ..., Q], , ..., n groups with sum Q, we get a solution for the instance of 3-Partition.Next, consider the subgraph 3-Partition instance has a solution, then we build a schedule Vice versa, if the Hamilton-3-regProblem Instance: A bipartite, 3-regular graph Question: Does The reduction is done in two steps. The first step transforms an instance Hamilton-3-reg into a new 4-regular graph H with the properties described in Lemma\u00a0H from Lemma\u00a0N-TreePack.In this section, we show that it is NP-hard to decide whether there exists a schedule of objective value at least 7. The reduction is from the following version of the Hamilton cycle problem; see Akiyama, Nishizeki & Saito Problem Hentclass1pt{minimaentclass1pt{minimaHamilton-3-reg as input and outputs a 4-regular bipartite graph H together with an edge special edge), so that the following holds: (i)Hamilton-3-reg, then the new graph H contains a Hamilton cycle that traverses the special edge If (ii)Hamilton-3-reg, then the new graph H has no Hamilton path starting in vertex u.If There is a polynomial time algorithm that takes an instance H then consists out of the following parts: There are two copies of H is bipartite and 4-regular, so it remains to prove claims (i) and (ii).The reduction is sketched in Fig.\u00a0C in H using the edge u, and traverse all the vertices of H which uses the edge For claim (i), assume that H has a Hamilton path u, we have to prove that P. Note that if P necessarily switches between P first encounters P switches between P which lie in For claim (ii), we prove the contrapositive. Assume that H be a 4-regular bipartite graph as described in Lemma\u00a0H, and let G,\u00a0w) of N-TreePack from H. An informal sketch of this instance  is depicted in Fig.\u00a0G has the vertex setG has the following edges and edge weights:U and Z, the graph G has exactly the same edges as the graph H. For every such edge e, we set Between the vertex sets i-th gadget of type L and has edges and edge weights as depicted in Fig.\u00a0For every i-th gadget of type R and has edges and edge weights as depicted in Fig.\u00a0For every gadgetC.Finally, the two edges Now let G,\u00a0w) allows some schedule i-th gadget of type L will consist of either one or two connected components under schedule fully-connected during the t-th time slot. If there are two connected components  be the instance described above. Every schedule of objective value 7 for  satisfies the following. (i)R is fully-connected during time slots 2 and 6, and semi-connected during each of the remaining five time slots.A gadget of type (ii)For each (iii)C is fully-connected during time slot 4, and semi-connected during each of the remaining six time slots.The gadget Let  be the corresponding N-TreePack instance. If H contains a Hamilton cycle which uses the special edge, then Let the graph entclass1pt{minimaW using R are fully-connected during time slots 2 and 6, and semi-connected otherwise.All gadgets of type L are fully-connected during time slots 1, 3, 5, and 7, and semi-connected otherwise.All gadgets of type C is fully-connected during time slot 4, and semi-connected otherwise.The gadget All edges All edges All edges All edges It is easy to see that a schedule t, which edges are scheduled and which gadgets are fully connected during the the t-th time slot H form a matching of H during the time slots 1,2,3,5,6, and 7, and form a Hamilton path of H during the time slot 4. By checking each of the cases Let mentclass2pt{minimH and the special edge G,\u00a0w) be the corresponding N-TreePack instance. If H contains a Hamilton path starting at vertex u.Let the graph entclass1pt{minimav, which are both in E(H) and active during the t-th time slot. The strategy of the proof will be to repeatedly deduce some conditions for So assume there exists a schedule t-th time slot both the gadget C are semi-connected. But of course at least one edge incident to t-th time slot. Hence First, recall Lemma\u00a0k vertices is acyclic, has k edges, and therefore has k connected components. But because R and the gadget C are semi-connected during time slot 1, this implies that every single gadget of type L is actually fully-connected during time slot 1. The same argument holds for time slot 7. In total, together with Lemma\u00a0L is fully-connected during the t-th time slot, if and only if Next, consider the graph L are semi-connected during time slot 4. For the sake of contradiction, assume L and R are semi-connected. We also have for all H starting at Finally, we claim By combining Lemmas\u00a0N-TreePack it is strongly NP-hard to decide whether there exists a schedule of objective value at least\u00a07. For All edge weights in the above reduction are in the set N-TreePack is strongly NP-hard, even if all edge weights are in Problem L. Figure\u00a0Edges of weight\u00a07 only show up in the gadget of type N-TreePack instances with optimal objective value\u00a06 and N-TreePack instances with optimal objective value\u00a07, we also get the following in approximability result.As it is NP-hard to distinguish between N-TreePack with worst case guarantee better than 7/6. Unless P=NP, there is no polynomial time approximation algorithm for In Sect.\u00a0N-TreePack on a graph with m edges, it can be decided in For an instance of E into set Let G after contracting the edge set G after contracting the edge set F is acyclic in graph The matroid F is acyclic in graph The matroid The matroid Recall that a base of a matroid is a maximal independent set. By construction, the bases of F is a base of F induces a spanning tree of G.If a set F is a base of F induces a spanning tree of G.If a set F is a base of F induces a spanning tree of G.If a set Now observe that scheduling an edge of weight 1 is equivalent to choosing in which of the three time slots 1,2 or 3 it is scheduled. Scheduling an edge 2 is equivalent to always schedule it in time slot 2 and choose whether it is scheduled in time slot 1 or 3. From these facts together with Lemma\u00a0By Lemma\u00a0mentclass2pt{minimlgorithm . \\documeBy a similar (but simpler) argument we can also decide in polynomial time whether t. By t.We introduce a greedy algorithm that maintains connectivity by always activating edges of the largest possible weight. Formally, we let c components, we turn it into a tree by adding a maximum weight subset A exists, the Greedy algorithm terminates. Now the Greedy algorithm starts its work by initializing n vertices and for every For every graph For the positive result, we consider the time slot mentclass2pt{minimn vertices with weights For the negative result, we consider the complete graph e Palmer\u00a0) says th(i)G is a cactus graph.(ii)N-TreePack instance  to optimality.For every choice For every connected graph N-TreePack instance into smaller instances that do not interact with each other, it is sufficient to prove the statement for two-connected cactus graphs. Hence we will assume that G is a cycle on n vertices, and we let G,\u00a0w) equals We first show that (i) implies (ii). Since cut-vertices split an H on the four vertices In order to show that (ii) implies (i), we first consider the graph G does contain a subdivision w(e) of the edges H; if an edge G,\u00a0w) satisfies Now let N-TreePack is fixed parameter tractable with respect to various parameters. As the problem is already NP-hard even for highly restricted graphs, we can only hope for positive parameterized complexity results for quite restricitive graph parameters, or when additionally the edge weights are restricted. Note that Theorems\u00a0N-TreePack, even if either the treewidth or the edge weights are bounded by a constant.In this section, we show that problem N-TreePack is fixed parameter tractable with respect to t the treewidth of the input graph.Problem t, there is a vertex t . As every edge incident to v has weight at most T. We introduce Boolean variables As the graph  theorem  implies N-TreePack is solvable in exponential time On input graphs T all graphs E|! cases. Each case is easily checked and evaluated in By Lemma\u00a0N-TreePack is fixed parameter tractable with respect to the size k of a feedback edge set. There is a kernel with Problem Note that the input graph mentclass2pt{minimNow the kernelization procedure is clear: As long as N-TreePack is tractable on instances that in a certain sense are close to the preemptive tree packing problem of Nash-Williams.The last theorem of this section shows that problem G,\u00a0w) be an instance of N-TreePack on m edges, so that k edges have weight at most k. Then an optimal solution can be found in Let  We have shown that"}
+{"text": "Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. In this paper, we solved some graph equations of detour two-distance graphs, detour three-distance graphs, detour antipodal graphs involving with the line graphs. The recent rapid growth in the Internet of things has necessitated the development of new approaches to persistent issues in wireless sensor networks. These issues include minimum obstacles in the end-to-end communication path, location accuracy, latency, and delay, among others. These problems can be mitigated by using the distance graph to create local algorithms, i.e., algorithms with minimum communication rounds. We study distance graph applications in wireless sensor networks with a focus on minimum path obstacles and high localization accuracy.A wireless sensor network (WSN) is a network of tiny wireless sensors that can sense a parameter of interest. The sensed data is forwarded to a base station through the formed ad hoc network of sensor nodes. There are many application areas of WSNs, including M2M communication and the Internet of Things (IoT). WSNs are a fundamental building block of smart homes, smart workplaces, and smart cities, among others. It has a lot of other essential purposes for modern technology, such as scientific research, rescue operations, and scientific discoveries. As sensors are a power constraint tiny devices, energy conservation for extending the network\u2019s lifetime is a challenging issue. A wireless sensor network\u2019s lifetime heavily depends on innovative schemes that mitigate energy consumption. The distance graph is used to form and localize an ad hoc network of sensor nodes so that sensed data can be forwarded to the base station with little energy cost.Therefore, finding the solutions to these graph equations is essential. A lot of research has been done by many researchers during the past fifty years, and their results have made a significant contribution in graph theory.X be a nontrivial finite connected graph. Every graph X with detour distance D defines a metric space. The n-distance graph of X, denoted by u and v are adjacent in u and v in this graph are adjacent if and only if detour n-distance graph of X. If n equals the detour diameter of X, then this graph is called the detour antipodal graph of X, which is denoted by X is said to be a detour self n-distance graph if Let G is the graph whose vertices correspond to the edges of G and wherein two vertices are adjacent in G.The line graph In this work, we consider the detour distance graphs. Specifically, we solve the graph equations involving detour two-distance graphs, detour three-distance graphs, detour antipodal distance graphs, line graphs, and the complement of graphs. In addition, we solve some equations involving two-distance graphs, three-distance graphs, and antipodal distance graphs with the graphs mentioned earlier.X such that n-distance graph equations, which can be found in [Harary, Heode, and Kedlacek first studied the two-distance graph. They investigated the connectedness of two-distance graphs. This graph and the relationship between the two-distance graph and line graph was further studied in ,6,7,8,9.found in . S. K Sifound in ,15,16,17found in ,19,20. Ifound in .Motivated by the results listed above, we solved some graph equations of distance graphs and line graphs. Other graph-theoretic terms and notations that are not explicitly defined here can be found in .G of these equations.First, we consider some graph equations of type The main result of solving graph equations involving detour two-distance graphs we prove in this section is the following:Theorem\u00a01.Let G be a graph. Then,If G is connected, then(a)(b)(c)(d)(e)(f)(g)(h)(i)Lemma\u00a01.Let Proof.\u00a0Clearly Proposition\u00a01.Let Proof.\u00a0Clearly Proposition\u00a02.Let G be a graph.If G is connected non-unicyclic, then If G is disconnected, then Proof.\u00a0G be connected non-unicyclic. Suppose that G is unicyclic, since G is connected, which is a contradiction to our assumption that G is non-unicyclic. Thus, Let G be disconnected. Then, Let \u25a1Proposition\u00a03.Let G be a connected unicyclic graph but not a cycle. Then,Proof.\u00a0G. Let this cycle be v be a vertex in G which is not in the cycle of G. Without loss of generality, we may assume that v is adjacent to Let If G is the graph other than these graphs, then by the argument of part (a), If G, the graph k. Clearly G is the graph obtained from By the structure of By part (c), If G is the graph other than these graphs, then the maximum length among all the cycles in If By part (e), By part (c), G is the graph other than the graph If By part (c), The proof is similar to the proof of part (h), since By part (e), By part (e), Therefore, By part (a) If G is the graph other than these graphs, then by the argument of part (a), If \u25a1Combining Propositions 1\u20133, we get the proof of Theorem 1.The main result on solving graph equations involving three-distance graphs we prove in this section is the following: Theorem\u00a02.Let G be a graph. Then,If G is connected, then(a)(b)(c)(d)(e)(f)(g)To prove the above theorem, we start with the following:Lemma\u00a02.Let Proof.\u00a0Clearly, Proposition\u00a04.Let Proof.\u00a0Clearly, Proposition\u00a05.Let G be a graph.If G is connected non-unicyclic, then If G is disconnected, then Proof.\u00a0G be connected non-unicyclic. Suppose that G is unicyclic, since G is connected, which is a contradiction to our assumption that G is non-unicyclic. Thus, Let G be disconnected. Then, Let \u25a1Proposition\u00a06.Let G be a connected unicyclic graph but not a cycle. Then,Proof.\u00a0G, the graph k. Clearly, By the structure of By part (a), If G is the graph other than these graphs, then the maximum length among all the cycles in If By part (c), By part (a), (f)-The proof is similar to the proof of part (b), since (h):(i)-The proof of part (i) and (j) are similar to the proof of parts (c) and (d), respectively,(j):since \u25a1Combining Propositions 4\u20136, we get the proof of Theorem 2.The main result on solving graph equations involving detour antipodal graphs we prove in this section is the following:Theorem\u00a03.Let G be a graph. Then,Lemma\u00a03.Consider the graph Lemma\u00a04.Let Proof.\u00a0The proof follows directly from the definition of a detour antipodal graph.\u2003\u25a1Proposition\u00a07.Let Proof.\u00a0Clearly Proposition\u00a08.Let G be either connected non-unicyclic or a disconnected graph. Then,Proof.\u00a0We need to consider the following cases.Case (i): Let G be connected non-unicyclic. Suppose that G is connected and unicyclic, which is a contradiction to our assumption that G is non-unicyclic. Hence, Case (ii): Let G be disconnected. Then, The proof follows from the above cases.\u2003\u25a1Proposition\u00a09.Let G be a connected unicyclic graph but not a cycle. Then,Proof.\u00a0(1):G such that G. We claim that G is k. Therefore, Clearly, (2):If G is the graph other than these graphs, then by the argument of part (a), If (3):If G is non-isomorphic to the above-mentioned graph. Then, by the similar argument used in the proof of part (1), we get Now, we assume that (4):By part (3), (5):G and G or By part (1), we have (6):By part (1) and Lemma 3, none of the graphs (7):G. Furthermore, G is unicyclic. Hence, none of G. By part (3), we have G.If (8):If Thus, By part (3), we have (9):If By part (3), we have (10):If G is the graph other than these graphs, then by the argument of part (a), If \u25a1Combining Propositions 7\u20139, we get the proof of Theorem 3.Given a set of wireless sensor nodes and connections, graph theory provides a useful tool to simplify the many moving parts of dynamic systems. In this work, we mainly focused on the study of detour distance graph equations. In particular, we solved some graph equations involving detour two-distance graphs, detour three-distance graphs, detour antipodal graphs and line graphs. This solution is believed to be useful for many researchers and businesses working in wireless sensor networks."}
+{"text": "Recently, several advances have been made on seeding methods for fast sequence comparison. We combine two such methods, syncmers and strobemers, in a novel seeding approach for constructing dynamic-sized fuzzy seeds and implement the method in a short-read aligner, strobealign. The seeding is fast to construct and effectively reduces repetitiveness in the seeding step, as shown using a novel metric E-hits. strobealign is several times faster than traditional aligners at similar and sometimes higher accuracy while being both faster and more accurate than more recently proposed aligners for short reads of lengths 150nt and longer. Availability: The online version contains supplementary material available at 10.1186/s13059-022-02831-7. Aligning Illumina sequencing reads to a reference genome is the first step in many analysis pipelines. Due to the fundamental role of short-read alignment in bioinformatics, there has been considerable work in this area. BWA\u00a0, 2, BowtA pioneering approach was the use of minimizers\u00a0, 16 as sseed-filter-extend approach, where the seeding and filtering are at the heart of an aligner\u2019s performance. In\u00a0 denote a k-mer substring at position i in S covering the k positions s. We will consider 0-indexed strings. We let subsequence of a string as a set of ordered letters that can be derived from a string by deleting some or no letters without changing the order of the remaining letters. A substring is a subsequence where all the letters are consecutive. Our fuzzy seeds produced from S are subsequences of S since they consist of two syncmers S. The syncmers are concatenated after their extraction to a string We use h to denote a hash function m and use We use 2-bit encoding to store nucleotides with 00, 01, 10, and 11 representing A, C, G, and T. With this bit encoding, each string is associated with a sequence of bits that can be interpreted as an integer. For example, k-mer subsampling method described in\u00a0 as E-hits. The connection to read alignment is immediate. A seed of length s is captured in a read of length r if the read starts at any of the G| if the length of the genome. Since every seed is captured with the same probability Let expected hit rate. The difference between E-hits and the expected hit rate is that the denominator is k-mers and 20 for minimizers with density 1/5  as defined in\u00a0, hence Eentclass1pt{minimain BLAST\u00a0. The E-vStrobealign has a peak memory usage of about 25\u201333 Gb for hg38 (Additional file Additional file 1: Supplementary notes and figures."}
+{"text": "N = 256, compared with the BP bit-flip-1 (BPF-1) algorithm at The Belief Propagation (BP) algorithm has the advantages of high-speed decoding and low latency. To improve the block error rate (BLER) performance of the BP-based algorithm, the BP flipping algorithm was proposed. However, the BP flipping algorithm attempts numerous useless flippings for improving the BLER performance. To reduce the number of decoding attempts needed without any loss of BLER performance, in this paper a metric is presented to evaluate the likelihood that the bits would correct the BP flipping decoding. Based on this, a BP-Step-Flipping (BPSF) algorithm is proposed which only traces the unreliable bits in the flip set (FS) to flip and skips over the reliable ones. In addition, a threshold  Polar code is the first error-correcting code  which haThe Successive Cancellation (SC) algorithm, which was proposed by Ar\u0131kan , is one To improve the original BP decoding performance, many methods to improve the BP-based algorithm have been proposed\u2014for example, the BP list (BPL)  decoder.T (CS-T) [T denotes the size of the CS. By\u00a0analyzing the behavior of the incorrect decoding results of the bit-flipping BP decoder with CS, a\u00a0BP decoder with multiple bit-flipping sets (BFSs) and stopping criteria (BP-MF-MC) was proposed [BP flipping algorithms identify and then flip error-prone positions to improve decoding performance. For\u00a0polar codes, bit-flipping strategies have been applied to both SC and BP decoding. However, the\u00a0principles of flipping strategies on SC and BP decoding are different due to their different decoding schedules. The\u00a0key to the BP flipping algorithm is to construct a flip set (FS), which consists of the error-prone bits. FS can accurately indicate the error bits, thus flipping the bits within FS can narrow the search space. Initially, the\u00a0FS was constructed in SC , which pT (CS-T) , where Tproposed . The\u00a0CS proposed  with a rosed [\u03a9) , where t decoder  was propA stepping strategy is proposed. We first analyze the behavior of FS and find that only a few bits in the FS could correct the error frame. Therefore, a\u00a0concept to evaluate the likelihood of bits correcting the trajectory of BP decoding is presented to judge whether the bits in FS should be flipped or not. The\u00a0judgement condition determines whether flipping the bits in the FS is helpful in correcting error\u00a0frames.Based on the stepping strategy, an\u00a0optimization algorithm for the BP flipping algorithm, the\u00a0BP step-flipping (BPSF) algorithm, is proposed. The\u00a0algorithm flips only unreliable bits in FS and steps reliable bits to shrink the number of flipping attempts necessary. Similarly, the\u00a0stepping strategy is also added into the GBPF-lgorithm ,18 to reIn addition, we notice that some effective flipping bits may be skipped over when the LLR magnitude is small. We further propose the enhanced BPSF-This paper aims to reduce the number of decoding attempts in the BP flipping algorithms. The main contributions are summarized as follows:The remainder of this paper is organized as follows. r, In this paper, we use calligraphic characters, such as N independent copies of binary-input discrete memoryless channels are converted to N split channels with different capacities [After channel combining and channel splitting, pacities . Some ofP , where N is the code length of the polar code and K represents the length of the information bits. Meanwhile, R = K information bits comprise r-bit CRC. The\u00a0set of information bits and frozen bits are denoted as n-th Kronecker power of Polar code can be represented as n matrix , and\u00a0F\u2297nThe BP decoding is initiated from the received value N sub-channels by channel splitting, defining i = 1, 2, \u2026, N. Let the LLR of A binary input memoryless channel N is represented by an n-stage DFG. We use  to indicate the nodes of the DFG, where i indicates node index and j indicates column index. The\u00a0leftmost nodes in the DFG mean j = 0, such as the blue and black nodes in the j = n, as\u00a0shown in the grey node column.The BP algorithm for polar codes is based on a DFG. A\u00a0polar code with code length j-th received bit. The\u00a0The classic BP DFG is depicted in  used in . Lj,i anThe maximum number of iterations The bit-flipping strategy is a feasible method with which to improve the performance of BP-based algorithms. Due to the parallelism of BP decoding, there may be more than one bit that could correct the error frame by flipping it. Not only can the real error bits correct the error frames, but\u00a0there are still other bits that can correct the error frames in the process of the iterative computation of the DFG . HoweverInitially, the\u00a0CS is used to identify unreliable bits in the SC flipping decoder, which is composed of the first bit index of each Rate-1 node . As\u00a0showFor the GBPF decoding ,18 algorSpecifically, the\u00a0GBPF flipping operation can be written\u00a0asThe oracle-assisted BP (OA-BP) decoder  knows whAlgorithm 1 BP flipping\u00a0algorithm.\u00a01:Input:\u00a02:Output:\u00a03:4:if CRC, which flips the left message The original flipping strategy used in BPF  is to flSimilarly, inspired by the GBPF-lgorithm ,18, we dThe BPSF-Algorithm 2 EBPSF-2\u00a0decoding.\u00a01:Input:\u00a0T2:Output:\u00a03:4:if CRC algorithm is close to the BPF-T = 39) algorithm in the average number of iterations. For T = 39, the EBPSF-1  outperforms the CA-SCL (L = 4) decoder by 0.13 dB when BLER = N = 512 is depicted in T = 60 and T = 60, the performance of the EGBPSF-1 (L = 2) decoder.When N = 64 is illustrated in T = 32, the EBPSF-2  and (L = 8). N = 256. The EBPSF-2  decoder by 0.02 dB at BLER = The two-bit flipping performance for To reduce the average number of iterations in the BP flipping algorithm, this paper proposes a BP flipping algorithm with the stepping strategy. To narrow the search space, the reliable bits are skipped by the stepping strategy to improve the accuracy of flipping bits. The magnitude of LLRs are used to determine whether the bits are reliable or not, skip over the reliable bits in the FS, and flip the unreliable bits to reduce the average number of iterations. Furthermore, to make the algorithm more robust, we propose the threshold"}
+{"text": "Nature 10.1038/s41586-022-04893-w Published online 4 July 2022Correction to: y-axis label of Fig. 5, where in \u201cmF\u201d appeared in error as \u201cmV\u201d; the label has been amended in the HTML and PDF versions of the article.In the version of this article initially published, there was an error in the top"}
+{"text": "Communications Biology 10.1038/s42003-022-03583-7, published online 29 June 2022.Correction to: The original version of this article contained errors in the text.In the original version of the Article, the third paragraph of the Introduction incorrectly stated \u201cLKB1 is also regulated by direct phosphorylation of eleven of the twelve AMPK-related kinases\u2026\u201d. The is now corrected to, \u201cLKB1 also regulates by direct phosphorylation eleven of the twelve AMPK-related kinases\u2026\u201dIn the Introduction section, page 2 \u201cprecipitates\u201d had been changed to \u201cprecipitate\u201d, which is now corrected.In the Results section, page 2, errors were introduced that have now been corrected:Fig. 1dI, e-g now reads Fig. 1di, e-gFig. 1dII, e-g now reads Fig. 1dii, e-gFig. 1dIII, e-g now reads Fig. 1diii, e-gIn the Discussion section page 11, \u201cFurther support for this proposal is provided by the rank order by the severity\u201d has been corrected to\u201cFurther support for this proposal is provided by the rank order of severity\u201dIn the Discussion section, page 11 a comma has been deleted after \u201cwhile by contrast,\u201d so that the sentence now correctly reads: \u201cwhile by contrast the peak of the Sustained Phase of both responses remained unaltered\u201d.These corrections have been made in the PDF and HTML versions of the Article."}
+{"text": "In the article titled \u201cRole of Baicalin in Anti-Influenza Virus A as a Potent Inducer of IFN-Gamma\u201d , there aThe corrected figure, as approved by the editorial board, is shown below."}
+{"text": "Selecting a subset of k-mers in a string in a local manner is a common task in bioinformatics tools for speeding up computation. Arguably the most well-known and common method is the minimizer technique, which selects the \u2018lowest-ordered\u2019 k-mer in a sliding window. Recently, it has been shown that minimizers may be a sub-optimal method for selecting subsets of k-mers when mutations are present. There is, however, a lack of understanding behind the theory of why certain methods perform well.a, b, n)-words, and an upper bound for minimizers. As a demonstration of our results, we modified the minimap2 read aligner to use a more conserved k-mer selection method and demonstrate that there is up to an 8.2% relative increase in number of mapped reads. However, we found that the k-mers selected by more conserved methods are also more repetitive, leading to a runtime increase during alignment. We give new insight into how one might use new k-mer selection methods as a reparameterization to optimize for speed and alignment quality.We first theoretically investigate the conservation metric for k-mer selection methods. We derive an exact expression for calculating the conservation of a k-mer selection method. This turns out to be tractable enough for us to prove closed-form expressions for a variety of methods, including (open and closed) syncmers, (supplementary methods are available at https://github.com/bluenote-1577/local-kmer-selection-results. os-minimap2 is a modified version of minimap2 and available at https://github.com/bluenote-1577/os-minimap2.Simulations and Bioinformatics online. We now define a local k-mer selection method.We will sometimes refer to a k-mer selection method as a selection method or just a method when the value of Definition 2.A method f is a q-local method if\u00a0for every\u2002of length\u2002after an appropriate shift in the position of the k-mers.q\u2009=\u20091 implies that the method can be defined by examining all k-mers and deciding if each k-mer is selected or not. We will always assume that In other words, a q-local method is just defined on Theorem 1. Let f be a q-local method. If two strings\u2002share a region of length\u2002, i.e.\u2002, then every k-mer in\u2002is also in\u2002and f(S) (if ignoring the index of the starting position).Proof. Follows easily from the definition of q-locality.\u25a1Let \u03a3 be our alphabet. We will be implicitly dealing with nucleotides , one can easily see density is equal to i is not near the edges (the start/end) of S. The issue near the edges is that in Definition 2, a k-mer near the start of S appears in less of the Given a long uniform random string nimizers .2.2.1Definition 5.Given a triple\u2002where w, k are integers and\u2002is an ordering on the set of all k-mers, a minimizer outputs the smallest k-mer appearing in a\u2002-mer, or equivalently a window of w consecutive k-mers.w-local method with a w-window guarantee by examining all windows of w k-mers and selecting k-mers inside this window. k and w are application-dependent parameters that control for density and k-mer size, so there is one free parameter which is the ordering From now on, when we specify the smallest value in a window, ties are broken by letting the leftmost k-mer be the smallest. A minimizer gives rise to a random minimizer to be a minimizer with the ordering defined by a random permutation. charged context.Somewhat surprisingly, the ordering, which can be string-dependent, plays a very important part of minimizer performance. We define a Definition 6Given parameters\u2002, a window of consecutive w\u2009+\u20091 k-mers (i.e. a\u2002-mer) is a charged context if the smallest k-mer is the first or last k-mer in the window.(Charged contexts). charging appears in A very similar definition of Theorem 2  position of the k-mer selected at the window of w k-mers starting at i. By the above paragraph, the expected number of k-mers is then just Mathematically, let w\u2009+\u20091 consecutive k-mers starting at i is first or last k-mer, or equivalently, if this window is a charged context. If the smallest k-mer is the first k-mer, then iX = i, but w\u2009+\u20091, the probability that the smallest k-mer is the first or last is simply The next key step is to notice that The most well-known class of local k-mer selection methods are minimizer methods, originally appearing in w and k. However, with a specific ordering, one can achieve provably better densities for the same parameters. For example, the miniception  example of a method that is 1-local and has a window guarantee. We also analyze the open syncmer defined in Definition 7Let  be parameters with s\u2009<\u2009k and\u2002. Considering a k-mer as a window of\u2002consecutive s-mers, a k-mer is selected if the smallest s-mer appears at position t in the window.(Open syncmer). may not have a window guarantee. Consider the string AAAAA\u2026 with t\u2009=\u20092 for any k, s. Remembering the leftmost s-mer is the smallest by convention, the smallest s-mer always occurs at the first position so no k-mers are selected. For t = \u00a01, -words method. The density of this method is W can be constructed, but we will not analyze such methods theoretically since these W are found by an optimization algorithm and thus hard to analyze. We will instead test against more sophisticated W empirically.They offer a simple form for While we have discussed intrinsic features of selection methods such as locality, density and window guarantee, we have not yet discussed the \u2018performance\u2019 of selection methods. It turns out that evaluating the performance of a method is subtle and depends on the task at hand. In certain contexts, methods cannot be compared because some tasks such as constructing de Bruijn graphs from minimizers  or countw, the assumption being that a method\u2019s performance is only reliant on the size of the window guarantee. This is not an unreasonable assumption for certain tasks, but it is not applicable to methods without a window guarantee.To compare methods, we will fix the density across methods and evaluate a precise notion of performance which we will define below. In previous studies on minimizers . Let i be a position in S which is away from the edges. Define the event\u2002representing whether or not a k-mer at position j is selected by f, and\u00a0the probability that some k-mer is selected from\u2002. We call\u2002the probability vector of f.. Define the conservation to be\u2002f overlapping the base and (ii) this k-mer is unmutated from S to S and The set Let iX be indicator random variables where iX = 1 if iX are not independent; if S, we get that i in S away from the edges.We now show that 3.3.1i, the k-mers covering i on Given the base i, an unmutated k-mer being one for which all bases are unmutated. These unmutated k-mers are candidates for being in Given some configuration, we will get k in \u03b8. This problem is well-studied; see Chapter 5.3 in From 3.3.2\u03b1, we getConditioning on a consecutive unmutated k-mers in S and lE but over x is arbitrary and can be thought of as the starting position of the first unmutated k-mer (the probability does not depend on x). Locality comes into play now; if f is a 1-local method, then the event f. Hence Theorem 3. Let \u00a0and f be a 1-local method. Then\u00a0If f is not 1-local, then\u00a0follows from the trivial upper bound\u2002f is not 1-local, then context dependency problem; if a k-mer is selected in S and the same k-mer is also in If 3.3.3Theorem 4. For\u2002i.i.d Bernoulli trials with success probability\u2002and\u2002For the case\u2002, the probability of\u2002successes is just\u2002Even though the successful runs problem is solved for general parameters, the probability formula is derived by manipulating generating functions and is a bit unruly. For Theorem 5. 1 be a 1-local method and fn be anLet f\u2002local method with n\u2009>\u20091 such that the densities of both methods are equal. That is, for a long uniformly random string S, . Then\u00a0f, by linearity of expectation, we haveProof. Given any local method x is unique in f(S) and doing the same for S, we can condition on Writing S is uniformly random, x. Therefore, the first term is independent of the method.Now notice that if never be true if x is not unique in S by the definition of 1-locality. However, for an n-local method, it is certainly possible for x is not unique in S. Hence, S is large, the theorem follows. \u25a1However, for 1-local methods, all 1-local methods have the same expected number of unique k-mers if S is uniformly random. The same idea in the proof can be re-applied to show that the average expected multiplicity over all k-mers (i.e. how many times it repeats in the f(S)) is also higher when using a 1-local method. We explore the consequences of this in Section 5.2.3.The above result show that 1-local methods may cause more repetitive matches than other methods such as minimizers. In fact, the above proof shows that Given that 1-local methods are superior for conservation, which is a measure of sensitivity, it is natural to ask if such methods have an inherent precision trade-off. In the context of alignment, k-mer matching precision is related to spurious k-mer matchings caused by repeat k-mers, as such matches would force an aligner to evaluate several candidate alignments. In general, unique k-mer matches are easier to handle computationally than repeat k-mer matches. It may therefore be more advantageous for a local selection method to select non-repetitive k-mers. We show that indeed, locality is related to repetitive k-mer selection.k, s, t be given and f be either a closed or open syncmer method. To calculate \u03b1 consecutive k-mers. Breaking these k-mers into s-mers, we get a window of k\u2009=\u200915 and w\u2009=\u200910. To achieve approximately the same density using an open syncmer, we need s\u2009=\u200910, and it is easy to show that this probability is very small. Since all s-mers are distinct and we assume a random ordering on all s-mers, the relative ordering of s-mers in this window is a uniformly random permutation in i in the window. Determining whether or not a k-mer is selected then amounts to analyzing a random permutation\u2019s smallest elements . If\u2002, then\u2002If f is a closed syncmer method, then\u00a0Corollary 1. We prove this theorem in We can also count open syncmers. Unfortunately, the number of permutations is only determined as a recurrence relation and the formula is not as nice. Theorem 7 is proved in Now given a permutation Theorem 7 Using parameters k, s, t as defined in Definition 7, let\u2002and\u2002be the number of permutations in\u2002such that for some window\u2002the smallest element is\u2002. Define\u2002. Then\u00a0(Successful permutations for open syncmers). We define\u2002as\u00a0where the subscript indicates falling factorial, and\u2002if\u2002t. In t was investigated on the performance of open syncmers, but no explicit conclusion was made about how to choose t. Below we prove a theorem that says that the parameter t should be chosen to be the middle position of a window of One can divide Theorem 8. Let\u2002. Then\u2002for any valid choice of t.t. By Theorems 3 and 8, we can rigorously justify the optimal value for t to maximize conservation. Thus, t is not actually a free parameter when optimizing for conservation.We prove Theorem 8 in w, k be parameters for a random minimizer method f. To calculate \u03b1 consecutive k-mers, we now have to look all k-mers in all windows containing any of these \u03b1 consecutive k-mers. As in the syncmer case, we will assume all k-mers are distinct.Let \u03b1 consecutive k-mers, we need to also know the ordering of the w\u20121 k-mers to the left and to the right of these \u03b1 k-mers because they are included in some window containing one of these consecutive k-mers. This gives us Given nS satisfying a general condition.Theorem 9 Given parameters\u2002with\u2002, let\u2002n such that for some windowbe the number of permutations in S\u2002, the smallest element is one of\u2002. Then\u00a0where\u2002and using\u2002to mean the falling factorial,(Successful permutations for random minimizers). \u03b1 consecutive k-mers since the p parameter describes the leftmost position of the first unmutated k-mer covering position i. Therefore, as before, The specific choice of parameters It was shown to us recently  that for\u03b1\u2009=\u20091, we get the desired result that the density is f is a 1-local method, which minimizers are not. We give an example that shows how context dependency leads to lower conservation in When We proceed by counting permutations corresponding to some k-mer being chosen by a random minimizer method. We first define a function a, b, n)-words method which selects k-mers based on their prefix. We prove this result in Theorem 10. under the -words method is\u00a0where\u2002if x\u2009<\u20090.We can also derive the probability vector for the previously  is defined in Section 3.1 as the upper bound on probability vectors. For the miniception method, it is not obvious how parameters affect d so we let k0 and w slightly until we get the density close to d. For the words method, we use two choices of W as W4 and W8 -words method, the closest choice of parameters leading to the most similar density is n\u2009=\u20092, 3 which gives density We first fix W4, W8 and the open syncmer methods perform well compared with the other methods. The large drop in conservation between the empirical random minimizer and the upper bound for the random minimizer indicates that context dependency plays a highly non-trivial role in conservation. We note that for d\u2009=\u20091/4, the -words method performs poorly as it does not take advantage of selecting k-mers with non-overlapping prefixes n\u2009=\u20090.The results in These results also suggest that the best methods already achieve W for each density. We note that since minimap2 was designed with minimizers in mind, we expect the benefits of switching k-mer selection methods to be dampened compared with designing an aligner with open syncmers in mind.We now investigate applications to read mapping. We modified minimap2 , a stateseeds to be matched onto the selected k-mers of the reference. Colinear sets of k-mer matches are collected into chains, and then dynamic programming-based alignment is performed to fill gaps between chains. Our modification was to swap out the k-mer selection method, originally random minimizers, to an open syncmer method instead. Our version of minimap2 can be found at https://github.com/bluenote-1577/os-minimap2.Minimap2 aligns reads using a seed-chain-extend procedure. Roughly speaking, this works by first applying a k-mer selection method to all reads and reference genomes. Selected k-mers on the reads are then used as We operate on four sets of real and simulated publicly available long-read datasets:https://tinyurl.com/uhuwvxb8 and their corresponding assemblies.Real microbial PacBio Sequel long-reads from PacBio, available at https://github.com/marbl/CHM13  and the corresponding assembly CHM13.Real human ONT nanopore reads from Simulated RNA (cDNA) ONT long-read data from Trans-NanoSim  in the dataset and compared the mappings for open syncmers versus minimizers. This is shown in For each alignment of a read, minimap2 computes a t\u2009=\u20093, the optimal parameter of t with t increases for open syncmer methods because the vectors t increases; see t increases is suggestive that goodness of chaining is indeed correlated with conservation, even for PacBio reads which have higher rates of indels than substitutions  ONT data, where we can analyze mapping precision due to having a ground truth. We chose to analyze such data because read lengths are shorter, and in After generating a set of reads from a transcriptome, we mapped the reads back to the genome (GRCh38) using the minimap2-x splice option. For every mapping, we take the primary alignment if the mapQ > 0. We designate a mapping successful if the transcript corresponding to the read overlaps the true gene, otherwise we designate it as an error. We only analyze genes found on the primary chromosomes of GRCh38 and ignore genes found on alternate loci.k to create more seed matches; this was also not investigated in .Increasing k-mer matching sensitivity by lowering k and choosing more conserved methods effectively do the same thing by increasing the number of seed hits. Larger versions of this subplot are shown in Open syncmers and minimizers have similar error/success curves as seen in the top-right of k versus using open syncmers, open syncmers allow for new parameterizations. While the quality of the mapping seems independent of lowering d = 1/7, we noticed that syncmers may offer a sizeable error-runtime improvement for small k, see d; this can also be seen in the top-left of d may be necessary in cases where a large number of genomes must be indexed by k-mers and memory is an issue.For the case of fixed density k is fixed. For large k, this is primarily due to indexing speed, which we did not attempt to optimize. For smaller k, this seems to be due to a larger number of repetitive k-mers and spurious matches as mentioned in Section 3.4. Syncmers take longer when t value is unique when Interestingly, we found that for even values of minished . This ismaximize sensitivity, which is related to quality, and minimize the number of repetitive k-mers in the indexed set, which is related to speed. Further research should investigate if this trade-off can be improved using new local-selection methods and how to engineer aligners that take advantage of the trade-off.In summary, we first described a new mathematical framework for understanding k-mer selection methods in the context of conservation, which allowed us to prove results pertaining to upper bounds, optimal parameter choices and closed-form expressions for conservation. We then investigated conservation empirically and then found that augmenting minimap2 with a more conserved method increases alignment sensitivity as predicted. However, such methods may give rise to more repetitive seed matches, increasing the computational time of alignment. To optimize for quality of mapping versus speed, one should A notable result of ours is that the best methods can already achieve > 0.96 of the upper bound for conservation for certain parameters, implying that major improvements in conservation are not possible. However, real genomes do not consist of i.i.d uniform letters. There is a mix of high-complexity and low-complexity regions in genomes, so techniques for better distributed selection of k-mers should be investigated . TheoretAn orthogonally related recent idea are strobemers , which hbtab790_Supplementary_DataClick here for additional data file."}
+{"text": "The proposed cost function is optimized using an iterative algorithm derived from the alternative direction method of multipliers. Moreover, we propose improved versions of the proposed algorithms by incorporating a smoothing penalty function into the cost function. We also introduce angular constrained forms of the proposed algorithms by considering a special case as follows. The imperfect error values are constant over all the projection angles, as in the case where the source of ring artifact is the non-uniform sensitivity of the detector. Real data and simulation studies were performed to evaluate the proposed algorithms. Results demonstrate that the proposed algorithms with incorporating smoothing penalty and their angular constrained forms are effective in ring artifact elimination.Ring artifact elimination is one of the popular problems in computed tomography (CT). It appears in the reconstructed image in the form of bright or dark patterns of concentric circles. In this paper, based on the compressed sensing theory, we propose a method for eliminating the ring artifact during the image reconstruction. The proposed method is based on representing the projection data by a sum of two components. The first component contains ideal correct values, while the latter contains imperfect error values causing the ring artifact. We propose to minimize some sparsity-induced norms corresponding to the imperfect error components to effectively eliminate the ring artifact. In particular, we investigate the effect of using different sparse models,  The sinogram data corresponding to the image containing the ring artifact is also contaminated by incorrect measurement values similar to the example shown in Ring artifact is one of the well-known image degradations that restrict the quality of X-ray computed tomography (CT) images . In addiThis paper is organized as follows. The related work is presented in Section 2. The proposed algorithms are detailed in Section 3. After that, we show the results of the experimental studies in Section 4. Finally, the conclusion is provided in 5.Pre-processing methods: remove the vertical stripes from the sinogram before image reconstruction.Post-processing methods: remove the ring artifact from the image after image reconstruction.In-processing methods: remove the ring artifact during image reconstruction.There are numerous methods that have been investigated to suppress the ring artifact. These methods can be classified into two general categories. The first category contains methods based on the modification of hardware, such as those detailed in , 13. TheA technique based on a combination of wavelet decomposition and Fourier filtering was investigated to eliminate the stripes from the sinogram . Also, a\u21130-norm/\u21131-norm regularization term to remove the ring artifact from the reconstructed images , where Ai denotes the system matrix corresponding to the i-th projection angle. Similarly, we express the projection data as i-th projection angle. Using these notations, the image reconstruction problem in the angular constrained form can be formulated as\u03b8, which originates from the constraint that values of elements in the imperfect vector are same for all the angles.Generally, it is clear from the different causes of ring artifact that the values of the imperfect vector in the projection data may be dependent on the measured angles. In other words, the imperfect values are variables for all the angles. In addition to this general case, we suggest studying a special case where the ring artifact originates from physical factors related to hardware, such as the existence of some imperfect detector bins. Then, the imperfect elements in \u21131-norm as an example of the sparsity-induced norm \u03c1 > 0 is a positive constant. Using the augmented Lagrangian function in The formulated cost function can be optimized using any iterative algorithm. For example, first-order primal-dual method, alternative direction method of multipliers (ADMM) , and pro\u03b1 > 0 denotes the step size, L is the maximum number of iterations in the GD method, and \u03bc = 1/\u03c1. It can be solved directly using a simple formula in closed form via the soft thresholding [The update of image sholding  functionAlgorithm 1\u21131-ring algorithm.Input the projection data \u03b1 > 0 and \u03c1 > 0).Set initial value for fork = 1, 2, \u2026, Kdo\u2003forl = 1, 2, \u2026, Ldo\u2003\u2003\u2003end\u2003\u2003\u2003\u2003endOutput the reconstructed image i.e.\u21130-norm, Huber \u21131-norm and Huber \u21130-norm. The result of the derivation shows the following. Almost same algorithms can be obtained for the cases of using four different norms, and the only difference among the four cases appears in the form of the proximity operator in Step 2. For clarity, the proximity operators corresponding to the four cases are summarized in \u21131-norm, \u21130-norm, Huber \u21131-norm, and Huber \u21130-norm by \u21131-ring, \u21130-ring, H\u21131-ring, and H\u21130-ring algorithms, respectively.We followed the same steps to derive three iterative algorithms corresponding to the remaining three sparsity-induced norms mentioned above, \u03b2 > 0 denotes the hyper-parameter that controls the strength of smoothing. In this work, we choose to use a smoothing penalty similar to Markov random fields (MRFs) [\u21131-norm case, followed by explaining how it can be changed to the other three norms. The cost function in the \u21131-norm case is given byUj denotes the set of eight neighboring pixels around the j-th pixel, and j-th pixel and the We propose to incorporate a smoothing penalty s (MRFs) . This isAlgorithm 2\u21131-smth-ring algorithm.Input the projection data \u03b1 > 0, \u03c1 > 0 and Set initial value for fork = 1, 2, \u2026, Kdo\u2003forl = 1, 2, \u2026, Ldo\u2003\u2003\u2003end\u2003\u2003\u2003\u2003endOutput the reconstructed image \u21131-smth-ring, \u21130-smth-ring, H\u21131-smth-ring, and H\u21130-smth-ring algorithms, respectively. In addition, we call a collection of these four algorithms using the smoothing penalty by improved algorithms to distinguish them from the algorithms without the smoothing.Similarly to the case without the smoothing penalty, the iterative algorithms corresponding to the other three norms mentioned above are given as follows: change the proximity operator in Algorithm 2, as shown in i.e. the formulation of k. Each element \u03bbr\u03b8 of the imperfect vector r) in every projection angle (\u03b8) based on each elements dr\u03b8 of the vector This section describes iterative algorithms for the angular constrained form where elements of imperfect error vector have the same values for all the angles, r = 1, 2, \u2026, R dofor \u03b8 = 1, 2, \u2026, \u0398 do\u2003for \u2003\u2003\u2003endendApplying the angular-independency constraint means that the update of r = 1, 2, \u2026, R dofor \u2003\u03b8 = 1, 2, \u2026, \u0398 do\u2003for \u2003\u2003\u2003endend\u21131-ring, cstr-\u21130-ring, cstr-H\u21131-ring, and cstr-H\u21130-ring algorithms) for the case without the smoothing, and  for the case with the smoothing.Using the update of \u21131-norm or Huber \u21131-norm is guaranteed for the following reason. These algorithms can be considered as an application of ADMM to the convex minimization subject to the linear constraint. However, the iterative algorithms using \u21130-norm or Huber \u21130-norm are not guaranteed to converge due to the non-convex nature of cost functions. However, as we will show in the next section, the algorithms using \u21130-norm or Huber \u21130-norm converge to nice approximate solutions in practice. Also, their power to eliminate the ring artifact is much stronger compared to the \u21131-norm based algorithms. This observation motivated us to keep the \u21130-norm based algorithms in this paper in spite of the lack of mathematical guarantee in the convergence. We note that similar behaviors, i.e. approximate solution with the \u21130-norm works better than the exact solution with the \u21131-norm, have been observed in other application areas of CS.The convergence of iterative algorithm using \u03bcm) thick scintillator was used for measuring the projection data. The number of projection data was 1800 over 180 degrees, and each projection data consisted of 1024 \u00d7 1024 pixels. From the conventional FBP reconstruction of this data, the central slice of the reconstructed 3D image was contaminated with strong ring artifact. Moreover, in the simulation data, we used a 2D slice obtained from a dataset of screening chest CT images. The dataset includes 68 volumes for various patients scanned using Hitachi CT-W950SR scanner. Each volume is composed of 25 to 31 transaxial slices, where each slice is composed of 320 \u00d7 320 (pixels) with a slice thickness of 10 (mm) and a pixel size of 1 \u00d7 1 (mm). The 2D chest slice was resized to 512 \u00d7 512 (pixels). The simulation studies were carried out with and without adding noise to the projection data. It is known that the statistical noise in the CT measurements follows Poisson distribution [b0 is the number of average photon counts transmitted from the x-ray source, and bi is the detected photons measured after attenuation by the scanned object at detector bin i. Then, the noisy projection data gi at detector bin i can be calculated using Eqs \u03c3, decomposition level L, and wavelet base function W). On the other hand, to correct the image by the M2 method, some parameters need to be adjusted, such as the ratio between the defective and background values R. Also, the size of the smoothing filters that remove the small to medium and large stripes in the sinogram  is required for executing the M2 method. In order to obtain satisfactory results with the M1 and M2 methods, we selected their parameters based on the best image quality in terms of RRMSE values besides visual evaluation. Furthermore, to study the effect of using the standard \u21132-norm on ring artifact removal, we compared our proposed algorithms with two algorithms using \u21132-norm for the data fidelity term with and without smoothing penalty. Additionally, the GD method was used for the optimization problem of these two algorithms, which we name \u21132 and \u21132-smth algorithms. All the algorithms were implemented using C++ platform on a machine with Intel(R) core(TM) i7\u20132670QM CPU @ 2.20 GHz processor and 6 GB RAM. The average execution time of the proposed algorithms for every iteration was 6.0 seconds.To evaluate the proposed algorithms, we performed experimental studies using real data in addition to simulation data. In the real data, some experiments for propagation-based phase-contrast imaging were performed by synchrotron radiation X-ray micro-CT , Japan , 36. A sribution . Assume \u03bcx and \u03bcz are the mean values of images \u03c3xz is the correlation coefficient value of image c1 = (k1*s)2 and c2 = (k2*s)2 where k1 = 0.01 and k2 = 0.03 and s is the dynamic range of the pixel values.To evaluate image quality achieved by the proposed algorithms, we used two image quality metrics throughout the simulation studies. Suppose that M) index , which c\u03c1 and \u03b4) control the degree of the ring artifact removal in the proposed algorithms. All the algorithms were implemented using the same values for these parameters \u03c1, \u03b4, N, and K for the following reasons: to obtain a fair comparison between the different algorithms and to show the effect of the different sparsity-induced norms on the ring artifact elimination. The parameter values used in our implementation are summarized as follows: L = 2, K = 2, 000, \u03b1 = 125 \u00d7 10\u22123, \u03c1 = 0.004, \u03b4 = 0.092, \u03b7 = 0.001. Also, the parameter values  and  were used for the correction by M1 and M2 methods, respectively. \u21132 and \u21132-smth algorithms for the first study case. The true slice, the corrupted image, the reconstructions using all the proposed algorithms, and the images corrected by using the M1 and M2 methods are shown in Figs In this section, we applied the proposed algorithms to the simulated projection data without statistical noise corresponding to the above-mentioned 2D chest slice. The simulated sinogram consisted of 512 (bins) \u00d7 1,000 (angles), where the standard parallel-beam geometry with 360\u00b0 angular range was assumed. We considered three different cases, each of which corresponds to a different setup of the non-uniform sensitivity bins and consequently a different ring artifact pattern in the image domain. The details are summarized as follows. In the first case, we assumed that some non-adjacent bins have non-uniform sensitivities producing the ring artifact. In the other two cases, some adjacent detector bins have non-uniform sensitivities producing the thick ring artifact of multiple pixel width where the maximum width was set to 3 (pixels). We assumed that the imperfect error value in each detector bin is constant with respect to the angle in the first and second cases, and varied with respect to the angle in the third case. Using the sinograms \u21132 and \u21132-smth algorithms. On the other hand, it is clear from the reconstructions shown in Figs \u21131-ring algorithm succeeds in eliminating most of the ring artifact except few rings located near the center. For example, we can notice that one ring appeared with low contrast in the first study case, while very small number of rings still appeared in the second and third study cases. Meanwhile, the reconstructions by \u21131-smth-ring algorithm illustrate that the remaining artifacts were smoothed well. The reconstructions by \u21130-ring algorithm produced ring-free images, though very little new artifacts were introduced in the second study case. Additional improvement with the smoothing penalty was able to efficiently suppress these remaining artifacts. It also produced high-quality image closer to the original image without any loss in the fine details. Furthermore, the reconstruction by H\u21131-ring and H\u21130-ring algorithms show that they provide similar results to those in \u21131-ring and \u21130-ring algorithms, respectively. However, the latter algorithms eliminate more ring artifacts and produce better results than the former ones. The residual artifacts were disappeared well with H\u21130-smth-ring algorithm and were smoothed well with H\u21131-smth-ring algorithm, where they still slightly appeared with low contrast. Moreover, it is notable from Figs From \u21131-smth-ring and \u21130-smth-ring algorithms and their angular constrained forms outperformed the other proposed algorithms.For quantitative evaluation, we measured the quantitative metrics (RRMSE and SSIM) between the original reference image and the reconstructed image by each algorithm. The obtained metric values are summarized in Tables Finally, from the above qualitative and quantitative evaluation, the proposed algorithms and their angular constrained forms, especially with incorporating the smoothing penalty, are effective in suppressing the ring artifact. They also achieve higher image quality compared with the other methods implemented in this work. 6 (counts/bin) was added to the sinogram of the first study case in the previous section. Using this sinogram, we reconstructed images by the proposed algorithms. The parameter values in the proposed algorithms were as follows: L = 2, K = 500, \u03b1 = 5 \u00d7 10\u22123, \u03c1 = 0.001, \u03b4 = 0.03 and \u03b7 = 0.01. Also, \u21131-smth-ring, 55.0 in \u21130-smth-ring, 75.0 in H\u21131-smth-ring, 45.0 in H\u21130-smth-ring, and 150.0 in the angular constrained forms. Moreover, the parameter values in the M1 and M2 methods were the same as in the case without noise. The true image, the corrupted image, and the reconstructions by the proposed algorithms and the compared methods are shown in Figs We also studied the case where projection data contains statistical noise in addition to the ring artifact. In the noisy data case, Poisson noise corresponding to 10\u21131-ring and \u21130-ring algorithms did not succeed in completely eliminating the ring artifact, where it only slightly decreased the intensity of some rings. The reconstructions by H\u21131-ring and H\u21130-ring algorithms produced similar results to those in \u21131-ring and \u21130-ring algorithms, respectively. Meanwhile, the remaining artifacts were weakened with \u21131-smth-ring algorithm. Also, they were suppressed with \u21130-smth-ring, H\u21131-smth-ring, and H\u21130-smth-ring, where the artifact slightly appeared with low contrast. It can be notable that the reconstructions by H\u21131-ring and H\u21130-ring algorithms contained less noise compared to \u21131-ring and \u21130-rings algorithms. The reason for this is the existence of the quadratic part in Huber \u21131-norm and Huber \u21130-norm cost functions in H\u21131-ring and H\u21130-ring algorithms.From the visual evaluation of the results, we can notice that the M1 and M2 methods produced similar results to those in the previously studied noise-free case. Furthermore, we can observe that the reconstructions by \u21130-ring and H\u21130-ring algorithms. They also removed most of the rings except some rings located near the center in both \u21131-ring and H\u21131-ring algorithms, although some new artifacts were introduced. Additionally, we can observe that the angular constrained forms of the improved algorithms could effectively remove the artifact and produce ring-free images.Concerning the results of the angular constrained forms of the proposed algorithms, it is clear that the angular constrained forms of the proposed algorithm could eliminate all the ring artifact with \u21131-ring or H\u21130-ring algorithms. Consequently, we plan to incorporate a statistical model in addition to the sparsity-induced norms for further improvement of the reconstruction with noisy projection data.To perform quantitative evaluation of the proposed algorithms, RRMSE and SSIM values were measured and presented in the last two columns in For additional evaluation of the proposed algorithms, we implemented the proposed algorithms with real data. We used the projection data corresponding to the central slice of the above-mentioned real data. We implemented the proposed method and the compared methods with this data. The results are shown in \u21132 and \u21132-smth algorithms and their angular constrained versions (cstr-\u21132 and cstr-\u21132-smth) still included the strong ring artifact. Since the real projection data is corrupted with noise, H\u21130-ring, H\u21130-smth-ring, and the angular constraint versions of H\u21131-ring and H\u21130-ring algorithms could remove most of the ring artifact well. Moreover, cstr-smth-H\u21131-ring and cstr-smth-H\u21130-ring algorithms almost completely removed the ring artifact leading to high-quality reconstructions. Finally, we would like to strengthen the following fact. Using \u21132-norm cannot suppress the ring artifact, whereas the combination of \u21131-or \u21130-norm and \u21132-norm as in Huber \u21131- and Huber \u21130-norms is able to remove the ring artifact. This means that the use of sparsity-induced norm is essential in the ring-artifact elimination problem.The results are summarized as follows. Most of the ring artifacts were removed well with the corrections using M1 and M2 methods. However, some remaining rings were still visible. These existing techniques worked well, but were not complete in this experiment. The reconstructed images with i.e. M1 and M2 methods. In summary, we can conclude that the sparsity-induced norms for the imperfect error components of the projection data in the data fidelity as well as the smoothing penalty can effectively eliminate the ring artifact.In this work, we developed a class of algorithms to eliminate the ring artifact from CT images. The first group of algorithms minimizes different sparsity-induced norms of the imperfect error components of the sinogram. In the second group of algorithms, we improved the first class of algorithms by incorporating the smoothing penalty into the cost function to remove the remaining ring artifact. Furthermore, we also introduced angular constrained forms corresponding to the proposed algorithms and their improved versions. The proposed algorithms are able to correct the ring artifact well during image reconstruction and need neither pre-processing nor post-processing steps. We evaluated the performance of these algorithms through a number of simulation and real data studies. In the simulation, we considered three different cases where different setups of the ring artifact patterns were simulated. Both the qualitative and quantitative evaluation results demonstrated that the improved versions of the proposed algorithms and their angular constrained forms are efficient in ring artifact suppression. They also provide significantly better results than the compared methods, S1 File(RAR)Click here for additional data file."}
+{"text": "Nature Communications 10.1038/s41467-022-34710-x, published online 16 November 2022Correction to: The original version of this Article contained an error in Fig. 4, in which in panel (b) the residues in the sequence presented were highlighted with a wrong color coding, i.e., the second \u201cS\u201d in the sequence \u201cNALVSRSKGTSKSNFIPFRDSKLTR\u201d was highlighted in pink instead of black. In addition, the arrows in panel (a) have decreased thickness to improve the visibility of the structure. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Nature Communications 10.1038/s41467-022-30856-w, published online 07 June 2022.Correction to: In the original version of this Article, the positions of \u201cMorphine\u201d and \u201cCodeine\u201d and the associated chemical structures in the morphinan pathway in Fig. 1a were swapped. These have been corrected in both the PDF and HTML versions of the Article."}
+{"text": "To overcome these issues, this paper proposes a x and y position based on inductive saliency between two sets of three-phase coils. The proposed idea is applied on a combined winding self-bearing machine which does not require additional suspension force winding. No additional search coil placement for Self-bearing machines do not contain physical bearings but magnetic bearings. Both rotor rotary and spatial positions displacement are required in these types of machines to control the rotor position while it is levitating. Self-bearing machines often use external sensors for  The remal axes) ,3,4.Conventional self-bearing machines typically comprise two sets of independent windings in the stator for producing torque and suspension force, i.e., separated winding (a torque winding and a suspension winding). For compact size self-bearing machines, combined winding that uses the same coils to create both suspension forces and torque current have been developed ,6.Position sensors for closed-loop rotor spatial  change. This is due to the unbalanced air-gap length between phases [Phase shown in , where Ressed by , where Lmovement ,9. Note n phases .n is equal to 1, m is equal to 2, and vice versa. Clark transform, Six-phase voltage models can be presented as two sets of \u03b1\u03b2n-axes  and 5)..\u03b1\u03b2n-axes, Kc, in  is used.The HF voltage characteristic model in stationary reference frame is represented by  and 7),,7), obtation see .x- and y-spatial rotor position displacement. This dependency will be used for rotor It will be shown in Finally, since shown in  exist amThis section presents the inductance dependency in rotor spatial position displacement   \u03b1\u03b21 refeL\u03b21\u03b21 in . Therefor is the per-unit air-gap length. x- and y-axes. The effect of In this subsection, inductance sensitivity analysis is performed. Air-gap length in each phase is modeled as in  using EuTaking the dominant components, per unit air-gap length is calculated in \u201320): (1: (120): x and y rotor position displacement, Equivalent air-gap area, tance to , taking tance to  is calculated in . The senx and y rotor position displacement from the simplified inductance model can be summarized as follows:x-axis rotor movement. For x-position self-sensing, main inductances are required.Main inductances, y-axis rotor movement. For y-position self-sensing, cross-coupling inductances are required.Cross-coupling inductances, Cross-coupling inductances, The main and cross-coupling inductances in the first and the second set of three-phase coils have opposite sensitivity to The conclusions of inductance variation in n, while the other set of three-phase coils current, m, are set to zero  is performed to verify the conclusions from the simplified reluctance model. A stacking factor of 0.95 is used for the stator with N35 grade NdFeB permanent magnet on the rotor. Self-bearing machine geometry and simulation conditions for FEA analysis are summarized in  to zero  and 26)Dos, Dis, to zero \u201330). Gi. GiDos, n = 1, m = 2, i = 1, j = 2. Note that the magnitude of the cross-coupling inductances between three-phase coil sets are much smaller (about 1/5 times) than the self inductances shown in The cross-coupling inductance between the first and the second set of three-phase coils, shown in ions see . Therefos is the differential operator. Park transform in  as in (Equations  and 7)  7) can bsform in  with ref \u03b1\u03b2-axes  where \u03b8i2) as in  to use d will be . The res will be , where Ifined in .x and y rotor position? This may be explained referring to , a, ax and rring to . The mainator of , VHF2\u03c0fHshown in  and 38)x and y rx and y rotor position are estimated, from the HF current responses, , to position, e.g., millimeter (mm), given HF injection conditions, i.e., x-axis offset constant to calibrate the x-axis referencing position. The procedure to select the self-sensing gains is as follows:x = y = 0 mm. first, ^ = 0 in  and 40)kgx and ksecond, Exciting both \u03b1\u03b22 with  as in Fisponses,  and 40)\u03b1\u03b21 and \u03b1sponses,  and (40)x and y rotor positions are estimated using (ed using  and 40)xy-positix- and y-axes is 0.1 mm. The center position of the rotor with respect to the stator is position controlled by the linear motion stage, and used as an absolute position reference during the This section shows the experimental results of the x = 0 mm and y= \u22121 mm, are shown in x and y positions, The self-sensing experiment conditions are summarized in ^, using  and 40)v\u03b11HF*, vy-positions while the x-positions are varied from \u22121 mm to 1 mm in incremental steps of 0.5 mm, see x-position variation while To further show viability of the y-position is varied while holding the x-position constant. y position as expected in (x- and y-position results are shown in ected in  and 38)y-positioRotor x- and y-rotor position, simultaneously utilizing both main- and cross-coupling inductance variation. The excitation frequency is carefully selected to minimize the interference to the closed-loop operation of the bearingless machine drive system. Demodulating the coupled HF current, The model for machine inductances\u2019 sensitivities with respect to the"}
+{"text": "Men with light eyes lack the dominant gene allele that codes for dark-brown eyes. Pairing with a woman who lacks the same allele must increase paternity confidence in these men, because any children with dark eyes would be extremely unlikely to have been fathered by them. This notion implies that men with light (blue or green) eyes should (1) prefer light-eyed women, especially in a long-term context, and (2) feel more threatened by light-eyed than by dark-eyed rivals. Yet because choosiness is costly and paternity concerns are entirely driven by the prospect of paternal investment, any such inclinations would be adaptive only in men who expect to invest in their children. Here I test these ideas using the data of over 1000 men who rated the facial attractiveness of potential partners, and the threat of potential rivals, whose eye color had been manipulated. Light-eyed men liked light-eyed women better (particularly as long-term companions), and feared light-eyed rivals more, than did dark-eyed men. An exploratory analysis showed that these large, robust effects disappeared in men who had felt rejected by their fathers while growing up\u2014suggesting that such men are not expecting to invest in their own children either. It is a wise father that knows his own child. The Merchant of Venice, Act 2 Scene 2\u2014 William Shakespeare,Males can never be certain they have fathered their mates\u2019 offspring. What they can do is adjust parental care to the probability of being genetically related to them Trivers, . There iand that this ability is highly imperfect.In our species, too, paternal investment is strongly related to paternity confidence reliably as to the other  permits to predict with high accuracy whether someone\u2019s eyes are brown or blue  genes than would light-eyed men with the opposite preference, or no preference. This leads to the prediction that, other things being equal, men with light eyes should be especially attracted to women with light eyes. This has been shown to be the case in a study with 44 male participants who were asked to rate, from photographs, the attractiveness of faces with blue or brown eyes  and either brown or dark brown (dark-eyed men: N\u2009=\u2009805), for a total of 1237 individuals; of these, 621 reported currently having a partner. Data were collected in accordance with guidelines approved by the local Psychological Research Ethics Committee; all participants gave informed consent.The total sample included 1440 men . With very few exceptions, participants were Italian; they were mostly recruited via links posted on Italian universities\u2019 online social networks and other social media, such as Facebook groups. Men who self-identified as heterosexual or bisexual with a preference for female partners were directed to the current study, whereas men who self-identified as homosexuals or bisexual with a preference for male partners were directed to a separate one. The analyses presented here include all participants whose eyes were either blue or green  term relationship, which of these two people would you prefer?\u201d Possible responses were \u201cthe one on the left\u201d and \u201cthe one on the right.\u201d The other questions were, \u201cFor a long- (short-) term relationship, how attractive do you find the person on the left?\u201d and \u201cFor a long- (short-) term relationship, how attractive do you find the person on the right?\u201d, each followed by a 0\u201310 scale going from \u201cnot at all attractive\u201d to \u201cvery attractive.\u201d Long-term and short-term relationships were defined as follows: \u201cBy a long-term relationship, we mean someone you may consider leaving your current partner for, or with whom you may like to create a stable relationship, leading to cohabitation or marriage, in case of a breakup with a current partner or if you are single\u201d; \u201cBy a short-term relationship, we mean a single date accepted on the spur of the moment, an affair within a long-term relationship, or a one-night stand.\u201dAt the end, participants completed a questionnaire which asked about their eye color and that of their parents and current partner, if they had one. . Each pair was followed by three questions. The first was, \u201cIf you suspected your partner was being unfaithful to you, which of these two men would you be more jealous of?\u201d Possible responses were \u201cthe one on the left\u201d and \u201cthe one on the right.\u201d The second and third questions were, \u201cHow jealous would you be of the man on the left?\u201d and \u201cHow jealous would you be of the man on the right?\u201d, each followed by a 0\u201310 scale from \u201cnot at all jealous\u201d to \u201cvery jealous.\u201dLight- and dark-eyed participants were not significantly different in any of the demographic characteristics measured in the study, such as age, ethnicity, education level, sexual orientation, partnership status, and mean partnership duration. Stimuli  and procedures  that were counterbalanced between subjects turned out to have been presented to light- and dark-eyed participants with the same frequency.  were not Italian or raised but not born in Italy. The pattern of results remained the same if the data of these participants were discarded. Only results directly relevant to the predictions of the paternity-uncertainty hypothesis are reported here; the complete set of results can be found in the Supplementary Materials.Men\u2019s preference for light-eyed women was computed as the number of choices of light-eyed female faces, relative to the total number of choices, in response to the question \u201cIf you were looking for a long- (short-) term relationship, which of these two people would you prefer?\u201d This index could range from 0 (light-eyed face is never chosen) to 1 .F\u2009=\u200993.33, p\u2009<\u20090.0001. Light-eyed men preferred women with light eyes more than dark-eyed men did, F\u2009=\u200937.30, p\u2009<\u20090.0001, \u03b72p\u2009=\u20090.03\u2014an effect which is about the size of juries\u2019 tendency to be more influenced by credible than noncredible witnesses \u2009=\u20098.49, p\u2009=\u20090.004.A repeated-measures ANOVA was carried out on these preferences, with a within-subject factor of relationship context  and a between-subject factor of own eye color . Light eyes were liked better in short- than in long-term partners, p\u2019s\u2009<\u20090.0001, one-sample t). This core preference for light eyes has also been found in women , choosing a light-eyed partner confers an extra selective advantage to a man if he is light-eyed but not if he is dark-eyed.Overall, light eyes looked more attractive than dark ones  to 1 .p\u2019s\u2009<\u20090.0001, one-sample t). These choices were analyzed with a univariate ANOVA with a fixed factor of own eye color . Crucially, having light eyes increased the perceived threat of light-eyed rivals relative to dark-eyed ones, F\u2009=\u200916.62, p\u2009<\u20090.0001, \u03b72p\u2009=\u20090.03.In a potential competitor, light eyes looked more ominous than dark ones \u2009=\u200913.10, p\u2009=\u20090.0003. \u2009=\u20090.87, p\u2009=\u20090.350.) As shown by separate ANOVAs, having light eyes significantly increased the preference for light-eyed partners in men who had felt accepted by their father, F\u2009=\u200952.97, p\u2009<\u20090.0001, \u03b72p\u2009=\u20090.07, but not in those who had felt rejected by him, F\u2009=\u20091.78, p\u2009=\u20090.183 \u2009=\u20097.69, p\u2009=\u20090.006; in participants who had felt rejected it was not, F\u2009=\u20091.49, p\u2009=\u20090.222. A similar effect emerged in the univariate ANOVA on partnered men\u2019s jealousy of rivals: paternal rejection  interacted with own eye color , F\u2009=\u20094.09, p\u2009=\u20090.044. That is, having light eyes increased the relative threat of light-eyed rivals more in men who had felt accepted by their father than in those who had felt rejected by him  interacted with own eye color , F1, 106\u2009=\u200913.1F1, 106\u2009=\u200913.1p\u2009<\u20090.0001; jealousy: beta\u2009=\u20090.142, p\u2009=\u20090.007); and that the effect was dampened by paternal rejection .Results were similar if paternal rejection was left in its original, continuous form rather than split along the median; and if attraction and jealousy were computed not as proportion of choices, but as differences between the ratings given to light vs dark eyes on the 0\u201310 scale. Multiple regression analyses Norman,  showed t2p\u2009=\u20090.03 vs 0.008, that is Cohen\u2019s d\u2009=\u20090.35 vs 0.18) or partialled out from one another. Second, as shown by separate ANOVAs, the effect of own light eyes was independently significant in men with light-eyed mothers, F\u2009=\u200913.75, p\u2009=\u20090.0002, and in men with dark-eyed mothers, F\u2009=\u20097.61, p\u2009=\u20090.006. Thus, the connection between having light eyes and liking light eyes shows up along with, not because of, sexual imprinting.Men are attracted to potential partners whose eye color resembles their own mother\u2019s , hence it is sensible to ask whether light-eyed men\u2019s preference for light-eyed women could be a mere byproduct of this inclination. Assortative mating might be direct, by eye color, or indirect\u2014most plausibly by ethnicity, which could create the illusion of assortative mating by eye color just because eye color and ethnicity covary. However, even disregarding the detail that all participants had the same ethnicity, neither interpretation stands up to scrutiny. First, the effect of own eye color on preference is observed for light-eyed men but not for dark-eyed ones. In Fig.\u00a0Here, I have put to a triple test the idea that light-eyed men should have evolved a particular preference for light-eyed women as potential partners and a particular concern with light-eyed men as potential rivals. I have done so with the help of the data of over one thousand men who rated the facial attractiveness of potential partners, and the threat of potential rivals, whose eye color had been manipulated. On this substantial sample, I found that light-eyed men see light-eyed women as more attractive than dark-eyed men do. The effect . Third, all these effects  ought to parallel men\u2019s expectation to invest in their children. Hence, on the grounds that men who have experienced less affective investment from their father tend to repeat this pattern with their own children , relationship context , and potential rival\u2019s eye color  were tested specifically by the study\u2019s design. The role of paternal rejection was not predicted ahead of time, implying that this finding ought to be regarded as exploratory. Yet, that a man\u2019s recollections of paternal rejection cancel, independently, all these effects suggests that such recollections do reflect a man\u2019s disinclination to invest in his future children.Note importantly that, via its impact on the fitness of children, paternal investment has an impact on the fitness of mothers as well. Thus, the paternal-uncertainty hypothesis by no means predicts that women should be neutral with respect to eye-color preference (indeed, they are not: Bressan & Damian, Considering that proper mirrors were unavailable for most of our evolutionary history, one may wonder how people\u2019s eye color could possibly inform their choices. One may think that the evolution of a preference for mates whose eye color looks like our own need not be more complex than that of a preference for people whose facial traits do\u2014which has been demonstrated repeatedly and begins well before adulthood (Richter et al., It has been argued (Rantala & Marcinkowska,"}
+{"text": "We explored the results of fixed point, coincidence point and coupled coincidence point for the mappings in an ordered metric spaces. Our results generalized and extended the well-known results in the literature. Some numerical examples are provided for justifying the results obtained.b-metric space which satisfies a generalized week contraction condition. Furthermore, these results are extended for two self mappings for obtaining coincidence point, coupled coincidence point and coupled common fixed point in the same context. A few examples are presented to support the findings.Some fixed point results are found for a self mapping in a partially ordered  It has a wide range of uses in mathematical research and scientific applications. It was first established by Bakhtin in [b-metric space and then applied their results to quadratic integral equations. Common fixed point results for generalized weak contractions in the same context was studied by Aghajani et al. [b-metric space were discussed by Aleksi\u0107 et al. [b-metric spaces was examined by Aydi et al. [b-metric space with necessary topological properties.A khtin in  and evenkhtin in . Later, khtin in , Allahyakhtin in  investigi et al. . Also, ti et al. . Some re\u0107 et al. . Common i et al. , Seshagii et al. , 24, 25 b-metric spaceIn this paper, we introduced the following generalized weak contraction condition which involve the altering distance functions y et al. , Bhaskarmentclasspt{minimay et al.  and Seshy et al. , 24, 25.mentclass2pt{minimy et al. , Huapingy et al. , Roshan y et al. , 19 and y et al. \u201323 for tIn the whole paper, we use the following nations for the altering distance functions: b-metric space.We start this section with the following fixed point result in a complete partially ordered Supposebe a complete partially ordered b-metric space withAssume that a continuous self mappingonis non-decreasing with respect toand satisfies the condition . If for somesuch thatthenhas a fixed point inmentclass2pt{minimThe proof is trivial for entclass1pt{minimaFurthermore the continuity of We have the following result in which the mapping According to Theorem\u00a02.1, a non-continuous self mappinghas a fixed point ifmeets the condition (6):n, i.e., As from Theorem\u00a0n, then  an an14) an1s) from . Accordi1s) from , we haveWe have the following result without the continuity property of Ifhas the property in Theorem\u00a02.6thatthen the weakly compatible mappingshave a coincidence point. Besides that, whenandcommute at their coincidence points, thenhave a common fixed point inn. Next to show that As from Theorem\u00a0}\u03bc. From , we haveb-metric space Consider the partially ordered Letbe a complete partially ordered b-metric space. Assume that a mappingsatisfies the condition  and,are continuous,has mixed-monotone property and commutes withSuppose, if for some such thatandthenandhave a coupled coincidence point inondition  and,\\doFrom Theorem 2.2 of , there w=\u03d6n+1 in , we get2,\u03c3=\u03b6n in , we get3Suppose that if hen from , we get and thus  holds. S1 thence  follows 1 thence .Now, we can deduce from  that \\doa 3.1 of . TherefoSupposebe a complete partially orderedb-metric space. Let a continuous mappinghas a mixed monotone property and satisfies the contraction conditions below for anysuch thatandandi.ii.whereandIf there existssuch thatandthenhas a coupled fixed point inA unique coupled common fixed point forandexists in Theorem\u00a02.9, if for everythere is somesuch thatis comparable toand toFrom Theorem\u00a0Now, assume the followingfrom Eq. , we get4Assume Iforin Theorem2.11, thenandhave a unique common fixed point inAssume that mma 2 of , we haveThe result can also be seen in the case of The same conclusions can also be seen as in Theorems \u00a0Although uence of , the conmentclasspt{minimasults of  as well Now depending on the continuity of a metric Let b-metric space. Assume that For If If Define a metric b-metric space with Suppose Suppose that Let Since, b-metric space, the existence and uniqueness of a fixed point for a self mapping which satisfies a generalized weak contraction condition with two rational auxiliary functions are discussed. These results are further generalized for two self mappings in the same context and proved the existence of coincidence point, coupled coincidence point and coupled common fixed points. Also, shown that these results are generalized the well known existing results in the literature. Some numerical examples are given to justify the obtained results.b-metric space to acquire triple, quadruple fixed points.These results can be extended by involving more mappings in partially ordered These contractions can be used to obtain a coincidence point, coupled coincidence point and coupled common fixed points for the mappings in various ordered metric spaces with required topological properties like monotone non-decreasing, mixed monotone, compatible etc.In complete partially ordered"}
+{"text": "The high longitudinal and lateral coherence of synchrotron X-rays sources radically transformed radiography. Before them, the image contrast was almost only based on absorption. Coherent synchrotron sources transformed radiography into a multi-faceted tool that can extract information also from \u201cphase\u201d effects. Here, we report a very simple description of the new techniques, presenting them to potential new users without requiring a sophisticated background in advanced physics. We then illustrate the impact of such techniques with a number of examples. Finally, we present the international collaboration SYNAPSE (Synchrotrons for Neuroscience\u2014an Asia-Pacific Strategic Enterprise), which targets the use of phase-contrast radiography to map one full human brain in a few years. Radiography was invented by Wilhelm Roentgen just a few hours after his discovery of X-rays ,2. To prSuch opportunities, however, remained largely unexploited for about one century. The detection of wave-like phenomena when electromagnetic radiation interacts with objects requires a special property called \u201ccoherence\u201d ,4,8. We Starting in the 1960s, unconventional synchrotron radiation X-ray sources became available, which had high coherence levels ,4. CoherThese facts notwithstanding, even today imaging with coherent X-rays is practiced only by a small portion of its potential user community. This limitation is partly caused by an insufficient understanding of the techniques, their foundations, and their effectiveness. Unfortunately, most descriptions of coherence-based radiography cannot be understood without a rather sophisticated physics background ,9.The primary objective of the present text is to fill this gap. We begin with a very simple description of coherence-based radiography, avoiding formalism and using elementary examples to introduce the essential notions and techniques. Then, we illustrate the practical use of such techniques with a few concrete cases. A discussion will follow, again in simple terms, of some advanced coherence-based imaging strategies. Finally, we illustrate the general potential impact of coherent radiography by presenting the recently inaugurated international project SYNAPSE , which tA complete treatment of the image formation process in radiography would require a detailed theory of X-ray scattering by the electrons in the objects ,4. One wOne could thus imagine the retrieval of the charge distribution from the images by inverse Fourier transforms, and from it, the derivation of the structural characteristics of the objects. However, the practice of radiography is very different from this idealized view, for both fundamental and practical reasons. In essence, the vast majority of radiography applications still rely only on absorption and on the visual inspection of the corresponding images. As mentioned, coherence-based imaging is used only, in a rather limited way, by a small community of specialists. When trying to export it beyond this restricted group, one cannot expect the audience to accept complex presentations. The objective of most clinical radiologists is just to \u201csee\u201d things in the objects, with as little processing and interpretation as possible. In their eyes, coherence-based techniques are justified only if they facilitate the observation of interesting features.And this is often true, as shown by the examples of Therefore, our first objective here is to understand how coherent X-rays produce the edge enhancement. The impact of this enhancement is vividly illustrated by The phenomena that improve the second image of Eo, propagating with the time t in the x-direction:\u03bb is the wavelength and v is the velocity. To introduce the idea of \u201cphase\u201d, we shall consider the following, the simple mathematical form of an electromagnetic plane-wave. This is a sinusoidal electric field of amplitude \u03c0/\u03bb)(x \u2212 vt) of the sine function in Equation (1). To verify that this function does propagate with time, note that E is the same for combinations of x and t that give the same phase. Consider for example the phase for x = zero, t = zero, which is zero. And the phase for x = \u0394x, t = \u0394t, which remains equal to zero if \u0394x \u2212 v\u0394t = zero, i.e., if v = \u0394x/\u0394t. This shows that the wave of Equation (1) propagates indeed with speed v. The \u201cphase\u201d of the wave is the argument  are in the 10\u22124\u201310\u22125 range or even smaller [What makes the refraction edge fringe pairs detectable in practice, as seen in  smaller .\u03b1 depends on the edge geometry and is typically not far from 1. A simple but tedious trigonometric calculation  shows th\u03b4 correspond to deviation angles in the 10\u22124\u201310\u22125 radians range: for a detector-object distance ro \u2248 1\u201310 m, they would give refraction fringe widths of the order of 10\u20131000 \u00b5m. So, the above values of This is in agreement with the empirical findings and with the typical detector spatial resolution, explaining why refraction edge enhancement can be observed. Note that 10\u20131000 \u00b5m is also the typical width of the edges for which refraction enhancement can be seen.\u03bb. More realistically, however, the beam consists of a band of wavelengths of width \u03b4\u03bb. In principle, this could decrease or even wipe out the edge enhancement caused by refraction.To start understanding X-ray coherence and its role in edge enhancement, let us consider the wavelengths of the X-ray beam in \u03bb defines the X-ray beam coherence. More specifically, it determines what is called the \u201clongitudinal coherence\u201d.This is expressed by saying that the bandwidth \u03b4\u03bb and the edge enhancement, consider that the wavelengths do influence refraction, since \u03b4 in Equations (2) and (3) changes with them (see \u03b4 makes (Equation (3)) the deviations \u03bc negligible and may impede the refraction edge enhancement. To understand the relation between the \u201clongitudinal coherence\u201d parameter \u03b4them see . For exa\u03bb \u2248 1 \u00c5 and with a bandwidth \u03b4\u03bb = 1 \u00c5, extending from 0.5 to 1.5 \u00c5. We see in \u03b4 roughly range from 10\u22126 to 10\u22125. Suppose that refraction enhancement applies to an edge of width w = 10 \u00b5m with a slanting angle \u03b1 = \u03c0/4. The optimized distance ro for the central wavelength \u03bb \u2248 1 \u00c5\u2014roughly corresponding to \u03b4 \u2248 2 \u00d7 10\u22126 and (Equation (3)) to \u03bc \u2248 2 \u00d7 10\u22126 radians\u2014is ro \u2248 w/\u03bc \u2248 5 m. Consider a typical synchrotron X-ray beam for imaging, centered at ro, the other wavelengths in the band 0.5\u20131.5 \u00c5 and their \u03b4-values. Short wavelengths, 0.5\u20131 \u00c5, correspond to narrower fringes than for the central wavelength, but to the same fringe positions. If anything, this increases the fringe visibility. Consider now, for this optimized Long wavelengths in the band, 1\u20131.5 \u00c5, correspond instead to broader fringes with less visibility. However, such wavelengths are more strongly absorbed by the material and contribute less to the fringes. These intuitive arguments, corroborated by abundant empirical evidence, reveal a fundamental fact : the fin\u03bb by filtering synchrotron radiation with additional devices, the so-called \u201cmonochromators\u201d. This is very good, since monochromators sharply decrease the X-ray flux. Avoiding them strongly increases the signal in the imaging experiment. Historically, this played a crucial role in the expansion of phase-contrast radiography [Therefore, one does not need to decrease \u03b4iography . These facts can be summarized by saying that synchrotron radiation possesses sufficient \u201clongitudinal coherence\u201d for refraction edge enhancement. However, this is only one of the two aspects of coherence. The second one is \u201clateral coherence\u201d, which is related to the geometry of the X-ray source. To introduce the notion of \u201clateral coherence\u201d, note that an excessively large source size in We shall further elaborate on \u201clateral coherence\u201d later. But we can immediately realize that for phase-contrast imaging the X-rays must possess sufficient levels of both kinds of coherence, longitudinal and lateral. And this is true for the synchrotron sources of today without requiring further measures like monochromatization. Let us now go back to ro is large enough (right-hand side of the figure), one also sees a fringe sequence like that in the bottom part of If absorption was the only active mechanism, then the detected image would simply consist of two regions with different intensities, as seen on the left-hand side of Elementary optics shows  that thero << \u03c1o, where \u03c1o is the distance between the X-ray source and the object. By deriving it, we can discover the origin of Fresnel edge diffraction.Specifically, Equation (4) is valid for the realistic case \u03bb. And dark fringes occur when the path difference equals an odd-integer multiple of \u03bb/2. Consider, in fact, a ray that reaches the detector after having been scattered by the edge. On the detector, its wave is combined with that of the rays that reach the same point without being scattered. Constructive interference, corresponding to bright fringes, occurs when the path difference equals an integer number of wavelengths ro. For a ray scattered by the edge and arriving at the position z on the detector, the path is (ro2 + z2)1/2.The object-detector path for rays without scattering is z = \u0394z, is \u03bb/2. Thus:\u03bb << ro, gives: The path difference for the first bright fringe is zero. And that for the adjacent dark fringe, occurring at The practical detection of a Fresnel diffraction fringe sequence is possible in practice only under certain conditions. These include sufficient spatial resolution and high coherence. z. From Equation (4), we see that \u0394z increases with ro. Thus, one can again compensate for the limited spatial resolution of the detector by placing it farther away from the object.Specifically, the spatial resolution of the detector must be sufficient to distinguish adjacent fringes, i.e., it must be better than \u0394\u03bb in Equation (4). Assume once again that the X-ray beam is not \u201cmonochromatic\u201d but has a bandwidth \u03b4\u03bb. This \u201cblurs\u201d the inter-fringe distance from \u0394z to \u03b4\u0394z and could make the fringes impossible to detect. Concerning \u201clongitudinal coherence\u201d, we must consider the presence of z does not exceed the inter-fringe distance itself: \u03b4\u0394z < \u0394z. From Equation (4) we get:The fringe sequence is still visible if the \u201cblurring\u201d \u03b4\u0394z < \u0394z is satisfied if:Thus, the requirement \u03b4\u0394Equation (7) is the condition for \u201clongitudinal coherence\u201d in this particular case.z-direction? In addition, there is also a source geometry condition for \u201clateral coherence\u201d. So far, our analysis implicitly assumed an X-ray source with a small size. What happens if the source has a large transverse dimension, for example in the In essence, the emission of each source point produces an individual diffraction pattern. The superposition of all patterns can wash out the fringes, making it impossible to detect them. Hence, we find here again that \u201clateral coherence\u201d requires a small source.ro is large enough to compensate for the limited spatial resolution of the detector. There is, however, an important difference between the two kinds of fringes. For a slanted edge, the fringe pair caused by refraction and the fringe sequence caused by diffraction can be combined. Both become visible if ro is increased. On the contrary, we see in ro and diffraction fringes for large values [The visibility of a diffraction fringe sequence continues to improve as e values . In the practice of coherence-based radiography, refraction fringe pairs are most frequently observed whereas diffraction fringe sequences are seldom seen. This is due to the fact that complicated edge shapes yield complex diffraction sequences, difficult to observe. Whereas refraction fringe pairs are typically simple and intense, and therefore easy to see.ro. The best approach is to boost the visibility of refraction fringe pairs, which are most effective in producing edge enhancement. Note again, however, that this optimization is not universal and must be repeated for each object.These empirical facts can be exploited to optimize the image quality by tuning The practical way to implement edge-enhanced radiography is by using the geometry of The simple online geometry of the top part of n is very close to 1 [The technical problem with this approach is finding suitable lenses for X-rays. The devices for visible light, such as focusing mirrors or refractive lenses, cannot be easily transferred to the X-ray wavelength range. We have seen that X-ray refraction is very weak, since the index of refraction ose to 1 . And theAs a consequence, special focusing devices must be invented and realized for X-rays: this is a crucial problem in the evolution of advanced radiography towards high spatial resolution. Major progress was made in recent years ,24,25,26The two top pictures a specifii-th zone equals i full wavelengths:Constructive interference at the focal point F occurs if the difference in the path between the rays passing through the center and the \u03bb in Equation (8) implies that the typical size of X-ray FZPs is much smaller than for visible-light FZPs. Fabricating such minuscule devices is not easy [iMAX of i, as high as possible. The presence of not easy ,22,23,24MAX of the outermost zone:The same equation gives for the width \u0394rMAX \u2248 (\u03bbiMAXf)1/2, which gives iMAX \u2248 rMAX2/(\u03bbf), so Equation (9) implies:Equation (8) shows that the FZP radius is rMAX requires a very narrow outermost zone width \u0394MAX, which is very difficult to fabricate. This difficulty is augmented by the weak X-ray absorption of the blocking zones, which requires them to have a large thickness. Therefore, the outermost zones must be radially narrow but very thick, i.e., with a high \u201caspect ratio\u201d [This is a key result: a large FZP radius t ratio\u201d ,22,23,24The mechanical fragility of such features makes fabricating FZPs for X-rays a very challenging task. This was successfully implemented, as shown in One might be surprised that this lens works for X-rays, since it uses two reflections at near-normal incidence, which should be very weak at short wavelengths. The secret is the use of multilayer coatings that increase X-ray reflectivity. The feasibility of this approach was demonstrated by successful tests, as reported in Ref. .Finally, The combination of focusing/magnification with coherence-based imaging can be also improved by adding a phase-controlling element to an FZP microscope, as shown in the bottom part of Our previous discussion was focused on edge enhancement by refraction, which as mentioned dominates most applications of phase-contrast radiography. But other interesting coherence-based techniques exist that deserve at least a first look, as we shall discover in Let us start with a general empirical definition of coherence: \u201cthe property that makes it possible to detect wave-like phenomena\u201d. To analyze its essential aspects, we can use anyone of such phenomena. Here, we shall select the simple case of diffraction by a narrow circular pinhole . This is\u03bb, as shown in Pinhole diffraction produces a detectable pattern of circular bright-dark fringes only if the radiation has a sufficient level of coherence. What are the corresponding conditions? Let us start with a point-like source that emits only one wavelength \u03bb, as in the right-hand image of ro\u03bb/d, where d is the pinhole diameter.Let us now relax these conditions, assuming that the source is not \u201cmonochromatic\u201d but emits a wavelength bandwidth \u03b4\u03bb \u201cspreads\u201d this inter-fringe distance to ro\u03b4\u03bb/d, blurring the fringe pattern. Which ceases to be visible when the spread becomes comparable to the distance between two adjacent fringes.The bandwidth \u03b4ro\u03b4\u03bb/d < ro\u03bb/d, or:Thus, the requirement for the pattern to be observable is This is in this case the condition for \u201clongitudinal coherence\u201d, qualitatively equivalent to that of Equation (7). Note that this condition is not very stringent. As a curiosity, applied to sunlight it explains why we can observe wave-like phenomena in everyday life, such as the beautiful colored fringes of soap bubbles. Indeed, the detection bandpass of our eyes guarantees that Equation (11) is satisfied for the solar spectrum that we can see. \u03be and with an angular beam divergence corresponding to a solid angle \u03a9.In addition to \u201clongitudinal coherence\u201d, there is a \u201clateral coherence\u201d (source geometry) condition for seeing the pinhole diffraction fringes. We assumed so far a point-like source, but \u03c1o the distance between the source and the object, the solid angle corresponding to the pinhole area \u03c0d2/4 is \u2248 (\u03c0d2/4)/\u03c1o2. Therefore, the portion \u03b7 of the emitted power that contributes to diffraction is:The angular divergence implies that only a portion of the source emission passes through the pinhole and participates in diffraction. Look at \u03a9 decreases, \u03b7 increases: a larger portion of the source emission contributes to the diffraction pattern, improving its signal-to-noise ratio. Conversely, if \u03b7 decreases more of the emission is wasted as far as pinhole diffraction is concerned. As the divergence \u03be of the source. Each source point acts as an emitter and produces a diffraction pattern centered at a specific position on the detector. The overall pattern is the superposition of all these individual patterns. And it could be no pattern at all, i.e., fringes may no longer be visible. Let us now bring into the picture  the fini\u03be(ro/\u03c1o). Fringes are still visible if this distance is smaller than that between adjacent fringes, \u2248ro\u03bb/d. So, the approximate condition to see the fringes is \u03be (ro/\u03c1o) < ro(\u03bb/d), or:To analyze this point, note in \u03c1o\u03bb/\u03be on the pinhole plane can contribute to diffraction, i.e., it is \u201claterally coherent\u201d. Equation (13) can be interpreted as follows: only radiation emitted within an area of diameter \u03b7: By combining Equations (12) and (13), we discover an important upper limit for the parameter \u03b7max is called the \u201ccoherent power fraction\u201d and measures how much \u201claterally coherent\u201d radiation emits the source. In other words, it gauges the level of \u201clateral coherence\u201d. The quantity \u03be and/or the angular divergence \u03a9 decrease. This illustrates the role of the source geometry in phase-contrast imaging. Note that the coherent power fraction, and therefore the \u201clateral coherence\u201d, increases if the source size \u03be of a synchrotron radiation X-ray source corresponds to the cross-section of the electron beam circulating in the accelerator. This cross-section, and therefore \u03be, are typically very small thanks to the sophisticated accelerator technology of today [Practically speaking, the size of today ,4,9. The\u03a9 of synchrotron sources is also very small. This is a phenomenon caused by Einstein\u2019s relativity, which produces laser-like beams of X-rays [Likewise, the angular divergence f X-rays ,4,9.\u03bb. And are much more difficult to satisfy for short X-ray wavelengths than for visible light. This explains why coherence-related applications started for X-rays only in the recent decades, whereas they have been present for centuries in visible optics.In essence, synchrotron X-ray sources reach high levels of longitudinal and lateral coherence, fully suitable for phase-contrast radiography. This solved a big historical problem. Both the conditions for \u201clongitudinal coherence\u201d (Equations (7) and (11)) and for \u201clateral coherence\u201d (Equation (14)) depend on the wavelength \u03be. Before concluding our elementary discussion, we must discover a fundamental limit affecting \u201clateral coherence\u201d. Consider a hypothetic procedure  to artif\u03be decreases. Elementary optics shows that the minimum value of the product \u03be2\u03a9 equals \u03bb2. Thus, the coherent power fraction \u03b7max defined by Equation (14) cannot exceed the value \u03c0/4.However, pinhole diffraction increases the angular divergence of the radiation as \u03c0/4 cannot be surpassed by improving the instrumentation. When a source reaches this limit, it has full \u201clateral coherence\u201d. This is a fundamental property of physics, called \u201cdiffraction limit\u201d. The maximum value Many of the synchrotron sources of today reach the diffraction limit at least in part of their emitted spectrum of wavelengths. This is true, in particular, for the new class of X-ray sources called \u201cfree-electron lasers\u201d . Concrete applications of coherence-based radiography impact many different areas of science and technology. The examples are becoming very numerous: selecting a subset is not trivial. We shall concentrate here on some of our results in materials science, the life sciences, and cultural heritage, selecting examples that provide a good idea of the power and flexibility of the novel radiography techniques.\u03b4 (defining the refractive index n with Equation (2)) and \u03b2, the absorption coefficient. Before introducing such examples, we can anticipate that the dominating mechanism for all of them is once again refraction-induced edge enhancement. Absorption also contributes to the images, but its effects are weaker. This can be understood from \u03b4 and absorption for \u03b2\u2014are limited. We see, however, that the effects of absorption are comparatively weaker. So, by not exploiting contrast mechanisms other than absorption one would miss excellent research opportunities, as clearly illustrated by the following examples.Both parameters are small, so the corresponding effects\u2014refraction, interference, and diffraction for Edge-enhanced radiographs taken with non-monochromatized synchrotron radiation reach excellent signal-to-noise ratios and contrast levels. This can be exploited to detect minute object details that are practically invisible in conventional absorption radiography. Furthermore, it opens the door to dynamic experiments, which image-evolving systems on short time scales.Tsai, W. L. et. al. (1996) reports a relevant example of such time-evolution studies . The invIt is known, for example, that in some cases electrodeposition of metal coatings yields poor results: visually unattractive rough-looking surfaces. A mechanism was proposed long ago to explain these failures and seek a remedy. But the hypothesized phenomenon was difficult for many to be accepted as plausible\u2014until coherent X-ray radiography demonstrated its existence with real-time movies.During electrodeposition, gas bubbles are formed close to the surface that is coated. The hypothesis was that the metal overlayer, under certain conditions, does not initially form on the substrate itself but on the surfaces of the bubbles. These then dynamically disappear, leaving cavities at the substrate-coating interface. Such leftover cavities can cause the poor quality of the coating.Experimental tests with phase-contrast movies demonstrated the validity of this hypothesis in a very direct way. Edge enhancement by refraction is indeed ideal to visualize bubbles. And metal coatings strongly absorb X-rays, becoming very visible. The combination of these features allowed taking real-time movies of the process, as shown in The results were unmistakable and illustrated the power of this type of X-ray imaging. The hypothesized phenomenon was clearly visible and could be analyzed in detail, in view of a possible optimization of the deposition parameters to avoid defects. No matter how hard to believe, the \u201cbuilding on bubbles\u201d mechanism could no longer be doubted after being directly seen . No dataVessels in living organisms are particularly difficult to image with conventional absorption-contrast radiography. In fact, the contrast is particularly weak between different organic tissues. This has very important consequences. For example, radiographic screening of heart diseases related to coronary arteries is still quite difficult, invasive, and not widely used.The negative consequences of limited contrast also impact life science research. Indeed, it makes it difficult to detect small vessels, which often play a fundamental role in physiological mechanisms.Tsai, Y. L. et al. (2002) presents a particularly challenging example of this problem . The expThe emitted power is indeed astonishing. If scaled up to a flying plane, the emission would likely cause it to crash. Thus, nature implements in fireflies an exceedingly effective light-producing process that could inspire human-oriented technologies.S)-2--4,5-dihydrothiazole-4-carboxylic acid, also known as \u201cfirefly luciferin\u201d. This requires supplying oxygen, but until recently it was not yet fully clear how this is accomplished in the firefly organ \u201clantern\u201d. Part of this organ is visualized in The phenomenon is not yet entirely explained and different hypotheses have been proposed for it. The emission takes place by breaking the compound . As it is well known, CAT produces three-dimensional radiographic pictures of objects with excellent flexibility in selecting the viewing mode. Thus, it has become a very widely used instrument for medical diagnostics.The foundation of CAT is the three-dimensional information present in a set of two-dimensional (\u201cprojection\u201d) radiographic images taken from different viewpoints. A typical CAT set consists of several thousand \u201cprojection\u201d pictures acquired in different directions, by rotating the radiography apparatus or, alternatively, the object. Pictures are normally taken at regular angular intervals.From a CAT set, well-established computer algorithms can reconstruct virtual images of different object parts, seen from different points of view and with adjustable depth penetrations. Over the past several decades, absorption-based CAT has become a very sophisticated and very powerful instrument.The advent of phase contrast in X-ray imaging triggered the obvious question: could it be implemented in the CAT mode? The issue was not trivial, since the information yielded by a \u201cphase object\u201d is not equivalent to that from an \u201cabsorption object\u201d. And the CAT reconstruction techniques had been specifically developed for absorption images. Could they be applied to phase-contrast images, and if yes to what extent?Once again, practical tests provided the answer. Phase-contrast tomography was successfully implemented in many cases, delivering useful and rather spectacular results ,28,38,39Phase-contrast tomography has become by now a routine technique. Its main practical problem is the need to take large sets of projection images, which increases the duration of the experiment. As we shall see in the last section of this text, excellent progress has been recently made to tackle this issue.Our previous discussion, mostly limited to X-ray refraction and/or absorption, was somewhat oversimplified. In fact, several other phenomena contribute to X-ray image formation. The corresponding, valuable information can be extracted with experimental strategies different from those described so far.For example, monochromatized synchrotron radiation can analyze phenomena occurring at specific wavelengths. And sophisticated techniques for spatial and/or spectral filtering of the X-rays can separate the different contributions to the images.One very relevant example is \u201cDiffraction Enhanced Imaging\u201d (DEI) ,40,41. WWhat will be the long-term impact of coherence-based radiography? Difficult to predict, for a number of reasons. But to have any impact at all, the new techniques must be massively applied to real problems in science and technology. Unfortunately, there exists in this domain a certain tendency to favor the development of experimental techniques over their practical applications. This is not good: unused techniques, no matter how clever and sophisticated, are of no value. And it is not easy to transform new techniques from mere feasibility tests to practical tools.This transformation is further complicated if the objective is medical diagnostics. In fact, such an objective is affected by many other technical and non-technical issues. The efforts towards broader practical applications are easier\u2014and desirable\u2014for materials science and biology. We shall illustrate these points with a specific and very relevant project: SYNAPSE, whose objective is to map large animal and human brains. Its ambition is to obtain comprehensive charts of all neuron cells and of their connections. One of the key achievements prior to SYNAPSE ,43 was mThe development of practical strategies to transform such a dream into reality reveals the formidable obstacles that separate feasibility tests from real-life experiments. These are the most important.Spatial resolution: the radiography techniques must be able to detect details of the objects on a scale suitable for brain mapping. One must consider two resolution levels. At the micron scale, the edge-enhancement techniques previously described are adequate and yield good general images of brain cells with some details. However, regions of special interest must be imaged with a better, nanometer-scale resolution. This is achieved with the microscopy techniques discussed in Total duration of the experimental program: mapping the Drosophila brain required a few years [ew years ,43. Mostew years  to engagImage contrast: microscopic soft tissue features in brain specimens such as organelles, axons, and synapses do not offer much contrast for X-ray imaging, even in the presence of edge enhancement. So, the contrast must be boosted by staining the objects [ objects ,43. The  objects . Radiation damage: this is a potential issue for all radiological studies at the cellular level. The problem is typically handled with empirical approaches, systematically checking the specimens for possible modifications. So far, the results have been negative, but systematic assessments are required.Data processing: the project of human brain mapping is primarily based on tomography and requires computer reconstructions of very many large tomographic image sets. The amount of data to be processed for SYNAPSE is enormous: it would largely exceed the present resources of organizations like Google. Once again, a coordinated effort over different countries appears necessary [ecessary . Data storage, availability, and security: the objective of SYNAPSE is to make its data available to all qualified researchers worldwide. But the sheer dimension of the information sets creates extreme problems. Access should be guaranteed without barriers and across national borders. But this creates formidable problems of data security. Once again, there is a big gap between feasibility tests and real experiments that handle real data.How can all these challenges be managed? SYNAPSE  is a conAt this time, SYNAPSE involves Japan, South Korea, China, Australia, Taiwan, and Singapore, with foreseen extensions to other countries. Its present partners are PAL  RIKEN/Spring-8, Shanghai/IoN , SSLS/NUS , Yong Loo Lin School of Medicine (NUS), the Institute of Physics of the Academia Sinica , NSSRC  and the Australian Synchrotron .SYNAPSE is built on the success of the previous program AXON (Accelerated X-ray Observation of Neurons). Which produced, in particular, important technical results as far as accelerating the image taking is concerned ,42,43. The SYNAPSE coalition was formally inaugurated early in 2020 with a ceremony in Singapore. In spite of the unforeseen problems caused by the Covid-19 pandemics, the programs initiated and already produced good results . The objSYNAPSE is also tackling the huge problems of data processing, storage, security, and availability. This is handled by a consortium of high-performance computing institutions in the participating countries, under the leadership of the National Supercomputer Center in Singapore ."}
+{"text": "PAC) reinforcement learning (RL) algorithm for Markov decision processes (MDPs) that intelligently maintains favorable features of both model-based and model-free methodologies. The designed algorithm, referred to as the Dyna-Delayed Q-learning (DDQ) algorithm, combines model-free Delayed Q-learning and model-based R-max algorithms while outperforming both in most cases. The paper includes a PAC analysis of the DDQ algorithm and a derivation of its sample complexity. Numerical results are provided to support the claim regarding the new algorithm\u2019s sample efficiency compared to its parents as well as the best known PAC model-free and model-based algorithms in application. A real-world experimental implementation of DDQ in the context of pediatric motor rehabilitation facilitated by infant-robot interaction highlights the potential benefits of the reported method.This paper offers a new hybrid probably approximately correct ( RL) algorithms can apply to a dynamical system modeled as a Markov decision process (MDP), few are probably approximately correct (PAC)\u2014meaning able to guarantee how soon the algorithm will converge to a near-optimal policy. Existing PACMDP algorithms can be broadly divided into two groups: model-based algorithms like  with a model-based (R-max) PAC algorithm, in order to give rise to a new PAC algorithm (Dyna-Delayed Q-learning (DDQ)) that combines the advantages of both.Typically, model-free algorithms circumvent the model learning stage of the solution process, a move that by itself reduces complexity in problems of large size. In many applications, however, model learning is not the main complexity bottleneck. Neurophysiologically-inspired hypotheses  have sugRL algorithms begins with the Dyna-Q algorithm  provides a smooth (er) transition from model-free to model-based, during the learning process . This is also distinct from another thread of research that addresses uncertainty and robustness in MDPs whose parameters are randomly (or even adversely) selected from a set and can vary over the instances when the same state-action pair is encountered  did not result in models of particularly large state and action spaces, but were particularly complicated by the absence of sufficient data sets for learning (HRI data can be collected) is usually limited to a few hours per month. There is a need, therefore, for reinforcement learning approaches that can maintain (or even guarantee) efficiency and accuracy even when the learning set is particularly small.Our own motivation for developing of this new breed of learning . This isPACRL algorithm in the form of a well-known theorem. The DDQ algorithm is introduced in PAC properties, and the analytic derivation of its sample complexity. Finally, DDQ outperforms its parent algorithms as well as the state-of-the-art model-base and model-free algorithms in terms of the required samples to learn near-optimal policy. Experimental results from application of DDQ in the context of early pediatric motor rehabilitation suggest the algorithm\u2019s efficacy and its potential as part of a child-robot interface mechanism that involves autonomous and adaptive robot decision-making. To enhance this paper\u2019s readability, the proofs of most of the technical lemmas supporting the proof of our main result are moved to the paper\u2019s Appendix.The paper starts with some technical preliminaries in MDPM is a tuple {S, A, R, T, \u03b3} with elementsS a finite set of statesA a finite set of actionsR: S \u00d7 A \u2192  the reward from executing a at sT: S \u00d7 A \u00d7 S \u2192  the transition probabilitiesdiscount factorA finite policy\u03c0 is a mapping \u03c0: S \u2192 A that selects an action a to be executed at state s. A policy is optimal if it maximizes the expected sum of discounted rewards; if t indexes the current time step and at, st denote current action and state, respectively, then this expected sum is written \u03b3 here reflects the preference of immediate rewards over future ones. The value of state s under policy \u03c0 in MDPM is defined asA state-action pair  under policy \u03c0:Note that an upper bound for the value at any state is MDPM has at least one optimal policy \u03c0* that results in an optimal value  assignment at all states; the latter is denoted Every The standard approach to finding the optimal values is through the search for a fix point of the Bellman equationRL) is a procedure to obtain an optimal policy in an MDP, when the actual transition probabilities and/or reward function are not known. The procedure involves exploration of the MDP model. An RL algorithm usually maintains a table of state-action pair value estimates Q  that are updated based on the exploration data. We denote Qt  the currently stored value for state-action pair  at timestep t during the execution of an RL algorithm. Consequently, vt(s) = maxaQt . An RL algorithm is greedy if it at any timestep t, it always executes action at = arg\u2009maxa\u2208AQt . The policy in force at time step t is similarly denoted \u03c0t. In what follows, we denote |S| the cardinality of a set S.Reinforcement learning , and the resulting estimated model subsequently informs the computation of the optimal policy. A model-free RL algorithm, on the other hand, would skip the construction of an estimated MDP model, and search directly for an optimal policy over the policy space. An RL algorithm is expected to converge to the optimal policy, practically reporting a near-optimal one at termination.Reinforcement learning algorithms have been classified as PAC) analysis of RL algorithms deals with the question of how fast an RL algorithm converges to a near-optimal policy. An RL algorithm is PAC if there exists a probabilistic bound on the number of exploration steps that the algorithm can take before converging to a near-optimal policy.Probably approximately correct , and letKt \u2286 S \u00d7 AMDPbe a set of state-action pairs labeled known. The known state-action is anMDPderived fromMandKtby defining new stateszs,afor each unknown state-action pair \u2209Kt, with self-loops for all actions, i.e.,. For all  \u2208 Kt, it isand. When an unknown state-action pair \u2209Ktis experienced,and the model jumps tozs,awith; subsequently,.Kt be set of current known state-action pairs of an RL algorithm t, and allow Kt to be arbitrarily defined as long as it depends only on the history of exploration data up to t. Any \u2209Kt experienced at time step t marks an escape event.Let Theorem 1Letbe a greedyRLalgorithm for an arbitraryMDPM, and letKtbe the set of current known state-action pairs, defined based only on the history of the exploration data up to timestept. Assume thatKt = Kt+1unless an update to some state-action value occurs or an escape event occurs at timestept, and thatQt \u2264 vmaxfor all  andt. Letbe the known state-actionMDPat timesteptand\u03c0t(s) = arg\u2009maxaQt denote the greedy policy thatexecutes. Suppose now that for any positive constant\u03f5and\u03b4, the following conditions hold with probability at least 1 \u2212 \u03b4for alls,aandt:. LetAoptimism:accuracy:complexity:sum of number of timesteps withQ-value updates plus number of timesteps with escape events is bounded by\u03b6 > 0. Then, executing algorithmon anyMDPMwill result in following a 4\u03f5-optimal policy on all buttimesteps, with probability at least 1 \u2212 2\u03b4.DDQ and the main contribution of this paper. Ddq integrates elements of R-max and Delayed Q-learning, while preserving the implementation advantages of both.This section presents Q-learning algorithm  Linelgorithm  with a mtype-1 update (model-free update), and to the one on line 52 as a type-2 update (model-based update). The latter offers a way for new model-related information to be injected into the model-free learning process. Type-1 updates use the m1 most recent experiences (occurances) of a state-action pair  to update that pair\u2019s value, while a type-2 update is realized through a value iteration algorithm (lines 43 \u2212 54) and applies to state-action pairs experienced at least m2 times. The outcome at timestep t of the value iteration for a type-2 update is denoted \u03f52 regulates the desired accuracy on the resulting estimate : the number of samples gathered for the update type-1 of Q  once l  = m1.\u2022 U : the running sum of target values used for a type-1 update of Q , once enough samples have been gathered.\u2022 b : the timestep at which the most recent or ongoing collection of m1  experiences has started.\u2022 Q . The flag is set to true initially, and is reset to true whenever some Q-value is updated. It flips to false when no updates to any Q-values occurs within a time window of m1 experiences of  in which attempted updates type-1 of Qi  fail.\u2022 n : variable that keeps track of the number of times  is experienced.\u2022 n : variable that keeps track of the number of transitions to s\u2032 on action a at state s.\u2022 r : the accumulated rewards by doing a in s.\u2022 We refer to the assignment in line 31 of Algorithm 1 as a estimate . A type-DDQ algorithm is tuned via the m1 and m2 parameters. One can practically reduce it to Delayed Q-learning by setting m2 very large, and to R-max by setting m1 large. The next section provides a formal proof that DDQ is not only PAC but also possesses the minimum sample complexity between R-max and Delayed Q-learning in the worst case\u2014often, it outperforms both.The execution of the Q-learning is incomparable .Before formally stating the Definition 3An event whenand at the same timel = m1orn = m2, is called an attempted update.Definition 4At any timesteptin the execution ofDDQalgorithm the set of known state-action pairs is defined as:s, a) known, the set Kt will be partitioned into two subsets:In subsequent analysis, and to distinguish between the conditions that make a state-action pair , timesteptis called a successful timestep for  if atteither update type-1 happens toQ or the number of times that  is visited reachesm2.\u03f51. Defining rewards as positive quantities prevents the Q-values from becoming negative. At the same time, state-action pairs can initiate update type-2 only once they are experienced m2 times. Together, these conditions facilitate the establishment of an upper-bound on the total number of successful timesteps during the execution of DDQ:Recall that a type-1 update necessarily decreases the Q-value by at least Lemma 1The number of successful timesteps for a particular state-action pair  in aDDQalgorithm is at most. Moreover, the total number of successful timesteps is bounded by\u03ba.Proof. See Lemma 2The total number of attempted updates inDDQalgorithm is bounded by |S\u2016A|(1 + \u03ba).Proof. See Lemma 3LetMbe anMDPwith a set of known state-action pairsKt. If we assume that for all state-action pairs \u2209Ktwe have, then for all state-action pairs in the known state-actionMDPit holdsProof. See m1 big enough and applying Hoefding\u2019s inequality allows the following conclusion  experiences a successful update of type-1 with its value changing fromQ toQ\u2032, and that there existssuch that\u2200s \u2208 Sand\u2200t\u2032 < t,. Iffor\u03ba = |S\u2016A|(1 + 1/(1 \u2212 \u03b3)\u03f51), thenwith probability at least.Proof. In m2, and the number of iterations for the value iteration part of the DDQ algorithm in order to obtain a desired accuracy.The following two lemmas are borrowed from  with verLemma 5Proposition 4)) Suppose the value-iteration algorithm runs onMDPMforiterations, and each state-action value estimateQ is initialized to some value between 0 andvmaxfor all states and actions. LetQ\u2032 be the state-action value estimate the algorithm yields. Then. estimate ofRandT, withn \u2265 m2, in the form ofandrespectively. WithCa constant and for all state-action pairs, choosingwith probability at least. Moreover, for any policy\u03c0and for all state-action pairs,with probability at least.Proof. Combine  \u2208 S \u00d7 A, we have:with probability at least.Proof. See DDQ; however, for the complexity condition of Theorem 1 to be satisfied, one needs to show that during the execution of m1 as in Lemma 9With the choice ofm1as in, and assuming theDDQalgorithm at timesteptwith \u2209Kt,l = 0 and, we know that an attempted type-1 update ofQ will necessarily occur withinm1occurrences of  aftert, say at timestep. If  has been visited fewer thanm2till, then the attempted type-1 update atwill be successful with probability at least.Proof. See Lemma 10Lett be the timestep when  has been visited form1times after the conditions ofwere satisfied. If the update at timesteptis unsuccessful and at timestept + 1 it is, then  \u2208 Kt+1.Proof. See DDQ algorithm can be derived in a straightforward way. Note that a state-action pair that is visited m2 times becomes a permanent member of set Kt. Therefore, the number of escape events is bounded by |S\u2016A|m2. On the other hand, DDQ as the minimum among the two bounds.A bound on the number the escape events of ism i.e.  suggest Lemma 11During the execution ofDDQ, with the assumption thatholds, the total number of timesteps with \u2209Kt (i.e. escape events) is at most.Proof. See PAC properties of the DDQ algorithm and provides a bound on its sample complexity.Next comes the main result of this paper. The statement that follows establishes the Theorem 2Consider anMDPM = {S, A, T, R, \u03b3}, and let, and\u03b4 \u2208 . There existandwithand, such that ifDDQalgorithm is executed,Mfollows a 4\u03f5-optimal policy with probability at least 1 \u2212 2\u03b4on all butoptimism condition, we start by proving that Proof. We intend to apply t = 1, the value of all state-action pairs are set to the maximum possible value in MDPM. This implies that t = n \u2212 1. 3) At timestep t = n, all t = n. For these state-action pairs, 1) At For all M exept for t and all state-action pairs, which directly implies Note that accuracy condition, first writeTo establish the s, a) \u2208 Kt, there can be two cases: either \u03b2 \u2264 3\u03f51. If If  \u2208 Kt, \u03b2 \u2264 3\u03f51 with probability at least a = \u03c0t(s) and mirroring \u03b1 = 0  is bounded by \u03ba + min  with probability Finally, to analyze \u03b4 and therefore the DDQ algorithm is PAC. Substituting \u03b6 into In conclusion, the conditions of DDQ algorithm to its parent technologies. It proceeds with additional comparisons to the state-of-the-art in both model-based 6 , the lowest bound on the sample complexity is |S\u2016A|/\u03f52 (1 \u2212 \u03b3)7, achieved by UCB Q-learning (MDP).The lowest known bound on the sample complexity of a model-based lgorithm ). For thlearning   deterministically transports the agent to state + with reward 0.5 + \u03f5\u2032 (with \u03f5\u2032 > 0). Let a be any of the other A\u2212 1 actions (represented by dashed lines). From any state i \u2208 {1, \u2026, N}, taking action a will trigger a transition to state + with reward 1 and probability pia, or to state \u2212 with reward 0 and probability 1 \u2212 pia, where pia \u2208 {0.5, 0.5 + 2\u03f5\u2032} are numbers very close to 0.5 + \u03f5\u2032. For each state i \u2208 {1, \u2026, N}, there is at most one a such that pia = 0.5 + 2\u03f5\u2032. Transitions from states + and \u2212 are identical; they simply reset the agent to one of the states {1, \u2026, N} uniformly at random.To perform a fair and meaningful comparison of these algorithms to MDP such as the one shown in i \u2208 {1, \u2026, N} is independent of the other states; specifically, it is the action marked by the solid arrow if pia = 0.5 for all dashed actions a, or the action marked by the dashed arrow for which pia = 0.5 + 2\u03f5\u2032, otherwise. Intuitively, this MDP is hard to learn for exactly the same reason that a biased coin is hard to be recongized as such if its bias  is close to 0.5  policy of M in terms of the required samples. As expected, the required samples decrease  in m (m = 600). For that reason, we cap m at 600 which requires 7,770 samples on average for Mormax to learn the optimal policy. Yet another important performance metric to record for a model-based RL algorithm is the number of times it needs resolve the learned model through value-iteration, since the associated computational effort is highly dependent on this number. For Mormax, the average number of times it performs model resolution is 12.06.We empirically fine-tune the parameters of Mormax and UCB Q-learning algorithms to maximize their performance on learning the near optimal (4ly) in m  until thc2 parameter. The value of c2  is the most common Markovian model because some internal parameters of the human partners such as intent are not directly observable    or an MDDP)  part of six 1-h infant-robot social interaction sessions with a 10 month old subject, and data in the form of video are collected and annotated. In the six sessions the robot was remotely controlled and its actions were chosen by a human operator who was observing the interaction. The I which is a random variable that indicates the improvement as a result of using DDQ optimal policy and is expressed as DDQ algorithm is used (as it was in last two rehabilitation sessions), and t-test with releasing the constraint of equal standard deviation for the two group , one can confidently attest that it is possible that a DDQ policy can outperform a human-driven social interaction strategy.To put the figures of wo group  in orderRL algorithm that captures favorable features of both model-based and model-free learning and most importantly preserves the PAC property can not only alleviate the cognitive load and time commitment of human caregivers when socially interacting in play-based activities with infants who have motor delays, but potentially also improve motor rehabilitation outcomes. One such algorithm which has been implemented and pilot-tested within an enriched robot-assisted infant motor rehabilitation environment is the DDQ. The DDQ algorithm leverages the idea of earlier Dyna-Q algorithms to combine two existing PAC algorithms, namely the model-based R-max and the model-free Delayed Q-learning, in a way that achieves the best (complexity results) of both. Theoretical analysis establishes that DDQ enjoys a sample complexity that is at worst as high as the smallest of its constituent technologies; yet, in practice, as the numerical example included suggests, DDQ can outperform them both. Numerical examples comparing DDQ to the state of the art in model-based and model free RL indicate advantages in practical implementations, and experimental implementation and testing of DDQ as it regulates a robot\u2019s social interaction with an infant in a game of chase hints at possible advantages in rehabilitation outcomes compared to a reactive yet still goal-oriented human strategy.The design and implementation of an"}
+{"text": "Twisted Ring-LWE, which replaces the canonical embedding by an extended form. By doing so, we allow the Ring-LWE problem to be used over maximal real subfields of cyclotomic number fields. We prove that Twisted Ring-LWE is secure by providing a security reduction from Ring-LWE to Twisted Ring-LWE in both search and decision forms. It is also shown that the twist factor does not affect the asymptotic approximation factors in the worst-case to average-case reductions. Thus, Twisted Ring-LWE maintains the consolidated hardness guarantee of Ring-LWE and increases the existing scope of algebraic lattices that can be considered for cryptographic applications. Additionally, we expand on the results of Ducas and Durmus  on spherical Gaussian distributions to the proposed class of lattices under certain restrictions. As a result, sampling from a spherical Gaussian distribution can be done directly in the respective number field while maintaining its format and standard deviation when seen in Several works have characterized weak instances of the Ring-LWE problem by exploring vulnerabilities arising from the use of algebraic structures. Although these weak instances are not addressed by worst-case hardness theorems, enabling other ring instantiations enlarges the scope of possible applications and favors the diversification of security assumptions. In this work, we extend the Ring-LWE problem in lattice-based cryptography to include algebraic lattices, realized through twisted embeddings. We define the class of problems  Lattice-based cryptography comprehends the class of cryptosystems whose security is based on the conjectured intractability of hard lattice problems such as the Shortest Independent Vectors Problem (SIVP), the Shortest Vector Problem (SVP), and the Closest Vector Problem (CVP)\u00a0,2. The mn a power of two. The fact that R to its dual, denoted R, with no loss in their underlying worst-case hardness guarantees\u00a0[Although the Ring-LWE hardness results hold for any number field\u00a0,9, its marantees\u00a0.R considering a power basis, since the transformation to the associated vector subspace H isomorphic to H and computing the inverse transformation with respect to the canonical embedding\u00a0[Another advantage of power-of-two cyclotomic number fields is that the sampling of error terms can be performed directly in the ring mbedding\u00a0. For genmbedding\u00a0,12.There are several works in the literature exploring properties of number fields used in the foundation of some cryptosystems based on ideal lattices. An example is a quantum polynomial-time algorithm to find a small generator of a principal ideal in the ring of algebraic integers of cyclotomic rings\u00a0, which ap prime, which was proposed for NTRU Prime\u00a0[Although these weak instances are not addressed by worst-case hardness theorems\u00a0, new proRU Prime\u00a0, and sugRU Prime\u00a0. In thistwisted embeddings. Since the canonical embedding is a special case of twisted embeddings, this replacement maintains the consolidated results for Ring-LWE. Twisted embeddings have been useful in coding theory, since they allow the construction of algebraic lattices with improved properties for Rayleigh fading channels, providing high density, maximum diversity, and great minimum product distance\u00a0[In this context, we extend the Ring-LWE class of problems to embrace more general algebraic constructions of lattices which allow additional factors on the embedding coordinates. We replace the canonical embedding by distance\u00a0,34,35.Twisted Ring-LWE problem, in which the error terms are sampled in the space H isomorphic to We extend the Ring-LWE problem by replacing the canonical embedding with twisted embeddings on both the search and decision variants. As a result, we obtain the m is odd, and m is even, corresponds to a distribution with the same format in the space H, but linearly wider in the ring dimension. This occurs because the lattice obtained from the ring H. Examples of ideal lattices equivalent to p-th cyclotomic number fields. Since power-of-two cyclotomic rings have been widely used in cryptographic applications, we consider parameterizing the Ring-LWE problem with the ring of integers of the maximal real subfield of a cyclotomic number field. We discuss the limitations of using maximal real subfields in a public-key encryption scheme\u00a0[H, their Ring-LWE instances can be efficiently converted between themselves.As a result, algebraic constructions from coding theory via twisted embeddings can also be used in cryptographic applications based on the Ring-LWE problem. In this work, we focused our attention on the algebraic construction of rotated d Durmus\u00a0 showed tr fields\u00a0, and ther fields\u00a0, and then scheme\u00a0 using thn scheme\u00a0. Finallyn scheme\u00a0. In factThis paper is organized as follows. n, the asymptotic factors are not affected by the change of embeddings.nd Regev\u00a0, and alsm, denote by In this section, we introduce concepts, results and notation to be used throughout the paper. For a positive integer number space H.Frequently, lattices are defined in the Euclidean space  context\u00a0,9, it isDefinition\u00a01.Let subspace is defined as(Space H)H endowed with the inner product obtained as a restriction of the standard inner product of We consider The norm .Let  canonical basis of H as an n-dimensional , if E with rank n. Equivalently, basis  as follows. Let n-dimensional distribution We extend this definition to elliptical Gaussian distributions in The smoothing parameter is a lattice parameter defining the width beyond which a discrete Gaussian starts to behave similarly to a continuous distribution\u00a0. It is rDefinition\u00a03.For an n-dimensional lattice\u039band positive real  smoothing parameter (Smoothing parameter)n, normalizing the Gaussian function discrete Gaussian distribution over For any In this section, we summarize concepts and results from algebraic number theory, presenting as an example the case of cyclotomic number fields and their maximal real subfields. Details can be found in\u00a0,40.algebraic) number field\u00a0K is a finite extension of the field K is a degree of K, denoted K. In general, if K and L are number fields such that An Example\u00a02.For  maximal real subfield of K be a number field. A map involution of K if Let K, satisfies trivial (it is the identity); otherwise, the involution is said to be non-trivial. If K is its maximal real subfield\u00a0[The subfield subfield\u00a0.K be a number field of degree n. There are exactly n distinct monomorphisms (of fields) from K to Let real if complex. If n as K to canonical embedding from K into the subspace H is the homomorphismA monomorphism  problem\u00a0,9.signature of K. We say that K is totally real when K is totally complex when K is said to be a CM-field if it is totally complex and has degree two over its fixed field by the involution F\u00a0[The pair lution F\u00a0.Any cyclotomic number field K is said to be a Galois number field if, for every x over K. In this case, the set of automorphisms Galois group of K over K to The number field K be a Galois number field. For every trace and norm of any element Let K that are the root of a monic polynomial in ring of integers of K, denoted by K is a number field of degree n, its ring of integers has a n elements, which is called an integral basis of K. If The set of all elements in a number field n elements. The same holds if fractional ideal of K, which is a subset of K satisfying the condition that K, including its ring of integers, is a K. If m-th cyclotomic number field, then K is a monogenic number field.If codifferent ideal, that is, the dual ideal of the ring of integers. Frequently, the codifferent ideal is also denoted by different of K. In general, the dual ideal of any fractional ideal K is the fractional ideal K, defined asThe fractional ideal (x) of \u03b8  -LWE hardness, namely the decision version of the Shortest Vector Problem (GapSVP), the Shortest Independent Vectors Problem (SIVP), and the Discrete Gaussian Sampling (DGS) problem, which is denoted  field K\u00a0.Definition\u00a04.\u039b and length For an approximation factor LWE, the DGS problem can be stated as follows: given an K be a number field with ring of integers K, and let K, let In order to define the Ring-LWE distribution and the computational problems associated with it, let Definition\u00a07.For  is the homomorphism (Twisted embeddings)F is totally positive, then Since sition\u00a01\u00a0.Proposition\u00a01.If M is a free .If M iK to K, then H.Twisted embeddings can be extended from n isometric to both Consider the natural extension of the trace function a under the canonical embedding are simply M of rank n can be seen as a full-rank lattice directly in the Euclidean vector space \u00a0(ii)\u00a0Proof.\u00a0By definition, Twisted Ring-LWE, or simply Ring-LWEIn this section, we propose an extended version of the Ring-LWE problem, adopting twisted embeddings rather than the canonical embedding. We refer to this new class of problems as  problem\u00a0, providie is randomized by a distribution K a number field with an involution, F its associated fixed field, e is randomized by a distribution K.In the Ring-LWE distribution, the error Definition\u00a011.For a totally positive element  Twisted Ring-LWE distributionwhere a is uniformly randomized in (Twisted Ring-LWE distribution)Analogously to Ring-LWE\u00a0, which iy et al.\u00a0 and the y et al.\u00a0.Definition\u00a012.For a positive real Definition\u00a013.Let  Ring-LWE hardness consists in two reductions: Theorem\u00a03.Let K be an arbitrary number field of degree n with ring of integers \u00a0[m is odd, and m is even. Then, the reduction modulo Durmus and Ducas proved a special case when a spherical Gaussian distribution with width eorem\u00a04)\u00a0. In ordem is odd and m is even. Also, let H be:In the statement of Theorem\u00a04, let Theorem\u00a04.Let \u00a0, and thes Q(\u03b62k)\u00a0, and therime p\u22655\u00a0. The casrime p\u22655\u00a0, and Ducrime p\u22655\u00a0. In the Let Proposition\u00a03Let , realized in Proposition\u00a03, is given byThe generator matrix of the H.As an immediate consequence of Theorem\u00a05, in Corollary\u00a01 we prove that the construction for the Corollary\u00a01.Let Proof.\u00a0In the realization of the ven by M . Since Op prime, to analyze the practical impacts of instantiating the Ring-LWE problem over the ring of integers of K in the compact public-key cryptosystem of Lyubashevsky, Peikert, and Regev\u00a0[In this section, we use the fact that nd Regev\u00a0  for efficient polynomial multiplication. For example, for Notice that, in our case, c such that q in comparison with CRT-based algorithms for power-of-two cyclotomic number fields [expansion factor, a property introduced by Lyubashevsky and Micciancio [f isg after reduction modulo f. By computing the expansion factor of q such that the coefficients do not wrap around after arithmetic operations, avoiding the occurrence of decryption errors.Thus, d Seiler . Althougr fields ,46. Anotcciancio . The expf.In order to analyze the expansion factor of Lemma\u00a04.If g is a polynomial in q in order to avoid the coefficients to wrap around after polynomial operations. This also leads to an increase in the length of system parameters and memory/bandwidth requirement for transmission of public parameters.For the case K does not increase as a power-of-two, one may want to find a ring instantiation that closely achieves a target security level. For example, to obtain a ring dimension between 700 and 800, the required for achieving 128-bit security [p ranges from the 223-th to the 252-th prime number, comprehending 29 possible choices.In the positive direction, since the dimension of security , possiblK is the maximal real subfield of a cyclotomic number field, whose dimension is K is the maximal real subfield of a cyclotomic number field. Moreover, we present future research possibilities related to the Twisted Ring-LWE problem.In a nutshell, we have discussed some practical impacts of instantiating the Twisted Ring-LWE problem when In this paper, we introduce an extension to the Ring-LWE class of problems, namely The Twisted Ring-LWE Problem ,9. The Rbeddings  rather tH via twisted embeddings. This generalizes the results of Ducas and Durmus in Theorem 5 [As a result, we broaden the scope of number of algebraic lattices that can be used for lattice-based cryptosystems, including those algebraic constructions of lattices that allow additional factors on the embedding coordinates. This type of construction has been useful in coding theory, since they allow the construction of algebraic lattices with improved properties for Rayleigh fading channels, providing high density, maximum diversity, and great minimum product distance ,34,35. Nheorem 5  and the p-th cyclotomic number fields. We analyze instantiating the Ring-LWE problem using maximal real subfields of p-th cyclotomic number fields in a public-key encryption scheme [p-th cyclotomic number fields grows exponentially.An example of a construction of the n scheme . By doinn scheme  and provH, without resorting to change of representation from Lyubashevsky, Peikert, and Regev  suggesteWe also leave as future work detailing how to connect Twisted Ring-LWE instantiations over different number fields, if the ring of integers of both number fields leads to equivalent lattices under twisted embeddings. By doing so, we can connect an instance on a power-of-two cyclotomic number field to an instance of a maximal real subfield as both rings of integers lead to a construction of the vidowitz . As a co"}
+{"text": "In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive capacity. As fundamental limit theorems of probability theory, the classical law of the iterated logarithm (LIL for short) plays an important role in the development of probability theory and its applications. The original statement of LIL obtained by Khinchine  is for aAs is well known, the linear processes are especially important in time series analysis and they arise from a wide variety of contexts (cf. Hannan ). Applicc denotes a positive constant, which may take different values whenever it appears in different expressions.A natural question is: can LIL of linear processes be realized under Peng\u2019s framework? The main purpose of this paper is to establish the law of iterated logarithm for linear processes generated by IID random variables in sub-linear expectation space. In the classical case, the LIL of partial sum is established by decomposing the linear process. We will find that this way is also valid for proving LIL for linear process in the sub-linear expectation space, though there are some differences. Intuitively, sub-linear expectation and related non-additive probabilities (Capacities) generated by them plays a decisive role in our proof. In the sequel, To state the result, we shall first recall the framework of sub-linear expectations. We use the framework and notation of Peng ,18,19. LDefinition\u00a01.A function 1.\u00a0Monotonicity: 2.\u00a0Constant preserving: 3.\u00a0Sub-additivity: 4.\u00a0Positive homogeneity: The triple Remark\u00a01.(i) The sub-linear expectation Definition\u00a02.(i)  Let whenever the sub-expectations are finite. A sequence of random variables (ii) (Independence) In a sub-linear expectation space whenever (iii) (IID random variables) A sequence of random variables It is obvious that, if Next, we introduce the capacities corresponding to the sub-linear expectations.Definition\u00a03.A set function V: 1.\u00a02.\u00a0.A set It is called to be sub-additive if A. ThenA sub-linear expectation V being replaced by In addition, a pair If of Zhang ).Definition\u00a04.(a) A sub-linear expectation .(a) A (b) A function V: (c) A capacity V: c1. Continuity from below: c2. Continuity from above: It is obvious that the continuity from above and sub-additivity imply the continuity from below, and the continuity from the below and sub-additivity imply the countable sub- additivity. Therefore, we call a sub-additive capacity to be continuous if it is continuous from above. Set In this section, we shall study the LIL of linear processes under association assumption in the sub-linear expectation space. For any First, we give the definition of strictly stationary sequence under the sub-linear expectation.Definition\u00a05.Next we give the main results: the law of the iterated logarithm for linear processes in the sub-linear expectation space.Theorem\u00a01.Suppose that Define the linear process by where Remark\u00a02.If Remark\u00a03.In particular, according to Proposition 4.1 in Zhang , for theIn order to prove the main results, we need the following Lemmas. The first one was the convergence part of the Borel\u2013Cantelli Lemma.Lemma\u00a01.Let .Let {AThe second Lemma on the exponential inequality is Lemma 2.1 of Zhang .Lemma\u00a02.Let where .Let {ZThe following Lemma is a law of iterated logarithm under sub-linear expectation.Lemma\u00a03.Let Proof.\u00a0Obviously, (4) can be directly derived from Theorem 3.11 and (4.29) in Zhang .\u2003\u25a1Lemma\u00a04.Let Proof.\u00a0Note that to prove , it suffBy the definition of Let now that\u2211k=1n\u2212E^[ing that\u2211k=1n\u03b5k\u2264\u2211x, where First, to estimate I2, by , we get<1. Theng\u03f5(\u00b7)\u2208Cl,I2, by , a, a21), a<\u221e,thensupn and are also a natural generalization of the LIL under classical additive probability. The key to the main results of this paper is an exponential inequality. If we can establish the corresponding exponential inequalities for negative dependent (ND) sequences, then we can obtain the LIL of linear processes generated by stationary ND sequences under sub-linear expectation. ND sequences are weaker than independent sequences. Therefore, it is an impending problem to study the theoretical properties of ND sequences in sub-linear expectation, which is the subject of future research."}
+{"text": "R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator property. In the present paper, we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains.A commutative ring  A non-zero ideal R). The domain R is called (finitely) stable if every non-zero (finitely generated) ideal of R is stable. By definition, invertible ideals are stable and this implies that Dedekind domains are stable and Pr\u00fcfer domains are finitely stable. On the other hand, stable domains need neither be noetherian, nor one-dimensional, nor integrally closed. For background on stable rings, their applications, and for results till 2000 we refer to the survey [Motivated by a paper of Bass , Lipman,e survey  by Olbere survey , 44\u201347.R is a BF-domain  if a = bc with set of atoms of H and we say that H is atomic if every non-unit is a finite product of atoms. Two elements associated if a = bc for some k is a factorization length and the set a is called the set of lengths of a. For convenience, we set system of sets of lengths of H,Let elasticity is accepted if H ishalf-factorial if it is atomic and monoid if it is atomic and each element of H is divisible by only finitely many non-associated atoms, andan FF-monoid if it is atomic and all sets of lengths are finite.a BF-We say that the H is atomic but not half-factorial, then we have By definition, an atomic monoid is half-factorial if and only if H is cancellative, H. We denote byseminormal closure of H, and bycomplete integral closure of H.Suppose that H is seminormal  if A is a divisorial ideal  if A is an s-ideal if A = AH. If s-ideal of H, then prime s-ideal of H if for all s-ideal I of H let radical of I. The monoid H is said to beMori if it satisfies the ascending chain condition on divisorial ideals,Krull if it is a completely integrally closed Mori monoid,monoid if the intersection of all non-empty prime s-ideals is non-empty,a G-primary if strongly primary if finitely primary (of rank s and exponent \u03b1) if H is a submonoid of a factorial monoid Then H be a primary Mori monoid, H is strongly primary.) Mori monoids and strongly primary monoids are BF-monoids.Finitely primary monoids and primary Mori monoids are strongly primary.  primary, seminormal, completely integrally closed) if its monoid R is primary if and only if R is one-dimensional and local. The domain Rfinite character if every non-zero element is contained in only finitely many maximal ideals.has divisorial if every non-zero ideal is divisorial.is h-local if R has finite character and every non-zero prime ideal of R is contained in a unique maximal ideal of R.is By a One-dimensional Mori domains have finite character by [S be an integral domain such that R is an order in S if S is a finitely generated R-module. Moreover, the following statements are equivalent if R is not a field [R is an order in a Dedekind domain.R is one-dimensional noetherian and the integral closure R is a finitely generated R-module.Let quadratic if R-module between R and S is a ring. If R. Thus every quadratic extension is an integral extension.The extension 3.In this section, we first gather main properties of stable domains \u20133.5. TheR be a domain. A non-zero ideal stable if it is invertible as an ideal of the overring R. The domain is called finitelystable if every non-zero (finitely generated) ideal of R is stable. Since invertible ideals are obviously stable, Dedekind domains are stable and Pr\u00fcfer domains are finitely stable. Conversely, if R is completely integrally closed and stable, then R and R is a Dedekind domain. Recall that R is an almost Dedekind domain if R is a Dedekind domain if and only if R is a stable almost Dedekind domain. In particular, every almost Dedekind domain that is not a Dedekind domain is not stable. For an example of an almost Dedekind domain that is not a Dedekind domain we refer to [Let Proposition 3.1.Let R be a domain that is not a field. Then the following statements are equivalent.R is a one-dimensional stable domain.R is a finitely stable Mori domain.R is a stable Mori domain.Proof.This is due to Gabelli and Roitman. More precisely, the equivalence of (a) and (b) is proved in [R is a Pr\u00fcfer domain. Next we consider the local case.Examples given by Olberding in , 46 showCorollary 3.2.Let R be a local domain that is not a field.The following statements are equivalent.R is a one-dimensional stable domain.R is a primary stable domain.R is a stable Mori domain.R is a strongly primary stable domain.If these conditions hold and (b) (c) age 2 of ).(d) R be a domain. By Let R is a local domain whose ideals are 2-generated, then R is finitely stable with stable maximal ideal (e.g. see R is noetherian). Nevertheless, such a domain is  neither half-factorial nor an FF-domain. In what follows, we present suitable counterexamples.Note that if e.g. see  and the K be a quadratic number field with maximal order p be a prime number such that p is split (i.e. p\u2009=\u20092.) Let K with conductor S is a local domain whose ideals are 2-generated and there are precisely two maximal ideals of S. It follows from [S is not half-factorial.  R is noetherian, and thus R is one-dimensional by R is not integrally closed. Since R is not integrally closed, we have that (b) R-module by R is finitely stable.Consequently, R is a one-dimensional stable domain by R is 2-generated by (c) R is said to be weakly Krull ifA domain afrullah , 3, and Theorem 3.7.Let R be a domain with, and suppose that R is either weakly Krull or Mori. Then R is stable if and only if every ideal of R is 2-generated. If this holds, then R is an order in a Dedekind domain.Proof.R is 2-generated, then R is stable by R be stable.If every ideal of R is weakly Krull. Then, for every R is weakly Krull, this implies that R is Mori by [Let us first suppose that R is Mori in both cases. Using R is one-dimensional. Therefore, R is 2-generated. \u25a1Thus Corollary 3.8.Let R be a seminormal G-domain and suppose that R is either Mori or one-dimensional. Then R is stable if and only if every ideal of R is 2-generated. If this holds, then R is an order in a Dedekind domain.Proof.R is a seminormal G-domain, Since Example 3.9.K be a field, Y an indeterminate over K, and X an indeterminate over K(Y). Then R is not a valuation domain. By There exist integrally closed one-dimensional local Mori domains which are neither valuation domains nor finitely stable. Let R is a local two-dimensional domain with maximal ideal R is stable as well by [R is not Mori by There exists a seminormal two-dimensional local stable domain. Let R is seminormal. Indeed, we know D is seminormal. Now clearly R is seminormal in D. Therefore, R is seminormal.R which is a BF-domain, whence R is a finitely stable BF-domain that is not Mori . In SecH be a cancellative monoid and K a quotient group of H. An ideal system on H is a map Let r be an ideal system on H. A subset r-ideal if rI = I. Furthermore, a subset r-ideal of H if there is some cJ is an r-ideal of H. We denote by r-ideals, and we define r-multiplication by setting r-multiplication is a reduced semigroup with identity element H. Let r-ideals, r-invertible fractional r-ideals, and r-invertible r-ideals of H with r-multiplication. We denote by s-ideals of H, by r-r-ideals of H, and by r-r-ideals of H. We say that r is finitary if We refer to , 32 for s-system, the v-system, and the t-system. For every ideal system r, we have r is finitary, then H has finite r-character if each r-ideals of H.We will use the R be a domain with quotient field K and r an ideal system on R \u2003for all \u2003(b)\u2003for all \u2003(c)\u2003The following statements are equivalent.2.\u2003is half-factorial. \u2003(a)\u2003for all \u2003(b)\u2003for all \u2003(c)\u2003Ifandfor every, then \u2003(d)\u2003H is half-factorial and for every nonprincipalit follows that \u2003(e)\u2003Proof.H is finitely primary of rank one, there is some Since 1.(a) mq is a product of a atoms of H and b atoms of H. We infer that 1.(b) 1.(c) H is strongly primary and r-H is r-local, we have that I is a non-empty s-ideal of H, then 2. Note that r-ideal of H, there is some 2.(a) mHq is an r-product of a atoms of r-product of b atoms of 2.(b) 2.(c) 2.(c) H is half-factorial. Let 2.(d) 2.(e) A is principal. Then A = uH for some Case 1. A is not principal. Then Case 2. Observe that some of the semigroups . Thencatenary degree and the monotone catenary degree of H. By definition, we have H is factorial if and only if H is cancellative but not factorial, then, by [H is half-factorial and that Let transfer homomorphism if the following two properties are satisfied.A monoid homomorphism (T 1) u = vw, (T 2) If H is said to be a transfer Krull monoid if it allows a transfer homomorphism \u03b8 to a Krull monoid B. Since the identity map is a transfer homomorphism, Krull monoids are transfer Krull, but transfer Krull monoids need neither be commutative (though here we restrict to the commutative setting), nor Mori, nor completely integrally closed. The arithmetic of Krull monoids is best understood (compared with various other classes of monoids and domains), and a transfer homomorphism allows to pull back arithmetical properties of the Krull monoid B to the original monoid H. We refer to the surveys [A monoid  surveys , 28 for H is half-factorial, then All Dedekind domains are transfer Krull and stable. However, there are orders in Dedekind domains that are transfer Krull but not stable  and therWe start with a result on the finiteness of the catenary degree of weakly Krull Mori domains.Theorem 5.1.Let R be a weakly Krull Mori domain.For every, andif and only ifandis local.andIf, thenis a Mori monoid and it is half-factorial if and only if it is transfer Krull.Proof.R is a weakly Krull Mori domain, we have t-Let Since the catenary degree of a coproduct equals the supremum of the individual catenary degrees [Since See [Since H with There are primary Mori monoids H be a finitely primary monoid of rank H and some system H is said to bestrongly ring-like if Let The concept of strongly ring-like monoids was introduced by Hassler , and thenumerical monoid is a submonoid of value monoidA Proposition 5.2.Let R be a local stable Mori domain with. Thenis finitely primary of rankand it is strongly ring-like. If s\u2009=\u20092, thenand if s\u2009=\u20091 and, then the elasticityis accepted withProof.R is one-dimensional. By [R is 2-generated by Proposition 3.5.4, whence R is noetherian. If R, then s\u2009=\u20092, then s\u2009=\u20091. Since By R be a one-dimensional local Mori domain with R is stable, then, by Let Lemma 5.3.Let R be a Mori domain and a G-domain and let I be a divisorial stable ideal of R. Thenfor someProof.I is divisorial and R is a Mori domain, we have that Since every overring of a G-domain is a G-domain, Example 5.4(Stable orders in number fields). 1. Let R is 2-generated, R is a stable order in the Dedekind domain Let K be an algebraic number field, R is stable by a result of Greither [R and 2. Let s and exponent \u03b1, with all notation as in s\u2009=\u20091 and by R in a quadratic number field whose localization n but the catenary degree Next we discuss the catenary degree of finitely primary monoids, which has received a lot of attention in the literature. Let ure  holds. By (a) R is a one-dimensional Mori domain, we have that (b) R is a one-dimensional Mori domain, we have that R is of finite character. Furthermore, if R. Let R is a Mori domain and t-finitely generated and locally principal and R.(c) (d) R is a Mori domain, we have that (d) (e) (f) 2. If Thus the claim follows from R be as in Let R is a semilocal domain, then R is not semilocal, then the statements for R. If R is any order in an algebraic number field, then R can be transfer Krull without being half-factorial [By Theorem 5.10.Let R be a stable order in a Dedekind domain.The following statements are equivalent.is transfer Krull.is transfer Krull.is half-factorial.is half-factorial.cmon(I*(R))<\u221e.has finite elasticity if and only ifis bijective. If this holds, then the elasticity is accepted.Proof.1. This is an immediate consequence of R is an order in a Dedekind domain, R is a weakly Krull Mori domain with non-zero conductor. By 2. Since 3. By [Thus the assertion follows from In Remark 5.11(Structure of sets of lengths and of their unions).R is an order in a Dedekind domain, then sets of lengths of (Structure of sets of lengths) If H be an atomic monoid. For every (Structure of unions of sets of lengths) Let is the union of sets of lengths containing k. The structure theorem for unions of sets of lengths states that there is a bound M such that almost all sets Remark 5.12(On catenary degrees).Remark 5.13. We compare the arithmetic of stable orders with the arithmetic of seminormal orders in Dedekind domains. Note that stable orders need not be seminormal  and semR be a seminormal order in a Dedekind domain and let \u03c0 is bijective, then \u03c0 is not bijective, then \u03c0 is bijective. For stable orders, only one implication is true .R in a Dedekind domain such that The Statements 1.(c) and 1.(d) of L be the field with 16 elements, let X be an indeterminate over L and let R is a local divisorial half-factorial Cohen-Kaplansky domain such that Let Proof.R is a half-factorial local Cohen-Kaplansky domain, K-basis of L and R. Note that R is divisorial by [E of R let S(E) is a K-subspace of V and T(E) is a K-subspace of L.By [A and B are proper ideals of R, then Claim: If A and B be proper ideals of R. First let Let Now let A and B of R such that I = AB. It follows by the claim that K-subspace W of S(A). We infer that Assume that a\u2009=\u20091. Then Case 1: a\u2009=\u2009y. Then Case 2: Case 3: Case 4: Case 5: Case 6: Case 7: Remark 5.15(Transfer Krull does not imply stability). If R is an order in a Dedekind domain with R such that R has ideals which are not 2-generated. Thus, R is not stable.We construct a seminormal one-dimensional local noetherian domain X be an indeterminate over L, and K-basis of L. Then R-module. Since R is noetherian, and hence Let R itself is local and one-dimensional. Moreover, R is transfer Krull by [Since x0 is the constant term of x), and thus if R is seminormal.Now if y0 is the constant term of y). If Note that x1, y1 be the linear coefficients of x respectively y. Then Assume to the contrary, that"}
+{"text": "The Editors-in-Chief have retracted this article because there appear to be anomalies in four of the figures, specifically Figure\u00a05, Figure\u00a06A, Figure\u00a06C and Figure\u00a08A. The Editors-in-Chief therefore no longer have confidence in the data presented. The authors have been invited to submit a new manuscript for peer review. Xialong Tang stated on behalf of all co-authors that they do not agree with this retraction."}
+{"text": "We have studied one of the most common distributions, namely, Lindley distribution, which is an important continuous mixed distribution with great ability to represent different systems. We studied this distribution with three parameters because of its high flexibility in modelling life data. The parameters were estimated by five different methods, namely, maximum likelihood estimation, ordinary least squares, weighted least squares, maximum product of spacing, and Cram\u00e9r-von Mises. Simulation experiments were performed with different sample sizes and different parameter values. The different methods were compared on the generated data by mean square error and mean absolute error. In addition, we compared the methods for real data, which represent COVID-19 data in Iraq/Anbar Province. The Lindley distribution was proposed in 1958 by Lindley  studied \u03b8, and the second is gamma distribution with 2 and \u03b8, that is,The Lindley distribution is made up of mixing two continuous distributions with different weights; the first is exponential distribution with Thus, the resulting function is as follows:w = \u03b8/(\u03b8 + 1); hence, the probability density function (p.d.f.) is as follows:Lindley  used w =Ghitany et al.  introducParameter estimation of the two-parameter Lindley distribution was conducted by many researchers, such as Al-Bayati , Sharafiw = \u03b1\u03b8/(\u03b1\u03b8 + \u03b2) was used, as follows:The three-parameter Lindley distribution (THPL) was proposed by Shanker et al. ; the weiFigures W\u22121(.) denotes the negative branch of the Lambert W function.The quantile function of the three-parameter Lindley distribution is given by the following:We present five well-known methods to estimate the parameters of the three-parameter Lindley distribution, including maximum-likelihood (ML), ordinary least-squares (OLS), weighted least-squares (WLS), maximum product of spacing (MPS), and Cram\u00e9r-von Mises (CVM).x =  under the three-parameter Lindley distribution can be written as follows:The log-likelihood of the positive vector of observations \u03b8, \u03b1, and \u03b2, by solving the following nonlinear equations:Shanker et al.  derived We can also obtain MLE by maximising  via fminX(1) \u2264 X(2) \u2264 \u22ef\u2264Xn)( are the order statistics of a random sample from any probability distribution. The ith-order statistic has the mean and the variance as follows:Suppose that F(xi) represents the theoretical c.d.f. of the observation xi)( of the distribution under study and \u2131(i) represents the empirical c.d.f. which is usually estimated by OLS and WLS were proposed in 1988 by Swain et al. . We can F(xi) in the previous equation by its c.d.f. defined in equation  in the previous equation by its c.d.f. defined in equation  \u2212 F(xi \u2212 1) and F(x(0)) = 0; F(xn + 1) = 1.MPS was derived by Cheng & Amin in 1979 ; the ideF(xi) in the previous equation by its c.d.f. defined in equation .Note that if there is a tie, we cannot find the natural logarithm of CVM was proposed by MacDonald in 1971 . The ideF(xi) in the previous equation by its c.d.f., which was defined in equation  values, p values are greater than 0.05, indicating that the data follow the three-parameter Lindley distribution.We note that all We draw p.d.f. and c.d.f. of the three-parameter Lindley distribution based on the following:According to equations  and 30)30), the We note that the behaviour of the estimated functions is relatively close to that of the empirical functions. This finding is a good indication that the estimated models can represent the COVID-19 data.The parameters of the three-parameter Lindley distribution (THPLD) were estimated by five different methods. A simulation study was performed, and these methods were compared using MSE and MAE. All estimators were consistent because their MSE and MAE values decrease as the sample size increases. The MPS and WLS methods were good in small samples. MPS, MLE, and WLS were good in medium samples. MLE and MPS were good in large samples.On the practical side, the results indicated that the COVID-19 data follow the three-parameter Lindley distribution. The p.d.f. and c.d.f. were estimated based on the five methods, and then, these functions were drawn. The graphics indicated that the behaviour of the estimated functions is close to the empirical functions."}
+{"text": "The cost for a single test can be controlled to ~1 dollar. This strategy provides a competitive solution for real-time, sensitive, selective, and large-scale application in cold-chain food quarantine.Due to the friendly temperature for virus survival, SARS-CoV-2 is frequently found in cold-chain foods, posing a serious threat to public health. Utilizing an interdigitated microelectrode chip modified with an antibody probe and integrating dielectrophoresis enrichment with interfacial capacitance sensing, a strategy is presented for the detection of trace level spike-protein from SARS-CoV-2. It achieves a limit of detection as low as 2.29\u2009\u00d7\u200910 More typical examples have been showing their destructive power, such as large outbreaks of hepatitis A3 and norovirus infection5. As expected, these viruses are detected in various foods as well as water7, which exacerbates the spread of the disease. Therefore, the viral contamination detection in food poses a more great challenge in the recent decade8.The contamination of pathogens in food and the environment has always been a serious problem worldwide for food safety, entry-exit quarantine, epidemic prevention, and public health management. Although viral epidemics are less reported for food safety compared with bacteria9. Although there is not yet a direct evidence to indicate the foodborne characteristic of SARS-CoV-2, food contamination of SARS-CoV-2 has presented a risk for virus spreading, which attracts considerable attention in many countries12. SARS-CoV-2 virions adhering on the solid surface are reported to be stable, with a viability up to longer than 72\u2009h (on plastic)13. As a matter of fact, besides the wet markets providing a breeding ground for the virus14, positive identification of SARS-CoV-2 on cold-chain foods are frequently reported in China recently, including the confirmed SARS-CoV-2 virions on plastic packing. Due to the below 0\u2009\u00b0C temperature during the cold-chain transportation, the viruses can have a longer survival time than in room-temperature environment. On the other hand, the virus concentration may be of trace level, while a large number of samples need to be tested. Therefore, sensitive, fast, and low-cost SARS-CoV-2 detection is urgently needed for cold-chain foods.Since winter 2019, the outbreak of a so-called coronavirus disease 19 (COVID-19) has become a global pandemic, with the culprit being a new SARS coronavirus (SARS-CoV-2)8. Because the culture process is very time-consuming, PCR-based methods have become a mainstream approach15. Numerous works on various virus detection by PCR or reverse transcription-PCR (RT-PCR) in food have been reported, including hepatitis A17, hepatitis E18, and norovirus17. Although PCR techniques have been developed over the past 30 years, the operation is still complicated, and the required turnaround time cannot be shorter than several hours15. Based on the good specificity and versatile sensing mechanisms, bio-probe-based sensors for virus detection are becoming more practicable in recent years as promising approaches21. Also, due to the high specificity, reproducibility, and stability, antibody-based detections of causative agents are continually adopted in food safety detection23.For virus detection in food, there are mainly two types of techniques, culture/counting methods and polymerase chain reaction (PCR)-based methods26. As a result, S-protein (S1 subunit) is selected as a preferred biomarker for SARS-CoV-2 detection29. Because the S-protein existing on the periphery of the virion is exposed on the food surface independent of body infection and viral assembly, at a quantity more than viral RNA itself, it can act as a good biomarker for food contamination of SARS-CoV-2. For specific recognition of certain antigens, the antibody is considered as a promising probe due to the usually high affinity between the antigen and antibody30.A SARS-CoV-2 virion binds directly with its receptor through spike (S-) protein on its surface, and the subunit of S1 serves as the receptor-binding domain\u22126\u2009ng/mL, while the time from sample to result is as short as 20\u2009s due to effective target enrichment embedded into the detection process. Meanwhile, the detection is specific against the interferences, demonstrating a satisfactory selectivity in S-protein recognition. This report constructs a cost-effective immunosensor as well as a simple detection strategy for real-time, selective, and large-scale screening of SARS-CoV-2 for cold-chain food quarantine.Here, a method for trace S-protein (S1 subunit) detection associated with cold-chain food is developed for real-time SARS-CoV-2 contamination screening. An anti-SARS-CoV-2 S-protein antibody is immobilized on a low-cost interdigitated microelectrode (IDME) chip. Then, an alternating current (AC) signal is applied to the IDME to induce a dielectrophoresis force on the protein particles. Thus, the S-proteins are rapidly driven toward the IDME surface in the nanofluid and captured by the antibodies. Utilizing the electrical double layer capacitance at the IDME surface as an ultra-sensitive indicator, the limit of detection (LOD) reaches 1031, which is abundant in the antibody. Sodium (Na1s) and phosphorus (P2p)  solvent. The presence of P2p at the bare IDME  should be first verified. Al (Al2p) is dominant at the IDME surface before functionalization Fig. , demonst2p) Fig.  are accoDME Fig.  could be2 to 105\u2009Hz is acquired to reflect the change on the IDME surface during functionalization by an electrical method. The impedance distinctly increases after antibody modification, but changes little after blocking \u2009=\u2009\u22122.66lg\u2009X (ng/mL), demonstrates an excellent semi-log linear relationship between the target concentration and the response from 10\u22125\u2009ng/mL until 10\u22121\u2009ng/mL, with a correlation coefficient (R2) of 0.994. With the cut-off line (Y\u2009=\u2009\u22122.05%) defined as a response value three standard deviations from the background, the LOD is calculated to be 2.29\u2009\u00d7\u200910\u22126\u2009ng/mL plugging the cut-off value into the calibration equation. This LOD is at an ultra-low level. The dose response as well as the calibration demonstrates a quantitative performance of the sensor, with a wide linear range.For calibration using dose response Fig. , the resFor a qualified sensor, selectivity for the target is the most important performance. In this work, the acquired effective response is verified in three ways: (1) comparing the response from functionalized sensors with that from dummy sensors when S-protein is the target of the test, (2) comparing the response from S-protein with that from the background of 0.1\u00d7 PBS, and (3) comparing the response from S-protein with that from the interferences. Here, the dummy sensor is defined for an IDME chip without antibody functionalization to verify the probe\u2019s effectiveness.\u22121\u2009ng/mL is equivalent to the response from S-protein at 4.27\u2009\u00d7\u200910\u22124\u2009ng/mL calculated using the calibration line, then the selectivity ratio of this sensor is calculated to be 234:1 (10\u22121\u2009ng/mL:4.27\u2009\u00d7\u200910\u22124\u2009ng/mL).According to the comparison result Fig. , the res\u22123\u2009mg/mL, which most possibly exist at the food surface dissociated from various bacteria. In this test, the spiked S-protein is 10\u22124\u2009ng/mL. Although the concentrations of nontarget molecules are 10-fold higher than that of S-protein, the response is only a bit larger than that in PBS without impurities , the interfacial capacitance will increase as illustrated in Supplementary Material  force, S-protein particles are attracted towards the sensor\u2019s surface and captured by the antibodies in 20\u2009s. Also, the response acquisition is completely integrated into the target enrichment process, thus the response time is shortened to 20\u2009s, a duration meeting the real-time detection demand on site. Besides, the LOD of this detection reaches an ultra-low level, i.e., 10Another merit of this strategy is the high specificity. The selectivity for S-protein against the interference is calculated to be 234:1. Not only common organic molecules but also various matrices as backgrounds are verified to be nonresponsive, with known or unknown components. Therefore, the sensor has demonstrated the required specificity to identify the S-proteins from practical samples with complex backgrounds.The cost for a single sensor device is estimated to be ~1 dollar. As a result, this sensor is designed to be a disposable chip. Meanwhile, the impedance analyzer for capacitance detection is also inexpensive and lightweight. As discussed previously, the detection operation as well as the pretreatment is simple, only including dilution and centrifugation steps. Therefore, this sensor can be operated by a layperson. Based on the above characteristics, the platform and method for S-protein detection provide a promising solution for large-scale applications in cold-chain food quarantine requiring a quick response, low LOD, high specificity, user-friendly operation, and low cost as well.36. Compared with most techniques for preconcentration needing an extra incubation or equipment, AC electrokinetic (ACEK) effects can manipulate nanoparticles efficiently to realize target enrichment rapidly without extra processes or devices39. For relatively large molecules such as proteins, DEP force, an important ACEK effect, has been demonstrated as a dominant force applied on the particles41. In this work, an IDME chip is used as a physical device to induce the DEP effect. DEP force can be expressed as a function of electric field , directly reflects the S-protein adsorption level, by which the S-protein concentration in the solution can be indicated. Using an IDME of micron-scale, dC/dt is a competitive parameter to reflect the tiny change at the electrode interface44. Therefore, ultra-trace S-protein detection can be expected. In practice, the lab-prepared sensors may have inconsistency due to different effective electrode surfaces and total recognition sites. Here, the normalization by the initial capacitance  is purchased from Cellregen (Beijing) Life Science and Technology Co., Ltd, which is recombinant and expressed by the prokaryotic system with the host of 2  , a small piece of a certain sample of ~8\u00d78\u2009mm2 is first cut-off, and 10\u2009\u03bcL S-protein of 1\u2009ng/mL is spread over it. After the solid sample is incubated for 12\u2009h in a closed tube at 4\u2009\u00b0C, 990\u2009\u03bcL of 0.1\u00d7 PBS is added into the tube. Then, the solution is sufficiently agitated and centrifuged at 3000\u2009r.p.m. for 10\u2009min. The supernatant from this mixture with a theoretical S-protein concentration of 10\u22122\u2009ng/mL is ready for further dilution to obtain the final samples with theoretical concentrations of 10\u22123 and 10\u22124\u2009ng/mL. During pretreatment of the salmon slice, an additional centrifugation at 5000\u2009r.p.m. for 10\u2009min is necessary to remove the abundant interference, and the floating lipid layer should be excluded when the supernatant is collected. To obtain the corresponding backgrounds for these practical samples, a similar process is performed except for the S-protein spreading and incubation steps.The test procedures mainly include incubation, extraction, and centrifugation steps (as shown in Fig. S41, and the voltage is optimized to be 100\u2009mV according to the optimization (described in Fig. SC/dt can be calculated and analyzed. To demonstrate the sensor\u2019s repeatability and consistency, all the data are presented with error bars, which represent the standard deviation obtained from three sensors of the same batch.The frequency of the AC signal is set to be 100\u2009kHz according to a previous studyFurther information on research design is available in the Supplementary InformationReporting Summary"}
+{"text": "X be an abelian variety of dimension g over a field k of characteristic g modules over p > 0 and k is perfect, we have also a p-adic analog of covariant Dieudonn\u00e9 module g modules over the ring of Witt vectors Let Definition 1.1:L is an R-lattice in L has an R-basis that is an Given rings u is given by A; equivalently, there exists a u-stable Zarhin There exists a u-stablelattice(b)There exists a u-stablelattice(c)If p > 0 and k is perfect, then there exists a u-stablelattice(d)If p > 0 and k is perfect, then there exists a u-stablelatticeThe following restatement of (b) answers a question implicit in ref. , Remark Corollary 1.3.LetThen there exists a matrixsuch that, for everythere is a-basis ofon which the action of u is given by A, and such that, if p > 0 and k is perfect, there is a W-basis ofon which the action of u is given by A.X, u) in characteristic p > 0 cannot always be lifted to characteristic 0 Themoduleis free of rank h.(ii)If p > 0 and k is perfect, then themoduleis free of rank h.(iii)For eachthemoduleis free of rank h.(iv)Themoduleis free of rank h.(v)If p > 0 and k is perfect, then themoduleis free of rank h.Proof:(i)This is ref. , Theorem(ii)jE of M induces an jE-linear and K-semilinear automorphism of jM. By jM is free.The following proof is essentially a combination of the proofs of ref. , Proposix on On the other hand, by ref.  (p. 96), of ref. , Theorem(iii)\u03bb of \u03bb. Since Fix These induce decompositionsh over h over By (i), (iv)We have (v)Similarly, this follows from (i), (ii), and (iii). __Proof of Theorem 1.2:(a)k up to isogeny. By ref. [u is contained in a subring of iE. Then X is isogenous to iY with iE-stable i, then we may take E. By P. Then u-stable We work in the category of abelian varieties over  By ref. , Theorem(b)V as in (a). We havep = 0. Then u-stable Given (c)E. By P. Then u-stable As in the proof of (a), we reduce to the case in which (d)V be as in (c). We have u-invariant Let u, we consider a R-stable r stable for every (1)R is contained in a subring of iE, then the proof of R-stable lattice exists.If (2)X is an elliptic curve such that R-stable R cannot act on a two-dimensional Serre observed that if (3)R is assumed to be commutative, then the conclusions of Y is an elliptic curve such that B, and If R is commutative. For each nonzero The ideal R-stable V in U, and hence equal to U. Thus we obtain a Suppose that there is an It is an isomorphism sincef in R-stable Since In"}
+{"text": "Howevet al. ,7. This et al. ,9 insighSenescence evolves because natural selection \u2018cares less about\u2019 late life than about early life ,11. Thisx; of a newborn's probability of still being alive at that age, xl; and of her instantaneous rate of production of offspring at that age given she is alive, xb; for simplicity assume asexually reproducing female populations. Life histories can also be modelled for discrete intervals, where the simplest case is a birth-pulse population with all reproduction occurring on the birthday; this assumption makes the following equations exact [x entering interval X of unit length; Xl = xl be a newborn's probability of survival to the beginning of interval X; and Xm be the number of daughters she produces at the beginning of interval X, given she is alive.An age-structured life history  is a schns exact , p. 16; ns exact , p. 403.x at time t surviving to be censused for the first time at time t + 1, for pre-birth censusing is r is the intrinsic rate of increase, the population's exponential growth rate once in stable age distribution, calculated as the unique real root of the Euler\u2013Lotka equation:Further quantities can be derived: interval age-specific survival probability is notation , p. 814.X, add a bit to interval fecundity X at which the gene's effect occurs. This embodies the general approximationHamilton  considerr versus r and, as mentioned, considered age-specific interval survival and fecundity, parameterized as X and can be ignored for our purposes. The numerators are monotonically decreasing functions of the interval X at which the gene acts, vindicating the insight of Haldane, Medawar and Williams that natural selection cares less about late than about early life , can rise with age in rapidly shrinking populations; these tend to go extinct anyway [et al. used the sensitivity r, but genes that multiplicatively reduce interval average hazard rate, thus used the sensitivity The partial derivative on the right is a fitness sensitivity, or selection gradient, or indicator of the force of selection. Applying this approximation requires choosing the fitness measure yway [R0 ; thus Da\u2202ln\u2061\u03bc\u00afX) ,9.Hamilton's assumption that genes multiply ntuitive , p. 191:a), can in fact rise with age under some conditions; however, it still must decrease with age in initially non-senescing age distribution is a right eigenvector w of the matrix A; the (st)age-specific individual reproductive values also form a left eigenvector v of the matrix A; the dominant eigenvalue is j; i; and \u2329w,v\u232a is the eigenvectors' dot product. Caswell summarizes: \u2018The effect  assumes additive genetic effects on survival probability, while equation (1.6a) assumes multiplicative genetic effects on survival probability; see [et al. repeat a subtle mischaracterization by Caswell [a) and (1.9b) as a \u2018reformulation of\u2019 equations (1.6a) and (1.6b), and write, still implying equivalence, that \u2018For any given (st)age of a life cycle, the force of selection on an increase in the reproduction or mortality of that (st)age is proportional to the product of two key components: (i) the stable age distribution of individuals at that (st)age and (ii) the reproductive value of individuals that the (st)age contributes to the population (new offspring or their surviving selves)\u2019 [b) \u2018shows why reproductive value is apparently missing from\u2019 equation (1.6b): \u2018reproductive value at birth \u2026 is scaled to equal 1\u2019 [et al. observe in life-history data [r to proportional hazards (equation 1.7) equals Stage-structured life histories are modelled in discrete time using population projection matrices \u20135; discr Caswell  showed tation of ,1.8\u2202\u03bb\u2202aiulation\u2019 , p. 529. Caswell , p. 534,RVX\u2260VX+1 . Caswellequal 1\u2019 , p. 540.Click here for additional data file."}
+{"text": "Hinks TSC, Cureton L, Knight R, et al. Azithromycin versus standard care in patients with mild-to-moderate COVID-19 (ATOMIC2): an open-label, randomised trial. Lancet Respir Med 9: 1130\u2013402021; \u2014The appendix of this Article has been corrected and the data in the following Results text is now corrected: \u201c\u2026while systemic corticosteroids were co-prescribed in 13 (9%) receiving azithromycin\u201d. These corrections have been made to the online version as of Sept 2, 2021, and will be made to the printed version."}
+{"text": "Persons with autism spectrum disorder (ASD) have impaired mentalizing skills. In this study, a group of persons with ASD traits (high-AQ scores) initially received sham tDCS before completing a pre-test in two mentalizing tasks: false belief and self-other judgments. Over the next week, on four consecutive days, they received sessions of anodal electrical stimulation (a-tDCS) over the right temporo-parietal junction (rTPJ), a region frequently associated with the theory of mind. On the last day, after the stimulation session, they completed a new set of mentalizing tasks. A control group (with low-AQ scores) matched in age, education and intelligence received just sham stimulation and completed the same pre-test and post-test. The results showed that the high-AQ group improved their performance (faster responses), after a-tDCS, in the false belief and in the self-other judgments of mental features, whereas they did not change performance in the false photographs or the self-other judgments of physical features. These selective improvements cannot be attributed to increased familiarity with the tasks, because the performance of the low-AQ control group remained stable about one week later. Therefore, our study provides initial proof that tDCS could be used to improve mentalizing skills in persons with ASD traits. The human brain has developed extraordinary mentalistic capacities, far superior to those of other species of primates, to deal with our complex social world. The so-called \u201ctheory of mind\u201d (herein ToM) is a cognitive skill that allows us to navigate the social world while continuously tracking our own and others\u2019 mental states and engaging in social reasoning ,2. ToM iWe can distinguish two main neural networks involved in mentalizing processes: the affective ToM, which is mainly responsible for emotional empathy, and the cognitive ToM, which is assumed to compute others\u2019 mental states, dissociating them from ours and enabling our complex social reasoning capabilities ,5,6. EspSince autism is characterized by impaired cognitive ToM, some studies have explored the brain functional organization of persons with ASD, compared to control persons, while dealing with ToM tasks. For instance, neuroimaging studies by ,21 askedThe study of the efficiency of non-invasive brain stimulation to improve social cognition both in control individuals and in persons with ASD is a growing field. According to a recent review , some stAn alternative technique is transcranial direct current stimulation (tDCS). Although tDCS has the significant drawback of offering much less focal stimulation than rTMS, it also has some advantages, such as having relatively long-lasting effects\u2014about an hour after 12 min of stimulation \u2014a generaAs we have seen, evidence of the therapeutic efficacy of non-invasive brain stimulation to improve social cognition in persons with autistic traits is still scarce. In this study, we developed for the first time a multisession intervention with anodal tDCS over the right TPJ in persons with high-AQ scores. We measured their performance in validated mentalizing tasks before and after the treatment. A group of low-AQ persons served as controls, receiving sham tDCS and performing the same mentalizing tasks in two sessions with the same time delay as the high-AQ group. For this study, we selected two well-known tasks that are representative of cognitive ToM skills, that is, the false belief task and the self-other judgment task, which are associated with activations in the rTPJ. Both tasks involve a dissociation between representations of the self and representations of the other. The false belief paradigm consists of presenting stories in which a protagonist performs an action based on a false belief because he/she is unaware of a critical event, which the reader/listener knows. For example, \u201cMary puts her chocolate in the top drawer of the table, and while she was at the school, her mother moved it to the bottom drawer of the table. When Mary comes back home, will she look for the chocolate in the top drawer?\u201d To correctly answer this question, participants need to recreate the outdated belief of the protagonist to understand her actions (looking in the top drawer) even though they know the chocolate is actually in the bottom drawer. These stories are contrasted with stories of \u201cfalse photos\u201d that also require the representation of outdated content but do not involve monitoring the characters\u2019 beliefs. For example, \u201cAn old photo showed a house with a front door and two windows on the sides. In 2010 one of the windows was replaced with a new door. Did the old photo show the two doors?\u201d Therefore, false belief stories and false photographs are similar in their general difficulty, logical complexity and inhibitory demands, but differ in the need to think about someone\u2019s thoughts  ,22,34. WThe second task involves self-reference or other-reference judgments of physical or mental features. The participants were asked to judge to what extent a physical characteristic  or a mental characteristic  applies to you (self-reference) or to a famous person (other-reference). This task requires that the participant know the other\u2019s mental states , which frequently differ from our own . We predAs for the low-AQ group, it serves as a passive control (with participants receiving only placebo stimulation) to assess whether there is any improvement between the initial and the final test of the mentalizing tasks, as a simple consequence of familiarization or learning. The expectation is that their performance would remain stable in ToM tasks. p = 0.0001), and in the EQ scores  = 16.225; p = 0.0001). However, they did not differ in age  = 3.253; p = 0.079), or Raven scores  = 0.870; p = 0.357). Forty-two Spanish-speaking participants, 21 with high-AQ scores and 21 with low-AQ scores serving as the control group, were selected. All were right-handed, had normal or corrected-to-normal visual acuity and had signed an informed consent form. Participants were screened via safety guidelines for transcranial stimulation  and the 2 and the current intensity was 2 mA, which involves a current density of 0.08 mA/cm2. The sham sessions had identical electrode setup and timing, except that real stimulation only took place during the first 30 s. Afterward, participants completed a survey regarding the tolerability of stimulation and guessing the stimulation condition. None of the participants reported special discomfort, and all believed they had been stimulated.The active stimulation sessions consisted of 20 min of anodal tDCS over the right TPJ, with the cathode electrode placed at the vertex, that is, at the CP6 and Cz positions in the 10/20 international localization system, respectively . The elep = 0.602). Belief task. In this task, a repeated measures factorial design was used, with 2 Test (Pre-test vs. Post-test) \u00d7 2 Modality  \u00d7 2 Response polarity (Yes vs. No) as within-participant factors and 2 Group (high-AQ vs. low-AQ) as a between-participant factor. Two sets of 20 stories (A and B) were used in a counterbalanced way for the pre-test and the post-test sessions. Set A consisted of the original stories created by , translaSelf-other judgment task. In this task, the design included 2 Test (Pre-test vs. Post-test) \u00d7 2 Reference (You vs. Other) \u00d7 2 Feature  as within-participant factors and 2 Group (high-AQ vs. low-AQ) as between-participant factor. Two sets of self-other questions were adapted from an earlier version used by . ParticiIn each task set, there were 20 items in each type of question , which is a total of 80 items. Participants issued a judgment on a scale of 1\u20134 . To encourage participants to engage in the task, they were told that their judgments would be compared with the answers given by the famous persons in various interviews, and they would receive an \u2018accuracy score\u2019 at the end of the task. This \u2018\u2019score\u2019\u2019 was randomly generated and displayed on the screen at the end of the task. t-tests), to assess the effects of the test (pre-test vs. post-test) for each experimental condition in each group, and to contrast the two groups (high-AQ and low-AQ) for each experimental condition. Global analyses of variance (ANOVAs) were performed in each task for reaction times and accuracy (only in the belief task), including Group (high-AQ and low-AQ), Test (pre-test and post-test) and the specific variables of each task: Modality (belief vs. photo) in the belief task and Feature  and Reference (you vs. other) in the self-other task. To explore the resulting interactions, separate ANOVAs were applied to each group separately, followed by pairwise comparisons  which focused on the variables with theoretical interest: Group \u00d7 Modality \u00d7 Test. However, the statistics referring to response polarity are offered in the p = 0.032; \u03b7\u00b2 = 0.110), suggesting certain familiarization with the task that was independent of the stimulation protocol. However, the crucial Test \u00d7 Group interaction was not significant (F < 1), which means that the learning effect was similar in both high-AQ and low-AQ participants . There was a slight improvement from the pre-test  to the post-test , which was statistically significant  = 4.947; icipants . Furtherp = 0.232). Furthermore, the t-test contrasting high-AQ and low-AQ for each experimental condition substantiated a significant group difference for the false belief items in the pretest session  = 2.946, p < 0.005), while the two groups did not differ in the false photo items  = 0.878, p = 0.354). As for the RTs, the high-AQ group showed a nonsignificant trend to respond more slowly than the low-AQ group  = 1.47; p = 0.0001; \u03b7\u00b2 = 0.295 (slower responses in the pre-test than the post-test), and Modality: F  = 6.092; p = 0.018; \u03b7\u00b2 = 0.132 . Most important, the interaction Test \u00d7 Group was also significant  = 7.597; p = 0.009; \u03b7\u00b2 = 0.160), since the difference between pre- and post-test was much larger in high-AQ  than in low-AQ participants . To explore this interaction in detail, separate ANOVAs were performed for the high-AQ and the low-AQ group. There were significant main effects of Test: F  = 16.765; p = 0.005; \u03b7\u00b2 = 0.532) and Modality  = 5.785; p = 0.026; \u03b7\u00b2 = 0.224). However, these effects were qualified by the crucial Test \u00d7 Modality interaction  = 6.265; p = 0.021; \u03b7\u00b2 = 0.239), illustrated in p < 0.0001), but not for false photo stories (t (20) = 1.972, p = 0.063). As for the low-AQ group, neither the main effects of Test or Modality nor their interaction were statistically significant .For the high-AQ group, there was a main effect of Test  = 22,713; p = 0.075). However, the between-group t-tests for each experimental condition obtained a significant difference: in the first session, high-AQ participants responded more slowly to you-mental questions  than low-AQ participants  = 2.173, p < 0.036). Significant main effects were obtained for Test: F  = 21.295; p = 0.0001; \u03b7\u00b2 = 0.347 (faster responses in the post-test than in the pre-test), Reference: F  = 106.926; p = 0.0001 \u03b7\u00b2 = 0.728 (faster responses for you than for other) and Feature: F  = 11.553; p = 0.002; \u03b7\u00b2 = 0.224 . In this task, only the reaction time was used as a dependent measure. The high-AQ group showed a nonsignificant trend to respond more slowly than the low-AQ group  = 3.33; p = 0.030; \u03b7\u00b2 = 0.112, which indicates that high-AQ and low-AQ participants responded differentially in the pre-test and post-test sessions depending on the features of the task. Finally, there was a Group \u00d7 Feature \u00d7 Reference interaction: F  = 4.828; p = 0.034; \u03b7\u00b2 = 0.108. To explore these interactions, new ANOVAs were performed for the high-AQ and the low-AQ groups separately. However, these main effects were modulated by important three-way interactions. Especially relevant was the Test \u00d7 Group \u00d7 Feature interaction: F  = 5.063; p < 0.0001; \u03b7\u00b2 = 0.479 (post-test faster than pre-test), Feature: F  = 23. 419, p < 0.0001, \u03b7\u00b2 = 0.539  and Reference: F  = 43.663, p < 0.0001, \u03b7\u00b2 = 0.686 (you faster than other). However, a significant Test \u00d7 Feature interaction was also obtained: F  = 4.503; p = 0.047, \u03b7\u00b2 = 0.184, indicating that whereas for the mental features, responses were significantly faster in the post-test  than in the pre-test  = 4.239; p < 0.0001), for the physical features, the post-test and pre-test  did not differ significantly: t (20) = 1.483; p = 0.154. This means that the beneficial impact of stimulation was selective over those items that demand the evaluation of mental features. This was corroborated by the fact that the effect of Test in the high-AQ group was constrained to the combination of other-mental: t (20) = 4.239; p = 0.0001, while it did not reach significance in the combination of you-mental: t (20) = 1.692; p = 0.106. The analysis of repeated measures with the high-AQ group alone showed robust main effects of Test: F  = 18.381, p = 0.0001; \u03b7\u00b2 = 0.783; that is, faster responses were found for you  than for other , although this effect was modulated by an interaction with Feature: F  = 4.544; p = 0.046; \u03b7\u00b2 = 0.185, since responses to you-physical  were faster than responses to other-physical . Importantly, there was no significant effect of Test  = 3.648; p = 0.071) or its interaction with any other factor, which means that there was no appreciable familiarity or learning effect for low-AQ participants, which serve as controls  = 72.050; controls . We explored the relationship between self-report measures and performance measures. Specifically, the correlations between the scores in AQ and EQ and the reaction times in the tasks were computed for the pre-test session. This procedure is justified, because at this stage both the high-AQ and low-AQ groups passed exactly the same protocol, before undergoing any treatment with tDCS. As This study showed for the first time that a multisession excitatory stimulation on the social brain of persons with high levels of autistic traits (high-AQ scores) improves their performance on representative mentalizing tasks. Anodal tDCS was applied over the right temporo-parietal junction, a significant region with ToM functions, in four consecutive sessions, and participants\u2019 performance in false belief and self-other distinction tasks was measured before and after the treatment. High-AQ participants improved after treatment (faster responses) exclusively in those tasks requiring mentalizing; that is, in false belief judgments and you-other distinction of mental features. Interestingly, persons with high AQ did not modify their performance in the tasks with little or no demand for ToM, such as the false photograph or you-other distinction of physical features. This suggests that the beneficial effects of a-tDCS in persons with ASD traits are specifically related to mentalizing processes and cannot be attributed to general learning or familiarity with the tasks. This was corroborated by the fact that in the low-AQ control group that received no active stimulation, there was no improvement in the ToM tasks.As expected, performance was better in the false photo than in false belief trials; that is, responses were faster and more accurate. This was true for both groups of participants and is consistent with previous results in the literature . It may The effect of a-tDCS on false belief performance in the high-AQ group is especially relevant here. It suggests that the stimulation of rTPJ has a very selective effect on mentalizing processes and does not affect the false photo task, despite being comparable in logical complexity  and inhibitory demands. The critical difference is that, unlike false belief, the false photo task does not require thinking about someone\u2019s thoughts. Nonetheless, the impact of a-tDCS on performance was limited to response times and did not affect the accuracy of the false belief judgments. This could be due to the fact that the false belief task was simple enough to induce a ceiling effect that prevents further improvements with the treatment. In future studies with ASD participants, the use of an implicit false belief task embedded in naturalistic social contexts ,45 couldBoth participants with high AQ and participants with low AQ scores responded faster to self-referred questions than to other-referred questions. This could indicate the additional cost of mental perspective taking (putting myself in someone else\u2019s shoes) or it could simply be a matter of familiarity (I know myself better than I know anyone else). More important are the differences observed between the two groups of participants. First, the a-tDCS applied to the high-AQ group selectively improved the response speed to questions about mental features referring to another person, while the control group\u2019s performance did not change in any task. That is, stimulating rTPJ in persons with high levels of autistic traits have a selective effect on those questions that are more demanding of ToM inferences. We did not obtain a similar improvement in questions referred to oneself, despite the fact that previous studies have reported that persons with ASD also have impaired self-reference functions . HoweverAs stated above, this study is a basic demonstration that a-tDCS applied over rTPJ could improve social cognition in persons with autistic traits. However, as such the study has some limitations that we want to highlight for future research. First, in this study, the high-AQ cut-off score was 30, rather than the standard 32 usually reported in the literature. Second, there are general limitations to non-invasive brain stimulation; for instance, the stimulation is applied to a specific cortical region, whereas potentially relevant subcortical regions cannot be directly stimulated; in addition, the stimulation on the target region overlaps with neighboring regions . These lOur findings demonstrate the efficacy of tDCS applied to persons with ASD traits, to improve their performance on representative social cognition tasks. We can establish two general consequences of this study. First, it confirms that the rTPJ used as a target for stimulation is functionally involved in the attribution of mental states to others and oneself, which are basic skills of cognitive ToM, necessary to properly navigate the social world. Second, it serves as initial proof that multisession anodal tDCS could be used to improve social cognition in persons with ToM deficits."}
+{"text": "X family of distributions. For the practical illustration, we introduced a new special sub-model, called the new generalized-Weibull distribution, to describe the new family\u2019s significance. For the proposed family, we introduced some mathematical reliability properties. The maximum likelihood estimators for the parameters of the new generalized-X distributions are derived. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. To assess the efficiency of the proposed model, the new generalized-Weibull model is applied to the coating machine failure time data. Finally, Bayesian analysis and performance of Gibbs sampling for the coating machine failure time data are also carried out. Furthermore, the measures such as Gelman-Rubin, Geweke and Raftery-Lewis are used to track algorithm convergence.As is already known, statistical models are very important for modeling data in applied fields, particularly in engineering, medicine, and many other disciplines. In this paper, we propose a new family to introduce new distributions suitable for modeling reliability engineering data. We called our proposed family a new generalized- Within the area of reliability engineering and other related fields, modeling of data related to lifetime events is very crucial. A range of probability models, such as Weibull, gamma, exponential, etc., are available for modeling lifetime data. However, in many cases, these classical models are not suitable for modeling lifetime data, and there is always a clear need for modified forms of these existing distributions. Therefore, the researchers have introduced new families that are more advantageous than the old ones. For more reading about statistical distributions using different approaches; see .In the literature, the Weibull distribution is the most outstanding one that has broadly been used in reliability engineering and in other various areas of research; see, for instance, . AlthougThe foremost goal of this research is to introduce a new flexible modification of the Weibull model by means of inducting one additional parameter. The induction of the additional parameter leads to the greater flexibility to enhance goodness-of-fit to reliability data. In fact, we show empirically that the new extension of the Weibull distribution offers the best fit to the coating machine failure time data than the two-parameter, three-parameter, and four-parameter competitive distributions (see section 5). The practical example really shows that the proposed distribution is a good alternative candidate for modeling reliability data.X (NG-X) family. A random variable X is said to follow a NG-X family, if its cumulative distribution function (cdf) is given by\u03b8 is an extra shape parameter, and F is the baseline cdf which may depend on the parameter vector X distributions can provide best fit to reliability engineering data. The corresponding density function isNow we introduce the proposed family of distributions called a new generalized-S and the hf h of NG-X distributions are given byThe reliability function -X distributions approach, we introduce a new form of the Weibull model called, a new generalized Weibull (NG-Weibull) distribution. Furthermore, we consider maximum likelihood (Non-Bayesian) and Bayesian procedures in order to estimate the unknown parameters of the NG-Weibull model. In the Bayesian discussion, we consider different types of symmetric and asymmetric loss functions such as squared error loss, weighted squared error, precautionary, K-loss, and modified squared error loss function to estimate the unknown parameters of the NG-Weibull model. Since all the parameters are positive, we use gamma prior distributions. Bayesian 95% credible and highest posterior density (HPD) intervals  are obtX family. Some mathematical properties of NG-X distributions are derived in Section 3. Section 4 is specified for obtaining the estimates using the maximum likelihood estimation, and the Monte Carlo simulation study is also provided in the same section. Section 5 is concerned with the goodness of fit of the proposed distribution. In this section, we showed that NG-Weibull model provides fit to reliability engineering data. Section 6 offers the Bayesian analysis. The future research directions are provided in Section 7. Some concluding comments are presented in Section 8.This paper is outlined in the following manner: In Section 2, we define a NG-\u03be = . Then, a random variable say X is said to follow the NG-Weibull distribution, if its cdf is given byLet The density function corresponding to The reliability function and hf of the NG-Weibull distribution are given byIn the X distributions, which include identifiability, quantile function, random number generation, rth noncentral moments, and the Renyi entropy with numerical illustrations. A characterization theorem extending the NG-X class of distributions in terms of the hf is also provided.In this part of the paper, we derived the mathematical properties associated with the NG-X distributions. To prove the identifiability property of the NG-X distributions, we have to show that \u03b81 = \u03b82. Let \u03b81 and \u03b82 be the two parameters having the NG-X distributions with cdfs given by G and G, respectively. From the definition of identifiability, we haveThe identifiability is an important statistical property that a model must obey to make sure that the inference should be precise. In this subsection, we prove the identifiability property of the NG-Theorem 1.The quantile function of NG-X distributions is given bywhere F\u22121is the quantile of the distribution with cdf F(x), 0 < p < 1, and W(z) gives the principal solution for w in z = wewProof.p < 1, we must solve the following equation for Q(p)Let 0 < y = F(Q(p)). Using software like MATHEMATICA, if we solve the equation below for yLet ThusNotation:If the cdf of the Weibull distribution is given bywe writeif Y is a NG-Weibull random variable.Some numerical values of the quantile measure are provided in U \u223c Uniform, then random numbers from NG-X distributions can be obtained fromF\u22121 is the quantile of the distribution with cdf F(x), and W(z) gives the principal solution for w in z = wew.If Theorem 2.The rthNon Central Moments of NG-X distributions can be expressed aswhere \u03a9i,k, n, qis defined as in the proof of the theorem, E[\u22c5] denotes an expectation, and U \u223c Uniform.Proof. From subsection 3.3, we know if U \u223c Uniform, then the following random variableF\u22121 is the quantile of the distribution with cdf F(x), and W(z) gives the principal solution for w in z = wew, follows the NG-X family of distributions.F(x) distribution. For a power series raised to a positive integer r \u2265 1, we have\u03b4r,i are obtained from i = 1, 2, \u2026; see [E(\u22c5) is an expectation. By the binomial series, we can writeAccording to , we can , \u2026; see . Thus weBy using integer powers of the Lambert W function we can writeBy the binomial series we can writePutIt follows thatSome numerical description of the ordinary moments are presented in Theorem 3.The Renyi entropy of the NG-X distributions, for \u03b4 \u2260 1, \u03b4 > 0, can be expressed aswhere X is a random variable with cdf F(x) and pdf f(x), and \u03a9k,q, ris defined as in the proof of the theorem.Proof. Recall the pdf of NG-X distributions is given byg(x)\u03b4 where \u03b4 \u2260 1 and \u03b4 > 0. By the binomial series we can writeWe first find an expansion for By the binomial theorem we can writeBy the power series representation for the exponential function, we can writePutIt follows thatTherefore, the Renyi entropy ishf, of a function, F, that can be differentiated twice satisfies the following differential equationIt is clear that X type distribution. The result here is inspired by [In this section, we present a Kumaraswamy NG-pired by . First, Definition:We say a random variable X follows a Kumaraswamy-G type distribution if its cdf is given bywhere G is some baseline distribution, x \u2208 Supp(G), and \u03be is a vector of parameters in the baseline distribution whose support depends on G.Remark:Note that if we take \u03bb = 1 and \u03c6 = 2 inof [then we get the cdf in the above definition. 2 inof , then weG type distribution is given byg is the pdf of the baseline distribution. Clearly the hf of the Kumaraswamy-G type distribution is given byThe pdf of the Kumaraswamy-Theorem 4.Letbe a continuous random variable. The pdf of X isfor some baseline distribution with pdf g and cdf G, if and only if its hazard rate function h(x) satisfies the following differential equationwith boundary condition h(0) = 2g(0).Proof. If X has pdf as stated in the theorem, then the differential equation as stated holds. Now if the stated differential equation holds, thenG type distribution.X type distribution is obtained from the above theorem by letting the baseline pdf and cdf given in section 1.Clearly, a characterization of the Kumaraswamy NG-X parameters using the maximum likelihood estimation approach and providing a comprehensive Monte Carlo (MC) simulation study to assess the maximum likelihood estimators (MLEs) performance.This section is devoted to estimating the NG-x1, x2, \u2026, xn be the observations of a random sample of size n taken from the NG-X distribution with the parameter vector \u0398 = T. For \u0398, the log-likelihood function (LLF) is given byLet The partial derivatives of the LLF are given by\u03b8 and \u03be of the NG-X distributions can be obtained by maximizing The MLEs of the unknown parameters optim R-function with the argument method = \u201cL-BFGS-B\u201d. We made 1000 MC-iterations using different sizes of the samples as follows, n = 25, 50,\u2026,1000. We computed the average MLEs, the associated mean square errors (MSE), biases and absolute biases. For the first set of MC simulation results, the plots MLEs and MSE are provided in In the following sub-section, we assess the behavior of the MLEs of NG-Weibull distribution by means of the MC simulation study. The process is carried out by maximizing the LLF using the In this section, we evaluate the usefulness of the NG-Weibull distribution by means of analyzing reliability engineering data taken from . The datTo figure out about the goodness of fit amongst the competitive distributions, we consider certain goodness of fit measures such as Cramer-Von-Mises (CM) statistic, Anderson Darling (AD) statistic, and Kolmogorov-Smirnov (KS)statistics alongside with its p-values.Corresponding to the coating machine failure time data, the model parameters\u2019 estimated values with standard errors in the parenthesis are presented in QQ) plots are presented in In support of the goodness of fit measures given in Furthermore, for the coating machine failure time data, we calculated the KS statistic values of the NG-Weibull and other considered models. Then, we utilized the parametric bootstrap approach , and booIn this section, we consider different types of symmetric and asymmetric loss functions such as squared error loss function (SELF), weighted squared error loss function (WSELF), modified squared error loss function (MSELF), precautionary loss function (PLF) and K-loss function (KLF). These functions associated with Bayesian estimators and posterior risks are reported in For more detail, we refer to \u201318. Next\u03b1, \u03b3 and \u03b8 of NG-W distribution have independent prior distributions as\u03b10, \u03b11, \u03b30, \u03b31, \u03b80 and \u03b81 are positive. Consequently, the joint prior density function is formulated as follows:Assume that the parameters \u03b6 asFor simplicity, let us define the function L(data) isThe joint posterior distribution defined from \u03b1, \u03b3, \u03b8) and K is given asTherefore, the joint posterior density function can be expressed by\u03b1,\u03b3 and \u03b8 assuming that \u03a8 =  = , can be given byi, j, k = 1, 2, 3,i \u2260 j \u2260 k and \u03a8i is the ith member of a vector \u03a8.Moreover, the marginal posterior density functions of 1, \u03a82, \u03a83) =  is obtained via minimizing the expectation of loss function under the marginal posterior density as follows:Under the marginal posterior density function as in However, in practice, because of the intractable integral in relation 1, \u03a82, \u03a83) = , which is associated with the NG-Weibull distribution and j;  as in \u03b7 \u2208 , the (1 \u2212 \u03b7)100% credibility interval In the Bayesian framework, interval estimation can be done via credibility interval conception. Consider the parameter vector \u03a8 = 100%  HPD interval for \u03a8j, j = 1, 2, 3 is the simultaneous solution of the following integral equationsThe HPD interval is a kind of credibility interval with a specific restriction. The  and observed data k, are as follows:It is clear from Eqs Starting with an initial estimate Draw Draw Draw \u03b1, \u03b3, \u03b8) and initial parameter vector \u03a80 = c, the posterior samples are extracted by above Gibbs sampler where the full conditional distributions are given asIn case of the NG-Weibull distribution, by considering the parameter vector \u03a8 = , Geweke (G) and Raftery-Lewis (RL) for checking the convergence of the Gibbs algorithm are provided in The statistical decision theory helps to address the state of uncertaintyand provides potentially a sound framework for dealing with problems of bio-medical, reliability, actuarial, economic and financial decision-making. Among the applied fields, the reliability engineering has received a serious consideration. In the field of reliability theory, modeling of lifetime data is very crucial. The data related to the lifetime of electronic product or any entity, etc., are usually positive and skewed to the right. In lifetime analysis and reliability theory, the failure rate function  is a prominent reliability characteristic. Among the possible failure rate functions, the unimodal, modified unimodal or bathtub-shaped failure rate curves are well-known in reliability literature. The classical models are not so flexible to model such complex forms of data.Due to the importance and application of the statistical models in reliability, medical and financial sciences, a reasonable work has been done in the literature aiming to improve the characteristics of the classical models. Although the new improvement has achieved the respective goal, unfortunately, the numbers of parameters have been increased, and the estimation of parameters, statistical inference and derivation of mathematical problems become complicated.To provide a better description and best fitting to the reliability data, therefore, in the present study, a new family of distributions has been studied. The key goal of introducing the class of distributions is to improve the characteristics of the classical distributions.From the above theory and discussion, it is quite clear that the researchers are always in search of new flexible distributions. Therefore, to introduce new flexible distributions and bring further flexibility in the model proposed in this paper, we suggest to introduce modified forms of the proposed model. As a future research direction, we suggest to introduce new models useful for modeling data in reliability engineering and financial sciences.As we stated above that the statistical models with bathtub-shaped failure rate function are very useful in reliability engineering. Here, we suggest a new modification of the proposed distribution to model lifetime data with a bathtub-shaped failure function.F = 1 \u2212 e\u03b3x\u03b1 \u2212 \u03b7x\u2212, be the cdf of the three-parameter modified Weibull (MW) distribution, where \u03be = . Then, a random variable say X is said to follow the new generalized modified Weibull (NGM-Weibull) distribution, if its cdf is given byLet The corresponding pdf and hf are given byDifferent plots for the failure rate function of the NGM-Weibull distribution are provided in \u03b1 = 1.2, \u03b3 = 1.2, \u03b8 = 0.01, \u03b7 = 0.08 (red line), (ii) modified unimodal for \u03b1 = 4.8, \u03b3 = 0.3, \u03b8 = 0.1, \u03b7 = 0.1 (green line), and (iii) bathtub-shaped for \u03b1 = 3.5, \u03b3 = 1, \u03b8 = 0.1, \u03b7 = 4.6 (black line). Since, the NGM-Weibull captures all the important forms of the hf, therefore, the NGM-Weibull distribution can be a good candidate distribution to model complex form of the reliability engineering data. In the future, therefore, we are intended to model lifetime and reliability data having unimodal, modified unimodal and bathtub-shaped failure rate behavior.From the plots provided in Furthermore, in the practice of actuarial and financial sciences, the heavy-tailed distributions are useful for modeling heavy-tailed financial data sets. Heavy-tailed distributions are those, whose right tail probabilities are heavier than the exponential distribution, and satisfiesX family.Here, we suggest a new heavy-tailed distribution to provide the best description of the heavy-tailed financial data set. The new heavy-tailed distribution can obtained by using the Burr-XII (B-XII) distribution as a special case of the NG-F = 1 \u2212 (1 + xc)k\u2212, be the cdf of the two-parameter B-XII distribution, where \u03be = . Then, a random variable say X is said to follow the new generalized B-XII (NGB-XII) distribution, if its cdf is given byLet The corresponding pdf is given byc = 1.2, k = 1.5, \u03b8 = 1.2 (red line), (ii) c = 1.4, k = 0.8, \u03b8 = 1.4 (green line), and (iii) c = 1.6, k = 0.3 and \u03b8 = 1.6 (black line).Different plots for the pdf of the NGB-XII distribution are provided in c and \u03b8, the NGB-XII distribution tends to a heavy-tailed distribution. Henceforth, the NGB-XII distribution can be a good candidate distribution to model heavy-tailed financial and other related data sets. In the future, therefore, we are intended to use the proposed method to introduce new heavy-tailed distributions.From the plots provided in X family. The MLEs of the model parameters along with some mathematical properties, are derived. Based on the proposed approach, a new modified form of the Weibull model called an NG-Weibull distribution is introduced and studied in detail. The NG-Weibull model is very versatile and is able to cater to the different patterns of failure rates. Due to the flexible behavior of the hf, the proposed model is capable to describe adequately the failure behavior of several lifetime datasets, particularly reliability engineering data. The usefulness of the NG-Weibull distribution is proved by analyzing the coating machine failure time data. We performed Bayesian estimation and estimated the model parameters using five different loss functions. The diagnostics measures such as the Gelman-Rubin, Geweke, and Raftery-Lewis are discussed to evaluate the MCMC procedure in the Bayesian analysis. As a future work, new models based on the proposed approach will be introduced to model complex form of reliability engineering and heavy-tailed financial data sets.Due to the great importance of statistical distributions in modeling data in reliability engineering, we introduced and studied a new family of distributions, called a NG-"}
+{"text": "Scientific Reports 10.1038/s41598-021-82611-8, published online 11 February 2021Correction to: The original version of this Article contained an error in the title of the paper, where \u201cto measure\u201d was incorrectly given as \u201cto detect of\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Information file."}
+{"text": "The Funding statement had an error in the reference of one project. Instead of PTDC/EMD-TLM/4644/2021, it should be PTDC/EMD-TLM/7289/2020.This work was supported by UID/BIM/50005/2019 and PTDC/EMD-TLM/7289/2020, a project funded by Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia - Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior (FCT-MCTES), through Fundos do Or\u00e7amento de Estado . CSL also acknowledges FCT-MCTES fellowship PD/BD/135045/2017.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher."}
+{"text": "Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer. Recently, network-based Markov models of DNA sequence evolution have been introduced along with model-based methods for reconstructing phylogenetic networks. For these methods to be consistent, the network parameter needs to be identifiable from data generated under the model. Here, we show that the semi-directed network parameter of a triangle-free, level-1 network model with any fixed number of reticulation vertices is generically identifiable under the Jukes\u2013Cantor, Kimura 2-parameter, or Kimura 3-parameter constraints. Typically, the goal of a phylogenetic analysis is to find a tree that describes the evolutionary relationships among a set of taxa. However, because trees, as directed graphs, have acyclic skeletons, they cannot represent reticulate evolutionary events, such as hybridization, introgression, and lateral gene transfer. Recognizing this limitation, it has become increasingly common to use phylogenetic networks in order to more accurately describe the history of some sets of taxa\u00a0. In Gross and Long  to determine the unrooted skeleton of N as well as which vertices (edges) are hybrid vertices (edges).To illustrate the implications of Theorem Our proof is largely combinatorial, as we are able to use the algebraic results for small networks obtained in Gross and Long  and Holldistinguishable and precisely what it means for the network parameter of a class of models to be generically identifiable.We begin this section by defining the graph theoretic terminology that we will use throughout the paper. Then, in Sect. (rooted binary) phylogenetic networkN on a set of leaves skeleton of a phylogenetic network is the undirected graph that is obtained from the network by removing edge directions.A tree vertex if it has in-degree one and out-degree two. A vertex is a reticulation vertex if it has in-degree two and out-degree one, and the edges that are directed into a reticulation vertex are called reticulation edges. Let rooted phylogenetic tree.A vertex is a level of a phylogenetic network is the maximum number of reticulation vertices in a biconnected component of the network. Of particular interest in this paper are level-1 networks, which can also be characterized as phylogenetic networks where no vertex belongs to more than one cycle in the network\u2019s skeleton .Note that deciding whether a mixed graph, a graph with some edges directed and others undirected, is a semi-directed network can be done in quadratic time in the number of edges [Corollary 4 of\u00a0Huber et\u00a0al. ]. The untriangle-free level-1 semi-directed network is a level-1 semi-directed network where every cycle in the unrooted skeleton has length greater than three. We will also refer to level-1 semi-directed networks with exactly one reticulation vertex as k -cycle networks, where k is the length of the unique cycle in the unrooted skeleton.In a semi-directed network, the reticulation vertices are the vertices of indegree two and the level is defined the same as for a rooted phylogenetic network. A A,\u00a0B non-empty. An edge e in a network separatesA and B if every path (not necessarily directed) between any e. If e separates A and B then we call e a cut-edge and we say  split.We finish these preliminaries with one additional bit of graph theory terminology that will be useful throughout. Let n-leaf rooted binary phylogenetic network. For the description below, we assume that the network belongs to the set of tree-child networks  the underlying substitution process is known as the -S\u00e1nchez . Howeverconstraints. For example, we will refer to the image of model associated tounder the Jukes\u2013Cantor constraints.In order to not overload the word \u201cmodel,\" we will refer to these restrictions on the transition matrices as We end this section on network-based Markov models by noting that there exist other natural extensions of tree-based Markov models. For example, in Francis and Moulton , the autN for the group-based models considered in this paper. We will see that for a given set of constraints , if N is the semi-directed network attained from N does not depend on the location of the root. Then, we show that the associated model does not change if we suppress degree two vertices or remove parallel edges in the network. Thus, the phylogenetic semi-directed network N contains all of the information necessary to recover In this section, we show how to associate a model mentclass2pt{minime and f are incident to a vertex of degree two and that the Markov transition matrices For a tree-based phylogenetic model under the Jukes\u2013Cantor, Kimura 2-parameter, or Kimura 3-parameter constraints, we may relocate the root and suppress vertices of degree two without changing the underlying model .n-leaf r-reticulation triangle-free level-1 semi-directed networks are distinguishable. In order to show this, we will require a number of results concerning 4-leaf networks which we prove in Lemma Our aim is to prove Theorem Q), a single triangle network (DT), or a 4-cycle network (4C), and compare the resulting varieties. We only need to consider four possibilities for each of toric fiber product argument that is described in the remark following Proposition 4.5 in Gross and Long If (ii)If (iii)If (iv)If (v)If (vi)If (vii)If See Table\u00a0Let mentclass2pt{minimThe proof of Lemma In order to reduce the total number of invariants required to prove each part, we take advantage of the symmetry between networks. As an example, suppose that the statement in part (vii) is false. Then there must exist two double-triangle networks with distinct skeletons, In order to prove some parts of the lemma, we require two or more invariants to distinguish all of the relevant networks, though all parts can be proven using some combination of just the following six polynomial invariants:https://github.com/colbyelong/DistinguishingLevel1PhylogeneticNetworks,we provide the code to verify that these polynomials vanish or do not vanish on the referenced varieties as claimed.Small trees catalog  for the K2P and K3P constraints we require a set of invariants that vanishes on exactly one of the single-triangle networks. The set ullivant .To prove (v), we require a set of invariants that vanishes on one of the tree varieties, but on none of the double-triangle network varieties, and a set of invariants that vanishes on one of the single-triangle networks varieties, but on none of the double-triangle network varieties. The set For (vi), we must first show that there is a set of invariants that vanishes on one of the double-triangle network varieties but on none of the 4-cycle network varieties. The set The invariant We also need a result on 4-leaf networks that does not fit into Table\u00a0common split if non-trivial if conflicting if For networks Let (i)when (ii)when The invariant Note that 4-cycles have no non-trivial splits, so we just need to compare trees, single-triangle networks, and double-triangle networks. Moreover, Table restriction of a network to a subset of leaves.Finally we require Lemma\u00a0N be an\u00a0n-leaf semi-directed network on\u00a0restriction of N to A is the semi-directed network A (where undirected edges are treated as bidirected) and then suppressing all degree two vertices and removing parallel edges.Let Lemma n-leaf semi-directed networks on\u00a0Let f contained in Let and Long , it is sLemma\u00a0N/X the network x. Observe also that If n-leaf semi-directed networks and If The next lemma follows immediately from Lemma\u00a0n-leaf semi-directed networks on\u00a0Let\u00a0n-leaf triangle-free level-1 semi-directed network on C a cycle in C. Then the partition induced by C is the partition x is separated from C by below the reticulation vertex if C. If C then we also say that x is below the reticulation vertex for any Let meet at a cycle C if each leaf in C. We say that they induce a cycle in t-cycle network. Note that if the set of leaves We say a set of three or more leaves N, i.e., this cycle is unique in\u00a0N. Denote this cycle by Observe that if n-leaf triangle-free level-1 semi-directed networks on refines\u00a0a,\u00a0b that are contained in different sets in\u00a0Let\u00a0We recall a combinatorial result from\u00a0Ba\u00f1os  on four-N be an\u00a0n-leaf triangle-free level-1 semi-directed network on\u00a0N such that\u00a0(Lemmas 12 and 13 of Ba\u00f1os ) Let\u00a0N bn-leaf triangle-free level-1 semi-directed networks on Let Let\u00a0a,\u00a0b,\u00a0c,\u00a0d all meet at a with d is below the reticulation vertex in To see this, first consider any We thus have that for Now consider any two leaves Suppose that every cycle in e in b such that e separates b from A. If e separates A from B, then Let u be the vertex in e nearer to A. If u is on a cycle, then denote this cycle by b (since C via e). If j, then the corresponding edge C is an edge that is further away from b than e and which separates A from b, contradicting the choice of e. So we may assume that the partition subdivideA  contains all of B and also none of A, which would imply that A and B. As every cycle in A and B. But this contradicts the fact that Furthermore See Fig.\u00a0a.u is not on a cycle, let f and g be the other edges incident to u. By choice of e, neither f nor g can separate A from b. Thus there is at least one element u via f, and at least one element u via g. As e does not separate A from B, there is at least one u via either f or g, say  f. Then let f, with Y the set containing b. Observe that If See Fig.\u00a0b. \\documTheorem\u00a0n-leaf triangle-free level-1 semi-directed networks on\u00a0Let We prove the claim by induction on mentclass2pt{minimn. We first show that we may assume that any set of 4 leaves that induces a 4-cycle in So now assume that different 4-cycle or a double-triangle, then by Lemma\u00a0Indeed, suppose this is not the case, and consider some arbitrary mentclass2pt{minimOtherwise, mentclass2pt{minimSo we may now assume that any set of 4 leaves that induces a 4-cycle in Firstly, if entclass1pt{miniman leaves. Thus by the induction hypothesis, if Secondly, suppose that n-cycle network, that is, Finally, suppose that\u00a0mentclass2pt{minimWe are now ready to prove Theorem\u00a0Theorem 2 The network parameter of a network-based Markov model under the Jukes\u2013Cantor, Kimura 2-parameter, or Kimura 3-parameter constraints is generically identifiable with respect to the class of models where the network parameter is an n-leaf triangle-free, level-1 semi-directed network with n-leaf triangle-free level-1 semi-directed networks on\u00a0Let We have shown that triangle-free level-1 semi-directed networks are generically identifiable under the Jukes\u2013Cantor, Kimura 2-parameter, and Kimura 3-parameter constraints. This means that, given a long enough multiple sequence alignment that evolved on a network of this class under one of these models, this network is, with high probability, the only network from the class that coincides with the given data. Roughly speaking, this means that the data provide sufficient information to reconstruct the network. To prove this result, we employed a blend of algebraic and combinatorial methods to show that any pair of networks are geometrically distinguishable.Previously, it had been shown that networks cannot be identified from certain substructures. For example, networks cannot be inferred from their displayed trees since more than one network can display the same set of trees (Gambette and Huber On the algebraic front, the computations reveal differences between the relationships between the network ideals under the JC constraints and the relationships between the ideals under the K2P and K3P constraints that would be interesting directions for further exploration. In Hollering and Sullivant , the autAdditionally, from an algebraic perspective, we note that adapting the random search strategy described in Hollering and Sullivant  is what Finally, a major open problem, which is the larger setting for this paper, is to determine whether generic identifiability results such as these can be extended to higher level networks. We expect finding the necessary invariants for the increased number of non-unique induced 4-leaf subnetworks will be challenging. Furthermore, the complexity of the combinatorial part of the proof will explode for higher levels. This question is open not only for the group-based models studied in this paper, but also for the general Markov model, which has just started to be studied in the context of networks Casanellas and Fern\u00e1ndez-S\u00e1nchez ."}
+{"text": "The findings suggests that respondents\u2019 good self-appraisal of coping resources could moderate the impact of adversities on their future quality of life. Interventions for promoting positive psychological growth among middle-aged and older adults should cover four domains, i.e. event-related factors, environmental factors, personal factors, and cognitive and coping responses. Traditional Chinese wisdom emphasizes the importance of understanding the bad (\u2018Yin\u2019\u2014the shady side) and the good (\u2018Yang\u2019\u2014the sunny side) aspect of life events. Future research may explore the Yin Yang perspective on life-threatening experiences and its applications in cross-cultural quality of life studies in the era of globalization.The current study explores the interaction effect of adversities and self-efficacy at baseline on quality of life (QoL) at follow-up among middle-aged and older Chinese women. 531 women were interviewed in 2008 and 226 of them were re-interviewed a year later using Quality of Life Ladder (QoLL), General Self-Efficacy Scale (GSE), List of Threatening Experiences (LTE), Somatic Complaint Scale, and self-rated health. Respondents\u2019 mean age at baseline was 55.7 . Over a year\u2019s time, respondents had a decline in quality of life and self-rated health (p\u2009<\u2009.001), experienced more life-threatening events (p\u2009<\u2009.05) and somatic complaints. The hierarchical multiple regression model, employed in the study, identifies three predictors of future quality of life after adding the interaction term \u2018Previous LTE\u2009\u00d7\u2009Previous GSE\u2009\u00d7\u2009Previous household income\u2019 \u2014 previous quality of life , previous LTE , and the interaction term . This model explains 34.1% of the variance of future quality of life (Adjusted R Studies have suggested that emotional distress or post-traumatic stress disorder is ubiquitous in affected communities after disasters such as the current Covid-19 pandemic  Dependent variableThe Quality of Life Ladder (QoLL), which is a single item leader-shaped visual analogue scale, was adopted to assess a participant\u2019s level of quality of life level. The score anchors from \u2018(0) worst possible\u2019 to \u2018(10) best possible\u2019, indicating that the higher the score, the better the quality of life Cantril, . BowlingB)Independent variablesThe List of Threatening Experiences (LTE) is a modified 6-item inventory of life events by reporting the number of threats that respondents have experienced in the last 12\u00a0months   : a single-item measure asking respondents to rate their health as \u20185\u2009=\u2009Very Good\u2019, \u20184\u2009=\u2009Good\u2019, \u20183\u2009=\u2009Fair\u2019, \u20182\u2009=\u2009Poor\u2019, or \u20181\u2009=\u2009Very Poor\u2019.Sociodemographic variables include age and monthly household income.All participants were sent a self-administered questionnaire, which was formulated in English and then translated into Chinese. The Chinese version was back-translated to English again to examine whether the contents were well-translated. The questionnaire used for data collection was the Chinese version, and these Chinese-translated measurement tools have been tested in a pilot study. Thirteen adult learners filled the Chinese-translated questionnaire to test the inter-correlation among items of the questionnaire. Results of the pilot study was satisfactory  scale, 0.512 for List of threatening experiences (LTE), and 0.857 for Somatic complaint scale (SCS)). As the LTE is just a checklist for calculating the number of critical life events rather than a measurement scale, the low Cronbach\u2019s score did not affect its reliability. Details of the measurements are as follows:Using IBM SPSS version 25, the changes of score in measurement tools over time were examined by t-test, ANOVA, and Chi-square test. Hierarchical multiple regression analysis was applied to explore how independent variables and covariates at baseline predicted quality of life at follow-up. The regression model also examined the interaction effect of financial resources, self-efficacy, and life-threatening experiences at baseline on quality of life at follow-up.The research protocols were approved by the ethics approval committee of the University where the study was conducted (Project No.: 07/1.12). Informed consent was sought from all respondents who participated in this study.t\u2009=\u20092.733, df\u2009=\u2009516, p\u2009<\u20090.01), the result of Little\u2019s Missing Completely at Random (MCAR) test \u2009=\u20095.073, p\u2009=\u20090.407). In other words, the missingness is completely unsystematic and unrelated to the study variables.A total of 531 middle-aged and older Chinese female learners participated in the baseline survey in 2008 and 42.7% (n\u2009=\u2009226) of them returned their questionnaires at follow-up in 2009. Though the attrition for follow-up was high, there were no statistical differences in the key measures including LTE, GSE, SCS, and SRH between the remaining group and the drop-out group. Despite a relatively lower QoL mean score in the drop-out group compared with the remaining group . However, after adding LTE and GSE at baseline in the equation (Block 2), the quality of life and LTE at baseline were found to be strong predictors of future quality of life . The LTE factor can explain an additional 2.5% of variance of future quality of life. After adding the interaction term \u2018LTE at baseline\u2009\u00d7\u2009GSE at baseline\u2009\u00d7\u2009Household income at baseline\u2019 in Block 3, three key predictors of future quality of life were found: previous quality of life , previous LTE , and the moderation effect of \u2018LTE at baseline\u2009\u00d7\u2009GSE at baseline\u2009\u00d7\u2009Household income at baseline\u2019 . The model can explain 34.1% of the variance of future quality of life .From the results of hierarchical multiple regression analysis  and opportunity (j\u012b \u6a5f)  is identical with the Western concept of crisis, and that is to tell a latent danger  indicates a critical moment for better or worse, and that is like the meaning of \u2018crisis\u2019 in English \u2014 \u2018the moment in which a decision was about to occur\u2019 (Graf, Maercker and Zoellner\u2019s  Janus-Fa Zimmer, . For exa Zimmer, . The meaer Mair, . On the r\u2019 Graf, : 599. Thr\u2019 Graf,  because r\u2019 Graf, . This inr\u2019 Graf, . That shr\u2019 Graf, . The Yinr\u2019 Graf, . The conr\u2019 Graf, , and by r\u2019 Graf,  has applThere are several limitations to this study. Firstly, respondents of the current panel study were drawn from a large-scale lifelong educational program, instead of the whole population of Hong Kong. This may generate a biased result as active learners tend to perceive their psychological well-being and self-efficacy more positively. Even so, because the program is a government-funded territory-wide community project, which has a wide coverage in Hong Kong HKSAR, . The cur"}
+{"text": "Synthetic lethality (SL) is a promising gold mine for the discovery of anti-cancer drug targets. Wet-lab screening of SL pairs is afflicted with high cost, batch-effect, and off-target problems. Current computational methods for SL prediction include gene knock-out simulation, knowledge-based data mining and machine learning methods. Most of the existing methods tend to assume that SL pairs are independent of each other, without taking into account the shared biological mechanisms underlying the SL pairs. Although several methods have incorporated genomic and proteomic data to aid SL prediction, these methods involve manual feature engineering that heavily relies on domain knowledge.Here, we propose a novel graph neural network (GNN)-based model, named KG4SL, by incorporating knowledge graph (KG) message-passing into SL prediction. The KG was constructed using 11 kinds of entities including genes, compounds, diseases, biological processes and 24 kinds of relationships that could be pertinent to SL. The integration of KG can help harness the independence issue and circumvent manual feature engineering by conducting message-passing on the KG. Our model outperformed all the state-of-the-art baselines in area under the curve, area under precision-recall curve and F1. Extensive experiments, including the comparison of our model with an unsupervised TransE model, a vanilla graph convolutional network model, and their combination, demonstrated the significant impact of incorporating KG into GNN for SL prediction.https://github.com/JieZheng-ShanghaiTech/KG4SL.: KG4SL is freely available at Bioinformatics online.Supplementary data are available at  Complex biological systems cannot be composed by a large number of genes acting independently, but rely on the interactions between genes which can be further classified into enhancing and suppressive effects . The supin silico knockouts using metabolic network models. A spectrum of computational methods has been proposed for SL prediction. These methods can be categorized into three classes. The first class involves simulating 2MF  might latently invalidate the assumption of independency. For instance, poly (adenosine diphosphate-ribose) polymerase 1 (PARP1) and breast cancer 1 (BRCA1) are a famous SL gene pair, leading to the first clinically approved SL-based cancer drug, PARP inhibitor . PARP1 a2MF and GRSMF] have injected some genomic and proteomic data to facilitate the SL prediction, and the results of these studies have underscored the significance of integrating additional information. Meanwhile, GNN-based methods can also encode such information as input features. However, these methods extracted features manually based on domain knowledge and some features might be left out. Therefore, to attain a more comprehensive set of features to improve the performance of SL prediction, we need a new method capable of automatic knowledge integration and feature extraction.A subset of existing methods [e.g. SVM, random forests (RFs), SLE are defined as triplets Knowledge graphs (KGs) are a type of multi-relational graph, where nodes and edges have different types. A KG is denoted by wo nodes . By incoHere, we propose a novel KGNN-based method for SL prediction, named KG4SL, which utilizes KG MP as a back-end. We approach the independency issue by injecting various factors including biological processes, diseases, compounds etc. that could be pertinent to SL, into our KG. Our model comprises three parts. In the first part, we derive a gene-specific subgraph from the original KG for each gene. In the second part, we conduct MP on the gene-specific subgraph, to automatically associate genes with factors that could be decisive in identifying an SL pair. In the third part, we define a decoder to reconstruct gene\u2013gene similarity in a supervised fashion. To the best of our knowledge, this is the first framework to integrate KG with GNN for SL prediction. We compared our model with 10 state-of-the-art methods for SL prediction, and our model outperformed all the baselines in area under ROC curve (AUC), area under precision-recall curve (AUPR) and F1. Another contribution of our work is that we studied the impact of KG, which suggests that introducing a KG combined with MP process in GNN can significantly improve the performance of SL prediction.In this section, we first introduce the data and the problem of SL prediction. Then, we present the details of the proposed KG4SL model.http://synlethdb.sist.shanghaitech.edu.cn/v2/#/; SynLethDB ,  and . And the other 8 relationships are associated with drug and compounds. Besides, 7 out of 11 kinds of entities are directly related to genes, i.e. pathway, cellular component, biological process, molecular function, disease, compound and anatomy. They are in the format of . These entities can be reached from genes in one hop, whereas the other three kinds of entities  can be reached from genes in two hops. After removing isolated nodes, the final graph of SynLethKG contains 54 012 nodes and 2 231 921 edges as shown in The 24 relationships in n is the number of genes involved in the SL pairs. In this SL matrix S, an entry ie and gene je, and 0 otherwise. Note that gene pairs with entry value 0 are unknown pairs, some of which could be potential SL pairs not yet discovered. The KG SynLethKG is denoted by eV and a set of relationships rV. Each edge in the KG is defined as a triplet r between head entity h and tail entity t, where Formally, the SL data can be modeled as a matrix S and the KG G, the problem we aim to solve is to predict the SL relationship between gene ie and gene je. To achieve this goal, we propose a GNN-based model to learn a scoring function ie and gene je is an SL pair, where W, A and b denote the learnable parameters in function F.Given the SL matrix The overall framework of KG4SL is laid out in 2.3.1Given an SL-related gene, we first construct a weighted subgraph from the KG. Identifying relevant nodes and determining the edge weights are two key operations to construct the gene-specific weighted subgraph.e is the central node/entity and N(e) is the set of neighbors of e (i.e. entities directly connected to e). In SynLethKG, the size of N(e) varies greatly among the entities. For example, network hubs may have thousands of relations, whereas some nodes are less studied and thus have a limited number of neighbors. In this work, we sample a fixed number of k neighbors for each entity to characterize its local structure and we repeat this process for H hops . An example of 2-hop subgraph with neighbor sampling size k\u2009=\u20094 in each hop can be seen in Assume that ie, je), the weight for an edge i\u2019es subgraph is computed by e is one of the entities in the subgraph of ie, and je and relation g is an inner product function. Here, je.In a gene-specific subgraph, we can assign different weights for edges to describe the importance of the relations. For an SL pair ; hyper-parameters \u03b1,d, k, h and epoch;Output: \u00a01: Initialization:eW;2: entity embedding matrix rW;3: relation embedding matrix 4: step \u2190 0;5: while step < epoch do6: \u2003\u2003for \u00a0doGene-specific Subgraph(ie);7: \u2003\u2003\u2003Gene-specific Subgraph(je);8: \u2003\u2003\u20039: \u2003\u2003\u2003for\u2002m\u2002do10: \u2003\u2003\u2003\u200311: \u2003\u2003\u2003\u2003for\u2002h\u2009=\u20091,2,\u2026,H do12: \u2003\u2003\u2003\u2003\u2003for \u00a0do13: \u2003\u2003\u2003\u2003\u2003\u200314: \u2003\u2003\u2003\u2003\u2003\u200315: \u2003\u2003\u2003\u2003\u2003end for16: \u2003\u2003\u2003\u2003end for17: \u2003\u2003\u2003\u200318: \u2003\u2003\u2003end for19: \u2003\u2003\u2003Compute the predicted probability 20: \u2003\u2003\u2003Compute the loss 21: \u2003\u2003end for22: \u2003\u2003step \u2190 step + 1;23: \u2003end whileIn this section, we first introduce the state-of-the-art baseline methods and their implementation details, and then we compare our model with the baselines, followed by an analysis of the influence of the KG. The KG4SL model was implemented with Python 3.6 and Tensorflow 1.15.0. We adopt AUC, AUPR and F1 as the evaluation metrics.3.1.1We compare KG4SL with the following baselines:2MFSL  (rk (GCN)  is the mGraphSAGE , RW-based baselines  and GNN-based baselines . We evaluated DeepWalk, Node2Vec, LINE using CogDL  into the GNN model. Many existing methods view each SL pair as an independent sample from a latent representation, but this assumption is an oversimplification in the biological context of cancer cells. KG can bring additional information such as biological processes which could be crucial for discovering new SL pairs. By injecting the KG, our model was capable of harnessing the aforementioned issue, without manual feature engineering. Extensive experiments have been conducted to examine the impact of KG. The results show that both KG and MP in GNN are essential for boosting the model performance. Therefore, KG4SL represents a breakthrough in applying supervised machine learning to SL prediction.Our future work will focus on the following directions. First, we plan to further improve our model, using the strategy of contrastive learning, which is a self-supervised approach to learn graph representation. Secondly, the degrees of some nodes in a KG might be very large, while sampling a fixed-sized neighborhood may not fully capture the neighborhood topological structures of the nodes. To address this issue, it will be a highly desirable future work to contrast multiple receptive fields for a given node, to learn a more robust and enriched embedding. Moreover, inspired by the recently proposed KG attention network . By insp"}
+{"text": "The authors have been informed of some errors that occurred in the published paper. The errors are listed as:\u2022In the M&M section in the main text, the word \u201cperformed\u201d has been changed to \u201crecruited\u201d.\u2022Some references have been modified in the text.\u2022The type of randomization has been corrected as the random number table.\u2022The Mann-Whitney test was added in the statistical analysis section.\u2022The statistical test which has been used in Table I was added as a table subtitle.\u2022The study results were re-analyzed, and some p-values were modified in the text and table, especially in Table IV.The authors wish to apologize for these errors.http://journals.ssu.ac.ir/ijrmnew/article-1-813-en.html&sw=(http://doi.org/10.29252/ijrm.15.4.231).The online version of the article has been updated on September 4, 2021 and can be found at"}
+{"text": "Procedia-Social and Behavioral Sciences. Spain is the country with the highest volume of production. It is concluded that research on ELHI use does not have an established line of research, due to its recent creation and the lack of related research. The bibliometric analysis specifies that the research is oriented towards knowing the level of acceptance and application of the pedagogical method in the teaching and learning processes.E-learning is conceived as a purely virtual training approach. Different learning styles have been proliferated in recent years, especially now, due to the impact of COVID-19 in the educational field. The aim of this study is to discover the evolution of e-learning in higher education (ELHI) in scientific literature indexed on the Web of Science. Co-word analysis and bibliometric analysis was performed. A total matrix of 1261 documents was analyzed through SciMAT software. The results revealed that studies on ELHI are written in English and presented by conference papers. The main source of publication for the conferences is EDULEARN proceedings, while the journal source is  Information and communication technologies (hereinafter ICT) are deeply rooted, widely accepted, and developed in today\u2019s society . The fieIn this sense, new technological means have made it possible to generate new learning environments and methodologies ,5. In adAs a consequence of technological development in the field of education, the digital competence of teachers and students is presented as a relevant factor for the development of good practices with ICTs ,9,10. ThE-learning can be found within the broad spectrum of innovative learning methodologies. This training approach is conceived as a virtual instruction, carried out through content management platforms to carry out the teaching and learning process in a digital environment . This trThere are several advantages that e-learning has over other, more traditional teaching methods . E-learnThis type of teaching allows greater communicative interaction between educational agents, by being able to emit messages through the platforms established by educational centers . In addiDespite the potentialities reflected, e-learning also has limitations or disadvantages . This inAfter analyzing the literature on e-learning, it was observed that there are no studies that have analyzed the construct in a comprehensive manner. This is, from a bibliometric perspective, based on the scientific mapping of published studies. This problem, which has arisen in the impact literature, is intended to minimize with this work, presenting the importance and evolution of the concept of e-learning, specifically in higher education spaces. This research also offers the themes that e-learning runs through, as well as the way forward in coming years, revealing trends that are on the rise.Due to the importance of the subject today, the purpose of this work is to know the evolution of e-learning in the higher education stage in the scientific documents registered in the Web of Science (WoS) database.In this research, the concepts \u201ce-learning\u201d and \u201chigher education\u201d (ELHI) in WoS are studied. The analysis of this work was developed through scientific mapping ,35,36,37The purpose of this research is to reveal the evolution of ELHI through the analysis of WoS export documents. In addition, it focuses on knowing how scientific production performs and evolves, as well as specifying the most influential topics and authors.2 index [The research methodology used is bibliometrics. Bibliometrics allows to analyze different bibliographic characteristics in documents and the analysis of diverse features of scientific activity. This kind of analysis is important to scientific publications as a tool that allows qualifying the quality of the knowledge-generating process and the impact of this process on the scientific background . Specifi2 index . This isn \u2265 13); knowledge area (n \u2265 89); type of document (n \u2265 70); institutions (n \u2265 12); authors (n \u2265 5); source of origin (n \u2265 34); countries (n \u2265 74); citation (the four most cited references \u2265 100). These actions reported 1305 publications. The cut-off values for the criteria are established with those results whose nodes are formed by more than one document or value.The research procedure has been carried out in several stages: (1) selection of the database to be analyzed (WoS), considered the most important scientific database; (2) choice of keywords under study (\u201ce-learning\u201d and \u201chigher education\u201d); (3) construction of the search equation (\u201ce-learning\u201d (TITLE) AND \u201chigher education\u201d (SUBJECT)). Several inclusion criteria were also applied: year of publication ; language  that have been prepared under the criterion of documentary similarity.All presented analysis was carried out with the citation reports tool of WOS and SciMAT software.The set of documents related to ELHI in Web of Science is 1261. The start of production dates back to the year 2000. From that date until 2010, the growth in the volume of documents was high (being increasing and constant throughout the period). In 2011 the scientific production decreased compared to the previous year, but in 2012 and 2013, it increased again. From that same year until 2017, the production was constant (concerning quantity). However, in 2018 and 2019, production fell to levels close to 2008. Peak production occurred in 2015 .The language, mainly used by researchers, is English. All other languages are far removed from it .The studies on ELHI are collected mainly in the knowledge area Education Educational Research, being far from the other areas .Both papers and research articles are the main types of documents used by researchers to show their findings. The number of papers stand out, confirming the fact that this field of study is of a recent appearance in the scientific community .The Universitat Oberta de Catalunya is the leading institution in ELHI-related studies. The fact that the most prolific universities are Spanish stands out .The author with the highest level of scientific production on ELHI is Pelet, J.E. The rest of the authors are at a close distance, which shows the variety and number of authors who study the field under analysis .The main sources collecting research on ELHI are two books of conference proceedings, with EDULEARN as the main reference. This fact coincides with the data offered previously on the source of production. In this case, the main journal that publishes studies on this subject is Procedia Social and Behavioral Science .Two countries are the reference countries in this field of study in scientific production. Spain is in first place, closely followed by England .In ELHI\u2019s field of study, the most widely cited work has 234 citations . The secThe evolution of keywords shows the number of keywords collected in a given period. In addition, it also shows the keywords that go out and come in a certain period. In this study, the level of keyword matching between contiguous periods is low, and it increased from its beginnings until 2019. This shows that the line of investigation is not established, although it is beginning to be established .The academic performance presents the most valuable subjects in each of the established time periods. These values are based on bibliometric indicators of various kinds . Academic performance is shown according to established time periods. In the first interval (2000\u20132011), the subject with the highest bibliometric value is \u201ceducation\u201d. In the second interval (2012\u20132015), \u201ce-learning\u201d is the most important. In the third interval (2016\u20132019), it is \u201cextension\u201d and \u201cstudents\u201d .Thematic diagrams provide data on the relevance of the different topics in a given time period. The coordinate axis shows the level of centrality and density. The former analyzes the relational strength of external links. The second analyzes the relational strength of internal links. The study of the three diagrams shows that no single theme is repeated as the driving force in the three periods. Only \u201csatisfaction\u201d stands out, which appears in the second and third periods .In the first interval (2000\u20132011), the driving themes are \u201cperceived-usefulness\u201d, which is related to \u201cimpact\u201d, \u201ctechnology-acceptance-model\u201d, and \u201cuser-acceptance\u201d; \u201ce-readiness\u201d, which is based on \u201cmeasuring-e-readiness\u201d, \u201ccultural-aspects\u201d, and \u201cIT\u201d; and \u201con-line\u201d which is oriented towards \u201cqualitative-differences\u201d, \u201cknowledge-work\u201d, \u201cteaching-quality\u201d, \u201ctechnology\u201d, \u201csatisfaction\u201d, \u201cconceptions\u201d, \u201cteaching/learning-strategies\u201d, and \u201cface-to-face\u201d. In this period, although ELHI is analyzed, it seems that the research interest is more oriented towards distance learning than e-learning.In the second interval (2012\u20132015), the driving themes are \u201cused-acceptance\u201d, which is related to \u201cperceived-ease\u201d, \u201cextension\u201d, \u201cnational-culture\u201d, \u201cinformation-technology\u201d, \u201cmodel\u201d, \u201cbehavioral-intention\u201d, \u201cself-efficacy\u201d and \u201ctechnology-acceptance\u201d; and \u201csatisfaction\u201d, which focuses on \u201cinformation-systems-success\u201d, \u201ccontinuance-intention\u201d, \u201cinstructor\u201d, \u201ccritical-success-factors\u201d, \u201cweb\u201d, \u201cmanagement\u201d, and \u201cweb-based-e-learning-system\u201d. In this period, the evaluation and acceptance of the e-learning method, mainly oriented to technological resources, takes on an important nuance.In the third and final interval (2016\u20132019), the driving themes are \u201cDeLone\u201d which is related to \u201cMcLean-model\u201d, \u201cinformation-systems-success\u201d, \u201cattitudes\u201d, \u201ce-learning-system\u201d, and \u201cmanagement-systems\u201d; \u201cextension\u201d, which is oriented towards \u201cunified-theory\u201d, \u201cdeterminants\u201d, \u201cstudents-behavioral-intention\u201d, \u201cinformation-technology\u201d, \u201ctechnology-acceptance-model\u201d, \u201cuser-acceptance\u201d, \u201cusage\u201d and \u201cvariables\u201d; \u201cintention\u201d which is based on \u201cacceptance\u201d, \u201cinformation-systems-continuance\u201d, \u201ctrust\u201d, \u201ccomputer\u201d, \u201cmodel\u201d, \u201cadoption\u201d, \u201cself-efficacy\u201d and \u201cperceived-ease\u201d; \u201csatisfaction\u201d, which relates to \u201ce-learning-success\u201d, \u201cstudents-perspective\u201d, \u201cpublic-administration-education\u201d, \u201cquality-of-e-learning-system\u201d, \u201ccritical-success-factors\u201d, \u201cperformance\u201d, \u201ccontext\u201d and \u201cuse\u201d; and \u201cbehavioral-intention\u201d which focuses on \u201ctechnology-acceptance\u201d, \u201cTAM\u201d, \u201csystem-characteristics\u201d, \u201cperspective\u201d, \u201cpreservice-teachers\u201d, \u201cstructural-equation-modeling\u201d, \u201cuniversity-students\u201d, and \u201cperceived-usefulness\u201d. In this period, the e-learning method is more relevant, the behavior of the subjects when faced with the pedagogical method and the relationship between the people involved in the pedagogical act. Furthermore, in this period, the themes \u201cMOOC\u201d, \u201cgamification\u201d, \u201cblended-learning\u201d, and \u201cMoodle\u201d must be taken into account, given that their location in the diagram places them as unknown themes. In other words, the topics may become the next driving force, or they may disappear from the scientists\u2019 lines of research.The scientific evolution provides information on the relationship between the themes of the recognized contiguous periods. To establish these relationships, the Jaccard index has been taken into account. The relationships can be of two types: continuous line and discontinuous line. The thickness of the lines shows the strength of the relationship between the themes.The scientific evolution of ELHI presents a conceptual gap. This is due to the fact that there is not one theme that is repeated in the three periods. Even so, two lines of research can be glimpsed, on the one hand that established by \u201cmodel-user/acceptance-extension/behavioral-intention\u201d and\u2014on the other\u2014that of \u201cstudents-e/learning-students\u201d. In other words, studies in this field of study are mainly oriented towards the acceptance of the pedagogical model and in the students themselves. Furthermore, as can be seen in The author considered as the driving force in the ELHI study is Gullu, F. , becauseThe ELHI field of study is relatively young, as it began in 2000 according to WoS. From that date to 2019, the level of production was irregular, with a great deal of incidence by the scientific community from 2000 to 2010, and then remaining constant over time. Since 2018, there was a downward trend in production, although with the health crisis caused by the COVID-19, it will probably rise again, given that it is currently the model used to develop all types of education, both university and non-university levels.The studies on ELHI are written in English and presented in conference papers. The area of knowledge where research is based on is Education Educational Research. The most important institution in this field of study is the Universitat Oberta de Catalunya , with Spanish institutions being the most productive. Pelet, J.E. is the author with the largest number of productions, although Gullu, F. stands out as the most relevant in this field of study. The main source of publication for the conferences is EDULEARN proceedings, while the journal source is Procedia Social and Behavioral Sciences. Spain has the largest scientific production on ELHI. The most cited manuscript is , with 23If we look at the co-word analysis, we can see that this field of study does not have a solid line of investigation recognized, given that the level of coincidence of key words between the established periods is low. Even so, it can be seen that a line of research is beginning to be established in this field of study, given that, over time, the number of key words coinciding between periods is increasing.Academic performance reiterates and confirms this fact, given that there is not one theme that repeats in all three periods, not even in two. This analysis shows that the topics dealt with in this field of research are oriented towards education, online teaching, and students.With regard to the most relevant topics in this field of study, it is shown that there is an evolution over time, with varying interest and focus on the part of the researchers. In the first period, interest is focused more on distance learning than on online learning itself, given that it uses terms that are not typical of the e-learning method. In the second period, this fact changes radically, given that interest is focused on the assessment and acceptance of e-learning by those involved in this teaching process. In the third period, the line of the second period is maintained a little, although the researchers extend their field of interest to the intention of those involved in the training process.Over the next few years, the themes of \u201cMOOC\u201d, \u201cgamification\u201d, \u201cblended-learning\u201d and \u201cMoodle\u201d should be kept in mind when researching the use of e-learning in higher education, and could be the next driving force.The thematic evolution once again confirms what was indicated previously\u2014that is to say, there is no solid and stable line of research in this field. Moreover, there is a conceptual research gap related to ELHI. Even so, there are two lines that have focused more interest on the part of the scientific community. These timelines are \u201cmodel-user/acceptance-extension/behavioral-intention\u201d and \u201cstudents-e/learning-students\u201d. In other words, studies in this field of study are mainly oriented towards the acceptance of the pedagogical model and in the students themselves.It can be concluded that research on the use of ELHI does not have an established line of investigation. This bibliometric study indicates that the subject is quite new in the Web of Science database. That is to say, studies on this line of research have begun to be registered recently. The bibliometric analysis specifies that the research is oriented towards knowing the level of acceptance and application of the pedagogical method in the teaching and learning processes. This information offered here can guide researchers and professors in their work. The prospective of this research consists of offering the scientific community new trends in this field of study. In addition, the aim is to show the educational community the latest trends on this method of teaching and learning.As for the limitations of this research, we must say that there are several. Firstly, generating the database in WoS requires a great deal of effort for researchers. This is because the entire scientific production must be read to determine whether it follows the inclusion criteria set out in the PRISMA  protocol. Secondly, the time distribution has been carried out, taking into account the criterion of equity. An attempt has been made to collect an even number of manuscripts in each of the established time periods. Thirdly and finally, the criteria for inclusion have been established at the discretion of the researchers, which have sought to present results that are in line with each other in terms of size and relevance. In this case, the data shown in this study should be considered with caution. The change in the inclusion criteria may slightly change the data shown in this research. Future lines of research include analyzing the e-learning method in other educational stages, such as compulsory secondary education, baccalaureate, or vocational training."}
+{"text": "D. The networks need not be binary, so vertices in the networks may have more than two parents and/or more than two children. In general, in order to make the resulting network acyclic, additional arcs not in D must also be contracted. This paper shows how to choose D so that the resulting acyclic network is \u201cpre-normal\u201d. As a result, removal of all redundant arcs yields a normal network. The set D can be selected based only on the geometry of the network, giving a well-defined normal phylogenetic network depending only on the given network. There are CSD maps relating most of the networks. The resulting network can be visualized as a \u201cwired lift\u201d in the original network, which appears as the original network with each arc drawn in one of three ways.As phylogenetic networks grow increasingly complicated, systematic methods for simplifying them to reveal properties will become more useful. This paper considers how to modify acyclic phylogenetic networks into other acyclic networks by contracting specific arcs that include a set  A phylogenetic tree is a directed tree whose vertices represent biological species, whose leaves typically correspond to known extant species, and whose branchings indicate speciation events, usually by genetic mutation. As such, internal vertices have in-degree one and out-degree at least two (except for the root with in-degree zero). In the last decades it has become clear that other events such as hybridization and lateral gene transfer are also important in evolution, even though they are not easily modeled using phylogenetic trees One measure of the complexity of an acyclic X-network and Suppose N is a rooted tree, then (a) If N is normal, then (b) If N is regular, then (c) If N is tree-child, then v is unbounded.(d) If n indicates that normal networks are potentially a more tractable network type than regular or tree-child. Also indicative of their tractable nature is the fact  N, from which properties of N. The wired lift is not a subnetwork of N in the usual sense.If entclass1pt{minima Willson  show thaN, even though there is usually no CSD map from N to N with each arc drawn in one of three different ways. Thus we can visualize the resulting normal network by looking at a redrawn diagram of N. The current author thinks such visualizations can provide a tool for better understanding complicated networks.Section\u00a0Section\u00a0X-network N, to find a related, uniquely determined, normal X-network, which I will denote N. The fast program PhyloSketch  is regarded as directed from u to v, so we call u a parent of v and v a child of u. We assume N is a simple graph: there are no loops ; and there is at most one arc  for Let corresponding undirected graphUnd(N) edges and are not directed. In this paper, N will always refer to a directed graph unless otherwise specified.If in-degree of a vertex v in N, denoted indeg(v) or indeg , is the number of arcs , i.e. the number of parents of v. The out-degree of a vertex v, denoted outdeg(v) , is the number of arcs  , i.e., the number of children of v.The v may have We shall not assume that our directed graphs are binary. Thus a vertex leaf is a vertex root is a vertex v is hybrid or reticulate if u of v is a tree-child if v,\u00a0u) is the only arc coming into u. A vertex v is trivial if A u and v are vertices, a path or, for emphasis, a directed path from u to v is a sequence of vertices i, length of the path is the number n of arcs. Note that the arcs are uniquely determined by the vertices in the list since N is a simple graph. No two successive vertices can be the same since there are no loops. We say the path contains arc segment.  is a simple directed graph; Let X-networkN is an X-directed graph An V is a finite set (the set of nodes or vertices).(N1) A (the set of arcs) is a finite set of ordered pairs  with u and v distinct members of V.(N2) root, is a node with in-degree 0.(N3) (N4) The map (N5) Each leaf is a vertex with in-degree 1 and hence has a unique parent.(N6) The image of (N7) v.(N8) For each v to some leaf.(N9) For each acyclicX-network is an X-network that also satisfiesAn N has no cycles.(N10) phylogeneticX-network to be an acyclic X-network that contains no trivial vertices.Following Steel , we defiThese assumptions are not intended to be the minimal possible; rather, they tell the properties we will utilize the most.p(x) or p. The arc of form x-arc. If x is not specified, any such arc will be called an X-arc.If N is an X-network. By (N4) and (N6) we may identify X with the set of leaves.Suppose u to v then we write X-network is acyclic, then u and v we have If there is a directed path from X-networks or two X-directed graphs X-isomorphic iff there exists a map Two f is one-to-one and surjective.(i) (ii) (iii) (iv) N and In this situation, cl (or cl(v) when N is understood) for cluster of v. Note that v, cl(v) is nonempty.For each It is immediate that if N.Let N be an X-labeled graph. An arc  is redundant or a short-cut if there exists a path a,\u00a0b). Thus, there is no lengthening or a lengthening path of . Examples will be seen in several figures later, such as Fig.\u00a0Let We shall have need of the following result:N is an acyclic X-network. Suppose there is a directed path in N from a to b. Then, a directed path in N from a to b of maximal length contains no redundant arc.Suppose P in N of maximal length k. If the result is false, we may assume that for some P by replacing the segment Since the vertex set is finite and there are no cycles, there is an upper bound to the length of a path. Suppose X-networks which will be of interest:There are several types of X-network N is tree-child  is the power set of X;(1) the cluster map N has no redundant arcs; and(2) (3) X-network N is normal  N contains no redundant arc.(2) Sometimes there are small differences in the definition of a network. In Baroni et\u00a0al.  and WillN and X-networks. One interesting way to compare them is their Robinson-Foulds distanceCl(N) and X-networks X, it is a metric on the collection of regular X-networks  denote the result of contracting every arc  such that N, for some p(x) is hybrid and has out-degree one. Then in S(N) the arc N will have been contracted, and S(N) will not satisfy (N5). Thus in S(N) a leaf can be hybrid. Moreover, any trivial vertices will have been suppressed.If The following result shows that two normal networks N is a normal X-network, then S(N) is a regular X-network and (1) If X-networks and (2) Suppose X-network N, if  is an arc and N is normal then S(N) remains normal and hence is a regular network (Willson (1) For any  Willson .X-networks. (2) If X-networks, it can be used to compare how well various networks of various types \u201capproximate\u201d a given network. For example, if N is a complicated acyclic X-network and T and X-networks that are rooted trees, then T might be a better approximation to N than The X-network N into a normal X-network In this paper we will be \u201csimplifying\u201d an acyclic X-directed graphs. A connected surjective digraph (CSD) map (Willson Let  Willson  \\documen(C1) digraph map).(C2) For each arc (C3) For each (C4) u,\u00a0v in V such that (C5) For each N. Thus in the undirected graph Und(N) of N, if W and edge set (C6) For each N and Note that if X-networks. A CSD-map leaf-preserving if for each Let V such that (C7) x-arc x-arc (C8) the If  Willson  that theX-network\u201d refers to what in this paper is an X-directed graph satisfying (N1), (N2), (N3), (N4), (N6), (N7), (N8), and (N9). Thus the networks in Willson  which contains D and is strongly closed. Hence, we are able to define X-network that results from contracting the arcs of D and also the other arcs needed for acyclicity. The sections after this one will rely on the iterated use of this construction. The fundamental problem studied in this paper is, roughly, how to choose D so that we can find a normal network from Here is a summary of this fundamental section: The basic tool used in this paper is that of successively contracting arcs in an X-network. Suppose V. Let [v] denote the equivalence class of V under Let quotient digraphAs in Willson  the quot(1) (2) (3) For each u] and [v] be in (4) Let [We will denote this quotient digraph by connected if each equivalence class [v] is connected in N. An equivalence class [v] is convex if, whenever N with both i, convex if each equivalence class [v] is convex.The equivalence relation root-preserving if the equivalence class leaf-preserving providedThe relation (1) if u such that (2) for any X-networks. A CSD-map leaf-preserving if for each Let V such that (1) x-arc x-arc (2) the The following result is similar to Theorem\u00a0X-network. Let V, and let Let X-network.(1) (2) The natural map a to b in N, then there is a path from First we prove (1). (N1) and (N2) are immediate. (N4) is immediate since u] and hence an arc from some N.Each N there is a path in N from v to v] to Let v] is a leaf of v is not a leaf of N, then there is a path in N from v to v] is a leaf, it follows Suppose [N from Suppose in u] has in-degree 0. By (N8) there is a path from u, say u] has in-degree 0, it follows that u] has in-degree 0, it follows For (N7), suppose . (C2) is immediate since if v] is connected as well.We now prove (2). (C1) is immediate since every vertex of (C7) restates that N is acyclic.We do not claim that projection from N to We will refer to the map X-network. Let D be a subset of A. Define a relation V by saying vertices a and b satisfy Let D be a subset of A. A path D-path provided that for each i, Droot-preserving if whenever D-path, then every path from a is a D-path.Let X-network. Let D be a subset of A. ThenLet (1) D contains no X-arc.(2) D is root-preserving.(3) v the trivial path at v shows D is a subset of A, it is clear that each equivalence class is connected. This proves (1).(1) For any vertex v under Write D contains no X-arc, then for each (2) If D is root-preserving. We must show that the equivalence class N such that (3) Assume that v] if D is understood) denote the equivalence class of v under equivalence relation determined by D. It is clearly the smallest equivalence relation u,\u00a0v) satisfying Let X-network. Let D be a subset of A. Assume D contains no X-arc and D is root-preserving. Then the quotient digraph X-network. Moreover, the projection Let By Theorem\u00a0D contains no X-arc and is root-preserving, we will write quotient X-network of N under D and refer to its formation as contracting or merging the arcs of D. In general, N is acyclic.Henceforth if It is not hard to program a computer to find X-network N. Let D contains no X-arc. Note the root Figure\u00a0X-network. A subset closed if it satisfies the following: Suppose i satisfying a,\u00a0b) is an arc and Let D is not closed since In Fig.\u00a0X-network. Let D is closed then each equivalence class of Let D is closed. Let v] is convex. Write N where Suppose D is not closed.Figure\u00a0u,\u00a0v) is merged, the number of vertices drops by one, reducing the resolution. In Fig.\u00a0D contained 4 arcs, and the number of vertices dropped from 13 in (a) to 9 in (b). On the other hand, if Figure\u00a0X-network. A subset strongly closed if it satisfies the following: Suppose there are vertices V with k such that K.Let X-network. Let D is strongly closed, then D is closed. Hence D is root-preserving.Let D is strongly closed. Suppose there is a sequence (not necessarily a path) a to b. Then D is strongly closed, for D is closed.Suppose D is root-preserving. By Theorem\u00a0D that is closed but not strongly closed. Indeed, Figure\u00a0D is strongly closed, then The next result shows that, if X-network. Assume X-arc. If D is strongly closed, then Suppose D is strongly closed. By Theorem\u00a0D is root-preserving. By Theorem\u00a0X-network. Suppose D is strongly closed, each arc Write D we can construct a uniquely determined strongly closed set K that contains D.The following theorem shows that from a given X-network and Let (i) K is strongly closed, and(ii) (iii) for every strongly closed K is the unique minimal strongly closed subset of A containing D.Thus A. Let We define a sequence V such that n by If A is a finite set, the chain K contains C that contains C must contain K. By construction D is a set of arcs in the X-network N, the strong closureD is the smallest set K of arcs that contains D and is strongly closed. By Theorem\u00a03.7K is uniquely determined.If The next theorem is the main result of this section.X-network. Assume X-arc. Let K(D) be the strong closure of D. Let Let X-network.(1) v] of (2) Each equivalence class  to [b]. Then in N there is a g-path from a to b.(4) Suppose there is a path in Write N. Since i, either (1). Let (2) (3) Since (4) Suppose X-network. Let b is not a leafD is strongly closed and contains no X-arcs.Let D contains no X-arcs since such were specifically excluded. Note that if i, either X-arc in D, no It is immediate that D is strongly closed, suppose there are vertices V such that D. Then To see that X-network. Let b is not a leafLet X-network.(1) (2) For every b is a leaf.(3) For every arc (4) p(x) for some (5) No vertex of (6) (1) follows from Theorem\u00a0N from v to (2) By Lemma D it follows that Since b is not a leaf. If For (3) suppose u,\u00a0v) is an arc of v is not a leaf. There exists b is not a leaf since For (4) suppose (c. Then For (5) write For (6), note v is trivial if X-network v with unique child c. When this happens, p(x) is trivial, it has a unique parent u(x). By Theorem\u00a0u(x) satisfies p(x) can be merged with u(x) and hence removed. We state this as a theorem:Recall that a vertex X-network and p(x) for Suppose X-network.(1) (2) There is a leaf-preserving CSD map (3) X-network.(4) (5) E contains no X-arcs. It is easy to see that E is strongly closed. Hence, X-network, proving part of (1).It is immediate that N to u(x) did not have out-degree one in u(x)] does not have out-degree one in u(x)] is not trivial. Thus, There are leaf-preserving CSD maps A very similar network was described in Willson  by a difX-network N, and Fig.\u00a0N and much simpler than N. Vertices in N with the same cluster.Figure\u00a0X-network N all its redundant arcs to form Our goal in this paper is the construction of normal networks which by definition contain no redundant arcs. A crucial step will be removing from an N is an X-network, let N by removing all redundant arcs. More precisely, if A by removing all arcs redundant in N.If X-network. Then X-network.Suppose The proof is straight-forward and is omitted.f may not induce a CSD map from X-network M. Let M has no redundant arcs, while N has two redundant arcs, indicated by dashes. The projection map N without the dashed arcs, and If N to In the same figure, one sees easily that there is no CSD map from N is an acyclic X-network. For each Suppose v to N. By Theorem\u00a0v to N of maximal length contains no redundant arc, hence lies in v to N from v to x, proving Suppose X-networks. Suppose wired lift of N is described. It provides a method for visualizing N. In this section we modify and generalize the notion so that connected map. This will let us obtain wired lifts from a process that includes both CSD maps and removing redundant arcs.Let  Willson  a wired X-networks, and let f is a connected map Let (K1) (K2) (K3) for all (K4) for each (K5) for each f is a connected map while in general it is not a CSD map.It is immediate that a CSD map is connected, but a connected map need not be CSD. Suppose V. A  wired lift of f (or of N) is a pair Let (W1) For each arc u,\u00a0v) representspre-arc of (W2) For every arc representative arcs since each represents an arc of Call the members of V. Thus for all Note that the collection of all backwards mapg is a map f is a CSD map, for each u,\u00a0v) exists, and Suppose There are several situations that give rise to wired lifts. We describe three of them in the next theorem. A fourth will be given in Theorem\u00a0X-networks, and let Let (1) Let (2) Suppose (3) Let f can be regarded as a map (1) and (2) are immediate from the definitions since a CSD map is connected. For (3), note that N. An example is shown below in Fig.\u00a0N except that each arc may be wide solid, thin solid, or thin dashed. Suppose u,\u00a0v) a wide solid arrow if N and each vertex of g-paths using allowed steps, which we will now describe.Given a connected map X-networks, with f. If u and v are in V, we say there is an allowed step from u to v if either Let X-networks, with f. Let V defined by Let N there is a sequence of vertices (1) In N such that, for i such that (2) There is a sequence of vertices Suppose there is a sequence of type (1). If Conversely, given a sequence of type (2), if the allowed step from generalized path or g-path from a to b in We will call a sequence of either type a X-networks. Let f.Let N (of type (2)). Then (1) Suppose N from a to b.(2) Suppose If there is an allowed step from Conversely suppose In Willson  there waN; thus if we ignore thickness and dashing and include all arcs with their indicated directions, whether thin, wide, or dashed, the diagram exhibits N. A vertex of f(10) of f(15) has inverse image Figure\u00a0f(16) to f(1). The corresponding path in N from 16 to 1. Similarly the g-path 21,17,4 shows that in The dashed arcs are not permitted on g-paths, and wide solid arcs must be followed in their direction. Thin solid arcs can be followed in either direction. Thus, 16, 10, 8, 9, 15, 1 is a g-path showing that X-networks. Suppose f is nevertheless a connected map and there is a wired lift of f. Consequently, we are able to visualize simplifications of Suppose X-network. Write Suppose for (i) (ii) (1) f.(2) f is well defined since To see (1), note that For (2), to prove (W1) suppose For (W2), given any arc f on the diagram of In the situation of Theorem\u00a0u,\u00a0v) if (1) a thin solid arc  if (2) a thin dashed arc  if (3) a wide solid arc  an obstacle if (1) v is not a leaf, and (2) every child of the vertex v in v may be regarded as an \u201cobstacle\u201d to N being pre-normal.Let We must ignore redundant arcs when deciding our strategies concerning which arcs to merge. To make these decisions we need to have a notion of in-degree and out-degree that does not count redundant arcs.v is a vertex of an X-network N. The non-redundant in-degree of v, denoted nrindeg(v), is the number of non-redundant arcs ; hence it is the number of parents of v by non-redundant arcs. If non-redundant out-degree of v, denoted nroutdeg(v), is the number of non-redundant arcs , hence the number of children of v by non-redundant arcs. If v is not a leaf, then by Theorem\u00a0Suppose v of N is nonr-hybrid if c is a nonr-child of v if  is a non-redundant arc; we also say v is a nonr-parent of c. A nonr-child c of v is a nonr-tree-child of v if nonr-path if no arc A vertex v is a pre-normal obstacle iff (1) v is not a leaf, and (2) every nonr-child of v is nonr-hybrid.It is immediate that X-network with redundant arcs. Note that 8 is an obstacle since both its children 12 and 13 are nonr-hybrids. But 9 is not an obstacle since the only nonr-parent of 10 is 9 and Figure\u00a0X-network N is obstacle-free if it contains no pre-normal obstacle.An N is an acyclic X-network that is obstacle-free. Then X-network and N is pre-normal.Suppose v that is not a leaf, there is a non-redundant arc  with c is a tree-child of v. Since N is pre-normal. By hypothesis, for every vertex X-network is always pre-normal, but a pre-normal network need not be tree-child.Theorem\u00a0X-network N, when we seek a normal network M, we know by Lemma 2.2 that S(M) will be regular; by (1) in the definition of regular network, S(M) is SCD. We are therefore seeking a network that is very close to being an SCD network, and it is plausible to start with the very general SCD network Theorem\u00a0N be an acyclic X-network. Suppose c is an obstacle. An allowable 1-fold parent chain of c is a path d is via a redundant arc). An obstacle c is of type 1 if c has an allowable 1-fold parent chain. If c has type 1 and Now we show that there are different types of pre-normal obstacles. Let c is an obstacle and allowable k-fold parent chain for c is a nonr-path d distinct from c is of type k ifSuppose c is not of type (a) c has an allowable k-fold parent chain.(b) k-fold parent chain writeIn this situation, for this N be an acyclic X-network. Then every pre-normal obstacle c has a unique type.Let It is clear that the type, if it exists, is unique.c which has maximal length k. Write this path as d other than k-fold parent chain of c, so c has type at most k. If, instead, q of d other c has type Consider a path from c is not a leaf hence must have a nonr-child e. Since c is an obstacle, e has a nonr-parent q must start c to q, hence a nonr-path from c to q to e, showing that  is redundant, a contradiction. Hence some such c has an allowable If no such The following result shows a simple way to remove a type 1 obstacle:N is an acyclic X-network and c is a type 1 obstacle with allowable 1-fold parent chain p,\u00a0c, where p has nonr-tree-child Suppose c is an obstacle, it is not a leaf, so D contains no X-arc. Moreover, D is strongly closed since  is not redundant, and X-network. Note p,\u00a0c],\u00a0d). If q is any parent of d in N other than p, then  is redundant since d is a nonr-tree-child of p. Hence by Theorem\u00a0d. Thus the lengthening must include the nonr-parent p of d and there is a path in N with non-redundant arcs from q to p to d. Since q,\u00a0d) is redundant in Since k. The next result assumes for simplicity that D is strongly closed.The result above often generalizes to obstacles of type N be an acyclic X-network with pre-normal obstacle c of type k. Suppose k-fold parent chain, where D is strongly closed. Form d and Let D contains no X-arcs since c is not a leaf. By Lemma d becomes a nonr-tree-child of d becomes a nonr-tree-child of d. Note that The following lemma shows that, often, once an obstacle is removed, it does not reappear when subsequent arcs are merged.p,\u00a0c) is a non-redundant arc in the acyclic X-network N and p and c. Let a,\u00a0b) is a non-redundant arc in N and b is a nonr-tree-child of a  (2) There is a leaf-preserving CSD map (3) N is normal, then (4) If E contains no X-arc because a leaf does not have out-degree one. Since E is clearly strongly closed, X-network. (1) and (2) follow as in Theorem\u00a0u is trivial, then Note that N is tree-child, N by removing one trivial vertex t with parent q and child c. In q obviously still has a tree-child, the same one as in N. We must show that q has a tree-child in t has a tree-child in N which must be c so c has no other nonr-parent than t in N. Hence q in c which has no other nonr-parent and is therefore a tree-child. This proves For (4) we first show that since N by the removal of a single trivial vertex t with parent q and child c. The only possible redundant arc in q,\u00a0c). If it is redundant, there is a path in q to c other than the arc, hence a path in N from q to c not through t. Such a path of maximal length by the proof of Theorem\u00a0c has a nonr-parent besides t. This contradicts that N was normal, since t in N has no tree-child. For (4) we must also prove that X-network N, to compute a uniquely determined normal X-network. We first compute a uniquely determined pre-normal acyclic X-network pre-normalization of N. The computation uses the procedure PRENORM described below. Briefly, if N is not already a pre-normal acyclic X-network, we compute c we compute its type k and find all the allowable k-fold parent chains for c. Let D(c) be the union of c. Let D be the union of the D(c) for all the obstacles c. We then compute We now show how, given an Here is a more detailed description of the computation of height of r. Thus N is acyclic and pre-normal; otherwise, r is 1 more than the number of times the procedure passes through steps 5 , 6, 7. The height r is a crude indicator of the complexity of the calculation. The examples in this paper satisfy The network output by the procedure will be denoted The next theorem shows that the procedure works.X-network.Let N. ThenApply procedure PRENORM to X-network (1) The procedure terminates and outputs an acyclic N.(2) (3) The projection N that contains no dashed arcs.(4) Let N and X-network which contains no trivial vertices. If it contains no obstacles, it is pre-normal by Theorem\u00a0c. For each obstacle c of type k and each allowable k-fold parent chain c the set X-arc since the obstacle c cannot be a leaf. Hence D(c) contains no X-arc, so D contains no X-arc. By Theorem\u00a0X-network, which we expect will be pre-normal by Lemmas If the procedure returns D is nonempty, so more arcs are contracted and N is finite, the procedure must terminate. This proves (1).Each time step 5 is utilized on The procedure never involves a choice, such as favoring some obstacles or some allowable parent chains over others. Hence (2) is true.We wish to see (3). If For (4), since X-network, we remove the redundant arcs to form normalization of N. The next theorem records its basic properties.Since N is an X-network. Let Suppose X-network containing no trivial vertices, hence a phylogenetic X-network.(1) N.(2) The definition of (3) The projection N to (4) The composition N which may contain dashed arcs.(5) There is a wired lift of (6) X-network by Theorem\u00a0N. Then (3) follows from Theorem\u00a0For (1) note There is an interesting variant of the procedure PRENORM. Define the procedure VARIANT PRENORM to be exactly like PRENORM except that step (5c) is replaced byk-fold parent chain c, and let  The procedure terminates and outputs an acyclic (2) The projection N that contains no dashed arcs.(3) There is a wired lift of Let X-network containing no trivial vertices, hence a phylogenetic X-network.(4) (5) The projection (6) The composition N.(7) There is a wired lift of a variant prenormalization of N and is denoted C records the particular choice of allowable k-fold parent chain for c made in step  c of type k there is more than one allowable k-fold parent chain, then (2) If for some obstacle u and v are vertices of (3) If (4) u and v are vertices of (5) If (6) If (7) If c of type k, E contains exactly one allowable k-fold parent chain for c, while D contains all allowable k-fold parent chains for c. Then (2) is obvious and (3) follows from (1). For (4), go through the proof of Theorem\u00a0K(E), it necessarily must be added also to K(D). Then (5) follows from (4). For (6), the vertices of (1) is true since for a given obstacle A calculation of Other variants making other choices of parent chains are possible as well.N in Fig.\u00a0N has four more distinct clusters than the tree This example continues Example\u00a0N in Fig.\u00a0N is already SCD. Consider D is strongly closed, and we find v, N contains the arc .The projection map f is a connected map. Figure\u00a0N. The thin solid arcs show immediately that there were identifications Let mentclasspt{minimaN contains vertices with clusters N. In this example, It is easy to compute that X-network N with a single obstacle 16 of type 3. N is seen by changing all thin solid or dashed arcs to wide solid. N is easily verified to be already SCD, so N is 11, 14, 17, 16; another is 13, 14, 17, 16. The chain 13,14,16 is not an allowable parent chain because  is redundant. To find Figure\u00a0N. When these arcs are removed from u,\u00a0v) such that As maps of vertex sets The wired lift of This section contains two examples from real biological data.N be their graph. A wired lift of N is seen if each arc in Fig.\u00a0N, which contains 31 vertices (of which eight are hybrid), and 38 arcs. We find Gl\u00e9min et\u00a0al.  study pen et\u00a0al.  to indicN for the angiosperm genus Viola in their Fig.\u00a0D contains 4 arcs. u,\u00a0v) can map to the same arc Marcussen et\u00a0al.  exhibit N than s et\u00a0al.  in theirD has 3 rather than 4 arcs, leading to one more vertex in N as well as does If we use instead VARIANT PRENORM, there are two possible normal networks N by Theorem\u00a0Both such Both variant normalizations satisfy Further comments concerning this example are given in Sect.\u00a0Comparison ofandX-network. It is interesting to contrast X-networks depending only on the geometry of N. Both allow vertices of N to have in-degree greater than 2 or out-degree greater than 2, and both apply quite generally.s et\u00a0al. . Both arN. A vertex v is visible if there exists v. This set of visible vertices forms the initial vertex set of N, as is done in Francis et\u00a0al. , where u and v are distinct visible vertices of N, precisely when N and there is no third visible vertex w such that u could be present because of directed paths in N from u to u to The arcs of N is for the Viola genus of Marcussen et\u00a0al.  are visible and hence they do not appear in N, and (c) there is no other path from 22 to 18 containing a third visible vertex. Similarly N. Thus these three distinct arcs in N involving 13 and 14.Consider again Fig.\u00a0n et\u00a0al. . The diaN that appear in g-paths; the thin solid arcs tell what arcs must be merged to obtain the normal network g-paths lets us understand In contrast, the arcs of Software The author has written software using Xcode which implements the calculation of Future work One can ask whether there are other classes of networks besides normal networks for which a similar construction could be used to simplify a network N into one of this other class. Suppose, given an X-network N, we sought a tree-child X-network C. Since a tree child network may contain redundant arcs, we should like a construction that depends only on the geometry of N and yields a CSD map"}
+{"text": "Scientific Reports 10.1038/s41598-021-89417-8, published online 12 May 2021Correction to: The original version of this Article contained errors.In the PDF version, Table 1 was incorrectly sized resulting in the loss of the final two columns of data: \u201cDIF\u201d and \u201cBMI\u201d. The HTML version was unaffected.F statistics, where F  and F  were incorrectly given as F\u2009=\u2009 and F\u2009=\u2009 respectively.In addition, there was a repeated error in the The original Article has been corrected.The conclusions of the Article remain unchanged."}
+{"text": "Meniscoid lesions have been reported in patients with chronic ankle injuries, especially in soccer athletes, and such lesions cause soft-tissue impingement and pain. To our knowledge, we are the\u00a0first to report a meniscoid lesion in the ankle joint presenting as a long-term sequela of avascular necrosis of the talus that developed in childhood.In this paper, we describe a 55-year-old\u00a0Caucasian male patient who presented with a 1-year history of intermittent locking, \u201cgiving way,\u201d weight-bearing pain, and swelling over the anterior aspect of the ankle joint. Imaging showed a rare case of avascular necrosis of the talus associated with an unstable plica-like lesion that was removed arthroscopically after unsuccessful conservative treatment.We demonstrate that unstable meniscoid lesions of the ankle joint can be treated successfully with arthroscopic debridement. We obtained satisfactory short-term clinical results at the 2-year follow-up, even though advanced osteoarthritis was present. Avascular necrosis (AVN) of the talus is a challenging condition to treat, and is usually associated with\u00a0major disabilities in patients. Fracture of the talus is the most common cause of AVN, accounting for up to 75% of cases . AnatomiA 55-year-old Caucasian male presented for consultation with a 1-year history of intermittent locking, \u201cgiving away,\u201d weight-bearing pain, and swelling over the anterior aspect of his right ankle that had recently been aggravated. The patient was a sedentary worker and non-athlete. He stated that he had experienced right ankle trauma at 8\u00a0years old, following an accidental fall from a height that was never investigated or treated. His pain and\u00a0swelling had disappeared after several months, and the patient never had any further symptoms until recently.Physical examination revealed pain over the anterior aspect of the ankle joint. No snap was audible, and no lateral instability was exhibited. Provocative tests of the flexor hallucis longus were painless, dorsiflexion was slightly limited and painful,\u00a0and forced plantar flexion was full and painless. Moreover, we noted pain with a\u00a0single leg squat. There was no proprioception impairment, postural control difficulty, or strength deficit. Shortening of the right inferior limb was measured to be approximately 1\u00a0cm.Plain radiographs Fig. a and b sAfter 6\u00a0months of conservative treatment, including rehabilitation, pain medication, and intraarticular corticoid injection, the patient still had the same complaints. Surgical arthroscopy was chosen for debridement. An ambulatory arthroscopic intervention was performed under general anesthesia. A tourniquet was applied for hemostasis. Two portals were used: anterolateral and anteromedial. At the time of surgery, no instability was seen during anesthesia. Upon arthroscopic examination through the anterior medial portal, an unstable band of white, meniscus-like tissue accompanied by an unstable 1.5\u00a0cm ossicle Fig. a\u2013d was fThe follow-up radiograph Fig. a and cliet\u00a0al. in 1950 [et\u00a0al. [et\u00a0al. [et\u00a0al. [et\u00a0al. [Meniscoid lesions in the ankle were first reported in the literature by Wolin  in 1950 . Other s in 1950 . Acute i in 1950 . We have in 1950  identifi in 1950 . McCarro [et\u00a0al.  advocate [et\u00a0al.  that chi [et\u00a0al.  and has  [et\u00a0al. , in the  [et\u00a0al. , 14, whe [et\u00a0al. .In this case report, we present a case of an unstable preexisting meniscoid lesion accompanied by an unstable ossicle as the long-term sequela of AVN of the talus. This case initially\u00a0developed in childhood and became more symptomatic in adulthood. Both lesions led to fibrous and osseous impingements that were removed arthroscopically. The treatment was a success, with the patient complaining of only very rare pain and swelling at the 2-year follow-up. This result supports the role of arthroscopy in symptomatic meniscoid lesions in the ankle joint as a first line of surgical treatment. However, for later end-stage ankle arthritis, more invasive measures such as tibiotalar fusion may be needed."}
+{"text": "Scientific Reports 10.1038/s41598-018-24414-y, published online 23 April 2018Correction to: This Article contains an error in Figure\u00a01A. As a result of a mistake in figure assembly, the band for p-MLKL is incorrect. The correct Figure\u00a0This change does not affect the conclusions of the Article."}
+{"text": "One of the major approaches in such a study is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a novel two-phase framework has been proposed for inverse QSAR/QSPR, where in the first phase an artificial neural network (ANN) is used to construct a prediction function. In the second phase, a mixed integer linear program (MILP) formulated on the trained ANN and a graph search algorithm are used to infer desired chemical structures. The framework has been applied to the case of chemical compounds with cycle index up to 2 so far. The computational results conducted on instances with  In computational molecular biology, various types of data have been utilized, which include sequences, gene expression patterns, and protein structures. Graph structured data have also been extensively utilized, which include metabolic pathways, protein-protein interaction networks, gene regulatory networks, and chemical graphs. Much attention has recently been paid to the analysis of chemical graphs due to its potential applications to computer-aided drug design. One of the major approaches to computer-aided drug design is quantitative structure activity/property relationship (QSAR/QSPR) analysis, the purpose of which is to derive quantitative relationships between chemical structures and their activities/properties. Furthermore, inverse QSAR/QSPR has been extensively studied , 2, the descriptors and correspond to feature vectors in machine learning. Using these chemical descriptors, various heuristic and statistical methods have been developed for finding optimal or nearly optimal graph structures under given objective functions  denote the set of integers i with Let graph stands for a simple undirected graph, where an edge joining two vertices u and v is denoted by uvH are denoted by V(H) and E(H), respectively. Let V of vertices and a set E of edges. For a vertex v in H is denoted by degreev is defined to be distanceu and v in H. The diameterH is defined to be the maximum distance between two vertices in H; i.e., P.A Centers of trees For a tree T with an even  diameter d, the center is defined to be the vertex v  is designated as the root. Let T be a rooted tree, where for two adjacent vertices u and v, vertex u is called the parent of v if u is closer to the root than v is. The heightv in T is defined to be the maximum length of a path from v to a leaf u in the descendants of v, where v in T. Figure\u00a0mentclass2pt{minimDegree-bounded trees For positive integers a,\u00a0b and c with T denote the rooted tree such that the number of children of the root is a, the number of children of each non-root internal vertex is b and the distance from the root to each leaf is c. We see that the number of vertices in T is T is T, we denote the vertices by T, let j such that j such that i,\u00a0j) of vertices T. We call proper if the next conditions hold: T such that For each pair of vertices T with Each subtree Note that a proper set Branch-height in trees In this paper, we introduce \u201cbranch-height\u201d of a tree as a new measure to the \u201cagglomeration degree\u201d of trees. We specify a non-negative integer k, called a branch-parameter to define branch-height. First we regard T as a rooted tree by choosing the center of T as the root. Figure\u00a0T.leafk-branch: A non-root vertex v in T such that A non-leafk-branch: A non-root vertex v in T such that v has at least two children, and for each child u of v it holds that k-branch a k-branch. Figure\u00a0k-branches of the rooted tree A entclass1pt{minimak-branch-path: A path P in T that joins two vertices u and u and k-branch and P does not contain the root or a k-branch as an internal vertex.A k-branch-subtree of T: The subtree of T that consists of the edges in all k-branch-paths of\u00a0T. We call a vertex  in T a k-internal vertex  if it is contained in the k-branch-subtree of T and a k-external vertex  otherwise. Let k-internal and k-external vertices  in\u00a0T.The k-branch-tree of T: The rooted tree obtained from the k-branch-subtree of\u00a0T by replacing each k-branch-path with a single edge. Figure\u00a0k-branches and non-leaf k-branches are leaves and branching points in the k-branch-tree.The mentclass2pt{minimk-fringe-tree: One of the connected components that consists of the edges not in the k-branch-subtree. Each k-fringe-tree v in the k-branch-subtree, where v. Note that the height of any k-fringe-tree is at most\u00a0k. Figure\u00a0k-fringe-trees of the rooted tree A entclass1pt{minimak-branch-leaf numberk-branches in T. For the trees The mentclass2pt{minimk-branch heightT: The maximum number of k-branches along a path from the root to a leaf of\u00a0T; i.e., k-branch-tree The mentclass2pt{minimk-branch height for chemical cyclic graphs . The core of a chemical cyclic graph G is defined to be the induced subgraph G that consists of vertices in a cycle or the vertices in a path joining two cycles. A vertex in the core (not in the core) is called a core vertex . The edges not in the core of a chemical cyclic graph G form a collection of trees T, which we call a non-core tree. Each non-core tree contains exactly one core vertex and is regarded as a tree rooted at the core vertex. The k-branch height of a chemical cyclic graph G is defined to be the maximum of k-branch heights over all non-core trees. We observe that most chemical graphs G with at most 50 non-hydrogen atoms satisfy Even though this paper deals exclusively with acyclic graphs, we formally introduce the For convenient reference, we summarize the graph-related notation used throughout this paper in Table\u00a0We represent the graph structure of a chemical compound as a graph with labels on vertices and multiplicity on edges in a hydrogen-suppressed model. Let adjacency-configuration of the atom pair. Choose a set We introduce a total order < over the elements in We use a hydrogen-suppressed model because hydrogen atoms can be added at the final stage.v and a bond-multiplicity m is assigned to an edge e, respectively. For a notational convenience, we denote the sum of bond-multiplicities of edges incident to a vertex A tuple chemical graph over (i)H is connected;(ii)(iii)A chemical graph H is an acyclic graph. Similarly for other types of graphs for H.Let bond-configuration of an edge G to be a tuple u and v of e. Let We define the In summary, we give the notation on modeling chemical compounds used throughout this paper in Table\u00a0feature vectorf(G) that consists of the following 11 kinds of descriptors. We choose an integer In our method, we use only graph-theoretical descriptors for defining a feature vector, which facilitates our design of an algorithm for constructing graphs. Given a chemical acyclic graph General chemical graph descriptorsn(G): the number |V| of vertices.H divided by G.G.Descriptors for vertices of certain degreei in H, where the bond-multiplicity of edges incident to a vertex v is ignored in the degree of v.Descriptors for branch-leaf number and branch-heightG.G.Descriptors for vertex labelsDescriptors for the number of bondsm.Descriptors for adjacency-configurationsG.Descriptors for bond-configurationsG.Note thatK of descriptors in our feature vector K descriptors are not independent in the sense that some descriptors depend on the combination of other descriptors. For example, descriptor a(G) the observed value of the property G. As the first phase, we solve (I) Prediction Problem with the following three steps.We review the framework that solves the inverse QSAR/QSPR by using MILPs , 21, whiPhase 1.Stage 1: Let K. We call f(G) the feature vector of f(G) a descriptor of G.Stage 2: Introduce a feature function a(G) for many chemical graphs in\u00a0Stage 3: Construct a prediction function j-th descriptor j-th descriptor, In this paper, we use the range-based method to define an applicability domain (AD)  to our iIn the second phase, we try to find a vector agamochi , Chiewvaagamochi  showed tLetbe an ANN with a piecewise-linear activation function for an input vectordenote the number of nodes in the architecture anddenote the total number of break-points over all activation functions. Then there is an MILPthat consists of variable vectors, and an auxiliary variable vectorfor some integerand a setofconstraints on these variables such that:if and only if there is a vectorfeasible to, 21) Let Let21]) See Appendix\u00a0\u201cmentclass2pt{minimadmissible if there is a chemical graph q. For the class q so thatA feasible solution A vector Afterwards, for the classes of chemical graphs with cycle index\u00a01 and\u00a02, Ito\u00a0et\u00a0al. [A vector t}f(G)=x . Let \\dom\u00a0et\u00a0al.  introduco\u00a0et\u00a0al.  and Zhu\u00a0o\u00a0et\u00a0al.  presenteInverse Problem for the inverse QSAR/QSPR by treating the following inference problems.As the second phase, we solve (II) (II-a) Inference of VectorsInput: A real Output: Vectors (II-b) Inference of GraphsInput: A vector Output: All graphs The second phase consists of the next two steps.Phase\u00a02.The second requirement may be replaced with inequalities Stage\u00a04:\u00a0 Formulate Problem (II-a) as the above MILP Stage\u00a05:\u00a0 To solve Problem (II-b), enumerate all (or a specified number) of graphs In practical applications, there would be many criteria that a target chemical compound needs to satisfy rather than a single chemical property G such thatG is at most 4;The maximum degree in k-branch height k; andThe k-fringe-tree in G is bounded.The size of each The reason why we restrict ourselves to the graphs in k-branch height and the size of 2-fringe-trees. According to this, over 55%  of acyclic chemical compounds with up to 100 non-hydrogen atoms in PubChem have the maximum degree 3 ; and nearly 87%  of acyclic chemical compounds with up to 50 non-hydrogen atoms in PubChem have the 2-branch height at most 1 . This implies that k-branch height and the k-branch-leaf number for a branch-parameter k.In this paper, we choose a branch-parameter H such thatH is at most 3 when The maximum degree of a vertex in n(H) of vertices in H is The number H is The diameter The The  holds.To design Stage\u00a04 for our class More formally, given specified integers G so that the number G with Design of Stage\u00a05, i.e., generating chemical graphs x 0 to 2 \u201324. All To conclude the description of the target graph class to be inferred by the inverse QSAR/QSPR framework developed in this paper, we summarize the global parameters in Table\u00a0G in the class In this section, we describe an idea of formulating an MILP H is as follows. See a rooted tree T including the root T as the H.From the tree T and replace each of the edges H.Next, we choose some edges in the tree k as the H. The resulting tree is a required rooted tree H.Finally, we append to the tree Our new idea of constructing an acyclic graph T of In our MILP, we prepare a binary variable for each of the vertices and edges in e with a path F of directed edges between the vertices in F in our MILP. When an edge To represent a replacement of an edge F and the set of rooted trees at the vertices in scheme graphWe call the graph that consists of all the above graphs H with H in Fig.\u00a0H in Fig.\u00a0Figure\u00a0In this paper, we obtain the following result.Letbe a set of chemical elements,be a set of adjacency-configurations, where, andGiven non-negative integers,,,,and, there is an MILPthat consists of variable vectorsandfor an integerand a setof constraints onxandgwith sizesuch that:is feasible toif and only ifforms a chemical acyclic graphsuch thatandNote that our MILP requires only See Appendices\u00a0n(G) is larger than around\u00a020.Previous methods of inferring chemical graphs \u201319 use aTreat acyclic graphs with a certain limited structure that frequently appears among chemical compounds registered in the chemical database; andG from the process of computing the vectors.Instead of manipulating acyclic graphs directly, first compute the frequency vectors In (a), we choose a branch-parameter G that have a small 2-branch number such as G with This section introduces a new dynamic programming method for designing an algorithm in Stage\u00a05. We consider the following aspects: mentclass2pt{minimT to be a vector that consists of the frequency of each chemical element T. We are given a vector G to be inferred.We design a method in (b) based on the mechanism of dynamic programming in the following way. Define a frequency vector We first construct a set m, as illustrated in Fig.\u00a0m to obtain the frequency vector m.We next combine two chemical rooted trees G with p trees in m is equal to the given vector G with m.Our algorithm for generating a chemical acyclic graph G with With a slight modification, the algorithm can generate a chemical acyclic graph G with Appendix\u00a0Kow), boiling point (Bp) and heat of combustion (Hc). We executed the experiments on a PC with Two Intel Xeon CPUs E5-1660 v3 @3.00GHz, 32\u00a0GB of RAM running under OS: Ubuntu 14.04.6 LTS. We show 2D drawings of some of the inferred chemical graphs, where ChemDoodle version 10.2.0 was used for constructing the drawings.We implemented our method of Stages\u00a01 to\u00a05 for inferring chemical acyclic graphs and conducted experiments to evaluate the computational efficiency for three chemical properties Results on Phase\u00a01.  We implemented Stages\u00a01, 2, and 3, in Phase\u00a01 as follows.Kow, Bp, HcStage\u00a01. We set a graph class Kow, Bp and Hc;n(G) of non-hydrogen atoms over the compounds G in G in G in a(G) for G in\u00a0Table\u00a0f that consists of the descriptors defined in \u201cStage\u00a02. We used a feature function K: the number of descriptors for the chemical compounds in data set Activation: the choice of activation function;a,\u00a0b,\u00a01) consists of an input layer with a nodes, a hidden layer with b nodes and an output layer with a single node, where a is equal to the number K of descriptors;Architecture: (L-time: the average time (in seconds) to construct ANNs for each trial;test test From Table\u00a0Stage\u00a03. We used scikit-learn version 0.21.6 with Python 3.7.4 to construct ANNs $$i\\in 1,$$\\end{do$$i\\in 1,$$\\end{doFor each chemical property Results on Phase\u00a02.  We implemented Stages\u00a04 and 5 in Phase\u00a02 as follows.Set the 2-leaf-branch number Fix the instance size Set the diameter Set the maximum degree Kow, Bp, HcFor each instance size Based on the above setting, we generated six instances for each instance size Stage\u00a04. In this step, we solve the MILP IP-time: the time (sec.) to an MILP instance to find vectors We observe that most of the MILP instances with Tables\u00a0g\u00a0et\u00a0al.  could soa\u2013c illustrate some chemical acyclic graphs G with Figure\u00a07a\u2013c illustrate some chemical acyclic graphs G with Figure\u00a08Stage\u00a05. In this stage, we execute our new graph search algorithms for generating target graphs h in Step\u00a02 and an execution of Steps\u00a01 and 3 for h in Steps\u00a02 and 3 and We introduce a time limit of 10 minutes for each iteration When no feasible vector pair is found by the graph search algorithms, we output the target graph G-LB: a lower bound on the number of all target graphs G such that G has been found from the vector G-time: the running time (sec.) to execute Stage\u00a05 for a given feature vector Previously, an instance of chemical acyclic graphs with size Tables\u00a0m\u00a0et\u00a0al. . For them\u00a0et\u00a0al.  and Zhu\u00a0m\u00a0et\u00a0al.  was arouAn additional experiment We also conducted some additional experiment to demonstrate that our MILP-based method is flexible to control conditions on inference of chemical graphs. In Stage\u00a03, we constructed an ANN Kow, Bp, HcKow, Bp and Hc, it is possible to infer a chemical acyclic graph G that satisfies a target value G illustrated in Fig.\u00a0In this paper, we introduced a new measure, branch-height of a tree, and showed that many chemical compounds in the chemical database have a simple structure where the number of 2-branches is small. Based on this, we proposed a new method of applying the framework for inverse QSAR/QSPR \u201319 to thWe implemented our new method and conducted some experiments on chemical properties such as octanol/water partition coefficient, boiling point and heat of combustion.The resulting method improved the performance so that chemical graphs with around 50 non-hydrogen atoms and around diameter 30 can be inferred. Since there are many acyclic chemical compounds having large diameters, this is a significant improvement.It is left as a future work to design MILPs and graph search algorithms based on the new idea of the paper for classes of graphs with a higher rank. Recently, a method for inferring a chemical cyclic graph with any rank has been designed by Akutsu and Nagamochi  based on"}
+{"text": "J. Appl. Cryst. (2021), 54, 317\u2013332]Peterson, Olds, McDonnell & Page Peterson, Olds, McDonnell & Page [ are corrected and clarified, respectively.Errors and ambiguities in the article by  Illustrated formalisms for total scattering data: a guide for new practitioners  and \u03c1(r)] that are defined identically by Keen  ; the powers of ten, although implicitly present, could be ignored in practice. They are now more commonly tabulated in fm , 1(f), 2(e), 2(f), 3 [GK(r) and T(r)] and 4 [GK(r) and T(r)] of Peterson et al. , GPDF(r) or \u03c1(r)] are unaffected as the scattering length units cancel out.Neutron scattering lengths were typically given in units of 10 al. 2021. This ha al. 2021; the funQ limit of total scattering structure factors is related in a complex way to thermodynamic functions and fluctuations  most ofKeen 2001 and by MKeen 2001 and is f al. 2021]. The fi al. 2021. It is uKeen 2001 and Pete al. 2021. Since tKeen 2001], whilstKeen 2001. These l al. 2021, which a al. 2021 with verS(Q), FPDF(Q) and GPDF(r) etc., which are divided through by \u2329bcoh\u232a2], are useful when comparing with models and calculations, the functions FK(Q), GK(r) etc., which are not scaled by \u2329bcoh\u232a\u22122, permit a much more direct and unambiguous assessment of absolute data normalization when correcting experimental data. FPDF(Q) and GPDF(r) are more challenging in this regard as their respective Q- and r-dependent asymptotes to the origin make determination of the low-Q and low-r trends less obvious \u2018by eye\u2019. S(Q) should also be used cautiously; although it is unitless this hides the fact that scattering factors are incorporated within the function, and even though many S(Q) have a low-Q limit that is close to zero this does not mean that zero is the limiting value by definition.The above discussion also highlights another important point. Although the scaled functions . Typically when correcting data, a \u2018good\u2019 low-Q limit is often much harder to achieve than a \u2018good\u2019 high-Q limit. This is especially the case for time-of-flight neutron diffractometers where data corrections are usually more challenging in the lower-Q regime. The low-Q limit of S(Q) should approximately equal c)]. The low-r levels of GK(r) = \u2212\u2329bcoh\u232a2 and gPDF(r) = 0 . Here a back-transform correction has been applied to direct these PDFs to their theoretical values for r < 1\u2005\u00c5; encouragingly these values are maintained to much higher r, including in the gaps between the first few low-r peaks. For completeness, plots of FPDF(Q) and GPDF(r) are shown in Figs.\u00a02e) and 2f), respectively.As a worked example of this, we show in Fig. 2et al.  will not be symmetric and centred in gPDF(r) . Symmetet al. (2021et al. (2021et al. (2021We have worked together on this corrigendum to try to ensure that these corrections to the Peterson  al. 2021 paper ar al. 2021 are not  al. 2021, thus un al. 2021, but it  al. 2021. We as a al. 2021 and Pete al. 2021 with thi"}
+{"text": "The Laurent\u2013Stieltjes constants of Let  Let Dirichlet L-functionStieltjes constants or generalized Euler constants. In the particular case when L-function Riemann zeta functionL-functions. This gives rise to the widely used name \u201cStieltjes constants\u201d for these coefficients.Let L-functions have also been studied by many authors. We introduce some of their results in the following section.The asymptotic behavior of : Briggs , Mitrovi: Briggs , Israilo: Briggs , Matsuokmentclasspt{minima: Briggs , Knessl : Briggs , Adell [entclass1pt{minima: Briggs ). The stL-functions. We consider functions in a class larger than the Selberg class. We first introduce the Selberg class In this paper, we are interested in investigating the Stieltjes constants of more general f be an arithmetic function, and denote by f. We say the Dirichlet series Let p:All functions L-functions K. The sum of the parameters degree of the L-function Notable examples of functions in refer to , Chap. 6generalized Laurent\u2013Stieltjes constants or the Laurent\u2013Stieltjes constants of the extended Selberg class. In this paper, we study these coefficients and give an upper bound of From now on we keep our focus on Our main theorem is stated as follows.Q be the positive real number appearing in condition\u00a0n witha satisfies Let L-functions have many applications not only in analytic number theory, but also in algebraic number theory and even fields outside of number theory. They can be used to determine zero-free regions for Finally we remark that the Laurent\u2013Stieltjes constants of zeta and sis, see .L-functions. She gave the following upper bound for q and for every The first explicit upper bound for y Briggs , which wy Briggs  and Isray Briggs . In 1985mentclasspt{minimad author  extendedhowed in  that thiK be a number field and Dedekind zeta functionK, K, h(K) the class number of K, R(K) the regulator of K, K and D(K) the discriminant of the extension K. The second author [L-functions, has been studied so far. For more details see for example [L-functions in the extended Selberg class.Finally, let tion. In  they ared author  studied  example , 20. ThiIn order to prove our main result, we first show a proposition and two necessary lemmas. Recall the notation used when we defined mentclass2pt{minimLet For the standard case when we assume entclass1pt{minimaNow without entclass1pt{miniman be an integer with Let D is the positively oriented rectangular path passing through the vertices A and T are sufficiently large numbers. Let us now divide D into the line segments By Cauchy\u2019s formula, we can writementclass2pt{minimBy Lemma\u00a0Next we consider the integral over Thus, for fined in . This comentclass2pt{minimFor mentclass2pt{minimPut \u03bbm. From , we havea be a real number satisfying Now we are ready to prove our main theorem. We again putBy Proposition"}
+{"text": "Nature Plants 10.1038/s41477-021-01014-9, published online 15 November 2021.Correction to: In the version of this article initially published, there were errors in the Fig. 1 color key. In the key, \u201cCortex\u201d should have been by the blue bar, rather than yellow, and \u201cEndodermis\u201d by the yellow bar, rather than blue. The errors have been corrected in the html and PDF versions of the article."}
+{"text": "Much research has attested to the benefits of intergenerational programs (IGPs) for older and younger participants, but there is a lack of understanding about what motivates them to participate and to persevere. We conducted structured interviews with 83 older (mean age = 77) and 96 younger (mean age = 23) participants who participated in 13 IGPs in Israel, some involving specific topics, and some providing assistance to older adults. Using a mixed-methods approach, we analyzed differences in motivation across generations and program types and compared initial and ongoing motivation to participate. We found differences regarding motivation by age group and program type: Among older participants, interest in the specific subject was a more prevalent motivation in topic-focused groups, while receiving support was more common in assistance groups. Among young persons, motivations relating to obligation, such as receipt of a financial scholarship, and the wish to help others were the most prevalent motivators. Ongoing motivation was often explained by positive intergenerational relationships and enjoyment. For older adults, offering more diverse topic-focused activities may motivate greater participation. For young adults, integrating IGPs within more and different settings, and promoting IGPs as opportunities to help others are potential motivators. Intergenerational programs [IGPs] are types of human services that involve ongoing and organized interactions between members of younger and older age groups for the benefit of all participants . They arThe negative physical and mental health impact of social isolation and loneliness on older adults has been widely studied ,6,7, yetResearch has also identified challenges, including uneasiness experienced by young people when encountering older people with dementia or frail older adults . AnotherAlthough the motivation of participants to take part in IGPs has not been studied specifically, several studies have mentioned the willingness of participants to continue participating in IGPs, e.g., . In one study, university faculty members worked in collaboration with a team of older volunteers to develop, deliver, and evaluate an undergraduate intergenerational course about aging . The oppThe limited available literature principally describes the motivation of older adults, who generally report more benefits than young adults in IGPs . Little In this paper, we aim to address the lacuna in the research regarding the motivation of younger and older individuals to participate in IGPs. Addressing this gap aims to provide organizers of IGPs with new insight into the recruitment and retention of participants. Our research questions are: (1) What motivates young and older participants to participate in IGPs? We examined both initial motivation and ongoing motivation for both groups. (2) How do the different types of motivation relate to young and older participants\u2019 background characteristics? (3) For young participants, we also examined whether they perceived their involvement as voluntary or obligatory.We sought to include all the types of community-based IGPs offered in the greater Tel Aviv, Israel metropolitan area by contacting national and municipal offices and diverse not-for-profit organizations. We learned of additional programs through snowballing. Our data were generated from 13 programs. We included only IGP programs that were organized by community-based organizations, in contrast to school-based, and were conducted at community centers or participants\u2019 homes, rather than in school buildings or long-term care settings.We categorized the 13 community-based IGPs found in greater Tel Aviv based on their most salient content and goals: (1) \u201cTopic-focused programs,\u201d which involved the performing arts such as theater and dance, the study of Jewish texts, a photography course, and a bridge club; (2) \u201cAssistance groups\u201d designed to provide one-on-one support with daily activities for older persons, including visits to their homes, documentation of their life stories, in-home computer assistance, or assistance with pet care. Young participants and older participants met about once weekly on average. While all programs were aimed at improving intergenerational relationships, the topic-focused programs provided meaningful recreation rather than personal assistance. Some programs recruited young persons from among specific groups, e.g., university students, soldiers. Young participants either volunteered or participated non-electively as part of their military, pre-military, national service, or academic course work. Some young participants received a financial or housing scholarship for their participation. Older participants were referred to some IGPs by social services workers, or by word of mouth, or responded to publicity about opportunities to participate in such programs.The study was approved by the ethics committee of Tel Aviv University. After informed written consent was obtained, questionnaires were either completed during personal interviews by trained interviewers (~80%) or were self-administered.The questionnaires first inquired into participants\u2019 demographic background. The subjective health of older participants was measured using the global self-rated-health item on SF-36 , using aWhy did you choose to participate in the activity?What motivates you to continue to take part in the activity and persevere in it?Is the activity a mandatory or voluntary task for you?Motivation for participation in the IGP was queried via three questions:The third question was addressed only to young participants. While the last question requested a binary (Yes/No) response, all young participants were also asked to specify the elective or non-elective nature of their involvement. These clarifications and responses to open-ended questions enabled us to identify the organizational framework within which 91 (out of 96) young participants participated in the IGPs. This study used a mixed-methods approach, combining quantitative and qualitative analyses. The research question as to what motivated young persons and older persons to participate in IGPs was first examined qualitatively. We then used the themes reached to code the responses of each participant. We used descriptive analyses of frequencies and cross-tabulation to respond to the research questions.Qualitative analysis. We used a thematic approach to understand participants\u2019 motivations for participating in IGPs . To adhet-tests to examine the relationships between background information and motivational factors. Because of the exploratory nature of those analyses and the use of multiple comparisons, we applied a criterion of p-value of 0.001 for presentation of significant findings. Quantitative analysis. We used chi-square and 79 = 3.34, p = 0.001).We interviewed 83 older persons and 96 young persons. For older participants, the mean age was 77.07 (SD = 7.07), and 83.1% were women. Of the older participants, 46 (55.4%) participated in the topic-focused groups and the rest in the assistance groups. Young participants reported a mean age of 23.49 (SD = 6.25), and 66.7% were women. Of the young participants, 32 (33.3%) participated in the topic-focused groups and the rest in the assistance groups. Age and gender were not significantly associated with type of IGP in either age group. Older participants in the topic-focused IGPs reported better health (mean = 3.42) than those in the assistance groups -IM) or \u201cI really like theater and the subject is very interesting for me. When I was young, I participated in a number of plays and then I did not [further] develop this [interest]. And it intrigued me and I wanted to try and see how it would go\u201d (#84-F-80-TF-IM) or \u201cIt is relaxing and good. This photography is relaxing and there are beautiful things to photograph in this country\u201d (#25-F-70-TF-OM).Satisfaction and joy, OM. \u201cI enjoy every moment, a great pleasure\u201d (#198-F-76-TF-OM) or \u201cThe activity gives me pleasure\u201d (#176-F-78-TF-OM). \u201cThe joy I have in my heart, I love it. It\u2019s love\u201d (#87-F-79-TF-OM).Intergenerational interactions and friendship, IM and OM. \u201cThey give me meaning in life, content. I am getting to know these wonderful youth\u201d (#143-F-90-assistance-IM) or \u201cIt interests me to be among the youth\u201d (#184-F-77-TF-IM) or \u201cI love being close to the younger generation, I feel young in spirit and love to dance\u201d (#197-F-78-TF-IM) or \u201cThe fact that it gives me pleasure, I feel with them \u2026 they opened up to me. I tell about my life and they tell me about their life, they are like my granddaughters. I feel like I have expanded the family\u201d (#171-F-77-assistance-OM).Receiving support , IM and OM. \u201cI asked for someone to come to me because I am alone. There are afternoons when I don\u2019t even have anyone to talk to. I wanted someone to come so that I will have someone to talk to and who will help me with all sorts of things I need\u201d (#142-M-83-assistance-IM) or \u201cI wanted someone to teach me [about] a computer. I have a computer and did not know how to use it. When the kids were little, I avoided the computer and now I really like this device and just want to know how to develop [using] it. Bringing someone in costs a lot of money; [A volunteer organization] had a course and they stopped it \u2026 the best thing is to have someone come and sit by you and guide you, that\u2019s the best\u201d (#44-F-75-assistance-IM) or \u201cIt gives me a lot, I am very satisfied. I always say, [when] Ron returns he is the best. I love him, it\u2019s not like a woman\u2019s love, it\u2019s like a mom and son\u2019s love. He does everything for me when he can. He helps me a lot. I give him a score of one hundred\u201d (#17-F-85-assistance-OM).Invited to participate, IM. \u201cRachel asked me to attend, so I agreed. I do not know the specific neighborhood, so it was interesting for me. It\u2019s nice to be with young people; They instructed us nicely\u201d (#30-F-80-TF-IM) or \u201cI did not choose [the IGP], my friend, Rhonda, who works here at the club, teaches gymnastics or something here, told me that there is this activity and I said I would come and check it out\u201d (#99-F-74-TF-IM).Activity/Having something to do, IM and OM. \u201cEver since I retired, against my will, I started looking for what to do. To my great joy, I received a gift from the job from which I had been fired, a personal computer, and I said to myself, what am I doing now?! What do I do in life? Then I started writing my life story. It took me 10 years. After that, I started writing short stories and participated in a creative writing class. And then I did research on a family that perished in the Holocaust; No one knew about the others\u2019 existence, and finally the second generation found each other. It\u2019s a life story of this family. So now I\u2019m looking for activities, and each time a different activity. \u2026Then I heard about the community theater, and I said, \u2018Oh!\u2019 Now I have something to do\u201d (#89-M-77-TF-IM) or \u201cA friend told me it exists; It\u2019s something I\u2019ve never done before. I have time now, something I have never had in my life. So, I came, I had a nice time, so I stayed. Everything was so light. Without major goals. Had it not been interesting, I would have left, but it was fine, so I stayed\u201d (#104-F-70-TF-IM) or \u201cBecause [otherwise] it\u2019s a day with no activities\u201d (#81-F-79-TF-OM).Sense of commitment, OM. \u201cIt\u2019s a responsibility, as soon as I get into something, then I take it upon myself to complete it. I take on a new challenge every year, and every time I take on such a challenge I keep going until the end. I intentionally take on all sorts of things every year that present a challenge for me \u201c(#79-F-71-TF-OM) or \u201cIt\u2019s a matter of character; I will not leave in the middle\u2026\u201d (#92-F-70-TF-OM).Philanthropy/Desire to help young persons, IM and OM. \u201cBecause it fulfills me, it\u2019s my life. It is important for me to pass on to the young people the values with which I grew up\u201d (#36-F-82-assistance-IM) or \u201cIt is my pleasure that I can teach young people and pass my knowledge on to them\u201d (#36-F-82-assistance-OM).Obligation, reported both as IM and OM. \u201cObligation\u201d refers to young participants\u2019 reports that IGP participation was a non-elective activity. \u201c[I participated] because it is mandatory to make a personal commitment and this activity was the most convenient and appropriate for my schedule\u201d (#199-F-16-TF-IM). The obligation may have been part of national service enlistment, army service, in those units that require it, or as a condition for receipt of a financial study or housing scholarship, etc. \u201cThe military required that we participate\u201d (#7-M-21-assistance-IM) or \u201cI committed to the activity at the beginning of the year so I persevered with it\u201d (#199-F-16-TF-OM).Interest in the subject matter, IM and OM. \u201cI have been participating in community theater for three years in a row in this course. There are quite a few frustrations and challenges in this \u2026 but I do it because it is the only production in the theater department that allows all students to participate in a creative way, and writing is also one of the things that interests me and this is the only course that allows one to write. Plus, it allows me to perform on stage\u201d (#111-F-25-TF-IM) or \u201cI was interested in learning bridge\u201d (#185-M-16- TF-IM) or \u201cBoth the stories themselves and the enthusiasm of the older women motivate me to continue\u201d (#34-M-19-assistance-OM).Philanthropy/Helping others, IM and OM. \u201cIt was important for me to do something for the community before I graduate from university\u201d (#52-M-27-assistance-IM) or \u201c[I liked] the idea of a year of contribution to the State, in the framework of a year of national service, the understanding that I am helping and really contribute where I am needed\u201d (#137-F-19-assistance-OM).Satisfaction with the activity and enjoyment of the activity, OM. \u201cPersonal satisfaction\u201d (#7-M-21-assistance-OM) or \u201cI really, really enjoy it \u2026. love to come to meetings with Hanna\u201d (#51-F-19-assistance-OM).Intergenerational interactions and friendship, IM and OM. \u201cI chose to take part in the activity because I also believe in the goals of the activity; I think it is important to get the generations closer. In addition, the older generation has a lot to contribute to us, the younger generation. There is something to learn from them\u201d (#203-F-16-TF-IM) or \u201cI connected to that woman and that moving life story of hers, and also the need to feel the same feeling of satisfaction when I walk away knowing I made her smile and enjoy those moments\u201d (#133-F-24-assistance-OM).Personal or professional value/experience, IM and OM. \u201cI worked at [another volunteering organization that provides a scholarship] for three years, and I wanted to diversify a little for myself. I got a lot out of it, I do not shy away from older persons, like many people who flinch\u201d (#154-F-26-assistance-IM) or \u201cFor me it\u2019s part of personal development \u2026 it gives me answers and questions about my life\u2026it connects me to the world I study, the whole subject of coaching. It gives [or] connects me to the spiritual side of what I am learning. Gives me a perspective that is more human, in the Jewish point of view and less religious \u2026 It is more a matter of a humane, philosophical outlook. This is a field that interests me very much\u201d (#80-M-44-TF-OM) or \u201cI think I derive something from it \u2026 I\u2019m getting to know a population that I hadn\u2019t had much contact with. It\u2019s seeing different perspectives. I guess it\u2019s also somewhere nice to have another circle of friends, both from my side and from hers\u201d (#151-M-28-assistance-OM).Sense of commitment, OM. \u201cI began the activity so I will finish it. It is not fair to stop in the middle, also to the old woman\u201d (#60-F-20-assistance-OM) or \u201cCommitment to the group, desire to learn to direct and gain experience\u201d (#124-F-31-TF-OM).177 = 4.04, p < 0.001, see Overall, the most common motivational factors that prompted older participants to become involved in IGPs  were intTo understand the extent to which young participants\u2019 involvement was actually voluntary or mandatory, we cross-tabulated the organizational frameworks  under which the young participants participated by their reports of the activity being voluntary or mandatory\u2014both in the open-ended questions about their motivation to volunteer and in a question that directly addressed whether their activity was voluntary or mandatory. As shown in p \u2264 0.001 are reported.Since the examination of the relationships between reported sources of motivation and background variables was exploratory and involved multiple comparisons, only relationships that were found to be significant at a level of 79 = 3.45, p = 0.001). Similarly, older participants who reported sense of commitment as a motivational source were younger than older participants who did not report so . Older persons who reported receiving support as a motivation for participation reported worse health status than those who did not . No relationships with gender fit our criteria. For young participants, none of the relationships fit our criteria. Age, gender, and health. Older participants who reported interest in the topic as a motivational source were younger than older participants who did not report such interest . Conversely, older participants in the topic-focused IGPs were more likely to report interest in the topic as their motivation (73.9%) as compared to those in the assistance group . Among young persons, those who were in the assistance groups were more likely (56.3%) to report that the activity was motivated by philanthropy  as compared to those in the topic-focused groups .Type of activity. Among older participants, those who were in the assistance groups were more likely (70.3%) to report that the activity was motivated by need for support and companionship as compared to 2.2% in the topic-focused groups  school project, academic course, n = 23, (3) condition for financial scholarship, n = 23, and (4) purely voluntary activity not related to a formal framework, n = 10. As summarized in 23 = 27.25, p < 0.001). Philanthropy/helping others was often a motivation reported by actual volunteers (80%) and by those providing a year of military, pre-military, or national service (63%), as compared to those receiving a financial scholarship (34.8%) or those in a school-related activity . Interest in the subject was most often mentioned by actual volunteers (80%) and by those in school-related activities (60.9%), but much less so among those receiving financial scholarships (17.4%) or those enlisted in military, pre-military, or national service . We compared young persons\u2019 reports of motivation in terms of the four organizational frameworks through which they participated: (1) pre-military, military, or national service, The most striking finding was that about 90% of the young participants were in educational or enlisted-service frameworks that mandated \u201cvoluntary\u201d activity, either in IGPs or in other endeavors. This is especially illuminating in view of the fact that we located the young participants not through those educational or occupational frameworks but through the IGPs. This suggests that the vast majority of young persons in IGPs, at least those in the geographical area under study, are not truly volunteers. This finding corroborates previously reported complaints by organizers of IGPs concerning the difficulty of recruiting young persons . Our resThe distinction between \u201cobligatory\u201d and \u201cvoluntary\u201d, however, is somewhat obscure in this context. Over half of the young participants belonging either to a pre-military, military, or national service organization, and many of those receiving a financial scholarship that required participation, described their involvement as \u201cvoluntary.\u201d This is probably due to two types of reasoning. The first is that the choice of enrolling in the organizational framework is usually voluntary, i.e., participants choose to take the specific course or to apply for the financial scholarship that comes with conditions; the second, reported in some of the verbal responses to our open-ended questions, is that participants have the option to choose from several \u201cvoluntary\u201d activity options. Participants who felt that they \u201cchose\u201d to enlist in national service, or \u201cchose\u201d the academic course that required participation, or \u201cchose\u201d the particular IGP from a number of options, considered their participation voluntary.Among older persons in the assistance programs, 70% said they were motivated by a need for support and companionship. In a sense, individuals among these older persons were compelled to participate because they required help and/or were lonely, and the IGP was the only available solution. In addition, close to 30% of all older participants said they joined because they were invited to attend, suggesting that observers perceived a need for intervention, and 10% said they enrolled because it gave them something to do, suggesting a need for occupation. Similarly, the findings point to significant relationships between the background variables of age and health status and the source of motivation to participate in IGPs. Thus, for some older persons, involvement in an IGP, while not mandatory, was in some way dictated by their life circumstances.Reported motivational factors differed between young and older participants in several ways. The sources of motivation of \u201cobligation\u201d, \u201dphilanthropy\u201d , and \u201cvaluable experience\u201d  were mentioned mostly by young participants. In contrast, the factors of \u201cbeing invited to participate\u201d, \u201creceiving support\u201d and \u201chaving something to do\u201d were mentioned only by older participants. Some motivational factors were reported by both young and older participants, including \u201cinterest in the subject matter\u201d, \u201csatisfaction and joy derived\u201d (or anticipated) from the activity, \u201cintergenerational interactions and friendship\u201d, and \u201csense of commitment.\u201d The differences we found partly reflect the different life experiences of the respective generations. For example, older, but not young participants, reported the need for support and the need to fill available time. The differences also reflect that a large proportion of the IGPs under study were devoted to providing assistance to older persons, which relates directly to the altruistic motivations expressed among young participants and the need for support expressed among older participants. For older participants who were involved in the topic-focused groups, interest in the subject matter was often a key motivation. We found that motivational factors change with time during the course of IGPs. The motivations of satisfaction and joy, as well as intergenerational interactions and friendship developed into ongoing motivations as the programs continued, whereas other motivational factors, such as interest in the subject matter (among older and young persons) and personal/professional value (among young persons) tended to decrease. To some extent, this suggests that the success of the IGPs in our study provided the motivation needed to promote continued participation. The implications of the motivational factors that emerged in this study should be investigated in future studies. For example, were young persons who cited enjoyment of intergenerational interactions and friendship as ongoing motivations to participate in IGPs more likely to manifest a decrease in ageist attitudes or an increase in interest in pursuing a career involving older adults? Were older persons who cited enjoyment of intergenerational interactions and friendship as ongoing motivations more likely to report a decrease in feelings of isolation and loneliness? As both young and older participants cited \u201cinterest in the topic\u201d as a motivating factor, offering more diverse topic-focused activities may motivate greater participation, in addition to integrating IGPs within more and different settings, and promoting IGPs as opportunities to help others.A study of an American IGP, \u201cThe Experience Corps\u201d ,30, in wWe aimed to recruit all IGPs in the greater Tel Aviv metropolitan area. Therefore, the study is limited to programs in the cultural context of Israel. We also limited the IGPs to those in the community, rather than in schools. As participants volunteered to participate in the research, the data may represent a bias towards more successful experiences in IGPs. Another limitation is the use of qualitative analysis to determine the distribution of sources of motivation, whereas future research should validate those findings via quantitative questionnaires based on our findings, which are likely to provide more precise estimates. These limitations notwithstanding, this study is innovative in examining in depth young persons\u2019 motivation to participate in IGPs, in examining the complex meaning of \u201cvolunteering\u201d in this context, in comparing young and older persons\u2019 motivations to participate, in studying how those motivational factors change during the course of IGPs, and in examining community-based rather than school-based IGPs. The study is strengthened by convergent results vis a vis the few studies available on the topic of motivation to participate in IGPs and by its use of a larger sample than most studies of IGPs, thus offering valuable guidance for future planning of IGPs. The findings highlight the crucial need for motivational analysis prior to initiating an IGP. In our study, the often-proclaimed virtues of IGPs, such as promotion of intergenerational understanding and encouragement of altruistic community involvement, emerged as insufficient without the weight of additional self-interest or external requirements as motivational factors. Most topic-focused programs provided some self-interest in the form of offering an experience that would further knowledge or experience in a particular topic, but among such IGPs, most young participants were bound by additional obligatory frameworks. In the assistance groups, the self-interest of older participants was evident, and although more than half of young participants in the assistance groups reported philanthropy/altruism as a motivational factor, it is likely that many would not have participated without having been obligated to do so. These findings are important because they challenge the general perception that recruiting \u201cvolunteers\u201d is an inexpensive means of improving intergenerational relationships and remedying social problems. Rather, the results suggest that significant funding or embedding IGPs in a compulsory framework may be needed. The motivational factors of \u201csatisfaction\u201d, \u201cinterpersonal relationships\u201d, \u201cidealism/sense of philanthropy\u201d, and \u201cinterest in the topic\u201d appear to need a boost from a different realm. These complexities need to be considered in planning IGPs and evaluating their outcomes. Future research should examine correlations between the motivations of dyads in one-on-one IGPs and within specific topic-based groups. Future work could also include a cost/benefit analysis of IGPs by following cohorts on a longitudinal basis, exploring participants\u2019 ongoing and changing sources of motivation, and also the long-range impact on participants, such as the percentage of young participants who go on to pursue careers involving older adults."}
+{"text": "Neurodevelopmental disorders (NDDs) are conditions affecting a child's cognitive, behavioural, and emotional development. Appropriate and validated outcome measures for use in children with NDDs in sub-Saharan Africa are scarce. The aim of this study was to validate the Communication Profile Adapted (CP-A), a measure developed in East Africa to assess caregivers' perception of communication among children with NDDs.We adapted the CP-A for use in Ethiopia, focusing on the communicative mode (CP-A-mode) and function (CP-A-function) scales. The CP-A was administered to a representative sample of caregivers of children with NDDs and clinical controls. We performed an exploratory factor analysis and determined the internal consistency, test-retest reliability, within-scale, known-group, and convergent validity of the identified factors.N = 300 participants . Within the CP-A-mode, we identified two factors ; the CP-A-function scale was unidimensional. Combining both scales into one summary variable  resulted in a scale with excellent internal consistency and test-retest reliability . Testing known-group validity, the CP-A-total scores were significantly higher for controls than cases . Convergent validity assessment indicated that scores were negatively and moderately correlated with clinical severity .Our analysis included The CP-A is a valid tool for the assessment of communication among children with NDDs in Ethiopia. It holds promise as a brief, quantitative, and culturally appropriate outcome measure for use in sub-Saharan Africa. The CP-A assesses caregivers' perceptions of their child's abilities and activities for communication, and participation in family and community events  and King's College London (HR-16/17\u20133489). In addition to validation of the CP-A, the data collection comprised further questionnaires, the validation of which are reported in Borissov et al. .Participants were 300 caregivers with long-term responsibilities for children aged 2\u20139 years, attending either the general paediatric or child mental health clinic of the two hospitals. The paediatric clinics consecutively recruited children with physical health conditions for the clinical control group. The mental health clinics consecutively recruited children with either NDDs alone or with a comorbid mental health condition for the case group, in accordance with the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5)  after initial test data collection. All participants provided written informed consent.Eligible families were approached by the attending clinician at either clinic and given a flyer with information about the study. Data collection and consent taking was done by clinic nurses who worked independently from the clinicians supporting the families. A subgroup of 40 caregivers was invited for a retest of an average of 19.6 days  and communicative function (CP-A-function) were selected for validation in this study, see Items' responses refer to a 0\u20134 Likert scale where [0] stands for \u2018never\u2019, [1] \u2018rarely\u2019, [2] \u2018sometimes\u2019, [3] \u2018usually\u2019, and [4] \u2018always\u2019. Participants were shown a visual ladder representation of this scale with 0 being the lowest and 4 the highest rung .N\u00a0=\u00a024) and ASD (N\u00a0=\u00a050). General psychiatrists working in the two hospitals rated the child's condition, based on the DSM-5 severity ratings, as [1] \u2018mild\u2019, [2] \u2018moderate\u2019, or [3] \u2018severe\u2019. A structured questionnaire was used to collect caregiver-reported demographic information.Clinician-assigned severity levels were available for a subgroup of participants with a diagnosis of ID  as cognitive interviews indicated that the direct translation of the term \u2018behaviour\u2019 was unclear to respondents. The original CP-A response scale comprised 8 rungs of ladders; this was shortened to 4 rungs  after cognitive interviewing indicated that participants could not meaningfully differentiate between the small increments of the original ladder. Within the CP-A-function, the original version of the scale did not just require a response using the ladder but also asked the extent to which the item is a problem for the respondent. This second part was removed to improve consistency as well as administration ease and time. In its original format, the CP-A asked both questions on how the child communicates with the respondent, and how the respondent communicates with the child. Caregivers participating in the cognitive interviews had difficulty distinguishing between these questions. In response, the section on how the caregiver communicates with the child was removed, focusing solely on the mode of communication of the child.Within the CP-A-mode, the content of question 1j was changed to Data collection took place in Yekatit 12 and St Paul's Millennium Medical College general paediatric and child mental health clinics. To allow for the participation of non-literate caregivers, instruments were administered through face-to-face interviews by nurses who had received training in data collection procedures and questionnaire administration. Participating caregivers were reimbursed for their travel costs. Data were double entered using Epidata, version 3.1  in the CP-A were replaced by median imputation  CP-A-mode, (ii) CP-A-function, and (iii) CP-A-total were examined with the use of item exploratory factor analysis (EFA)  guidelines   was evaluated through Cronbach's alpha  included children who did not meet the criteria to be in either the case or clinical control group  and those for whom diagnostic information was incomplete (full details in online Supplementary Table S3).Our sample included s.d.\u00a0=\u00a07.1).p\u00a0<\u00a00.001), with a higher proportion of females among cases, and residence (p\u00a0<\u00a00.001), with more cases living in urban areas. Furthermore, we report significant differences in religion, (p\u00a0=\u00a00.004), observing a higher proportion of Muslims among cases compared to controls, relationship to the child (p\u00a0<\u00a00.001), where caregivers in the case group were more often mothers, and occupation (p\u00a0=\u00a00.02), with a higher proportion of housewives among cases.Statistically significant differences between cases and controls were observed for the caregivers' gender (s.d.\u00a0=\u00a02.0). Among children, comparison across cases and controls showed significant differences in age (p\u00a0<\u00a00.001), with cases being older than controls, and gender (p\u00a0<\u00a00.001), with a higher proportion of males in the case group in line with the observation that NDDs are more common in boys .62% of children were male, with an average age of 4.9 years . The correlations between items and promax-rotated common factors are displayed in a \u2018Facial expression\u2019, c \u2018Gestures\u2019, d \u2018Body movements\u2019, e \u2018Looking or use of eye gaze\u2019, f \u2018Pointing\u2019, and h \u2018Showing you objects\u2019 loaded more strongly on factor 1. Items b \u2018Making noises \u2019, g \u2018Showing you pictures\u2019, j \u2018Speaking Amharic\u2019 and l \u2018Behaviour\u2019, instead loaded on factor 2. Factor 1 generally corresponds to physical communication, while factor 2 to verbal communication. Item g \u2018Showing you pictures\u2019 presented moderate loadings for both factors  that were maintained throughout different rotation methods. Item l had a negative loading on verbal communication, indicating that caregivers of children with poor verbal communication tended to highlight the use of behaviour as the main mode of their child's communication.The Scree-test and eigenvalues  suggested a 2-factor solution for the CP-A-mode , suggesting that the function items assessed a single construct. All items loaded positively on the factor, see For communicative function, the Scree-test and eigenvalues  suggested a 1-factor solution. The model had a good fit to the data , suggesting that all items of the analysed CP-A scales can be meaningfully subsumed under a single construct reflecting overall communication activities. All items, besides Item l, loaded positively on the factor .Similarly, for the CP-A-total the Scree-test and eigenvalues  indicated a 1-factor solution. The model had a good fit to the data (\u03c1) between the CP-A-mode's verbal communication and physical communication scores was significant and moderately positive . Similarly, the correlation between the CP-A-mode and CP-A-function scores was significant and moderately positive , further justifying the adoption of the CP-A-total as a unidimensional summary scale  and verbal communication . This holds true also for the CP-A-function  and CP-A-total , d estimates for CP-A-mode's factors were medium when unadjusted and small when accounting for covariates. Estimates were large for CP-A-function and CP-A-total across both scenarios  as well as verbal communication . Similar results were obtained for the CP-A-total . For the CP-A-function, the point estimate of the correlation was in the same direction and of similar magnitude (\u03c1\u00a0=\u00a0\u22120.23) but was not significant (p\u00a0=\u00a00.59) \u00a0\u2a7e\u00a00.78; verbal communication: 6 items, \u03b1\u00a0=\u00a00.72, 95% CI\u00a0\u2a7e\u00a00.69). Excellent internal consistencies were obtained for the CP-A-function  and the CP-A-total . Assessing internal consistency separately for cases and controls suggested that levels remained acceptable for the CP-A-mode's physical communication , but were low for verbal communication . The internal consistency remained excellent for CP-A-function  and CP-A-total  , demonstrating moderate to a substantial agreement among items. For CP-A-function and CP-A-total, the agreement was moderate to near perfect for all items   and verbal communication . Excellent test-retest reliability was observed for the CP-A-function  and CP-A-total  , supported by findings of strong correlations between the identified factors. As hypothesised, children with NDDs (cases) scored lower than clinical controls. Moreover, scale scores were negatively correlated to clinical severity ratings of NDDS, indicating that children with more severe NDDs used fewer modes of communication and applied fewer functions of communication. We observed acceptable to excellent internal consistency as well as test-retest reliability. Overall, these results demonstrated the validity and reliability of the CP-A-mode, function, and communication-total scales.This paper reports the first validation study of the CP-A, a caregiver-reported tool for the assessment of children's communication. Our aim was to address the need for a psychometrically sound, brief, and culturally appropriate outcome measure for use in Ethiopia. We investigated two sections of the CP-A: communicative mode and function. Within communicative mode we identified two factors, i \u2018Sign language\u2019, j \u2018Speaking English\u2019, and m \u2018Other\u2019, most responses were equal to 0 (i.e. \u2018never\u2019), suggesting these items have little relevance in assessing communicative mode within our sample. For item i this is likely due to the fact that none of our participants was reported to have hearing loss. Furthermore, formal sign language has received very limited implementation in Ethiopia so far \u2019 and j \u2018Speaking Amharic\u2019. Item g \u2018Showing you pictures\u2019 showed more moderate loading, with substantial cross-loading on factor 1. Item l \u2018Behaviour\u2019 had a strong negative correlation with factor 2, suggesting that caregivers of children who did not express themselves verbally were more likely to report their child's behaviour as a form of communication. This finding is in line with theoretical notions that see verbal acts and behaviours as equivalent in function  and did not include a control group, results suggested sensitivity to change, as scores in the activities for communication sections, including communicative mode and function, were significantly higher post-intervention compared to pre-intervention  still scores higher than the case group. The clinical severity assessment was carried out by general psychiatrists, with no specialist expertise in the assessment of child NDDs. Nevertheless, diagnosis and assessment of children with NDDs part of postgraduate training in psychiatry in Ethiopia and the psychiatrists involved in the study were experienced in making these diagnostic assessments. Psychiatrists used their clinical judgement rather than standardised tools to assess the severity of impairment of the children since there are no validated standardised clinical severity assessment scales available in Ethiopia to support the assessment of severity. Furthermore, the limited educational or supportive service provision available for children with NDDs in this setting means that reports from other professionals are not available to inform severity assessments. Thus severity is based on a single report from the caregiver during the clinical encounter and observations of the psychiatrist of the child in a clinical setting. Severity scores were collected for a small sample only, covering a limited range of complex communication needs. This study was conducted as part of a larger project focusing on NDDs. Most cases included in our study had ASD or ID, rather than a wider group of complex communication needs and developmental disabilities for which the CP-A was also developed (e.g. sensory impairments). Lastly, participants were help-seeking families recruited in Addis Ababa. Our sample had an overrepresentation of urban families and may not be fully representative of the Ethiopian population.i \u2018Sign language\u2019), should be re-evaluated. Future research should further examine whether the CP-A-mode, CP-A-function, and CP-A-total are sensitive to change induced by interventions. Lastly, future studies may also wish to consider other sections of the CP-A not included in the current evaluation.Further research could test our factor structure for the CP-A-mode and CP-A-function through confirmatory factor analysis. Recruitment of cases should be extended to a wider range of complex communication needs. In such studies, the relevance of items reflecting characteristics of developmental disabilities with no representation in our sample (i.e. This work is the first investigation to explore the validity of CP-A, an open-access measure developed in and for the African context. The communication mode and function and their combined scales met the validity and reliability criteria as a measure for the assessment of caregiver-perceived activities for communication. We tested this among children with NDDs and concomitant complex communication needs in Ethiopia. We recommend the further validation of this scale. The CP-A has potential for application in intervention studies on NDDs across sub-Saharan Africa as a brief, quantitative, and culturally appropriate outcome measure."}
+{"text": "We investigate the analogues, in  Being interested in the maximum order of d(n), he defined highly composite integers n to be those for which In , Ramanujmentclass2pt{minimf, and observe that a generic polynomial f in We consider the question of maximising the divisor function in the function field setting. Let highly composite polynomial of degree n if We call Highly composite polynomials of a given degree are not necessarily unique. For example, all linear polynomials in f be a highly composite polynomial of degree n and suppose otherwise, so that There is (at least) one new highly composite polynomial at each degree. Indeed, let If See \u201cAppendix\u201d for an illustrative table of highly composite polynomials in We first investigate a family of highly composite polynomials nujan in ), which x-superior highly composite polynomial, or just x-SHC, if for all h is an x-semi-superior highly composite polynomial, or x-SSHC, if for all x-SHC or x-SSHC for some superior highly composite or semi-superior highly composite, respectively.Let x-SHC, then it is x-SSHC. Moreover, any polynomial h which is x-SSHC is highly composite, since if Clearly, if n by Eq.\u00a0 we have x of an x-SSHC,After defining a particular set for the parameter lettingwe are able to determine the structure of the superior highly composite polynomials.x-SHC polynomial, namely There is one, and only one, S, then S and the set of superior highly composite polynomials, given by If Let and that of the semi-superior highly composite polynomialsx-SSHC polynomial, namely the polynomial If d in Eq.\u00a0.x-SSHC polynomials of the form h given by If equation , \\documeh(x) is x-SSHC and g is also x-SSHC.If Let This family of semi-superior highly composite polynomials is not too sparse, so we can use it to construct polynomials at every degree which make the divisor function close to its maximum. In particular, if we let h be an x-SSHC polynomial of degree Let s in Eq.\u00a0, and h bN in Theorem\u00a0N in the form presented in Theorem\u00a0From the final sentence of part\u00a02 of Theorem\u00a0We begin by showing, contingent on some auxiliary lemmas proven subsequently, thath is unique.If h.Else, if For each From , we can j, so by Lemma\u00a0If s,\u00a0r) such that j, so by Lemma\u00a0Otherwise, if h is in fact a finite product.Notice in both cases that This leads us first to the proof of Theorem\u00a0x-SHC. Moreover, if x-SHC, and moreover, if If S, and let S and the set of superior highly composite polynomials, given by Let For Then we move to the proof of Theorem\u00a0If x-SSHC polynomials are precisely the E, which we can rewrite as x and y, we have y, we have for h(x) is the (distinct) superior highly composite polynomial immediately preceding If mentclass2pt{minimh(x) be x-SSHC and g is also x-SSHC.Let entclass1pt{minimaFor Finally we conclude by proving the auxiliary lemmas used in the proof of Proposition\u00a0j, then If j, then Else, if Let If Else, if Let ands,\u00a0r) such that Let r,\u00a0s) and  distinct. If Suppose otherwise, so that Now Since the family of semi-superior highly composite polynomials is not too sparse, we can use it to construct polynomials at every degree which make the divisor function close to its maximum, and thus prove Theorem\u00a0h is highly composite, so h is x-SSHC, and so for any If entclass1pt{minimaentclass1pt{minima"}
+{"text": "Obtaining valuable clues for noncoding RNA (ribonucleic acid) subsequences remains a significant challenge, acknowledging that most of the human genome transcribes into noncoding RNA parts related to unknown biological operations. Capturing these clues relies on accurate \u201cbase pairing\u201d prediction, also known as \u201cRNA secondary structure prediction\u201d. As COVID-19 is considered a severe global threat, the single-stranded SARS-CoV-2 virus reveals the importance of establishing an efficient RNA analysis toolkit. This work aimed to contribute to that by introducing a novel system committed to predicting RNA secondary structure patterns  that leverage syntactic pattern-recognition strategies. Having focused on the pseudoknot predictions, we formalized the secondary structure prediction of the RNA to be primarily a parsing and, secondly, an optimization problem. The proposed methodology addresses the problem of predicting pseudoknots of the first order (H-type). We introduce a context-free grammar (CFG) that affords enough expression power to recognize potential pseudoknot pattern. In addition, an alternative methodology of detecting possible pseudoknots is also implemented as well, using a brute-force algorithm. Any input sequence may highlight multiple potential folding patterns requiring a strict methodology to determine the single biologically realistic one. We conscripted a novel heuristic over the widely accepted notion of free-energy minimization to tackle such ambiguity in a performant way by utilizing each pattern\u2019s context to unveil the most prominent pseudoknot pattern. The overall process features polynomial-time complexity, while its parallel implementation enhances the end performance, as proportional to the deployed hardware. The proposed methodology does succeed in predicting the core stems of any RNA pseudoknot of the test dataset by performing a 76.4% recall ratio. The methodology achieved a F1-score equal to 0.774 and MCC equal 0.543 in discovering all the stems of an RNA sequence, outperforming the particular task. Measurements were taken using a dataset of 262 RNA sequences establishing a performance speed of 1.31, 3.45, and 7.76 compared to three well-known platforms. The implementation source code is publicly available under knotify github repo. The RNA molecule, being the intermediate representation of the information flowing from DNA to proteins, holds a crucial role in many biological processes. Recent studies reveal that its detailed structural analysis is of utmost importance. The RNA structure is often depicted by a 2-D representation of the base-pairing nucleotide  known as the \u201csecondary structure\u201d, which conduces to the more-complex construction 3-D representation, termed the tertiary structure. The substantial role of RNA in the expression of proteins, along with its contribution to the gene expression regulation, catalysis, and site recognition, requires the enlightenment of its territorial structure, which is associated with considerable biological functionalities.More specifically, non-coding RNAs (ncRNAs) are functional RNA molecules transcripted from DNA but not translated into proteins. The latter must not be misinterpreted as not enclosing important information or contributing to any biological operation. Current evidence implies that ncRNAs transcribe most of the genomes of mammals and other complex bions, to contradict the widespread assumption that proteins transcribe most genetic information. Their purpose is to fulfill diverse catalytic and structural functions, along with regulating gene expressions at the transcriptional and post-transcriptional level.The literature contains a considerable number of publications discussing the prediction of RNA secondary structure. The employed methodologies are mainly based on dynamic programming algorithms, thermodynamic models, stochastic methods, and syntactic pattern-recognition techniques. A thorough analysis of the related work is presented in The article is organized at the following sections. In Non-coding RNAs (ncRNAs) are functional RNA molecules that are transcripted from DNA but not translated into proteins. This is not to say that ncRNAs do not provide knowledge or serve a purpose. Although it has been generally assumed that proteins transcribe most genetic information, recent evidence suggests that ncRNAs transcribe most of the genomes of mammals and other complex bions. Their purpose is to fulfill diverse catalytic and structural functions and regulate gene expressions at the transcriptional and post-transcriptional level.RNA is the cornerstone of various biological processes; it carries genetic information that is encoded into four distinct nitrogenous bases, i.e., adenine (A), cytosine (C), guanine (G), and uracil (U). As a messenger , it actsContrary to DNA, RNA features a single-stranded molecule resulting in a solid inclination of its bases to interact in two principal ways, either perpendicular to their planes (stacking) or hydrogen-bonded within the base planes (pairing). Those interactions form base pairs via hydrogen bonds between the corresponding nucleotide, i.e., the standard set of RNA base-pairs  known as Watson\u2013Crick base-pairs  and the According to the literature, there is a strong correlation between the structure of a RNA molecule and its function ,11,12 toTurnip Yellow Mosaic virus  \u2190 EMPTY_SET\u2003\u2003endforfunction EARLEY_PARSER\u2003\u2003INITIALIZE(input_string)\u2003\u2003n \u2190 LENGTH(input_string)Start \u2192 \u2022S, 0), Sets[0])\u2003\u2003ADD_TO_SET((\u2003\u2003for i \u2190 from 0 to n\u2003\u2003\u2003\u2003for each state in Sets[i]\u2003\u2003\u2003\u2003\u2003\u2003if (state is not completed)\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003if (RIGHT_TO_DOT(state) is a nonterminal)\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003PREDICTOR\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003else\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003SCANNER\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003endif\u2003\u2003\u2003\u2003\u2003\u2003else\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003COMPLETER\u2003\u2003\u2003\u2003\u2003\u2003endif\u2003\u2003\u2003\u2003endfor\u2003\u2003endfor\u2003\u2003return Sets\u03b1\u2022 C\u03b2, j), i, grammar)function PREDICTOR((B \u2192 \u03b4) in GRAMMAR_RULES\u2003\u2003for each , Sets[i])\u2003\u2003\u2003\u2003ADD_STATE_TO_SET, i, input_string)function SCANNER((B \u2192 \u2003\u2003if (a is input_string[i])\u03b3 a \u2022\u03b4, j), Sets[i+1])\u2003\u2003\u2003\u2003ADD_STATE_TO_SET, i)function COMPLETER((A \u2192 \u03b3\u2022 A \u03b2), j) in Sets[x]\u2003\u2003for each , Sets[i])\u2003\u2003\u2003\u2003ADD_STATE_TO_SET RNA sequence is parsed using a CFG parser in order all trees that include a pseudoknot to be produced; (ii) all derived trees are then traversed to identify additional base pairs around the pseudoknot; and (iii) the optimal tree is selected via the criteria of minimum energy and the maximum number of base pairs of the pseudoknot. These three main tasks of the proposed methodology see  are thorAs exhibited in The proposed methodology of detecting pseudoknots in sequences of nitrogenous bases representing RNA rests on syntactic-pattern-recognition techniques and specifically on an efficient CFG parser. Consequently, it is vital to select the right primitive patterns. In the case of RNA recognition, the most-typical option is to represent the nitrogenous bases adenine, cytosine, guanine, and uracil as single characters \u201cA\u201d, \u201cC\u201d, \u201cG\u201d, and \u201cU\u201d, respectively. These characters in sequence constitute an RNA representation. Hence, in our case, where a grammar parser is proposed to recognize pseudoknots in RNA, the proposed grammar vocabulary contains only the four terminal symbols T = {\u201cA\u201d, \u201cC\u201d, \u201cG\u201d, \u201cU\u201d}, with each one representing a distinct base: adenine, cytosine, guanine, and uracil, respectively. Therefore, every RNA sequence may linguistically be represented as a string containing the terminal symbols, e.g., UAGGC or AUGGCCGUACG.The task to syntactically recognize a given pattern may actually be converted into using an appropriate pattern grammar, in order to parse the linguistic representation of the original patterns. The design of the pattern grammar may have a significant impact on the recognition\u2019s result. Therefore, the formation of the CFG to be used is an important subtask in implementation having as the underlying model syntactic-pattern-recognition techniques. Hence, the design of an efficient grammar is indispensable in order to describe the syntax of the pseudoknot within any arbitrary RNA sequence. It is well known that CFGs are adequate to represent structural features. The core stems. The second column of \u2205 is the empty set. Hence, L may produce strings of length greater than zero as A, UA, CCGGAU, etc.L is the non-terminal symbol that will produce sequences of bases forming the two interior loops of the pseudoknot, i.e., sequences of bases between C and U as well as between G and A. Non-terminal L may produce strings belonging to set D is the non-terminal symbol that will produce sequences of bases between the two crossing base pairs, i.e., between bases U and G in this example. Using non-terminal symbols K and N, L may recognize substrings of terminal symbols of length zero to two, i.e., hub repo .C \u2026U G \u2026\u2026A. Then, rules 19, 18, and 22 were used to recognize the bases between C and U, i.e., C G C C U G \u2026\u2026A. After that, rules 24, 29, and 34 were used to recognize the empty string between the U G bases of the core stems. Finally, rules 16, 17, 17, 17, and 23 were used to recognize the bases between C and U, i.e., C G C C U G A U U U G A. The integration of this substring in the initial RNA sequence and the process of decorating the pseudoknot with additional base pairs is explained in The parse tree produced by the parsing of substring \u201cC G C C U G A U U U G A\u201d is shown in The proposed methodology parses all substrings, beginning with the one that starts with the first sequence symbol and features the minimum potential length. Iteratively, the length is extended by one symbol to include the entire initial RNA sequence finally. In the same iterative fashion, string starting points are augmented to exclude the previous set starting symbol. The parsing is over when the substring\u2019s length to be parsed deteriorates further than a predefined threshold . This methodology, considering that Context-free grammar was selected with the view of augmenting it with attributes (forming an attribute grammar) in order to store probabilities and to manage to prune parse trees during the parse-tree construction process, in future work. In order to enhance the performance of the proposed system, an alternative implementation of the first task was proposed using a brute-force algorithm. This approach traverses the input string in order to spot all possible base pairs and then traverses all base pairs so as to identify couples of base pairs, which potentially form the core stems of a pseudoknot, i.e., consisting of two helical segments that are bound by two single-stranded sections or loops. The brute-force approach achieved a performance speed of 2.55 compared to the implementation that makes use of the context-free grammar at the first task. The speedup, though, comes at the cost of the overall extensibility that the grammar approach provides. In any case, both proposed implementations are faster than two well-known platforms . Performdecoration. Having detected the core stems U\u2013A and C\u2013G at positions 9 and 11 and 5 and 10, respectively, all bases in both pseudoknot loops,  and 11 to 15 (right loop)) were examined to identify against forming base pairs with bases outside the pseudoknot loops. Hence, base pairs belonging in the left loop were checked out if they may form base pairs with bases at positions 17 to 19, while bases belonging in the right loop were examined to match the ones at positions 1 to 4. In both the left and the right loops of the pseudoknot, the base pairs at positions 8\u201317, 7\u201318 and 4\u201311, and 3\u201312 were sequentially detected, respectively. Once the parse trees are generated following the methodology described in the previous subsection, all trees are traversed to decorate the pseudoknot with additional base pairs. The proposed system permits the user to optionally select the existence of base pairs U\u2013G in the pseudoknot\u2019s loops. At the same time, the existence of bulges or interior loops in the loops of the pseudoknot is part of our future work.According to the literature, multiple methodologies have been presented that tackle the problem of RNA base-pair prediction, with the prevalent ones being the (i) method of minimum free energy , which dThe proposed system employs a hybrid model of optimal tree selection, combining principles originating from the two most-prevalent techniques, i.e., the method of maximum pairing and that of MFE, to predict the pseudoknot pattern of any RNA secondary structure accurately yet in an efficient way. MFE is cost-effective in terms of performance; initially, all trees are sorted by the number of base pairs around the detected pseudoknot, and MFE applies only to the ones ranking the top score of the base-pairs count. This is a heuristic that outperforms the MFE original approach.H-In order to select the best candidate from the set of secondary structures, our method chooses the one with the minimum free energy. To carry out this important task, a module from HotKnots  was incotally in , and refAccording to the literature, the prediction of pseudoknots of any arbitrary RNA sequence is a NP-complete problem. On the one hand, free-energy-minimization algorithms proposed to provide pseudoknot predictions invoke dynamic programming to rank high regarding their computational cost, while their precision decreases proportionally to the length of the input sequence. On the other hand, existing heuristic approaches lack generalization capabilities when being tested under different datasets. In this setting, we introduced a novel hybrid strategy to pick the RNA sub-sequence that is the most-probable pseudoknot expression. According to The proposed implementation is hybrid itself as well. By invoking Python and C code routines, a performant, scalable yet easy-to-use, and extended software package was implemented. Python was used to provide high-level flexibility and out-of-the box features such as flexible parallelization capabilities, sub-process supervision, and file management, while C nailed the parsing task by minimizing the memory footprint and maximizing CPU utilization.The input sequence was sliced into multiple sub-sequences  the accuracy of the pseudoknot\u2019s core stems prediction, (ii) the capability to predict the base pairs existing in the ground truth dot-bracket (confusion matrix), and (iii) the execution time.i, j) is equivalent to , , , and , as proposed in [posed in .The measurements divided per RNA sequences\u2019 length are presented in The percentage of pseudoknot\u2019s core stems exact prediction per platform is also shown in The percentage of pseudoknot\u2019s core stems exact prediction per platform for all groups of length of RNA sequences is also shown in We benchmarked our framework on the sequences of To evaluate the overall performance, we focused on the precision, the MCC, and the F1-score. The latter is the harmonic mean of the PPV and the recall. Our methodology outperformed on average all methods in regards to precision metric having 0.784, while Knotty was 0.729, IPknot 0.718, Hotknots 0.706, and IHFold 0.608. Regardingthe F1-score and the MCC metrics, Knotty outperformed on average all methods with a F1-score equal to 0.807 and a MCC equal to 0.569. The proposed methodology had an accuracy very close to Knotty . In addition, HotKnots scored F1-score = 0.738 and MCC = 0.452, while IPknot  and IHFold  had lower accuracy on both the F1-score and the MCC.The above-mentioned results are also shown in In The last metric that was used in order to compare the proposed methodology with other platforms is that of execution time. In The execution time required per platform is also shown in In Total execution time required per platform for the four groups of different RNA sequences\u2019 length is also shown in Recently, COVID-19 evolved into a severe global threat. This virus\u2019 connection to RNA is one of the most-prominent artifacts justifying the requirement of concrete and accurate RNA-analysis toolkits. This study introduced an innovative methodology to detect H-type pseudoknots in RNA secondary structures accurately and performantly. The method is based on Early\u2019s parser, which, given an RNA sequence in the form of a string, produces a space of all possible parse-trees, each one expressing a potential pseudoknot structure. The optimal tree is picked through a hybrid model combining pairing maximization and free-energy minimization for each context\u2013tree pair. The evaluation of the proposed algorithm demonstrated its outperformance to the task of pseudoknot prediction, paving the way for our future work endeavours: (i) discovering even more complex patterns such as pseudoknots enclosing bulges or hairpins, (ii) building advanced searching algorithms leveraging common patterns of the secondary structure of RNA, and (iii) creating an open web platform to make our work accessible to all researchers. The work in ,91 may b"}
+{"text": "In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell\u2013Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations. A,B, etc. No tilde will be used on constants. If A is written as x and y with differentials X, where X may be scalar real variable x, scalar complex variable X, or vector/matrix complex variable X and The following notations will be used in this paper: Real scalar variables, whether mathematical variables or random variables, will be denoted by lower-case letters, such as x,  and Ex are fixeussed by . A modifussed by , and it X may be real scalar x, complex scalar X, or complex vector/matrix a is a fixed real scalar anchoring point, a is measured in In early 2000, the second author introduced a generalized entropy of the following form:plied by  in time-plied by  used a pplied by  discusseplied by  studied In the present article, the term \u201centropy\u201d is used as a mathematical measure of uncertainty or information characterized by some basic axioms, as illustrated by . Thus, iShannon entropy x be a real scalar variable and let x and a is a fixed real scalar constant, x as a mathematical model or as a statistical model. The model x is replaced by m is the relocation parameter. For Let ation of  under thd, this gives the Fermi\u2013Dirac density, and for Fermi\u2013Dirac and Bose\u2013Einstein densities are also available from the same procedure. In this case, the second factor Equation  becomes In model-building situations, if X be a X be X from the point of location X from u. Consider the following constraints:X is a Let he modelf3(X)=C3[Lemma\u00a01.Let For the proof of this result, as well as for other similar results, see . We willLemma\u00a02.Let X be real where, for example, where .s by using a real type-1 beta integral. Hence, for s by using a real type-2 beta integral, we have the normalizing constant Consider Observe that the model in (9) is a multivariate generalized real type-1 beta model, (10) is a multivariate generalized real type-2 beta model, and (11) is a multivariate generalized real gamma model. For sis; see . The modons; see .h-th moment of the ellipsoid of concentration for an arbitrary h. That is, for From the normalizing constants ion, see . Then, [Theorem\u00a01.For the Note\u00a01.We can relax the condition Note\u00a02.Consider a function over all p matrix with distinct real scalar variables u is an important quantity in statistical literature. Hence, we will impose restrictions in terms of moments of u. Consider the optimization of Mathai\u2019s entropy in (4) over all densities X is a Y, and, hence, Z is a s-integral by using a real scalar type-1 beta integral; for s-integral by using a real scalar type-2 beta integral; for s-integral is evaluated by using a real scalar gamma integral. Then, the normalizing constants are the following:Let Observe that (21) and (22) are available from (20). Similarly, (20) and (22) are available from (21). In other words, all densities in (20)\u2013(22) are available through the pathway parameter Note\u00a03.If a location parameter p matrix with distinct elements p matrix-variate densities a is a fixed scalar constant. In order to avoid having too many symbols, we will use the same notations of e, we have S-integral by using a real matrix-variate type-1 beta integral for Let S-integral by using real matrix-variate type-1 beta, type-2 beta, and gamma integrals. The final expressions will be the following:Let us consider the matrices Note\u00a04.If a location parameter is needed, then replace X with h-th moment of this determinant u for an arbitrary h is needed, then this moment can be written down by looking at the normalizing constants in (32)\u2013(34). For h-th moment is the following: Let Both sides have the same distribution. Similarly, for Note\u00a05.Note that Note\u00a06.If A, its transpose will be written as A is called Hermitian. Any complex matrix A can be written as A is Hermitian, then A is A is written as For a matrix ain, see .Lemma\u00a03.Let Lemma\u00a04.Let where p-dimensional complex domain. This ellipsoid is an important quantity in statistical analysis, as well as in various other situations. When u is the generalized distance of u. Consider the following constraints: For a is a fixed location, and s is s-integral by using a real scalar type-1 beta integral for As a first problem, let For een from . Observep matrix with distinct complex scalar variables as elements. Let A. Consider the optimization of Mathai\u2019s entropy in (4) for the density p. Then, proceeding as in the real case, we end up with the following densities: For Let q, then we can take p and q interchanged and A and B interchanged. We obtain results parallel to the ones above for the case of Note that (50) can be considered as a multivariate version of the complex Maxwell\u2013Boltzmann and Rayleigh densities for p with distinct complex scalar variables as elements. Let p. Then, proceeding as in the real case, we have the following densities:Let tE[|detAX\u02dcBX\u02dc*A12given by . The stah-th moment of the absolute value of the determinant h. Then, from (54), we have the following: For q, then we can obtain results for p with q and A with B.As in the real case, we can consider the In this paper, it is shown that a large number of statistical densities belonging to the pathway family  of densi"}
+{"text": "Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different \u2018higher-order\u2019 discrete time crystals with integer and, surprisingly, even fractional n\u2009>\u20092. We characterize these  non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.Discrete time crystals are periodically driven systems characterized by a response with periodicity  Discrete time crystals are typically characterized by a period doubled response with respect to an external drive. Here, the authors predict the emergence of rich dynamical phases with higher-order and fractional periods in clean spin-1/2 chains with long-range interactions. A DTC is a nonequilibrium phase of matter breaking the discrete time translational symmetry of a periodic  drive. In the thermodynamic limit, the defining feature of an n-DTC is a subharmonic response at 1/nth of the drive frequency (n\u2009>\u20091), which is robust to perturbations and which persists up to infinite time12. Following the first seminal proposals8, DTCs have been widely investigated both theoretically and experimentally23.Due to its foundational and technological relevance, the study of condensed matter systems out of equilibrium has attracted growing interest in recent years, accounting among others for the discovery of dynamical phase transitionsn\u2009=\u20092). This fact naturally emerges from the dimension 2 of the local Hilbert space of the spins6, and can be generalized to n-DTCs in models of n-dimensional clocks25. Another well-studied setting is that of bosons in a gravitational field bouncing on an oscillating mirror9, where the single-particle Hilbert space dimension is infinite (as the particle\u2019s position is continuous) and where n-DTCs with arbitrary integer26 and fractional27n have been shown.In this context, most work has focused on spin-1/2 systems, which have largely been shown to exhibit a 2-DTC where at every Floquet period each spin (approximately) oscillates between the states 8. Alternatively, in clean  systems, heating can be escaped with all-to-all interactions28, or significantly slowed down with long-range interactions32. Very recently, ref. 32 has provided the theoretical framework to study Floquet, clean, long-range interacting systems, in which novel prethermal phases of matter are expected. While their framework allows for the possibility of n-DTCs with n larger than the size of the local (or single-particle) Hilbert space, their concrete examples are limited to n\u2009=\u20092. From our analysis below, we see that part of the difficulty in numerically observing what we call \u201chigher-order\u201d DTCs may lie in their emergence at system sizes that are typically beyond the reach of exact diagonalization.In these systems, heating to a featureless \u201cinfinite temperature\u201d state is typically avoided by introducing disorder, which leads to a (Floquet) many-body-localized (MBL) phasen-DTCs with integer and, remarkably, even fractional n\u2009>\u20092 . These novel dynamical phases give rise to a peculiar fragmentation of the magnetization spectrum, which is intriguingly reminiscent of the plateau structure of the fractional quantum Hall effect.Here, we overcome this limitation by considering a system amenable to a set of complimentary methods, which enable us to discover an unusually rich dynamical phase diagram hosting a zoo of novel, exotic  nonequilibrium phases of matter. More specifically, we show that a clean spin-1/2 chain in the presence of long-range interactions  limit, and finally show that the physics observed extends far beyond the fine-tuned limit. We note that our work is distinct from traditional MBL DTCs, which do not have such a semiclassical limit. On a conceptual level, our analysis is closer to that of equilibrium statistical physics, where, for example, the ferromagnetic phase in the Ising model is best understood in a mean-field description, which is exact in the limit of all-to-all interactions. In our out-of-equilibrium and clean setting, the existence of a conceptually simple mean-field limit is particularly valuable, and highlights profound differences between the clean DTCs considered here and the pioneering works on MBL DTCs.N spins in the thermodynamic limit (N\u2009\u2192\u2009\u221e), driven according to the following time-periodic Hamiltonianjth spin, periodic boundary conditions are assumed, and both \u210f and the drive frequency have been set to 1. J measures the strength of a power-law interaction with characteristic exponent \u03b1, \u03bb is the strength of a nearest-neighbor interaction, and \u03c0h is the average over one drive period of the monochromatic transverse magnetic field. The Kac normalization \u03b1\u2009=\u2009\u03bb\u2009=\u20090), in which the underlying complex physics is reduced to its essence and most easily interpreted.We consider a one-dimensional chain of z-polarized state J\u2009=\u2009\u03bb\u2009=\u20090, for which the magnetization t\u2009=\u20090, 1, 2, \u2026 reads h is the system\u2019s characteristic frequency. The essential question to diagnose a n-DTC is whether, upon switching on the interactions, there exists a finite range of h for which the system\u2019s characteristic frequency \u03bd remains instead locked to a constant value 1/n\u2009<\u20091, signaling the stability of the DTC to perturbations of the drive. In the following, we answer this question affirmatively not only for the well-known n\u2009=\u20092 case, but, if the interactions are sufficiently long range, also for integer and even fractional n\u2009>\u20092, corresponding to the higher-order DTCs. Note, the 33. This issue, however, disappears for the higher-order n-DTCs that, because the Hamiltonian lacks any n\u2009>\u20092), must indeed be a \u201cgenuine\u201d manifestation of time-symmetry breaking.The dynamics from an initially mentclass2pt{minim\u03b1\u2009=\u2009\u03bb\u2009=\u20090), which allows for a conceptually simple semiclassical interpretation of the various dynamical phases. The dynamics of the system is in this case described by a semiclassical Gross\u2013Pitaevskii equation (GPE) for the complex fields \u03c8\u2191 and \u03c8\u2193 \u2009=\u20091, \u03c8\u2193(0)\u2009=\u20090), and the corresponding Fourier transform h is plotted in Fig.\u00a012, the 2-DTC results in the system characteristic frequency \u03bd being locked to 1/2 for h\u2009\u2248\u20091/2. Surprisingly, the same locking occurs at frequencies 1/n with integer and fractional n\u2009>\u20092 , giving rise to a fragmentation of the spectral line of h\u2009\u2248\u20091/n. Each of these plateaus signals a higher-order  DTC, the width of the plateau being a signature of the DTC\u2019s robustness to drive perturbations. The \u201chalos\u201d surrounding the plateaus in Fig.\u00a0The dynamics of the magnetization  the GPE  from an \u03bd\u2009=\u20090 for h\u2009\u2248\u20090 signals the tendency of the spins to remain aligned along z in a dynamical ferromagnetic phase (F). This corresponds to macroscopic quantum self-trapping of weakly driven bosons in a double well34, which can in fact be exactly mapped to the LMG limit .The plateau at N. This allows a scaling analysis extended up to large system sizes, showing a progressive emergence of the spectral line plateaus for an increasing number of spins N. For the standard 2-DTC, the plateau is clearly visible already for N\u2009\u2a86\u200910, whereas, crucially, for the 4-DTC it appears only for N\u2009\u2a86\u2009100  is highlighted with red markers. For a weak drive h\u2009\u2248\u20090, the spins tend to remain aligned along z in a dynamical ferromagnetic phase (a), giving rise to a Poincar\u00e9 map which closely resembles the phase portrait of undriven bosons in a double well34. For h\u2009\u2248\u20091, the micromotion consists of approximately an entire revolution of the spins around the Bloch sphere per period, with a preferential z alignment restored at stroboscopic times despite the detuning in the magnetic field strength (b). For h\u2009\u2248\u20091/n and n\u2009=\u20092, 4, 8 in (c), (d), and (e), respectively, the n-DTC results in the presence of n \u201cislands\u201d in the phase space, which the system visits sequentially jumping from one to the next at each drive period. In n drive periods, the system visits all the n islands once, and the magnetization m completes one oscillation.The stroboscopic dynamics generated by the GPE  can be ch\u2009\u2248\u20093/8 the system behaves as a n-DTC with fractional n\u2009=\u2009q/p\u2009=\u20098/3 (f). In this case, the system cyclically visits q islands of the phase space in q drive periods. Differently from a q-DTC, however, during this time the magnetization m completes p oscillations, resulting in a characteristic frequency p/q. Finally, for larger interactions J the Poincar\u00e9 maps become chaotic (as in ref. 12), signaling thermalization35.Furthermore, for Since the island-to-island hopping that underpins the subharmonic response holds for any point of any island, the islands themselves can be interpreted as stability regions of the DTCs with respect to perturbations of the initial state. The Poincar\u00e9 maps also provide an interpretation of the subdominant frequencies visible as halos around the plateaus in Fig.\u00a010. It becomes thus of primary importance to assess the role of the interactions also for the higher-order DTCs. To this end, as a concrete example, in Fig.\u00a0J on the 4-DTC. If the interaction is weak, a slightly mistaken magnetic field strength h\u2009=\u20091/4\u2009+\u2009\u03f5, with \u03f5\u2009\u226a\u20091, originates in envelopes  with period ~1/\u03f5, resulting in the Fourier transform \u03bd\u2009\u2248\u2009h and in trivial dynamics (a). Crucially, stronger interactions can compensate the mistake in the flipping field (b): the envelopes in m(t) disappear, the peak in \u03bd\u2009=\u20091/n, and the discrete time symmetry is broken. The time-glassy character of the DTC is observed in a small aperiodic modulation of the magnetization on top of the subharmonic response.It is well established for the standard 2-DTC that the robust subharmonic response hinges on the interaction being sufficiently strong. The fact that interactions are necessary for the robustness of DTCs is critical, as it underpins the many-body nature of the DTCs and it justifies their classification as nonequilibrium phases of matterJ,\u2009h) plane (c). The 4-DTC phase opens up from the integrable point J\u2009=\u20090, h\u2009=\u20091/4 for increasing interactions, in analogy with the opening of the standard 2-DTC from J\u2009=\u20090, h\u2009=\u20091/216. This opening, which in dynamical system theory would be referred to as Arnold\u2019s tongue, confirms that larger interactions J allow the higher-order DTCs to bear larger detunings in the field h. However, at even larger J\u2009\u2a86\u20090.8 semiclassical chaos sets in and the time crystalline order is broken irrespectively of h. To see this, we introduce a decorrelator 35.The subharmonic peak magnitude entclass1pt{minima\u03b1\u2009>\u20090) and nearest-neighbor (\u03bb\u2009>\u20090) interactions. In this case, the system is no longer described as a collective spin, and spin-wave excitations are rather generated. To account for them, we adopt a spin-wave approximation (see \u201cMethods\u201d), in which the central dynamical variable is the density of spin-wave excitations \u03f5(t)bk are bosonic creation and annihilation operators for the spin-wave excitations with momentum k.As shown, the DTCs rely on the interactions being sufficiently (but not too) strong. Crucially, in contrast to the standard 2-DTC, higher-order DTCs also necessitate the interactions to be sufficiently long range. We now probe the robustness of the higher-order DTCs along yet a different direction in the drive space, exploring the effects of non-all-to-all interaction on higher-order DTCs, particularly assessing their stability upon breaking the mean-field solvability of the dynamics with power-law (\u03bb\u2009=\u2009\u03b1\u2009=\u20090), no spin-wave excitation is generated and \u03f5\u2009=\u20090 at all times. When departing from such a limit, two scenarios are possible , for which we consider the spin-wave approximation consistent, or (ii) \u03f5 rapidly grows to values\u2009\u2a86\u20091, for which the spin-wave approximation breaks down. Although the method is not exact and may fail to capture the very long-time physics, it suggests that (i) and (ii) correspond to prethermalization and thermalization, respectively37.In the LMG limit  \u03f5 \u03bb and \u03b1), whereas thermalization quickly sets in for shorter-range interactions  plane plotting the amplitude of the subharmonic peak \u03f5\u232at in Fig.\u00a0n-DTC is stable for a whole region of the parameter space surrounding the LMG point (\u03b1\u2009=\u2009\u03bb\u2009=\u20090), that is, if the interactions are sufficiently long range. The DTC is also robust to arbitrary perturbations to the initial state, as long as the initial spin-wave density \u03f5(0) is sufficiently small, as we have checked by injecting a small amount of spin-wave excitations to the initial state. For completeness, in the Supplementary Note\u00a0hz. We found in this case that the expected prethermal nature of the DTC is only changed quantitatively, with the heating time scaling exponentially with the ratio of the driving frequency  and the energy scale hz. Finally, we note that the time-glassy character of the DTCs is maintained throughout their whole stability region. In particular, we find small peaks at incommensurate frequencies that do (do not) vary when slightly perturbing the drive .We observe that the higher-order DTCs are stable  for sufficiently long-range interactions  Hilbert space. The dynamical phase space fragments to host many higher-order d2(t)44m\u2009=\u2009\u0394\u03b8\u2009=\u200910\u22126. The decorrelator time average T is the total simulation time, for example, T\u2009=\u2009103 in Figs.\u00a0We quantify the sensitivity to the initial conditions of Eq.  with a d37 and the Supplementary Material therein, to which we redirect the reader for further details. In a DTC evolving from an initially z-polarized state Z-axis tracks the orientation of the collective spin at all times. This tracking is encoded in the condition \u2329SX\u232a\u2009=\u2009\u2329SY\u232a\u2009=\u20090, from which the dynamics of the rotating frame is obtained self-consistently. The Holstein\u2013Primakoff transformation from spin degrees of freedom to bosonic degrees of freedom is then performed as N ordinary differential equations similar to Eqs. (26) and (29) in the Supplemental Material of ref. 36, describing the rotation of the new reference frame and the dynamics of the spin waves at the various momenta.Here, we briefly summarize the idea behind the spin-wave approximation, which is thoroughly explained in refs. 36. First, ref. 36 considers a constant-in-time Hamiltonian, whereas the parameters of the Hamiltonian in the present work are time-dependent. As a consequence, the parameters in the system of ordinary differential equations become time-dependent. Second, ref. 36 considers a nearest-neighbor interaction on top of an all-to-all one, whereas we consider the more general case of nearest-neighbor interaction on top of a power-law one. The 36 is therefore substituted by a more generic Finally, we remark the main differences between the implementation of the spin-wave approximation in our work and in ref. Supplementary Information"}
+{"text": "Unfortunately this is computationally impractical, particularly if data reconstruction is iterative or the acquisition protocol is dynamic. We develop a flexible statistical linear model analysis to be used with multi-frame PET image data to create valid bootstrap samples. The technique is illustrated using data from dynamic PET studies with fluoro-deoxyglucose (FDG) and fluoro-thymidine (FLT) in brain and breast cancer patients. As is often the case with dynamic PET studies, data have been archived without raw list-mode information. Using the bootstrapping technique maps of kinetic parameters and associated uncertainties are obtained. The quantitative performance of the approach is assessed by simulation. The proposed image-domain bootstrap is found to substantially match the projection-domain alternative. Analysis of results points to a close relation between relative uncertainty in voxel-level kinetic parameters and local reconstruction error. This is consistent with statistical theory.PET imaging is an important diagnostic tool for management of patients with cancer and other diseases. Medical decisions based on quantitative PET information could potentially benefit from the availability of tools for evaluation of associated uncertainties. Raw PET data can be viewed as a sample from an inhomogeneous Poisson process so there is the possibility to directly apply bootstrapping to raw projection-domain  The work here is stimulated by (Positron emission tomography (PET) is a well-established radiotracer imaging technique, extensively relied on in both secondary and tertiary clinical care settings, as well as in medical research. As the role of quantitative PET in clinical decision making evolves, it is likely that there will be an increasing interest in the availability of practical methods for evaluating uncertainty associated with the results reported for an individual patient. There is already a significant literature on variance assessment for PET. Much of this work has concentrated on the development of analytic approaches based on the linear approximations to the reconstruction process \u2013 see, for example, . The potlated by , who uselated by , with thlated by  proposede.g. dynamic PET studies. In this setting suitable modeling of the dynamic data enables us to identify an associated set of residuals that can be manipulated to construct a viable model-based image-domain bootstrapping procedure.The work here develops a more flexible procedure for image-domain bootstrapping. This new approach is applicable in situations where there may be a complex temporal structure in the measured PET data \u2013 a near-constant temporal structure is intrinsic to the method used in . In addiThe technical framework for the methodology is set out in 2.N \u00d7 T array, {ijz; i = 1, ., N, j = 1, \u2026, T} . Here N represents the number of voxels in the field of view and T is the number of time-frames in the PET acquisition. ijz is the reconstructed PET-measured tracer concentration value at the 3-D voxel co-ordinate, ix, at a time jt corresponding to the mid-point of the j\u2019th time-frame of scanning. We begin by providing a formal mathematical description of the model, highlighting the various unknowns that must be estimated before it can be used for bootstrapping.The input data for the approach is a 4-D dynamic PET dataset represented by an 2.1.ijz be denoted ij\u03bc and X = {k\u03bc, k = 1, 2, \u2026, K}, that have the ability to approximate local mean values, ij\u03bc. The method used to identify X is described in ijz is expressed as a sum of systematic and random terms. The basic version is given byLet the true mean and variance of the PET measurement jx is the j\u2019th row of X and i\u03b1 is a vector of unknown coefficients. Note that the systematic part of ijz, here ij\u03bc, is approximated by a linear form. The model is referred to as a generalized linear model because errors are allowed to be non-Gaussian and the scale factors, ij\u03c3, are not assumed constant  and temporal (j\u03d5) factors. The constraint on \u03d5 is required for identifiability. A key part of ij\u03f5 is related to a sub-ordinate Gaussian variable, ij\u03b7, by a (unknown) Q-transform. In statistical parlance, the inverse of Q defines the normal-quantile plot for the collection of measurement errors  = 1. Monotonicity of Q is a requirement for the distribution of the measurement errors to be well-defined; it does not restrict the flexibility of the model to adapt to arbitrary distributional forms for the error. Strict monotonicity implies that the quantile mapping is invertible. If the model errors have a continuous distribution - a very plausible approximation for PET and many other types of medical imaging data - then Q must be strictly monotone. The sub-ordinate Gaussian \u03b7-process, \u03b7 = {ij\u03b7, i = 1, 2, \u2026, N, j = 1, 2, \u2026, T}, is assumed to have independent temporal components, matching the formal Poisson structure of PET ,t errors . We assue of PET , and a ce of PET . Note thblished.  providesij\u03ba as a surrogate variable for representing deviations from the product form of the variance and the assumed distributional structure. This leads to a more elaborate generalized linear modelQ(\u00b7\u2223\u03ba) is strictly monotone for each fixed \u03ba-value and is assumed to be slowly varying as a function of \u03ba. For identifiability, a scaling constraint involving Q is also required. For this with h2(\u03ba) = var(Q(\u03b7\u2223\u03ba)), we require Q does not vary with \u03ba. If Q(\u00b7\u2223\u03ba) corresponded to a scaled Gamma distribution then, based on 2 be proportional to \u2223\u03ba\u2223, i\u03c3 proportional to While the model in based on , \u03ba wouldorted by . Thus thorted by . Regardl\u03b7 can be written in the form of a Kronecker tensor product, \u03a3N \u2297 TI, where \u03a3N is a N \u00d7 N matrix representing the spatial correlation pattern and TI is an T-dimensional identity matrix. Spatial stationarity implies that the covariance can be diagonalized using the Fourier transform  of detected events. If events are binned into count arrays, this is equivalent to drawing a random sample from a multinomial distribution with eN trials and probabilities proportional to the observed counts in binned array. Each simulated count array is processed to produce a bootstrap reconstruction, z*. Repeating the process BN times leads to a projection-domain bootstrap sample, list-mode re-sampling, we do not use it here. Note that as the count-rate increases, there will be little percentage difference between counts produced by either sampling method.This approach involves random sampling (with replacement) from the number  is readily expressed in terms of the associated model coefficient - i.e. i\u03b8 = f(i\u00b7\u03bc) = f(ix\u2032\u03b1) \u2261 g(i\u03b1). Recall that a basic property of maximum likelihood is that if i\u03b1 then i, c.f.\u03b8  = \u03a3K = [X\u2032WX]\u22121. iD is a spatially invariant transformation of the error process and also of the underlying sub-ordinate Gaussian process \u03b7. Thus for N \u00d7 K array, D, with rows iD\u2019s, is strictly stationary in a spatial sense. Now if the error in D has the Kronecker product form \u03a3N \u2297 \u03a3K, where \u03a3N is the spatial covariance of \u03b7. Thus simulated realizations of D can be produced by creating a N \u00d7 K array whose rows are independent samples from a K-dimensional Gaussian with zero mean vector and covariance \u03a3K and then transforming the columns of the array by multiplication by the matrix N \u00d7 K dimensional array using i\u2019th row. An obvious modification of this would be to use the full set of We propose a novel 2.3.X, is specified and after that consider the other elements.As indicated earlier, the model in The goal in basis selection is to choose a configuration that is physiologically interpretable and has the ability to approximate the measured time-course data at all voxels in the volume. A clustering scheme is used to identify clusters of time-courses that have self-similar shapes. If a basis can be found to represent the average time-course in such clusters, then it can be expected that a simple scaling of the representation for the average will fit individual time-course data in the cluster. In light of this, the basis selection is optimized so that the set of cluster means are well represented. But because the number of clusters is quite small  relative to the number of voxels, evaluation of the objective function for assessment of any candidate basis set based on the reduced cluster-mean data is computationally efficient. A generalized cross-validation criterion is used as an objective function for basis set assessment. Backwards elimination, a well-established type of greedy algorithm in statistical model selection , is usedlC, l = 1, 2, \u2026 L}, with the property that the data in each cluster has a similar shape pattern: i.e. if i \u2208 lC then for a suitable constant ia, ijz \u2248 i\u03bcjla where j = 1, 2, \u2026, T is the mean time-course for the l\u2019th cluster. Step 2 takes the collection of mean time-course patterns associated with each of these clusters as an initial set of basis elements Detailed implementation of the above basis selection scheme substantially follows . The proX fixed, an unconstrained weighted least squares procedure, with a simple fixed temporal weighting scheme, is used for estimation of i\u03b1\u2019s in \u03d5-values areWith j\u2019th time-frame and m is taken to be a fraction (0.1) of the maximum of these jdt and j\u03b6\u2212te, with \u03b6 the decay constant for the radio-tracer isotope, is the standard tracer decay factor. While the estimates of i\u03b1 based on these simple weights may not be optimal, under general conditions weighted least squares estimates are unbiased and also consistent, as the scale of the error diminishes  = \u2212\u221e and \u03bal) seems to be quite adequate. As Q is piecewise constant, its variance is also piecewise constant - ijh = lh for lh given \u03c3 and \u03d5 is\u03c3, \u03d5 and h. This defines K is the number of columns of X. This is to ensure there is adjustment for the bias arising from fitting the \u03b1-coefficients at each voxel. Such adjustments are standard in most parametric model fitting settings - see ; the second comes from a more recent breast cancer imaging trial with 18F-labeled Fluorothymidine (FLT) (We present two dynamic PET imaging studies of cancer patients. One is from a series reported in  and invone (FLT) . The studraws on .3.1.C, can be described by a convolution between the local arterial blood concentration supplied by the output of the left-ventricle (LV) of the heart, pC, and the corresponding impulse-response, or so-called tissue residue function R. ThusThe basic principle of most tracer imaging studies with PET is that the tracer\u2019s interaction with the local tissue is linear and time-invariant. While there are situations where this assumption is not valid, it is very reasonable for FDG and FLT. The arterial supply is the primary system for transport of tracer to tissue, so linearity and time-invariance implies that the true tissue concentration, pC = pC (s \u2212 \u0394x) where pC(t) is the LV blood concentration and \u0394x is a suitable delay. From basic principles of blood-tissue exchange . This is a version of the form used in \u03b1-coefficients are constrained to be non-negative. In the NPRM setting, the backwards elimination scheme in LX by elements based on non-parametric residue modeling of the cluster mean data \u2013 i.e.There is a substantial literature on modeling techniques for PET time-course data. Most of this focuses on the analysis of region of interest data, see, for example, . But thecer flux .kR, k = 1, \u2026, K}, i.e.As the basis elements are represented in terms of residue functions, Here a very short duration (less than 5 seconds) spiked residue is used to represent the AIF, a constant residue is used for the Patlak term.ET is the study duration and let BT for 0 < BT < ET represent a realistic upper-bound for large-vessel travel-time \u2013 for human PET studies with FLT and FDG, a value BT of around 5 to 10 seconds is reasonable physiologically. The residue over the observed time-frame of the study, , is decomposed in terms of vascular (BR), in-distribution (DR) and extraction (ER) components asIn the NPRM approach, decomposition of the voxel-level residue is used to create summaries variables for mapping tracer kinetics. Suppose iK(x). This is a measure of flux (see further BV(x), as well as the in-distribution flow, DK(x), and volume, DV(x), are recovered from BR and DR asThe apparent rate of extraction of tracer atoms by the tissue is measured by DV(x)/DK(x). However this does not take account of variation in the time of arrival of the tracer to the local tissue. To address this we use a flow-weighted average of mean transit-times associated individual sub-TACs \u2013 i.e. MTT(ix) = \u03a3kikwMTTk where MTTk = \u0394k + DkV/DkK with DkK and DkV obtained from k\u2019th component residue (kR). Here the weights, which are normalized to sum to unity, are proportional to the flow contributions from the different component tissues represented at the i\u2019th voxel, iki.e w \u221d ikKDk\u03b1 for k = 1, 2, \u2026 K. Thus MTT is written asBy the central volume theorem , the meaw(ix) = \u03a3kikw\u0394k. In the case that the individual delays are all the same, \u0394w(ix) will constant across voxels.\u0394k1, k2, k3, k4). The impulse response function (a.k.a tissue residue) for the model is a mixture of exponentialsbf), this gives rise to a model representation of the tissue time-course (TC) asWhile a non-parametric approach is used for specification of sub-TAC residues, it is useful to record what the above summary parameters correspond to in the 2-compartmental model of Huang and Sokoloff, see . This mooR defined over the interval  bySuppose we introduce a simple linear residue BT \u2192 0, oR becomes very spiked at 0. For small BT and the convolution of oR with the AIF is approximately bCpf(t). As a result, for sufficiently small BT, the 2-compartmental model can be given a residue representationCR(t) = oR(t) + (1 \u2212 bf)CI(t). Decomposing CR as described in K1 = (1 \u2212 bf)k1 and O(x) indicates that corresponding terms vanish as x \u2192 0. If k4 = 0 then \u03bb2 = 0. Here as BT \u2192 0 with ET large (so e\u03bb1ET\u2212 is negligible) the residue summaries for the 2-C model becomeNote k3 and k4 are zero, the 2-compartment model reduces to the 1-compartment Kety-Schmidt model (iK = 0 (no retention), BV = bf, DK = K1 and 15O-labeled water.When both dt model . Here thz). Individual bootstrap realizations e.g. such as those reviewed in  and T = 31 time-frames extending over a 90 minute period. The time-frame sequence is: 1(1 min) preinjection, 4(20 sec), 4(40 sec), 4(1 min), 4(3 min) and 8(5 min). The bootstrapping technique is used to evaluate sampling variation in computed metabolic images.PET studies with FDG play a major role in the diagnosis and management of many cancers . Spence reportediK) and extraction (iK/K1), in the tumor region. Standard errors demonstrate that variability is very much related to the scale of the metabolic variable. This pattern is likely a consequence of the overall pseudo-Poisson characteristic of PET data so areas with high metabolic values  also have greater absolute variance. We examine this more formally in iK/K1) values. As described in . The data considered here are from a patient studied at baseline (before chemotherapy). The study was conducted on a 74-plane scanner using a 3-D acquisition process and ML reconstruction. The 4-D PET data set consists of an imaging volume with N = 168 \u00d7 168 \u00d7 74 voxels (2.97 \u00d7 2.97 \u00d7 2.01mm3) and T = 45 time-frames of acquisition over one hour. The time-frame binning sequence was: 16(5 sec), 7(10 sec), 5(30 sec), 5(1 min), 5(3 min) and 7(5 min). Note that more than half of the temporal sampling is focused on the first 2.5 minutes of the 1-hour acquisition. This is in part because the kinetics of FLT  are faster than those of FDG. The left-ventricle of the heart was used to directly recover a blood time-course, which after approximate adjustment for metabolites provided an arterial input function, pC, used for kinetic analysis.Cellular DNA is replicated during cell division so that its concentration in rapidly proliferating tumor tissues can be expected to be higher than in normal tissue. PET FLT imaging has the potential to provide an approximate measure of DNA concentration and for this reason FLT imaging may be able helpful for diagnosis and treatment planning with certain cancers. Our data is from a multi-center American College of Radiology Imaging Network clinical imaging trial (ACRIN 6688) which conducted dynamic PET-FLT imaging of breast tumor before and during neoadjuvant chemotherapy. The goal was to see if PET-FLT imaging could give an early indication of the tumor response \u2013 trial results are reported in . The ACRBN = 500 image-domain bootstrap replicates were used for evaluation of sampling variation in computed metabolic images. Metabolic images and associated bootstrap estimates of their voxel-level standard errors are in dV), flow(Kd) and flux (iK) show significant enhancement in the tumor region. In a compartmental modeling framework, all three parameters have been suggested as appropriate ways to quantify FLT time-course data (iK/K1) appear quite stable as is the associated uncertainty measure. VOIs for tumor and contra-lateral normal breast were also accessed. The tumor region had 1280 voxels extending over 16 slices ; the normal VOI is not quite as large - 1054 voxels - but with a very similar shape. The bootstrap estimated histograms of the sampling distribution of the 95th percentile of the metabolic parameters in the VOIs are shown in bV). These differences are highly significant when formally assessed via the bootstrap information.Data were processed using the same methods as used for the brain study. rse data . Standar\u03ba-bins shows that as \u03ba-increases, there is increasing conformity to the Gaussian. As discussed in \u03ba is proportional to the shape parameter and as that parameter increases the Gamma distribution formally converges to a Gaussian. Thus the data are in line with  are needed to evaluate the true target variance with reasonable accuracy. Bootstrapping techniques involve simulation and the number of such simulations (BN) also needs to be considered. Apart from the computation, in practice the storage requirements associated with retention of bootstrap samples may also be a factor. We will report studies in which both modest and large numbers of bootstraps are examined.The purpose here is to evaluate the performance of the novel image-domain bootstrapping technique for PET and make comparisons with the more computationally intensive, but fully non-parametric, projection-domain approach. Assessment of variance estimators is somewhat complicated because we do not have an analytic formula for the true target variance. Hence a number of replicate simulations  reconstruction only, but iterative ML and analytic reconstruction are considered in the 1-D case. Dynamic aspects of both 1-D and 2-D studies are based on results obtained for the FDG brain and FLT breast cancer data presented in 4.1.\u03c0], discretized to a 183 \u00d7 181 sinogram array of distances and angles. Note the \u03c0-periodicity of the parallel beam Radon transform restricts the angular extent of the projection domain. As shown in R\u03c4. This dose is specified so that the voxel-level noise in the reconstructed data matches the apparent voxel-level noise level of the real data. Independent Poisson count simulation from each element of the scaled sinogram array yields the synthetic projection-domain data (y). Each frame of the sinogram data is reconstructed analytically using a standard filtered backpojection (FBP) procedure with the raw ramp-filter result smoothed by convolution with a Gaussian resolution filter. The resolution filter bandwidth is required to be common across all time frames and by grid-search its value is selected in order to minimize the average squared error difference between the estimated and true activity summed over frames. This choice of bandwidth is to ensure that the uptake image is objectively adapted to the study dose , the image-domain and the approximate image-domain bootstraps are acquired. i = 1, 2, \u2026, N. Here ip\u03c3 is the true standard deviation of the p\u2019th metabolic parameter estimate for the i\u2019th voxel; R2 exceeds 0.9 for all metabolic parameters and for both FDG and FLT simulations \u2013 values for flux (iK) are shown in Quantitative comparisons between the estimated and true standard deviations were assessed on a voxel-by-voxel basis using a simple linear regression analysis and also in terms of an overall root mean square error (RMSE) measure. Regression analysis considered the relation between the true standard deviation, estimated by replication, with the corresponding values evaluated by the bootstrap methods. These regression analysis models are expressed asa, b, c), in p\u2019th metabolic parameter estimate at voxel i for the s\u2019th replicate data for the bootstrap estimate, the RMSE is given byThe regression parameters,  but not for other parameters . RMSE values for the approximate image-domain bootstrap are consistently the largest. However it needs to be appreciated that, in light of the typical standard error of the true standard deviation, the significance of any of these differences is small. Standard errors are reported as The RMSE values for projection-domain and image-domain methods are denoted iK) is also shown in i.e. the voxel indicator (i) is replaced by an indicator of the ROI. Similar to the voxel case, bootstrap estimates perform very well. There is no evidence that these results are substantially impacted by the size-distribution or positioning of ROIs. The non-parametric and image-domain method (with BN = 25 replicates) have very similar RMSE reliabilities both for FDG and FLT. Both bootstraps tend to under-estimate the true ROI mean standard deviation. However, the amount of bias is small - on the order of 10\u201314% across the different kinetic parameters. Recycling is found to lead to more unreliable values - largely due to a greater systematic over-estimation of the true ROI standard deviation - on the order of 20% for most parameters. But the overall indication from the 2-D experiments is that image-domain bootstrapping scheme is very well aligned with the non-parametric projection domain approach and provides a viable mechanism for assessments of uncertainties at both the voxel and ROI level.For this analysis a nested sequence of grids were used to construct a range of ROIs with different sizes and tissue heterogeneity characteristics. 4.2.x = 1, 2, ., N (even) and T = 1, 2, \u2026, T. Here 0 < xa \u2264 1 is a known attenuation factor and the matrix \u03b2K : NR \u2192 NR and \u03b2K has the form of a discrete convolution. Letting x \u2208 NR, \u03bd = \u00b11, \u00b12, \u2026, N/2. With \u03b2 > 0, the action of \u03b2K is to smooth the vector x. If y is a realization of a Poisson with mean \u03c4\u03b3, then an unbiased estimate of the underlying source distribution \u03bb is obtained by adjusting for the y-data by the attenuation factor and applying a least squares (LS) inversion procedure. This result is then smoothed to achieve consistent mean square error performance. As FBP is essentially equivalent to LS in the 2-D setting xt = xty/xa.Letting hS has a discrete Fourier representation, zfbp)( and z are efficiently computed using the 1-D FFT. Adapting (zml) estimation characteristic as a function of dose for the 1-D Poisson deconvolution model, and the corresponding MSE characteristic of 2-D PET reconstruction.If Adapting , the EM Toeplitz . In d-diorted in  show thaN = 128. The temporal patterns are matched to those arising in the 2-D simulations. Spatial patterns are indicated in \u03b2\u03b1jK\u2019s, and the attenuation pattern. Reference dose-values R\u03c4 were again chosen so that the qualitative variability of simulated 1-D data matched that seen at the voxel-level in the real FDG and FLT data. Five dose levels, \u03c4 = R\u03c4/5, R\u03c4/2.5, R\u03c4, 2.5R\u03c4, 5R\u03c4 were examined with FDG and FLT. In the 1-D setting a more extensive bootstrapping process was used . Simulated data were reconstructed using FBP and iterative ML techniques. Raw frame-by-frame reconstructions were smoothed by convolution with a Gaussian kernel. Similar to the 2-D case, bandwidth was common across all frames, and its value was optimized according to the mean square deviation of the estimated total uptake from the true known source. Due to the implicit regularization associated with raw ML reconstruction , whose standard deviation by the image-domain methods are consistently lower than reported by the projection-domain bootstrap, there is remarkably close alignment between the methods.The estimates of the \u03b1-coefficients should be approximately W is the diagonal matrix with elements j = 1, 2 \u2026, T. The NPRM kinetic analysis procedure involves fitting the model \u03b1-coefficients are non-negative. By \u03b8 = , are simple functions of the constrained \u03b1-coefficients. Assuming the unconstrained \u03b1-coefficients are sufficient for the constrained values, \u03b8 can also be regarded as a function of the unconstrained coefficients. Hence we can consider the estimated kinetic parameters as functions of the unconstrained \u03b1-coefficients g : KR \u2192 PR (P = 6). By application of the delta method, e.g.  that have a linear dependence on the constrained \u03b1-coefficients. Hence \u03b1\u2113 may depend on the local \u03b1-value. In spite of this, the analysis suggests a relation between the voxel-level parameter standard deviation and the standard deviation of the measurement. In the simulation setting, the square-root of the weighted mean square reconstruction error can be used as an assessment of measurement error: 1\u03b3p1 as well as the quality of fit of the model measured by the R2 statistic. The model fits are remarkably good (most in excess of 80%) particularly for . With MTT the model pattern is continues to be remarkably accurate for FLT; but not for FDG. On the other hand the model variance pattern for extraction (iK/K1) is still very reasonable for FDG but not for FLT. While these analyses give an understanding of the behaviour of voxel-level kinetic parameter variability, they also help to provide some underpinning for the basic theoretical heuristic for the approximation used to recycle the image-domain bootstrapping. Further studies were conducted in 1-D in order to evaluate the accuracy of the bootstrapping techniques as a function of the size of the imaging domain (i.e.K/T). But in PET, dose constraints mean that reconstruction error will increase with temporal sampling. So the ability to manipulate relative RMSE performance merely by increased temporal sampling would be unrealistic.The relation between voxel-level parameter standard deviation and reconstruction error was also examined. Our analysis is motivated by the approximation used in constructing the recycling process for the simplified image-domain bootstrap in od, e.g. , the covg domain . Remarkag domain , the pri5.The work has presented a novel image-domain approach to bootstrapping PET data having a dynamic component. The method is based on a novel general linear model approximation of the dynamic source distribution in which the error is described in terms of a sub-ordinate Gaussian process that is assumed independent across time-frames and stationary in the imaging space. In addition the distribution of error is allowed to adapt to the local skewness of the data. Thus there is no requirement for the method to be modified depending on whether an analytic or iterative data reconstruction process is used. This removes a number of potentially limiting assumptions used in . The booOur methodology is illustrated by application to real examples involving the use of dynamic PET imaging for the purpose of mapping metabolic parameters of tissues in the field of view. The general linear modelling analysis technique enables us to create bootstrap replicate data sets for analysis. Application of the NPRM kinetic mapping technique to the bootstrap data provides voxel-level estimates of metabolic parameters and their associated uncertainties (SEs). Numerical studies motivated by these examples compare the image-domain bootstrapping approach to the more computationally demanding but fully non-parametric projection-domain approach . Image-dhttps://cran.r-project.org) in the near future. In comparison to projection-domain bootstrapping, in which each bootstrap replicate requires reconstruction of simulated list-mode data; computation of image-domain bootstrap replicates are negligible. But of course significant computation is required to setup the image-domain bootstrapping model. For the 3-D data sets analyzed in The current analysis is implemented in  - an opee.g. National Cancer Institute (https://www.cancerimagingarchive.net), do not to our knowledge include any list-mode information. Thus the analysis of image uncertainty using data from such archives can only be based on a suitable image-domain bootstrapping approach, as we have described here.Of course as computing capabilities grow and it becomes standard to retain list-mode data for dynamic PET studies, non-parametric projection-domain bootstrapping may become practical as well. Indeed this would be an ideal circumstance because the theory underpinning the non-parametric approach is very well developed . But curFor situations where retention of extensive bootstrap samples is prohibitive, we have proposed a novel recycling process as an approximate image-domain bootstrapping approach. While the RMSE performance of this approximation is not as good as a full bootstrap, the results are still quite reasonable. Importantly our studies indicate that the performance of the image-domain simulation techniques are not impacted by whether or not the reconstruction methodology is analytic (FBP) or iterative (ML).It would be interesting to use the methods here to examine multiple studies with a similar anatomy on the same scanner, in order to develop a practical scanner-specific understanding of the study-to-study stability of the image-domain model estimates. If list-mode data were available, it would also be possible to use the projection-domain bootstrap to gain some insight into this. Specifically such a bootstrap could be used to create replicate projection-domain scanning data that could be used to estimate image-domain model parameters. The collection of model parameters obtained across bootstrap replicates would then provide a direct assessment of their sampling characteristics.There are a number of other medical imaging modalities where subject-specific assessment of uncertainty in quantitated imaging measurements are not currently available and the techniques here might be useful. For example, dynamic imaging with MR  or CT are routine in the clinical management of cancer and stroke and the structure of datasets is substantially similar to dynamic PET. This will be a focus for future work."}
+{"text": "Nature Communications 10.1038/s41467-020-15812-w, published online 20 April 2020.Correction to: The original version of this Article contained errors in Figure 2b, where the y-axis was labelled \u201ccm\u201d when the unit should have been \u201cmm\u201d, and the y-axis error bars should have been omitted. These have been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Communications Biology 10.1038/s42003-021-02017-0, published online 27 April 2021.Correction to: In the original version of the Article, reference 61 was incorrectly given as: \u201cNikolai. Trait-based range expansion aided in the global radiation of Crocodylidae (2019).\u201dGlob. Ecol. Biogeogr. 28, 1244\u20131258 (2019).\u201dThis has been corrected in the HTML and PDF versions of the Article to: \u201cNicola\u00ef, M. P. J. and Matzke, N. J. Trait-based range expansion aided in the global radiation of Crocodylidae. In addition, the reference to \u201cNikolai and Matzke\u201d in the third paragraph of the Discussion has been corrected to \u201cNicola\u00ef and Matzke\u201d in the text in the HTML and PDF versions of the Article."}
+{"text": "The deep Q-network (DQN) is one of the most successful reinforcement learning algorithms, but it has some drawbacks such as slow convergence and instability. In contrast, the traditional reinforcement learning algorithms with linear function approximation usually have faster convergence and better stability, although they easily suffer from the curse of dimensionality. In recent years, many improvements to DQN have been made, but they seldom make use of the advantage of traditional algorithms to improve DQN. In this paper, we propose a novel Q-learning algorithm with linear function approximation, called the minibatch recursive least squares Q-learning (MRLS-Q). Different from the traditional Q-learning algorithm with linear function approximation, the learning mechanism and model structure of MRLS-Q are more similar to those of DQNs with only one input layer and one linear output layer. It uses the experience replay and the minibatch training mode and uses the agent's states rather than the agent's state-action pairs as the inputs. As a result, it can be used alone for low-dimensional problems and can be seamlessly integrated into DQN as the last layer for high-dimensional problems as well. In addition, MRLS-Q uses our proposed average RLS optimization technique, so that it can achieve better convergence performance whether it is used alone or integrated with DQN. At the end of this paper, we demonstrate the effectiveness of MRLS-Q on the CartPole problem and four Atari games and investigate the influences of its hyperparameters experimentally. Reinforcement learning (RL) is an important machine learning methodology for solving sequential decision-making problems. In theory, by interacting with an initially unknown environment, the RL agent can learn the optimal action policies at different states to maximize the cumulative expected return . UnfortuCurrently, there are three main categories of research work on improving DQN. The first category mainly focuses on how to estimate action values accurately. For example, Hasselt et al.  proposedIn traditional RL, Q-learning algorithms often use linear functions to approximate action values, which have better stability and fewer hyperparameters to be trained than DQNs . In partIn our previous work , we propThe remainder of this paper is organized as follows. In this section, we briefly review the related theories and algorithms of our MRLS-Q, including the Markov decision process (MDP), DQN, and LS-DQN. In addition, we also describe some notations that will be used throughout this paper.\ud835\udcae, \ud835\udc9c, P, r, \u03b3\u232a, where \ud835\udcae is the state space, \ud835\udc9c is the action space, P \u2208  and r \u2208 \u211b are the state-transition probability and the immediate reward from the state st to the next state st\u2032 by taking the action at, and \u03b3 \u2208 , i.e.,J(\u03c0) is usually defined in the form of discount return [s0 is the initial state, whereas J(\u03c0) is hardly calculated by using the above equation directly, since P is unknown in RL, and st\u2032 and rt can only be obtained by the agent's interaction with the environment.For a given MDP, the goal of RL is to learn the optimal policy \u03c0), i.e.,\u03c0\u2217=argmaxQ\u03c0 to measure the performance of \u03c0 when the initial state and action are st and at. In this paper, we assume that \ud835\udcae is continuous and \ud835\udc9c is discrete. For this kind of MDP problems, to overcome the curse of dimensionality, Q\u03c0 is often approximated by linear function approximators or deep neural networks.To tackle this problem, RL usually resorts to estimating the action value DQN is probably the most important algorithm in deep RL. It combines the Q-Learning algorithm with deep neural networks and uses the experience relay for breaking the correlation among samples and training network parameters.t, the agent firstly uses the \u03f5-greedy policy to select the action at as\u03f5 is the exploration factor, \u0398t\u22121 is the policy network parameter, and Q is approximated by this network. Then, after taking at, the agent moves to the next state st\u2032, obtains the reward rt, and stores  into the experience replay buffer \ud835\udc9f, where dt \u2208 {0,1} denotes that st\u2032 is the terminal state or not. Next, by using the minibatch \ud835\udc9f randomly, the algorithm calculates the loss of the policy network ast\u22121 to \u0398t. For example, by using the SGD method [t\u22121 is updated as\u03b1 is the learning rate and \u2207t\u22121\u0398 denotes \u2202L(\u0398t\u22121)/\u2202\u0398t\u22121.The DQN algorithm can be summarized as follows. At the current step D method , \u0398t\u22121 isLS-DQN is a hybrid approach, which combines the traditional LSPI or FQI algorithm with the DQN algorithm. By enjoying the stability and efficiency of LSPI or FQI, it can obtain better performance than DQN.tL in the policy network astL is the ith column vector of \u0398tL. Besides, A and b are defined as follows:tL by using FQI, since it is a batch shallow RL algorithm that computes iterative approximations of the Q-function using regression. For brevity, we will not discuss the FQI algorithm in this paper.The LS-DQN algorithm can be briefly summarized as follows. Whenever the agent runs DQN some steps, it uses LSPI or FQI to retrain the last layer of the policy network once. The retraining consists of the following three substeps. Firstly, by recalculating all samples in the experience replay buffer with the current network parameters, the policy network generates a new dataset eir work , the algIn this section, we will introduce the detailed derivation and the practical implementation of our proposed algorithm, respectively. Our algorithm, the MRLS-Q algorithm, can be used not only alone but also as the last layer of DQN.MRLS-Q is a new Q-learning algorithm with linear function approximation, but it is more similar to the DQN algorithm rather than the traditional Q-learning algorithm. It uses the experience replay and the minibatch training mode, separates the linear function approximator into a policy approximator and a target approximator, and uses the state features rather than the state-action features. Besides, it uses an average RLS method for updating parameters.t, the agent also uses the \u03f5-greedy policy to select the action at as equation  is approximated by the policy approximator as\u03d5(st) \u2208 \u211bN is the feature vector of st, \u0398t\u22121 \u2208 \u211bN\u2009\u00d7\u2009|\ud835\udc9c| is the policy approximator parameter, in(a) denotes the index of a in \ud835\udc9c, and \u0398t\u22121) is the in(a)th column vector of \u0398t\u22121. Then, the agent takes at, moves to st\u2032, obtains rt, and stores  into the experience replay buffer \ud835\udc9f.First, we introduce the agent's interaction with the environment. At the current step equation . Note he\ud835\udc9f at the nth step, and let \u03bb \u2208 22) as foPt=At\u22121. By using the Sherman\u2013Morrison formula for 27) into t\u22121\u0398.As reviewed in If the loss function of MRLS-Q is defined by equation , by usinRecall the fact that we once used quations  and 24)k\u03d5\u00aft\u03d5t\u00afT quations  and 20)k\u03d5\u00aft\u03d5t\u00afT In addition, from equation , we can Using equation  yields11), the Using equations  and 40)40), we cTherefore, we can rewrite equation  as(42)\u0398tt in MRLS-Q.It shows that L1 regularization term into the above equation, i.e.,\u03b7 is the regularization factor and sgn(\u00b7) is the sign function.However, although RLS has a fast convergence rate, it often suffers from overfitting. In recent years, there has been extensive research on this problem. Based on Ek\u015fio\u011flu's work , we add t\u22121\u0398 can be calculated by the automatic differentiation package of PyTorch or TensorFlow directly. Besides being used alone, MRLS-Q can also be used as the last layer of DQN, since it uses the same loss function and experience replay as DQN. However, there is still an obstacle to the combination of MRLS-Q and DQN. As the training goes on, the parameters of the DQN network are continuously changing, and the outputs of the same inputs are changing as well. Thus, we cannot use the inputs of the DQN's last layer as the features of MRLS-Q directly. In order to alleviate this kind of change and integrate MRLS-Q into DQN, we present a new method to define the feature function of MRLS-Q asXtL \u2208 \u211bM\u00d7NL\u22121 is the output matrix of the DQN's penultimate layer and \u03bd is a small hyperparameter to prevent the denominator becoming zero.Based on the above derivation, the pseudocode of MRLS-Q is summarized in In this section, we use two sets of experiments to demonstrate the effectiveness of MRLS-Q. Our experiments are divided into two sections. In In this set of experiments, we firstly verify the performance of MRLS-Q on the CartPole-v0 problem, which is from the OpenAI Gym. For comparison purposes, we build a new algorithm called Adam-Q, by replacing equation  with the4 random samples in the CartPole's state space, by using eight scikit-learn RBFSamplers [\u03f5 is initialized to 0.95 and is gradually decreased to 0.01 over 1000 steps. (3) The discount factor \u03b3 is 0.99. (4) The capacity of the experience replay buffer \ud835\udc9f is 104, and the minibatch size is 32. The learning starts when the number in \ud835\udc9f reaches the minibatch size. (5) The policy approximator parameter \u03980 and the target approximator parameter t each step. Note that the performances of both algorithms will get worse if we increase the update steps, since the CartPole problem is very simple and both algorithms converge fast. (7) The max norm of \u2207t\u22121\u0398 is clipped to 1 by the L2 norm. (8) The two algorithms run five times and 100 episodes for each time. In each episode, each algorithm runs 200 steps at most. (9) Besides, in Adam-Q, the learning rate, \u03b21, and \u03b22 of Adam are 0.001, 0.9, and 0.999; in MRLS-Q, the initialization P0, the forgetting factor \u03bb, the regularization factor \u03b7, and the approximation factor k are 0.5I, 1, 10\u22125, and 1/32, respectively. The average result of this experiment is shown in To compare the performance between MRLS-Q and Adam-Q, the experimental settings are summarized as follows. (1) Both algorithms use 400 radial basis functions (RBFs) for action-value approximation. These RBFs are generated from 10Samplers  with ker\ud835\udc9f| \u2208 {500,1000,5000,10000}, P0 \u2208 {0.1I, 0.2I, 0.5I, I}, and k \u2208 {(1/2), (1/8), (1/32), (1/128)}, respectively. The other settings of these experiments are the same as what we did for MRLS-Q in the previous experiment. The average results of these experiments are presented in Figures \ud835\udc9f has a significant influence on the performance of MRLS-Q. The larger capacity will result in the better performance, since big \ud835\udc9f is helpful to remove the correlation between the observed transitions. From P0, whereas too big P0 will make MRLS-Q become unstable and too small P0 will make MRLS-Q converge slowly. From k also has a significant influence on MRLS-Q. From equation (k will make Pt update with higher strength. If state feature values change greatly, k should be set to a big value.To investigate hyperparameter influences on MRLS-Q, we test |equation , bigger \u03b21, and \u03b22 of Adam are 0.0000625, 0.9, and 0.999; in the last layer of Hybrid-DQN, the initialization P0, the forgetting factor \u03bb, the regularization factor \u03b7, the approximation factor k, and \u03bd are 0.1I, 1, 10\u22128, 1/2, and 10\u221212, respectively. Note that here we use a big k to update Pt for adapting to the feature change.In this set of experiments, we verify MRLS-Q as the last layer of DQN on four Atari games: Pong-v0, Breakout-v0, SpaceInvaders-v0, and RiverRaid-v0, which are from the OpenAI Gym. Here we choose the traditional DQN algorithm with the Adam optimizer for comparison. For Adam-DQN and in the second to fifth layers of Hybrid-DQN, the learning rate, The average evaluation results are presented in L1 regularization technique to prevent overfitting, and propose a new method to define the feature function for alleviating the feature change of the same state and integrating MRLS-Q into DQN. Experiment results on the CartPole problem demonstrate that MRLS-Q has better convergence than Adam-Q and reveal the hyperparameter influences on MRLS-Q. In addition, experiment results on four Atari games demonstrate that DQN can improve convergence and stability by integrating with MRLS-Q.How to improve convergence and stability of the DQN algorithm is one of the key issues in deep RL. In this paper, we propose MRLS-Q, a linear RLS function approximation algorithm with the similar learning mechanism to DQN. MRLS-Q can be used not only alone but also as the last layer of DQN. Similar to LS-DQN, the Hybrid-DQN with MRLS-Q can enjoy rich representations from deep RL networks as well as stability and data efficiency of the RLS method, but it can seamlessly integrate MRLS-Q and thus is easier to use. In MRLS-Q, we use the experience replay to break the correlation between training samples, present an average RLS optimization method to improve the convergence performance and reduce the computational complexity, employ an"}
+{"text": "Data analysis in real life often relies mainly on statistical probability distributions. However, data arising from different fields such as environmental, financial, biomedical sciences and other areas may not fit the classical distributions. Therefore, the need arises for developing new distributions that would capture high degree of skewness and kurtosis and enhance the goodness-of-fit in empirical distribution. In this paper, we introduce a novel family of distributions which can extend some popular classes of distributions to include different new versions of the baseline distributions. The proposed family of distributions is referred as the Marshall-Olkin Weibull generated family. The proposed family of distributions is a combination of Marshall-Olkin transformation and the Weibull generated family. Two special members of the proposed family are investigated. A variety of shapes for the densities and hazard rate are presented of the considered sub-models. Some of the main mathematical properties of this family are derived. The estimation for the parameters is obtained via the maximum likelihood method. Moreover, the performance of the estimators for the considered members is examined through simulation studies in terms of bias and root mean square error. Besides, based on the new generated family, the log Marshall-Olkin Weibull-Weibull regression model for censored data is proposed. Finally, COVID-19 data and three lifetime data sets are used to demonstrate the importance of the newly proposed family. Through such an applications, it is shown that this family of distributions provides a better fit when compared with other competitive distributions. Selecting a suitable statistical distribution for modeling and analyzing data is of great importance in order to achieve more accurate decisions. Over the years, many statistical distributions have been proposed to fit different shapes of the data. Applying classical distributions to fit these data sets may lead to inaccurate results. Hence, the need for modifying the standard distributions is clearly evident.Recently, many methods have been proposed to obtain more flexible distributions that can reflect the data behavior in many situations more accurately. Adding a new parameter to existing distributions is one popular method that has attracted more attention in literature.  proposedX from a baseline distribution and such variable has a cdf G. Then, for the MO family, its cdf and its probability density function (pdf) are, respectively, given by\u03b1 > 0 is the shape (tilt) parameter, \u03c4 is a vector of parameters for the baseline model. The MO transformation has some attractable characteristics which can add more flexibility to any baseline distribution. This encouraged many researchers to apply the MO transformation to common classical distributions such as the Pareto distribution by \u22121 and G))c(i+1)\u22121, the pdf for MOW-G family with \u03b1 > 1 is obtained byNow by using Pt,m is defined by , with a parameter c can be respectively defined for an arbitrary G(x) asAt this point, the cdf and pdf for the exponentiated-G (Exp-G) distribution, denoted by Then, a linear combination of the Exp-G density functions serves as a way of expressing the pdf of the MOW-G family. Hence, starting from the properties of the Exp-G class of distributions, some features of the MOW-G family of distributions can be obtained. Such features have been investigated in several studies such as, \u201336, amonYj is a random variable from Exp-G distribution with parameter (c(i + 1) + m + r), then the rth moment of the MOW-G family is given by\u03c9j is defined in Let Yj is a random variable from Exp-G distribution with parameter (c(i + 1) + m + r) and \u03c9j is defined in The moment generating function of the MOW-G family can be derived in term of the Exp-G distribution as followssth incomplete moment for MOW-G family is obtained as followssth moment for the Exp-G distribution with parameter (c(i + 1) + m + r) and \u03c9j is defined in The Q(p), 0 < p < 1, of the MOW-G family is as followsThe quantile function, Therefore, the median is given byThe R\u00e9nyi entropy for the MOW-G family is given by\u03b1 < 1, (fMOWG(x))R can be obtained using For 0 < Therefore,Now, using G)R\u2212 and ))R(c\u22121)+ci, the R\u00e9nyi entropy for the MOW-G family for \u03b1 \u2208 , is expressed asPt,m is defined in Applying Eqs  and 12)12), resp\u03b1 > 1 and using Now for A is defined in Applying \u03b1 > 1, the R\u00e9nyi entropy for the MOW-G family is written asPt,m is defined in Thus, for x1, x2, \u2026, xn from MOW-G distribution with order statistics xn1: < xn2: < \u2026 < xn:n. Then the distribution of the qth order statistics of MOW-G distribution is given byConsider the random sample \u03b1 \u2208  and after some algebra, the distribution of the qth order statistics of the MOW-G is expressed as followsThen, for for \u03b1 > 1, we can obtainz is defined in Similarly, for c(i + 1) + m + r). Thus, many proprieties of these order statistics can be achieved from the proprieties of the Exp-G.From Eqs  and 25)25), we cx1, x2, \u2026, xn follows a distribution associated to the MOW-G class, with a parameters vector \u03c6 = , where \u03c4 represents the vector of parameters of the baseline distribution G, then the log-likelihood function (\u2113) is defined byTo obtain the estimators for the parameters of any member from the MOW-G family, the maximum likelihood method can be applied. That is, if we have The complexity of the above log-likelihood makes it difficult to solve analytically. Therefore, we take the derivative of \u03c6 can be acquired by obtaining the solutions in iterative way of the above nonlinear equations using the well-known Newton-Raphson method or any other numerical method. Instead, employing any standard non-linear optimization technique, the log-likelihood in Thus, the MLEs of the parameters vector \u03b3 and scale parameter \u03b4. For each distribution, the simulation is performed over the number of iterations, nsimu = 1000. Four distinct sample sizes n = 25, 50, 100, 200, 500 are considered with the following cases for the true parameters, \u03b8tru.For MOW-E:For MOW-W:For evaluating the performance of the MLEs, some simulation studies is conducted for the two particular members of the MOW-G family namely; MOW-E distribution with rate parameter \u03bb and MOW-W distribution with shape parameter We compute the mean square errors (MSEs) and biases of the MLEs of the parameters based on 1000 iterations, whereThe R programming language  has beenn increases, which indicates that the estimates are consistent. This provides evidence that the maximum likelihood method has a good performance when estimating the parameters of the proposed family.The \u201coptim\u201d function in R software is used to achieve all estimation results. The results of the simulation study are reported in Tables Four real-world data sets with the exponential and Weibull distributions as the G, are considered to investigate the flexibility of the proposed MOW-G family. The first data set is fitted to MOW-E distribution and compared with Marshall Olkin-G defined by , 38 and \u2113), Akaike information criterion (AIC), Bayesian information criterion (BIC), consistent Akaike information criterion (CAIC), Cram\u00e9r-von Mises (W*), Anderson-Darling (A*), Kolmogorov-Smirnov (KS) and P-value statistics. These statistics or criteria are widely used to assess the performance of a distribution in modeling a data set. Smaller values of these statistics, indicate a better fit.The proposed model is compared with other models according to some criteria, include the value of the log likelihood function  will have the LMOW-W distribution with the following pdf and survival function respectively\u03b1, c, \u03b2 are defined in \u03c3 > 0 is the scale parameter and The regression model can be obtained by considering the log MOW-W (LMOW-W) distribution in which the location parameter depends on some explanatory variables For the standardized random variable Xi of the ith individual in the sample, for i = 1, \u2026, n, and considering a set of p covariates such that vi = T, where the 1 is for the intercept term, the location-scale regression model relating to the response variable yi = log(xi) with the explanatory variable vector v can be mathematically described from the LMOW-W as followszi has density function in \u03c3, \u03b1, c, \u03b2 > 0 and \u03c4 = T are the unknown regression coefficients of the p explanatory variables. To illustrate, yi has the location parameter \u03bc = T of the location parameter is described by the linear model \u03bc = \u03c4V, such that V = T is a known model matrix.Assuming the survival time n observations (y1v1), \u2026, , assume that F and C be the sets of individuals for which the response variable yi is the log-lifetime and log-censoring, respectively. Considering the non-informative censoring such that the observed lifetimes and censoring times are independent, the random response is determined by yi = {log(xi), log(ci)}. Then, the log-likelihood function for the vector of parameters \u03b6 = T from model (f(yi) is the density function in S(yi) is the survival function in Yi. Thus, the log-likelihood function for \u03b6 defined asr is the number of uncensored observations (failures) and For an independent sample of om model  can be o\u03b6. For this case, numerical non-linear optimization procedures are commonly applied. The optim function in R can be used in order to find the MLEs.The log-likelihood function in v1 which represents the two-arms . Therefore, the LMOW-W regression model is considered asz1, \u2026, z96 are independent random variables with pdf in The LMOW-W regression model is applied to fit data from an earlier study by , which cThe results from LMOW-W model are compared with some alternative regression models, namely; the log-Weibull (LW) in , the logResults in Weibull-G family introduced in  has advaS1 Appendix(PDF)Click here for additional data file.S1 Text(TXT)Click here for additional data file."}
+{"text": "To the Editor:I enjoyed very much reading the article by Revilla-Mart\u00ed et al. , describ"}
+{"text": "Introduction: The omnipolar electrogram method was recently proposed to try to generate orientation-independent electrograms. It estimates the electric field from the bipolar electrograms of a clique, under the assumption of locally plane and homogeneous propagation. The local electric field evolution over time describes a loop trajectory from which omnipolar signals in the propagation direction, substrate and propagation features, are derived. In this work, we propose substrate and conduction velocity mapping modalities based on a modified version of the omnipolar electrogram method, which aims to reduce orientation-dependent residual components in the standard approach.Methods: A simulated electrical propagation in 2D, with a tissue including a circular patch of diffuse fibrosis, was used for validation. Unipolar electrograms were calculated in a multi-electrode array, also deriving bipolar electrograms along the two main directions of the grid. Simulated bipolar electrograms were also contaminated with real noise, to assess the robustness of the mapping strategies against noise. The performance of the maps in identifying fibrosis and in reproducing unipolar reference voltage maps was evaluated. Bipolar voltage maps were also considered for performance comparison.Results: Results show that the modified omnipolar mapping strategies are more accurate and robust against noise than bipolar and standard omnipolar maps in fibrosis detection . They present better correlation with unipolar reference voltage maps than bipolar and original omnipolar maps .Conclusion: The modified omnipolar method improves fibrosis detection, characterization of substrate and propagation, also reducing the residual sensitivity to directionality over the standard approach and improving robustness against noise. Nevertheless, studies with real electrograms will elucidate its impact in catheter ablation interventions. Diagnosis and treatment of a wide range of atrial arrhythmias, including atrial fibrillation, require extraction of substrate and propagation features from intracardiac electrograms (EGMs) . This strategy identifies as fibrosis  method tries to cope with the problems affecting unipolar and bipolar measurements  by using two clique configurations: square and triangular cliques. These modifications are hypothesized to improve the accuracy and robustness of the voltage and CV estimates and to reduce the error induced by the b-EGMs dependence on catheter orientation, which is not fully compensated by the OP-EGM approach. Specifically, the aims of this study are: (1) to assess the estimates of CV and propagation direction within each clique with the proposed MOP-EGM method as compare to the ones obtained by the original OP-EGM; (2) to propose mapping strategies based on omnipolar EGMs estimations to characterize the atrial substrate; and (3) to assess the ability of the proposed maps in detecting a fibrotic patch and in reproducing unipolar voltage maps.IKr) was selected 1.6-fold greater than the original right atrial model , the L-type calcium current (ICaL), the inward rectifier potassium current (IK1), the ultrarapid outward potassium current (IKur) and the slow delayed rectifier potassium current (IKs) (see APD90) (248 vs. 111 ms), in concordance with experimental data . Simulations were run in ELVIRA software  conditions was simulated by dividing it into adjacent square elements whose centers were separated 0.1 mm. Within the tissue slice, a circular patch with a diameter of 2 cm was defined, whose center was at the center of the 2D tissue. Inside this circular patch, a diffuse fibrosis pattern was randomly defined following a uniform distribution. All the non-fibrotic nodes were assigned the Courtemanche cellular model stabilized during 1 min at basic cycle length (BCL) 500 ms  see , as in pIKs) see . Twenty IKs) see . The intIKs) see . AlthougIKs) see , therefoN \u00d7 N high-density multi-electrode array (MEA) (N = 15), where the inter-electrode distance was d = 2 mm. The simulated tissue geometry, including the MEA location and the fibrotic patch, is shown in i, j) within the MEA, is referred to as electrode 1. The rest electrodes of the clique are numbered from left to right and bottom to top. Therefore, electrodes 2, 3, and 4 correspond to locations , , and , respectively.Recording electrodes were distributed over the simulated tissue, mimicking a The simulated electrode grid is located so that its central electrode corresponds to the center of both the tissue slice and the fibrotic patch, and the MEA is rotated by an angle \u03a8 with respect to the tissue fiber orientation. Three different MEA orientations with respect to the tissue preferential direction were considered: \u03a8 = 0\u00b0, \u03a8 = 30\u00b0, and \u03a8 = 45\u00b0, which are illustrated in z = 1 mm distance from the tissue surface. This represents a plausible compromise between recording realistic amplitude EGMs and the real clinical setting situation where there is no guarantee of maintaining a perfect electrode-tissue contact during the mapping.The MEA grid was placed at ui, j(t) were simulated as generated by the propagation wave when passing by electrodes located at sites ,  of the grid. They were computed in a volumetric tissue-blood model with a temporal resolution of 1 ms, as in Martinez-Mateu et al. . Bipolar EGMs Bipolar signals, as defined in Equation (1), are used to compute bipolar voltage maps for performance comparison, as described in subsections 2.12, 2.13.i, j) in its lower left corner, i, j) electrode position, see black arrows direction variations in The omnipolar methodological developments assume a locally plane wave propagation within a clique, with a velocity vector Examples of unipolar and bipolar EGMs used in this study, corresponding to the case when the global propagation direction of the wave and MEA direction form an angle \u03a8 = 0\u00b0, are shown in tc be the reference time at which the center c of the selected square is activated. Assuming constant velocity within the arrangement, the activation times at the four electrodes are:Let us consider any four-electrode clique within the MEA, like the one in t) be the unipolar voltage waveform generated by a plane wave when passing by a given position at time t = 0. When one or more electrodes within the square of t) passage, the following u-EGMs and b-EGMs are modeled as:Let \u03d5(x direction (b12(t) and b34(t)), y direction (b13(t) and b24(t)), as well as along the directions of its diagonals (b14(t) and b23(t)). Depending on the waveform arrival time to each electrode tm, the activation time of each b-EGM bmn(t) corresponds to the passing of the wave by the middle point between electrodes m and n. Therefore, relative delays  occur between the different bmn(t).It should be noted that bipolar signals in Equation (4) are derived within each clique along um(t) = \u03d5(t \u2212 tm) around tm = tc, we can approximate:By using the Taylor's series expansion of tmn = tn\u2212tm are the differences between activation times at electrodes m and n, m, n \u2208 {1, 2, 3, 4}, and \u0394tm = tm\u2212tc are the differences between activation time at electrode m and the reference activation time of the center of the square. By replacing Equation (2) in Equation (6) and operating, the following b-EGMs expressions are derived:where \u0394bmn(t), showing the previously mentioned delay between the different bipolar signals. If we relate b12(t) and b13(t), measured in different x and y directions, we obtain:From these expressions we can relate the second order approximations of the different pairs of b-EGMs y-direction (1\u20133) is a scaled version of the b-EGM along x-direction (1\u20132) by a factor x-direction), b13(t) = 0, while for \u03b8 = 45\u00b0, the delay is \u03c4 = 0, meaning that both bipolar EGMs in the x- and y- directions are activated at the same time. Similarly, if we relate b12(t) with b34(t), both along the x-direction, we obtain:Equation (13) shows that the b-EGM along d/v, when the propagation is orthogonal to the direction of the electrode pairs (\u03b8 = 0\u00b0).Equation (14) shows that b-EGMs along parallel directions have the same amplitudes (as expected), and the delay t), and the electric field (E-field) at the extracellular-myocardial interface. Let us consider a locally plane myocardial surface, defined by its normal unit vector The purpose of the OP-EGM method is to obtain EGM amplitude and propagation features which are invariant to the relative angle between the propagation direction and the catheter  is a vector containing the available b-EGMs, D is a matrix of interelectrode distances, and \u03f1 \u2208 {\u25a1,\u25b3} denotes the clique type, square (\u25a1) or triangular (\u25b3), respectively. In case of square clique, as the one illustrated in b\u03f1(t) \u2261 b\u25a1(t) contains six b-EGMs, D\u03f1 \u2261 D\u25a1 is a 2 \u00d7 6 matrix, reported below. Similarly, in case of triangular configurations, as the clique 1 in b\u03f1(t) \u2261 b\u25b3, 1(t) contains three b-EGMs, D\u03f1 \u2261 D\u25b3, 1 is a 2 \u00d7 3 matrix, also shown below.where D\u25b3, 1 were obtained for the other three-electrode configurations of the clique shown in Expressions similar to From Equation (15) we see that the projection of the E-field along the inter-electrode distance results in the corresponding b-EGM. Since measured b-EGMs will be affected by noise and model mismatch errors, we can use the least-squares criterion to estimate the electric field c of each \u03f1-type clique, describes a loop trajectory in the 2D plane. Under the assumption of locally plane and homogeneous wave, E\u22a5(t) \u2248 0 within the clique, so that The evolution over time of the N \u00d7 N is the size of the MEA, there will be (N \u2212 1) \u00d7 (N \u2212 1) = N2 \u2212 2N + 1 estimates of x(t) and \u00cay(t) of the electric field can be expressed as linear combinations of the two b-EGMs along x- and y- directions, respectively:If where the approximated terms make use of Equations (7\u201310).v. Such delay represents the difference in the wavefront arrival time to the middle point of each bipole.Equations (18\u201322) show that the two electric field components within each clique have a different amplitude, depending on the propagation angle \u03b8. In addition, for triangular cliques, there is also a delay between both components, which is also a function of the propagation angle \u03b8 and the conduction velocity magnitude In the formulation of Equation (15), no delay is considered among the b-EGMs. However, when estimating the electric fields making use of measured b-EGMs, the different bipolar signals are activated at their corresponding wavefront arrival times, thus having a delay among them, as expressed in Equations (7\u201312).x(t) and \u00cay(t), for plane wave propagation and to that level of approximation. Consequently, the x(t) and \u00cay(t) in Equation (18) is the summation of two terms which have a delay between them: Equations (7\u201310), respectively. It is well known that the summation of delayed components result in smoothed estimates,  we found that there are no delays between \u00cax(t) and \u00cay(t) components. This misalignment will be reflected at the x(t) and \u00cay(t), in this study we propose a modified version of the least squares estimator of E\u03f1(t), where the b-EMGs in the clique are previously time-aligned. For that purpose, both in square and in triangular configurations, the time delay \u03c4mn between each independent bipolar signal bmn(t), mn \u2208 {12, 34, 13, 24} and the b-EGM with the highest amplitude within the clique bmax(t) was estimated by maximizing their cross-correlation:For the triangular cliques, Equations (19\u201322) show that, in general, there is a delay between \u00cabmn(t) was then advanced by \u03c4mn so that it is aligned with bmax(t). Figure 5 shows examples of E-field estimated with and without previous alignment.Each b-EGM c, and the projection of the electric field in that direction \u00cap(t). The unipolar voltage signal c: E(t) is expressed as E(t) along the propagation direction is given by:OP-EGM approach estimates propagation direction by finding the angle E(t) with its estimate according to Equations (18\u201322) and solving:The estimated conduction angle c maximizing the previous cross-correlation, the propagation angle estimate is:If For square cliques, considering the estimates of the E-field components for plane wave propagation in Equation (18), the expressions in Equation (3) and the fact that Using a similar procedure for triangular cliques, as clique 1 in x(t) and \u00cay(t) are estimated from properly aligned bipolar signals, then we obtain This result points out that the estimate of \u03b8 is biased in general for triangular cliques. Nevertheless, if the electric field components \u00cauc(t) = u1(t). For triangular cliques, the signal from the electrode corresponding to the vertex of the right angle is chosen, so that uc(t) = uk(t), k = {1, 2, 3, 4} for each of the four triangles indicated with the same k-th index, respectively, in In the reference omnipolar method introduced by Deno et al. , it is nAlternatively, we propose in this work a more robust approach, where the estimation of umax(t), by computing the maximum cross-correlation between them. In this way, the four aligned u-EGMs uk(t \u2212 \u03c4k), k \u2208 {1, 2, 3, 4}, are obtained;each of the four u-EGMs is aligned with respect to the one with the highest amplitude, denoted as t) is calculated by averaging the four aligned u-EGMs uk(t \u2212 \u03c4k);the average signal \u016b(t) is computed and used as estimate of the time derivative of \u016b, as they are expected to be proportional under the assumption of locally plane wave: v can be estimated by computing the ratio of the peak-to-peak (pp) amplitudes of p(t), as proposed by Deno et al.  of p(t):In order to avoid the large sensitivity to noise that be expected from an estimation based on peak-to-peak amplitudes, we propose here a more robust estimate of For square cliques, by using Equation (18) in Equation (24) and if the propagation direction is well estimated (x(t) and \u00cay(t), and assuming that the propagation direction is well estimated , using the approximations with delays in Equation (19) for \u00caThis equation shows that the misalignment of i, j, (q)(t), where q \u2208 {1, 2, 3, 4} refers to each of the four possible triangles when using triangular clique configuration, were defined by projecting t) within the corresponding clique onto the following directions:In this work, OP-EGM signals \u03c6me) direction was derived as: Emax of the electric field, proposed by Deno et al.  of the loop described by t) within the depolarization interval. The resulting OP-EGM signal The principal direction Let us consider y(t) and \u00cax(t) components with the delay approximation in Equation (19) and time aligning them, we obtain the aligned version It should be noted that there are no second-order terms in Equation (32), unlike the expressions of b-EGMs (see Equations 7\u201312). Again, alignment prevents attenuation at the Figure 6, for both clique configurations and the three MEA orientations, with and without the previous alignment of b-EGMs.whose amplitude is properly estimated. Examples of the omnipolar EGM signals here introduced are observed in s \u2208 {me, pca, pca\u22a5}, we computed the peak-to-peak amplitude pca approach, we also created maps based on the root sum square of the voltage in the first and second principal components, For each OP-EGM signal introduced in this work r) of both values, as well as their maximum (m) were also considered so as to have a performance reference based on bipolar signals:We also built bipolar maps based on the peak-to-peak amplitudes All the voltage maps were computed for each orientation of the MEA, and by using both clique configurations analyzed in this study. Omnipolar voltage maps were also performed from aligned b-EGMs. We obtained color-coded maps where a pixel corresponds to a clique .v-values and arrows representing angular direction \u03b8 of the estimated velocity vectors v in each clique. Plotted v-values were estimated by using both OP-EGM approach of the Equation (28) proposed by Deno et al.  measurement configurations  within the MEA, maps performed with this configuration present higher spatial resolution.It should be noted that maps performed with square cliques present the same resolution as bipolar maps, both providing \u00ae catheter  in 27 different mapping points at intervals with no recorded EGMs. All noise segments were normalized in order to guarantee the same power level, coinciding with the observed average power. One hundred different realizations of this recorded noise were randomly added to each of the simulated b-EGMs x and y directions of the MEA. As a result, we generated one hundred noisy bipolar signals along each of the two directions, n, the different modalities of voltage and conduction velocity maps were computed, obtaining 100 different maps from noisy b-EGMs. These mapping strategies were tested regarding fibrosis detection, as well as voltage map reproducibility. The previous procedure was repeated for six different noise levels, scaling the noise realizations so that they had standard deviations \u03c3n \u2208 {3, 6, 14, 28, 42, 55} \u03bcV. The standard deviation of the recorded noise ranged from 1.2 \u03bcV to 11 \u03bcV, with an average value of 2.4 \u03bcV, lower than those reported in Unger et al. , receiver operating characteristic (ROC) curves were used. Two ground-truth masks of fibrosis were created for bipolar and omnipolar maps, having the resolution of square and triangular cliques and indicating whether a clique lay within the fibrotic or the normal tissue. A 14 \u00d7 14 ground-truth mask was used to evaluate bipolar and omnipolar maps with square cliques. A value of 1 was assigned if the four electrodes defining the square clique lay in the fibrotic area, and a value of 0 was assigned if all of them lay in the non-fibrotic area. Cliques with some electrodes inside and some outside the fibrotic patch were not considered in the evaluation. Similarly, a 28 \u00d7 28 ground-truth mask was used to assess omnipolar maps performed with triangular cliques, considering if the three electrodes defining the triangular clique lay in fibrotic or non-fibrotic tissue.true positive denotes the number of cliques correctly identified as fibrotic, false negative represents the number of missed cliques in the fibrotic area, true negative stands for the number of cliques correctly identified as non-fibrotic and false positive is the number of cliques incorrectly detected as fibrotic. The accuracy (ACC) was defined as the number of cliques correctly identified as fibrotic or non-fibrotic divided by the total number of cliques. The maximum ACC was used as a measure of the overall fibrosis detection ability of a given map. In addition, the sensitivity and specificity with the threshold achieving the maximum ACC were also computed.Both ground-truth masks used in this study are illustrated in p and Spearman's rank \u03c1s correlation coefficients. A p \u2264 0.05 was required to have statistical significance. Reference voltage maps were obtained by following two sequential steps:The ability of the voltage mapping strategies in reproducing the spatial distribution of reference maps was also evaluated. We created peak-to-peak amplitude maps of u-EGMs, and resampled them to match the spatial resolutions of bipolar and omnipolar pixel maps (with both square and triangular cliques). To quantify the agreement of each voltage map with the substrate characterization given by the reference map, we used both Pearson's \u03c1N \u00d7 N peak-to-peak amplitude map of u-EGMs ui, j(t),  \u2208 {1, \u2026, N}, was performed placing three interpolated values between any two adjacent electrodes, along both MEA directions, thus increasing the total number of pixels to (N + 3 \u00b7 (N \u2212 1)) \u00d7 (N + 3 \u00b7 (N \u2212 1)). The original and interpolated maps for N = 15 are shown in A bicubic interpolation of the N \u2212 1) \u00d7 (N \u2212 1) and 2\u00b7(N \u2212 1) \u00d7 2\u00b7(N \u2212 1) reference maps, matching the dimensions of bipolar and omnipolar maps with square cliques, and omnipolar maps with triangular cliques, respectively. Resulting resampled pixel maps from N = 15, for the case when \u03a8 = 0\u00b0, are illustrated in The interpolated pixel map was later resampled so as to obtain  between each noisy map and the respective noise-free map. In case of voltage maps, we calculated:s \u2208 {b-m; b-r; o-me; o-me, a; o-pca-r; o-pca-r, a}. Analogously, for velocity maps, we computed:where s \u2208 {o; o-m; o-m, a}.with o and the modified \u03b8o-m omnipolar method. Angle differences, \u03f5\u03b8, between propagation direction maps obtained from noisy realizations and those obtained from noise-free signals (considered as the reference) were computed for each omnipolar approach and noise level. The mean and standard deviation of the angle differences in each map were obtained and averaged for all noise realizations.We also studied the effect of noise on the estimation of the propagation direction with both the original \u03b8All performance measurements were reported jointly for the three MEA orientations considered in this study, thus assuming that the relative angle of the propagation direction with respect to the catheter is not known a priori.i, j) electrode positions. All the E-field loops were estimated with and without previous time alignment of b-EGMs, as proposed in subsection 2.6 (denoted as Ea(t) and E(t), respectively). In the top three rows, cliques were chosen in a non-fibrotic area with plane wavefront. Rows A\u2013C correspond to the clique  =  for \u03a8 = 0\u00b0, \u03a8 = 30\u00b0 and \u03a8 = 45\u00b0, respectively. The estimated local propagation angles with the proposed MOP-EGM method were i, j) =  with \u03a8 = 0\u00b0 in i, j) =  with \u03a8 = 30\u00b0 in i, j) =  with \u03a8 = 45\u00b0 in (B), (C), (D) and (E)].The effect of the proposed alignment is evident in both upper and lower panels. In square cliques, the E-field peak value for the aligned versions is clearly higher than for the non-aligned ones. On the other hand, in triangular cliques the alignment of b-EGMs proves to improve the estimation of the propagation direction. These is clearly seen especially in those areas where the local propagation direction differs from the dominant directions of the MEA [see panels i, j) as in s \u2208 {me, pca, pca\u22a5}, in square and triangular cliques, with and without alignment of b-EGMs. These results show that the OP-EGM signals produced by the two modalities are quite similar in most of the cases. Square cliques reveal that n = 28\u03bcV (right columns). In the latter case, only one of the 100 noisy realizations was shown. The omnipolar maps are presented without and with the alignment of b-EGMs. These results reveal that combined bipolar maps obtained as the root sum square or the maximum voltage of both MEA directions, Vb-r and Vb-m, shown at row A, present better fibrosis detection performance than omnipolar maps without alignment, illustrated at upper and lower rows in me and pca, respectively. However, omnipolar maps with previous time alignment of b-EGMs (upper and lower rows in The different bipolar and omnipolar voltage mapping strategies are illustrated in A) and with the proposed approach (without (row B) and with (row C) alignment of b-EGMs) are presented in CVo-m and CVo-m, a) than the standard approach (CVo). Moreover, the standard approach tends to overestimate conduction velocity values, when compared with the MOP-EGM method.Velocity maps obtained with the reference OP-EGM method  achieve values \u03c1p = 0.87 and \u03c1s = 0.87 when square cliques are used and b-EGMs alignment is performed. As a reference, Vb-r and Vb-m present correlations of \u03c1p = 0.86 and \u03c1p = 0.83, respectively. Regarding CV maps, the MOP-EGM version proposed in this work  presents indeed comparable performance in fibrosis detection to combined bipolar voltage maps , and better performance than both omnipolar voltage maps and than the original OP-EGM approach to estimate conduction velocity (CVo).AUC, ACC, Pearson \u03c1p, A, omnipolar voltage and CV maps are less affected by noise than bipolar maps for noise levels greater than or equal to \u03c3n = 28\u03bcV. Note that the proposed time alignment of b-EGMs improves fibrosis detection performance and robustness to noise of the MOP-EGM maps, when comparing them to their unaligned versions. The highest ACC was obtained by CV maps computed with the MOP-EGM method in square cliques, including prior alignment of b-EGMs (CVo) proved to be unstable with noise, both in square and triangular clique configurations. As shown in panel B, voltage maps performed with the MOP-EGM method, including b-EGMs alignment, and with square cliques, Similar results are observed in The RMSE between maps computed from noisy b-EGMS and those computed with noise-free b-EGMs are depicted in o and \u03b8o-m for square and triangular cliques, considering jointly all three MEA orientations. These results show that propagation direction maps performed with square cliques are less affected by noise than those performed with triangular cliques, regardless of the omnipolar approach. However, for noise levels lower than \u03c3n = 28\u03bcV, direction maps with the MOP-EGM approach \u03b8o-m exhibit a smaller mean bias than those using the original method \u03b8o.Vo-me, Vo-pca-r, Vo-me, a, Vo-pca-r, a, CVo-m and CVo-m, a) performed with square cliques. The accuracy in fibrotic patch detection reached the values ACC = 91, 99, and 100% using Vo-me; ACC = 91, 100, and 100% using Vo-pca-r; and ACC = 100, 91, and 91% using CVo-m, when \u03a8 = 0\u00b0, \u03a8 = 30\u00b0 and \u03a8 = 45\u00b0, respectively. When previous time alignment of b-EGMs is performed, accuracy achieves values ACC = 100, 91, and 92% for both Vo-me, a and Vo-pca-r, a, while ACC = 93, 100, and 100% when using CVo-m, a, for the same catheter orientations.Finally, In this work, we investigated the performance of different substrate and velocity mapping modalities based on the OP-EGM method, and on the here proposed MOP-EGM approach, in characterizing and detecting fibrotic areas. For that purpose, we used a 2D multi-electrode array over an atrial tissue simulated with the Courtemanche cellular model.ex vivo  always improves the fibrosis detection ability of the omnipolar voltage and conduction velocity maps. The latter provide a characterization of the atrial substrate comparable to bipolar voltage maps combining b-EGMs along Most studies to detect fibrosis rely on bipolar voltage mapping , we observe a reduction of the omnipolar voltage values. In addition, in tissue areas where the wavefront propagation is curved, the electric field is overestimated when the local propagation direction becomes parallel to one of the two main directions of the catheter (as when \u03a8 = 45\u00b0). As this happens in an area of healthy tissue, it causes a higher overall accuracy in fibrotic patch detection. The reverse occurs when these curved areas are oblique to the MEA (as in \u03a8 = 0\u00b0), providing underestimated voltages and decreased fibrotic detection accuracy.v, in Equation (29), has an inverse relationship with the magnitude of the estimated E-field, while in voltage estimation (equations in subsection 2.9), the dependence is direct. In addition, in those areas where the wave propagation is curved, velocity is overestimated when the MEA is in the same direction as the tissue (\u03a8 = 0\u00b0). Therefore, the fibrotic patch is globally better detected for this configuration. On the other hand, if catheter becomes oblique to the tissue (\u03a8 \u2260 0\u00b0), areas of curved propagation appear underestimated, thus reducing the overall fibrosis detection performance for those configurations. When b-EGMs are time-aligned, both MOP-EGM based voltage and velocity maps continue to be sensitive to the orientation between MEA and tissue, but to a lesser extent if compared to their unaligned versions. As a result, improved fibrosis detection, better voltage estimations and less degradation by noise are observed in average when using the MOP-EGM approach. The remaining dependence with \u03a8 is not predicted by the mathematical model based on the plane-wave assumption, but the sampling frequency of the b-EGMs (1 kHz) could be behind this observation.As for the orientation dependence of velocity maps, the opposite behavior is observed, with velocity estimation increasing for \u03a8 \u2260 0\u00b0. This is explained by the fact that The basic assumption of plane and homogeneous propagation within each clique represents an intrinsic limitation of the omnipolar methodology, requiring the use of high spatial resolution multi-electrode catheters (like the one considered in this study). Moreover, the hypothesis of a plane myocardial surface in the area defined by the clique is questionable in non-compacted myocardial regions or in the atrial appendage. Nevertheless, those areas will be identified with 3D electroanatomic mapping systems . Moreover, the proposed MOP-EGM maps need to be evaluated over real data, where the effect of electrode size, inter-electrode distance and variable tissue-electrode contact will be present. The validation of these methods In this work we showed that voltage mapping strategies based on the MOP-EGM method are able to discriminate fibrotic from healthy tissue. For low noise levels, they attain comparable performance to maps obtained by combining the b-EGMs amplitudes along the two directions of the catheter, but clearly outperform bipolar maps when noise is added. On the other hand, omnipolar CV maps reveal higher fibrosis detection accuracy than voltage maps, specially when the modifications proposed in this work were applied. The fibrosis detection performance of voltage and velocity maps benefit from prior intra-clique time alignment of b-EGMs as proposed in the MOP-EGM approach. In addition, the use of square cliques outperforms the triangular ones.me) and the one based on principal component analysis (pca) yield similar results, in terms of detection accuracy and correlation with unipolar voltage maps. Similar conclusions are drawn when b-EGMs are affected by noise extracted from real signals.As for the different approaches to estimate the omnipolar voltage from the E-fiel loop, both the one based on maximal excursion  Ethics Committee. The patients/participants provided their written informed consent to participate in the study.JR, AA, PL, and JM designed the study and analyzed the results. JR, PL, and JM wrote most of the manuscript. SR, LM-M, and JS performed the electrophysiological simulations. SL provided the clinical data. PL and JM supervised and formalized the project. JR developed the software and performed the required computations. All authors critically revised the manuscript and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher."}
+{"text": "S be a set of states of a physical system and p(s) the probability of the occurrence of an event when the system is in state S-probability. If a set P of S-probabilities is ordered by the order of real functions, it becomes a poset which can be considered as a quantum logic. In case the logic P is a Boolean algebra, this will indicate that the underlying physical system is a classical one. The goal of this paper is to study sets of S-probabilities which are not far from being Boolean algebras by means of the addition and comparison of functions that occur in these sets. In particular, certain classes of so-called Boolean posets of S-probabilities are characterized and related to each other and descriptions based on sets of states are derived.With many physical processes in which quantum mechanical phenomena can occur, it is essential to take into account a decision mechanism based on measurement data. This can be achieved by means of so-called numerical events, which are specified as follows: Let  In axiomatic quantum mechanics, orthomodular partially ordered sets and generalizations of them are considered as \u201cquantum logics\u201d that determine the behaviour of a physical system. In particular, if the quantum logic is a Boolean algebra, then one will have reason to assume that one deals with a classical physical system. The elements of a quantum logic can also be interpreted as events, and a Boolean algebra then as the equivalent of a classical field of events as known from probability theory.numerical event .S be a set of states of a physical system and p(s) the probability of the occurrence of an event, when the system is in state p from S to  is called a numerical event, or alternatively more precisely an S-probability. If ordered by the order S-probabilities becomes a partially ordered set (poset) that can be conceived as a quantum logic. In this paper, we study different kinds of such quantum logics, especially those that are not far away from being Boolean algebras. For this end, we provide the following notions.Let P be a set of S-probabilities including the constant functions 0 and 1, partially ordered by the order of functions. We will call disjoint, in symbols p and q, respectively, considered as real functions.Let P of S-probabilities is called specific if if if A set R of subsets of some set R, one has R and R. If A and B are disjoint, R having characteristic 2, i.e. Condition (2) seems natural in respect to dealing with probabilities, and as for (3), this condition is motivated by classical fields of events (yet for the time being limited to considering the sum of disjoint events). Conceiving such a field of events as a Boolean ring S-probabilities p and q are called orthogonal, in symbols S-probabilities in general are not), this property is known to be Boolean . We extP with an antitone involution is called Boolean, if A poset S-probabilities are Boolean posets.According to this definition, specific sets of p,\u00a0q of a set P of S-probabilities and denoting their infimum by Writing P be a set of S-probabilities satisfying (1) and (2) and let P in the following sense: If P then P and P then P and Let P. Then, P and Let Finally, we recall the definitions of two structures of numerical events which we will later relate to specific sets of numerical events.P of S-probabilities is called a generalized field of events (in short GFE) (cf. Dorninger ((4)if If a GFE satisfies (5)if then it is called an algebra ofS-probabilities (cf. Beltrametti and Ma\u0327czy\u0144ski (A set orninger ), if it \u0327czy\u0144ski  and Belt\u0327czy\u0144ski ).r to be 0.Condition (4) is a special case of condition (5)\u2014just assume S-probabilities, investigate their interrelations and closeness to Boolean algebras, and indicate when they will actually be Boolean algebras. Moreover, we will consider the question whether  sets of S-probabilities will belong to a Boolean subalgebra of a specific set of S-probabilities and we will characterize specific sets of S-probabilities by states.The goal of this paper is to characterize various classes of specific sets of S-probability p is called varying, if p is neither An S-probabilities are varying , the elS-probability is varying often comes up independently or can be achieved by adding further experimental data directed to this purpose.As for data won by experiments: That an S-probabilities that are varying. An S-probability is called complementary if P of S-probabilities with 0 and 1 will be called complemented if all of its elements are complementary. Further, we recall that a poset P with complementation orthoposet.Now, we will turn our attention to specific sets of P of varying S-probabilities has the following properties: (i)P is complemented and hence an orthoposet,(ii)if (iii)P is a GFE.A specific set (i)r being a varying S-probability. Therefore, If (ii)P being complemented, If (iii)If Let P be a set of S-probabilities satisfying (1) and (2). Then, all elements of P are varying if and only if P is complemented.Let P are varying, then P is complemented according to the proof of Proposition\u00a0P to be complemented. Let P is varying.If all elements of if if is called a concrete logic .S-probabilities are exactly the complemented Boolean GFEs. They all are concrete logics.The specific sets of varying P be a set of S-probabilities and P to be a specific set of varying S-probabilities. By Proposition\u00a0P is a complemented GFE. Conversely, assume P to be a complemented Boolean GFE. Then, as mentioned in Remark\u00a0P are varying. Further, if S-probabilities are orthoposets and hence, Boolean GFEs are Boolean orthoposets. As mentioned in Tkadlec .S-probabilities is a concrete logic, its elements can be represented by functions which have only the values 0 or 1. So, these S-probabilities must be varying from the outset. If S is finite, Theorem\u00a0S-probabilities are Boolean algebras, since finite Boolean orthoposets are Boolean algebras. So to distinguish between a classical and a quantum mechanical behaviour by measurements in the form of numerical events, one would need data from S-probabilities for a continuous set S of states.Since any specific set of varying S-probabilities and algebras of S-probabilities.Next, we turn our attention towards the connection of specific sets of varying S-probabilities that are Boolean.The complemented Boolean GFEs are exactly the algebras of S-probabilities was already shown in Dorninger .S-probabilities are orthomodular posets with a full set of states, and vice versa . Furthe Traczyk ). To be S-probabilities are exactly the infimum faithful algebras of S-probabilities.The specific sets of varying S-probabilities by Boolean rings, in line with Theorems\u00a0Returning to the motivation of the definition of specific sets of S-probabilities which is a Boolean algebra can be conceived as a Boolean ring if one extends S-probabilities p and q by assuming within the pointwise addition of the functions p and q that An infimum faithful algebra of P be a set of S-probabilities. We consider the following conditions: (6)If (7)if (8)if Condition (6) can be motivated by regarding a classical field of events as a Boolean ring R for which it is the case that S-probabilities that satisfy condition (6) as specific (join-specific) sets of S-probabilities. If (1), (2) and (7) hold, P is called a structured set ofS-probabilities (cf. Dorninger and L\u00e4nger (P is known as a weakly structured set ofS-probabilities (cf. Dorninger and L\u00e4nger (Let d L\u00e4nger ), and ifd L\u00e4nger ).S-probabilities:S-probabilities,S-probabilities (satisfying (6)),S-probabilities (for which (7) is distinctive),S-probabilities (characterized by (8)).Now, we define the following classes of sets of We have P be a set of S-probabilities and P is a specific set of S-probabilities. If Let We have P be a specific set of S-probabilities which is also a weakly structured set of S-probabilities and assume Let S-probabilities is a proper subclass of the class of S-probabilities which on its part is a proper subclass of the class of weakly structured sets of S-probabilities unless one assumes that only specific sets of S-probabilities are taken into account.The class of structured sets of As for the inclusions to be proper, in agreement with Lemma\u00a0S-probabilities are exactly the elements of First, assume S-probabilities are away from being Boolean algebras. A first reference to this can be a subclass of Next we will discuss the question how far S-probabilities are exactly the infimum faithful algebras of S-probabilities.(cf. Dorninger and L\u00e4nger ) The comS-probabilities P is finite, it is a Boolean algebra, because, as already mentioned, finite Boolean orthoposets are Boolean algebras. Further, P is a Boolean algebra if it is orthocomplete (cf. Tkadlec (P has to belong to P.) Moreover, if P is a lattice . (To be Tkadlec ). That Pd L\u00e4nger , a strucS-probabilities are characterized to be Boolean algebras by specifying some structural properties\u2014for an overview of these papers see Dorninger  classes of algebras of orninger \u2014and therlukowski , Navara lukowski , Pt\u00e1k .S-probabilities P is a Boolean algebra but if a  subset of P belongs to a Boolean subalgebra of P. If this were the case, this would indicate that one locally deals with a classical physical system. To answer this question, the existence of some further S-probabilities in P will have to be asked for, but the knowledge of P in detail will not be important.Sometimes it is not of interest if a whole algebra of S-probabilities P is given. If P wherein S-probabilities is orthomodular. So, let us suppose that P.So let us assume that a subset r et\u00a0al. ), and asr et\u00a0al. , every aP can only assume the values 0 and 1 .P with an antitone involution.We begin by extending the commonly known notion of a state to the class of bounded posets specific state on a bounded poset s from P to  satisfying the following conditions for all if if If for P, then a specific state on P satisfying (S5)if is called a pseudostate on P (cf. Dorninger and L\u00e4nger (A d L\u00e4nger ).setTof specific states on P is called full if for setTof specific states on P is called uniform if for disjoint r.  with Assume From this, we can conclude that f is an isomorphism from P onto f(P). Hence, P is isomorphic to a member of Conversely, let S-probabilities are exactly the bounded posets with an antitone involution in which the join of two disjoint elements exists and which have a full set of pseudostates, which in the light of Lemma\u00a0As shown in Dorninger and L\u00e4nger  up to isS-probabilities are exactly the bounded posets with an antitone involution in which the sum of two disjoint elements equals their join and which have a full set of pseudostates.Up to isomorphism, the S-probabilities are exactly the orthomodular posets having a full set of states.Theorems\u00a0To find out whether quantum mechanical effects can occur in a physical or technical system, various classes of sets of numerical events were studied, i.e. data-sets obtained by surveying the system which then form or contribute to the underlying quantum logic. In particular, sets of numerical events, called specific sets, were analyzed that are located at the threshold between classical and quantum behavior, a situation that can be characterized by the fact that in case of a classical physical system the underlying logic is a Boolean algebra. The interrelations of specific sets of numerical events and their closeness to Boolean algebras were ascertained and the question was answered when an unstructured set of numerical events can be a part of a Boolean algebra. Moreover, specific sets of numerical events were characterized by the states they admit."}
+{"text": "The action of Steenrod algebra on the cohomology of Given an  Khovanov homology\u00a0-module M we define the Borel equivariant cohomology of XX using the convention described above. In particular, we have In order to state and prove the next result, we need to set up some notation and recall some basic facts from homological algebra. If G-map reduced Borel cohomology of X, to beThere is a natural m-periodic link diagram of a link M, the equivariant Khovanov homology Let To begin with, observe thatM. We haveNext, let mentclasspt{minimamentclasspt{minimamentclasspt{minimantly, by\u00a0\\documentWe remark that the same argument as in the proof of Theorem\u00a0m-periodic annular link and let m-periodic diagram of M, it holdsLet k is a family of natural transformations between functors Given two generalized cohomology theories The Steenrod algebra For a prime Coming back to Khovanov homology we make the following observation, see\u00a0, 35.k over L and Let knotkit package\u00a0). package\u00a0 implemen package\u00a0. We remaThe next statement shows that Steenrod operations commute with group action.m-periodic link and Let m-periodic diagram of Cohomology operations are natural, so they commute with the group action on cohomology of p. The cohomology ring of Z. Write X, if Y, when Recall that X be a p a prime. There exists an isomorphism of graded , 40 Let As an immediate corollary of Theorems\u00a0p-periodic link with L denoting the quotient link. For any Let p, the modpSteenrod algebra, i.e. the algebra of stable Let I is admissible if degree of I, excess of I, I we associate the cohomology operation I is admissible if degree of I, excess of I, I we can associate a cohomology operation For unstable elements, For a graded Equivariant annular Khovanov homology p be a prime. p-periodic link and L is the quotient link, then for any If p-periodic link L denotes the quotient link.For a Let This is an immediate corollary of\u00a0[Smith inequalities given in Theorems\u00a0We have the following chain of inequalities"}
+{"text": "The invention of public-key cryptography (PKC) by Diffie and Hellman in 1976 is one of two milestones marking the beginning of modern cryptography. The security of a PKC system requires that it should be infeasible to compute the private key from a given public key, which in turn is typically guaranteed by the difficulty in solving some cryptographic-friendly mathematical problems. Among those problems, the integer factorization and discrete logarithm problems play pivotal roles in the development of public-key cryptography. In particular, the assumption that there is no polynomial time  algorithm that solves the above two problems constitutes the basis for the security of almost all currently used public-key cryptosystems, such as RSA and ElGamal. However, Shor\u00a0[As a response to the quantum crisis, the research community has made many efforts to post-quantum cryptography (PQC) that are believed to resist quantum computer attacks. Lattice-based cryptography is one of the main directions in this area, and has become the most promising PQC candidate for standardization.The research of lattice-based cryptography dates back to the seminal work of Ajtai\u00a0, which fFor current applications and standardization, key exchanges, public-key encryptions (PKEs) and signatures are the most desired lattice-based cryptosystems, where the first two are often used to ensure information secrecy, while the last provides information authentication. Note that public-key encryptions are equivalent to two-round key exchanges, also known as the key encapsulation mechanism (KEM). In the following, we focus on lattice-based PKEs/KEMs.f and its trapdoor f\u22121 are generated as the public key and private key. A plaintext m is encrypted as c = f(m), and the ciphertext is decrypted as m = f\u22121(c). The NTRU scheme and its variants follow such an approach. In the second approach, an approximate commutative function fs and a random input a are generated, the public key is ) and the private key is s. A plaintext m is encrypted as c1 = gr(a), c2 = gr(b) + E(m), where r is a random element, g is an approximate commutative one-way function and E is the encoding of an error-correction code. The ciphertext  is decrypted as m = D(c2 \u2212 fs(c1)), where D is the decoding of an error-correction code. The correctness of decryption is guaranteed by the approximate commutative property (gr(b) = gr(fs(a)) \u2248 fs(gr(a)) = fs(c1)) and the error-correction code. Learning with errors (LWE) problem-based PKE/KEM schemes and their variants follow such an approach.The design principle of lattice-based PKEs/KEMs follows two approaches: a trapdoor one-way function and an approximate commutative one-way function. In the first approach, a trapdoor one-way function The standardization of PQC has received substantial support from national funding agencies, such as the European Union projects PQCrypto and SAFEcrypto. The USA National Institute of Standard and Technology (NIST) started the post-quantum standardization project in 2012, organized a worldwide \u2018competition\u2019 in 2016 and plans to deliver draft standards before 2024. After two rounds of evaluation, seven schemes were accepted as the round-three candidates on 22 July 2020, of which five are lattice-based schemes. In 2017, the International organization for standardization started a study project of post-quantum cryptography named SD8.Most LWE-based PKE schemes such as Kyber and LAC follow the Lindner-Peikert framework\u00a0 up to thKyber\u00a0 is one oLAC\u00a0 uses sevet\u00a0al.\u00a0[By observing the asymmetries in lattice-based cryptosystems, Zhang and Yu et\u00a0al.\u00a0 proposedet\u00a0al.\u00a0[One important application of lattice-based PKEs/KEMs is to build authenticated key exchange (AKE), which could provide additional authentication to the established session key. There are several generic ways to construct AKE from lattice-based PKEs/KEMs. In the PKE setting, Xue and Lu et\u00a0al.\u00a0 proposedet\u00a0al.\u00a0 presenteet\u00a0al.\u00a0, which h"}
+{"text": "In CRYPTO 2019, Chen et al. showed how to construct pseudorandom functions (PRFs) from random permutations (RPs), and they gave one beyond-birthday secure construction from sum of Even-Mansour, namely  K is a uniformly random string with enough entropy, if for any input x, Random numbers are widely used in engineering practice. In particular, randomization is central to cryptography. One can generate random numbers by using physical random sources such as chaos-based  and quanIn theory, PRFs can be obtained from one-way functions ,6, but tAbout m independent n-to-n-bit keyed functions from m independent ideal random functions, its advantage does not depend on m. However, in this case the distinguisher still needs to make at least Fortunately, we can give positive answers to these questions. First, we prove that k randomly sampled from x.Second, we tweak the construction the work . A tweakFollowing the idea in , we solvx is an n-bit input, and n-bit uniformly random strings. Furthermore, we can tweak the construction t is a tweak, and x is an n-bit input.In this paper, we enhance the security of SoEM22  by showiP asx are the same as those in Equation (1). We tweak this new construction asx, and t are the same as those in Equation (2).Chen et al.  first cox (resp. the tweak t) in Equations (2) and (4) by an n-bit nonce N (resp. a message M), one can obtain two parallelizable beyond-birthday secure nonce based MACs asMoreover, from our two constructions of tweakble PRFs, we can give two nonce based MACs for variable length messages. In particular, when one replaces the input t is a tweak, and x is an n-bit input. Later, Dutta [P is a random permutation, and t, and x are the same as those in (7). Compared with Equations (7) and (8), our constructions in Equations (2) and (4) are parallelizable.Based on two random permutations i et al.  construcr, Dutta  gave a bP) asK is an n-bit key, x is an n-bit input, and 2 is a primitive element in the finite field K over n-bit uniformly random strings. However, all these two constructions were proved beyond-birthday secure only in the single-key setting. Compared with them, Equation (3) is parallelizable and can be proved beyond-birthday secure in the multi-key setting.Chakraborti et al.  construca et al.  proved tK is an n-bit key, N is an n-bit nonce, M is a variable length message, and Besides, Chakraborti et al.  also gavD who has access query to the primitive oracle P and to the construction oracle D is to distinguish which construction oracle it interacts with. Set p query-response tuples for the primitive oracle, and q query-response tuples for the construction oracle. Then, D interacts with The basic technique to prove the BBB security of our constructions is the H-Coefficient technique ,21. As aIn general, all possible transcripts are divided into bad transcripts and good transcripts. The key to use the H-Coefficient technique is to define bad transcripts in the ideal world with a low proportion. Furthermore, one also needs to show that the probability of any good transcript in the ideal world is close to its probability in the real world. After observing the transcript, the distinguisher will use this information to test whether it is compatible with P is large enough. Let P, and this idea allows that P, and P. Since For any good transcript, to prove that its probability in the real world is almost close to the one in the ideal world, it needs to show that the number of choices for unfixed maps of  idea in ,22 to coThe rest of this paper is organized as follows. In n-bit strings by s is sampled uniformly from S. For any sets q and N such that For any n-bit permutation-compatible set if n-bit permutation-compatible set n-bit permutation-compatible set For any function U and U is disjoint with x in Given two sets Definition\u00a01Let n be a positive integer. Assume that . M be any binary string with M as s bits, and Next, we briefly describe an example of h family ,23 for sRemark\u00a01.The keyed hash family One important tool used in our proofs is the H-Coefficient technique , which cr independent random permutations, and n-bit uniformly random strings. Then based on r public permutations Let m keyed functions m independent ideal random functions m independent keys. In this case, let As shown in Let (i)(ii)The security proofs in both multi-key and tweakable settings are similar. Therefore, we prove these two cases in a unified approach. For two independently and randomly sampled functions r independent random permutations. In this case, let D interacts with the construction oracle . LetN-size set S. When one samples S without replacement, N, Assume that there are The following lemma is useful in our proofs.Lemma\u00a02.Let A, B, C, and N be positive integers satisfying Proof.\u00a0In this section, we prove that the construction rm(n) in , namelyLet To show the security of Theorem\u00a01.Let m independent random keys, and randomly samples two independent random functions In the multi-key setting, one sets Corollary\u00a01.Let Corollary 1 shows that the construction Similarly, given an Corollary\u00a02.Let Assume that Finally, let Corollary\u00a03.Let Assume that for any message l is a constant, then If Proof of Theorem\u00a01.For convenience, we follow some notations in ,17 in thWe denote(B-1): (B-2): (B-3): (B-4): (B-5): (B-6): (B-7): (B-8): (B-9): (B-10): (B-11): (B-12): (B-13): An attainable transcript Otherwise, we call The proportion of all bad transcripts in the ideal world is upper bounded by the following lemma.Lemma\u00a03.Let Proof.\u00a0y is sampled uniformly and independently from i) is denoted by Here we assume that there exists no repeated items in For each  that in ,17,22. HIn Lemma 4, we show that the probability of any good transcript Lemma\u00a04.Let Proof.\u00a0Given a good transcript The next goal is to lower bound Proposition\u00a01.Let Proof.\u00a0By definition, we have We use The way to compute those in  so that Finally, by Lemmas 1, 3, and 4, Theorem 1 can be proved.\u2003\u2003\u25a1In this section, we first use one bidirectionally efficient random permutation Let As mentioned before, one can simultaneously show that the above two constructions are beyond-birthday secure in the multi-key and the tweakable settings by proving the BBB security of the \u201cunified\u201dfunction,Theorem\u00a02.Assume that Same to Corollary 1, the following corollary holds.Corollary\u00a04.Assume Similarly, given an Corollary\u00a05.Assume Denote Corollary\u00a06.Assume l is set to a constant, then Let Proof of Theorem\u00a02.In this proof, we follow some notations in ,17 for cWe also denoteNow we define four parameters for transcript (C-1): (C-2): (C-3): (C-4): (C-5): (C-6): (C-7): (C-8): (C-9): (C-10):(C-11): (C-12): (C-13): (C-14): (C-15): (C-16): (C-17): For sets An attainable transcript Otherwise, i) for Let Lemma\u00a05.Let Proof.\u00a0p permutation pairs from the interaction between distinguisher D and P. For each distinct construction query y is sampled uniformly and independently from Let The probabilities of For For y for each Finally, by combining the upper bounds on In this part, we prove that for any good transcript Lemma\u00a06.Assume that where Proof.\u00a0Given a good transcript We first introduce some subsets of Proposition\u00a02.Let Proof.\u00a0By the definition of these five subsets, it holds that We use The next goal is to lower bound P is fixed on exactly p input-output pairs from U to V. For each For each P is fixed on exactly Now, we can define two disjoint collections P such that the event Let Let Recall that Similarly, it also holds that By the definition of Set Proposition\u00a03.With notations as above, one has(i)\u00a0All sets in (ii)\u00a0Proof.\u00a0We first prove (i). From the fact Next we prove (ii) by enumerating all possible cases. For For Now we define two disjoint union sets Let Conditioned on For each Definition\u00a02.We say (1)\u00a0(2)\u00a0(3)\u00a0(4)\u00a0The next lemma shows that for each Lemma\u00a07.Assume that where Proof.\u00a0We count all possible pairs in a \u201cgood\u201d set step by step as follows. First, we decide all possible pairs for After choosing After choosing S is unordered.When we finish the choice of all possible cases for Furthermore, P is well-defined by the definition of S:S, we define two subsets of P, P is fixed on For a fixed P is fixed on p input-output pairs from U to V, P.Until now, the random permutation Note that once the items in (i)(ii)Let k, and the second condition can exclude at most Now we count the number of all possible distinct tuples Let (i)(ii)Recall that k, and the second condition can exclude at most Now we count the number of all possible distinct tuples Let m be the number of all distinct tweaks appearing in m distinct tweaks. We denote m distinct tweaks asLet (i)For each (ii)For each For convenience, Except these two conditions, each Overall, by combining , 35), , , and 3737, one hombining  and 38)(38)p\u2033(\u03c4\u00afBy combining  and 40)40), we cLower bounds on Putting , 43), a, a43), aPr[Tre=\u03c4\u00afCombing all these facts together, the proof of Lemma 6 is finished.\u2003\u2003\u25a1Finally, by Lemmas 1, 5 and 6, Theorem 2 follows.\u2003\u2003\u25a1s Even-Mansours, namelys independent random permutations, and s\u00a0n-bit uniformly random strings. Obliviously, this generalization is at least as secure as In this paper, we first prove the BBB security of the construction"}
+{"text": "Cell Death and Disease 10.1038/s41419-020-02835-w, published online 6 August 2020Correction to: The original version of this article unfortunately contained a mistake. After publication of the article, the authors noticed an unintentional error in Fig. 2f. As shown in Fig. 2f, the representative transmission electron microscopy image of \u201cOL-shSec23a\u201d was identical to the image of \u201cPOL-vector\u201d. The authors have confirmed that the image of \u201cOL-shSec23a\u201d was mistakenly presented in the original Fig. 2f. This error was caused by unintentionally misplacing the representative image. Nevertheless, this error does not change the conclusion or the discussion of the article. The authors apologize for any inconvenience this error may cause. The corrected Fig. 2f is provided below. The original article has been corrected."}
+{"text": "Whether intergroup conflict is a necessary condition for the evolution of human prosociality has been a matter of debate. At the center of the debate is the coevolutionary model of parochial altruism\u2014that human cooperation with in-group members has coevolved with aggression toward out-group members. Studies using the intergroup prisoner\u2019s dilemma\u2013maximizing difference game to test the model have repeatedly shown that people do not exhibit out-group aggression, possibly because of an inappropriate operationalization and framing of out-group aggression. The coevolutionary model predicts out-group aggression when the actor understands that it will lead to the in-group\u2019s benefit. However, in the game, such an aspect of out-group aggression that benefits the in-group is typically not well communicated to participants. Thus, this study tested the hypothesis that out-group aggression in the game would be promoted by a framing that emphasizes that attacking out-group members enhances the in-group\u2019s gain. Results of two laboratory experiments with 176 Japanese university students in total showed that such a framing did not promote out-group aggression and individuals invested more money to cooperate with in-group members only, avoiding the strategy of cooperating with in-group members to harm out-group members. These results do not support the coevolutionary model. To understand the nature of intergroup conflict, researchers from diverse disciplines, such as sociology, political science, economics, and other social sciences, have conducted studies to unravel its causes6. In social psychology, intergroup conflict has been attributed to intergroup bias8, which is the human tendency to behave altruistically or cooperatively toward members of the group to which they belong  and/or competitively or aggressively toward members of the group to which they do not belong . Various theories have been proposed as a psychological explanation of it11.Intergroup conflict, including the extreme case of war, is ubiquitous in human social life14. However, based on an evolutionary perspective15, the absence of out-group aggression in previous studies may be due to the lack of a critical condition, such as a cue that attacking the out-group would increase the benefit to the in-group. Thus, the current study introduces such a cue to an experimental game paradigm and examines whether out-group aggression emerges.Recent experimental studies in social and evolutionary psychology have revealed that intergroup bias mainly stems from in-group cooperation, and out-group aggression rarely occurs in economic games16. Intergroup bias in minimal groups\u2014in which no conflict of interest, negative stereotypes, or face-to-face interactions within or between groups exist\u2014has been consistently observed in student17 and non-student samples18 across various cultures20. Evolutionary and social psychologists have formed several hypotheses on the evolutionary origin of intergroup bias22.Intergroup bias is present even between arbitrarily created experimental groups 24, which holds that humans simultaneously acquire in-group cooperation and out-group aggression. Choi and Bowles15 used an agent-based simulation and showed that agents who displayed both in-group and out-group aggression thrived, suggesting that in-group and out-group aggression co-evolved. The validity of the CO model has been examined using various datasets, ranging from ethnohistorical and archaeological25 to experimental27, although evidence for the model has been mixed30.One of the evolutionary hypotheses explaining intergroup bias is the coevolution model (CO model)22 is the assertion of the existence of out-group aggression. Previous studies have typically employed the intergroup prisoners\u2019 dilemma\u2013maximizing difference game (IPD\u2013MD)12 to test the CO model experimentally. In the IPD\u2013MD, players are randomly divided into two groups. They receive a fixed amount of money from the experimenter. They decide how much to keep for themselves and to invest in the two pools: the within-group and the between-group pools. The total amount of money invested in the within-group pool by the members of the group is doubled and divided among in-group members equally. However, the total amount of money invested in the between-group pool is doubled; all in-group members receive an equal split and out-group members lose half the amount of the money . Specifically, any investment in the between-group pool includes harming out-group members, i.e., out-group aggression. If people are inclined to pursue self-interest, they would keep the entire amount of the initial endowment for themselves. If people are inclined only to cooperate with in-group members, they will invest their money in the within-group and/or between-group pools, without distinguishing between the two pools. Meanwhile, if people intend to cooperate with in-group members and harm out-group members, they would invest in the between-group pool that reduces the resource of out-group members.A feature that distinguishes the CO model from other evolutionary models of intergroup bias31. Nevertheless, several studies have revealed that individuals, in general, invest more money in the within-group pool than in the between-group pool35. This pattern was also observed when researchers modified the game to encourage investment in the between-group pools41. Their findings offer conflicting evidence for the CO model: the empirical evidence does not suggest that individuals simultaneously acquire the tendency for in-group cooperation and out-group aggression.The CO model predicts that individuals are inclined to invest more in the between-group pool than in the within-group pool in the IPD\u2013MDBehavioral evidence from studies using the IPD\u2013MD does not support the CO model. Nonetheless, in-group and out-group aggression not evolving together would be a premature conclusion given the uncertainty of whether out-group aggression in the IPD\u2013MD  corresponds to the operationalization of this concept in the CO model. Thus, the present study argues the vital importance of revisiting whether the IPD\u2013MD offers contextual cues to elicit out-group aggression that is arguably acquired during evolution.43, and evolutionarily acquired psychological mechanisms are often characterized as domain-specific44. For instance, the percentage of accuracy in performing logical reasoning tasks increases when the task is framed to detect norm violators46. That is, \u201ccheater detection\u201d is thought to be an adaptive reasoning system specific to the domain of social exchange47. Previous studies have identified various domain-specific psychological systems47, including theory of mind48, intuitive physics49, and folk biology50. Moreover, intergroup bias is also considered a domain-specific feature51.Human minds are thought to have domain-general and domain-specific features52, and negative attitudes toward immigrants, who are associated with the possibility of unknown pathogens54. Cues of an important social exchange situation may also facilitate cooperation in a prisoner\u2019s dilemma game56. If intergroup bias stems from an evolutionarily acquired domain-specific mindset51, then out-group aggression may be triggered by the cue of an adaptation task, such as intergroup conflict.Situational cues that imply a certain adaptive task reportedly activate a corresponding domain-specific mindset and behavior. For instance, disease priming, which induces pathogen infection threat assessment, leads to the preference for a symmetrical face, which indicates a high-functioning immune system15 described out-group aggressions predicted by the CO model as in-group-benefitting behavior. One of the main causes of intergroup conflicts is the competition for resources, such as food, territory, and mating opportunities59. The in-group-benefitting aspect of out-group aggression is an important tenet of out-group aggression in the CO model. Several evolutionary models and simulations suggest that out-group aggression might evolve when individuals gain resources from an out-group60. Moreover, people display hostile intergroup behavior when out-group resources can be acquired61; people also tend to be sensitive to threats arising from hostile intergroup relationships63. This suggests that out-group aggression is favored when it benefits the in-group.Choi and Bowles12. Thus, the in-group-benefitting aspect of out-group aggression seems to be missing in the IPD\u2013MD, and this might be why previous studies using the game have yielded inconsistent results with the CO model.However, out-group aggression in IPD\u2013MD seems to show a discrepancy with how it has been theoretically defined in the CO model. Specifically, previous studies using the IPD\u2013MD have operationalized out-group aggression as simply reducing the payoff of out-group members: investment in the between-group pool is typically framed as merely about increasing and decreasing payoffs for in-group and out-group members, respectivelyThe present research aimed to test the framing effect in an IPD\u2013MD. Specifically, if out-group aggression in an IPD\u2013MD  is framed such that it leads to financial gain for the in-group, then out-group aggression would emerge, which provides empirical support for the CO model.64, for example, the gain or loss framing on risky decision making65, attribute framing on evaluation64 and goal framing on cooperation66. Furthermore, the framing effect has been observed for evolutionary acquired domain-specific psychology67. This study examines whether out-group aggression would emerge when the contribution to the between-group pool is framed as having benefits to the in-group. Specifically, this study formulated two conditions that varied in the framing of the between-group pool: a control condition and a steal framing condition. In the former, the instructions on the two pools were identical to that of a basic IPD\u2013MD. In the latter condition, the investment in the between-group pool was framed such that it led to moving money  from an out-group to their own group.Previous studies have revealed the framing effect on human decision making31 proposed the \u201cweak\u201d and \u201cstrong\u201d hypotheses of out-group aggression based on the CO model: the amount invested in the between-group pool should be interpreted not only in terms of its absolute amount but also as a relative amount compared with the amount invested in the within-group pool, and \u201ca larger contribution to the between-group pool relative to the within-group pool may be interpreted as negative attitude toward the out-group, an equal contribution to both pools as indifference regarding the out-group\u2019s welfare, and a smaller contribution to the between-group pool as positive attitude toward the out-group\u201d13 (p. 2). Based on the CO model, a negative attitude toward the out-group can be expected to lead to aggressive behavior in the steal-framing condition. Therefore, the present study set the \u201cstrong\u201d hypothesis (hypothesis S) as follows:The current research tested two hypotheses regarding the framing effect on out-group aggression. B\u00f6hmIn the steal condition, individuals would contribute more to the between-group pool than to the within-group pool.68, steal framing may nonetheless lead to a less positive attitude. Therefore, the current study set the \u201cweak\u201d hypothesis (hypothesis W) as follows:Even if hypothesis S is not supported, as in previous studiesIndividuals in the steal condition would invest more money in the between-group pool than those in the control condition.69. Preference tends to be stable regardless of the actions and reactions of an interacting partner. Meanwhile, belief refers to an expectation about others\u2019 behavior. If the framing affected the investment in an IPD\u2013MD, then whether the effect would be attributable to changes in preferences and/or beliefs merits investigation.The research aimed to further explore how the steal framing would influence out-group aggression. Framing effects in experimental economic games can be divided into effects of changes in preference and beliefStudy 1 was reviewed and approved by the ethical committee at Kochi University of Technology. In accordance with the Declaration of Helsinki, all participants provided written informed consent.The study was advertised in a large student-participant pool at Kochi University of Technology, and 73 participants (34 women) voluntarily participated in the current study. Their mean age was 19.53\u00a0years (SD\u2009=\u20091.12).Upon arrival at the experimental lab, participants were given a participant ID and instructed not to share it with anyone. They were then escorted individually to an experimental cubicle, in which they completed the study on a computer without the physical presence of others. Once they were seated, they received instructions about the IPD\u2013MD. Participants were first randomly divided into two groups, and each was given 600 JPY by the experimenter. Next, they had a one-shot interaction in which they each decided how much of the 600 JPY to keep for themselves and to invest in the within- and inter-group pools. The amount invested in the within-group pool was doubled by the experimenter and the total was distributed equally to all members of the participants\u2019 own group.Participants were randomly assigned to one of the two framing conditions  and received different instructions on the between-group pool. In the control condition, they were informed that the total amount invested in the pool would be doubled and then distributed equally among in-group members regardless of their contribution. Moreover, they were told that out-group members would lose half the amount of money that in-group members received. The only difference between the control and the steal framing condition was whether the money invested in the between-group pool increased the in-group resource or decreased the out-group resource, as per the experimenter. For the control condition, the instructions mentioned that the experimenter increased the in-group\u2019s money and decreased the out-group\u2019s money. Specifically, in a game between Groups X and Y, each of which has five participants, if Participant A from Group X invests 100 JPY in the between-group pool, the experimenter doubles the amount of money and distributes it equally among the five participants. Therefore, all participants in Group X, including participant A, would receive 40 JPY each. Simultaneously, the experimenter deducts 20 JPY from each of the five participants in Group Y. Meanwhile, in the steal condition, the amount of money invested in the between-group pool moves from the out-group to the in-group. For example, if Participant A of Group X invests 100 JPY in the between-group pool, all members of Group X, including A, would receive 20 JPY each. They receive an additional 20 JPY that is taken from out-group members. In other words, the amount of money deducted from Group Y is given to Group X. Thus, the payoff structure of each individual was identical in both conditions. The word \u201csteal\u201d was not used in the instructions including the steal framing condition. The participants were told that all of them would decide simultaneously and that they could complete the game only once. It was also emphasized that the rules of the game were the same for out-group members. After reading the instructions about the IPD\u2013MD, the participants input their decisions on a computer screen.The participants then completed a post-experiment questionnaire. They first answered the comprehension and manipulation check questions. The tool contained three comprehension check questions: (C1) \u201cWhose money does the investment in the within-group pool increase?\u201d (C2) \u201cWhose money does the investment in the between-group pool increase?\u201d and (C3) \u201cWhose money does the investment in the between-group pool increase?\u201d They selected one of the following options: \u201cincrease (decrease) the money of my group as a whole,\u201d \u201cincrease (decrease) the money of others\u2019 group as a whole,\u201d \u201cincrease (decrease) the money of both groups,\u201d \u201cincrease (decrease) the money of neither group,\u201d or \u201cdon\u2019t know.\u201d For the manipulation check, they were asked the following question: \u201cWho received the money subtracted from the members of the other group owing to the investment in the between-group pool?\u201d They answered this with one of the following options: \u201cthe money went to my group,\u201d \u201cthe experimenter collected the money,\u201d or \u201cI don\u2019t know.\u201dAfter the comprehension and manipulation checks, the participants inferred how other members of their own group and the other group had completed the game. Specifically, they were asked how much other members of their ingroup and outgroup had kept and invested in the within- and between-group pools, in units of 50 JPY. For exploratory analyses, the study administered items measuring identification with the in-group and out-group and social dominance orientation (see ps\u2009>\u20090.05). The participants\u2019 understanding of the rules of the game was satisfactory. The correct response rate for the manipulation check was 94.5%. In the control condition, 89.2% of the participants answered correctly, and 10.8% answered incorrectly or chose \u201cI don\u2019t know.\u201d All participants in the steal condition answered correctly. The correct response rate between the two conditions showed no significant difference . As most of the participants correctly answered the comprehension and manipulation check questions, we did not conduct data exclusion. Data exclusion based on these questions did not change results in a meaningful manner \u2009\u00d7\u20092 (pool: within- vs. between-group) mixed ANOVA. The results showed a significant main effect of pool, F\u2009=\u200914.33, p\u2009<\u20090.001, \u03b7p2\u2009=\u20090.17. The main effects of framing \u2009=\u20090.54, p\u2009=\u20090.465, \u03b7p2\u2009=\u20090.01) and the interaction effect \u2009=\u20090.004, p\u2009=\u20090.953, \u03b7p2\u2009<\u20090.001) were insignificant.On average, participants kept 397.26 JPY SD\u2009=\u2009191.10), invested 147.95 JPY (SD\u2009=\u2009171.28) in the within-group pool, and invested 54.79 JPY (SD\u2009=\u2009103.47) in the between-group pool. The means and standard deviations of their investments under different conditions are shown in Fig.\u00a091.10, int(71)\u2009=\u20090.74, p\u2009=\u20090.46, d\u2009=\u20090.17). In the steal condition, the participants invested a significantly lower amount in the between-group pool than the within-group pool \u2009=\u20092.75, p\u2009=\u20090.009, d\u2009=\u20090.68). Therefore, hypotheses S and W were not supported. Using G*Power 3.169, sensitivity analysis of a two tailed t-test (power\u2009=\u20090.8) for hypothesis S revealed that the detectable effect size was 0.665 and that for hypothesis W was 0.48. This suggests that the observed effect sizes, especially for hypothesis S, were not big enough for the current study to detect.The mean amount of investment in the between-group pool was 45.94 JPY (SD\u2009=\u2009100.95) in the control condition and 63.89 JPY (SD\u2009=\u2009106.64) in the steal condition, with no significant difference between them \u2009=\u200929.26, p\u2009<\u20090.001, \u03b7p2\u2009=\u2009. 29. The main effect of framing \u2009=\u20091.90, p\u2009=\u20090.173, \u03b7p2\u2009=\u20090.03) and the interaction effect \u2009=\u20090.16, p\u2009=\u20090.690, \u03b7p2\u2009=\u20090.002) were not significant. Thus, the steal framing did not alter the expectation about how other in-group members would complete the game.Although the effect of the framing manipulation was not significant, we examined the participants\u2019 inferences about other in-group and out-group members\u2019 investment decisions \u2009=\u200923.15, p\u2009<\u20090.001, \u03b7p2\u2009=\u20090.25. The main effect of framing \u2009=\u20091.09, p\u2009=\u20090.299, \u03b7p2\u2009=\u20090.02) and the interaction effect \u2009=\u20091.55, p\u2009=\u20090.217, \u03b7p2\u2009=\u20090.02) were not significant. This indicates that the framing did not alter the behavioral expectation of out-group members.Further, the A 2 (framing)\u2009\u00d7\u20092 (pool) mixed ANOVA on the estimated amount of money invested by out-group members revealed a significant main effect of pool, Both hypotheses were not supported in Study 1: results showed that steal framing did not increase out-group aggression in IPD\u2013MD. Thus, even when out-group aggression was framed as being beneficial for the in-group, the CO model was not empirically supported.68; except for Halevy et al.40. As per the sensitivity analysis, the hypotheses were not supported, possibly due to the small sample size. Thus, we conducted Study 2 with more participants and re-tested the hypotheses.Study 1 had fewer than 40 participants in each condition, smaller than the number of participants recruited in the majority of studies that used the IPD\u2013MDStudy 2 was reviewed and approved by the ethical committee at the Kochi University of Technology. In accordance with the Declaration of Helsinki, all participants provided written informed consent.Study 2 intended to recruit 50 participants for each condition. A total of 107 Japanese undergraduate students signed up for the study . Their mean age was 18.87\u00a0years (SD\u2009=\u20091.18). Participants were recruited from a large participant pool at Kochi University of Technology with an emphasis on monetary incentives. The procedure and materials were identical to those in study 1.ps\u2009>\u20090.05). The correct response rate for the manipulation check item was 91.3%. In the control condition, 83.3% of the participants answered it correctly, and 16.7% answered it incorrectly or chose \u201cI don\u2019t know.\u201d All (100%) the participants answered correctly in the steal condition, and the difference was significant (Fisher\u2019s exact test: p\u2009=\u20090.003). The exclusion of participants in the control condition who failed to answer the questions correctly did not change the results of subsequent analyses in a meaningful way. Thus, results without data exclusion are reported here \u2009=\u20097.72, p\u2009=\u20090.007, \u03b7p2\u2009=\u20090.07) and a significant interaction effect \u2009=\u20094.06, p\u2009=\u20090.047, \u03b7p2\u2009=\u20090.04). In contrast, the main effect of framing was not significant, F\u2009=\u20092.06, p\u2009=\u20090.154, \u03b7p2\u2009=\u20090.02. Post hoc comparisons using the Holm method revealed that the amount of investment in the within-group pool was higher in the steal condition than that in the control condition (p\u2009=\u20090.014), but the difference in investment in the between-group pool between the two conditions was not significant (p\u2009=\u20090.518). In addition, the amount of investment between the within- and between-group pools in the control condition did not significantly differ (p\u2009=\u20090.581). Meanwhile, the difference in the steal condition was significant (p\u2009=\u20090.001).The participants, on average, kept 352.43 JPY (SD\u2009=\u2009202.84) for themselves and contributed 156.31 JPY (SD\u2009=\u2009170.31) and 91.26 JPY (SD\u2009=\u2009150.72) to the within- and between-group pools, respectively \u2009=\u20090.68, p\u2009=\u20090.497, d\u2009=\u20090.13). In the steal condition, the amount invested in the between-group pool was significantly lower than that in the within-group pool \u2009=\u20093.18, p\u2009=\u20090.003, d\u2009=\u20090.70). Therefore, hypotheses S and W were not supported. Sensitivity analysis of a two tailed t-test (power\u2009=\u20090.8) for hypothesis S revealed that the detectable effect size was 0.558 and that for hypothesis W was 0.408. This suggests that the observed effect sizes, especially for hypothesis S, were not big enough for the current study to detect.The mean amount of investment in the between-group pool was 100.93 JPY (SD\u2009=\u2009156.76) in the control condition and 80.61 JPY (SD\u2009=\u2009144.63) in the steal condition, with no significant difference between them \u2009=\u200915.32, p\u2009<\u20090.001, \u03b7p2\u2009=\u20090.13) and the interaction effect \u2009=\u20095.36, p\u2009=\u20090.023, \u03b7p2\u2009=\u20090.05) were significant. Meanwhile, the main effect of framing was not significant, F\u2009=\u20092.8, p\u2009=\u20090.097, \u03b7p2\u2009=\u20090.03. Post hoc pairwise comparisons with the Holm method revealed that the level of inferred investment in the between-group pool was not different between the two framing conditions (p\u2009=\u20090.52). In contrast, the inferred investment in the within-group pool in the steal condition was significantly higher compared with that of the control condition (p\u2009=\u20090.005). These results showed that although steal framing increased the inference of cooperation among in-group members, it did not increase the inference that other in-group members would attack out-group members.We examined the participants\u2019 inferences about other in-group and out-group members\u2019 investment decisions \u2009=\u20097.19, p\u2009=\u20090.009, \u03b7p2\u2009=\u20090.07) and pool \u2009=\u200915.35, p\u2009<\u20090.001, \u03b7p2\u2009=\u20090.13) were significant. The interaction effect was not significant \u2009=\u20093.7, p\u2009=\u20090.057, \u03b7p2\u2009=\u20090.04). Thus, steal framing generated an inference that out-group members would no longer pursue self-interest, but this did not mean that they would invest more in out-group aggression.The same ANOVA on the inferred investment out-group members revealed that the main effect of framing  does not promote out-group aggression.Previous studies using experimental economic games, such as the public goods game, have shown that framing can change behavior68. These findings support another evolutionary model of intergroup bias, namely, bounded generalized reciprocity (BGR)74. The BGR model holds that in-group bias stems from cooperation with in-group members rather than aggression toward out-group members75. The BGR model assumes that people have an intuitive belief that indirect reciprocity exists within the group, and that acting cooperatively toward in-group members is of vital importance to establishing a good reputation. However, individuals do not suppose that out-group members are part of the system of indirect reciprocity, and consequently, they are not motivated to display altruistic behavior to earn a reputation not only with respect to out-group members but also strangers. In other words, the BGR model assumes that humans do not act altruistically toward out-group members, not that they proactively attack them. Although the current study did not aim to validate the BGR model, the results are consistent with the model.In the current study, regardless of the framing condition, the amount of investment in the between-group pool was not higher than that in the within-group pool, consistent with previous findings77. For example, B\u00f6hm et al.36 showed that, although not the framing manipulation, the amount of investment in the between-group pool increases when it can prevent attacks from the out-group. Additionally, the framing instruction used in Weisel and Zultan68, which supports the \u201cweak hypothesis\u201d in IPD\u2013MD, seems to have an in-group defense-like phrase. Further research could investigate whether out-group aggression can occur by setting framing characterized by a defensive function.Out-group aggression can emerge when it can defend an ingroup78 but also for the conflicting empirical findings80. These do not necessarily mean, however, that humans have not evolutionarily acquired any aggressive tendency toward out-group members. There may be several types of out-group aggression76 that are possibly suited for the CO model, for example, preemptive strikes81 and proactive or reactive aggression82. A theoretical and empirical examination of the types of aggression directed toward out-group members is necessary.The CO model has been criticized not only for its theoretical assumptions84, the effect size of d\u2009=\u20090.17 obtained in study 1 was relatively small. Additionally, the effect size of d\u2009=\u20090.13 obtained in study 2 was in the opposite direction of study 1, and the combined effect size of study 1 and 2 was close to zero (d\u2009=\u20090.04, see There are other two limitations. First, framing manipulation was used to emphasize that out-group aggression increases the benefit of the in-group, but it is not clear whether the framing changed the participants\u2019 perception as intended. That said, participants in the steal framing condition might see the investment in the between-group pool as a means to decrease the benefit of the out-group rather than increase the benefit of the in-group. In that case, they might refrain from investing money in the between-group pool because it would be socially undesirable. Second, as per the sensitivity analysis, the effect may not have been detected because the sample size was small. Compared to the effect sizes obtained in previous meta-analyses on the gain\u2013loss framingSupplementary Information."}
+{"text": "In intensive transactional analysis psychotherapy (ITAP), intensity is obtained with both technical expedients and the relational manner with the patient. In ITAP, the therapist modulates pressure and support commensurately to the patients' ego strength. In the present article, we contrast two clinical cases of young adults in which ego strength produced different therapy outcomes and processes. We present excerpts of the psychotherapy process that illustrates technical aspects of ITAP as well as the therapist's attitude that we describe as holding. We show quantitative therapy outcomes consisting of effects size values of changes in Clinical Outcome in Routine Evaluation\u2014Outcome Measure scores in baseline, treatment, and follow-up phases and qualitative outcome evaluated with the Change Interview at the end of the therapy. In the patient with high ego strength, we observed a rapid improvement and a complete recovery at the end of the therapy, whereas the results of the patient with low ego strength were less consistent . We conclude that quantitative and qualitative outcome data, together with process observations, are required to have a complete picture of therapy effectiveness. Moreover, we conclude that qualitative ego strength is not a limitation for the use of expressive therapy such as ITAP, but rather, it is an important variable that should be considered to dose confrontations and support. Intending to increase intensity in therapeutic intervention, intensive transactional analysis psychotherapy (ITAP) is short-term psychodynamic psychotherapy that integrates transactional analysis Berne,  with briimpulse is a manifestation of the Id  are explored, comparing them with relational experiences with the therapist in psychotherapy sessions (therapeutic relationship) and with past relationships in which repetitive relational patterns may have been formed as an effect of traumatic experiences. Thus, in the ITAP model, psychic functioning is described as interconnections of impulse, anxiety, and defenses, which have originated in past relationships and which can be enacted in here-and-now relationships (current relationships and/or therapeutic relationship) . CORE-OM global scores allowed the classification of the patients on the basis of their distress level: healthy (score <0.6), low-level (score between 0.6 and 1.0), mild (score between 1.0 and 1.5), moderate (score between 1.5 and 2.0), moderately severe (score between 2.0 and 2.5), or severe (score >2.5). Moreover, four subscales allowed the evaluation of four outcome variables: well-being, psychological problems , functioning , and risk (risk to self and others). The Italian version of the CORE-OM shows good acceptability, internal consistency, and convergent validity . The CORE-OM is a widely used scale for the routine evaluation of psychotherapy outcomes ; (b) how likely these changes would have been without therapy (from 1 = unlikely to 5 = likely without therapy), and (c) how important he/she feels these changes to be (from 1 = slightly important to 5 = extremely important).Psychotherapy outcome was evaluated qualitatively through The Change Interview, a semi-structured interview that provides qualitative descriptions from patients of perceived change reported at the end of the therapy  diagnosis was provided for each patient, and they were asked about the goals of their therapy before starting the treatment. For both patients, this was the first experience of psychotherapy, and they were not treated pharmacologically.well-integrated structure according to the OPD-2 diagnosis. She was a 25-year-old female student. In her therapy, she focused mainly on her relational difficulties. She reported having difficulties in regulating her emotions with others. On the one hand, she suffered because sometimes she was aggressive with others, and then, she felt guilty as a consequence of this aggressiveness. On the other hand, she perceived not being free to express herself with her family, and she wanted to feel free to make her own decisions. She also suffered from anxiety and loss of concentration. In addition to these emotional difficulties, she wanted to cope with the loss of her dog (which was living with her ex-partner). With regard to the diagnosis, she saturated the DSM-5 criteria for dysthymic disorder and generalized anxiety disorder  and clinical training as psychotherapists and three advanced students. Two of the experienced researchers also had specific training as psychotherapy supervisors. The students participated in research team/clinical supervision groups, and they were also involved in data collection and analyses.Patients were recruited from a waiting list of students who had psychological or relational difficulties and were voluntarily referred to therapy as part of a larger clinical study. The patients were voluntary students attending the same university as the research team, but they had no direct connection with the research team. The Ethical Committee of the University of Padua approved the research protocol. Before entering treatment, all patients received detailed descriptions of the research protocol, and they were informed that they were free to leave the research protocol at any moment without consequences for the continuation of their therapy. In the informed consent, a specific section for the use of video-recorded sessions was included, and it was specified that patients would not be identifiable on the basis of the material presented in scientific publications.Baseline included 5 weekly evaluations in 5 consecutive weeks before the beginning of the therapy ; (b) treatment included weekly evaluations realized immediately before each session ; (c) follow-up included evaluations realized at 1, 3, and 6 months after the end of the therapy. For each assessment, patients filled out the CORE-OM in the clinical psychology laboratory and in the presence of an external research assistant. During the first follow-up, a researcher carried out the Change Interview to collect qualitative data concerning patients' subjective perception of changes. Patients were informed that the therapist had no access to any research data provided.For the evaluation of psychotherapy outcome time series, longitudinal data were collected in three different phases: (a) The treatment followed the procedures described in the ITAP manual  were dropped unless they had specific communication value. In brackets, we reported the position in the intrapsychic triangle  and interpersonal triangle . Regarding the therapist's interventions, the positions to which the therapist moves are preceded by the symbol \u2192 . In few cases, interventions escape from triangle classifications. Thus, we provided few additional categories. \u201cAw\u201d refers to therapists' interventions aimed at stimulating aspects of awareness in the patients (\u2192Aw) and the patient's responses indicating the acquisition of aspects of awareness (Aw); \u201cE\u201d refers to empathic interventions; \u201cAl\u201d refers to therapists' interventions aimed at the alliance. According to the consensual qualitative research method : she recently encountered a dog similar to the one she had to leave with her ex-boyfriend and became sad. The therapist aims to bring out the impulses activated in this episode by comparing the patient's defensive modes (D) in the here-and-now of therapy (T) to the emotions related to the loss of the dog (I). The patient is able to achieve a greater awareness regarding her tendency not to face conflict situations by giving in to the will of others (such as leaving her beloved dog to her ex-boyfriend).What did you feel in that moment? [\u2192 I/C]T: I don't know how to express it, I mean it was really a strange thing\u2026a lump in my throat\u2026 [A/C]M: How was this lump in the throat for you? [\u2192 A/C]T: Nice and bad\u2026Nice because it was nice, I mean, ah, it took my back to another world in a moment \u2026 And bad because once it's finished you think in any case \u201cWho knows what will happen to my dog\u2026\u201d [D/C]M: As if you'd realized that that scene isn't there anymore?\u2026 How did you feel in that moment? [\u2192 I/C]T: Ah, the darkness takes you [I/C]M: You mean, this scene was sad? [\u2192 I/C]T: Yes, yes, also. Even now that I'm talking about I feel the darkness returning, yes \u2026 [I/T]M: Yes, but you're laughing a lot [\u2192 D/T]T: Ah I know, well, unfortunately it's a bad habit of mine, laughing [D/T]M: No, I have the impression that there's a part of you that's sad, and another part that says \u201cNo, no, come on, everything is ok, laugh about it\u201d [\u2192 D/T]. But a part of you is sad [\u2192 I/T]T: Ah yes, I can't get rid of it, I mean I can't get rid of a piece of my life, get rid of some memories. No? [Aw/C]M: But the memories are sad\u2026 [\u2192 I/T]T: Ah yes, but, but you've got to deal with them [D/T]M: And how do you deal with them? IF you deal with them by laughing and then they come back [\u2192 D/T].T: Ah\u2026 I don't know another way\u2026 I mean the time, I've always said \u201cIn time things will pass\u201d, sure enough time has passed a lot, ah, I mean that \u2026 [D/T]M: Yes of course. I was concerned about the part, actually, that is worried \u2026that then becomes darkness \u2026 [\u2192 A/T]T: I hope not. I mean, I hope that\u2026 this doesn't happen, I hope so. I mean every day of my life \u2026 to do things that make me so satisfied that I don't think of anything else, no? [D/T]M: I have the impression that not thinking about it creates a, sort of, barrier for a bit [\u2192 D], then something bigger comes along \u2026 [\u2192 I/T]T:\u2026Yes, yes, I've thought about this \u2026 [Aw/T]M: the barrier collapses and everything that wasn't there before comes along \u2026 [\u2192 D/T]T: \u2026Yes, yes, it's true \u2026 [Aw/T]M: And I'm worried about this, because the barrier of doing stuff so as not to feel what there is over here [mimes a barrier with the hand], it holds up a little, a little and then by dint of doing this you get all of the manifestations , and then, as is natural, it collapses. And when it collapses it's a month and a half, two, of darkness. [\u2192 D/T]T: \u2026What are you in contact with? [\u2192 I/T]T: I don't know what, I don't know what this thing inside of me is, I'm trying to bring out something that's inside me that I don't know. [D/T]M: On a cognitive level yes, I have the impression that you don't know. On an emotional level how are you, when you think of these things? Actually, when do you feel this thing?\u2026Let's try to remain there, to listen to what's there, behind that barrier that I was talking about before \u2026[\u2192 I/T]T: I don't know, because I was different, I was like other people, as if I was talking about other people, a lot of things have changed, so I can no longer reflect myself in what I was. I have really changed personality so I can't remember anything at all. [D/T]M: [Silence] What is it that's coming back then\u2026? [\u2192 I/T]T: The sensations come back, of nostalgia. I mean, it's the emotions that come back up, nostalgia, anger, it's not the memory\u2026 The emotions, I mean the impotence.[I/T]M: What are you feeling now, the impotence?[\u2192 I/T]T: Yes. [I/T]M: Is that what you couldn't get a handle on? [\u2192 I/C]T: Yes, exactly maybe the impotence of not having - I as I do generally - I mean that I let things go rather than assert myself on things, I don't assert myself on things \u2026 Because I don't want to get to a discussion\u2026 [I/C]Like when S. says to me \u201cOh, the dog's staying with me, because I can provide it with more things\u201d\u2026 [Aw/C]M: And you want that dog?[\u2192 I/C]T: Yes, I want it [I/C], but I can't, I made this choice [D/C]\u2026M: \u2026Yes, yes\u2026 on a cognitive level it seems very clear: \u201cI chose this\u201d.T: Ok, on an emotional level. Ah no, because clearly it wasn't good for me.M: And that thing there comes and returns, cyclically [\u2192 I/C].T: \u2026now I am starting to reason in a much more selfish way [Aw/C]M: [the patient talks about how recently she is feeling the necessity to assert herself in various contexts] \u2026Ah there you are, if you could think in a selfish way when you're with L?[\u2192 I/C]T: Ah I'd like to give him a slap it's different [I/C]\u2026but there as well, what's the point of it\u2026?[D/C]M: There's the sense of listening to what you feel. That's it, what you feel. As a fantasy, if you could what would you do to this L?[\u2192 I/C]T: Ah, I'd gladly give him a few slaps [I/C]M: \u2026[the patient stimulated by the therapist expresses her anger through the use of fantasies]You knocked it down, and you knocked it down, and you knocked it down\u2026 and now, luckily, it's coming up, it's coming up, it's coming up\u2026T: I had enough\u2026That strength I\u2026 I've always had it inside.[Aw/P]M: Very good, meanwhile let's try to understand what there is underneath it, that reservoir that stayed there and let's start to knock it out, and to process it\u2026Have you seen that we've caught our fish: you are very angry with him still \u2026 Can you accept it?T: Yes![Aw/T]M: In the therapy extract, we can observe some elements that indicate a good level of ego strength in the case of Maria. First of all, it can be observed that anxiety is present at manageable levels and is mainly discharged at the level of the striated muscles . As typically happens with this type of manifestation of anxiety, the defenses are of an evolved type and concern the recognition of emotional aspects on a cognitive level with an avoidance of the actual emotion (the patient smiles while telling a sad episode so as not to come into contact completely with the sadness) or the repression . Finally, we see that Maria manages to understand the therapist's interventions without getting too anxious and easily acquires aspects of awareness.This excerpt is taken from the third session. The patient starts with an episode from his own past (P) in which he recounts a situation where he had been very frightened, and his fear had not been accepted sufficiently. The patient easily links the terror he felt in P with the terror he currently feels during his anxiety crisis (C). The therapist encourages Fabio to focus on his emotions in recalling that episode in the here-and-now of the session (T), helping the patient to recognize some defensive tendencies and to get in touch with his own impulses of sadness (I).I was on my way home and there was someone there, I met someone who was like, \u201cHey there, who are you?\u201d Ah I got scared for a moment no, pretty scared for a child\u2026Then this person I saw - then maybe I imagined - that he was following me from behind, so I had a moment and started running. [I/P]F: T: How scary![\u2192 I/P]Oh yes quite so\u2026 there was nothing there, it was in the middle of nowhere, to get home, that is there are only fields and so I was alone there\u2026 And then I was like this [indicates a child's height], the other guy was like this [indicates an adult's height]\u2026 [I/P]F: T: And so you were very scared [\u2192 I/P]F: Yes, exactly [I]T: And so every time you went that way, you relived that fear? [\u2192 I/P]F: Yes pretty much [I]T: Have you ever had a chance to talk to anyone about that moment?\u2026 was your fear somehow acknowledged? [\u2192 I/P]F: Yes, it was acknowledged, but I couldn't find a solution. So\u2026.T: Ok.My dad told me, he said, \u201cLook, don't worry about it\u2026\u201d I mean, a reassurance that's a little too rational, that's all.F: He didn't listen to you. (he hugs his belly)T: F: Exactly.That kid was still worried [I/T].T: Yes, terrified [I/T]F: Terrified. By others?[\u2192 I/C]T: Well, in this case yes, well now that you mention it this terror maybe with the panic attack comes back a bit when\u2026 for example in a deserted street like I told you\u2026 [I/C].F: Is this memory useful to you? I mean, this connection that you're making? [\u2192 Aw]T:  Well, it's useful because I see a similarity between the terror felt in both cases. [I]F: \u2026The terror of the child being left alone with maybe someone following him in the fields\u2026 \u2026 [I/P]T: Yes. (I/P)F: And terror of the adult who, on the other hand, how can I put it, connects, links up\u2026 \u2026[\u2192 Aw of the link between I/P and I/C]T: Yes.F: with the terror of the child. [Aw of the link between I/P and I/C]T: F: Because it is the same terror in those moments when the panic attack\u2026 in fact I feel like a child\u2026 I feel in the middle of the fields, lost, small\u2026 helpless even. [Aw]T: Small, helpless, scared.F: Scared.\u2026Where are we now, out of these things? [\u2192 I/T]T: in this moment, sadness [I/T]F: as if we had also evoked the sadness of when you were a child\u2026 That child was feeling so many things [\u2192 I/T]T: \u2026Yes, quite\u2026 I've always made things complicated. [D/T]F: You're judging yourself [\u2192 D/T]T: Yeah, my parents told me I was complicating things [D/P]. And now I just remembered that around elementary school - these episodes are all around elementary school - I had to go\u2026 [D/T]F: Can I stop you for a moment? [\u2192 Al]T: Yes. [Al]F: I think it's useful to stop, otherwise we'll move on to more cognitive aspects\u2026 [\u2192 Al]. Remember that it' s all right, it's all right. [\u2192 E]\u2026 But it's like we're jumping a little bit away from these emotions [\u2192 D/T]T: Ah ok [Al]F: It's not a judgment, no one is to blame, it's okay. [\u2192 E]. But I think it's useful for you to stay on these emotional issues that have emerged very clearly and very strongly [\u2192 Al], otherwise there's a chance we'll do it the way we did it  [\u2192 D/T]T: Oh, okay, I get it, yeah, you mean, just distance yourself right away\u2026 [Aw/T]F: Distance yourself immediately. Instead we found out that that child was angry, scared, feeling helpless [\u2192 I/P]\u2026 Now you're feeling these emotions here [\u2192 I/T]T: Ah [sigh] [A/T]F: Ah [sigh] [E/T]T: Ah, it's not simple\u2026[A/T]F: It's not simple [E/T]. As far as I can stand them, how can I say this, I'm there, I'm with them, it's a way to be with that child too\u2026we here maybe have the chance to be with that child. IfT: not, we'll leave him alone one more time. [\u2192 Al].Ah ah, ok. Yes that's ok. [Al]F: Mm? Do you have it, are you seeing it?T: Yes.F: And what's it like?T: I don't know, I'm picturing him locked in a corner with some bars\u2026 crying. [I/T]F: Ah, ok. Mm. And as you see him, what can you do? Now, that you're older. [\u2192 I/T]T: \u2026 [the therapist explores a possible Impulse]Well, I'd give him a hand and caress him, let's say\u2026 [I/T]F: Does he feel it? [\u2192 I/T]T: Yes. [I/T]F: And how is he? [\u2192 I/T]T: Ah, warmer, more relaxed [I/T]F: Listen to yourself for a second. Don't use words, there's no need to explain [\u2192 I].T: Ok. [Silenzio] [I]F: Listen to yourself. How's your breathing, how's your body, how is this sensation of warmth? [\u2192 I]T: Calmer, more relaxed. With fewer things running through my mind [I/T]F: Calmer, more relaxed. The warmth calms. [\u2192 I/T]T: Yes. Ah yes, the thoughts as well. [Connects I and D]F: It calms your thoughts as well.T: Yes.F: So even the thought of that child with the hand calms you down.T: Ah yes. Pretty much, yes. But my ears are ringing [A/T]F: Yeah. Okay. All right. It's okay, it's okay. We're working on some important stuff\u2026 [E/T]T: Ah ok [E]F: So there is a realignment of your structure right now [\u2192 Aw]. Do you follow me? [\u2192 Al]T: Ah ok. Yes yes yes yes yes. Yes yes yes yes \u2026.[A/T] F: Have your ears started ringing? [\u2192 A/T]T: My ears have started ringing [A/T]F: Was there also a feeling of movement a little bit inside? I mean 'oops'! [\u2192 A/T]T: Yes, exactly yes [Aw].F: You' re becoming aware of yourself in a different way from the way you were before, you're in contact with a part of yourself, emotionally and physically, as you weren't before\u2026[\u2192 Aw].T: \u2026In this second therapy extract, we can observe certain elements that are indicative of a low level of ego strength in Fabio's case. It can be noted that the anxious manifestations also involve cognitive-perceptive aspects (ringing in the ears), as well as those concerning the striated muscles (being stuck to the chair) Abbass, . To dealvs. treatment phases, baseline vs. follow-up phases, and treatment vs. follow-up phases  of change in CORE-OM scores  from baseline mild range of distress. As shown in mild range to the healthy range of distress. Thus, CORE-OM scores show a complete recovery for Maria.Maria's CORE-OM scores at baseline were in the clinical range, except for the functioning score that was in the normal range , as well as in subscales well-being (ES = 2.44) and psychological problems (ES = 2.99). A large ES was found for the functioning subscale (ES = 1.28), and a medium ES was also observed for the risk subscale (ES = 0.75).This description was confirmed in statistical analysis. In \u201cbaseline vs. follow-up\u201d comparison.Similarly, in \u201cbaseline vs. follow-up\u201d comparisons, very large ESs were observed in CORE-OM total scores (ES = 2.88), in the well-being (ES = 4.03) and psychological problems subscales (ES = 1.01), and a large ES was observed in the functioning subscales (ES = 1.01). Only a small ES was found in the risk subscale (ES = 0.75) for the \u201cbaseline healthy to the low-level range of distress in the follow-up phase . In line with this description, non-relevant changes were observed in the \u201ctreatment vs. follow-up\u201d comparisons, indicating the maintenance of achieved CORE-OM scores.The described improvements were maintained in follow-up evaluations, except for the risk subscale score that increased slightly in the last follow-up (6 months), influencing the global score of distress that moved from the low-level to the mild range of distress. A partial recovery of previous scores was achieved after the 18th session, but it remained in the mild range of distress.Although Fabio reported severe symptomatology and the therapists evaluated his personality as being low structured, Fabio's total scores compared with Italian normative data were within the nonclinical range at the beginning of the therapy. As shown in The peculiar evolution of this case was also reflected in the statistical evaluations see . In \u201cbasIn \u201cbaseline vs. follow-up\u201d comparisons\u2014which is less influenced by fluctuations in the score during the therapy\u2014a large ES indicating improvement was observed for the well-being subscale (ES = 1.08). However, very large and large deteriorations in ES were observed, respectively, for the functioning (ES = \u22121.62) and risk subscales (ES = 1.23), whereas non-relevant changes were observed in the psychological problems subscale and in the CORE-OM global score.vs. follow-up\u201d comparisons where a medium ES was obtained for the CORE-OM global score (ES = 0.57), the well-being subscale (ES = 0.84), and the psychological problems subscale (ES = 0.54), whereas a medium ES of deterioration was maintained for the risk subscale (ES = \u22120.54), and non-relevant changes were observed for the functioning subscale.The partial recovery achieved after the 18th session was maintained in follow-up evaluations. This recovery can be statistically observed in the \u201ctreatment Although quantitative data indicated a positive outcome for Maria and a negative outcome for Fabio, the qualitative evaluation of the psychotherapy outcome realized using the Change Interview method accounts for a very positive outcome for both patients. They reported several changes classified as very important and extremely important, and they considered many such changes as being unlikely without the therapy. Interestingly, most of the reported changes are in line with the declared aims of ITAP. They concern interpersonal relationships , emotion regulation , and the improvement of self-representations achieved through contact with self-relevant impulses. Detailed results of the Change Interview are reported in what works for whom approach, our final aim was to reflect on the possibility that intensive interventions may be differently efficacious in helping patients with different levels of psychic structure integration.In the present study, we contrasted two clinical cases of patients with different levels of ego strength (or different levels of psychic structure integration) treated with ITAP, a new psychotherapy approach that aims toward the intensification of therapist intervention through the integration between transactional analysis and brief psychodynamic approaches. Following the If we consider ITAP outcomes evaluated using quantitative measure, CORE-OM data account for clearly different outcomes in the clinical cases analyzed in the present study. Maria\u2014the patient with a well-integrated psychic structure\u2014obtained a complete recovery, with a rapid improvement in early sessions and the maintenance of these results in follow-up evaluations. This pattern of change corresponds to a typical trajectory of change previously described in the literature  for patients with less ego strength.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The studies involving human participants were reviewed and approved by Ethical Committee Psychology University of Padua (number 1703). The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.IM: study planning, data analysis, and manuscript writing. AM: process material preparation. FS and MS: therapy provision, study planning, and ITAP conceptualization. EB: study planning and realization of change interview. AG: manuscript revision and supervision. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Nature Communications 10.1038/s41467-021-24787-1, published online 22 July 2021.Correction to: The original version of the Source Data associated with this Article included an error in the sheet for Supplementary Figure 1, which contained two incorrect data points. The correct content of cell C15 is \u20182.0048\u2019 instead of the original, incorrect \u20182.1224\u2019 and the correct content of cell D37 is \u20184.5090\u2019 instead of the original, incorrect \u20184.4090\u2019. The HTML has been updated to include a corrected version of the Source Data.Updated Source Data"}
+{"text": "A dichotomy theorem for the complexity of deciding whether a graph has a 1-frugal colouring with k colours was found by McCormick and Thomas, and then later extended to restricted graph classes by Kratochvil and Siggers. We generalize the McCormick and Thomas theorem by proving a dichotomy theorem for the complexity of deciding whether a graph has a t-frugal colouring with k colours, for all pairs of positive integers t and k. We also generalize bounds of Lih et al. for the number of colours needed in a 1-frugal colouring of a given t-frugal colourings, for any positive integer t.A  G is t -frugal if, for every c, the colour c is assigned to at most t vertices of N(v). We consider only proper colourings.A colouring of a graph G with sufficiently large maximum degree has a Frugal colourings were introduced by Hind, Molloy, and Reed in 1997 . Their molouring . Their wolouring .t for which a graph has a t-frugal colouring with a given number of colours, we fix t and focus on the number of colours needed for a t-frugal colouring. The t -frugal chromatic number of G is the smallest positive integer k, such that there exists a t-frugal k-colouring of G, and is denoted by Rather than focussing on the values of t-frugal colourings of planar graphs and outerplanar graphs. For planar graphs, they showed Amini, Esperet, and van den Heuvel  examinedinjective colouring, distance 2 colouring, colouring the square, and L-labelling; for example, see [G is G by adding edges between all pairs of vertices at distance 2 in G.The case ple, see , 12, 26.ple, see . Similarple, see ,\u00a0pages 1G is planar, then:G is a Wegner  conjectu settled , 25. In vatipour  establisand Reed  later shh et al.  proved aG be a Let The proof of this theorem appears in Sect.\u00a0k-colouring. Their result was later strengthened by Kratochv\u00edl and Siggers [k-colouring [k-colouring is NP-complete. By contrast, it follows from Brooks\u2019 Theorem (applied to the square) that any graph with maximum degree at most k-colouring.McCormick and Thomas  determin Siggers . The proows from . The proolouring . Kratocht and k by proving:We generalize the theorem of McCormick and Thomas  to all pt-frugal k-colouring is solvable in polynomial time. If t-frugal k-colouring is NP-complete.If The proof of this theorem appears in Sect.\u00a0t and k, the existence of a t-frugal k-colouring can be described in monadic second-order logic. Hence, by Courcelle\u2019s Theorem [For all integers  Theorem , the exid must be assigned different colours are discussed in [L-labellings, which generalize L-labellings, are surveyed in [We conclude this section by briefly mentioning some related work. Locally injective colourings which need not be proper colourings are considered, for example, in , 20, 28.ussed in , 27. Resveyed in , 6G is called G can be transformed into A graph t-frugal k-colouring can be decided in linear time for graphs of bounded treewidth, hence in particular for t-frugal chromatic number of a n vertices. However, since t-frugal chromatic number can be computed in linear time [As noted in the previous section, the existence of a entclass1pt{minimaear time .In this section, we prove Theorem\u00a0G be a u be a vertex of G. Let Let G be a there exist two adjacent vertices of degree 2;u with there exists a vertex  Let G beUsing this lemma, we now prove Theorem\u00a0The case h et al. . Hence, G is a proper t-frugal colouring of G. Since If For convenience, let:G by induction on G be a n vertices. Our strategy is to delete a vertex w to obtain H can be coloured by induction. We then seek to extend the colouring of H to G by assigning a colour to w. We will show that the number of colours which are excluded as options for the colour of w is less than the number of colours which are available; hence, an extension exists. For a vertex w in G, let t-frugal colouring of H to a proper t-frugal colouring of G. Colours are excluded if they are used to colour a vertex adjacent to w, or are used t times in the neighbourhood of some neighbour of w. Therefore, w in G.We colour w be a vertex with degree 1. Clearly, H can be t-frugally coloured with t-frugal colouring of H can be extended to a t-frugal colouring of G.Suppose first that v and w, such that H can be coloured using w and v have degree 2, and w can violate the frugality condition for v. Therefore, the neighbour of v at distance 2 from w can be disregarded which leads to the slightly improved bound H can therefore be extended to a t-frugal colouring of G.Next, suppose that there are vertices u, such that u and x, and let By Lemma\u00a0x contains the neighbourhood of u, because no two vertices of degree two are adjacent and x is the only possible neighbour of u which does not have degree two. (Note that u and x are not necessarily adjacent.) Since H with x contains the neighbourhood of u, we have H can therefore be extended to a t-frugal colouring of G.Suppose that H is t-frugally coloured using x and y to u.Suppose that H can therefore be extended to a t-frugal colouring of G.First, suppose that c be a t-frugal colouring of Now, suppose that u is not adjacent to a vertex with colour c(x), then either u can be recoloured, so that c can therefore be extended to a t-frugal colouring of G.If u is adjacent to a vertex with colour c(x), then we have:c can therefore be extended to a t-frugal colouring of G.If Finally, suppose that This completes the proof. P-colouring is formally defined as follows.The decision problem Problem:P-colouring, Instance: A graph G.Question: Is there a proper t-frugal k-colouring of G?P-colouring clearly belongs to NP for all integers P-colouring for each NP-completeness of d Thomas  .P-colouring, for all pairs of positive integers t and k. We first treat some special cases, and then derive the general result from them.We will extend the result to P-colouring is NP-complete.The transformation is from 3-colouring.G be an instance of 3-colouring. We construct an instance P-colouring from G as follows. First, consider the graph H with vertices x, y, and z, such that x is adjacent to y, and the vertices y and z are connected by three paths of length two. For each H as follows. For each vertex u, such that H in which the vertices x, y, and z of H, respectively. Let Let mentclass2pt{minimv, ordered arbitrarily.As above, let Claim 1: In a 2-frugal 3-colouring of the vertices for must receive the same colour.It is sufficient to show that We refer to the colour used to colour the vertices Claim 2: can be coloured, such that, forand use different colours.i, i is even, and colour 3 when i is an odd. Then, since Without loss of generality, we may assume that the colour of Claim 3: Ifuandvare adjacent inG, then the colour of is different than the colour of By construction, c of G is given. To extend this to a 2-frugal 3-colouring c(v) be the colour of c is a proper colouring, and from Claim 3. Therefore, Suppose a 3-colouring c of G from c(v) be the colour of c will assign different colours to u and v. Therefore, c is a proper 3-colouring of G.Finally, suppose a 2-frugal 3-colouring P-colouring is NP-complete. Therefore G be a graph. The corona ofG with respect toG by, for each vertex v of G, creating a copy of v is adjacent to each vertex of its copy of Let P-colouring polynomially transforms to Let G be an instance of P-colouring. The instance of G is the graph H which is the corona of G with respect to G has a t-frugal k-colouring if and only if H has a k-colouring.Let c of G, a colour x, and a vertex c that the colour x appears in the neighbourhood of v.For a colouring c be a t-frugal k-colouring of G. Clearly, c can be extended to a proper colouring H by, for each v using each of the x appears in the neighbourhood of v is exactly c is t-frugal, we have k-colouring of H.Let k-colouring of H. We claim that the colouring c of G induced by t-frugal k-colouring. To see this, observe that for every x must be used exactly once in H associated with v. Since c is a t-frugal k-colouring of G.Now, let We can now prove Theorem\u00a01.2.P-coloured if and only if it contains no edges. If P-coloured if and only if it is bipartite with t. If t using Lemma\u00a0If d Thomas  and indu"}
+{"text": "Under the assumption that covalent bonds are rigid, it is possible to compare the estimations of rigidity based on anisotropic and isotropic B-factors. This is done by computing the difference of the mean-square displacements (Delta-u) of atoms A and Z along the covalent bond A\u2013Z, which must be close to zero for a rigid bond. The analysis of a high-quality set of protein structures, refined at a resolution better than  0.8 Angstroms, showed that Delta-u is significantly close to zero when anisotropic B-factors are used, with an average 60% Delta-u reduction. This reduction is larger for larger B-factors and this suggests that care should be taken in data-mining procedures that involve isotropic B-factors, especially at lower resolution, when anisotropic B-factors cannot be determined and when the average B-factor increases.The online version contains supplementary material available at 10.1007/s00726-021-02985-x. The benefits of high-resolution macromolecular crystal structures have been repeatedly described  are available, the mean-square displacement (u) of an atom is the same in all directions around the atomic average position, and the rigidity of the bond A\u2013Z can be monitored by the function BA and BZ are the B-factors of atoms A and Z). With anisotropic B-factors (U), the Delta-u function must consider that the mean-square displacement (u) of an atom is not the same in all directions, and it must be computed as:which must be close to 0\u00a0\u00c5, according to the Hirshfeld rigidity test : on average, it is 0.0108 (0.0001) \u00c5 smaller. This difference is larger for side-chain bonds [0.0157 (0.0002) \u00c5] than for main-chain bond [0.0061 (0.0002) \u00c5]. Only for 13% of the bonds, the isotropic Delta-u is slightly smaller than the anisotropic Delta-u and most of these cases concern the C\u2013N backbone bonds. This percentage is smaller for side-chain bonds (10%) than for backbone bonds (17%).In general, and as expected, anisotropic This is certainly not surprising. In fact, given the assumption that covalent bonds are rigid, this reflects the better modeling of atomic dispersion around the equilibrium positions in anisotropic refinements. In other words, the rigidity of covalent bonds is better accounted for by anisotropic B-factors refinements, especially for side-chains, which tend to be more flexible.Delta-u are equal, on average, to 0.0075 (0.0001) and 0.0184 (0.0001) \u00c5, the deviation from rigidity of the covalent bonds is reduced by 60% when anisotropic B-factors are refined. This improvement is remarkable and somehow surprising by its amount.However, the added value of the work presented here is the fact that this is a quantitative comparison, which points out that, given that the anisotropic and isotropic Delta-u shown in Fig.\u00a0Delta-u increases considerably, from values close to 0\u00a0\u00c5 up to 0.04\u00a0\u00c5, the anisotropic Delta-u increases much less, only from 0.006 to 0.007\u00a0\u00c5 to about 0.01\u00a0\u00c5. This confirms that the covalent bond rigidity is drastically better monitored by anisotropic B-factors.This can be appreciated also by the relationship between the anisotropic and isotropic Delta-u tend to be larger for atom pairs that have a larger average isotropic B-factor Below is the link to the electronic supplementary material."}
+{"text": "Nature Communications 10.1038/s41467-020-16601-1, published online 1 June 2020.Correction to: The original version of this Article contained an error in Figure 2, where the horizontal axis value \u20181600\u2019 in panel (a) was incorrectly labelled as \u20181200\u2019. This has now been corrected in both the PDF and HTML versions of the Article."}
+{"text": "In the original article, there were errors. A correction has been made to:The legend in was\u201314.96 percentage points higher among the poorest mothers than among the richest mothers\u201d, it should actually say \u201cIn 1993, the SII was\u201314.96, i.e., the prevalence of the outcome was 14.96 percentage points higher among the poorest mothers than among the richest mothers\u201d.Also, in the presentation of the results of Table 3, a minus sign is wrongly placed. Where it reads: \u201cIn 1993, the SII was\u201314.96, i.e., the prevalence of the outcome I apologize for these mistakes on behalf of all co-authors."}
+{"text": "Communications Biology 10.1038/s42003-021-02145-7, published online 10 June 2021.Correction to: y axis was titled, \u201cChange from 1600 (%)\u201d. The correct y axis title is \u201cChange from 1600 \u201d. The correct version of Fig. 2 is:The original version of this Article contained an error in Fig. 2, in which the which replaces the previous incorrect version:y axis was titled, \u201cChange from 1600 (%)\u201d. The correct y axis title is \u201cChange from 1600 \u201d. The correct version of Fig. 3 is:The original version of this Article also contained an error in Fig. 3, in which the which replaces the previous incorrect version:Both errors have now been corrected in the HTML and PDF versions of the Article."}
+{"text": "The application of intermaxillary traction is often accompanied by the unexpected movement of dentition, especially anchorage teeth. The aim of this study was to comprehensively compare the influence of cross-sectional shape of ribbon arch wires with edgewise and round wires on intermaxillary traction in Class II malocclusion treatment using FEA simulation.The dentofacial structure was simulated in finite element software. A retraction force of 1.5\u00a0N was applied to different cross-sectional orthodontic arch wires: a ribbon wire (0.025\u2009\u00d7\u20090.017-in. and 0.025\u2009\u00d7\u20090.019-in.), a rectangular wire (0.017\u2009\u00d7\u20090.025-in. and 0.019\u2009\u00d7\u20090.025-in.) and a round wire (\u03a6 0.018-in. and \u03a6 0.020-in.).Among the three groups, ribbon wire (0.025\u2009\u00d7\u20090.017-in. and 0.025\u2009\u00d7\u20090.019-in.) exhibited the lowest displacement in the X-axis  and Z-axis . However, the 0.025\u2009\u00d7\u20090.017-in. ribbon wire showed the highest Y-axis displacement. In the round wire group, \u03a6 0.020-in. wire displayed less rotation than \u03a6 0.018-in. wire, where the sagittal, frontal and occlusal rotation of \u03a6 0.020-in. wire was almost half of that of \u03a6 0.018-in. wire. The movement of the first molar region was intermediate between the ribbon arch group and the round wire group. Notably, the values of the 0.025\u2009\u00d7\u20090.017-in. arch wire displacement, which were higher than those of any other group, peaked at 0.019\u00a0mm in the central incisor region with a spike-like shape. The deformation range of the \u03a6 0.018-in. wire group was the largest in this study.The cross-section of the arch wire influenced force delivery in Class II intermaxillary traction. With the same shape, a larger cross-sectional area led to less mandibular dentition movement. For the rectangular arch wire and ribbon arch wire groups, since the height and width were inverted, the vertical displacement of anchorage teeth in the ribbon wire group was reduced, but the possibility of buccal tipping in mandibular anterior teeth also increased. Class II malocclusion, which is associated with a convex soft tissue profile caused by either mandibular retrognathism or excessive growth of maxilla, constitutes a significant diagnostic percentage of the patients seeking orthodontic treatment \u20134. AmongPrevious studies have characterized the geometry and size effects of orthodontic arch wires on the ultimate orthodontic treatment outcomes , 9. BracCompared with contemporary edgewise wires, the cross-section of ribbon arch wires represents an inversion of height and width. Historically, the ribbon arch, the first orthodontic appliance coupled with brackets, was considered the progenitor of edgewise appliances and earned popularity in the 1920s . The utiIn addition, there is a paucity of data from investigations into the role that the cross-sectional shape plays in maxillomandibular traction. The reason for this lack of data could be the great challenge in identifying tooth movement and deformation under the coexistence of sophisticated anatomical structures and various orthodontic elements . Finite The aim of this study was to comprehensively compare the influence of the cross-sectional shape of ribbon arch wires with edgewise and round wires on intermaxillary traction in Class II malocclusion treatment using FEA simulation.The study protocol was designed in compliance with the Helsinki Declaration and approved by the ethical committee of the Fujian Medical University Union Hospital. Through medical history interviewing and oral examination, a 20-year-old healthy male volunteer with a healthy craniofacial structure and complete dentition with normal crown root ratio and a normal occlusion, was selected for this study. Before inclusion in this study, this volunteer signed an informed consent form.The finite element (FE) model was based on the computed tomography  data, which referred to the sectional images of the volunteer from the upper rim of the condyle to the lower edge of the mandible in digital imaging and communications in medicine (DICOM) format. The CT data were collected and imported to the processing software  to further obtain a virtual model of the maxilla and mandible in Geomagic Studio . Along with the outer surface of the mandible, the periodontal ligament (PDL) was constructed at 0.25\u00a0mm thickness. The central area of alveolar bone was cancellous bone surrounded by 1.5\u00a0mm thick cortical bone.Rectangular wire  and round wire  were scanned and these scans were entered into software . Using the same method, the matching brackets, buccal tubes and slots were modelled virtually. The ribbon wire (0.025\u2009\u00d7\u20090.017-in. and 0.025\u2009\u00d7\u20090.019-in.) was constructed based on the rectangular wire with height and width inverted. The rectangular wires and round wires were coupled with a 0.022\u2009\u00d7\u20090.028-in. slot, whereas the ribbon wire was inserted into the 0.028\u2009\u00d7\u20090.022-in. slot, which was designed for the purpose of fitting the upright arch wire. An anterior hook of 2.5\u00a0mm height was built and positioned between the maxillary lateral incisor and canine while the tubes were placed in the first mandible molar and second premolar. In addition, stainless steel ligature wires were tied to the brackets from the second premolar of the mandible right to the left second premolar. Those orthodontic appliances were assembled appropriately on the buccal side of dentition and are shown in Fig.\u00a0A nonlinear elastic finite element analysis was performed in Ansys Workbench 15.0 . The Coulomb friction coefficient between the ligature and brackets was assumed to be 0.2 with reference to other experimental data. Each anatomical component and orthodontic appliance was simulated with ten-node tetrahedral elements and assumed to have isotropic homogenous linear elastic characteristics. The sizes of the elements in the PDL, tooth and bone were set as 0.5\u00a0mm, 1\u00a0mm and 2\u00a0mm, respectively, in order to simplify the finite element model, which included both small element size in the PDL and a large volume of the bone and the teeth. The FE model with different arch wires consisted of 616,006\u2013650,197 nodes and 321,732\u2013325,321 elements in total while the numbers of nodes/elements were 56,376/30,327 for teeth, 243,141/120,459 for the PDL, 199,834/111,827 for bone and 116,655\u2013150,846/58,534\u201367,280 for the remaining components, including tubes, brackets and different arch wires. Young\u2019s modulus and Poisson\u2019s ratio of cortical bone, cancellous bone, teeth, PDL, arch wires, brackets and tubes were determined from previous studies \u201323 and aA traction force of 1.5\u00a0N was applied from the maxilla anterior hook between the canine and lateral incisor to the hook of buccal tubes in the mandible first molar. The application of retraction force would initiate the movement of teeth, which could be defined by the displacement rotation of teeth, and the stress redistribution of the PDL. All the movement was suppressed for the nodes located in the bottom of the mandible segment.There were two coordinate systems utilized in this study. For a single tooth, the x-axis, was referred to the mesio-distal direction , the y-axis referred to the buccal\u2013lingual direction  and the z-axis to the vertical direction . For other large volume components , the displacement of teeth was recorded on the basis of a standard coordinate system with the x-axis as the anterior\u2013posterior direction, the y-axis as the medial\u2013lateral direction, and the z-axis as the superior\u2013inferior direction, whereas the anterior, medial, and superior directions were defined as the\u2009+\u2009x,\u2009+\u2009y, and\u2009+\u2009z directions, respectively. Rotation movement was decomposed into three planes of motion , and the corresponding directions  were predetermined as positive.The buccal cusps of the mandibular posterior teeth and the edge of anterior teeth were lined virtually as buccal lines, while the lingual cusps of mandibular posterior teeth and the cingulum of anterior teeth were connected as lingual lines. The movement of the lingual line and buccal line was recorded.The results of 46 teeth in terms of force component distribution, displacement and rotation movements in three directions are shown in Table For the rectangular wire group, with increasing wire size, there was a descending trend in the displacement in the Y-axis and Z-axis. The displacement of the 0.017\u2009\u00d7\u20090.025-in. wire in the Z-axis direction was 9.17\u00a0\u03bcm and that of the 0.019\u2009\u00d7\u20090.025-in. wire was 9.13\u00a0\u03bcm. Among the three groups, ribbon wire (0.025\u2009\u00d7\u20090.017-in. and 0.025\u2009\u00d7\u20090.019-in.) exhibited the lowest displacement in the X-axis  and Z-axis . However, the 0.025\u2009\u00d7\u20090.017-in. ribbon wire showed the highest Y-axis displacement. The \u03a6 0.018-in. round wire also showed higher Z-axis displacement (9.44\u00a0\u03bcm) and Y-axis displacement (5.96\u00a0\u03bcm) than \u03a6 0.020-in. round wire .In the rectangular wire group and ribbon wire group, the rotation motion for 46 teeth in the sagittal, frontal and occlusal planes was \u2212\u20090.002\u00b0, 0.020\u00b0, and 0.021\u00b0, respectively. In the ribbon wire group, the frontal rotation was higher than that in the rectangular and round wire groups, especially the 0.025\u2009\u00d7\u20090.017-in. group, which exhibited 0.042\u00b0 of rotation. In the round wire group, \u03a6 0.020-in. wire displayed less rotation than \u03a6 0.018-in. wire, where the sagittal, frontal and occlusal rotation of \u03a6 0.020-in. wire was almost half that of \u03a6 0.018-in. wire.Figure\u00a0The detailed displacements  of mandible teeth after the application of 1.5\u00a0N retraction force is shown in Fig.\u00a0The displacements of the buccal line and lingual line in different groups are shown in Fig.\u00a0In the rectangular wire group (0.017\u2009\u00d7\u20090.025-in. and 0.019\u2009\u00d7\u20090.025-in.), the maximum displacements of the buccal line and lingual line were 15.98\u00a0\u03bcm and 15.91\u00a0\u03bcm, respectively. The movement of the first molar region was intermediate between the ribbon arch group and the round wire group. In the ribbon arch group, the lingual line displacement in the first molar region was 0.008\u00a0mm, which was also the lowest among the corresponding results of all the studied groups. Notably, the values of the 0.025\u2009\u00d7\u20090.017-in. arch wire displacement, which were higher than those of any other group, peaked at 18.55\u00a0\u03bcm in the central incisor region with a spike-like shape. In the 0.025\u2009\u00d7\u20090.019-in. group, the displacements ranged from the first molar to the central incisor of the buccal line, and the lingual line was lowest among the studied groups. In the round wire group, the displacement ranging from the first molar to the central incisor of the buccal line and lingual line was higher than those of the rectangular and ribbon arch groups. The movement induced by the \u03a6 0.020-in. wire was 16.11\u00a0\u03bcm, which was lower than that induced by the \u03a6 0.018-in. wire (17.18\u00a0\u03bcm).The deformation range between maximum deformation and minimum deformation in different groups after the application of 1.5\u00a0N retraction force is summarized in Fig.\u00a0The high prevalence of Class II malocclusion in patients prompted the wide usage of intermaxillary elastic traction. However, scarce data and few documented details are available regarding the influence of arch wire geometry during the maxillomandibular traction procedure. In the present study, we principally aimed to simulate the dentofacial structure via FEA to explore the effect of arch wire cross-sectional shape on Class II intermaxillary traction.Often, the changes in vertical and horizontal vectors caused by Class II intermaxillary traction involve anchorage loss , 24, 25.I) of the rectangular wire is equal to \u201ch3w/12\u201d (where \u201ch\u201d refers to the height of the cross-section and \u201cw\u201d refers to the width); I of the round wire is equal to \u201c\u03c0r4/64\u201d (where \u201cr\u201d refers to the radius of the cross-section) [Based on the FEA model in this study, differential results were observed in the arch wire group with different cross-sections in terms of mandibular first molar movement. The mechanics of arch wires have been recognized as one of the contributing factors of anchorage loss but have not been fully investigated . Theoretsection) . When thsection) . In addiIn this FE study, the remarkable execution of the ribbon wire in minimizing the vertical and horizontal displacements provided the basis for reviving the ribbon wire. The good performance of the ribbon wire in anchorage control could be attributed to the relatively greater height of the arch wire cross-section. A greater height tended to enlarge the moment of inertia and provide more rigid support to the occlusal plane. To our knowledge, only Inami et al. reported a minimum vertical bowing effect with a ribbonwise lingual appliance . HoweverThere were very similar results displayed by different arch wire groups in which the PDL around the distal root endured the most stress. Previous studies also revealed the relatively high occurrence of root resorption in the distal root of the mandibular first molar in orthodontic treatment . In the The displacement results of the buccal line and lingual line as well as the displacements of mandibular dentition also demonstrated that there was an association between cross-sectional geometry and mandibular tooth movement in Class II intermaxillary traction. Monlasser et al. stated that the importance of the arch wire cross-section in mechano-therapy should be appreciated since the force level in the vertical direction was amplified from 16 to 120% when the 0.014-in. arch was replaced by the 0.016-in. . In the Arch deformation is directly correlated with the resistance to sliding, and permanent wire deformation heavily encumbers tooth movement efficiency . From thThere were some limitations in this study because this experiment was conducted entirely using computer software. For instance, the setting of biological characteristics may differ from the real properties in vivo. Future studies, especially clinical trials, should be conducted to investigate the effect of arch wire geometry in vivo.Within the limitations of this FEA, the cross-section of the arch wire exerted an influence on force delivery in Class II intermaxillary traction. With the same shape, a larger cross-sectional size led to smaller mandibular dentition movement. For the rectangular arch wire and ribbon arch wire groups, since the height and width were inverted, the vertical displacement of anchorage teeth in the ribbon wire group was reduced, but the possibility of buccal tipping of mandibular anterior teeth also increased."}
+{"text": "Cell Death & DifferentiationCorrection to: 10.1038/s41418-020-00681-zhttps://www.nature.com/articles/s41418-020-00669-9) needs to be added to the start of paragraph 3, after \u2018Hauck et al\u2019. In addition, there was a typo in \u2018Hauk et al\u2019. The correct name is \u2018Hauck et al\u2019. The journal and\u00a0authors apologize for the errors. The original article has been corrected.The original version of this article unfortunately contained an ommission in the references\u00a0that\u00a0occured\u00a0in production. A reference to this paper ("}
+{"text": "Recently found zero-determinant (ZD) strategies have substantially been investigated in evolutionary game theory. The original memory-one ZD strategies unilaterally enforce linear relationships between average pay-offs of players. Here, we extend the concept of ZD strategies to memory-two strategies in repeated games. Memory-two ZD strategies unilaterally enforce linear relationships between correlation functions of pay-offs and pay-offs of the previous round. Examples of memory-two ZD strategy in the repeated Prisoner\u2019s Dilemma game are provided, some of which generalize the tit-for-tat strategy to a memory-two case. Extension of ZD strategies to memory- SinceIn 2012, Press and Dyson discovered a novel class of memory-one strategies called zero-determinant (ZD) strategies . ZD straRecently, properties of longer memory strategies have been investigated in the context of repeated games with implementation errors \u201345. In gIn this paper, we extend the concept of ZD strategies to memory-two strategies in repeated games. Memory-two ZD strategies unilaterally enforce linear relationships between correlation functions of pay-offs at the present round and pay-offs at the previous round. We provide examples of memory-two ZD strategy in a repeated Prisoner\u2019s Dilemma game. Particularly, one of the examples can be regarded as an extension of TFT strategy to a memory-two case.n case with n \u2265 2 is discussed. Section 6 is devoted to concluding remarks.The paper is organized as follows. In \u00a72, we introduce a model of repeated game with memory-two strategies. In \u00a73, we extend ZD strategies to the memory-two strategy class. In \u00a74, we provide examples of memory-two ZD strategies in a repeated Prisoner\u2019s Dilemma game. In \u00a75, extension of ZD strategies to a memory-. 2N-player repeated game. Action of player a \u2208 {1,\u2026, N} is described as \u03c3a \u2208 {1,\u2026, M}. We collectively denote state n with n \u2265 2.) Strategy of player a is described as the conditional probability \u03c3a when states at last round and second-to-last round are a when the state is t, and we have defined the transition probability\u03b4 = 1 .  Actions of both players at t = 0 and t = 1 are sampled from uniform distribution. In t = 100000. We can see that the linear relation . Then, we find that her PD matrix iss1\u232a(st) = \u2329s2\u232a(st) [Here, we introduce a memory-two ZD strategy which can be called an extended tit-for-tat (ETFT) strategy. We consider the situation when player 1 takes the following memory-two strategy:\u2329s2\u232a(st) , equatioq.We provide numerical results about the ETFT strategy. Parameters and strategies of player 2 are set to the same values as those in the previous subsection. In We can understand feelings of the ETFT player as follows. We find that, when the previous state is  or , ETFT behaves as TFT. When the previous state and the second-to-last state are TFT-ATFT :4.11T1, because T1 = 1. Therefore, it is expected that ETFT-2 is less successful than ETFT.It should be noted that a slightly modified version of ETFT:. 4.3R > T + S, which corresponds to the condition that mutual cooperation is favourable to the period-two sequence  \u2192  \u2192  \u2192 \u00b7 \u00b7 \u00b7 [Here, we introduce another memory-two ZD strategy which can be called a fickle tit-for-tat (FTFT) strategy. In this subsection, we assume 2 \u2192 \u00b7 \u00b7 \u00b7 . We consequation ). FTFT cq.We provide numerical results about the FTFT strategy. Parameters and strategies of player 2 are set to the same values as those in the previous subsections. In . 4.4R > T + S and 2P < T + S. In memory-one strategies, there exists the following memory-one ZD strategy:Here we assume that 2As an extension of ZSS, we can consider the following memory-two strategy:q.In . 4.5As in memory-one cases , possibl. 5n (n \u2265 2) case. By using the technique of this paper, extension of Akin\u2019s lemma  case is straightforward.In this paper, we extended the concept of ZD strategies in repeated games to memory-two strategies. Memory-two ZD strategies unilaterally enforce linear relationships between correlation functions of pay-offs and pay-offs at the previous round. We provided examples of memory-two ZD strategies in the Prisoner\u2019s Dilemma game. Some of them can be regarded as variants of TFT strategy. We also discussed that extension of ZD strategies to a memory-Before ending this paper, we make two remarks. First, in our numerical simulations, we investigated only simple situations which correspond to well-mixed populations and without evolutionary behaviour. It has been known that evolutionary behaviour can drastically change when populations are structured \u201352. TherThe second remark is related to the length of memory. Recently, it has been found that long memory can promote cooperation in the Prisoner\u2019s Dilemma game ,54. Our Click here for additional data file."}
+{"text": "Scientific Reports 10.1038/s41598-021-94505-w, published online 22 July 2021Correction to: In the original PDF version of this Article a previous rendition of Figure\u00a01 was published. The original Figure\u00a0This error has now been corrected in the PDF version of the Article; the HTML version was correct from the time of publication."}
+{"text": "Correction to: Translational Psychiatry 10.1038/s41398-022-01795-3, published online 26 January 2022The original version of this article unfortunately contained a mistake in Figure 2. Unfortunately, the direction of the label is incorrect. Currently it reads \u201cSignificant effects of Group: TS \u2013 NTS\u201d. The correct title is in fact \u201cSignificant Effects of Group: NTS \u2013 TS\u201d. All other details in the paper, including the reporting of results and discussion of findings are correct as published. The original article has been corrected."}
+{"text": "GW as post-Hartree-Fock methods. We found GW to be the most accurate of these three approximations for the ionization potential, by far. Going beyond GW by adding more diagrams is a tedious and dangerous activity: We tried to complement GW with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (WTDHF), and with a GW density-matrix (\u03b3GW). Only the \u03b3GW result has a positive impact. Finally using an improved hybrid functional for the non-interacting Green\u2019s function, considering it as a cheap way to approximate self-consistency, the accuracy of the simplest GW approximation improves even more. We conclude that GW is a miracle: Its subtle balance makes GW both accurate and fast.We use the GW100 benchmark set to systematically judge the quality of several perturbation theories against high-level quantum chemistry methods. First of all, we revisit the reference CCSD(T) ionization potentials for this popular benchmark set and establish a revised set of CCSD(T) results. Then, for all of these 100 molecules, we calculate the HOMO energy within second and third-order perturbation theory (PT2 and PT3), and,  GW approximation   is curreximation  for elecximation  for neutv. Here we name the second-order perturbation theory, PT2, and the third-order perturbation theory, PT3. Going beyond the third-order has seldom been attempted . With GW we denote here the one-shot GW appoximation that does not include self-consistency; in the literature it is sometimes denoted as 0W0G. 2 IP was more than 1\u00a0eV off the trend. We present here a complete recalculation of the CCSD(T) reference IPs for the GW100 benchmarkHowever, before doing so, we will revisit the CCSD(T) reference IPs. We observed that the set from .The GW100 benchmark is hence to be the boxing ring in which we want to scrutinize the quality of the different MBPT approximations  ionization potentials for GW100, we set up new CCSD(T) reference values of the IPs for the GW100 benchmark set. Benchmarking the MBPT Strategies compares the performance of the different approximations based on a standard Hartree-Fock starting point. MBPT From an Improved Mean-Field Starting Point shows an attempt to approach MBPT self-consistency with tuned hybrid functionals. Finally the conclusions are drawn in Conclusion. Hartree atomic units are used throughout this work. The numerical values are made available as Supplemental Material, under the wide-spread machine- and human-readable JSON file format.The article is organized as follows: In In MBPT, the central quantity is the one-electron Green\u2019s function. The Green\u2019s function describes the time-propagation of an additional particle in the electronic system: an extra electron for propagation forward in time, or a hole for propagation backward in time. The Green\u2019s function contains a great deal of information. For instance its diagonal is the electronic density, and, most interesting for us, its poles are the ionization energies .G0 is known, the exact Green\u2019s function G can be obtained thanks to the Dyson equation:p and q, have been dropped for simplicity.Once an approximate Green\u2019s function G0 to G. If the Hartree-Fock approximation (HF) is used for G0, then \u0394\u03a3 coincides with the missing correlation part of the self-energy \u03a3c.The operator \u0394\u03a3 stands for the self-energy difference. It performs the humongous task of connecting G0, it can be expressed analytically:p and q are molecular orbital (MO) indices, \u03f5p and \u00b1 i\u03b7 is a vanishing imaginary number that ensures the correct analytic behavior of G0. G0 is diagonal in the corresponding MO basis.When a mean-field approximation is selected for In practice, we make the further approximation that the self-energy difference is also diagonal in the MO basis:is field .I is the identity operator, it becomes clear that the diagonal approximation of \u0394\u03a3 will induce a diagonal approximation to G, since G and therefore also Recasting the Dyson G correspond to the zeroes of the term in between the brackets in p index that corresponds to occupied states is \u03f5HOMO = \u2212 IP. The HOMO energies reported in this work are obtained with this procedure, which is often referred to as the \u201cgraphical solution\u201d of the quasiparticle equation .Let us start gradually and begin with the formulation of the HF approximation in terms of Goldstone-Feynman diagrams. In the upper panel of r) = G is the electronic density. From the Hartree Goldstone-Feynman diagram, we can immediately see that the Hartree potential is local in space and in time, since the entry and exit points are identical. The exchange diagram , labeled WTDHF.Adding more diagrams in l effect . We willW together with an unscreened interaction v. The complete second-order diagrams with two W wiggly lines has been very recently considered in Ref.  reference set.In their work providing CCSD(T) reference values for the GW100 molecules, Krause asis set . Close iThe CCSD(T) benchmark values for the ionization potentials, which have been used by all GW100 studies up to now, were done by the authors of Ref. . using aconvenient choice, it may not lead to the most accurate CCSD(T) energy. For example, in the case of in this case. Indeed, GW calculation matched the experimental ionization energy better than the \u201cbenchmark\u201d CCSD(T) calculations did.While using the lowest energy UHF solution determined via such a stability analysis, can be a very evel see . While ievel see , so the  of Ref. , in termet al. accidentally used sulfur instead of selenium in their calculation. The most noticeable updates are SO2, MgO, cytosine, and uracil with changes larger than 0.4\u00a0eV.In this work we have re-calculated the frozen-core CCSD(T) energies for the entire GW100 set, however we chose to use GAUSSIAN 16  with de, includiet al. with an MAE of 0.09\u00a0eV. However, this correct MAE is hiding a few terrible outliers, such as SO2, MgO, cytosine, and uracil.Our revised IPs improve very much the consistency of CCSD(T) with the related method named equation-of-motion coupled-cluster (EOM-IP-CCSD). Indeed, Lange and Berkelbach  have evaNow, comparing our updated CCSD(T) to Lange\u2019s EOM-IP-CCSD yields not only an improved MAE of 0.06 eV, but also fixes all the mentioned outliers. The deviations between the updated CCSD(T) and EOM-IP-CCSD never exceed 0.30\u00a0eV.As our updated CCSD(T) set very much improves the consistency across the methods and the comparison to experiment when experimental data are available, we have confidence that our updated values are a genuine improvement. We remind the Reader that all the numerical values are reported in the Supplemental Material.G0 in G0 is maybe not the optimal Green\u2019s function.A noticeable source of misunderstanding between the different MBPT flavors is the starting mean-field approximation used for the non-interacting Green\u2019s function G, best W\u201d, is very effective for periodic systems  or on a semi-local approximation yields very decent results . In \u2202\u03a3c/\u2202\u03c9 is sometimes positive, which is not allowed for the exact self-energy. Remember that Z introduced in GW only contain single poles as shown for GW in Eq. 47 of Ref. ), MgO is more intriguing. It was very good with GW (\u22120.08\u00a0eV compared to CCSD(T)) and deteriorates very much with GW + \u03b3GW. BeO, which is chemically similar to MgO, is quite different in terms of its deviation, with a deviation of only 0.01\u00a0eV for GW + \u03b3GW with respect to CCSD(T).Finally, we evaluate the effect of the first-order correction to the Hartree and Fock exchange terms, as depicted in GW. However, we can state that with GW being already very good, it is a difficult task to improve over it. Adding diagrams may destroy the subtle balance, which makes GW so successful. Among all the additions we considered, only GW + \u03b3GW can be considered as a systematic improvement.Of course, we did not explore all the possible combinations of diagrams beyond It is attractive to calculate Green\u2019s functions self-consistently for several theoretical reasons. First, this is a systematic way to include more diagrams . The GreHowever for practical reasons, self-consistent calculations are rarely carried out and one rather uses a one-shot approximation on top of a mean-field calculation. In the previous Section, we only used an HF mean-field for comparison reasons.G0. For molecules, it has been identified , a global hybrid functional which mixes the PBE exchange energy and the Hartree-Fock exchange energy in a 1:3 ratio . In the box plot reported in At this point, there is a cross-road between chemistry and physics methods again. When performing a perturbation theory based on a mean-field different from HF, the Brillouin theorem breaks down  and firsG0 is an approximation to the self-consistent G. As a consequence, no first-order terms appear in PT2 and some Goldstone-Feynman diagrams should be removed from the original PT3. The static diagrams (\u201cA\u201d diagrams in Cederbaum\u2019s notation) are corrections to the Hartree and Fock exchange terms (See Then we consider that the PBEh(0.75) Green\u2019s function erms See . If PBEhHence, GW@PBEh(0.75) in GW calculations of Caruso and coworkers  Green\u2019s function. The GW + SOSEX somewhat improves compared to GW + SOSEX@HF. But it is still deteriorating the results compared to the simpler GW approximation. Next, we test GWTDDFT where W was obtained from time-dependent DFT using the same functional as for G0. Again the results are disappointing.Finally, we make an attempt at combining a better non-interacting Green\u2019s function with the additional diagrams we tested in Section IVB. In GW + \u03b3GW. If G0 was the self-consistent GW Green\u2019s function, the \u03b3GW diagrams would vanish. Remember that the \u03b3GW diagrams are not present in Hedin\u2019s equations, which are obtained for a self-consistent G. GW + \u03b3GW is very similar to GW. Besides MgO, which behaves badly again, the similarity between the error distribution of GW and GW + \u03b3GW is compelling.Last, we consider In this study, we have conducted a comprehensive benchmark of the MBPT performance for the calculation of the IP of molecules. Our boxing ring was the GW100 set introduced by one of us  a few yeGW, and several methods beyond GW. Among the classical approximations, GW is clearly the winner. Then our attempts to improve over GW by adding more diagrams have been unsuccessful, besides the GW + \u03b3GW diagrams that add corrections to the Hartree and Fock exchange expectation values.Based on the same HF starting point, we evaluated the 100 HOMO energies of GW100 for PT2, PT3, GW@PBEh(0.75) with a claimed MAE of 0.15\u00a0eV.Then starting from an improved mean-field (here we chose PBEh(0.75)), deteriorates the classical approximations, PT2 and PT3. Contrarily, GW improves with a more realistic starting mean-field. Our champion is then GW is the fact that its in a featherweight class: GW, when combined with the resolution-of-the-identify, has an attractive N4 scaling. GW now routinely runs on molecular systems with several hundreds of atoms   or equatof atoms ."}
+{"text": "Zinkiewicz et al. was published as a Letter in NanoLetters.On March 8th, 2021, the manuscriptentitled \u201cExcitonic Complexes in n-Doped WSgnexp in Numerical values placed in the column"}
+{"text": "We also give a general method for transforming any such family to an \u03b5-almost-strongly universal family of hash functions. The latter families can then, among other applications, be used in the Wegman\u2013Carter MAC construction which has been shown to provide a universally composable authentication method in QKD protocols. As Polynomial Hash has found many applications, our constructions and results are potentially of interest in various areas.Authentication plays a critical role in the security of quantum key distribution (QKD) protocols. We propose using Polynomial Hash and its variants for authentication of variable length messages in QKD protocols. Since universal hashing is used not only for authentication in QKD but also in other steps in QKD like error correction and privacy amplification, and also in several other areas of quantum cryptography, Polynomial Hash and its variants as the most efficient universal hash function families can be used in these important steps and areas, as well. We introduce and analyze several efficient variants of Polynomial Hash and, using deep results from number theory, prove that each variant gives an  Key establishment protocols, in which cryptographic keys are securely exchanged between parties over a public channel, usually use methods from public-key cryptography, like Diffie\u2013Hellman key exchange (DH) and elliptic-curve Diffie\u2013Hellman (ECDH); see  for a co\u03b5-almost-strongly universal hash function and then encrypted with a one-time pad. The application of the Wegman\u2013Carter paradigm in QKD was originally proposed by Bennett and Brassard [\u03b5-almost-strongly universal (\u03b5-ASU) family of hash functions, and a secret encryption key (a sequence of random one-time pads). A\u00a0message is authenticated by first hashing it with the shared hash function and then encrypting the resulting hash value with the shared encryption key (shared one-time pad). The resulting encrypted hash value, called an authentication tag, is transmitted together with the message (as a pair). Upon receiving this pair, the legitimate party recomputes and validates it. Such a MAC algorithm is information-theoretically  secure, that is, even an adversary who has unbounded computational power cannot forge the MAC with probability greater than the collision probability of the hash function family [Studying the security of QKD has become a topic of great importance .growing (rather than quantum key distribution) protocol. The Wegman\u2013Carter MAC construction has been shown in [\u03b5-ASU hash function families because these families are the main ingredient in the Wegman\u2013Carter construction .Because, in the authentication of the classical channel, the legitimate parties need to share some initial small secret information in advance as described above, QKD is sometimes called a quantum key shown in  to be unshown in \u201321, and Polynomial Hash (PH) and its variants for authentication of variable length messages in QKD systems. Since universal hashing is used not only for authentication in QKD but also in other steps in QKD like error correction and privacy amplification [\u03b5-almost-\u0394-universal (\u03b5-A\u0394U) family of hash functions which has found various important applications, for example, Galois/Counter Mode (GCM) [\u03b5-A\u0394U and so can be used in various applications. Furthermore, we propose a general method by which any \u03b5-A\u0394U hash function family can be transformed to an \u03b5-ASU family. Therefore, the Polynomial Hash variants constructed in this paper can all be transformed to \u03b5-ASU families which makes them useful for various applications including authentication of variable length messages in QKD.In this paper, following \u201324 we prfication , 25\u201330, de (GCM)  (which ide (GCM)  (which ide (GCM) \u201343 for vn, \u03b5-A\u0394U families to \u03b5-ASU families. In Sect.\u00a0The rest of this paper is organized as follows. In Sect.\u00a0n is a positive integer, p is a prime, n defined as q elements, where q is a prime power. Also, Throughout the paper, Finding (the number of) solutions of univariate and multivariate polynomial equations over fields and rings is a fundamental problem in mathematics, computer science, and related areas with many applications in various domains. In this paper, by a polynomial we mean a univariate polynomial. As a classical example, one can mention the Fundamental Theorem of Algebra which gives the exact number of solutions of polynomial equations over the field of complex numbers.Letbe a non-zero polynomial of degreewith complex coefficients. Then the equationhas, counting multiplicities, exactlydcomplex solutions. Equivalently, the field of complex numbers is algebraically closed.There are about a hundred proofs(!) of the Fundamental Theorem of Algebra . See 4646 for \u201cosolution of the polynomial congruencen has at most n solutions. Similarly, every multivariate polynomial congruence in k variables modulo n has at most By a n)? The answer is no; there is no direct analog of the Fundamental Theorem of Algebra for polynomial congruences. Let us see some examples. The following result, proved by D. N. Lehmer [A natural question is whether the Fundamental Theorem of Algebra can be applied to the ring . Lehmer , gives a(Lehmer\u2019s Theorem)LetThe linear congruencehas a solutionif and only ifwhereFurthermore, if this condition is satisfied, then there aresolutions.Note that the generalization of Lehmer\u2019s Theorem to higher degree multivariate polynomial congruences is a challenging problem. In fact, even the quadratic version addressed by Cohen  has mucha and b are integers, has zero, one, or more solutions .(Lagrange\u2019s Theorem)Given a primep, letbe a polynomial with integer coefficients such thatsaid to be of degreed). Then the polynomial congruencehas at mostdsolutions.Lagrange\u2019s Theorem can be extended from the prime field e, e.g., ):Letbe a field andbe a non-zero polynomial of degreewith coefficients inThen the polynomial equationhas, counting multiplicities, at mostdsolutions inTherefore, it has at mostddistinct solutions inIt would be useful to compare the above results:Setting exact number of complex solutions of polynomial equations over the field of complex numbers, but Lagrange\u2019s Theorem and Theorem\u00a0upper bounds for the number of solutions over the prime field and arbitrary fields, respectively.While Theorem\u00a0The proof of the Fundamental Theorem of Algebra is totally different from the proof of Lagrange\u2019s Theorem and Theorem\u00a0The following observations are useful, specially when discussing the Polynomial Hash and its variants: absolutely distinct if Note that Lagrange\u2019s Theorem does not hold for composite moduli. For example, the quadratic congruence Vandiver  obtained(Vandiver\u2019s Theorem)Letbe a commutative ring with identity. Letbe a polynomial with coefficients insuch thatThen the polynomial equationhas at mostdabsolutely distinct solutions.a and b are said to be absolutely incongruent modulo n if n.Taking Vandiver  derived . For generalization to prime power moduli, an upper bound for the number of solutions can be obtained using the following result .Supposeis an integer andsis a solution of the polynomial congruenceThen we have the following cases: Ifthenscan be lifted in a unique way fromtoThat is, there is a uniquewhich generatessand which satisfies the polynomial congruenceIfthen: Ifscan be lifted fromtoinpdistinct ways.Ifscannot be lifted fromton, letd). Denote by Given a positive integer IfthenThe proof easily follows from the basic properties of congruences.\u2003\u25a1Therefore, by Lemma\u00a0Using Lagrange\u2019s Theorem and Theorem\u00a0Letbe an integer. Thenp there will be 0, 1, or p solutions modulo p solutions modulo Clearly, if Is there a better upper bound for  Stewart , and to  Stewart . But we  Stewart , 45 (in (Konyagin\u2019s Theorem)Letbe an integer. ThenFurthermore, ifandthenSo far, we have very good upper bounds for the number of solutions of polynomial congruences modulo prime powers. Now, we generalize these upper bounds to arbitrary moduli. For this we need the following tool .Letbe a polynomial with integer coefficients. Also, letbe positive integers, pairwise coprime, and letThen the polynomial congruencehas a solution if and only if each of the polynomial congruenceshas a solution. Moreover, ifanddenote the number of solutions of  is at most D do not collide too often). Formally, H is universal if for any two distinct H is an \u03b5-almost universal (\u03b5-AU) family of hash functions if for any two distinct \u03b5-AU family, for a sufficiently small \u03b5, is close to being universal.The family R is a finite additive Abelian group. The family H is a \u0394-universal family of hash functions if, given a randomly chosen hash function from H, the difference of the hash values of any two distinct elements of D is uniformly distributed in R. Formally, H is \u0394-universal if for any two distinct H is an \u03b5-almost-\u0394-universal (\u03b5-A\u0394U) family of hash functions if for any two distinct k, the operation \u2018\u2212\u2019 can be replaced by \u2018\u2295\u2019 (XOR), and H is also called \u03b5-almost XOR universal (\u03b5-AXU) or \u03b5-otp-secure.Suppose H is a strongly universal (or 2-wise-independent) family of hash functions if, given a randomly chosen hash function from H, the hash values of any two distinct elements of D are independent and uniformly distributed in R. Formally, H is strongly universal if for any two distinct H is an \u03b5-almost-strongly universal (\u03b5-ASU) family of hash functions if for any two distinct h from H, R), andh from H, hard to guess even if The family H is \u03b5-ASU if for any two distinct Equivalently, Let H be an \u03b5-AU family of hash functions, which maps blocks of length 2l to blocks of length l. At each round of tree hash, the message is split into blocks of length 2l and each block is hashed with some n rounds of tree hash, the collision probability is Because many universal hash functions only work on fixed length messages, it is often necessary to extend the domain of the hash function to work on longer messages. Wegman and Carter  introduc1\u2212(1\u2212\u03b5)n . HoweverForletbe almost-universal families of hash functions whereand defineThenHhas the following property: IfisAU andisAU, thenHisAU.IfisAU andisA\u0394U, thenHisA\u0394U.IfisAU andisASU, thenHisASU.\u03b5-AU hash family with an \u03b5-A\u0394U or \u03b5-ASU hash family to create an efficient \u03b5-A\u0394U or \u03b5-ASU family. We can also use this result to create a Merkle\u2013Damg\u00e5rd like paradigm for universal hash functions. Let \u03b5-AU and let l for any positive l, and is The last two parts of this result can be used to pair an efficient d Tsunoo , and a md Tsunoo .H is an \u03b5-AU family of hash functions, then by hashing a message with two independent keys and concatenating the results, the probability of collision is lowered to n hash values to get a collision probability of n, the size of the key only increases by n values. Not only does this save key material, it reduces memory accesses, thus potentially improving performance.Often the collision probability of a hash function may be larger than desired. For this reason, there are several techniques for reducing the collision probability of a hash function family. If ms c.f. , 64), re, reH is \u03b5-A\u0394U families to \u03b5-ASU families. Because for authentication in QKD systems we need efficient \u03b5-ASU families, our result implies that constructing such families boils down to constructing efficient \u03b5-A\u0394U families. Our result is a generalization of the following result by Etzel et al. [Now, we prove a general result for transforming l et al.  which seLet the familybe a \u0394-universal family of hash functions, whereKis the key space andRis a finite additive Abelian group. Then the familywhereand \u2018+\u2019 denotes the group addition operation, is strongly universal.In order to generalize the above result, we also need the following result (see ):LetGbe an Abelian group, and letbe independent random variables which take on values inG. If one ofis uniformly distributed inG, then the sumis also uniformly distributed inG.G, under which the sum G.More generally, Sherstnev  gave necNow, we are ready to prove our result.Let the familybe an\u03b5-almost-\u0394-universal family of hash functions, whereKis the key space andRis a finite additive Abelian group. Then the familywhereand \u2018+\u2019 denotes the group addition operation, is\u03b5-almost-strongly universal.H is \u03b5-almost-\u0394-universal, we haveFor any two distinct \u03b5-A\u0394U family of hash functions which has received much attention is Polynomial Hash (PH), which is used for hashing variable length messages. The idea is that we put the message blocks as the coefficients of a polynomial and then evaluate the polynomial at the secret key, where all operations are done in a specific field or ring. In this section, we introduce and analyze several efficient variants of Polynomial Hash and then compare our results with available results. As Polynomial Hash has found many applications, our constructions and results might be of interest in various areas.An Here we introduce five variants of Polynomial Hash  and analyze their universality using results from Sect.\u00a0Polynomial Hash Over Ring of Integers Modulon(PH-IM): In this family, message blocks n, the key x is in (PH-IM)Given an integer Lethas the prime factorizationwhere\u2019s are prime andfor alli. Then we have the following cases: The family PH-IM isalmost-\u0394-universal.Ifnis square-free, then the family PH-IM isalmost-\u0394-universal.Ifandfor alli, then the family PH-IM isalmost-\u0394-universal.i, then the polynomial congruenceWe only prove the last part; the proofs for other parts are similar. Let Polynomial Hash With Probability At LeastZero Collision (PH-ZC): Let p be an odd prime and k be a positive even integer not divisible by p. Denote the set of even elements of E and the set of odd elements of O. In this family, message blocks E or are all in O, the key x is in E; the definition and the result over O are similar. Formally,(PH-ZC)p and a positive even integer k not divisible by p, we defineGiven an odd prime The family PH-ZC isalmost-\u0394-universal. Furthermore, with probability at leastthe collision probability is exactly zero.b is odd then the polynomial congruenceb is even then it has at most k solutions. On the other hand, by Lagrange\u2019s Theorem, for every d solutions. Now, using Theorem\u00a0b is odd, and has at most kd solutions if b is even.Let b is odd and possibly in other cases : In this family, each message block x are in (PH-PF)p,Given a prime The family PH-PF isalmost-\u0394-universal.Same as above, just use Lagrange\u2019s Theorem or Theorem\u00a0arbitrary non-negative integers as long as no two messages have all their corresponding blocks congruent modulo p or modulo n. See Theorem\u00a0It is important to note that we do not have to restrict the message blocks to be in Polynomial Hash Over Prime Fields With Arbitrary Message Blocks (PH-PA): Let A be a subset of A have all their corresponding coordinates congruent modulo p. In this family, each message m is in A, the key x is in (PH-PA)p,Given a prime The family PH-PA isalmost-\u0394-universal.p (by the definition of the set A) so the assumption of Lagrange\u2019s Theorem is satisfied. Also, note that Theorem\u00a0Same as above, just use Lagrange\u2019s Theorem. Note that when we find the difference of the two polynomials, at least one of the coefficients is non-zero modulo Polynomial Hash Over Finite Fields (PH-FF): In this family, each message block x are in (PH-FF)q elements, where q is a prime power,Given the finite field The family PH-FF isalmost-\u0394-universal.Same as above, just use Theorem\u00a0Using Theorem\u00a0any\u03b5-A\u0394U family, in particular the families studied in this paper, can be transformed to\u03b5-ASU families which makes them useful for various applications including authentication of variable length messages in QKD. This can be done by adding a uniform valueto the hash functions, whereRis the range of the corresponding hash functions.Polynomial Hash is widely attributed to Wegman and Carter , Dietzfe\u03b5-almost-\u0394-universality of these families. As discussed in detail in Remark\u00a0So far, only the families PH-PF and PH-FF have been introduced in the literature but, unfortunately, there is a growing number of papers that explicitly or implicitly have used the Fundamental Theorem of Algebra to prove the d,d multiplications and d additions since, by Horner\u2019s rule, d multiplications and d additions, while hashing the same message using most other universal hash function families needs more computations, for example, hashing it using MMH\u2217 [The evaluation of a polynomial ing MMH\u2217 , 72, 73 \u2217 and its variants) which hash fixed length messages  Polynomial Hash can be used for hashing variable length messages because each message block becomes the coefficient of the polynomial, and so is independent of the key.Unlike most other universal hash function families   . See Remark\u00a0We do not have to restrict the message blocks to be in In some of these variants with probability at least We do not need large prime numbers or finite field arithmetic anymore  using results from Sect.\u00a0Although in QKD the legitimate parties need to share some initial small secret information in advance for the authentication of the classical channel, each round of QKD provides substantially larger fresh key materials, part of which can be used for authentication in the next round of QKD. Furthermore, keys generated in each round of QKD are completely independent of all prior keys and messages , 6, 74. We connected Polynomial Hash and QKD with deep results in number theory. This may motivate more work in these areas.Our study of Polynomial Hash over The above techniques and results on the Polynomial Hash and its variants and comparing them with what were known before, reveals some remarks:"}
+{"text": "As a result, we obtained the p-type thermoelectric figure of merit up to 0.96\u00a0at 300\u00a0K, indicating that the boron monolayer is a promising p-type thermoelectric material.A heavy element is a special character for high thermoelectric performance since it generally guarantees a low lattice thermal conductivity. Here, we unexpectedly found a promising thermoelectric performance in a two-dimensional semiconducting monolayer consisting of a light boron element. Using first-principles combined with the Boltzmann transport theory, we have shown that in contrast to graphene or black phosphorus, the boron monolayer has a low lattice thermal conductivity arising from its complex crystal of hexagonal vacancies. The conduction band with an intrinsic camelback shape leads to the high DOS and a high  ZT = S2\u03c3T/\u03ba, where S is the Seebeck coefficient, \u03c3 is the electrical conductivity, \u03ba is the thermal conductivity including both electronic and lattice contributions, and T is the absolute temperature, respectively  light elements with high vibration frequency and 2) large atomic weight difference forbids the anharmonic scattering. In this regard, we intended to think that is there possibility to achieve promising thermoelectric transport in other single-layer crystal consisting of light elements? In recent years, boron, one of the carbon\u2019s nearest neighbors, demonstrated the polymorphism in two-dimensional crystals, which are called borophene. However, most of the boron monolayers were found to be metallic by experiment or theory. Interestingly, Hu et al. recently proposed a series of semiconducting boron monolayers formulated by the connected network of hexagonal vacancies   using projector-augmented wave (PAW)  pseudopoon (mBJ)  functionn-type doping while down for the p-type. However, within this approximation, the Seebeck coefficient can be calculated independent of carrier relaxation time \u03c4, while the evaluation of electrical conductivity still requires the knowledge of \u03c4. In this regard, we employed deformation potential theory based on effective mass approximation to calculate \u03c4  under a constant relaxation time approximation as implemented in BoltzTraP . A rigidculate \u03c4 . At lastculate \u03c4  package culate \u03c4 , and a cet al  is located in the interval between \u0393 and Y points. In consistent with previous calculation, the VBM is dominated by the out-of-plane pz orbitals while the CBM is attributed to the in-plane s+px,y orbitals   . Thus, tow 1ps\u22121 . Figure ZT values for both the n- and p-doped boron monolayer as a function of the carrier concentration at room temperature. Obviously, the p-type thermoelectric performance is superior to n-type due to the excellent p-type power factor. Combined with the relatively low lattice thermal conductivity, the optimal p-type ZT value of the boron monolayer reaches 0.96\u00a0at an optimal carrier concentration of about 1 \u00d7 1012\u00a0cm\u22122, which is a recorded value among single-layer materials consisting of light elements. Our results indicate that the semiconducting Combining the electronic and phonon transport properties, we evaluated the thermoelectric performance of the n-type Seebeck coefficient arises from the camelback shape of the lowest conduction band, while the highly degenerate valence band with small effective mass leads to the high hole mobility and long relaxation time, which contributes to the superior hole transport performance. Importantly, we found relatively low lattice thermal conductivity in the boron monolayer, \u223c20\u00a0W/mK at 300\u00a0K, as compared with graphene or phosphorene also consisting of a light element. This is primarily ascribed to the complex unit cell with the hexagonal vacancy. Finally, we obtained an optimal p-type ZT of about 0.96\u00a0at 300\u00a0K in this boron monolayer, indicating its potential as p-type thermoelectric materials.We have investigated the thermoelectric performance of a semiconducting"}
+{"text": "Communications Biology 10.1038/s42003-021-02449-8, published online 29 July 2021.Correction to: In the original version of the Article, the title contained an error and incorrectly spelt \u201cpolyploid\u201d as \u201cpolypoid\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Nature Communications 10.1038/s41467-020-19264-0, published online 02 November 2020.Correction to: y-axis was incorrectly labelled as \u2018ApoE in RIPA\u2019 instead of \u2018ApoE in FA\u2019. This has been corrected in both the PDF and HTML versions of the Article.The original version of this Article contained an error in Fig. 5b, in which the"}
+{"text": "Translational Psychiatry 10.1038/s41398-021-01257-2, published online 18 February 2021Correction to: The original version of this article unfortunately contained an error. The authors recommend adding a phrase at the end of the section \u201cGene\u2013environment interactions, epigenetic factors, and demographic characteristics\u201d.In doing so, the phrase \u201cfor instance, the aforementioned interaction between 2R- and 3R-repeat MAO-A variants  and child abuse was associated with violence and antisocial behavior only in Caucasians but not in individuals from other ethnic group\u201d changes to \u201cfor instance, the aforementioned interaction between 2R- and 3R-repeat MAO-A variants  and child abuse was associated with violence and antisocial behavior only in Caucasians but not in individuals from other ethnic group; however, as this study did not control for gender, it is likely its results could be pertinent to non-Caucasians, as well\u201d. The original article has been corrected."}
+{"text": "A number of methods have been proposed for face reconstruction from single/multiple image(s). However, it is still a challenge to do reconstruction for limited number of wild images, in which there exists complex different imaging conditions, various face appearance, and limited number of high-quality images. And most current mesh model based methods cannot generate high-quality face model because of the local mapping deviation in geometric optics and distortion error brought by discrete differential operation. In this paper, accurate geometrical consistency modeling on B-spline parameter domain is proposed to reconstruct high-quality face surface from the various images. The modeling is completely consistent with the law of geometric optics, and B-spline reduces the distortion during surface deformation. In our method, 0th- and 1st-order consistency of stereo are formulated based on low-rank texture structures and local normals, respectively, to approach the pinpoint geometric modeling for face reconstruction. A practical solution combining the two consistency as well as an iterative algorithm is proposed to optimize high-detailed B-spline face effectively. Extensive empirical evaluations on synthetic data and unconstrained data are conducted, and the experimental results demonstrate the effectiveness of our method on challenging scenario, e.g., limited number of images with different head poses, illuminations, and expressions. Point cloud, skeleton, and mesh grid are the widely used man-made shape type for face reconstruction. Lu et al.  present Ii from a camera is \u22121 denotes the inverse operator of \u03a0. The camera operator i = 1, 2, \u2026, n. And i of BP imaging from si, Ri, and ti denote scale, rotation, and translation parameter in projection \u03a0i. The ith projection operation is simplyOur problem modeling is illustrated in Ri,  expresses the first two rows of Ri.F\u22121 denote the inverse operator of F. It is thus clear that different embedding F determine different face shapes. According to the geometric optics of BP imaging, a image point via the operatorIi in the i-th view is mapped to surface S, and then is mapped to texture space byi, i = 1, 2, \u2026, n generate discrete and inconsistent rays mapping in texture space because of the discrete and different images domains, as well as the noises, seen in Let F according to from multiple images. If all images are the captures of a same Generally, the problem is how to determine # is a composition operator of fitting and sampling, to handle the inconsistency. It firstly fits a texture function based on the discrete texture and parameters mapped from one image, and then samples texture intensity values at unified parameter points {uj}j=1 : Np.First, that satisfiesn and 1st-order partial derivative in the first formulation, and the equivalence relation among albedo \u03c1, normal n, light direction l, and image intensity Second, it satisfiesWe refer to Equations (5) and (6) as 0th- and 1st- order consistence equations in 3D surface reconstruction respectively. Generally, researchers solve any one of the two consistence problem to reconstruct 3D surface, classically, by multi-view stereo . The surface function isRm,n(u) = Nm,4(u) \u00b7 Nn,4(v) andThe human face is assumed to be a uniform B-spline surface F is C2, meaning that it can approximate the true shape in arbitrary uv precision with deterministic k-ordered partial derivative k = 1, 2, and b denotes a 3MN \u00d7 1 vector storing B-spline control points, and T|u denotes a sparse 3 \u00d7 3MN matrix stacking the 0th-order coefficients at parameter We give a more brief formulation of 0th-order representation as follows:f landmark points on human face as shown in u(li) is the parameter point of the i-th feature point, i = 1, 2, \u2026, f. The landmarks cover a sparse structure of face.In fact, we needn't consider all 3D points mapping to 2D images when estimating a operator \u03a0. Instead, we only consider F w.r.t u and v areThe 1st-order partial derivatives of T1|u and T2|u denote the matrixes stacking the 1st-order coefficients w.r.t u and v, respectively.Similarly, we give a more brief formulation of 1st-order partial derivative as follows:u can be computed by the cross productTherefore, the surface normal vector at u and v, respectively areT11|u and T22|u denote the matrixes stacking the 2nd-order coefficients w.r.t u and v, respectively. The 2nd-order information can be used for smooth control during optimization.And similarly, the 2nd-order partial derivatives w.r.t. Based on face surface embedded with B-spline function, we present the pinpoint 0th- and 1st-order geometric consistency conditions in the following section.F by solving 0th-order consistence of Equation (5) or 1st-order consistence of Equation (6). Generally, two consistency conditions are combined for face reconstruction considering that estimating abundant consistent points in images is limited and that the estimated normals are unfaithful. Furthermore, how to obtain the accurate registration of 0th- and 1st-order information is the most important to high-detailed B-spline reconstruction.Reconstruction problem is to compute The well-registered textures are low-rank structures of the back projection texture charts. But in practice, they can be easily violated due to the presence of partial occlusions or expressions in the images captured. Since these errors typically affect only a small fraction of all pixels in an chart, they can be modeled as sparse errors whose nonzero entries can have arbitrarily large magnitude.ei represent the error corresponding to image Ii such that the back projection texture charts F, and free of any corruptions or expressions. Also combining with 0th-order representation of B-spline face in Equation (7), the formulation (5) can be modified as follows:E = .Let However, the solution # to sample Np dense parameter points {uj}j=1 : Np on the domain The resolution of reconstruction is determined by the density of correctly estimated normals. To enhance the resolution of B-spline surface, we use operator (\u00b7)i = 1, 2, \u2026, n and j = 1, 2, \u2026, Np.Then the well-registered and dense texture are obtained bynj as well as light li can be computed from the shading (intensity) of charts According to Lambertian illumination model seen in Equation (6), dense normals Finally, the high detailed reconstruction must satisfyThe problems of both 0th-order consistence and 1st-order consistence are difficult to solve. For , Jacobian matrices w.r.t. i}i=1 : n, surface parameters F (or b), and texture parameters D) need to be computed, but they are difficult to be solved simultaneously. We adopt to optimize them by turns, instead.In Equation (6), three kind of parameters including camera parameters {\u03a0si, rotation Ri and translationti of landmarks for each image Ii, i = 1, 2, \u2026, n based on the and SVD method .According to linear transformation from 3D to 2D in Equation (1), we can estimate scale f denote a 2nf \u00d7 1 vector stacking f landmarks of n images, and P denote a 2nf \u00d7 3f projection matrix stacking n views of parameters siRi, , and t denote a 2nf \u00d7 1 vector stacking f translation. The update of b can be implemented by solving:#l is a sampling operator that selects B-spline coefficients of landmarks at parameters {u(li)}i=1 : f, and (\u00b7)# selects B-spline coefficients at {uj}i=1 : Np. In fact, T#l is a 3f \u00d7 3MN matrix that stacks T|u(li), i = 1, 2, \u2026, f, and f \u00d7 3MN matrix that stacks T11|uj (or T22|uj), j = 1, 2, \u2026, Np.Let b and b0. It helps eliminate affect of geometric rotation brought by 0st-order warping, and guarantee a smoothness changing during optimization. Particularly, \u03b6 cannot be too small, otherwise a fast changing may bring a local optimal.The second item also work as a regularization measuring the distance of local information between faces i is determined by Equation (2) when \u03a0i and b is known. Then texture chart with noise is obtained by applying consistent parameter sampling i = 1, 2, \u2026, n, and j = 1, 2, \u2026, Np.Firstly, texture charts based photometric stereo method is used to estimate the local normals. Secondly, a normals driven optimization strategy is proposed to optimize the B-spline face.n texture charts are input into Mn\u00d7Np for estimating the initial shape M = LSvia SVD  can be rewritten asNp \u00d7 3Np diagonal matrix that stores 3Np reciprocals of lengths of the normals {nj}j=1 : Np; and (\u00b7)# is a selection operator that selects 3Np rows of 1st-order coefficients at parameter {uj}j=1 : Np; and b0 represent the control points of a B-spline template face. Particularly, symbol \u2297 denotes a composite operator of cross product, which makes w \u2297 v = , where w and v are 3Np \u00d7 1 vectors containing Np normals.We normalize h may not guarantee an unique solution of high-dimension b; and (2) the system is not simply linear, which is difficult to be solved. Therefore, a frontal constraint based on template b0 is applied to make a unique solution; And a strategy of approximating to linearization is also proposed to make a linear solution.However, there exists two issues: (1) the low-dimension x- and y-component:T#xy stacks 0th-order coefficients at parameter {uj}j=1 : Np corresponding to x- and y- components. Operator (\u00b7)#sxy also sets the coefficients corresponding to z- components to zeros.The frontal constraint is a distance measurement condition between surface O1 is not a simple linear form, for which an approximating to linearization is proposed.Particularly, the first item O1 can be rewritten as a linear-like formulation:According to the characteristics of the cross-product \u2297, the first item in \u2297 makes a 3Np \u00d7 1 vector Np \u00d7 3Np sparse matrix [w]\u2297 = diag, where Particularly, the operation [\u00b7]b is a known parameter, e.g., as b0, for L|b, the minimization of ||h \u2212 L|b0 \u00b7 b|| will be a linear system. That is also true for R|b.If h \u2212 L|b0 \u00b7 b|| to optimize the control points in parameter space of v by fixing u, and use ||h \u2212 R|b0 \u00b7 b|| to optimize in parameter space of u by fixing v.In fact, we can use formulation ||u and v parameter spaces by turns. The two iteration items are rewritten as1|b0 (or \u039b2|b0) is a 3Np \u00d7 3Np diagonal matrix that stores 3Np reciprocals of lengths of tangent vector uj}j=1 : Np. During this procedure b0 is updated step-by-step. As shown in u, v) are updated until n.A practical skill is to optimize the control points on O2, the final formulation of optimization consists of two items as follows:b0 is initialized by value of b0. Then we can solve b and update b0 orderly by minimizing (a) and (b) in Equation (18) iteratively until convergence.By integrating with An iterative algorithm is presented for this practical solution in Algorithm 1. Processes of 0th-order consistence and 1st-order consistence are separately conducted in the inner loop. And the outer loop guarantees a global convergence on two consistence problem.n2f2MN), and that of both Equations (18.a) and (18.b) are O, (18.a), and (18.b), SVD for estimating camera parameter, and Robust PCA for Equation (17). In detail, the computational complexity for solving Equation (16) is O(In this section experiments are presented to verify our automatic free-form surface modeling method. We first describe the pipeline to prepare a collection of face images of a person for B-spline face reconstruction. And then we demonstrate the quantitative and qualitative comparisons with recent baseline methods on projected standard images from ground truth 3D data (Zhang et al., The ground truth data are from the space-times faces (Zhang et al., The wild data (Huang et al., To verify the accuracy of automatic surface reconstruction, discrete points are sampled from the generated continuous free-form shape, and are compared to the traditional discrete reconstructions, e.g., work by Kemelmacher and Seitz  and RothS1, S2, S3, and S4 by using their corresponding images, and the fifth session S5 is based on images with different expressions. Each session contains 40 images with various illumination and different poses. Reconstruction results are compared with the re-implemented method Kemel_meth by Kemelmacher and Seitz (We conduct five sessions of reconstructions: the first four are used to reconstruct expression nd Seitz  and Rothnd Seitz . Kemel_mTo compare the approaches numerically, we compute the shortest point-to-point distance from ground truth to reconstruction. Point clouds are sampled from B-spline face and aligned according to absolute orientation problem. As done in work of Roth et al. , mean EuThe visual results in C2 differentiable parametric surface while the other two are discrete model. Conclusively, 0th- and 1st-order consistency modeling using B-spline surface is efficient to reconstruct parametric surface of individual face.We give statistics of characteristics of the results generated by the three methods in Our method is also tested based on real unconstrained data. Unconstrained data mean that the images are captured under uncertain condition, and the faces in the images are different in expression, pose and illumination condition. It is difficult to build the geometrical consistency for reconstruction using such data. Unlike the experiments in the work by Kemelmacher and Seitz  using huA label the results generated by the reimplemented Kemel_meth, and let B label the results generated by the reimplemented Roth_meth, and let C label the method Seta_meth of deep learning by Sela et al. (D label our results. Particularly, the input for Seta_meth is one image selected from the 35 images. Images in column 1, 5, and 8 are corresponding mean textures and two views of images respectively. By comparing these results, we observe some phenomena as follows:A and D show more vivid details than B, e.g., eyes and nose of Colin Powell. But in an other viewpoint, D shows more credible shape than A, e.g., the eyes and the forehead of Colin Powell, and the forehead and the mouth of Donald Rumsfeld.In frontal viewpoint, A loses the local information completely, but B, C, and D still maintain general geometrical shape of face. For all methods, reconstructing nose is a challenge because the geometric curvature of the nose varies greatly. When the images are not enough, the noise could be amplified. So B shows bad results at nose being limited by number of input images.When the normals are incorrectly estimated from a limited number of images, e.g., for Gloria Macapagal Arroyo, C is a approximately frontal face image selected. As the model of C is learning on a set of 3D face data, it may not handle the uncertain noise and identity of inputs. So the details in reconstruction by C don't look real, although their global shapes are stable and like human faces.The input of By comparison, our method steadily produces better looking results than others from different viewpoints in the dataset. Clear and vivid details can be seen at key components such as eyes, nose and mouth, forehead, and cheek.Visual face reconstructions for Colin Powell, Donald Rumsfeld, George W. Bush, Hugo Chavez, and Gloria Macapagal Arroyo are compared with other two methods, as shown in a et al.  and let B looks better. It could deal with 3D reconstruction with limited number of images. Because we may not obtain large amount of images for reconstruction as done by Roth et al. (A are mainly resulted from the inauthentic depth generated by integration method. And the bad results of B are caused by that the mesh template cannot build correct geometric consistency of number limited of unconstrained images and that the discrete differential operating on estimated noisy normal brings distortion errors. In contrast, we build pinpoint geometric consistency using B-spline surface. B-spline can smooth the noise in estimated normal better. So D can reconstruct correct face shape with little distortion, showing better result as a whole.All the above experiments prove that our method can build pinpoint geometrical consistency on the limited number of real unconstrained data. Our method may not be best method in area of 3D reconstruction from multiple images, as the results in the original work by h et al. , for somIn the comparison, we don't consider other deep learning methods based methods appeared in recent years (Dou et al., This study set out to present high-detailed face reconstruction from multiple images based on pinpoint 0th- and 1st-order geometric consistence using B-spline embedding. Based on the good consistence modeling in geometric optics, the method works well for data with different poses and expressions in the wild. The key contribution of this study is that surface modeling adapts the correct rays in geometric optics by using B-spline embedding. This makes the high-detailed B-spline modeling from a number limited of face images captured under wild condition become reality. The method could also be applied to expression tracking and assisting face recognition in a monitoring or robot system.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.WP and ZF has contributed equally to the core idea as well as the experiment design and results analysis. YS, KT, and CX has provided assistance in experiments and analysis, under ZF's supervision. Besides, KT and MF provided the research group with financial support and experimental equipments. KT and ZF are supportive corresponding authors. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Formulae for the c-subdifferential and biconjugate of the objective function of a general optimization problem are provided, too. We also characterize the total duality by means of the saddle-point theory for a notion of Lagrangian adapted to the considered framework.We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally convex topological space. Sufficient conditions for converse and total duality involving the even convexity of the perturbation function and  Another related interesting problem in conjugate duality theory is the notion of converse duality. It corresponds to the situation where there is no duality gap and the primal problem is solvable. This issue was investigated in the convex setting in [An important part of mathematical programming from both theoretical and computational points of view is the duality theory. Rockafellar (cf. ) developtting in  for Fenctting in .c-conjugation scheme and it was developed in [c-conjugation scheme is associated with the even convexity of such a function. Evenly convex sets (functions) are a generalization of closed and convex sets (functions), see, for instance, [evenly convex, e-convex in brief, if it is the intersection of an arbitrary family, possibly empty, of open halfspaces. Such sets have been employed to study the solvability of semi-infinite linear systems containing infinitely many strict inequalities in [e-convex if its epigraph is e-convex. According to [c-conjugation scheme is suitable for this class of functions in the sense that the double conjugate function equals the original one if it is proper and e-convex. This result can be seen as the e-convex counterpart of the celebrated Fenchel\u2013Moreau theorem. Concerning the usage of e-convexity in finance mathematics and consumer theory, we refer to [c-conjugate scheme in the direction of formulas for asymptotic functions and multi-marginal monotone sets can be found in [In this paper we propose a new dual problem to a general primal one defined on locally convex spaces by means of a generalized conjugation scheme and study converse duality for this primal\u2013dual pair. This pattern, which is inspired by a survey done by Mart\u00ednez-Legaz where generalized convex duality theory is applied to quasiconvex programming, is called loped in . In the loped in  \u2013 the usnstance, . Fenchelnstance,  a set evities in , whereasities in . Due to ities in , an exterding to , the c-crefer to ,12. Somefound in ,14, respc-conjugate duality theory, and the counterparts of some regularity conditions, i.e. conditions ensuring strong duality, from the Fenchel conjugate setting were obtained. Moreover, in [The theory developed in  motivateover, in  regulariover, in  we analyover, in  the Fencover, in  we used over, in  to derivtotal duality  from this general perspective. Moreover and extending in this way results from the convex setting [c-subdifferential and biconjugate of the objective function of a given general optimization problem. Motivated by [The purpose of the paper is twofold. First, we analyse the fulfillment of converse duality for a primal\u2013dual pair expressed via the perturbation function, where its even convexity will play a fundamental role. In order to avoid repetitive arguments, we have decided to derive the aforementioned converse duality in the general form, leaving as an application the natural particularizations into the previously mentioned special cases. As a second target, we address the problem of  setting , we provvated by , we highc-subdifferentials which allow to characterize total duality for a general primal\u2013dual pair. Moreover, the \u03f5-c-subdifferential of the objective function of the considered problem is expressed via the \u03f5-c-subdifferential of the considered perturbation function. Last but not least in Section\u00a0The layout of this work is as follows. Section\u00a02.X be a nontrivial separated locally convex space, lcs in brief, equipped with the Y be another lcs. By Let evenly convex, e-convex in short, if for every point e-convex hull of C, X containing C. For a convex subset X is a separated lcs, X is e-convex and every closed or open convex set is e-convex as well.According to , a set Ceffective domain of f and by epigraph and its graph, respectively. We say that f is proper if lower semicontinuous hull of f, which is the function whose epigraph equals f is lower semicontinuous, lsc in brief, if for all e-convex if For a function n see in , Ex.\u00a02.1e-convex hull of a function f. Based on the generalized convex conjugation theory introduced by Moreau [the coupling functionsc-conjugate of f, c of g, The y Moreau , a suitay Moreau . Let us c-elementary, and, in a similar way, functions of the form . In [X to c-elementary functions. Similarly, a function e if it is the pointwise supremum of sets of e of an extended real function g defined on W, denoted by g such that D.Functions of the form tary. In  it is shThe following counterpart of the Fenchel\u2013Moreau theorem for e-convex and eTheorem 2.1f is e-convex if and only if g is eLet recession cone of a nonempty convex subset The following lemma and proposition were shown in the finitely dimensional case in ,26, respLemma 2.2Let Proposition 2.3Let For convenience in Section\u00a0Definition 2.4functionally representable if A non-empty e-convex set Remark 2.1A non-empty e-convex set 3.c-conjugate Let lines of , we consinfimum value functionGDc). In , via theIn order to be able to provide a counterpart of (C5) for the pair ms \u2013 see ,18,20. RTheorem 3.1It always holds Proof.Let us take W. Then,)ction in\u00a0)cNext we present the counterparts of Lemma\u00a05.1, 5.2 and 5.3 from  that areLemma 3.2Proof.Fixing It holdsWe continue with a Moreau\u2013Rockafellar-type result involving the Lemma 3.3Proof.We have, for all Lemma 3.4If the e-convex hull of Proof.p,C is functionally representable by assumption, due to Remark\u00a0First, we see that  Theorem\u00a0epi\u03a8+fcc\u2032(x)Remark 4.1f is e-convex, f is not necessary in one sense of the equivalence.As a consequence of [total duality for We apply these results to ing (see ), total Proposition 4.6Let Proof.If  Furtherv(GP)\u2264\u03a6.Proposition 5.4One always hasProposition 5.5L if and only if Let us assume that Proof.L. From [Let  L. From , Sec.3 iL. From [\u2212\u03a6c) and\u03a6=suL.For the converse statement, since n, using\u00a0 and\u00a019)v(GP)=\u03a6=in6.\u03f5-duality statements from [In this paper we present new results regarding evenly convex (e-convex) functions, in particular converse and total duality statements for e-convex problems that extend their counterparts from the  convex case. Other results can be generalized to the current setting as well, for instance the nts from , howevernts from , Ex.\u00a02.1c-subdifferentials and c-subdifferential and biconjugate of the objective function of a given general optimization problem are provided, too. On the other hand, we extend the definition of the classical Lagrangian towards the e-convex setting by means of the c-conjugation scheme and relate the corresponding saddle-points to total duality. The results for general optimization problems can be specialized for constrained and unconstrained optimization problems as well.We extend in this article the notion of converse duality from the convex setting to e-convex optimization problems, providing a sufficient closedness-type regularity condition for it and an alternative formulation using the infimum value function. In order to prove the mentioned results we introduced the notion of functionally representable functions and we also gave a new Moreau\u2013Rockafellar type result for ec- and c-conjugation, other paths can be followed along this direction. On the other hand, the investigations from [We have restricted ourselves to closedness type regularity conditions, but taking into consideration , Sect.\u00a03ons from  on subdi"}
+{"text": "We study the problem of communicating over a discrete memoryless two-way channel using non-adaptive schemes, under a zero probability of error criterion. We derive single-letter inner and outer bounds for the zero-error capacity region, based on random coding, linear programming, linear codes, and the asymptotic spectrum of graphs. Among others, we provide a single-letter outer bound based on a combination of Shannon\u2019s vanishing-error capacity region and a two-way analogue of the linear programming bound for point-to-point channels, which, in contrast to the one-way case, is generally better than both. Moreover, we establish an outer bound for the zero-error capacity region of a two-way channel via the asymptotic spectrum of graphs, and show that this bound can be achieved in certain cases. Shannond DM-TWC ,4,5, andd DM-TWC ,7. Howevd DM-TWC ,9,10.In yet another seminal work, Shannon proposed and studied the zero-error capacity of the point-to-point discrete memoryless channel , also knn uses of the DM-TWC codebook pair. Note that the encoding functions depend only on the messages, and not on the observed outputs during the transmission, hence the name non-adaptive. When transmissions end, Alice and Bob observe the resulting (random) channel outputs . A rate pair achievable for the DM-TWC if an n. The non-adaptive zero-error capacity region of a DM-TWC non-adaptive zero-error sum-capacity of a DM-TWC The problem of non-adaptive communication over a DM-TWC can be formulated as follows. Alice and Bob would like to simultaneously convey messages The main objective of this paper is to provide several single-letter outer and inner bounds on the non-adaptive zero-error capacity region of the DM-TWC. The remainder of this paper is organized as follows. In V and edge set E. Two vertices adjacent, denoted as independent set in G is a subset of pairwise non-adjacent vertices. A maximum independent set is an independent set with the largest possible number of vertices. The size of a maximum independent set in G is called the independence number of G, denoted by complement of a graph G, denoted by G. We write n vertices, respectively.Let strong product  G and H is a graph such that(1)the vertex set of (2)two vertices The n-fold strong product of graph G with itself is denoted as Shannon capacity of graph G was defined in [Let (G)\u00d7V(H);two vertidisjoint union\u00a0G and H is a graph such that graph homomorphism from G to H, denoted by G, then H. We write G to the complement of H.The In , ZuiddamTheorem\u00a01.\u00a0\u2294 and the strong product \u22a0, and also contains the graph with a single vertex Let (1)\u00a0if (2)\u00a0(3)\u00a0(4)\u00a0Then, .\u00a0Let G As remarked in , 2\u0398(G) i of Alon , and als of Alon . In SectIn this subsection, we characterize the zero-error capacity of a discrete memoryless point-to-point channel, as well as the zero-error capacity region of a DM-TWC, in terms of suitably defined graphs. The point-to-point characterization is well known and goes back to Shannon , and thememoryless in the sense that ith channel use. Suppose that a transmitter would like to convey a message , and such a code is called uniquely decodable if R is called achievable if an n. The zero-error capacity of the channel is defined as the supremum of all achievable rates.A discrete memoryless point-to-point channel consists of a finite input alphabet confusion graph G, whose vertex set is the input alphabet n-fold strong product of graph G. Consequently, the zero-error capacity of a point-to-point channel is equal to the Shannon capacity of its confusion graph G. Note that there are infinitely many distinct channels with the same confusion graph, and all of these channels have the same zero-error capacity.A channel We now proceed to similarly associate a DM-TWC with a collection of confusion graphs, which would then be shown to characterize its zero-error capacity region. To that end, note that when Alice sends a letter Proposition\u00a01.Consider a DM-TWC In particular, we see that the capacity region Proposition\u00a02.If This further immediately implies:Proposition\u00a03.The strong product of two DM-TWCs Lemma\u00a01.Proof.\u00a0To prove this lemma, it is sufficient to prove that, for any dual graph homomorphism from (1)if (2)if It is easy to see that the dual graph homomorphism is a natural generalization of the standard graph homomorphism of two graphs, in the sense that they are both adjacency preserving. We write In this subsection we study the behavior of the zero-error capacity region of a DM-TWC under graph homomorphisms, generalizing a similar analysis from the point-to-point channel case . Let [{GLemma\u00a02.If Proof.\u00a0n for the DM-TWC Suppose \u03c6(an)=)one-shot zero-error capacity region, and the associated sum-rate as the one-shot zero-error sum-capacity. Recall that the one-shot zero-error capacity of a point-to-point channel is simply the logarithm of the independence number of its confusion graph; this quantity yields a lower bound on the zero-error capacity of the channel, and also provides an infinite-letter expression for the capacity when evaluated over the product graph. It is therefore interesting to study the analogue of the independence number in the two-way case, which in particular would yield an inner bound on the zero-error capacity region of the DM-TWC. For simplicity of exposition, we will focus here on the one-shot zero-error sum-capacity only.In this subsection, we consider the problem of zero-error communication over a DM-TWC with only a single channel use by the two parties \u00a0If (2)\u00a0(3)\u00a0S is an independent set of Proof.\u00a0The results follow directly from the definition of dual independent pairs.\u2003\u25a1Lemma\u00a03.Let (1)\u00a0(2)\u00a0(3)\u00a0(4)\u00a0Proof.\u00a0S and T. From Proposition 4 (2), we have(1) The lower bound follows from Proposition 4 (1) and the symmetry of S and T as the maximum independent sets of H and G respectively.(2) From claim (1) above, we have (3) From claims (1) and (2) above, we have(4) is a direct consequence of claim (1) above. The lemma follows.\u2003\u25a1By graph homomorphisms we immediately have:Proposition\u00a05.If J be an A and B, denote A. Now define Next, we shall provide an upper bound for a number . Let \u0393 bLemma\u00a04.Proof.\u00a0m and a set S, denote Suppose X, where Y similarly. The Shannon entropy of X is denoted by binary entropy function is written as conditional entropy of X given Y is written as mutual information between X and Y is conditional mutual information of Z is We recall some standard information-theoretic quantities that will be used in the sequel. Let Proposition\u00a06.(1) (2) (3) In this section, we provide single-letter outer bounds for the non-adaptive zero-error capacity region of the DM-TWC. First in It is trivial to see that Shannon\u2019s vanishing-error non-adaptive capacity region of the DM-TWC  and ande. Hence|Ai(S)|=\u2211 l(\u03bb) in . This coThe following is a trivial corollary of Lemmas 6 and 7.Corollary\u00a01.whereWe now provide a single-letter outer bound, in which the order of the minimum and the maximum in  is swappTheorem\u00a02.whereThe first intersection is taken over all DM-TWCs Proof.\u00a0The intersection over all n, we will show that:n, where n. The base case of n. Suppose that n. Following the same steps of  in  in teps of , we, we(22)I|Ai,Bi)2\u2264\u2211i=1nH(Yondition .By the definition of logl(\u03bb)}\u2265maxPX1,P we have\u2212logl(\u03bb)>mbining , weclose to , as desiD is a set of letters, n, and n. Let:I, and denoteIn this subsection, we present a construction of uniquely decodable codes via linear codes, which generalizes a known result for the binary multiplying channel . Let us detecting symbol, if detecting vector for detecting vector for Let Proposition\u00a07.Let Proposition 7 provides a sufficient condition for a uniquely decodable code, which is not always necessary (see Example 2). Nevertheless, this sufficient condition furnishes us with a way of constructing uniquely decodable codes by employing linear codes.Example\u00a02.Suppose that Assume that  channel .Theorem\u00a04.Let where To prove this theorem, we need the following lemma. The case that oved in \u00a0(2)\u00a0(3)\u00a0for each Proof.\u00a0A be a q-ary A. Recall that for every A with columns indexed by Let D} as in . Denote:On the one hand, the number of vectors Fq, see . Le. LeA . First we briefly review the probabilistic refinement of the Shannon capacity of a graph in type\u00a0n. For every type classP is the set of sequences of type P, that is, \u03f5-typical set of P isjoint type\u00a0conditional type\u00a0We first recall some basic notions and results from the method-of-types. Let Lemma\u00a011.\u00a0.\u00a0|Pn|\u2264\u00a0(2)\u00a0.\u00a0The liAccording to Lemma 11, it is easily seen that:arton in  via a noarton in .In this subsection, we derive an outer bound for the case when all Theorem\u00a05.Proof.\u00a0n. For any Suppose that n tends to infinity; (56) follows from  follows from Theorem 1 that each Now we are going to upper bound the cardinality of og|A||B|\u2264lim supn),where ; (55) foely have|Jn could outperform Theorem 2, see the following example.Example\u00a03.Consider the channel K\u00af5,C5;K\u00af,\u2026,K\u00af2 whown from  that \u0398, we, we64), her with , the proIn this paper, we investigated the non-adaptive zero-error capacity region of the DM-TWC and provided several single-letter inner and outer bounds, some of which coincide in certain special cases. Determining the exact zero-error capacity region of a general DM-TWC remains an open problem, and clearly a difficult one, since it includes the notorious Shannon capacity of a graph as a special case. Despite this inherent difficulty, the problem is richer than the graph capacity setting, and we believe it deserves further study in order to obtain tighter bounds and smarter constructions.A. We have also looked at some variants of the orthonormal representation. For example, we considered the case where each graph vertex a is labelled by a unit vector a and F, then the vector projections of F are orthogonal. However, proving sub-multiplicativity in any of these settings has so far resisted our best efforts.One appealing direction is to extend the Lov\u00e1sz\u2019s semi-definite relaxation approach in order to obtain tighter outer bounds, mimicking the graph capacity case. This, however, does not seem to be a simple task. In particular, one may ask whether the natural quantity fined in , which ufined in  is not afined in . In partIt would be also of much interest to consider the adaptive zero-error capacity of the DM-TWC. Allowing Alice and Bob to adapt their transmissions on the fly can in general enlarge the zero-error capacity region. As a simple example, note that a point-to-point channel with noiseless feedback is a special case of the DM-TWC (where Bob has no information to send). In , Shannon"}
+{"text": "Nature Communications 10.1038/s41467-019-11558-2, published online 14 August 2019.Correction to: The original version of this Article contained an error in Fig. 1c, in which the top SNP was incorrectly labelled \u2018rs4293358\u2019. The correct label is \u2018rs429358\u2019. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "In their study of the effect of an LCHF-diet on blood lipids, Bur\u00e9n et al. became worried because, after a few weeks, the participants\u2019 LDL-cholesterol (LDL-C) increased significantly . HoweverThe reason why high LDL-C is beneficial is most likely that LDL participates in our immune system by adhering to and inactivating all types of microorganisms and their toxic products, a little-known fact that has been documented in many ways by more than a dozen research groups ,6."}
+{"text": "No additional rigidity decline is observed when d_seq\u2009\u2265\u2009\u2009~\u200930 and this upper limit is very modest, close to 0.015\u00a0\u00c5.It was observed that the rigidity degree diminishes if the number of covalent bonds intercalated between the two atoms (This suggests that protein flexibility is not fully described by B-factors that capture only partially the wide range of distortions that proteins can afford.The online version contains supplementary material available at 10.1186/s12859-021-04393-0. Molecule flexibility is inherent in thermodynamic stability and chemical reactivity . In globStudies on protein flexibility have addressed numerous molecular features by means of several methodological approaches. Atomic resolution crystallography allowed the characterization of conformationally disordered atoms \u201310. TimeAnother source of information about protein flexibility is provided by the atomic displacement parameters\u2014usually referred to as B-factor (B)\u2014that monitor the positional displacements of the atoms around their equilibrium positions , 17. B-fHere a new and insofar unexplored aspect is considered: how does flexibility decrease when the separation between atoms increases. It can be expected that flexibility is minimal for covalently bound atoms and, more in general, for atoms close to each other, since close interatomic contacts tend to be rigid \u2014this is X and uY) must be identical. This means that their difference (Delta-u) must be equal to zero \u00c5:Flexibility degree can be monitored by means of the Hirshfeld test , which eOn the contrary, Delta-u far from zero \u00c5 is expected for atoms that do not behave as a rigid body and have displacements and dispersions around their average locations independent of each other.Atom pair separation is defined in two different ways. On the one hand, it is the Euclidean distance (d) between the atoms and, on the other, it is the number of covalent bonds intercalated between the atoms .It is observed that Delta-u values increase if d or d_seq increase. However, the dependence of Delta-u on d is likely to be due to the fact that d is proportional to d_seq. In fact, for a given value of d_seq, Delta-u does not depend on d.Moreover, it is observed that Delta-u tends to rich its maximal value at d_seq \u2248 30 and to be nearly constant for d_seq\u2009>\u200930. This maximal value is considerably smaller if the Delta-u values are computed with anisotropic B-factors than with isotropic B-factors, suggesting that the isotropic B-factors overestimate protein flexibility.The maximal Delta-u values are however very modest, close to 0.015\u00a0\u00c5, indicating that B-factors are rather unrelated, on average, to the stereochemical rearrangements, which are known to confer high flexibility to proteins, for example for exchanging buried water molecules with the external solvent.Delta-u values, Euclidean distances and covalent separations were computed for 6,794,404 pairs of atoms in 30 crystal structures, with covalent separation up to 50.The relationships between Delta-u and Euclidean distance or covalent separation are shown in Fig.\u00a0First, the flexibility of atom pairs is clearly overestimated by isotropic Delta-u. This is not unexpected, since anisotropically refined B-factors represent better the positional scatter of the atoms. It is however surprising that the difference between isotropic and anisotropic Delta-u is so large: for atoms 30\u201335\u00a0\u00c5 apart, the isotropic Delta-u (ca. 0.08\u20130.09\u00a0\u00c5) is about 4 times larger than its anisotropic counterpart (ca. 0.02\u00a0\u00c5); and for atoms separated by 30 covalent bonds it (ca. 0.065\u00a0\u00c5) is about 4 times larger than the anisotropic Delta-u (ca. 0.015\u00a0\u00c5).Second, a difference between Euclidean distances and covalent separation appears too. The Delta-us, both isotropic and anisotropic, tend to increase with Euclidean distance and the increase is rather linear for Euclidean distances larger than 10\u00a0\u00c5 . They adopt different fold types, a TIM-barrel for 1us0, essentially a \u03b2-barrel for 2b97, and a \u03b1-\u03b2-\u03b1 roll for 3ui4, and one of them, 1us0, is much larger than the others. These proteins show similar trends and there are no enormous differences between them; furthermore, the difference between the two enzymes is comparable to their difference from hydrophoibin, and the largest protein (1us0) is intermediate between the other two.Interestingly, this trend seems to be independent of protein dimension, type of fold, secondary structure composition or biochemical function. As an example, Fig.\u00a0Crystallographic B-factors are largely unable to monitor transitions amongst conformational sub-states. This has been observed, implicitly, in some previous studies. For example, according to a recent study, protein conformational entropy, defined as the movements of certain groups in proteins, is not monitored quantitatively by crystallographic B-factors . Also, iThese observations can be explicated as it follows. Crystal structures show the dominating and most stable protein conformation while alternative sub-states remain undetected, especially at low resolution. Some conformational disorder can be observed and refined experimentally only at high resolution \u201310. B-faAs a consequence, B-factors can be computed quite successfully in\u2014very\u2014small molecule crystals, independently of diffraction data, where B-factors monitor quite effectively atomic fluctuations. The vibrational component of the atomic displacement parameter can be computed with quantum chemistry computations in crystals with very small asymmetric units. For example, density functional theory (DFT)-based methods were used for crystalline l-alanine and crystalline urea , and denOn the contrary, protein crystallographic B-factors are affected by too many non-vibrational components and cannot be predicted by computing the energy of the environment of the atoms by means of quantum chemistry approaches, though it has been shown that protein B-factors are somehow correlated to packing density . At thisIt must be remembered too that most of protein crystal structure information is being produced at low temperature\u2014100\u00a0K\u2014and that a different flexibility might be detected at room temperature or at physiological temperature . HoweverThe above discussion does not imply that crystallographic B-factors are of limited value and disconnected from the physicochemical nature of proteins. For example, information about local flexibility can be extracted from B-factor analyses, for example for protein-DNA complexes , cold adWhile covalently bound atoms form a rigid structural unit, this rigidity, monitored through the Hirshfeld Delta-u , is prog30 crystal structures were extracted from the Protein Data Bank , 49 accoThe Delta-u values were computed with anisotropic B-factors (U)n is the unit vector from atom X to atom Y. These values are referred to as anisotropic Delta-u, to distinguish them from the isotropic Delta-u, computed with the isotropic B-factor equivalent, defined asaccording toby means of the following expression.All computations were performed with locally written software.Additional file 1. Table S1: List of the entries of the Protein Data Bank examined in the present article. Figure S1: Relationship between Delta-u and covalent separation in three equally populated subsets of the structures examined in the present communication."}
+{"text": "However, the binding of a TF to a gene does not necessarily imply regulation. Thus, it is important to develop methods to identify regulatory targets of TFs from ChIP-chip data.ChIP-chip data, which indicate binding of transcription factors (TFs) to DNA regions We developed a method, called Temporal Relationship Identification Algorithm (TRIA), which uses gene expression data to identify a TF's regulatory targets among its binding targets inferred from ChIP-chip data. We applied TRIA to yeast cell cycle microarray data and identified many plausible regulatory targets of cell cycle TFs. We validated our predictions by checking the enrichments for functional annotation and known cell cycle genes. Moreover, we showed that TRIA performs better than two published methods (MA-Network and MFA). It is known that co-regulated genes may not be co-expressed. TRIA has the ability to identify subsets of highly co-expressed genes among the regulatory targets of a TF. Different functional roles are found for different subsets, indicating the diverse functions a TF could have. Finally, for a control, we showed that TRIA also performs well for cell-cycle irrelevant TFs.Finding the regulatory targets of TFs is important for understanding how cells change their transcription program to adapt to environmental stimuli. Our algorithm TRIA is helpful for achieving this purpose. By organizing the genes in a genome into transcriptional regulatory modules (TRMs), a living cell can coordinate the activities of many genes and carry out complex functions. Therefore, identifying TRMs is useful for understanding cellular responses to internal and external signals. Advances in high-throughput tools such as DNA microarray ,2 and chGenome-wide gene expression analysis has been used to investigate TRMs controlling a variety of cellular processes in yeast -9. Clustet al. [et al. [et al. [On the other hand, the ChIP-chip technique was developed to identify physical interactions between TFs and DNA regions. Using ChIP-chip data, Simon et al.  investig [et al.  construc [et al.  construcSynechocystis sp [To overcome this problem, several algorithms have been developed to combine gene expression and ChIP-chip data to infer the regulatory targets of a TF. For instance, NCA  and MA-Nystis sp . Therefop-value to the binding relationship of a TF-gene pair. They found that if p-value \u2264 0.001, the binding relationship of a TF-gene pair is of high confidence and can usually be confirmed by gene-specific PCR. Therefore, we include a gene in the set B+ if the TF-gene binding p-value in the ChIP-chip data is \u2264 0.001, i.e. B+ consists of genes that are significantly bound by a TF. Further, a gene in B+ is assigned into B+R+ if it has a temporal relationship with the TF but into B+R- otherwise. A TF-gene pair is said to have a temporal relationship if the gene's expression profile is significantly correlated with the TF's regulatory profile possibly with time lags (see Methods). Our hypothesis is that the genes in B+R+ are more likely to be the regulatory targets of a TF than are the genes in B+R-. TRIA is developed to classify B+ into B+R+ and B+R-.Two previous papers ,19 used B+R+ and B+R- \u2265 25 (i.e. at least 25 genes in each group). The number of genes in each group (B+R+ and B+R-) is listed in Table We considered nine cell cycle TFs that have both sizes of B+R+ is shown to be more enriched than B+R- for specific MIPS functional categories with adjusted p-value < 0.05 (after the Bonferroni correction for multiple tests) using the cumulative hypergeometric distribution . In most cases (7/9), except for Abf1 and Ace2, the cell cycle genes are more enriched in B+R+ than in B+R-  from the binding targets (B+) of a TF. Then, we classify B+R+ into subsets Ai and Ri, where Ai (Ri) contains all genes whose expression profiles are positively (negatively) correlated with the TF's regulatory profile with a lag of i time points. Finally, we test whether the expression coherence of Xi is statistically higher than that of B+R+, where Xi = Ai or Ri. The expression coherence of genes in a set G (i.e. EC(G)) is defined as the fraction of gene pairs in G with a correlation in expression level higher than a threshold T [T was determined to be the 95th percentile correlation value of all pairwise correlations between 2000 randomly chosen genes in the yeast genome. Note that 0 \u2264 EC(G) \u2264 1. The cumulative hypergeometric distribution is used to assign a p-value for rejecting the null hypothesis EC(Xi) = EC(B+R+), where Xi = Ai or Ri (see the Appendix for details).TRIA has the ability to identify subsets of highly co-expressed genes among the regulatory targets of a TF. First, we use TRIA to identify the plausible regulatory targets  be the set of regulatory targets of a TF that are identified by TRIA but not by MA-Network (MFA) and S2 (T2) be the set of regulatory targets of a TF that are identified by MA-Network (MFA) but not by TRIA. We tested over-representation of the high-confidence TF binding motifs in S1 and S2 (T1 and T2). The cumulative hypergeometric distribution is used to assign a p-value to the motif enrichment (see the Appendix for details). We found that in four of the five (4/5) cases the high-confidence TF binding motifs are enriched in S1 with p-value < 0.001 but only two of the five (2/5) cases in S2 are enriched  cases in T2 is enriched  using the cumulative hypergeometric distribution. This result suggests that TRIA performed well for cell-cycle irrelevant TFs.In this paper, TRIA is used to identify regulatory targets of cell cycle TFs. For a control, we show that TRIA can also perform well for cell-cycle irrelevant regulators. In this regard, we apply TRIA to identify regulatory targets of TFs that are activated by amino acid starved stress. The genome-wide gene expression and ChIP-chip data under amino acid starved growth condition are download from ,19. As sThe development of TRIA was motivated by two biological observations. First, it is known that TF binding affects gene expression in a nonlinear fashion: below some level it has no effect, and above some level the effect may saturate. This type of behavior can be modeled using a sigmoid function. Therefore, we define a TF's regulatory profile as a sigmoid function of its expression profile as in previous studies -35. AlthIn this study, we use time-lagged correlation analysis between a TF and its binding targets to identify its regulatory targets. However, in some cases, TFs may interact with each other and together regulate a group of target genes. This issue will be addressed in the future. We will try to define an overall regulatory profile of a TF complex and apply TRIA to identify target genes that are co-regulated by the same TF complex.An algorithm called TRIA is developed to identify the plausible regulatory targets of a TF from its binding targets. Since the binding of a TF to a gene does not necessarily imply regulation, TRIA is used to solve this ambiguity. We validated the effectiveness of TRIA by checking the enrichments for functional annotation and known cell cycle genes. Moreover, the performance of TRIA was shown to be better than two published methods (MA-Network and MFA). Moreover, TRIA has the ability to identify subsets of highly co-expressed genes among the regulatory targets of a TF. In addition, TRIA has been successfully applied to identify high-confidence cell cycle TF binding sites  and to rThree types of data are used in this study. First, the ChIP-chip data of the cell cycle TFs under the rich media are downloaded from . Second,Temporal Relationship Identification Algorithm (TRIA) is developed to identify TF-gene pairs that have a temporal relationship. A cell cycle TF and its binding target are said to have a positively (negatively) temporal relationship if the target gene's expression profile is significantly positively (negatively) correlated with the TF's regulatory profile possibly with a time lag. It is known that TF binding affects gene expression in a nonlinear fashion: below some level it has no effect, and above some level the effect may become saturated. This type of behavior can be modeled using a sigmoid function. Therefore, we define a TF's regulatory profile as a sigmoid function of its expression profile as in previous studies -35.x1, ..., xN) be the gene expression time profile of cell cycle TF x and y1, ..., yN) be the expression profile of gene y. The regulatory profile RP(f(x1), ..., f(xN)) of TF x is defined as a sigmoid function:Let s is the sample standard deviation of RP = 0 and the alternative hypothesis H1: r(k) \u2260 0 by the bootstrap method (see the Appendix) and get a p-value p(k). The time-lagged correlation (TlC) of RP(r(j) that has the smallest p-value (i.e. TlC(RP(r(j) if p(j) \u2264 p(k) \u2200k \u2260 j). Note that -1 \u2264 TlC(RP(RP(RP(j time points if TlC(RP(r(j) > 0 &p(j) \u2264 pThreshold and (2) negatively correlated with a lag of j time points if TlC(RP(r(j) < 0 &p(j) \u2264 pThreshold. The pThreshold is chosen to ensure that we have at most a 5% false discovery rate (FDR) [x, after a lag of j time points, activates (represses) gene y if RP(j time points.Then we test the null hypothesis Hte (FDR) . We may B+R+ is statistically higher than that in B+R-. Following Banerjee and Zhang [We want to test whether the enrichment of the known cell cycle genes (identified in ) in B+R+nd Zhang , a modelWe calculate:N = na + nb, M = ma + mb, na(nb) is the number of genes in B+R+ (B+R-), ma(mb) is the number of the known cell cycle genes in B+R+ (B+R-), andwhere xa, xb such that xa \u2265 ma, which is taken as the p-value for rejecting the null hypothesis that enrichment of the known cell cycle genes in B+R+ is not statistically higher than that in B+R-.Then, we consider all possible combinations of EC) of sets B+R+, Ai and Ri are calculated, where Ai (Ri) contains all genes in B+R+ whose expression profiles are positively (negatively) correlated with the TF's regulatory profile with a lag of i time points.The expression coherence  = EC(B+R+)  > EC(B+R+)) is defined as in Equation (A1). N is the number of gene pairs in B+R+, M is the number of gene pairs in Xi, where Xi = Ai or Ri, na is the number of gene pairs in B+R+ that have correlations higher than the threshold T, and ma is the number of gene pairs in Xi that have correlations higher than the threshold T.We want to test whether the expression coherence of S1 (T1) and S2 (T2), where S1 (T1) is the set of regulatory targets of a TF that are identified by TRIA but not by MA-Network (MFA) and S2(T2) is the set of regulatory targets of a TF that are identified by MA-Network (MFA) but not by TRIA. Only 5 TFs  are studied for both TRIA and MA-Network. Only 8 TFs  are studied for both TRIA and MFA.The proportions of genes whose promoter regions contain the high-confidence TF binding motif are calculated for The high-confidence TF binding motifs were derived by using six motif discovery methods, under the requirement for conservation across at least three of the four related yeast species . The yeaS1 (T1) and S2 (T2). The cumulative hypergeometric distribution is used to determine the statistical significance. The p-value is defined as in Equation (A1), where N = 6229 is the number of genes in the yeast genome, M is the number of genes in G, where G = S1 (T1) or S2(T2) , na is the number of genes in the yeast genome that contain binding sites of a TF under study  and ma is the number of genes in G that contain binding sites of a TF under study .We tested over-representation of the high-confidence TF binding motif in N-k pairs of observations, Z = {zi: i = 1, ..., N-k and zi = (f(xi), yi+k)}. The correlation coefficient from the sample is calculated and denoted asWe observed r(k) \u2264 1. It is aimed to use these observations to test if r(k) is different from 0 significantly. Suppose the null hypothesis is H0: r(k)= 0 and the alternative hypothesis is H1: r(k) \u2260 0. We will apply the bootstrap method to perform this hypothesis testing based on the observations. Keeping the pair relationship of these N-k pairs to maintain the dependence between (f(xi), yi+k), zi are sampled with replacement N-k times to form a bootstrap sample, Z* = {zi*: i = 1, ..., N-k and zi* belongs to Z}. The correlation coefficient from the bootstrap sample Z* is computed and denoted as r*(k), -1 \u2264 r*(k) \u2264 1. Repeat the resampling procedure B times, we will observed r1*(k), r2*(k), ..., rB*(k). These bootstrap correlation coefficients are sorted to be p-value is the smallest value of \u03b1 for which the null hypothesis will be rejected based on the observation, the p-value for this test is estimated by the following:where I{\u00b7} is the indicator function whose value is one when the event is true and zero otherwise.where WSW developed the algorithm, performed the simulation and wrote the manuscript. WHL and BSC gave the research topic, provided essential guidance and revised the manuscript. All authors read and approved the final manuscript.Supplementary Table 1Click here for fileSupplementary Table 2Click here for file"}
+{"text": "John P. A. Ioannidis emphasizes the central role of prior probabilities . His conR, of 1.0 (a probability of 0.5), although his examples go as high as R = 2.0. A positive study must, by definition, increase the likelihood that the hypothesis is true. It might have been clearer had Ioannidis chosen to relate odds to odds or probability to probability; in both cases, a neutral study would produce a straight line along a 45-degree diagonal.Unfortunately, his formulation relates the post-study probability that the study's conclusion is true to the pre-study odds. The results might have been clearer had he also plotted the relation of odds to probability, a curvilinear relationship, assuming the study carried no information. Further, the various graphs are right-truncated at pre-study odds, R \u00d7 LR. For a single unbiased study, LR = (1 \u2212 \u03b2)/\u03b1. When incorporating study bias, u, as defined by Ioannidis, LR = (1 \u2212 \u03b2[1 \u2212 u])/(\u03b1[1 \u2212 u] + u). For a typical study with \u03b1 = 0.05 and \u03b2 = 0.2 , LR = 16. When R is less than 1:16 (a probability of 0.0588), the post-study odds will be less than one\u2014i.e., the study's hypothesis will be more likely false than true.The pre-study to post-study relation can more simply be expressed using the odds-likelihood form of Bayes rule\u2014i.e., the post-study odds equal the pre-study odds multiplied times the likelihood ratio (LR) of the study. Then, the equations for positive predictive value (PPV) become the simple product of R = 1. Then, LR would merely need to exceed one for the study's conclusions to be more likely true than false. At the common significance levels (\u03b1) of 0.05 and 0.01, the requisite study powers would merely need to exceed 0.05 and 0.01 respectively, corresponding to maximum type II error rates (\u03b2) of 0.95 and 0.99. Such lax requirements would almost always be met for a published study. Hence, the common belief that the vast majority of studies have valid conclusions would be correct if we can assume that the pre-study odds are truly uninformative. However, as Ioannidis suggests, this is unlikely to be the case.For non-Bayesians, statistical significance testing presumes uninformative prior probability\u2014i.e., Two more corollaries might be added. The higher the pre-study odds that the study's hypothesis is true, the lower the requisite power (study size and effect size) required to make the study's findings more likely true than false. When studies are published, the investigator should estimate the pre-study odds and report the LR implied by the observed effect.From the perspective of an epidemiologist or a statistician, the relevant question is whether the study's hypothesis is true\u2014i.e., is the probability of the hypothesis greater than 0.5? For clinicians and their patients, the relevant question is whether a particular strategy should be followed in an individual patient or a subset of similar patients. That decision (or recommendation to the patient) will depend on the pre-study likelihood of benefit in that patient and on the relative magnitude of benefits and risks of that strategy, if the diagnosis in that patient is uncertain. For many such decisions, the \u201cmore likely true than false\u201d criterion may not be the best decision rule. For serious diseases and treatments of only modest risk, post-study probabilities of considerably less than 0.5 may be sufficient to justify treatment .Ioannidis's provocative Essay is a timely call for careful consideration of published studies. The odds-likelihood formulation suggested herein may be helpful in providing a more intuitive model. Clinicians now need to take it to the next step."}
+{"text": "Multicategory Support Vector Machines (MC-SVM) are powerful classification systems with excellent performance in a variety of data classification problems. Since the process of generating models in traditional multicategory support vector machines for large datasets is very computationally intensive, there is a need to improve the performance using high performance computing techniques.In this paper, Parallel Multicategory Support Vector Machines (PMC-SVM) have been developed based on the sequential minimum optimization-type decomposition method for support vector machines (SMO-SVM). It was implemented in parallel using MPI and C++ libraries and executed on both shared memory supercomputer and Linux cluster for multicategory classification of microarray data. PMC-SVM has been analyzed and evaluated using four microarray datasets with multiple diagnostic categories, such as different cancer types and normal tissue types.The experiments show that the PMC-SVM can significantly improve the performance of classification of microarray data without loss of accuracy, compared with previous work. In recent years the use of DNA microarrays has resulted in the creation of large datasets of molecular information characterizing complex biological systems. Machine learning algorithms applied to DNA microarray data based on molecular classification approach have shown to have statistical and clinical relevance for a variety of cancer types . When apOne strategy to solve classification problems is for the computer to learn the input/output functionality from training data. The learning algorithm attempts to find the underlying target function which maps from the input to the output. The estimate of the target function is known as the solution of the learning problem, which is chosen from a set of candidate functions that map from the input space to the output domain. These candidate functions are known as hypotheses. The learning algorithm takes the training data as input and selects a hypothesis from the hypotheses. The learning algorithm must have the ability to correctly classify data that are not in the training set, known as generalization .When the learning problem deals with binary outputs, it is referred to as a binary classification problem, and when the problem deals with a finite number of outputs, it is referred as multi-category classification problem. In recent years, Support Vector machines (SVMs), a supervised machine learning algorithm is being used to solve many classification problems. SVM algorithm classifies the data by finding the optimal hyperplane between the classes of data. The focus is to maximise the margin between the parallel hyperplanes . The training data which lie on the optimal hyperplane are called support vectors. This maximum-margin classifier was proposed by Vapnik Chervonenkis theory . Many imlight T, \u03b1 = T and C is a constant. e is a vector of all ones. Q is the symmetric positive semi-definite matrix and entries Qi, j are defined aswhere Qi,j = yiyjK, i, j = 1,2 ..., N, \u00a0\u00a0\u00a0 (4)K denotes a kernel function, such as linear kernel, polynomial kernel and radial basis function (RBF). RBF kernel is used in the numerical experiments of this project.where Currently, decomposition method is one of the major methods to train SVM, in which only a subset of variable is considered per iteration. The subset, denoted as B, is called working set. If B is restricted to have only two elements, this special type of decomposition method is the Sequential Minimal Optimization (SMO). There are four steps to implement SMO :1 as the initial feasible solution. Set k = 1.1. Find \u03b1kis a stationary point of (2), stop. Otherwise, find a two-element working set B = {i,j}\u2282{1,..., l}. Define N \u2261 {1,..., l}\\ B, and  and  as sub-vector of \u03b1kcorresponding to B and N, respectively.2. If \u03b1ai,j = Kii + Kjj - 2Kij > 03. If B :Solve the following sub-problem with the variable\u03b1elseSolvesubject to constra int s of (5) to be the optimal solution of (4) and  Set k \u2190 k + 1 and go to step 2.4. Set After the PMC-SVM is trained, the decision functions are used to classify new datasets.mi, j, i, j = 1,...,k, for k categories, each denoted by Ci, i = 1,...,k. Each model mi, j is generated from categories Ci and Cj. A total of  submodels are generated from k categories in MC-SVM. For example, if we have 4 processors and 8 categories, 28 models will be generated, as shown in Figure Task decomposition is the first step for the parallel algorithm design. In multicategory classification of support vector machines, the algorithm will generate multiple binary SVM models, denoted by k0 submodels are assigned to p PEs, each PE performs the generation task of  submodels. A task scheduling algorithm is needed to determine which categories of data are used by each PE. The pseudocode of scheduling tasks is given as followsWhen Task scheduling algorithm// Task scheduling algorithm for PMC-SVM training// model_no: the index of models// p: the total number of PEs.// my_rank: processor index, 0<=rank <p// i, j: class index// k: total number of classesmodel_no = 0;for {for{model_no++;if(my_rank = = model_no % p);// processor with my_rank gets class i and class jget_data(i) // read class i dataget_data(j) // read class i datagenerate_bin_svm; // generate a submodel for category i and j}}With this scheduling algorithm, tasks are evenly distributed among multiple processors and achieve better balance.The Portable Batch System (PBS) is a flexible workload management system . It prov#PBS -S /bin/tcsh# Set up the cpus and memory#PBS -l ncpus = 4# Name this job \"job_svm\"#PBS -N job_svmrm job_svm.o* # Remove any PBS output files from previous runsrm job_svm.e* # Remove any PBS error files from previous runs# Do our job# make the makefilemake# run the svm-train, save the file to svm8.out/usr/local/appl/mpich-1.2.1/bin/mpirun -np 8 svm-train letter.scale >> svm.outCZ and YD initiated the project and carry out the design and analysis. PL and AR implemented the PMC-SVM and evaluated the performance. All authors contributed and approved the final manuscript."}
+{"text": "Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible  flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed.Saccharomyces cerevisiae serves as case study.We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units.We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules. In contrast to the above mentioned techniques, Petri nets provide useful unique visualisation techniques with possibilities for hierarchical modelling and for animation. Especially this aspect is of crucial importance for experimentalists and for the dialog between experimentalists and theoreticians.Carl Adam Petri introduced the basic concepts of Petri nets in his dissertation in the context of technical systems . He deveSignal transduction pathways exhibit some special properties. In contrast to metabolic networks, in signalling pathways there is no substance flow, but a signal flow, which is performed, for example, by phosphorylated and dephosphorylated protein forms. There are no stoichiometric reaction equations given, which dictate the net structure and define the arc weights. Modelling signalling pathways we have to work on another abstraction level than in modelling metabolic networks. Petri nets provide a generic description principle, applicable on any level of abstraction.In this paper we present a method, which enables the systematic deduction of the net structure from the known signalling processes in the cell, which are translated into logical terms as implication, conjunction, inclusive or exclusive disjunction, and negation. These terms can be translated unambiguously to Petri net components. The resulting model is a qualitative, discrete Petri net, which can be analysed for certain system properties to validate the model.S. cerevisiae and recall the necessary Petri net definitions. Then, we propose and discuss in detail a systematic modelling method with respect to signalling pathways. We focus on the analysis of signal flows and introduce for this purpose the new concepts of feasible t-invariants and of maximal common transition sets (MCT-sets). Feasible t-invariants stand for minimal self-contained subnets being active under a given input situation, while MCT-sets can be interpreted as smallest biologically meaningful functional units. Both concepts define a fully automatic net decomposition into biologically meaningful modules. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. We apply our modelling technique to the analysis of the pheromone response pathway in S. cerevisiae and discuss the results. Finally, we give conclusions indicating also further projects.In the following, we give a brief introduction into the mating pheromone response pathway in S. cerevisiae is reviewed, e.g., in [S. cerevisiae there are two different mating types of haploid cells, MAT\u03b1 and MATa. Cells of opposite mating type can mate, i.e., fuse to a diploid cell. This process is stimulated through small peptide pheromones, the \u03b1-factor and the a-factor, respectively. A haploid cell secretes the own factor and carries receptors for detecting a cell of opposite mating type via the other factor. When a yeast cell is stimulated by pheromone, secreted by a nearby cell of the opposite mating type, it starts a complex signalling pathway to undergo a series of physiological changes in preparation for mating. These changes are controlled and regulated through the pheromone signalling pathway, which is nearly the same in MAT\u03b1 and MATa cells.The signalling pathway of the mating pheromone response in e.g., in ,4,30. Ina cells, so the considered cells have an \u03b1-factor-specific cell surface receptor STE2, which is coupled to a heterotrimeric G-protein. This G-protein consists of the three subunits G\u03b1, G\u03b2, and G\u03b3, whereby the latter two can act as heterodimer G\u03b2\u03b3. A conformation change of the receptor catalyses an exchange of GDP to GTP in the G\u03b1 subunit leading to a dissociation of this monomer. If GTP is hydrolysed to GDP, the monomer reassociates with the dimer to the trimeric form of the G-protein [\u03b2\u03b3 subunits mediate a signal on the MAP kinase cascade by interacting with Cdc24 (Far1 transmitted), protein kinase Ste20, and scaffold protein Ste5. The Ste20, Ste11, and Ste7 kinases, which are activated serially, phosphorylate and activate itself the two MAP kinases Fus3 and Kss1. But, Fus3 attenuates the activation of Kss1 [In the following, we refer to this pathway in MAT-protein . The G-p of Kss1 . Fus3PP  of Kss1 . Pheromo of Kss1  or degra of Kss1 .P = {p1,..., pn} and transitions T = {t1,..., tm}, and directed arcs, which are weighted by natural numbers and connect only nodes of different type. Places model typically passive system elements as conditions, states, or biological species, i.e., chemical compounds as proteins. Transitions stand generally for active system elements as events, or chemical reactions as de-/activation. In graphical representations, places are depicted as circles and transitions as rectangles. Transitions without preplaces (postplaces) are called input (output) transitions and are drawn as flat rectangles. The arcs in the net describe the causal relation between active and passive elements. They are illustrated as arrows and labelled with their weight, if it is larger than one. Arcs connect an event with its preconditions, which must be fulfilled to trigger this event, and with its postconditions, which will be fulfilled, when the event takes place.Let us first recall some basic definitions of Petri nets. More formal definitions are given, e.g., in ,18,35. Pread arcs.The fulfilment of a condition is realised via tokens residing in places. Principally, a place in a discrete net may carry any integer number of tokens, indicating different degrees of fulfilment. If all preplaces of a transition are marked sufficiently (corresponding to the arc weights) with tokens, this transition may fire. If a transition fires, tokens are removed from all its preplaces and added to all its postplaces, each corresponding to the given arc weights. Thus, the tokens are the dynamic elements of the system. If a condition must be fulfilled, but the firing of an adjacent transition does not remove any tokens from it, these nodes are connected via two converse arcs. In the following, these arcs are represented by bidirectional arrows as a short-hand notation and are called From a biological viewpoint, the tokens residing in places indicate whether the corresponding chemical species is present, i.e., its concentration is above a certain concentration level (threshold) in the cell. This presence enables the chemical reactions modelled by the place's posttransitions to take place.m \u2208 marking of the net. Accordingly, the initial marking m0 of a net describes the system state before any transition has fired.A current distribution of the tokens over all places, usually given as C of a given Petri net is an (n \u00d7 m)-matrix . Every matrix entry cij gives the token change on the place pi by the firing of the transition tj. Thus, the incidence matrix does not reflect read arcs. A t-invariant is defined as a non-zero vector x \u2208 The incidence matrix C\u00b7x = 0. \u00a0\u00a0\u00a0 (1)realisable, if a marking is reachable, such that all transitions of the t-invariant are able to fire in a suitable partial order. Analogously, a p-invariant is defined as a non-zero vector y \u2208 A t-invariant represents a multiset of transitions, which have altogether a zero effect on the marking, i.e., if all of them have fired the required number of times, a given marking is reproduced. The invariant property holds for an arbitrary initial marking. A t-invariant is called y\u00b7C = 0. \u00a0\u00a0\u00a0 (2)y and any markings mi, mj \u2208 m0 by the firing of transitions, it holdsA p-invariant characterises a token conservation rule for a set of places, over which the weighted sum of tokens is constant independently from any firing, i.e., for a p-invariant y\u00b7mi = y\u00b7mj. \u00a0\u00a0\u00a0 (3)x are called the support of x, written as supp(x). Considering Equations (1) and (2), it is obvious that a sum of t-invariants (p-invariants) gives again a t-invariant (p-invariant). An invariant x is called minimal, if its support does not contain the support of any other invariant z, i.e.,The nodes corresponding to the non-zero entries of an invariant z : supp(z) \u2282 supp(x), \u00a0\u00a0\u00a0 (4)\u2204 invariant x is one.and the greatest common divisor of all non-zero entries of A net is covered by t-invariants (p-invariants), if every transition (place) participates in a t-invariant (p-invariant). A t-invariant (p-invariant) defines a connected subnet, consisting of its support, the support's pre- and postplaces (pre- and posttransitions), and all arcs in between.A \u21d2 (B \u2227 C) and (D \u2227 E) \u21d2 F, respectively. If there is a token on place A, the precondition A is fulfilled, and the corresponding posttransition may fire. This event will fulfil the postconditions B and C getting each a token. This example illustrates that the number of tokens in a net is not generally conserved. The fulfilment of condition F in Figure D and E.First, we want to define general network components in the language of Petri nets. Considering substructures, which model logical terms as a Petri net, an ordinary implication is a trivial case. Figure G \u21d2 (H \u2228 I) and (J \u2228 K) \u21d2 L, respectively. The two posttransitions of place G are in conflict, i.e., if there is one token on place G, both its posttransitions may fire, but only one of them can actually fire. This subnet represents an exclusive disjunction. Therefore, a nondeterministic behaviour results. In contrast to that, the pretransitions of place L are concurrent and can fire independently from each other, if any. With this subnet an inclusive disjunction is represented.Figure In all implications, presented in Figure y, which holds |supp (y)| = 2 may stand for a subnet, representing a negation by two places (A and \u00acA), see Figure p1 (A) and p2 (\u00acA) forming the p-invariant, i.e., the token depicted on place p1 circulates only between p1 and p2 by firing of t1 and t2, respectively. To preserve this invariant structure, the adjacent transitions t3 and t4, respectively, are connected via read arcs.A crucial point in signal transduction pathways are modifications of certain proteins, resulting in a functionally active or inactive form of these proteins. Many of them are activated by phosphorylation and deactivated by dephosphorylation, and act in different ways depending on their current state. A qualitative model allows by its structure to distinguish between different states of one protein. Modelling this situation, we use a subnet, which includes the different modifications (states) of one protein as places forming a p-invariant. A p-invariant Altogether, there are three cases in signal transduction models, which can be distinguished by their different use of read arcs:A does not lose its activity by interacting with a second substance B, see Figure \u2022 Case 1: A substance C triggers several events represented by transitions, which are independent of each other, see Figure \u2022 Case 2: A substance \u2022 Case 3: The above mentioned context of a p-invariant, see Figure G are in conflict. Thus this subnet represents an exclusive disjunction G \u21d2 (H \u2228 I). By applying read arcs in such a substructure, the posttransitions of the corresponding place are concurrent, i.e., independent from each other. Thus, the subnet in Figure C \u21d2 (D \u2228 E).The subnet presented in Figure Before turning to the next step, the model validation, let us summarise the main steps of the systematic model development:1. compilation of biological knowledge about the signalling pathway of interest, e.g., from the literature or by database search,2. translation of the interactions of relevant biological species into basic logical terms,3. transferring these logical terms into net components,4. assembling these net components to one Petri net,5. if necessary, include input and output transitions ensuring that there are no places without pre- or posttransitions in the net.The last but one point ensures that the developed Petri net is connected. The input and output transitions introduced in the last point make the net to a transition-bordered one. They represent the interface of the biological system to its surroundings.The input transitions of a transition-bordered Petri net cause unboundedness, i.e., there is no upper bound for the number of tokens in such a net. Therefore, the state space of the net, i.e., all reachable markings, is infinite, and the dynamic net properties cannot be decided by the computation of the reachability graph, which contains all reachable markings as nodes. But, we do get information about the model dynamics via the analysis of the net structure, represented by the incidence matrix. Thus, our approach to validate the model is mainly based on the net invariants. The definition of invariants, see Equations (1) and (2), was introduced in . The appP-invariants in signal transduction models represent also some kind of conservation relationship, however in the sense of the several modifications of a given species as introduced in Figure The next step is to consider all possible signal flows through the network represented by realisable t-invariants, and to check their biological meaning. All possible t-invariants can be computed as non-negative linear combination of the minimal ones, see Equation (1). In former case studies, which do not contain the special p-invariant construct, see Figure The calculation of t-invariants does not take into account the initial marking. Moreover, read arcs are not reflected in the incidence matrix. Therefore, the question arises, whether a minimal t-invariant is really realisable. We assume that read arcs are the only source for non-realisability, i.e., there is a sufficient token number in each of the minimal p-invariants in the initial marking.with read arcs. For example, the p-invariant-adjacent transitions t3 and t4 in Figure p1 and p2, respectively, is not reflected in the incidence matrix. If this kind of transitions is part of a t-invariant, whereby their preplaces (connected via read arcs) carry no tokens, they are actually not able to fire. Therefore, the minimal t-invariants have to be processed to get realisable t-invariants for a suitable marking.The use of read arcs corresponding to the first case described above is discussed in . For an In accordance with our objective of model validation, we are looking for minimal self-contained t-invariants, which are realisable in the initial marking, i.e., minimal multisets of transitions, which can fire in an appropriate order without the firing of the other transitions, not belonging to that t-invariant. Those t-invariants are called feasible t-invariants. To make a t-invariant feasible, all of its involved transitions have to be able to fire, i.e., for each of them it is true either that it is an input transition or that its preplaces enable it to fire. The latter case means that either the considered preplaces carry already sufficient tokens in the initial marking or these preplaces get sufficient tokens via the firing of other transitions involved in this t-invariant. We distinguish between realisable and feasible t-invariants, because the notion of realisability of a t-invariant is a general term of Petri net theory, referring to the reachability of a marking, where the t-invariant's transitions can fire. Feasible t-invariants are special realisable t-invariants, which are minimal ones concerning their realisability in the initial marking. They are introduced because of a special net structure, which causes the interruption of the t-invariant, when it leads for example to a p-invariant, which carries a special marking.z. Let us formulate this processing of the minimal t-invariants in a general form. For each read arc between a transition tj and an empty place pi of a p-invariant the following procedure has to be applied. Let t1,...,tk be all the pretransitions of pi, which are not connected via a read arc with pi, see Figure pi in the initial marking, a t-invariant is not realisable if it includes tj and excludes tl \u2200 l \u2208 {1,..., k}. The following combinations z of feasible t-invariants x and one non-feasible t-invariant y reestablish the given read arc between transition tj and place piTable z = x + y \u2200x \u2203 l \u2208 {1,...,k} : xl \u2260 0xj = 0with yj \u2260 0 \u2227 \u2200 l \u2208 {l,...,k} : yl = 0. \u00a0\u00a0\u00a0 (5)and x providing a token on the place pi one linear combination z is constructed. Appropriate combinations have to be performed iteratively, if there occur several read arcs in the net, which have to be bridged. The combined t-invariants do not hold the criterion to be minimal, see Equation (4). But, since only inevitable combinations of minimal t-invariants are constructed, see the restrictions in Equation (5), the resulting combined t-invariants are minimal with respect to their realisability in the initial marking. Moreover, they only have non-negative entries, because they are build as a sum of two t-invariants, which are defined as vectors in Note that for each feasible minimal t-invariant Feasible t-invariants define, similarly to the t-invariants, connected subnets, characterised by its support. Generally, these subnets overlap. They represent minimal self-contained subnets being active under a given input situation. So, each of these subnets stands for a possible signal flow in the net. The examination of the feasible  t-invariants for their biological plausibility is a central step of model validation. It has to be checked, whether each feasible t-invariant has a biological meaning and whether every modelled part of the considered signalling pathway is reflected in a corresponding feasible t-invariant .Finally, it has to be checked, whether the net is covered by t-invariants. This property ensures that every transition participates in a t-invariant, i.e., every biological atomic action in the model may take place as part of the basic behaviour of the net.meet at a minimal p-invariant with a corresponding place not carrying a token.While minimal t-invariants are computed based on the net structure only, feasible t-invariants are constructed with respect to the marking of the net. Summarising the discussion above, the following situations are possible: the minimal t-invariants can reach (1) from input to output transitions, (2) from input transitions to minimal p-invariants, (3) from minimal p-invariants to minimal p-invariants, or (4) from minimal to output transitions. The transitions of a t-invariant influence a minimal p-invariant in such a way that altogether its initial state is reproduced. Not every possible combination is considered to bridge a read arc and to connect minimal t-invariants. Such a procedure would lead to t-invariants reaching from input transitions to output transitions, only. As described above, those minimal t-invariants are combined, which maximal common transition sets (MCT-sets) by their occurrence in the minimal t-invariants: \u2200i, j \u2208 {1,...,m} the transitions ti and tj are grouped into the same MCT-set, if and only if they participate in exactly the same minimal t-invariants, i.e., all t-invariants x holdIn order to support the check of feasible t-invariants for their biological meaning, the transitions are grouped into so-called \u03c7{0}(xi) = \u03c7{0}(xj), \u00a0\u00a0\u00a0 (6)\u03c7{0} denotes the characteristic function, binary indicating if an argument is equal to zero. This support-oriented grouping leads to maximal sets of transitions, where each set of transitions \u03d1 holdswhereas x \u2208 X : \u03d1 \u2286 supp(x) \u2228 \u03d1 \u2229 supp(x) = \u2205, \u00a0\u00a0\u00a0 (7)\u2200X denotes the set of all minimal t-invariants x.whereas T, the set of transitions, which leads to a partition of T. The equivalence classes \u03d1 are the MCT-sets. Transitions, not contained in any t-invariant, form their own MCT-set. MCT-sets define subnets, but not necessarily connected ones. An example of a disconnected MCT-set will be given below in the presented model.The grouping according to Equation (6) represents an equivalence relation in The resulting MCT-sets are disjunctive and represent a possible decomposition of large biochemical networks into rather small subnets, which can be read as functional units. Because of the way, in which they are generated, each of the MCT-sets may represent a signalling unit or a building block with its own biological meaning. In the following, only those MCT-sets are considered, which contain more than one transition.S. cerevisiae. The Petri net in Figure In accordance with the elucidation above we developed a Petri net, modelling the signal transduction pathway of the mating pheromone response in \u03b1-factor (via Bar1), of the receptor Ste2 (endocytosis induced by Yck1 and Yck2), of G-protein subunits (via Sst2), of the MAPK cascade (via labelling for degradation), and of the regulation of transcription (via repression of the transcription factor Ste12).Proteins, protein complexes, and other chemical compounds are represented as places, and complex formation/cleavage, protein de-/phosphorylation, and other reactions by transitions. Tables complex2 (p17) does not lose its activity by firing of transition Ste11_phos_Ste7 (t18), i.e., in the MAPK-complex the protein Ste11 remains in its active form after activating the protein Ste7, see case 1. The place Fus3PP (p20) triggers several transitions Ste12_inhibit_phos t22), Ste12_phos (t24), Far1-phos (t31), and Sst2_phos (t34), which are independent of each other, see case 2. The place pair Kss1_phos (p38) and unphos_Kss1 (p39) forms a p-invariant as discussed in case 3.We take into account the above mentioned substructures, e.g., the place complex3 (p18), complex4 (p19), compl_without_Fus3 (p21), and the transitions Ste7_phos_Fus3 (t19), Fus3PP-release (t20), and binding_free_Fus3 (t21). By using this arc weight, it is ensured that the activation of the transition Ste7_phos_Fus3 (t19) depends on firing of transition Ste11_phos_Ste7 (t18), see Figure With one exception, there exist only arcs weighted by 1 because no substance flow with stoichiometric relations takes place, but signal flow is described by the model. This special arc is weighted by 2 to reduce the token number in the structural cycle, which is formed by the places inact_Far1 (p31) and Sst2_in_nucleus (p34), respectively, which symbolise that these proteins are already present in the cell in low concentration independently of a signal.In the initial marking there is one token residing in the place trimer_bound_to_receptor (p5) or which is dissociated in its subunits G_beta_gamma_dimer (p7) and G_alpha_GTP (p6). Therefore, both of these p-invariants include the place p5 in addition to one of the places p6 and p7, respectively. The places Kss1_phos (p38) and unphos_Kss1 (p39) indicate the modification of the involved kinase Kss1 and form the third minimal p-invariant according to case 3. Thus, all these minimal p-invariants can be interpreted in a biologically reasonable meaning.There are three minimal p-invariants in the net. Table Model validation, the places trimer_bound_to_receptor (p5) and unphos_Kss1 (p39) carry tokens ensuring that the minimal p-invariants contribute to the system behaviour.In the initial marking of the net there are some tokens already residing in special places. According to the elucidation in section MATalpha_cell(surrounding) (t1), receptor_synthesis (t3), binding_factor_to_receptor (t2), and receptor_conformation_change (t4). Therewith, this MCT-set represents the synthesis of Ste2, its binding to the present \u03b1-factor and its resulting conformation change. In Figure techn_input , compare Table For our model we got ten minimal t-invariants covering all transitions. As mentioned above, the transitions are grouped into MCT-sets, if and only if they participate in exactly the same minimal t-invariants, see Equation (6). If a huge number of t-invariants arises for a network, the concept of MCT-sets provides additional structure information. Due to their definition, MCT-sets represent sets of events, which occur only together. These sets, together with their pre- and postplaces and all arcs in between, should symbolise signalling functional units of the model with an own biological meaning, see Table G_beta_gamma_dimer (p7) remain in the net because of the minimal p-invariant 1. Therefore, the minimal t-invariants 3, 4, 5, and 6 do not fulfil the feasibility criterion, because they contain the MCT-set 3, but do not contain any transitions, which provide tokens at place p7, which is connected with the MCT-set 3 via read arcs. These non-feasible t-invariants have to be processed in the way explained above, see Equation (5). Only the minimal t-invariant 1 involves transition division  (t5), which provides tokens on place p7 and does not involve the MCT-set 3. Therefore, each of the four non-feasible t-invariants is combined with t-invariant 1. These combinations provide four feasible, non-minimal t-invariants. Table The necessarily in the net remaining read arcs endanger the feasibility, i.e., the realisability in the initial marking, of the minimal t-invariants. Following our modelling approach, minimal t-invariants are not feasible, if they involve a transition, which is connected via a read arc with an empty preplace, which does not get tokens by firing of other transitions involved in this t-invariant. To ensure the feasibility of all t-invariants, these non-feasible ones are joint with some others, which provide tokens on the critical preplaces. The read arcs adjacent to the place \u03b1 cell in the surroundings, causing a receptor conformation change (MCT-set 1). In t-invariant 1 the activated receptor causes the dissociation of the G-protein (transition t5), whose subunits reassociate to a trimeric form (transition t6). In the t-invariant 2 the proteins Yck1 and Yck2 are bound through Akr1 to the plasma membrane and phosphorylate the activated receptor. This leads to a receptor endocytosis (MCT-set 7) via an ubiquitination. The t-invariants 7 to 14 include a signal transduction via the G-protein (transition t5) and the MAP kinase cascade (MCT-set 3). A release and phosphorylation of the transcription factor Ste12 (MCT-set 4) is involved in the t-invariants 7 to 10. This leads in these t-invariants to a transcription of the pheromone response genes preparing the cell for mating, including a feedback via Bar1 and Sst2 (MCT-set 5). Far1 is transported out of the nucleus (MCT-set 2) in t-invariants 8 and 10, while it initiates the cell cycle arrest (transition t32) in the t-invariants 7 and 9. By containing MCT-set 6, the t-invariants 9 and 10 include a Ste12 repression via activated Fus3. In t-invariants 7 and 8, kinase Kss1 is activated and deactivated . This p-invariant 3 contributes also to the processes described in t-invariant 14, where Kss1 is phosphorylated and dephosphorylated . Generally, the t-invariants 11 to 14 represent signalling pathways, which do not lead to a mating of the cell. All these t-invariants consist only of the receptor activation (MCT-set 1) and the MAP kinase cascade (MCT-set 3). Only t-invariant 13 involves an additional activation of Ste12 (MCT-set 4), which is repressed via Kss1 (transition t43). The t-invariants 11 and 12 include a feedback inhibition via a protein degradation (transition t38), which is initiated through a phosphorylation of these proteins .We want to discuss the biological plausibility of the feasible t-invariants. Table Recapitulating, t-invariants 7 to 10 lead to a mating of the cell, while the other t-invariants enable the cell to regulate, and modulate a pheromone induced signal by attenuated response or response desensitisation.Altogether it can be summarised that the known signalling processes are represented in the feasible t-invariants.The Petri net model can serve as basis of theoretical knockout experiments. They can be constructed by deleting the corresponding place and adjacent transitions, modelling the absence of this compound in a null mutant. Animating the resulting net shows already where some token accumulations arise under the new situation. These affected compounds can characterise a null mutant. Theoretical knockout experiments by the Petri net model could point out, which compounds indicate a mutant and nominate possible indicators for biological exploration.Ste5(scaffold) (p11) and its adjacent transitions binding_to_Ste5 (t12) and Ste5_binds_Ste11 (t13). This results in the deletion of the MCT-set 3, see Table cell_fusion (t28) , and celI_cycle_arrest_in_G1 (t32) occur only in the feasible t-invariants 7 to 10, which were deleted. Thus, the Ste5 mutant cells modelled by that mutant net are neither able to arrest the cell cycle nor to undergo a cell fusion, because the corresponding transitions do not occur in the feasible t-invariants of the net.Furthermore, a deletion of transitions leads to a deletion of feasible t-invariants, at least in a net, which is covered by t-invariants. The remaining feasible t-invariants show, which events still take place in this new cell type. For example, it is known  that SteIn this paper we describe a systematic approach to model and analyse signal transduction pathways using qualitative Petri nets. We propose a step-wise model development via the translation of the biological interactions into logical terms, which then in turn are transferred into net components.We explain the model validation step with a strong focus on the invariant analysis. In our modelling approach, we use minimal p-invariants, e.g., for the representation of the switching behaviour representing a compound in its activated and deactivated form. These p-invariants are embedded into the whole network by read arcs. Therefore, minimal t-invariants have generally to be processed to get feasible t-invariants. According to the construction principle, feasible t-invariants correspond to minimal self-contained subnets active under a given input situation. So, feasible t-invariants have to be checked for their biological meaning.Furthermore, we define maximal common transition sets, which provide a decomposition of the net into not necessarily connected subnets. These structures can be interpreted as the smallest biologically meaningful functional units or building blocks of a given network.The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour by their fully automatic approach to decompose a given network into biologically meaningful modules. Please note that it is possible to build the MCT-sets based on the feasible t-invariants instead of the minimal ones. That makes sense in Petri nets, which contain more substructures of minimal p-invariants. MCT-sets provide a decomposition of the net into disjunctive subnets, and feasible t-invariants describe subnets, which can overlap.S. cerevisiae. The validated model denotes the known signal flows through the net, which are obtained by the invariant analysis. We are able to assign a reasonable biological meaning to all feasible t-invariants. These reflect correctly the signal transduction in such a system, i.e., the signal response behaviour. Thus, Petri net theory is also useful to model and analyse signalling pathways considering not a substance flow, but a flow of information  through the net.We illustrate this approach using the mating pheromone pathway in The Petri net model may serve as basis for theoretical knockout experiments. By deleting appointed places and adjacent transitions, null mutants can be modelled. The analysis results of the original net can be easily modified to get some information about the derived mutant cell.Having once validated the structure of the qualitative discrete Petri net, several applications and extensions are possible. The net may be refined and extended to a quantitative one by including known or estimated kinetic parameters , using continuous or hybrid Petri nets, respectively ,39.In this way, the resulting quantitative Petri net preserves the structure of the underlying net topology. Continuous Petri nets may be considered as a structured ODEs description. They can be evaluated by standard differential equation solvers. For a related case study see . Hybrid In this paper, we have chosen deliberately a rather small running example to be able to present all steps of the analysis procedure in full detail, which should help the reader to mimic the approach using his/her own case studies. It would be worth applying our approach to larger networks as presented in ,42.The development of the net has been done using the graphical Petri net editor and animator Snoopy  describeThe paper is a product of a strong co-operation between all three authors. The key concepts and case study has been elaborated by AS during the work on her diploma thesis. MH gave substantial and valuable contributions in the application of Petri net techniques. IK defined the topic and gave substantial contributions to the conceptional design of the research project. The editorial work has been done by all three authors. All authors read and approved the final manuscript."}
+{"text": "Oc\u2208R((N + nm) log n), where N is the size of the output patterns and (n \u00d7 m) is the size of the input with n time frames and m reaction coordinates. To date, this is the best time complexity for this problem. We next apply this to a \u03b2-hairpin folding trajectory and demonstrate that this approach extracts crucial information about protein folding intermediate states and mechanism. We make three observations about the approach: (1) The method recovers states previously obtained by visually analyzing free energy surfaces. (2) It also succeeds in extracting meaningful patterns and structures that had been overlooked in previous works, which provides a better understanding of the folding mechanism of the \u03b2-hairpin. These new patterns also interconnect various states in existing free energy surfaces versus different reaction coordinates. (3) The approach does not require calculating the free energy values, yet it offers an analysis comparable to, and sometimes better than, the methods that use free energy landscapes, thus validating the choice of reaction coordinates.  approach toward identification of global states. The approach is based on computing biclusters (or patterned clusters)\u2014each cluster is a combination of various reaction coordinates, and its signature pattern facilitates the computation of the Z-score for the cluster. For this discovery process, we present an algorithm of time complexity pproach:  The meth \u03b2-hairpin folding trajectory and demonstrate that this approach extracts crucial information about protein folding intermediate states and mechanism.The study of protein folding mechanisms continues to be one of the most challenging problems in computational biology. Currently, the protein folding mechanism is often characterized by calculating the free energy landscape versus various reaction coordinates, such as the fraction of native contacts, the radius of gyration, RMSD from the native structure, and so on. In this paper, the authors present a combinatorial pattern discovery approach toward understanding the global state changes during the folding process. This is a first step toward an unsupervised  approach toward identification of global states. The authors apply this approach to a  Understanding protein folding is one of the most challenging problems in molecular biology \u20137. The i\u03b2-strand hydrogen bonds, the number of \u03b1-helix turns, the hydrophobic core radius of gyration, and the principal components (PC) from principal component analysis th child) ignores the \u03b4-clusters. The algorithm is efficient due to the two following factors: (1) use of a data structure (D in the pseudocode below) to store the maximal biclusters, so that searching for an arbitrary one can be done quickly, and (2) terminating the tree traversal appropriately. The data structure suggested for use is a tree so that each query takes log n time. The terminating condition (line [2.4] of the pseudocode) is such that each leaf node corresponds to either the maximal bicluster defined by the \u03b4-clusters  j1 \u2264 j2 \u2026 \u2264 pj or its variants of the form q \u2264 \u03c1.We describe a simple recursive algorithm to solve this problem. This algorithm implicitly constructs a tree in a depth-first manner where (1) each level corresponds to a distinct Generate-Set shown below, describes the algorithm. Assume a function Add-set , which inserts R, a subset of integers between one and n, in a tree data structure D, along with the accompanying set C: then a query of the form if a set R exists in D takes O(log n) time. The initial call is Generate-Set ).The pseudocode of the recursive routine R,C,j)Generate-Set (j \u2264 0) then exit(1) If ((2) For Let Let D ), add C\u2033If ElseDAdd-set (3) Generate-Set  stored in D.The maximal biclusters are We first show that the algorithm is correct in computing all the maximal biclusters and next show that the algorithm runs in time linear with the size of the output.Correctness of the Algorithm. We first show that each computed  is a bicluster. By the construction, for each j, \u03b4-cluster. Thus  is a bicluster. Next, we have to show that it is maximal. Assume it is not. Then there exists ijv such that j,\u03b4-cluster. Then in the subroutine call Generate-Set  of the pseudocode , this set must have been created, leading to a contradiction. Hence, the assumption is wrong.j, \u03b4-cluster. Then in Step 3 of the subroutine call Generate-Set, dV corresponding to j\u2032 must have been included, leading to a contradiction. Hence, the assumption is wrong. Thus, all the computed sets are maximal biclusters. By similar arguments, it is easy to see that if there is any maximal bicluster defined on the data set, it must one of the computed R's.Next, assume there exists Complexity of the Algorithm. Assume the input elements are ij,\u03bd 1 \u2264 i \u2264 n, 1 \u2264 j \u2264 m. Consider the first step of computing the \u03b4-clusters for each j. The sorting of the elements i\u03bd, 1 \u2264 I \u2264 n takes O(n log n) time. The algorithm works by scanning the input from left to right, say i to I + s, where the set {i\u03bd , i+\u03bd1 ,\u2026, i\u03bds+ } is a maximal \u03b4-cluster. Then the input is scanned from i + 1, i + s + 1, i + s + 2,\u2026 onwards and so on. Thus, each data element is visited no more than twice. Assuming the comparison can be made in constant time, this step of the algorithm takes O(n log n + n) = O(n log n) time for each j.Generate-Set can be done in log n time. In the recursive-call tree structure (of the subroutine Generate-Set), each leaf node corresponds to a maximal bicluster. In a tree, the number of internal nodes is bounded by the number of leaf nodes and each leaf node is hit only as many times as the number of features in each pattern, thus assuming the output size is N  and the second step of the algorithm takes O(N log n) time. Thus, the time taken by the complete algorithm is O((nm + N) log n), where N is the size of the output and nm is the size of the input.Next, consider the second step of computing the maximal biclusters. Notice that the search in Step (2.4) of the subroutine"}
+{"text": "Nature Communications 10.1038/s41467-018-03311-y, published online 02 March 2018Correction to: In the original version of this Article, extraneous text not belonging to the Article was accidentally appended to the \u201cResults\u201d section. This error has now been corrected in both the PDF and HTML versions of the Article."}
+{"text": "We find that for any tripartite mixed state, the unified -entropy entanglement of assistance follows a polygamy relation. This polygamy relation also holds in multi-particle systems. Furthermore, a generalized monogamy relation is provided for unified -entropy entanglement in the multi-qubit system.We investigate the entanglement distribution in multi-particle systems in terms of unified ( Monogamy property has also been discussed in the device-independent quantum information processing4, condensed matter physics5 and black-hole physics7.Quantum entanglement is an important resource in quantum information theory. Different from classical correlations, this restricted shareability of entanglement in multi-particle systems is known as monogamy property. The more entanglement shared between two parties implies the less entanglement shared with the rest of the system. Monogamy property plays a crucial role in quantum cryptography: which restricts the quantity of information captured by an eavesdropper about the secret key to be extractedet al., who considered a three-qubit system ABC8, and showed that the amount of entanglement (which is quantified by the squared concurrence) between A and B, plus the amount of entanglement between A and C, cannot be greater than the amount of entanglement between A and the pair BC. Further, Osborne et al. proved the squared concurrence follows a general monogamy inequality for the N-qubit system1. Monogamy inequalities for different entanglement measures have been noted, such as concurrence12, entanglement of formation14, negativity19, R\u00e9nyi entropy entanglement21, and Tsallis entropy entanglement24. For the other physical resources, such as discord and steering, the monogamy property of them has also been discussed28.The study of monogamy property has a long history. The first monogamy relation was found by Coffman 30. Polygamy property was first provided by using the concurrence of assistance to quantify the distributed bipartite entanglement in multi-qubit systems30. Polygamy property has also considered in many entanglement measures, such as R\u00e9nyi entropy20, Tsallis entropy31 and convex-roof extended negativity19.As dual to monogamy property, polygamy property in multi-particle systems has arised many interests by researchersq, s)-entropy is an important entropic measure, which can be used in many areas of quantum information theory. In this paper, we investigate the entanglement distribution in multi-particle systems in terms of unified -entropy. We find that for any tripartite mixed state, the unified -entropy entanglement of assistance follows a polygamy relation. This polygamy relation also holds in multi-particle systems. Furthermore, a generalized monogamy relation is provided for unified -entropy entanglement in the multi-qubit system.Unified -entropy and discuss the properties of unified -entropy entanglement. In the second subsection, we give our main results. We summarize our results in the third subsection.This paper is organized as follows. In the first subsection, we recall the definition of unified -entropy is defined as32q, s\u2009\u2265\u20090 such that Given a quantum state s tends to 1, the unified -entropy converges to Tsallis entropy Tq(\u03c1)33When s tends to 0, the unified -entropy converges to R\u00e9nyi entropy Rq(\u03c1)34When q tends to 1, the unified -entropy converges to von Neumann entropy S(\u03c1)35When q\u2009\u2192\u20091 and s\u2009\u2192\u20090, we will use q\u2009=\u20091 and s\u2009=\u20091 to represent the limits in this paper. Now, let\u2019s consider the entanglement in terms of the unified -entropy. For any pure state A and B), the unified -entropy entanglement is defined as36q, s\u2009\u2265\u20090.Because the limits exist in the case of \u03c1AB, the unified -entropy entanglement can be defined via the convex-roof extension\u03c1AB with pi\u2009\u2265\u20090. It is straightforward to verify that For a mixed state 31. When 20. Especially, The unified 38\u03c1AB with pi\u2009\u2265\u20090.When q, s)-entropy entanglement, the unified -entropy entanglement of assistance -EOA) can be defined as\u03c1AB with pi\u2009\u2265\u20090. To understand -EOA better, consider a tripartite pure state 39. The entanglement supplier, Charlie, performs a measurement on his share of the tripartite state, which yields a known bipartite entangled state for Alice and Bob. Tracing over Charlie\u2019s system yields the bipartite mixed state q, s)-EOA.As a dual quantity to the unified  can be defined as\u03c1AB, concurrence and COA are known to have analytic formula40\u03bbi being the eigenvalues, in decreasing order, of matrix For a two-qubit mixed state \u03c1ABIn ref. q\u2009\u2265\u20091, 0\u2009\u2264\u2009s\u2009\u2264\u20091 and qs\u2009\u2264\u20093fq,s(x) has the formx\u2009\u2264\u20091.In ref. In this section, we will provide our main results. First, we have following result:\u03c1ABC in the Hilbert space q\u2009\u2265\u20091 and qs\u2009\u2265\u20091.Theorem 1. For any tripartite mixed state Proof: Let q, s)-entropy entanglement q\u2009\u2265\u20091 and qs\u2009\u2265\u20091, the unified -entropy is subadditive, that isFor any bipartite pure state Combining Eq.  with Eq.Thus, the proof is completed.q, s)-EOA in a tripartite quantum system. The upper bound of -EOA of A|BC can\u2019t be greater than the sum of -EOA of B|AC and -EOA of C|AB. In particular, for a tripartite pure state q, s)-entropy entanglement Theorem 1. Shows a simple but interesting polygamy relation of -EOA in the multi-particle system, and gives an upper bound of -EOA of q, s)-entropy entanglement Corollary 1. Shows a constrained relationship of -EOA becomes Tsallis entropy entanglement of assistance which has discussed in ref. Corollary 2. For any multi-qubit mixed state Before our second main result, we have following lemma:q\u2009=\u20092 and fq,s(x) in Eq.  in Eq.  satisfieq, s)-entropy entanglement of AB and Next, the following result will provide a lower bound of unified -entropy is subadditive for any q\u2009\u2265\u20091 and qs\u2009\u2265\u20091. Thus, the following equality holdsq, s)-entropy entanglement of AB and From the definition of unified  is an increasing function for q\u2009\u2265\u20092, 0\u2009\u2264\u2009s\u2009\u2264\u20091, and qs\u2009\u2264\u2009336.We also note thatOn the other hand, we haveCombine Eqs  and 33)33) with Putting Eq.  into Eq.q, s)-entropy entanglement for 8.Theorem 2 shows a monogamy relation for a multi-qubit pure state q\u2009=\u20092 and i\u2009=\u20091, 2 and Example 3: Consider a pure state lity Eq. .n-qubit system, where A1A2 isExample 4: Finally, let\u2019s consider a general W state lity Eq.  is \\doculity Eq.  holds foq, s)-entropy is an important generalized entropy in quantum information theory. Many entropies such as Tsallis entropy, R\u00e9nyi entropy, and von Neumann entropy can be seen as a special case for unified -entropy. In this paper, we have investigated the entanglement distribution in multi-particle systems in terms of unified -entropy. We find that for any tripartite mixed state, the -EOA follows a polygamy relation for q\u2009\u2265\u20091 and qs\u2009\u2265\u20091. This polygamy relation provides an upper bound for the bipartition A|BC, which also holds in multi-particle systems. Furthermore, for q\u2009=\u20092 and q, s)-entropy entanglement. This monogamy relation provides a lower bound for the bipartition Unified (Both monogamy property and polygamy property are fundamental properties of multipartite entangled states. We have studied the properties above in detail, and provided a two-parameters entropy function to study the entanglement distribution. We believe our result provides a useful methodology to understand the entanglement distribution of multi-particle entanglement."}
+{"text": "Scientific Reports 10.1038/s41598-017-18174-4, published online 19 January 2018Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cReflectors\u201d was incorrectly given as \u201cReectors\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Xiaoxi Li's name was omitted from the byline. In addition, the article did not correctly report the funding associated with the study. The article has since been corrected online.In the article \u201cPredictive Value of Serum miR-10b, miR-29c, and miR-205 as Promising Biomarkers in Esophageal Squamous Cell Carcinoma Screening\u201d,"}
+{"text": "Bogliubov-de Gennes equations are solved self-consistently to investigate the properties of bound states in chiral p-wave superconductive disks. It shows that either an s-wave or the mixed d- and s-wave state with odd-frequency and spin-triplet symmetry is induced at the vortex core, depending both on the chirality of the pairing states and on the vortex topology. It is also found that the odd-frequency triplet even parity (OTE) bound state can be manipulated with a local non-magnetic potential. Interestingly, with an appropriate potential amplitude, the zero-energy OTE bound state can be stabilized at a distance from the vortex core and from the local potential. Possible existences of the Majorana fermion modes are expected if the particle-hole symmetry property is applied to the zero-energy OTE bound state. Moreover, skyrmion modes with an integer topological charge have been found to exist. Sr2RuO4 is the first perovskite compound showing superconductivity without cupper-oxide planes1. Experimental and theoretical investigations suggest that its superconducting pairing state is most-likely a spin-triplet chiral p-wave state with the px\u2009\u00b1\u2009ipy symmetry5. In particular, Nelson et al.6 performed the measurements to confirm an odd-parity and spin-triplet Cooper pairing symmetry in Sr2RuO4 superconductor. The px\u2009\u00b1\u2009ipy state that has an intrinsic orbital angular momentum L\u2009=\u2009\u00b11 and breaks down the time-reversal symmetry has shown promising new physical properties under a applied magnetic field, e.g, the half-quantum vortices7, Majorana zero-energy modes8, Skyrmionic states10 and coreless vortices11, which is analog to the Anderson-Thouless vortices12 and Mermin-Ho vortices13 in the A phase of liquid 3He.The layered ruthenate superconductor Sr2RuO4, e.g., the odd-frequency spin-triplet s-wave pairings at a vortex core has been discussed by several research groups18. It is known that superconducting pairing amplitude has to be an odd function with respect to the permutations of electrons spin and position for equal times, as required by Pauli\u2019s exclusion principle. In an inhomogeneous system, translational invariance was broken-down, which would lead to couplings between the even- and odd-parity pairing states. With the spin rotation symmetry invariant, the pair amplitude of opposite parity must be opposite in the Matsubara frequency that defines the frequency of the relative motion of two electrons forming a Cooper pair19. A spin-singlet even-parity and a spin-triplet odd parity pairing correlation that is even in Matsubara frequency obeys that rule, and so is the odd-frequency spin-triplet s-wave pairing state.In addition, possible existences of odd-frequency spin-triplet even parity (OTE) states in the chiral p-wave superconductor p+ state in an atomic length scale, whereas it is not the situation for the occupied states for the vortex winding parallel to the p+ chirality18. Hence, on one side, one believes that the results18 strongly support for the existence of an odd-frequency spin-triplet s-wave core state in Sr2RuO4 for an anti-winding vortex. On the other side, we should ask a question on what is the essence of the bound state at a parallel vortex core. Below a vortex with positive vorticity in relative to the chirality of p+ -state is defined as a parallel vortex, and a vortex with negative vorticity is known as an anti-parallel one.In the chiral p-wave superconductor the structure of quasiparticle around a vortex core is closely associated with the bulk topology of the pairing states and the vortex topology. Indeed, it has been showed that an odd-frequency triplet s-wave core state has an identical spatial distribution as that of the local density of states at both zero-energy and finite energy levels for a single vortex winding antiparallel to the chirality of the Sr2RuO4. Alternatively, one may ask whether the odd-frequency spin-triplet s-wave state and the Majorana zero-energy excitation can exist at a distance from the vortex core. For this end, we use the Bogoliubov-de Gennes(BdG) model20 to solve the problem of a cylindrical chiral p-wave superconductor with a two-dimensional isotropic Fermi surface in the presence of a single vortex. We show that an odd-frequency spin-triplet s-wave core state exists for an anti-parallel vortex, in agreement with those reported in previous investigations18. However, we found out that the state at the core is dominated by the odd frequency triplet d-wave for a parallel vortex. We also investigate the effect of a local non-magnetic potential on the bound states. Remarkably, a zero-energy peak in the local density of states appears at a distance from the vortex core and from the local potential well. We found that the spatial distribution of the corresponding zero-energy local density of states(LDOS) peak fits well with that of a mixed odd-frequency spin-triplet s-wave and even-frequency p-wave amplitude. To our knowledge, this is the first zero-energy OTE pairing state coexisting with the bulk px\u2009\u00b1\u2009ipy pairing amplitudes in the chiral p-wave superconductor Sr2RuO4.Noticing also that almost all of the odd-frequency spin-triplet s-wave state and the Majorana zero-energy excitations are necessarily to be bound with an external topology defect  where the p-wave pairing amplitudes vanish or possess a local minimum. A second question arisen is if one can create an OTE bound state without involving local external topology defects in superconductor The paper is organized as follows. The mixed s- and d-wave state with odd-frequency and spin-triplet symmetry is induced at the vortex core in chiral p-wave superconductive disks and this bound state can be manipulated by introducing a local non-magnetic potential barrier are discussed in Sec. Numerical Results. Our results are summarized in Sec. Conclusion. Finally, in Sec. Theoretical Approach, we present in detail our theoretical approach and model.\u03bd\u2009=\u2009\u22121 we obtain the results (not shown) that are in good agreement with those in ref. We discuss first the properties of bound states around an axial vortex. For an antiparallel vortex with \u03bd\u2009=\u20091 . Therefore, states with even parity can exist around the vortex core. Importantly, the even parity triplet pairing state must be an odd function in frequency to satisfy Pauli\u2019s exclusion principle. Indeed, as shown in our calculations, the zero energy mode is an OTE s-wave pairing state, and the first occupied state is dominated by the odd-frequency triplet d-wave state.In the presence of a vortex with vorticity \u03bd\u2009=\u20091. To manipulate the odd-frequency triplet core states, we increase steadily the potential magnitude until to the gap closing occurs(The parameters are Pmax\u2009=\u20091.469\u2009eV). Here, the term \u201cgap closing\u201d refers to all of the pairing amplitudes we concerned vanish at the core center. We choose a non-magnetic potential with Gaussian distribution to study how a local potential affect the topology of the bound state. The non-magnetic potential changes the translation invariance properties of the system. As a result, pairing states with even- and odd-parity would coexist. This is one of the mechanisms for the existence of a triplet bound state with even-parity. We find a relative wide range of parameters  can work, provided that the radius of the non-magnetic potential of ring-shaped is neither too small nor too large, e.g. in the range of Sr2Ru4 disk, which gives a ring-shaped potential with height/amplitude of about electron-volts. Another way is to irradiate the sample with a non-paraxial x-ray with a desirable spot-size.We now discuss effects of a non-magnetic potential on the spectrum and bound state properties of the system. We focus to the case of a parallel vortex with 22.Figure\u00a0px\u2009\u00b1\u2009ipy state is \u03bd\u2009=\u20091 is applied to the superconductor sample. Here, \u0394+(r) and \u0394\u2212(r) are both real functions, which are evaluated from the simulations. The calculated \u0394+(r) and \u0394\u2212(r) are shown in Fig.\u00a0\u00b1 as \u0394x\u2009\u00b1\u2009i\u0394y. It is straightforward for us to show that \u0394x has, besides the one at the origin  of the polar coordinate, four zeros at , ) and at ), ) while \u0394y has zeroes at ), ) and at ), ). Where r1 is a radial length at which r2. Contour plots for |\u0394x| and |\u0394y| are shown in Fig.\u00a0\u2212 and \u0394+ are differentiable there must exists a closed loop L1 (L2) (white dashed lines) where the amplitude of \u0394\u2212(\u0394+) approaches to zero-value asymptotically. The intersections in L1 and L2 are the so-called \u201csingularities\u201d where the relative phase \u03b8x\u2009\u2212\u2009\u03b8y in the phase of \u0394x and \u0394y changes abruptly and discontinuously.As aforementioned, a formal expression for the pairing potential of the x and \u0394y lead us to think of topological defects, which opens possibilities for the induced vortex with distinctive topological index. As well-known, the relative phase \u03b8x\u2009\u2212\u2009\u03b8y must be an integer multiple of 2\u03c0 radians at an Abrikosov vortex core. For instance, as shown in Fig.\u00a0\u03b8x and \u03b8y change 2\u03c0 radians at the core of a single vortex with \u03bd\u2009=\u20091. Meanwhile, |\u0394x| and |\u0394y| vanish simultaneously at the vortex core. We checked our data carefully and confirmed that \u03b8x(\u03b8y) could be a \u03c0 winding at the half-vortex core. For instance, as shown in Fig.\u00a0\u03b8y is a 2\u03c0 winding while \u03b8x is a \u03c0 wingding at  and at . Also \u03b8x is a 2\u03c0 winding while \u03b8y is a \u03c0 wingding at  and at . Therefore, the resulting \u03b8x\u2009\u2212\u2009\u03b8y is a \u03c0 winding there. In contrast to it, \u03b8x\u2009\u2212\u2009\u03b8y changes only \u03c0 radians [Fig.\u00a0x and \u0394y amplitudes decays to zero [Fig.\u00a0p+ pairing states is knownn as a r1, while the half antivortex is on a circle with a radius of r2, forming the so-called skyrmion modes  in our static skyrmion mode, which would have a resonance spectrum in the local density of states  where the amplitude of \u0394+ tends to zero. It indicates that \u03b8x\u2009\u2212\u2009\u03b8y is a constant of C(r*) [Fig.\u00a0\u03b8x\u2009\u2212\u2009\u03b8y varies from 180 degrees to 0 degrees when electron local coordinates increase crossing through the cycle C(r*) in the second and fourth quadrants. Instead, it varies from 0 degrees to 180 degrees in the first and third quadrants. It increases that phases of \u0394x and \u0394y precede p\u2212 state will be reflected on the circle to its mirror state with an opposite chirality. Superposition of the incident with its mirror particles leads to transverse resonances in the LDOS spectra, as shown in the left panel of Fig.\u00a0Let us examine r*) Fig.\u00a0. \u03b8x\u2009\u2212\u2009\u03b8C(r*). Sandwiched between two superconductive domains, the cycle C(r*) where bulk p+ pairing amplitude vanishes may be regarded as an electronic subsystem of\u201dnormal state\u201d domain wall. Electrons scattered on the wall have suffered to two processes. One is the normal reflection. Another is the Andreev retroflection. At the temperature much lower than the superconducting transition temperature the Andreev reflection dominates. In fact, it is the Andreev reflection that assists the bound state carrying the local microscopic current screening the magnetic field of the spontaneous half-quantum vortices. Consider an incident electron with an angle \u03b1 measured from the polar axis. In general, the total current carried by the bound state can be expressed as n being an integer. Since each bound state with  has a mirror state of C(r*). Spatially inhomogeneous current distribution implies a time-dependent local electron density, according to the current continuality relationship. A resonant LDOS spectrum is obtained once the Fourier transformation has been performed with respect to the time variable.We discuss the major physical processes that lead to resonances in the spectra briefly by examining electrons scattered on p+-wave amplitude remains unchanged over the whole length scale. Hence, an identical r-dependence of the local electron density with that of a mixed s- and p-wave triplet amplitude  with p-wave amplitude. Very importantly, while the p-wave amplitude would be greatly suppressed with an increase of the scattering intensity of the non-magnetic impurities, the zero-energy odd-frequency triplet s-wave pairing amplitude that is insensitive to the scattering intensity remains unchanged. Then, using a TEM probe of s-wave superconductor the zero-energy odd-frequency triplet s-wave state can be tested as a zero-bias LDOS peak. When this happens the zero-energy LDOS signaled is a good indication of the Majorana excitation without an external magnetic topology defect.It is important to further note that the particle-hole symmetry of the system Hamiltonian remains hold even in the presence of an non-magnetic potential. By using this property, it is readily for us to prove that the Majorana condition We have investigated the properties of bound states in chiral p-wave superconductive disks. An odd-frequency triplet even parity (s- and/or d-wave) bound state or the zero-energy Majorana fermion is found at a single Abrikosov-type vortex core. The zero-energy OTE can exist at a distance from the external topological defect when a non-magnetic potential with appropriate amplitude has been included in the model Hamiltonian. Remarkably, half-quantum antivortex-vortex pairs and skyrmion modes are found to exist with the aid of the Andreev reflections. The topological charges have equal magnitudes but opposite signs for the 26 for the chiral p-wave superconductor Sr2RuO4 with pairing symmetry of px\u2009\u00b1\u2009ipy:m is the electron mass, e is the electron charge, and c is the speed of light in vacuum \u03bc is the chemical potential. A is the vector potentials. The gap equation of px\u2009\u00b1\u2009ipy-wave is written as20\u00b1 is the order parameter for the px\u2009\u00b1\u2009ipy-wave, g is the coupling constant, We begin with the BdG equationsHere,we use the gauge R under an axial vortex of vorticity \u03bd. In the cylindrical coordinate electron and hole quasi-particle wave functions We consider the problem of a chiral p-wave superconductor disk of radius \u03bcth Bessel function and \u03bc and \u03bc\u2032 have to satisfy the following relations in order to ensure a real gauge of the BdG model. For instance, \u03bc\u2009=\u2009\u03bc\u2032 when \u03bd\u2009=\u20091, \u03bd\u2009=\u2009\u22121, and \u03bd\u2009=\u20090 etc. Quasi-particle wave functions satisfy the normalization condition:Here From the self-consistent solutions, we can calculate the LDOS as28. With the same mechanism, the OTE bound states are allowable in a chiral p-wave superconductor. The odd-frequency spin-triplet s- and d-wave pair amplitudes are defined by Since an Abrikosov vortex breaks down the translation symmetry and leads to couplings between the even-parity and odd-parity pairing states, one expects then possibilities for an odd-frequency pairing bound state around the vortex even in a conventional spin-singlet s-wave superconductor. One of the manifestations of the bound state is the enhanced LDOS at the vortex core, as observed as a zero bias conductance peak in the scanning tunneling spectroscopy26 from a standard BdG model, from which the odd-frequency spin-triplet d-wave pair amplitude is given byIn analog to Eq., one canwhere We note that the particle-hole symmetry relationship \u03b2 is the standard deviation of the distribution. Different parameter values are used to adjust the location and potential intensity. The non-magnetic potential is extrmely located.This is the expression of normal distribution. nm, from which the coefficient in Eq. (R\u2009=\u2009500\u2009nm.In our calculation, we set the coupling strength t in Eq.  is \\docu"}
+{"text": "We provide a methodology for estimating counts of single-year-of-age live-births, fetal-losses, abortions, and pregnant women from aggregated age-group counts. As a case study, we estimate counts for the 254 counties of Texas for the year 2010.We use interpolation to estimate counts of live-births, fetal-losses, and abortions by women of each single-year-of-age for all Texas counties. We then use these counts to estimate the numbers of pregnant women for each single-year-of-age, which were previously available only in aggregate. To support public health policy and planning, we provide single-year-of-age estimates of live-births, fetal-losses, abortions, and pregnant women for all Texas counties in the year 2010, as well as the estimation method source code.The online version of this article (doi:10.1186/s13104-017-2496-x) contains supplementary material, which is available to authorized users. Estimates of pregnant populations in a geographic region can be critical to assessing public health risks, such as chemical exposure\u00a0, alcoholPregnant populations can be estimated from counts of live births, fetal losses and abortions. However, such data are often aggregated into 3\u20135\u00a0year age groups. Only a handful of studies provide single-year-of-age pregnancy estimates, including several addressing the prevalence of Down\u2019s syndrome\u00a0\u201310, fetaHere, we describe an interpolation method for estimating single-year-of-age pregnancy counts from readily available, aggregated year-age live births, fetal losses and abortion data. To demonstrate the method, we derive county-level estimates across the state of Texas for the year 2010.We summarize the notation for our analysis below.set of countiesset of single-year-of-age groups for which we estimate live birth/abortion/ fetal loss counts: set of aggregated year-age groups for which we have live birth/abortion/ fetal loss counts:Texas live birthsTexas abortionsTexas fetal lossesk\u00a0\u00a0\u00a0set of single-year age groups for which we estimate live birth/abortion/ fetal loss counts within the set of aggregated year-age group j in county icount of women in age group k in county icount of live births from women in age-group k in county icount of abortions from women in age-group k for entire countrycount of fetal-losses from women in age group j for entire statelive births from women in age-group proportion of year a woman is pregnant when she has a live birth: proportion of year a woman is pregnant when she has a fetal loss: proportion of year a woman is pregnant when she has an abortion: j in county ilive births from women in age-group j in county ifetal losses from women in age-group j in county iabortions from women in age-group i, at a single-year-of-age resolution \u00a0, and ders (DSHS)\u00a0. For aboxas DSHS\u00a0. For fetndations\u00a0 and use a et al.\u00a0. We provFurther, supplementary files for this subsection are provided in Additional files J, as a set of single-year age groups contained in the set k. For example, for We also define a subset, The National Vital Statistics System (NVSS)\u00a0 providesmentclass2pt{minimble from\u00a0. We descmentclass2pt{minimk, are proportional to the total live births in the entire state for that aggregated age-group, for all counties; i.e., We assume all live births in a county for aggregated age-group, Under this assumption, we do not associate live births across one aggregated age-group to another. For example, we do relate the number of live births from a mother of age [21\u201322) to those of age [22\u201323), since they both belong to the set Further, the estimates for this subsection are provided in Additional files The CDC recommends the use of national-average, as opposed to state-specific, fetal loss rates because most state reports of fetal deaths are limited to those with at least 20\u00a0weeks of gestation\u00a0; see alsk, from Ventura et al. \u00a0[k.As with live births, counts of fetal losses for single-year-of-age,  et al. \u00a0. The fet et al. \u00a0 are up t et al. \u00a0 does not et al. \u00a0, and divj is available from US Census Bureau\u00a0[i by multiplying j. We present Next, we use a piecewise-cubic Hermite interpolating polynomial (pchip) to determine single-year-of-age counts of national fetal losses.s Bureau\u00a0. The reds Bureau\u00a0. We, thuFurther, the estimates for this subsection are provided in Additional files Unlike fetal losses, the CDC does not recommend the use of a national abortion rate due to wide variations in modes of data collection in geographic and demographic sub-populations\u00a0. County-xas DSHS\u00a0. We use Further, the estimates for this subsection are provided in Additional files j for county i can be estimated as in\u00a0[Finally, the number of pregnant women of age ed as in\u00a0,1\\documeFurther, the details for this subsection are provided in Additional file j as We make several comparisons between our estimates and reported data to assess the accuracy of our method. First, we compare our live birth estimates from age mentclass2pt{minimSecond, the CDC reported a national fetal loss rate for women aged 15\u201344 in 2008 of 17.9 fetal losses per 1000 women\u00a0 reportedFinally, our estimate of 73,481 abortions among Texas residents in 2010 is close to the Texas DSHS report of 73,600\u00a0, yieldinAdditional file 1. This file contains the source information of all the input files we provide.Additional file 2. This file contains a summary of all the input and output files we provide.Additional file 3. This file contains aggregated live births for the 254 counties of Texas for the year 2010.Additional file 4. This file contains single-year-of-age live births for the entire state of Texas.Additional file 5. This file contains our estimated single-year-of-age live births for the 254 counties of Texas for the year 2010.Additional file 6. This file contains single-year-of-age national populations of women for the year 2010.Additional file 7. This file contains national aggregated fetal loss rates and corresponding populations of women for the year 2008.Additional file 8. This file contains single-year-of-age populations of women for the 254 counties of Texas for the year 2010.Additional file 9. This file contains our estimated single-year-of-age fetal losses for the 254 counties of Texas for the year 2010.Additional file 10. This file contains aggregated abortions for the 254 counties of Texas for the year 2010.Additional file 11. This file contains our estimated single-year-of-age abortions for the 254 counties of Texas for the year 2010.Additional file 12. This file contains our estimated single-year-of-age fractional pregnancy outcomes for the entire state of of Texas for the year 2010."}
+{"text": "An alternative error bound for linear complementarity problems for  The linear complementarity problem is to find a vector mentclass2pt{minimils, see .An interesting problem for the }\u2225x\u2212x\u2217\u2225\u221e , that ismentclass2pt{minimils, see  and the M is a P-matrices [B-matrices. Here a matrix B-matrix [S, with In , Garc\u00eda-matrices , which cB-matrix  if, for S-matrix  if there is set to be \u2212\u221e (\u221e) if\u03b2\u0303 can be very small, thus the error bound  a strictly diagonally dominant (SDD) matrix if M-matrix if its inverse is nonnegative and all its off-diagonal entries are nonpositive [First, recall some definitions and lemmas which will be used later. A matrix entclass1pt{minima\\documentM is a B-matrix, then et al. in [B-matrix, the following corollary can be obtained easily by Lemma\u00a0Remark here that when the matrix t al. in . Furtherentclass1pt{minimaLetbe amatrix that is not aB-matrix, and letwithsuch thatIfthenifthenwhere\u03b3satisfies (atisfies .Consider the family of S\u0305): B-matrix. Then bound , we can say that bound (From Example at bound  is more an bound . TherefoP-matrix linear complementarity problem, Chen and Xiang in [P-matrix M:To measure the sensitivity of the solution of the Xiang in  introducSimilarly to the proof of Theorem 2.4 in , we can Letbe amatrix andbe the matrix given in LemmaThenwhereandifentclass1pt{minimaSimilarly, by Corollary Letbe amatrix that is not aB-matrix, and letwithsuch thatIfthenifthenwhere\u03b3satisfies (atisfies .M is a In this paper, we give an alternative bound for mentclass2pt{minim"}
+{"text": "Parkinson\u2019s disease (PD) is a progressive brain disorder that interferes with activities of normal life. The main pathological feature of this disease is the loss of more than 80% of dopamine-producing neurons in the substantia nigra (SN). Dopaminergic neuronal cell death occurs when intraneuronal, insoluble, aggregated proteins start to form Lewy bodies (LBs), the most important component of which is a protein called \u03b1-synuclein (\u03b1-syn). \u03b1-Syn structurally contains hexameric repeats of 11 amino acids, which are characteristic of apolipoproteins and thus \u03b1-syn can also be considered an apolipoprotein. Moreover, apolipoproteins seem to be involved in the incidence and development of PD. Some apolipoproteins such as ApoD have a neuroprotective role in the brain. In PD, apoD levels increase in glial cells surrounding dopaminergic cells. However, elevated levels of some other apolipoproteins such as ApaA1 and ApoE are reported as a vulnerability factor of PD. At present, when a clinical diagnosis of PD is made, based on symptoms such as shaking, stiff muscles and slow movement, serious damage has already been done to nerve cells of the SN. The diagnosis of PD in its earlier stages, before this irreversible damage, would be of enormous benefit for future treatment strategies designed to slow or halt the progression of PD. This review presents the roles of apolipoproteins and \u03b1-syn in PD and how some of them could potentially be used as biomarkers for PD. PD is an age-related neurodegenerative disorder characterised by dopaminergic neural cell death in the SN of the brain Schapira . PD was Dopamine loss in PD brains is the reason for motor problems and, possibly, for the cognitive deficits seen in some patients. Motor symptoms of PD include: \u2018bradykinesia\u2019, which simply means slowness of movement and is the most common clinical feature of PD; a \u2018resting tremor\u2019 that disappears during sleep and voluntary movement; \u2018muscular rigidity\u2019 referring to limb resistance to passive movements such as flexion, extension and rotation around a joint; and \u2018postural instability\u2019 occurring in the late stage of PD as a result of reduced postural reflexes  mutations, or possibly because of problems in other organelles such as the proteasome system, or mitochondria, or as a consequence of cellular stress  and some others , including APOER2, MEGF7, VLDLR, LRP1 and LRP2 . Therefore, the CNS has its own lipid metabolism pathway. ApoE is the most frequent apolipoprotein in CSF and is secreted by astrocytes. ApoJ, as a small dense apolipoprotein with very low lipid content, is also secreted by astrocytes  can lead to PD. The three isoforms of apoE may also play different roles in the pathogenesis of \u03b1 synucleinopathies  that are reported in the familial form of PD. These \u03b1-syn N-terminal mutations occur in \u03b1-n tandem repeats and affect the conformation of \u03b1-syn and lead to \u03b1-syn aggregation and fibrillation Fig. . In addiMoreover, \u03b1-syn mutation can accelerate cell death by the effect on the MAPK pathway. \u03b1-Syn can interact with mitogen-activated protein kinases (MAPK) through its N-terminal domain, but its C-terminal domain is not involved in this interaction. The \u03b1-syn-MAPK interaction is important for regulation of the cell life cycle. \u03b1-Syn overexpression is accompanied by reduced active MAPK and increased \u03b1-syn-MAPK complexes and this can lead to neuronal death. These findings suggest that the inhibitory effect of \u03b1-syn on MAPK can be pathogenic in PD brains where \u03b1-syn is overexpressed Iwata . A mouseMutant \u03b1-syn can also induce mitochondria-dependent apoptosis to a higher extent than the normal protein. Mitochondria are one of the most important organelles in all cell types as they act as ATP machines that provide cells with the required energy content. In the secretory neurons, mitochondria are also involved in the maintenance of Ca2+ levels in a proper amount suitable for vesicle exocytosis and endocytosis in the presynaptic terminals. Therefore, mitochondrial dysfunction is directly linked to reduced cell viability. In dopaminergic neurons, secretion of dopamine can be reduced as a consequence of mitochondrial dysfunction, leading to oxidative damage and cell death through enhanced dopamine metabolism  may transfer to recipient cells. This is possible based on the ability of \u03b1-syn to interact with membrane lipids  aggregates much faster than full-length \u03b1-syn (\u03b1-synFL) and these kinds of aggregate are common in familial forms of PD. An in vitro experiment has proven that aggregation of \u03b1-synFL can be induced in the presence of \u03b1-syn\u0394C. Moreover, co-expression of \u03b1-synFL with \u03b1-syn\u0394C in rats can cause neuronal death as the consequence of elevated \u03b1-synFL aggregates while the expression of \u03b1-synFL by itself in the rat brain just leads to moderate aggregation without any neuronal death (Ulusoy et al. The formation of \u03b1-syn\u0394C is a normal process in cells that typically leads to accumulation of \u03b1-syn, but it is not toxic in the usual circumstance. However, in familial PD, the raised levels of both soluble \u03b1-syn and truncated forms are responsible for a greater number of inclusions and amount of cell death. Therefore, the amount of \u03b1-syn\u0394C levels in neurons is positively related to the synucleinopathy intensity. The sites of \u03b1-syn truncation at the C-terminus may be Asp119/Pro120, Asn122/Glu123 and Glu123/Ala124. It seems that \u03b1-syn cleavage is mediated by different proteases and the proteasome is believed to be responsible for the cleavage of \u03b1-synFL at the Asp119/Pro120 position, while calpain1 mediates the truncation of \u03b1-synFL at the Asn122/Glu123 position (Li et al. In conclusion, apolipoproteins that are involved in cholesterol removal from the cells and transport excess cholesterol to bile seem to have a protective role in PD. HDL particles are the major lipoproteins that remove cholesterol from the arteries and send them back to the liver. Therefore, HDL and ApoA1 as the main constituents of HDL are very important to prevent cardiovascular disease such as atherosclerosis, which is result of accumulation of extra cholesterol in the blood. ApoA1 is also has a protective role in PD. It is consistent with findings that show people who have lower heart rate variability are at a higher risk of PD (Alonso et al. AD, Alzheimer\u2019s disease; Apo, Apolipoprotein; BBB, Blood-brain barrier; CMA, Chaperone-mediated autophagy; CNS, Central nervous system; CSF, Cerebrospinal fluid; DLB, Dementia with Lewy bodies; HDL, High-density lipoproteins; kDa, Kilodalton; LBs, Lewy bodies; LDL, Low-density lipoproteins; MAPK, Mitogen-activated protein kinases; MAPT, Microtubule-associated protein tau; MW, Molecular weight; PD, Parkinson\u2019s disease; PEA, \u03b2-Phenylethylamine; PP2A, Protein phosphatase 2A; ROS, Reactive oxygen species; SN, Substantia nigra; TH, Tyrosine hydroxylase; VLDL, Very-low-density lipoproteins"}
+{"text": "In a recent work (Feischl et al. in Eng Anal Bound Elem 62:141\u2013153,  The central idea of isogeometric analysis (IGA) is to use the same ansatz functions for the discretization of the partial differential equation at hand, as are used for the representation of the problem geometry. Usually, the problem geometry ented in  for finihpk-adaptive algorithm.Since CAD directly provides a parametrization of the boundary D BEM in  and for D BEM in . Unlike D BEM in , 41 and D BEM in , 38, 42 D BEM in  for fast, and to  for some, and to , 25. TheFor standard BEM with discontinuous piecewise polynomials, a posteriori error estimation and adaptive mesh-refinement are well understood. We refer to , 11, 12 While this work focusses on adaptive IGABEM, adaptive IGAFEM is considered, e.g., in , 43. A rf is given and the density p-th order NURBS. The convergence order for uniform partitions of h-refinement of the underlying partition as well as the local smoothness of the NURBS across the nodes of the adaptively refined partitions. It reflects the fact that it is a priori unknown, where the singular and smooth parts of the density We develop and analyze an adaptive algorithm for the following model problem: Let etry. In , we analired. In , we obseWe prove that the adaptive algorithm from  is rate e, e.g., , 26, 27)lyzed in  instead tive BEM .T), but also accounts for the knot multiplicity. Moreover, for Technical contributions of general interest include a novel mesh-size function shown in , 29, 30,Throughout, all results apply for piecewise smooth parametrizations The remainder of this work is organized as follows: Sect.\u00a0}\u0393 Sect.\u00a0, the dis}\u0393 Sect.\u00a0, the mes}\u0393 Sect.\u00a0, B-splin}\u0393 Sect.\u00a0, and the}\u0393 Sect.\u00a0. Section}\u0393 Sect.\u00a0 from .Elements, partitionandLocal mesh-sizesanda,\u00a0b]. This gives rise to T are equivalent, where the equivalence constants depend only on Local mesh-ratiosPatchesandmentclass2pt{minimSuppose that we are given a deterministic mesh-refinement strategy We write For the proof of our main result, we need the following assumptions on There exists a constant h-ratios  are unifFor all Each sequence For an arbitrary initial mesh h-refinement based on local bisection .The proposed refinement strategy  used in , 25 satih-refinement procedure has been analyzed in  there exists some interval p, it is sufficient to consider the following subsetI as follows: Without loss of generality, we assume that the maximum of |F| is attained at some Step 3 We show that F\u00a0/\u00a0w with a polynomial F of degree p and the weight function w, which is also a polynomial of degree p and which satisfies Step 4 According to [rding to , it holdis shows\u00a0. \\documeThe proof of linear convergence\u00a0 will be Assumption\u00a0p, and x nor its neighbors result from h-refinement or from multiplicity increase. Then, x or one of its neighbors result from h-refinement and/or multiplicity increase. If only multiplicity increase took place, we getFor all h-refinement, while the multiplicity of all nodes T is obtained by h-refinement.Note that the construction of p, and h-refinement is considered.For any Local projection property\u00a0:\u00a0 For (ii)Local The Scott\u2013Zhang type operator  satisfieT, have support in All NURBS basis functions which are non-zero on ,p\u22641 and  to see\\dWe chooseLet limits ^{}\\sum _{zSince we use a different mesh-refinement strategy, we cannot directly cite the following lemma from . However DefineThe next lemma reads similarly as [f\u00a0:\u00a0 there is a constant Then,\u00a0 there holds convergence Suppose that V the weakly-singular integral operator\u00a0 for fixed f. The heart of the matter are the estimates We choose operator\u00a0. Moreove"}
+{"text": "We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in  X and Y be infinite-dimensional Banach spaces. If X and x, which is called the support of x. When the basis Let X and Y, respectively. If there exists C-dominates C does not matter, we will simply say that C-equivalent, and we can write it as Now, suppose that C-equivalent to C-subsymmetric. Similarly, if C-equivalent to each \u03f1 is a permutation of C-symmetric. Note that C-symmetry implies C-subsymmetry, which in turn implies C-unconditionality. In this paper, we use standard facts and notation from Banach spaces and approximation theory. For necessary background, see [A basic sequence mentclass2pt{minimmentclass2pt{minimM is a function that is continuous, nondecreasing, and convex with M is said to satisfy An Orlicz function The study of Orlicz sequence spaces was initiated with a certain specific purpose in Banach space theory. Lindenstrauss and Tzafriri  used theshown in  that eveMusielak-Orlicz function . For. For\\docion (ii)(iii)Let D is minimal in X if it is minimal in X equipped with the partial order \u227a, that is, if D is supported with respect to a basis We can say that X is a sequence A block basic sequence of a basic sequence Letbe a sequence of Orlicz functions, and letbe a weight. Forwe havewith norm inclusions.\u03c8. Then we have\u03c8, we get It is clear that (i)For a given sequence of signs (ii)The coordinate projection on (iii)Given (iv)we define the linear function Let us define some linear functions as follows: Given Letbe a sequence of Orlicz functions, letbe a weight, and letLetbe a sequence of signs. LetBbe a subset ofand let\u03c8be a linear map inThen we have the following: (i)andare norm-one operators frominto(ii)andare norm-one operators frominto(iii)is an isometry frominto(iv)The standard unit vectors form a 1-subsymmetric basic sequence in\u03c6, we get The proof of (i) is clear since it is a consequence of (ii) and Remark\u00a0Letbe a sequence of Orlicz functions, letbe a weight, and letSupposeis minimal inwith respect to the canonical basis. Thenwhereis determined by\u03c6 be the function in \u03d5 be the inverse function of \u03c8 restricted to H be the projection of A onto For given supremum  is attaiLetbe a sequence of Orlicz functions, letbe a weight, and letEvery normalized block basic sequence of the canonical basis ofis 1-dominated by the canonical basis of\u03c8, we get the following result.\u2003\u25a1Let a normalized block basic sequence be Letbe a sequence of Orlicz functions, letbe a weight, and letLetdenote the canonical basis ofSuppose thatforms a block basic sequence inThen there exists another block basic sequence formed bysuch that(i)for(ii)(iii)is a subsequence offor each(iv)(v)is 1-dominated byLet By defining the sequences Supposeis a sequence of Orlicz functions, is a weight, andLetdenote the canonical basis ofanddenote the canonical basis ofThen every symmetric normalized block sequence ofdominates\u03f1 of C-equivalent to all its subsequences and C-dominates Let Letbe a sequence of Orlicz functions, letbe a weight, and letLetdenote the canonical basis ofSupposeforms a normalized block basic sequence and satisfiesLetbe the sequence from Theorem\u00a0corresponding toThen for eachthere exists a subsequencethat isequivalent to the canonical basissuch thatiscomplemented in(i)The coefficients of (ii)The first part of the proof follows that of Lemma\u00a01 in . Let \\doi values between Let Let us prove that a block basic sequence P extend to a linear operator on P is the projection onto p and byP is bounded by P\u0303 in P\u0303 is the projection onto To show that ma\u00a015 in . Let us"}
+{"text": "In this paper, we introduce the concept of several types of groupoids related to semigroups, viz., twisted semigroups for which twisted versions of the associative law hold. Thus, if  Suppose that In particular, if d et\u00a0al. , Howie , the collection of all groupoids defined on a non-empty set X. Given arbitrary groupoids X acts as an identity in L(R) denote the collection of all groupoids linear groupoid. They showed that Kim and Neggers  introducQ-algebra, and showed that every quadratic Q-algebra X is a field with Some researchers studied on linear groupoids and quadratic groupoids in several algebras. Neggers et\u00a0al.  introducm and So  investigleft-twisted semigroup with respect to the map associator function of the groupoid Let dual left-twisted semigroup with respect to the map We may think of a dual equation of  as folloright-twisted semigroup with respect to the map Suppose we replace the Eq.  by3\\docudual right-twisted semigroup with respect to the map We may think of a dual equation of  as follomiddle-twisted semigroup with respect to the map If we replace the Eq.  by5\\docudual middle-twisted semigroup with respect to the map We may think of a dual equation of  as folloIf mentclass2pt{minimIfis a semigroup, then it is a  left-twisted semigroup.Consider Consider BCK-algebra which is also a right-twisted semigroup.Note that Example\u00a0In Example\u00a0Let There is no map such thatis a left-twisted semigroup.If we assume that there is a map Note that Proposition\u00a0entclass1pt{minimaIf a left-twisted semigroup has a right identity element, then it is a semigroup.Let mentclass2pt{minimDually, if a right-twisted semigroup has a left identity element, then it is a semigroup.Notice that mentclass2pt{minimThe groupoidis a middle-twisted semigroup with respect toif and only iffor anyGiven If we let X as follows:linear groupoid over a field X. We define its associator function Let Let Letbe a linear groupoid over a fieldXand its associator function defined byIfis a dual left-twisted semigroup with respect tothen it has the formorSince In Proposition\u00a0Let Note that Examples\u00a0Letbe a linear groupoid over a fieldi.e.,for allwhereare not all zero inX. Ifis a right-twisted semigroup with respect tothen it has one of the forms: (i) andandX, there exist Since Letbe a linear groupoid over a field X. If we define a mapthenis a dual right-twisted semigroup with respect towhenStraightforward. Letbe a linear groupoid over a fieldX, i.e.,for alland letIfis both a left-twisted semigroup with respect to a mapand a right-twisted semigroup with respect to a mapthenis an additive group of the fieldX.X. Since it is a left-twisted semigroup, given mentclasspt{minimaLetbe a linear groupoid over a fieldX, i.e.,for allwhereare not all zero. If we define a mapwherethenis a middle-twisted semigroup with respect toStraightforward. Let Letbe a group and(fixed). Define a binary operation \u201cG by If we define a mapwhereeis the identity ofG, thenis a dual left-twisted semigroup with respect toGiven n be a natural number. A group power property if there are x in G. For example, consider the dihedral group Let Letbe a group having thepower property. Define a binary operation \u201conGbyThenis not a left-twisted semigroup with respect to any mappingG such that Assume that Letbe a group having thepower property. Define a binary operation \u201conGbyThencan not be a right-twisted semigroup with respect to any mappingG. Since G such that Assume that Letbe a left-twisted semigroup with respect to a mapIfis anepimorphism of groupoids, i.e.,then there exists a mapsuch thatis a left-twisted semigroup with respect to the mapGiven f is an epimorphism, we haveGiven left-twisted-injective if X such that Let Letbe a left-twisted semigroup with respect to a mapIfis a left-twisted-injective epimorphism, then there exists a mapsuch thatis a left-twisted semigroup with respect to the mapf is onto, there exist f is left-twisted-injective, we haveFor any In Theorem\u00a0f byUsing the notion of this concept, we introduce an equivalence relation on the Cartesian product d-algebra BCK-algebra Consider a If we define a map f is an epimorphism, we have Thus, let Letbe an epimorphism of groupoids, whereandare left-twisted semigroups with respect toandrespectively. IfthenGiven an epimorphism mentclasspt{minimaFor the other types of twisted semigroups we have similar situations. In the case of a dual left-twisted semigroup, we obtain the following results.Theorem 3Letbe a dual left-twisted semigroup with respect to a mapIfis anepimorphism of groupoids, i.e.,then there exists a mapsuch thatis a dual left-twisted semigroup with respect to the mapdual left-twisted-injective if X such that Let Proposition 11Letbe a dual left-twisted semigroup with respect toIfis a dual left-twisted-injective epimorphism, then there exists a mapsuch thatis a dual left-twisted semigroup with respect to the mapf byThe corresponding relationship on (1)right-twisted semigroups: (2)dual right-twisted semigroups: (3)middle-twisted semigroups: (4)dual middle-twisted semigroups: The other four types go in entirely the same way. We list the relevant information. X be equipped with the product binary operation given by the formula Given one of the six types of twisted semigroups, let a subgroupoidof a dual left-twisted semigroupneed not be a dual left-twisted semigroup.In order to obtain varieties we must be able to claim that if Z be the collection of all integers. Then v is an integer. Then k. This means that k. Hence there is no mapping In Example\u00a0In this paper, we introduced the concept of several types of groupoids related to semigroups, viz., twisted semigroups for which twisted versions of the associative law hold. Besides a number of examples and a discussion of homomorphisms, a class of groupoids of interest was the class of groupoids defined over a field In the investigation of \u201cresidual associativity\u201d in groupoids one encounters a number of levels. The strongest version of such residual associativity is \u201cassociativity\u201d itself. Making a study of twisted semigroups, besides being of interest in itself, is also relevant in several other ways. One may wish to determine as precisely as possible how different twisted semigroups may differ from semigroups. Accordingly we note that the study of twisted semigroups, commenced in this paper, will prove to be a rich area for research both in itself and as embedded in the area of the study of \u201cgeneral theory of groupoids\u201d."}
+{"text": "We start with the second-order Lane-Emden equation Also, in  several et al. [et al. employed a monotonicity formula-based approach and gave a complete classification of stable and finite Morse index (positive or sign-changing) solutions to (For the fourth-order Lane-Emden problem ons (see ). The suequality , this win>0; see . These rmentclasspt{minima [et al.  and furt [et al. . This apd Grunau . It shoup>1; see . Finallyp>1; see , D\u00e1vila Thanks to the Liouville-type theorem with finite Morse index in , the autished in , they reIn this work, we are concerned with Liouville-type theorems for the nonlinear elliptic equation  for \\docThe paper is organized as follows. In Section\u00a0f:In order to state our results, we present first some assumptions on the nonlinearity (1) We easily verify that the following functions satisfy f can have an exponential growth at infinity. Therefore, clearly an adequate behavior of f at zero is needed to obtain the Liouville theorem. The unique and important nonexistence result for stable solutions of the non-homogeneous second-order equation  and (2) show that equation  has beenequation  does nottions of  are trivxponents  and --3.30\\docequation  by \\docuu be a stable solution to (The proof of Theorem\u00a0me as in , 6, 8. Nution to .Subcritical case:. By Proposition\u00a0Critical case:. By Proposition\u00a0u is not identically zero, then We now collect  and 3.2. By assuThe proof of Theorem\u00a0equation  by \\docuu gives The function x. Using  in the lng again , we get ution of , in the \u03b8 and combining it with (\u03f5 sufficiently small, we deduce Proof of 1. If u that the right hand side of (k large enough such that We proceed as in the proof of Proposition\u00a0Proof of 2. If hen from  and by YWe can proceed as in the proof of Proposition"}
+{"text": "In the original article, one of the co-author\u2019s names has been published incorrectly. The correct name should be K. Prabha."}
+{"text": "Second-order sideband generation in an optomechanical system with the coupling between a mechanical resonator and a two-level system is discussed beyond the conventional linearized description of optomechanical interactions. The features of two-color second-order sideband generation are demonstrated in this hybrid system. We discovery that the switch between one- and two-color second-order sideband generation is easily realized by shifting the detuning between the control field and the cavity field or the transition frequency of the two-level system. The efficiency of two-color second-order sideband generation increases monotonously with the control field strength. The coupling strength between the mechanical resonator and the two-level system plays a decisive role in the appearance of the two-color second-order sidebands. The two-color second-order sideband generation may provide measurement with higher precision in new degrees of freedom. The subject of rapid developments brings about significant value in both fundamental physics and practical applications, such as achieving high precision measurement7, slowing and storage of light pulses9, information processing11 and optomechanical induced transparency(OMIT)13. Micro-mechanical resonators14 are in combination with optical cavities, which presents some important \u00a0phenomena, such as phonon blockade16, phonon-induced transparency17, and high-harmonic generation18.Cavity optomechanics22 emerge, such as high-order sidebands24 and chaos26 which are achieved in the bichromatic driving regime by making use of numerical calculation method. In the perturbative regime that the probe field is weaker than the control field, an analytical method has also been proposed to describe the nonlinear interactions in an optomechanical system29. Here we use the perturbation method to study the second-order sideband generation in a hybrid optomechanical system with a two-level system coupled to the mechanical resonator.Recently, due to the nonlinear optomechanical interactions between the optical cavities and the mechanical resonators, a lot of interesting phenomena30, superconducting qubit circuits31, two-level defects32 and so on. There are three situations in a hybrid optomechanical system for the coupling among an optical cavity, a mechanical resonator and another object: a two-level system is coupled to both the cavity field and the mechanical mode33; a two-level atom is only coupled to the cavity field30 and a two-level system is only coupled to the mechanical resonator34. For the third situation, the hybrid optomechanical system has been utilized to complete both the classical and quantal researches, such as the appearance of the two transparent windows34 and tunable photon blockade35. For other similar systems, the discovery of some new applications in the double-electromagnetic-induced transparency (EIT)37 and double-OMIT39 has been presented subsequently. All of these results inspire us to explore second-order upper sideband of double frequencies in output spectrum, which is called two-color second-order sideband generation here.The hybrid optomechanical system may consist of an optical cavity, a mechanical resonator and other objects including two-level atoms40 and\u00a0provides measurement with higher precision in new degrees of freedom, such as charge measurement4 and force sensors41.In the present work, we show the two-color second-order sideband generation in a hybrid optomechanical system where a two-level system is only coupled to the mechanical resonator. The interpretation is given for the formation of two-color second-order sidebands and the features of two-color second-order generation are exhibited. The switch between the one- and two-color second-order sideband generation can be actualized by transforming the transition frequency of the two-level system compared to the mechanical-mode frequency, or the detuning between the cavity field and the control field, whose strength sets a direct influence on the efficiency of the second-order sideband generation. In addition, the coupling strength between the mechanical resonator and the two-level system determines whether two-color second-order sidebands can appear. The two-color second-order sideband generation may find potential applications in optical frequency comb\u03c9a, \u03c9b, respectively. The Pauli operator \u03c9q is the transition frequency of the two-level system. The coupling parameter between the cavity field and the mechanical resonator, which is coupled to the two-level system with coupling strength g, is \u03c7. Here we treat the interaction between the single-mode optical field and the mechanical resonator as radiation-pressure Hamiltonian. For simplicity, we assume that the mechanical resonator interacted with the two-level system is regarded as Jaynes-Cummings Hamiltonian, and we have no consideration on the direct interaction between the cavity field and the two-level system. The last term, where The hybrid optomechanical system consists of an optical cavity and a mechanical resonator coupled to a two-level system, which might be an intrinsic defect inside the mechanical resonator or a superconducting artificial atom, as shown in Fig.\u00a0U\u2009=\u2009expAlthough the Hamiltonian mentclass2pt{minim\u03c9c. When the strong control field and a weak probe field with frequency \u03c9p are applied to the optomechanical system, the whole Hamiltonian of the hybrid system can be written as\u03b5 is the Rabi frequency of the probe field, which describes the coupling strength between the probe field and the cavity field. In a frame rotating at \u03c9c, the Hamiltonian of Eq. , respectively.Considering the damping and environmental noise terms, the Heisenberg-Langevin equations of motion are read as follows:M0 which correspond to the values of the a, b, \u03c3\u2212, and \u03c3z, respectively.In this work, we consider the mean response of the hybrid system. By making use of the lowest-order correlation-truncation approximation, the operators in Eqs.  to 7) a a7) are To describe the process of the second-order sideband generation, we definefrom Eq.  by analy42 is not applied to expound the appearance of two transparent windows in the hybrid system where the mechanical resonator is coupled to a two-level system. For the sake of comprehending the physical processes of two transparent windows and two-color second-order sidebands, for simplicity, the single-photon and single-phonon excitations are taken advantage of exemplifying the transmission of photons in Fig.\u00a034. A typical \u039b-type three-level systems is composed of three states |0a, 0b\u232a, |0a, 1b\u232a, and |1a, 0b\u232a, where the subscripts a and b represent the photon and phonon states, respectively. However, the state |0a, 1b\u232a is split into two dressed states43 |0a, 1b+\u232a and |0a, 1b\u2212\u232a when the mechanical resonator is resonantly coupled to a two-level system, where the effective resonant frequency of the mechanical resonator becomes \u03c9b\u2009\u2212\u2009g and \u03c9b\u2009+\u2009g from \u03c9b which leads to two transparent windows due to the resonant matching between optical beat frequency \u0394 and the effective mechanical frequency. Here we consider the higher order upconverted processes42 of the control field that the control field absorbs two phonon or the anti-Stokes field absorbs a phonon to generate a second-order sideband which also exhibits two interference windows.The physical interpretation of the OMIT effecttp|2 and \u03b7 vary with \u0394 by solving Eq.  resonant with the frequency \u03c9q of the mechanical resonator, viz. Firstly, when we observe the case that the detuning between the transition frequency \u03b7 of the second-order sideband generation is very low with maximum 3%. If we consider the Stark field from the down converted process of the control field exciting the mechanical resonator, the Stark sideband further absorbs a phonon to generate a second-order sideband, whose efficiency is higher. In general, the down converted process of the frequencies is easier than the up converted process of the frequencies. As shown in Fig.\u00a0\u03b7 of second-order sideband at \u0394\u2009=\u20090.9\u03c9b is higher than the efficiency \u03b7 of second-order sideband at \u0394\u2009=\u20090.9\u03c9b. Regardless of the control field and the first-order sideband going through the up or down converted process to generate second-order sidebands, the condition that the two-level system is resonantly coupled to the mechanical resonator must be satisfied for the appearance of two-color second-order sidebands. Therefore, there is another variable the transition frequency \u03c9q of the two-level system utilized to switch the one- and two-color second-order sideband generation.In Fig.\u00a0\u03b7 of the second-order sideband generation for different values of the coupling strength g. The blue curve shows the value of the \u03b7 reaches its local minimum within a frequency window corresponding to about the line width of the cavity at \u0394\u2009=\u2009\u03c9b, which can also take place when the mechanical resonator is not coupled to a two-level system in an optomechanical system42. In fact, if the strength of the control field reduces appropriately, and the strength of the control field does not reach the condition of the appearance of OMIT, only a second-order sideband generates at \u0394\u2009=\u2009\u03c9b.In order to further verify the role of the coupling strength g between the two-level system and the mechanical resonator in the appearance of the two-color second-order sideband generation, Fig.\u00a0g that results from the Jaynes-Cummings coupling between the mechanical mode and the two-level system. That is to say, by transforming the coupling strength g between the mechanical mode and the two-level system, we can get two-color second-order sidebands at different frequencies of the output spectra. In addition, the different values of the coupling strength g also have an effect on the efficiency \u03b7 of two-color second-order sideband generation. For example, the efficiency \u03b7 of two-color second-order sideband generation at the coupling strength g/2\u03c0\u2009=\u200910 MHz is the highest, which illustrates the coupling strength should be moderate.For other curves in Fig.\u00a0\u03c9q of the two-level system and the detuning \u0394a between the cavity field and the control field, whose strength also affects the efficiency \u03b7 of two-color second-order sideband generation. The two-color second-order sidebands at different frequencies of the output spectrum can be observed from the second-order upper sidebands by controlling the coupling parameter g between the mechanical resonator and the the two-level system. Our finding of two-color second-order sideband generation maybe be an enlightenment of multi-color second-order sideband generation when the mechanical resonator is coupled to multi-level systems.In summary, we have expounded the second-order sideband generation in a hybrid system, consisting of an optical cavity and a mechanical resonator coupled to a two-level system via Jaynes-Cummings interaction. We give the explanation to two-color second-order sideband generation distinguished from one-color second-order sideband generation in the physical mechanism. It can be seen how to achieve the switch between one- and two-color second-order sideband generation by shifting the transition frequency \u03c9c\u2009\u00b1\u2009n\u0394 where n is positive integer. Instead of consideration on all frequencies of output fields, we are interested in the situation of the second-order sideband generation with n\u2009=\u20092. Here we use the perturbation method to deal with the Eqs. (It is very difficult for us to get an exactly analytical solution on nonlinear Eqs. \u201311. In tthe Eqs. \u201311, wherting Eq. \u201311, we c\u03c3z is a Hermitian operator, the relation In particular, it is pointed out that because d to Eq.  to simpl44After some derivation, we can obtain the values of \u03c9c\u2009\u00b1\u20092\u0394 is part of the output field with frequencies \u03c9c\u2009\u00b1\u2009n\u0394 and it has been studied in different optomechanical systems42. The term of The output field with frequencies"}
+{"text": "The approach relies on a pre-specified interval null hypothesis that represents the collection of effect sizes that are scientifically uninteresting or are practically null. The second-generation p-value is the proportion of data-supported hypotheses that are also null hypotheses. As such, second-generation p-values indicate when the data are compatible with null hypotheses (p\u03b4 = 1), or with alternative hypotheses (p\u03b4 = 0), or when the data are inconclusive (0 < p\u03b4 < 1). Moreover, second-generation p-values provide a proper scientific adjustment for multiple comparisons and reduce false discovery rates. This is an advance for environments rich in data, where traditional p-value adjustments are needlessly punitive. Second-generation p-values promote transparency, rigor and reproducibility of scientific results by a priori specifying which candidate hypotheses are practically meaningful and by providing a more reliable statistical summary of when the data are compatible with alternative or null hypotheses.Verifying that a statistically significant result is scientifically meaningful is not only good scientific practice, it is a natural way to control the Type I error rate. Here we introduce a novel extension of the  P-values abound in the scientific literature. They have become the researcher\u2019s essential tool for summarizing when the data are incompatible with the null hypothesis. Although p-values are widely recognized as imperfect tools for this task, the impact of their flaws on scientific inference remains hotly debated  where a < b are real numbers, then its length is |I| = b \u2212 a. The second-generation p-value, denoted by p\u03b4, is defined asI \u2229 H0 is the intersection, or overlap, between intervals I and H0. The subscript \u03b4 signals the reliance of the second-generation p-value on the interval null. Numerically, \u03b4 represents the half-width of the interval null hypothesis. The value of \u03b4 is driven by scientific context and should be specified prior to conducting the experiment. The first term in p-value to indicate inconclusiveness when the observed precision is insufficient to permit valid scientific inferences about the null hypotheses.Let p\u03b4 is the length of the intersection between the two intervals, divided by the length of the interval estimate, multiplied by the correction factor. When the interval estimate is sufficiently precise, defined here as when |I| < 2|H0|, the second-generation p-value is just the overlap fraction, |I \u2229 H0|/|I|. When the interval estimate is very wide, |I| > 2|H0|, the second-generation p-value reduces to 0.5 \u00d7 |I \u2229 H0|/|H0|, which is bounded by \u00bd.As described here, I| would represent an area or volume. Neither interval is required to be symmetric or of finite length. Although the vast majority of intervals in the literature are \u2018two-sided\u2019 with finite length, pathologies are possible when neither interval has finite length. If intervals I and H0 overlap but neither has finite length, e.g., overlapping one-sided intervals, the second-generation p-value will be zero or one, depending respectively on whether |I \u2229 H0| is finite or infinite (Remark 1 in Definition When measuring systolic blood pressure (SBP), the currently accepted recommendation is to report SBP to the nearest 2 mmHg when using analog or mercury devices ,18. Bloop-value based on \u03b4 = 2 mmHg, the maximum p-value over all possible null hypotheses in the range H0: 144 \u2264 \u03bc \u2264 148, and the traditional p-value for testing H0: \u03bc = 146.\u03bc0 \u00b1 \u03b4 = , has length |H0| = 2\u03b4 = 4 mmHg. So p\u03b4 isFor example, in Study 3, the upper confidence bound is 142.55 and the lower confidence bound is 147.45. The interval null, p\u03b4 of 0.7 means the data are inconclusive with a slight or weak favoring of null hypotheses. Intuitively, it means that 70% of the data-supported hypotheses are null hypotheses. Study 4 is an example where the correction factor comes into play. The length of the confidence interval, 8.82, is more than twice the length of the null interval, 4. Therefore, p\u03b4 is:A p\u03b4 of 0.5 means the data are strictly inconclusive. The role of the correction factor is discussed in Section 2.5.A p-values best describe p\u03b4, and the maximum p-value seem to account for this paradox. However, p\u03b4 has more desirable attributes in other circumstances, such as in Studies 3 to 6. Study 4 has a traditional p-value and maximum p-value of 1, but the data are clearly inconclusive. The second-generation p-value reflects this, with a value of 0.5, allowing for a more nuanced interpretation of \u2018inconclusive\u2019. In studies where the point estimate falls in the null range, but the confidence interval extends beyond  the maximum p-value does not properly convey what the data are saying, and the traditional p-value does not account for the range of null values, or the precision of the measurement tool. Studies 7 and 8 illustrate the case when the confidence interval is fully beyond the null space.The second-generation H0: \u03bca0 \u2264 \u03bc \u2264 \u03bcb0. The second-generation p-value, p\u03b4, has the following properties:Consider a general interval null hypothesis, say p\u03b4 is a proportion; a number between zero and one, inclusive.p\u03b4 is the fraction of data-supported hypotheses that are null hypotheses and therefore compatible with the null premise.p\u03b4 = 0, the data only support hypotheses that are scientifically or clinically meaningful, i.e., those that are meaningful alternative hypotheses.When p\u03b4 = 1, the data only support null hypotheses, i.e., those that are not scientifically or clinically meaningful.When p\u03b4 = \u2248 1/2, the data are strictly inconclusive. The degree of inconclusiveness is represented by p\u03b4 itself. For example, p\u03b4 = 1/8 and p\u03b4 = 7/8 both represent the same degree of inconclusiveness, but the balance between alternative and null hypotheses is reversed.When p\u03b4 has improved error rate control when the interval estimate I is a 100(1 \u2212 \u03b1) % CI. Under any null hypothesis within the interval null, the probability of observing p\u03b4 = 0 is less than or equal to \u03b1. This probability converges to zero as the sample size grows. Under any hypotheses beyond the interval null, the probability of observing p\u03b4 = 0 converges to one as the sample size grows.p\u03b4 may appear similar to that of a posterior probability of the null hypothesis. However, p\u03b4 is strictly not a posterior probability and it is not an estimate of the probability of the null hypothesis. Rather, p\u03b4 is simply the observed fraction of data-supported hypotheses that are null hypotheses; it is a descriptive statistic\u2014a simple proportion. Essential elements of a proper posterior computation, namely knowledge that some hypotheses are better supported than others and the degree to which some hypotheses inside the interval null should be favored over others, are not needed. Specification of the latter is controversial because it does not depend on the data at hand. Second-generation p-values are descriptive; they indicate when the study has generated data that rule out null or alternative hypotheses.The interpretation of p-values; this is why statistical significance is not scientific significance. The fourth property is strictly false for classical p-values; a p-value larger than the Type I Error probability \u03b1 is considered inconclusive. Large p-values never \u201csupport\u201d the null hypothesis; they just indicate the lack of strong evidence against it. This is the absence of evidence is not evidence of absence conundrum. The fifth property is also not strictly true for traditional p-values; when non-significant, the p-value is to be interpreted as inconclusive despite the temptation to do otherwise. A welcome feature of second-generation p-values is that they distinguish between data that are inconclusive (0 < p\u03b4 < 1) and data that are compatible with null hypotheses (p\u03b4 = 1). This ability is sorely needed in practice.The third property does not hold for traditional p-value converges to zero or one as the sample size grows, which means the procedure is inferentially consistent in the limit . One way to do this is to use the delta-gap, which is the distance between the intervals in \u03b4 units. Recall that \u03b4 is the half-width of the interval null hypothesis. If the CI was shifted to the right of the null interval, the delta-gap would be \u03b4 makes it unit free. The delta-gap ranking favors extremes in effect size, which is a logical complement to the second-generation p-value. Remember that second-generation p-values provide a quick and easy marker of when a study reaches a natural endpoint, i.e., when the data are compatible with only null hypotheses (p\u03b4 = 1) or only alternative hypotheses (p\u03b4 = 0). Two studies with equal second-generation p-values do not necessarily represent equal amounts of statistical evidence. For example, their likelihood functions may not be proportional. The same is true of classical p-values, of course \u22121 and P(H1\u2502Failed to Reject H0) = [1 + (1 \u2212 \u03b1)/\u03b2r]\u22121. The FDR and FCR for second-generation p-values are generally smaller than their hypothesis testing counterparts. Remark 20 in p-values decrease the FDR and FCR from classical p-values.In principle, the reliability of any inferential summary ought to be reported along with the summary itself. Neither is truly sufficient on its own. However, reporting the reliability can be difficult to do in practice for the reasons noted above. And while standards for reporting the FDR and FCR deserve further investigation and discussion, the key message is that second-generation We note that while estimates further from the point null are more reliable in the sense that their false discovery rates are lower, this does not mean that they are more \u2018important\u2019, more \u2018relevant\u2019 or more \u2018meaningful\u2019 in a scientific sense. A low false discovery rate means only that the results are more likely to replicate under identical conditions. The cause for this replication could be a true scientific finding or an unknown experimental flaw. Only careful investigation into the validity of the scientific experiment can determine which it is.p-value usage, despite its flaws, will persist. Science desires an easily digestible and reliable summary of whether the data are compatible with null or alternative hypotheses. Second-generation p-values are tailor made for this role. They are easy to apply and interpret; they can be used in conjunction with frequentist, Bayesian or Likelihood methods; and they exhibit excellent frequency properties. Moreover, they eliminate the haggling over ad-hoc adjustments to p-values that have become a real challenge in high-dimensional and data-rich settings.More than a century of experience tells us that p-values is that they can be small and yet also be associated with confidence intervals that include hypotheses or parameter values that are essentially null. In genomic studies with many thousands of variants, this has led to the detection of hundreds of variants with spurious significance. By introducing an interval null hypothesis of scientifically equivalent null hypotheses, second-generation p-values avoid the vast majority of the spuriously significant findings. By better reflecting the true nature of the null hypothesis in mathematical terms, statistical inference works better for science. Also, the width of the interval null need not be large, as the benefits of second-generation p-values will eventually be realized as the sample size grows.A well-known problem with classical p-values tend to have excellent behavior overall. Nonetheless, this should be explored in detail (See our \u201cFrequently Asked Questions\u201d in \u03b4) will require re-calculation of the second-generation p-value. To facilitate this, we encourage the reporting and discussion of the interval estimates upon which the second-generation p-value is based. We remind the reader that the second-generation p-value is not intended to be the final product, but rather a quickly digested summary measure. Understanding the force and implication of statistical results will always require attention to the details of the statistical analysis.Some challenges remain. The statistical properties of this new tool need to be explored and detailed in a variety of settings. Our preliminary findings detailed here, and in the web-supplement , indicatexactly correct . In this paper, we assumed that the broader statistical model holds because this is a routine assumption for p-value based inference. However, the robustness of the second-generation p-value to model misspecification is an important topic that deserves attention.Regardless of the analysis, caution should always be used when interpreting statistical findings. Just because a result is statistically less likely to be a \u2018false discovery\u2019 does not mean that the result is more \u2018important\u2019, \u2018relevant\u2019 or \u2018meaningful\u2019 in a scientific sense. It means simply that the results are more reliable and more likely to replicate under identical circumstances, even if those circumstances are in some way flawed. A statistical hypothesis is a specific, precise mathematical statement about an unknown parameter. And statistical hypotheses assume a probability model to perform computations. If that model fails, then the associated statistical hypotheses often fail to be valid translations of the scientific hypotheses. This is, in fact, one of the most common criticisms of point null hypothesis testing; the point null is almost never p-values will be encouraging researchers to define a scientifically relevant finding prior to examining the data. While this is already routine in some areas of biomedicine , it is not even on the radar in others. Nevertheless, second-generation p-values are a clear improvement over classical p-values. They are between 0 and 1. They have a straightforward interpretation. A second-generation p-value of 0 is properly interpreted as favoring alternative hypotheses. A second-generation p-value of 1 is properly interpreted as favoring null hypotheses. A second-generation p-value between 0 and 1 favors both types of hypotheses and is properly interpreted as inconclusive. The error rates for second-generation p-values are bounded by \u03b1 and converge to 0. Adjustments for multiple comparisons are obviated, and lower false discovery rates accompany observed results. In short, the second-generation p-value achieves the inferential properties that many scientists hope, or believe, are attributes of the classic p-value. Using second-generation p-values can only improve rigor, reproducibility and transparency across science.We anticipate that the major challenge in implementing second-generation S1 File(PDF)Click here for additional data file.S2 File(PDF)Click here for additional data file."}
+{"text": "European J Pediatr Surg Repvol 5, issue 1. DOI of the original article is10.1055/s-0037-1599796. The names should be listed with \"Sabine\u201d as first name and \u201cVasseur Maurer\" as family name.It has been brought to the Publisher's attention that the author's name \"Sabine Vasseur Maurer\" was not tagged correctly in the above-mentioned article, published in"}
+{"text": "Scientific Reports 10.1038/s41598-017-18413-8, published online 08 January 2018Correction to: lucius\u201d was incorrectly given as \u201c1ucius\u201d. This has now been corrected in the PDF and HTML versions of the Article.The original version of this Article contained an error in the title of the paper, where the word \u201c"}
+{"text": "In this paper, the idea of lacunary  The concept of statistical convergence  which isI-convergence is also an extended notion of statistical convergence ([A) is an ideal if I is additive, i.e.i.e.A is any non-empty set.Similarly, ergence  of realA lacunary sequence is an increasing integer sequence refer to \u201319 etc.\u03b8 will be determined by the interval Note: Throughout this paper, M if, for arbitrary i.e., A sequence I-convergent to A sequence et al. [For any lacunary sequence n et al. ) \\documeThe concept of a Musielak-Orlicz function is defined as t}M (see )  .M in We define a sequence We write it as I be a non-trivial admissible ideal such that x as follows: Example: Let Then we have, for each Letbe a PNS. Ifis lacunarystatistical convergent, then it has a unique limit.X which has two limits, Suppose For Take the following sets: Since I, from which it is clear that I [Now, let If Since For arbitrary Letbe a PNS. Ifxis lacunarystatistical convergent, then it is lacunarystatistical convergent ifFor given Therefore, Since \u03bb-statistically convergent to M with respect to \u03bd as We define Letbe a PNS. Ifxis lacunary\u03bb-statistically convergent toM, then it is also lacunarystatistically convergent toM.IfthenIfthenLetbe a PNS. Ifxis lacunary\u03bb-statistical convergent toM, then\u03bb-statistically convergent to M, then, for every Let I is admissible, we have Since Letbe a PNS. Ifxis lacunary\u03bb-statistical convergent, then it has a unique limit.Letbe a PNS. Ifxis lacunary\u03bb-statistically convergent, then there exists a subsequenceofxsuch that it is also lacunary\u03bb-statistically convergent toM."}
+{"text": "Protein crystal structures are potentially over-interpreted since they are routinely refined without any restraint on the upper limit of atomic B-factors. Consequently, some of their atoms, undetected in the electron density maps, are allowed to reach extremely large B-factors, even above 100 square Angstroms, and their final positions are purely speculative and not based on any experimental evidence.A strategy to define B-factors upper limits is described here, based on the analysis of protein crystal structures deposited in the Protein Data Bank prior 2008, when the tendency to allow B-factor to arbitrary inflate was limited. This B-factor upper limit (B_max) is determined by extrapolating the relationship between crystal structure average B-factor and percentage of crystal volume occupied by solvent (pcVol) to pcVol =100%, when, ab absurdo, the crystal contains only liquid solvent, the structure of which is, by definition, undetectable in electron density maps.It is thus possible to highlight structures with average B-factors larger than B_max, which should be considered with caution by the users of the information deposited in the Protein Data Bank, in order to avoid scientifically deleterious over-interpretations.The online version of this article (10.1186/s12859-018-2083-8) contains supplementary material, which is available to authorized users. In crystal structures, oscillation amplitudes of the atoms around their equilibrium positions are monitored by B-factors, which are related to the root-mean-square amplitude of oscillation  [Fenwick and co-workers designed a B-factor based order parameter, which approaches its maximal value equal to one for well ordered atoms, and approaches zero for highly disordered atoms. This order parameter, for single-conformer structural models, becomes unphysical (negative) when the sum of the B-factors of two atoms approaches 8\u03c0\u2248 79\u00a0\u00c52) .Unfortunately, it became common in recent years to deposit in the Protein Data Bank , 23, B-fThis might have severe consequences on the bioinformatics use of the B-factors. For example the quantitative relationships between local stereochemistry and B-factor (and flexibility) would be misinterpreted by considering protein moieties with unreliable structures.Traditionally, when crystallographers are unable to position atoms or residues based on electron density maps, they insert a series of warnings in PDB files. The \u201cREMARK 465\u201d, \u201cREMARK 470\u201d, \u201cREMARK 475\u201d, \u201cREMARK 480\u201d lines were used to list (i) the residues that are present in the SEQRES records but are completely absent from the coordinate section (REMARK 465); (ii) non-hydrogen atoms of standard residues which are missing from the coordinates (REMARK 470); (iii) residues modeled with zero occupancy (REMARK 475); and (iv) non-hydrogen atoms of residues modeled with zero occupancy (REMARK 480).Obviously, this is the result of a rather subjective decision, based on the visual analysis of the electron density maps. Some crystallographers prefer to include these \u201cinvisible\u201d protein moieties in their refinements, with the consequent inflation of the B-factors. An atom that cannot be precisely positioned tends to occupy a large portion of space to spread its electrons as much as possible.2 are often deposited in the Protein Data Bank and this has three major drawbacks. First, the occupancy and the B-factor fields merge in the PDB-formatted files, with consequent problem of readability: the string \u201c1.00 99.99\u201d becomes \u201c1.00100.00\u201d when the B-factor increases from 99.99 to 100.00\u00a0\u00c52. Second, at (sin\u03b8/\u03bb)\u2009=\u20092, the scattering power of at atom with B\u2009=\u20095, 20 or 80\u00a0\u00c52 is only 0.54, 0.08 or 0.0001 [2 is absolutely negligible. Ab absurdo, one might introduce several atoms of Fermium wherever possible in the asymmetric unit with B-factors extremely large without consequences on the R-factor, the free-R-factor and the electron density. Third, and this is a major concern, PDB file end users, which often are not crystallographers, might be induced to use structural data that are absolutely unreliable.Recently, B-factors larger than 100\u00a0\u00c5r 0.0001  and, as It is therefore necessary to have an estimation, at least semi-quantitative, of the highest B-factor values that can be considered to be acceptable and over which atoms can be considered to be non-localizable. Apparently, only a careful analysis of the electron density map allow one to solve this problem. This is however impossible in most bioinformatics applications due to the large amount of data that must be examined.ab absurdo, the B-factor of a \u201cliquid\u201d atom in a protein crystal. In practice, in this article, I analyze the relationship between the average B-factors of protein crystal structures and the percentages of crystal volume occupied by solvent, which can be estimated through the Matthews volume [B_max). Based on the analysis of a large and well selected set of protein crystal structures, it can be predicted that at very high resolution (better than 1.5\u00a0\u00c5), B_max is close to 25\u00a0\u00c52, which means that the average B-factor value should not be larger than 25\u00a0\u00c52 at that resolution, while larger values are observed at lower resolution. At very low resolution (worse than 3.3\u00a0\u00c5), B_max grows up to 80\u00a0\u00c52, which means, again, that the average B-factor value should not be larger than 80\u00a0\u00c52 at that resolution.It is impossible to define a physically meaningful threshold value, over which B-factors can be safely be used to decide that an atom must be excluded in the refined model: it would be a mere arbitrary threshold, based on some subjective assumption, for example \u201cless than 0.05%\u201d of the structure factor. On the contrary, it is possible to try to identify, s volume . In thiswww.rcsb.org). It is however important to observe that other criteria, slightly more or less stringent, would produce similar results , given the extreme-value distribution of pairwise protein sequence similarity scores [Protein crystal structures were downloaded from the Protein Data Bank , 23 accoy scores . Eight dProtein atoms were divided into 24 classes according to Li and Nussinov : atom typcVol) were computed with the rwcontents program of the CCP4 software suite [pcVol is computed as3.Percentages of crystal volume occupied by solvent  in a protein crystal structure and the percentage of volume occupied by solvent in the crystal (pcVol). By plotting B versus pcVol, it is then possible to extrapolate, through linear regression, the value of B (B_max) at pcVol\u2009=\u2009100%, when all the atoms contained in the crystal are, ab absurdo, in the liquid state.It is possible to compute the average B-factor  available for 2 and on the presence of missing atoms or residues . Therefore, it is possible to find four types of files: (i) those with large B-factors and with missing residues; (ii) those without large B-factors and without missing residues; (iii) those with large B-factors and without missing residues; and (iv) those without large B-factors and with missing residues.It is mandatory to use a set of protein crystal structures with a minimal fraction of atoms, the B-factors of which have been allowed to inflate \u2013 the common practice nowadays. For this reason, the entire PDB was analyzed and files were classified, based on the presence of atoms with B-factors larger than 100\u00a0\u00c5As it can be seen in Fig.\u00a0pcVol, assuming that these data are little affected by the modern tendency to allow B-factor inflation in the absence of interpretable electron density maps.It clearly appears that the tendency to allow B-factors to reach extremely high values became common only during the last decade. For this reason, only protein crystal structures deposited in the Protein Data Bank prior 2008 were used to analyze the relationships between B-factors and pcVol is shown in Fig.\u00a0The relationship between B-factors and pcVol increases  depends on the B-factor according toI observe here that the dependence of the B-factor on resolution is absolutely obvious. In fact the atomic form factor , they are nearly always smaller than 0.5 for the 24 atom types listed in the Methods. This depends on the considerable scatter of the average B-factors within each resolution range, which is not reported in Fig. BN), defined asBav is the average B-factor of a protein crystal structure and Bs is its variance. However, this is not possible here since the average BN is equal to zero by definition and, as a consequence, it is invariant and cannot depend on any other variable. When one analyzes a specific type of protein atoms, for example the backbone carbonylic carbon atoms, its average BN value can be different from zero. However, individual average BN values are nearly independent on resolution and pcVol, since the standardization is performed within a single protein crystal structure \u2013 this is actually the reason why this standardization is performed.The correlation coefficients between B-factors and pcVol and resolution  are shown in Table\u00a0B and pcVol are relatively small \u2013 they range between 0.23 and 0.51 \u2013 given the intrinsic variability of the B-factors; however, the slopes are statistically larger than zero for all atom types). B_max tend to increase if resolution decreases. In the highest resolution range (0.0\u20131.5\u00a0\u00c5) and when all the atom types are considered together, the average B-factor at pcVol\u2009=\u2009100% is only 25\u00a0\u00c52, while it is 80\u00a0\u00c52, in the lowest resolution range (3.3\u20134.0\u00a0\u00c5).The B-factors expected when CI) of the B_max values are also reported in Table n is the number of points, pcVolave is the average pcVol value andBobs is the observed value of the B-factor, Bcalc is the computed value of the B-factors  CIs are definitely vary large (nearly 20\u00a0\u00c52).B_max values are smaller for main-chain atoms than for side-chain atoms. For example, they range from 23 to 24\u00a0\u00c52 in the 0.0\u20131.5\u00a0\u00c5 resolution range, with an average value of 23\u00a0\u00c52, while the analogous values range from 20 to 40\u00a0\u00c52 for side-chain atoms, with an average value of 28\u00a0\u00c52. In general, main-chain B_max values are about 5\u00a0\u00c52 smaller that side-chain B_max values.B_max values tend to increase in going from sulfur, to carbon, to nitrogen and to oxygen atoms. For example, in the 0.0\u20131.5\u00a0\u00c5 resolution range, they are equal, on average, to 24\u00a0\u00c52 for sulfur atoms, to 26\u00a0\u00c52 for carbon atoms, and to 29\u00a0\u00c52 for nitrogen and oxygen atoms. It must however be observed that these differences are often statistically insignificant, given the quite wide variety of atom types per each chemical element, with the partial exclusion of sulfur.B_max values are observed for the side-chain sulfur atom of cysteine (atom type 13) or the N\u03b51 nitrogen atom of tryptophan (atom type 16). Interestingly, the side-chain sulfur atoms of methionine (atom type 14), which is more distant from the backbone than the side-chain sulfur atom of cysteine, is also associated with larger B_max values. For example, in the 0.0\u20131.5\u00a0\u00c5 resolution range, it is equal to 27\u00a0\u00c52, while that of cysteine is equal to 22\u00a0\u00c52.Minimal B_max values are observed for the side-chain nitrogen atom of lysine (atom type 20) and for the side-chain carboxylic oxygen atoms of aspartate and glutamate (atom type 23), which are at the end of long side-chains and are also, in general, largely exposed to the solvent. Interestingly, the side-chain nitrogen atoms of arginine have, in general, B_max values lower than the side-chain nitrogen atom of lysine and this might depend on the fact that the guanidinium moiety of arginine is larger and may for more hydrogen-bonds than the ammonium moiety of lysine.Maximal B_max values for a charged residue (lysine), a polar residue (serine), and an apolar residue (methionine). It clearly appears that B_max values tend to increases if the distance from the backbone increases. Lysine, which has the longest side-chain that ends with a cationic group, has, as expected, the largest B_max values at its extremity.Figure\u00a0B_max values were estimated from the analysis of protein crystal structures deposited until 2008 in the Protein Data Bank, when the tendency to allow B-factors to inflate arbitrarily was minimal. The analysis of a set of 2783 protein crystal structures deposited after 2014, assembled with the same criteria described in Methods, is summarized in Table\u00a0B_max, at low resolution a large fraction of the structures have an average B-factor larger than B_max. This depends on the fact that at high resolution only few atoms are invisible in the electron density maps and, as a consequence, few atoms have unreasonably large B-factors. On the contrary, at low resolution, several atoms are invisible in the electron density maps and have, as a consequence, extremely large B-factors. From the perspective of structural bioinformatics and of the users of the Protein Data Bank information, this means that nearly one half of the crystal structures refined at low resolution should be considered with extreme caution, since many moieties of them are not experimentally determined, but just modeled computationally. It is also interesting to observe that even at very high resolution about 15% of the protein crystal structures are likely to be incomplete, given their large average B-factor.B_max).Based on well controlled data sets, it is possible to estimate the maximal B-factor average values that are compatible with the crystalline solid state"}
+{"text": "Fetal electrocardiogram (FECG) extraction is very important procedure for fetal health assessment. In this article, we propose a fast one-unit independent component analysis with reference (ICA-R) that is suitable to extract the FECG. Most previous ICA-R algorithms only focused on how to optimize the cost function of the ICA-R and payed little attention to the improvement of cost function. They did not fully take advantage of the prior information about the desired signal to improve the ICA-R. In this paper, we first use the kurtosis information of the desired FECG signal to simplify the non-Gaussian measurement function and then construct a new cost function by directly using a nonquadratic function of the extracted signal to measure its non-Gaussianity. The new cost function does not involve the computation of the difference between the function of the Gaussian random vector and that of the extracted signal, which is time consuming. Centering and whitening are also used to preprocess the observed signal to further reduce the computation complexity. While the proposed method has the same error performance as other improved one-unit ICA-R methods, it actually has lower computation complexity than those other methods. Simulations are performed separately on artificial and real-world electrocardiogram signals. The fetal electrocardiogram (FECG) contains much important information about the health and possible diseases of the fetus, which reflects the complete view of the heart activities. Additionally, it is more sensitive than color Doppler ultrasound in the case of fetal acidosis and anoxia. With the analysis of the FECG, the doctor can discover fetal hypoxemia, umbilical abnormality, and other fetal abnormality situations timely and take early effective actions to ensure the health of the fetus. However, the FECG signal is considerably weaker than the maternal electrocardiogram (MECG) and is often embedded in the noise, MECG, baseline wandering, power line interference, and so forth. Accordingly, it is quite difficult to extract the FECG signal and further reduce the diagnostic accuracy.A number of methods have been reported for extracting the FECG signal, like filtering method , singulaTo overcome this problem, the independent component analysis with reference (ICA-R) is applied to extract the FECG \u201314, whicThe one-unit ICA-R is a special case of the multiunit ICA-R. It only separates one desired source signal every time. The only difference between the one-unit ICA-R and the multiunit ICA-R is that the former only extracts one desired signal, and the latter is based on the former and uses the orthogonalization method to extract multiple desired signals. If we use the deflationary orthogonalization method or symmetric orthogonalization method, which are widely used in ICA  to extraAlthough the one-unit ICA-R and multiunit ICA-R have a little difference, they share the same cost function. Additionally, they both use the same non-Gaussian measurement function that is used in the classical ICA algorithm to measure the non-Gaussian component of the extracted signal. The negentropy approximation is needed to compute the difference between the function of the extracted signal and the function of a Gaussian vector that has the same mean and variance as the extracted signal. This will consume plenty of time. The classical ICA algorithm has no information about the source signals, except that the non-Gaussian measurements and statistics are independent. However, the ICA-R has prior information about the desired signal, but the previous methods did not use such information to reduce the computational complexity of the negentropy approximation. The aim of this paper is to reduce the computational complexity for the one-unit ICA-R by taking advantage of the prior information of the desired ECG to simplify the negentropy approximation.This paper is organized as follows. x(t) = T is the observed signal, A is the mixing matrix with the size (n \u00d7 m), and s(t) = T is the source signal. The aim of the ICA is to estimate the source signal s(t) from the observed signal x(t) by computing the separating matrix W = T with size (m \u00d7 n). The estimated source signal can be expressed as follows:y(t) = T is the estimated source signal, which is the same as s(t) under ideal condition. However, under real condition, the shape of the waveforms of y(t) is close to s(t), except for the amplitude and sequence of the waveforms. The source signals s(t) are considered as non-Gaussian and mutually statistically independent. Accordingly, it has strong non-Gaussian properties. The mixing signals x(t) have strong Gaussian characteristics according to the central limit theorem. When the estimated source signal is close to the source signal s(t), it will have strong non-Gaussian properties. Thus, the ICA uses a non-Gaussian measurement function of the estimated source signals as a cost function  is avoided in J(y) to eliminate E{F(v)} to avoid further computing [E{F(y)} \u2212 E{F(v)}]. J(y) is a part of the cost function of the one-unit ICA-R. As a result, this will reduce computation complexity of the one-unit ICA-R.As the previous one-unit ICA-R methods involve the computation of the F used in one-unit ICA-R is a positive even function, the terms E{F(v)} and E{F(y)} are both positive in } has a maximum value, this equals [E{F(y)} \u2212 E{F(v)}], which has a maximum value. On the contrary, when E{F(y)} has a minimum value, this equals \u2212[E{F(y)} \u2212 E{F(v)}], which has maximum value.Since the nonlinear function itive in , and v hE{f\u2032(si)} \u2212 E{sif(si)} < 0, E{F(y)} has maximum value. Therefore, when E{f\u2032(si)} \u2212 E{sif(si)} < 0, we can determine that [E{F(y)} \u2212 E{F(v)}] has a maximum value based on the analysis described in the first paragraph of this subsection. Based on the above analysis, when E{f\u2032(si)} \u2212 E{sif(si)} < 0, then } \u2212 E{sif(si)} > 0, the non-Gaussian measurement function can be simplified asc = E{sif(si)} \u2212 E{f\u2032(si)}.Based on the analysis in  0, then  can be s0, then (Jy=\u03c1EFy\u2212Eunction (Jy=\u03c1EFy.Olified asJy=\u2212\u03c1EFy.F(y) was proposed for extracting the super-Gaussian and sub-Gaussian signal, respectively.a, b \u2208 R+. In [a = 1 in (y) and 1 \u2212 tanh2\u2061(y), respectively.In , the fol R+. In , Mi has ectively.Fsupy=1alR+. In [Fsupy=1alectively.Fsupy=1alR+. In [Fsupy=1alc in (si), which is described assi is a super-Gaussian signal with unit variance, E{si4} > 3. Then c < 0 in (If we use  as a nonc in  can be ec in (cEsifsi\u2212Ec in (cEsifsi\u2212Eterm in (cEsi2\u2212si4c < 0 in  as(33)Jyy = wTx is the extracted signal, x is the centered and whitened signal, and w is the separating vector. \u03c1 in  for the problem in , Newton's method is used to optimize L. The learning rule of the separating vector w is given by the following equation:\u03b7 is the learning rate:The one-unit ICA-R is used to extract one desired signal. The prior information that the desired signal is a super-Gaussian or a sub-Gaussian signal is easily obtained. The FECG and MECG are both super-Gaussian signals in general. Therefore, in the extraction of FECG, we can directly use  instead min\u2061\u2003\u2212Jy\u2248n (\u03c1^ in . \u03c1 is jumin\u2061\u2003\u2212Jy\u2248\u03c1 in (\u03c1(E{F(y)} \u2212 E{F(v)}). In the original algorithm, we have to additionally compute (E{F(y)} \u2212 E{F(v)}) in every iteration, which considerably consumes much more time compared with the improved algorithm.The main difference between the improved algorithm in  and the \u03c1 in  is just n Center the observed signals.(2)Whiten the centered signal.(3)\u03b3, convergence threshold \u03c2, parameter \u03c1, and the leaning rate \u03b7; generally let \u03c1 = 1, \u03b7 = 1.Choose a proper scalar penalty parameter (4)w0.Use  to initi(5)w0 \u2190 w0/\u2016w0\u2016.Normalize (6)\u03bc.Choose an initial value for (7)\u03bc by (Update the Lagrange multiplier \u03bc by .(8)w by (Update the separating vector w by .(9)w by Normalize the separating vector (10)wk+1 \u2212 wk\u2016, \u2016wk+1 + wk\u2016) \u2264 \u03c2, otherwise go back to step (7).Until min\u2061\u2009, A is mixing matrix, B is the whiten matrix, w is the separating vector of mixed signals after whitening, wTB is the global separating vector, M is the number of mixing signals, and maxj | pj| is to find the maximum valued among the elements in the vector p = . The extracted signal by proposed method can be described asp = , pk \u2260 0, we will have the extracted signal y = pksk, which is just rescaled signals of sk. It is obvious from  = log\u2009cosh\u2009\u2061(y) as the nonquadratic function and \u03b5 = E{(y \u2212 r)2} as the closeness measure function. Additionally, g(y) = \u03b5 \u2212 \u03be. We also use the corrected first derivative of g(y) as its first derivative. The corrected first derivative is given in [\u03c1, \u03b7, and \u03b3 all equal to one and perform 1000 trials for each data set.In the experiments, we select given in  as(42)\u2207wThe artificial signals include the power line interference with 50\u2009Hz, Gaussian noise, FECG, and MECG. The FECG and MECG are generated by using the ECG toolbox of Sameni . The ref4A=0.89250To quantitatively compare the performance of the proposed method and that of Mi's method , the IPIThe real-world ECG data was contributed by De Moor  and has In the Ch1 recording, the strong and slow heart belongs to the mother, while the weak and fast belongs to the fetus. Therefore, we can use the information about fetus in the Ch1 recording to construct reference signal for extracting the FECG. We use impulse series whose occurrence time is the same as that of the subpeaks in the first channel signal Ch1 as reference for extracting the FECG. The impulse series whose occurrence time is the same as the peaks of any channel signal were used as reference for extracting the MECG.The reference signal and the FECG signal extracted by both methods are shown in In this paper a fast one-unit ICA-R algorithm for extracting ECG is proposed by simplifying the non-Gaussian measurement method of the extracted signal. In the proposed algorithm, the nonlinear function of the extracted signal is directly used as non-Gaussian measurement function. This avoids having to compute the difference between the function of the extracted signal and the function of the Gaussian random vector with the same mean and variance as the extracted signal. Centering and whitening are also used to preprocess the observed data to avoid computing the observed signal covariance matrix. As a result, the computation complexity for the one-unit ICA-R algorithm is greatly reduced.The validity of the proposed algorithm is tested and compared to Mi's algorithm using artificial ECG data and real-world ECG data. Both experimental results demonstrate that the convergence rate of the proposed algorithm is two times faster than Mi's algorithm, while both methods have the same error."}
+{"text": "With a higher applied voltage in the c-LED, decreasing response time and rising time improve device performance, but a longer recombination time degrades luminescence efficiency. By using an m-LED with a stronger carrier localization and a low polarization effect, shorter response, rising, and recombination times provide more efficient carrier injection, transport, relaxation, and recombination. These advantages can be realized for high-power and high-speed flash LEDs. In addition, with a weaker carrier localization and a polarization effect in the c-LED, the slower radiative and faster nonradiative decay rates at a larger applied voltage result in the slower total decay rate and the lower luminescence efficiency. For the m-LED at a higher applied voltage, a slow decreasing nonradiative decay rate is beneficial to device performance, while the more slowly decreasing and overall faster radiative decay rate of the m-LED than that of the c-LED demonstrates that a stronger carrier localization and a reduced polarization effect are efficient for carrier recombination. The resulting recombination dynamics are correlated with the device characteristics and performance of the c- and m-LEDs.Based on time-resolved electroluminescence (TREL) measurement, more efficient carrier injection, transport, relaxation, and recombination associated with a stronger carrier localization and a low polarization effect in a nonpolar  The  current \u201313. Pola current , electro current , 10, poo current \u201313, and  current , 15 and  current  have alsd a-axes , 17, 18,d a-axes , and -c-n-polar)  can overcy droop . Withoutcy droop , 17, 18.nitrogen-polar InGaN/GaN LEDs with the opposite polarity were shown to provide the advantages of more efficient carrier relaxation and carrier recombination [m-LED are not well explored.Time-resolved electroluminescence (TREL) can explore the dynamic EL behaviors of carrier injection, carrier transport, carrier relaxation into active region, and carrier recombination at the excited states in LEDs . By TRELbination . Howeverm-LED in comparison with those of the c-LED by using currentz-voltage (I-V), electroluminescence (EL), external quantum efficiency (EQE), and TREL measurements. By using an m-LED to overcome the polarization effect, shorter response, rising, and recombination times demonstrate that a stronger carrier localization and a reduced polarization effect are efficient for carrier injection, transport, relaxation, and recombination. In addition, due to a weaker carrier localization and a polarization effect in the c-LED, the slower radiative and faster nonradiative decay rates at a larger applied voltage result in the slower total decay rate and the lower recombination efficiency. At a larger applied voltage, the more slowly decreasing and overall faster radiative decay rate of the m-LED than that of the c-LED demonstrates that a stronger carrier localization and a reduced polarization effect are efficient for carrier recombination.This study reports carrier transport and recombination dynamics associated with a stronger carrier localization and a low-polarization effect of the This paper is organized as follows. In section 2, methods are described. In section 3, results and discussions are reported. Finally, conclusions will be drawn in section 4.c- and m-LEDs were simultaneously grown on the c- and m-plane sapphire substrates, respectively, by a metal organic chemical vapor deposition (MOCVD) reactor. The LED structure comprises a 25-nm low-temperature (LT) GaN buffer layer, a 3.00-\u03bcm undoped GaN layer, a 1.50-\u03bcm n-type Si-doped GaN contact layer, 10-pair InGaN/GaN multiple quantum wells (MQWs) , an 15 nm AlGaN electron blocking layer, and a 0.25-\u03bcm Mg-doped p-GaN contact layer. The 25-nm LT-GaN buffers were grown on nitridized sapphires at 600\u00a0\u00b0C in H2. Except for the substrates, the structures of the two LEDs are the same.The I-V, EL spectrum, and EQE were measured with a source meter (Keithley 2614B), spectrometer , calibrated integrating sphere, and power meter. Without an ohmic contact, an indium dot melting on the sample surface was used as a contact for the probe station. For TREL measurement, a pulse generator (Tektronix AFG3152C) was used to generate 2.0\u20135.0 V, 0.5\u00a0\u03bcs pulse width, and 1 kHz repetition rate voltage pulses to the LEDs. The light output was focused and detected by a photosensor module containing a metal package PMT and a high-voltage power supply circuit (Hamamatsu H10721-210) operating directly on the surface of each LED. The same PMT voltages of the TREL measurement were applied for the two LEDs. The parasitic capacitance in the test circuit would introduce the same RC delay for the two LEDs. The transit EL signals were recorded by a digital oscilloscope (Agilent DSO 6052A) with a 500\u00a0MHz bandwidth. The overall resolution of TREL system is less than 2\u00a0ns. The detailed measurement was described in our previous study [us study .c- and m-LEDs, respectively. EL emission wavelength for the m-LED is much shorter than that for the c-LED. EL spectra of the c-LED just coincide with the lower energy shoulder of that for the m-LED. Both carrier localization effect [c-LED contribute to luminescence. The large difference of EL peak positions for the m-LED from that for the c-LED can\u2019t be discussed by only one effect. It can be due to the weaker QCSE or lower indium contents in the MQWs for the m-LED. The larger bandwidth of EL and the lower energy shoulder in the m-LED represent a stronger indium composition fluctuation and a stronger carrier localization. The broader bandwidth of EL in the m-LED could be due to the luminescence contributions from different indium compositions and indium clusters.Figure\u00a0n effect \u201323 and Qn effect  in the cm-LED could be due to the band-filling effect of higher energy states and a reduced polarization effect upon a forward bias.In addition, Fig.\u00a0I-V characteristics and normalized EQE, respectively, of the two LEDs. The turn-on voltages of c- and m-LEDs are 2.5 and 3.5\u00a0V, respectively. Although a slightly larger threshold, smaller slope of current under forward bias, and lower EQE of the m-LED suggest poorer device quality, a stronger carrier localization and a reduced polarization effect help the m-LED to exhibit better carrier transport and recombination dynamics, as shown later.Figure\u00a0c- and m-LEDs, respectively. After the voltage pulses are applied, different rising transit profiles for the two LEDs imply different behaviors of carrier injection and carrier transport. The rising part of the transit EL intensity of the c-LED shows a slower response and rise. Similar temporal behavior was observed in transition from free carrier to deep acceptor levels of a GaN/AlGaN LED [c-LED, the rising part of transit EL intensity for the m-LED shows a shorter response, steeply rising, and then decay within the first 100\u00a0ns. Similar temporal behavior, attributed to band-to-band emission, was observed in EL peak at 285\u00a0nm of a GaN/AlGaN LED [m-LED, carriers may transport from high energy states to lower energy states. It is noted that PMT has a better sensitivity and can amplify low signals. The intensity ratios of TREL transit profiles under the same bias for the two LEDs are different from those of EL spectra.Figure\u00a0lGaN LED  and in tlGaN LED . BecauselGaN LED . Without\u03c4response) can be determined by the time delay between addressing the device with a short voltage pulse and the appearance of EL. The rising time (\u03c4rise) is defined by the intercept of the tangents. Delay time (\u03c4delay) is the time delay in reaching both the maximum intensity of transit EL and the subsequent decay, when the voltage pulse is switched off . The recombination time (\u03c4recombination) can be determined by fitting the decay profile with a single exponential.As shown in Fig.\u00a0\u03c4response can be described as [As shown in Fig.\u00a0ribed as :Fig. 5Re\u03c4injection, \u03c4transport, \u03c4relaxation, and \u03c4\u2009'\u2009recombinaiton are the carrier injection time to the ohmic contact, carrier transport time from the ohmic contact to the active region, carrier relaxation time from the active region to the MQWs, and carrier recombination time in energy states, respectively. With the same contact material for the two samples, \u03c4injection can be assumed to be the same. Also, due to the faster mobility of nonpolar m-plane GaN [\u03c4transport of the m-LED should be shorter. Without polarization charges, a lower potential barrier makes the carrier relaxation efficiency of the m-LED better than that of the c-LED [\u03c4relaxation of the m-LED should be shorter. The weaker polarization effects in the m-LED increases the overlap of electron and hole wavefunctions and the \u03c4\u2009'\u2009recombinaiton is expected to be shorter, as shown later. This suggests that a weaker polarization effect in the m-LED helps carrier relaxation into MQWs and a stronger carrier localization helps carrier recombination in higher energy states. Hence, the shorter \u03c4response of the m-LED should be due to shorter \u03c4transport, \u03c4relaxation, and \u03c4\u2009'\u2009recombinaiton.where lane GaN , \u03c4transhe c-LED , so \u03c4rem-LED, shorter \u03c4response, \u03c4rise, \u03c4delay, and \u03c4recombination of the m-LED than those of the c-LED demonstrate that a stronger carrier localization and a reduced polarization effect of the m-LED are more efficient for carrier injection, transport, relaxation, and recombination. The advantages can be realized for applications of high-power and high-speed flash LEDs. Although a longer \u03c4recombination at a higher applied voltage shows a slower carrier recombination rate, it is shorter than \u03c4response and \u03c4rise.At the same time, at a higher applied voltage in the Ga- and N-polar LEDs [c-LED and the reduced polarization effect in the m-LED could be compared. The polarization-associated recombination dynamics in the c- and m-plane LEDs were also revealed by using bias-dependent EL, EQE, and TREL measurements.In a previous study, bias-dependent EL, EQE, and TREL measurements were conducted to compare the effects of carrier localization and QCSE on carrier transport and recombination dynamics of lar LEDs . It is nc-LED at 3.0V and the m-LED at 6.0V, shorter \u03c4response, \u03c4rise, \u03c4delay, and \u03c4recombination of the m-LED than those of the c-LED can be confirmed to demonstrate that a stronger carrier localization and a reduced polarization effect are efficient for carrier injection, transport, relaxation, and recombination.In addition, the injected current density may affect the carrier transport and recombination dynamics in LEDs. Because the carrier recombination is mainly from the ground states in the quantum wells, the injected current density may not affect it much. Under the same current density of the \u03c4) is the reciprocal of the total decay rate (\u03ba\u2009=\u20091/\u03c4), which is the sum of the radiative and nonradiative decay rates [The decay time  and (3).\u03ba, \u03bar, and \u03banr associated with recombination dynamics are shown in Fig.\u00a0c-LED at a lower applied voltage, a smaller deviation between \u03ba and \u03bar shows that the recombination dynamics are dominated by the \u03bar. With a higher applied voltage, the slower \u03bar and faster \u03banr result in the slower \u03ba.m-LED at a higher applied voltage, a steeply decreasing \u03banr is beneficial to device performance. In spite of the lower \u03b7 of the m-LED, the slower decreasing \u03bar and overall faster \u03bar of the m-LED than that of the c-LED demonstrates that a stronger carrier localization and a reduced polarization effect are efficient for carrier recombination. Because the c- and m-LEDs were simultaneously grown on the c- and m-plane sapphire substrates, respectively, the un-optimized growth condition for the m-LED leads to a faster \u03banr than \u03bar. The \u03bar should be enhanced by optimizing growth conditions for the m-LED separately. Also, an m-LED can be fabricated on an m-plane GaN substrate [c-LED at 3.0V and the m-LED at 6.0V, the faster \u03bar of the m-LED than that of the c-LED can be confirmed to demonstrate that a stronger carrier localization and a reduced polarization effect are efficient for carrier recombination, while the faster \u03banr of the m-LED can be due to an un-optimized growth condition and a higher defect density. The resulting recombination dynamics are correlated with the device characteristics and performance of the c- and m-LEDs.For the ubstrate . In addim-LED with a stronger carrier localization and a weaker polarization effect, shorter response, rising, and recombination times provide more efficient carrier injection, transport, relaxation, and recombination. By optimizing growth conditions to enhance the radiative recombination, the advantages in the m-LED can be realized for the applications of high-power and high-speed flash LEDs. In addition, due to a weaker carrier localization and a larger polarization effect in the c-LED, the slower radiative and faster nonradiative decay rates at a higher applied voltage together result in the slower total decay rate and the lower recombination efficiency. With a higher applied voltage in the m-LED, a slow nonradiative decay rate is beneficial to device performance, while the more slowly decreasing and overall faster radiative decay rate of the m-LED compared to that of the c-LED demonstrates that a stronger carrier localization and a reduced polarization effect are efficient for carrier recombination. The resulting recombination dynamics are correlated with the device characteristics and performance of the c- and m-LEDs.In summary, this study reveals that by using an"}
+{"text": "This paper presents a novel physics-driven spatiotemporal regularization (STRE) method for high-dimensional predictive modeling in complex healthcare systems. This model not only captures the physics-based interrelationship between time-varying explanatory and response variables that are distributed in the space, but also addresses the spatial and temporal regularizations to improve the prediction performance. The STRE model is implemented to predict the time-varying distribution of electric potentials on the heart surface based on the electrocardiogram (ECG) data from the distributed sensor network placed on the body surface. The model performance is evaluated and validated in both a simulated two-sphere geometry and a realistic torso-heart geometry. Experimental results show that the STRE model significantly outperforms other regularization models that are widely used in current practice such as Tikhonov zero-order, Tikhonov first-order and L1 first-order regularization methods. Linear regression has widespread applications in various fields such as engineering, healthcare, economics and social science, for predictive modeling, experimental design, or system optimization. Regression parameters are often estimated based on the static data set of explanatory and response variables. However, rapid advancement of distributed sensing and imaging technology brings the proliferation of high-dimensional spatiotemporal data, i.e., y\u2009=\u2009y and x\u2009=\u2009x in healthcare systems. Traditional regression is not generally applicable for predictive modeling in these complex structured systems.Linear regression is a widely used approach for modeling the relationship between explanatory variables y acquired by the ECG sensor network placed on the body surface, also named body surface potential mapping (BSPM)1x on the heart surface from BSPM y so as to investigate cardiac pathological activities 345For example, y\u2009=\u2009Rx\u2009+\u2009\u03b5) poses several challenges includingIn general, high-dimensional predictive modeling  such as BSPMs. It is often difficult to directly measure heart-surface potential mappings x. As such, inferring x needs a better knowledge of parameter matrix R. Fortunately, physical laws define the mechanisms of electrical propagation from the heart to the body surface. This, in turn, enables the derivation of parameter matrix R using physics-based principles .(1) Ill-conditioned system: Linear systems involving high-dimensional data y and x are commonly ill-conditioned. This is partly caused by unobserved x, and partly due to the fact that parameter matrix R is rank deficient . The condition number of R  is also shown to be large in high-dimensional predictive modeling  Spatiotemporal regularization: Ill-conditioned systems make the prediction more sensitive to noise factors  and approximation errors in parameter matrix R. For example, measurement noises can potentially cause a small change \u0394y in the observed data y. Considering the estimation of x changes to x\u2009+\u2009\u0394x, we will have the changes in the solution expressed as Rcond, the pseudo-inverse solution of x and y are spatially distributed and dynamically evolving over time, they have spatial and temporal correlations. Very little has been done to develop new spatial regularization methods that handle approximation errors through spatial correlations of dynamic profiles on the complex geometry , as well as new temporal regularization methods to increase model robustness to measurement noises and other uncertainty factors.(3) This paper presents a new spatiotemporal regularization model to tackle these research challenges and address ill-condtioned problems in high-dimensional predictive modeling. Our contributions in the present investigation are as follows:R. We developed realistic models of torso-heart geometries, numerically discretized them with the boundary element method, and then utilized physical laws  to derive the parameter matrix.(1) High-dimensional systems involve complex geometries, which challenge the derivation of parameter matrix R with a spatiotemporal regularization (STRE) method to build the high-dimensional prediction model. This approach leverages data from actual experiments to improve spatial and temporal regularity of the solutions, thereby making the final prediction closer to reality.(2) As physics-based models are deterministic and do not account for real-world uncertainties, we developed a physical-statistical approach that integrates physics-derived parameter matrix x. As such, they are not generally applicable because the electric field involves both positive and negative potentials. We developed a new method of dipole multiplicative update, which is inspired by the dipole assumption in electrodynamic physics. This new idea overcomes the drawbacks of existing multiplicative update methods, and provides a generalized approach to solve spatiotemporal regularization problems.(3) The proposed STRE model involves quadratic programming and high-dimensional data, which cannot be solved analytically. Iterative algorithms are commonly used such as the multiplicative update method which, however, requires the nonnegative constraint of (4) Few, if any, previous works focused on both spatial and temporal regularizations in inverse and forward ECG problems. We evaluated and validated the proposed STRE model in simulation as well as a real-world case study to map electric potentials from the body to the heart surface. Experimental results show that our method not only effectively tackles the ill-conditioned problems in high-dimensional predictive modeling, but also outperforms those regularization models widely used in current practice . This research work provides a new and effective approach to investigate disease-altered electric potentials from the body to the heart surface.The remainder of this paper is organized as follows: Section II introduces the research background. Section III presents our research methodology. Section IV describes the experimental design. Experimental results are shown in section V. Section VI concludes this paper.y\u2009=\u2009Rx\u2009+\u2009\u03b5, where x and y are spatiotemporal data, is generally ill-conditioned. For example, the inverse ECG problem in healthcare 7R  is a measure of relative sensitivity of the solution x to the observed data y . The pseudo-inverse solution of The high-dimensional predictive model, R, increase the model reliability and improve the prediction accuracy.Statistical regularization models such as Tikhonov and L1 regularization methods789The objective function of Tikhonov regularization is formulated aswhile the L1 regularization is formulated as2 and ||\u00b7||1 denote the L2- and L1-norm, respectively, \u03bb is the regularization parameter, and \u0393 represents the mathematical operator constraining x. Note that \u0393 is the identity matrix in zero-order Tikhonov and L1 regularization methods . Note that \u0393 is a discretized gradient operator in the first-order regularization methods. One of the most commonly used gradient operators is a bidiagonal matrix9Zero-order regularization is effective to shrink unreliable components of the estimator and achieve sparse solutions for high-dimensional predictive modeling. However, they are limited in the ability to handle measurement noises or approximation errors in ill-conditioned systems. Therefore, first-order regularization methods were proposed to address such limitations by constraining the gradient of the solution x in one column as {x(s1|t), x(s2|t), \u2026, x(sN|t)}T, and then applied the bidiagonal gradient matrix. Note that the alignment of spatiotemporal data in one column is not an effective way (maybe even incorrect) to compute the spatial gradients. As such, regularization results are not as satisfactory as expected.which is a central-difference approximation for the first-order derivative. However, this approximation does not account for the complex geometries of space-time dynamic systems, and is only effective for one-dimensional data. Most of previous works aligned x\u2009=\u2009\u2202x/\u2202n, where x denotes the dynamic potential distribution on the heart surface and n denotes the surface-normal vector7x, but ignores the gradient component on the the heart surface /\u2202\u03c4, where \u03c4 denotes the surface-tangent vector) and does not take into account the spatial correlations between adjacent regions. It is worth mentioning that spatiotemporal data from distributed sensing and imaging are generally spatially distributed and have spatial correlations13In the inverse ECG problem, another commonly used gradient operator is the normal derivative-operator of the potential distribution on the heart surface, \u0393et al.In addition, space-time systems are dynamically varying over time and have temporal correlations. For example, the human heart is a typical spatiotemporal system with cardiac electrical activities dynamically varying in both space and time15R by integrating the boundary element method with divergence theorem and Green\u2019s theorem. Second, we investigate the spatial regularization that handles approximation errors through spatial correlations of dynamic profiles on the complex geometry , as well as the temporal regularization to increase model robustness to measurement noises. Finally, we develop a new generalized method of dipole multiplicative update to solve the objective function of the proposed STRE model.As shown in y are generally obtained from the surface of a complex structured system such as BSPMs. Inferring the internal dynamic variable x  of these systems depends on the high-dimensional predictive modelingThe observed data R is the parameter matrix characterizing the interrelationship between x and y.where SB and heart surface SH18x on the heart surface and y on the body surface are related by the Laplace\u2019s equations derived from physics-based principles . Solving for the parameter matrix R involves tackling this Laplace\u2019s equation and calculating complex surface integrations, which are difficult to solve analytically in realistic torso-heart geometry. Thus, boundary element method (BEM)20SB and SH into triangle meshes, and divide the surface integrals into a series of numerical integrations over the triangle elements. Thus, the parameter matrix R is expressed as1819In the human body system, the heart represents the bioelectric source, and the torso is modeled as a homogeneous and isotropic volume conductor whose boundary consists of body surface A's and M's depend entirely on the torso-heart geometry. The rows of ABB, ABH and MBH correspond to the locations of different nodes on the body triangle-mesh SB. Similarly, the rows of AHH, AHB and MHH represent the locations of different nodes on the heart triangle-mesh SH. The different columns of all the matrices correspond to locations of triangle elements on the surface of integration.where the coefficient matrices, x in complex structured systems is an ill-conditioned problem, because the parameter matrix R is often with a large condition-number7R. For examples, the human body is modeled as a homogeneous volume conductor, and geometrical variations over time are assumed to be negligible. These assumptions may not hold true in real-world situations and will introduce uncertainties when predicting x22However, inferring s to overcome the drawbacks in existing methods.The spatiotemporal data acquired by distributed sensing and imaging systems are generally distributed in the space and have spatial correlations. In existing regularization methods, the constraint operator \u0393 or the penalty term does not account for the spatial correlations or the geometries of complex systems, but rather align the mesh nodes in one column or take the normal derivative operator. As such, they are limited in the ability to improve the spatial regularity. In this investigation, we propose to define the constraint operator \u0393 to be a spatial Laplacian operator \u0394s is computed by determining the Laplacian at each mesh node. In a two-dimensional square lattice with a lattice constant d as shown in xi denotes the value of dynamic variable x at node pi\u2009=\u2009, where  are location coordinates. According to Taylor\u2019s theory, xi is approximated as the sum of x0 and its derivatives at node p0\u2009=\u2009:The matrix \u0394Adding the above four equations yieldsx0 at node p0 is expressed asThus, the Laplacian of where xt(i) denotes the value of dynamic variable x at node pi at time t, and dij is the distance between pi and pj. Using linear interpolation, the value pi and pj, and pi, as shown in However, real-world geometries are complex and are generally discretized into irregularly triangulated meshes using the boundary element method20dij\u2019s over the neighbor nodes pj\u2019s of pi, and these neighbors pj\u2019s are the vertices of the triangles that include pi as one of the vertices. Thus, the Laplacian of xt(i) at pi in a 3D triangle mesh is defined aswhere ni is the number of neighbor nodes pj\u2019s of pi; pj\u2019s. According to s aswhere pi is defined asTherefore, the spatial regularity of three-dimensional triangle mesh at node N is the total number of mesh nodes.where x and y are dynamically evolving over time and have temporal correlations. However, few, if any, previous works have effectively dealt with the temporal regularization for high-dimensional predictive modeling in space-time systems \u2009=\u2009Rx\u2009+\u2009\u03b5, the two-body dynamic prediction problem). Therefore, we propose to define the temporal regularity asIn addition, spatiotemporal data T denotes the length of the overall time span of the spatiotemporal data, and w is a time window. Temporal correlation is stronger when two time points are close to teach other, and electric potentials at two time points that are far away from each other tend to have bigger differences. Therefore, the time window w is often chosen to be a small number. Adding the temporal constraints in where Combining the parameter matrix, spatial and temporal regularization as described in previous subsections, we formulate our STRE model by the following objective function\u03bbs and \u03bbt are the spatial and temporal regularization parameters, which can be chosen by the L-curve methodR, but also increase the model robustness to measurement noises in the time domain. Therefore, it is expected that the proposed STRE method will greatly improve the performance of high-dimensional predictive modeling in space-time systems.where x25xt is split into its positive part xt can be denoted as yt and xt to denote y and x here and later on. Then the term that only depends on vectxt in the objective function becomesThis objective function involves both spatial and temporal correlations, and is difficult to be solved analytically. Iterative algorithms are commonly used such as the multiplicative update method which, however, requires nonnegative constraint of I is an identity matrix whose dimension is the same as the Laplacian matrix \u0394s. We substitute where A+ and A\u2212 are the positive and negative parts of matrix A, whose definition is similar to that of where matrix In the present investigation, the proposed STRE model is implemented to predict the time-varying distribution of electric potentials on the heart surface from real-world sensor data of electric potentials on the body surface. The model performance is evaluated and validated in both a simulated two-sphere geometry and a realistic torso-heart geometry.R. A time-varying three-dimensional current dipole p(t)\u2009=\u2009(px(t), py(t), pz(t)) is placed at the center of the two-sphere geometry, which is defined ast ranges from 0\u2009ms to 300\u2009ms. Thus, the dynamic distributions of electric potentials on the inner surface x and outer surface y are calculated analytically by the equationswhere time \u03c3\u2009=\u20091 is the electric conductivity inside the outer sphere, rH(s) and rB(s) denote the location vectors from the center to the inner and outer spheres, respectively, and rH\u2009=\u20091.0 and rB\u2009=\u20091.5 are the radii of the two spheres.where y on the outer sphere calculated by \u03bbs\u2009=\u20090.015 and \u03bbt\u2009=\u20090.5 are chosen by the L-curve methodw is specified to be 2. In our simulation studies, Gaussian noises with mean zero and variance y. Five different noise levels  are added at each time, which correspond to noises with standard deviations \u03c3\u03b5\u2009=\u20090.1, 0.2, 0.3, 0.4, 0.5, respectively. At each noise level, the predicted potentials on the inner sphere will be compared with the true data  calculated by The proposed STRE model is implemented to predict the electric potentials t ranges from 0ms to 1000\u2009ms) on the heart and body surfaces, and the torso-heart geometry are obtained from the Center for Integrative Biomedical Computing (CIBC) at the University of Utahy are acquired from 367 sensors, which are located at 367 nodes on the body surface. Thus, a 367\u2009\u00d7\u2009257 parameter matrix R is generated. The STRE model is implemented to predict the potential distribution y. Regularization parameters \u03bbs\u2009=\u20092.0 and \u03bbt\u2009=\u20090.005 are chosen by the L-curve methodw is specified to be 2.Furthermore, we conduct experiments in the realistic torso-heart geometry, as shown in y to simulate the real-world uncertainties in this torso-heart geometry. The five noise levels are with standard deviations \u03c3\u03b5\u2009=\u20090.005, 0.01, 0.05, 0.1, 0.2, respectively. The estimated electric potentials on the heart surface from high-dimensional predictive modeling will be benchmarked with real-world sensor data of reference potentials.Similarly, five different noise levels  are added to the electric potentials on the body surface The performance metric, relative error (RE), is used to evaluate the model performance, i.e.,x denote the estimator and reference results, respectively. The performance of our STRE model is benchmarked with Tikhonov zero-order (Tikh_0th), Tikhonov first-order (Tikh_1st) and L1 first-order (L1_1st) regularization methods. In these first-order regularization methods, the matrix \u0393 is defined as the normal derivative operator of the electric potentials on the inner surface7where y of the outer sphere. Note that the proposed STRE model yields the RE of 0.006, which is significantly smaller than that obtained from Tikh_0th, Tikh_1st and L1_1st, which are 0.1475, 0.1026, and 0.1025, respectively.y of the outer sphere. In the present investigation, we replicated the experiment 20 times for each noise level, and thus the resulted RE is shown with a corresponding error bar . When the noise level increases from \u03c3\u03b5\u2009=\u20090.1 to \u03c3\u03b5\u2009=\u20090.5, the RE monotonically increases for all the methods. Specifically, the RE increases from (0.0670\u2009\u00b1\u20090.00057) to (0.0769\u2009\u00b1\u20090.0034) for the proposed STRE model, from (0.1557\u2009\u00b1\u20090.00058) to (0.2080\u2009\u00b1\u20090.005) for Tikh_0th, from (0.1037\u2009\u00b1\u20090.00031) to (0.1538\u2009\u00b1\u20090.0031) for Tikh_1st, and from (0.1046\u2009\u00b1\u20090.0004) to (0.1569\u2009\u00b1\u20090.0041) for L1_1st. Notably, the STRE model yields the smallest RE for all noise levels, and achieves the slowest increase of RE with respect to the noise level among various regularization methods.mV to 2.5\u2009mV. Note that the potential distribution on the inner sphere is dynamically varying over time, and t\u2009=\u2009150\u2009ms. y of the outer sphere. Note that the predicted potential mapping by the STRE yields a smaller RE of 0.006 compared to that of Tikh_0th , Tikh_1st  and L1_1st , which achieves the best performance to predict the reference potential mapping shown in \u03c3\u03b5\u2009=\u20090.5 in y of the outer sphere. Notably, the predicted potential mappings by Tikh_0th, Tikh_1st and L1_1st under this noise level show different color patterns from the results under the condition of no noise, and their RE\u2019s are 0.208, 0.1528 and 0.1569, respectively. However, the predicted mapping by the proposed STRE model closely preserves the color patterns of the results with no noise, and yields the smallest RE of 0.0769.Furthermore, As shown in y of the body surface. In the present investigation, our STRE model yields a much smaller RE of 0.0997 compared to that of Tikh_0th , Tikh_1st  and L1_1st . Note that the RE\u2019s of all the methods in this realistic torso-heart geometry are relatively bigger compared to the results in the simulated two-sphere geometry when no extra noise is added to y. This is mainly due to the fact that y are real-world BSPM data with measurement noises and other uncertainty factors in the inverse ECG problem, while that in the simulated two-sphere geometry are clean data calculated analytically by y on the body surface, we added different levels of noises to increase the real-world uncertainties on y. In the present investigation, we also replicated the experiment 20 times for each noise level, and thus each resulted RE is shown with a corresponding error bar . When the noise level increases from \u03c3\u03b5\u2009=\u20090.005 to \u03c3\u03b5\u2009=\u20090.2, the RE monotonically increases for all the methods. Specifically, the RE increases from (0.2386\u2009\u00b1\u20090.0105) to (0.4933\u2009\u00b1\u20090.0175) for the proposed STRE model, from (0.5570\u2009\u00b1\u20090.0025) to (0.8521\u2009\u00b1\u20090.0086) for Tikh_0th, from (0.9720\u2009\u00b1\u20090.0115) to (2.8261\u2009\u00b1\u20090.1835) for Tikh_1st, and from (1.2481\u2009\u00b1\u20090.0082) to (2.8994\u2009\u00b1\u20090.1849) for L1_1st, respectively. It is worth mentioning that the RE\u2019s increase dramatically when adding noises to y on the body surface, compared to the results in the simulated two-sphere geometry. This is mainly due to the fact that the realistic torso-heart geometry is much more complex and irregular. As such, the resulted high-dimensional prediction model tends to be more sensitive to noises. Nevertheless, our STRE model yields the smallest RE for all noise levels, and achieves the slowest increase of RE with respect to the noise level among various regularization methods in this realistic torso-heart geometry.mV to 15\u2009mV. Note that the potential distribution on the heart surface is dynamically varying over time, and t\u2009=\u200950\u2009ms. y of the body surface. Note that the proposed STRE yields the RE of 0.997, which is significantly smaller than that of Tikh_0th , Tikh_1st  and L1_1st , and yields the best performance to predict the reference potential mapping shown in \u03c3\u03b5 = 0.005 in y on the body surface. It is worth mentioning that the predicted potential mappings by Tikh_0th, Tikh_1st and L1_1st under this noise level show significantly different color patterns from Furthermore, As shown in x and y. This poses significant challenges for high-dimensional predictive modeling \u2009=\u2009Rx\u2009+\u2009\u03b5) in complex systems . First, inferring x needs a better knowledge of parameter matrix R that characterizes the physics-based interrelationship between x and y. Second, ill-conditioned systems make the predictions more sensitive to measurement noises and approximation errors in R. Third, very little has been done to develop new spatial regularization methods that handle approximation errors, as well as new temporal regularization methods to increase model robustness to measurement noises. Thus, there is an urgent need to tackle these research challenges and address ill-conditioned problems in high-dimensional predictive modeling.Advanced sensing and imaging technology lead to the proliferation of spatiotemporal data R. Second, we developed a physical-statistical approach that integrates physics-derived parameter matrix R with a spatiotemporal regularization method to build the high-dimensional predictive model. Third, we designed a new method of dipole multiplicative update, inspired by the dipole assumption in electrodynamic physics, to solve the generalized spatiotemporal regularization problems.In this paper, we developed a physics-driven spatiotemporal regularization (STRE) model for predicting dynamic behaviors in space-time systems. First, we developed realistic models of torso-heart geometry, and utilized the boundary element method and physics-based principles  to derive the parameter matrix The proposed STRE model is implemented to predict potential distribution on the heart surface using BSPM data. The model performance is evaluated and validated in both a simulated two-sphere geometry and a realistic torso-heart geometry. Experimental results show that our method not only effectively tackles the ill-conditioned problems in high-dimensional predictive modeling, but also outperforms those regularization models widely used in current practice . The present research work provides a new and effective approach to investigate disease-altered electric potentials on the heart surface in healthcare systems.How to cite this article: Yao, B. and Yang, H. Physics-driven Spatiotemporal Regularization for High-dimensional Predictive Modeling: A Novel Approach to Solve the Inverse ECG Problem. Sci. Rep.6, 39012; doi: 10.1038/srep39012 (2016).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "The distance k-domination number G is the minimum cardinality among all distance k-dominating sets of G. The first Zagreb index of G is defined as G is n-vertex trees with given distance k-domination number and characterize the extremal trees, which generalize the results of Borovi\u0107anin and Furtula (Appl. Math. Comput. 276:208\u2013218, n-vertex tree T, is that a sharp upper bound on the distance k-domination number Let  G. The eccentricity of v is defined as diameter of G is P is called a diameter path of G if the length of P is i from v in G, that is, privatek-neighbor of u with respect to D if pendent vertex is the vertex of degree 1.Throughout this paper, all graphs considered are simple, undirected and connected. Let first Zagreb indexsecond Zagreb indexA chemical molecule can be viewed as a graph. In a molecular graph, the vertices represent the atoms of the molecule and the edges are chemical bonds. A topological index of a molecular graph is a mathematical parameter which is used for studying various properties of this molecule. The distance-based topological indices, such as the Wiener index , 3 and tfound in \u201325. Manymentclass2pt{minimfound in \u201340.dominating set of G if, for any vertex domination numberG is the minimum cardinality of dominating sets of G. For distancek-dominating set of G if, for every vertex distancek-domination numberG is the minimum cardinality among all distance k-dominating sets of G )IfTis ann-vertex tree, different from the starthenforIn what follows, we present two graph transformations that increase the Zagreb indices.T be an n-vertex tree (u of v of w to the u (=v)  andThenu and v. ThenIt is obvious that Letuandvbe two distinct vertices inG. are the pendent vertices adjacent touandare the pendent vertices adjacent tov. Defineandas shown in Figure\u00a0Then eitherorentclass1pt{minimaFor a connected graphGof ordernwithG be a connected graph of order n. If G of order n if Let LetTbe ann-vertex tree with distancek-domination numberThenD be a minimum distance k-dominating set of T,Suppose that k-dominating set of T, which contradicts Clearly, k-dominating set according to the definition of k-dominating set of the tree If k-dominating set of T. Let k-dominating set of T, so the claim is true.We claim that In view ofk-domination number of a connected graph is an attractive problem. In Lemma\u00a0k-domination number of a tree is characterized. Namely, if T is an n-vertex tree with distance k-domination number Determining the bound on the distance n-vertex trees with distance k-domination number k-domination number mentioned in the above paragraph is sharp. Let k-domination number n-vertex tree with domination number were studied in [The Zagreb indices of mentclass2pt{minimTbe a tree onvertices. Thenif and only if at least one of the following conditions holds: Tis any tree onvertices;for some treeRonvertices, whereis the graph obtained by taking one copy ofRandcopies of the pathof lengthand then joining theith vertex ofRto exactly one end vertex in theith copy ofLetTbe ann-vertex tree with distancek-domination numberIfthenandwith equality if and only ifR on n-vertex tree with vertex set When LetGbe a graph which has a maximum value of the Zagreb indices among alln-vertex connected graphs with distancek-domination number andIfthenu and v are two distinct vertices in u and v, where D be a minimum distance k-dominating set of G. If k-dominating set of T. Hence, we assume that Suppose that n and distance k-domination number n-vertex tree T, then denote by In this section, we give upper bounds on the Zagreb indices of a tree with given order LetTbe ann-vertex tree andThenandThe equality holds if and only ifLet IfTis ann-vertex tree with distancek-domination numberthenwith equality if and only ifwhereAlso,with equality if and only ifwhereT. If k-dominating set of T, a contradiction to Assume that n-vertex tree If Since Let treeThenandwith equality if and only ifn. By Lemma\u00a0Assume that D be a minimum distance k-dominating set of T and T. Then k-dominating set, a contradiction. Note that T and Let k-dominating set of the tree Assume that If Since k-dominating set, a contradiction. It follows that D. If k-dominating set, a contradiction. Therefore, If Considering s be the unique vertex adjacent to i.e., Let Note that mentclass2pt{minimLetTbe a tree of ordernwith distancek-domination numberThenandwith equality if and only ifT. Define k-dominating set D of T such that Let T by applying Transformation Let By Lemma\u00a0D is a minimum distance k-dominating set of k-neighbors of x with respect to D in k-dominating set of tree k-dominating set of Suppose that By the definition of the first Zagreb index, we getIf If In what follows, we prove In view of Thus, However, the second condition is impossible. If Note that Hence, if Analogous to the analysis of the first Zagreb index, the second condition above is impossible. Thus,Besides, if k-domination number for k-domination number for T be an n-vertex tree with distance k-domination number Borovi\u0107anin and Furtula  proved\\mentclass2pt{minim"}
+{"text": "T, the boundary term B and a scalar field arXiv:1309.2698, Teleparallel theory of gravity and its modifications have been studied extensively in literature. However, gravitational waves has not been studied enough in the framework of teleparallelism. In the present study, we discuss gravitational waves in general theories of teleparallel gravity containing the torsion scalar  Therefore, GR and Teleparallel Equivalent General Relativity (TEGR) result in the same equations of motion.The observed late expansion of the universe can be described by either introducing an exotic form of energy (dark energy) or modifying gravity. In this framework, several modifications have been proposed \u20134 and, aT or R are taken into account [T and R, i.e. f\u00a0[f, where B is the boundary term\u00a0[However, difference between them arise in modified Lagrangians, where scalar fields coupled nonminimally to gravity or arbitrary functions of  account . Such mo account . In a mo f\u00a0, 9. Thisary term\u00a0, 11.In both GR and TEGR, gravitational waves (GW) have two independent polarizations, usually denoted as plus and cross modes. However, extra polarizations appear in modified theories. The perturbation theory in the post-Minkowski limit is a way to study the number of GW polarizations.z-direction as the propagation direction of GWs, they are plus b), longitudinal (l), vector-x (x) and vector-y (y) modes. These modes can be described by the independent NP quantities f(T), and in its scalar-tensor representation, are equivalent to that in GR and TEGR\u00a0[f(R) gravity, where the Lagrangian is an arbitrary function of Ricci scalar, three modes exist \u00a0[f, and have shown that the number of GW-modes depends on the form of it\u00a0[The other way is the Newman-Penrose (NP) formalism\u00a0, 13. Ado.g. Ref.\u00a0, 15). As.g. Ref.\u00a0, GWs in and TEGR\u00a0. In f(R)s exist \u00a0\u201320. Mode in Ref.\u00a0, where \\f(R), or of TEGR, like f(T). The main task is explaining dynamics by further degrees of freedom of gravitational field (with respect to GR or TEGR) instead of invoking dark components [f(R),because, in such a case, it is possible to reproduce the so-called Sanders potential with better precision. In this case, by a conformal transformation, it is shown that a model like T, but also boundary terms B and a scalar field An important remark is necessary at this point. Modified theories of gravity are taken into account to achieve a comprehensive picture of cosmic dynamics ranging from early inflation, up to large scale structure formation and current acceleration of the universe \u20134. The amponents . Howevermponents , the flaentclass1pt{minimassion in , could bThe present paper is organized as follows. The field equations of our modified teleparallel theory are derived in Sect.\u00a0B coupled to the scalar field [B is second order in perturbations; therefore, up to first order we have In teleparallel theories, vierbein fields describe gravity. Considering a set of orthonormal basis in each point of a generic manifold, the metric is given byar field . Let us F and E are two arbitrary functions of scalar field. For i.e.z as the direction of wave traveling. Taking l and b modes can be of the same order. Considering the weak field limit, we can adopt the NP formalism. To obtain the independent NP quantities, one can use the solution\u00a0 being an analytic function of T and B, one can expand it as followsIf from Eq.\u00a0, we get F(R) gravity can be easily recovered.In order to respect the local Lorentz symmetry invariance, we have to consider he paper\u00a0, 62\\docuthe mass  reduces Furthermore, the action . These sor . Equatie.g. torsion tensor becomes Under local Lorentz transformation m appear\u00a0, i.e.95\\n fields\u00a0, up to fone gets\u00a097\\documeFinally, let us consider the action containing the following termB and a further scalar field T. The conclusions we reached are the following. There is no extra polarization in TEGR and in f(T) theory with respect to GR as already shown in [B, beside the standard two modes of GR. One can also write the Lagrangian as a function of scalar torsion T and Ricci scalar R, however in order to study GW polarizations, it is better to decouple the Ricci scalar f. In f, extra massless and massive modes arise when the scalar torsion and the boundary term are non-minimally coupled as in the theory of The number of GW polarizations depends on the considered theory of gravity. In present work we have studied GWs in extended teleparallel gravity where a boundary term shown in . Here wehes (see  for a dif(T) gravity, showing the same gravitational modes as GR [In this perspective, the GW170817 event  has set es as GR , should es as GR , 15). In"}
+{"text": "Here, we provide a first-principle derivation of this HLL based on the gauge-theory approach. We start by considering massless Dirac fermions confined on the one-dimensional boundary of the topological insulator and interacting through a three-dimensional quantum dynamical electromagnetic field. Within these assumptions, through a dimensional-reduction procedure, we derive the effective 1\u2009+\u20091-dimensional interacting fermionic theory and reveal its underlying gauge theory. In the low-energy regime, the gauge theory that describes the edge states is given by a conformal quantum electrodynamics (CQED), which can be mapped exactly into a HLL with a Luttinger parameter and a renormalized Fermi velocity that depend on the value of the fine-structure constant  Further spatial  symmetries have been proposed in order to extend the periodic table of topological free-fermion systems4, and more recently inversion symmetry has also gathered attention6. However, time-reversal-invariant topological insulators are certainly the most studied so far8. These time-reversal-invariant topological insulators were theoretically proposed to occur in two-dimensional models involving a strong spin-orbit interaction10, and were then experimentally observed in HgTe quantum wells11. The spin-orbit interaction locks the spin and the chirality together and produces counter-propagating edge currents, giving rise to the quantum spin Hall effect. These topologically protected edge modes are right-handed and left-handed Dirac modes that always come in pairs, in agreement with the time-reversal symmetry of the bulk. Their dynamics is consistently described by a 1\u2009+\u20091-dimensional massless Dirac theory.Topological insulators represent a large family of materials characterized by gapped bulks and metallic edge states. The topological quantum numbers associated to the bulk depend on the discrete symmetries of the microscopic Hamiltonians, such as time-reversal, particle-hole and chiral symmetries13. In this picture, the strength of the interactions is encoded in the Luttinger parameter K, which depends on the value of the coupling constant g of the four-fermion term. Although many studies have pointed out for which values of K the interactions are relevant, it is still unclear how the constant g is related to the microscopic properties of the Dirac edge modes, such as their spin, electric charge, etc. The relevant open question is whether there is any fundamental way to derive the HLL from the universal properties of topological insulators.Moreover, it has been shown that local four-fermion interactions on the edge can transform the free-fermion phase into a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL)U(1) gauge field are free to propagate in all the three spatial dimensions that represent the physical space where the topological insulator is embedded, see Fig.\u00a015 plus the 1\u2009+\u20091-dimensional massless QED, also known as the Schwinger model17.The main goal of this paper is to provide an answer to this question. Firstly, we consider massless Dirac fermions constrained in one spatial dimension (the boundary), while the quantum excitations  of the U gauge fi19 and related 2D massive Dirac systems, such as silicene and transition metal dicalcogenides20, but to the best of our knowledge, it has not yet been employed in the description of one-dimensional systems, such as the edge currents of topological insulators. Notice that in ref.21, a projection of QED in 3\u2009+\u20091-dimensions to a 1\u2009+\u20091-brane was performed. However, a finite-size regulator was introduced to avoid ultraviolet divergences that appear when confining the system to one dimension. Therefore, the effective theory obtained is not scale invariant and cannot be conformal. In our approach, we found an explicit way to deal with the divergences, such that we obtain the CQED without any regulator. Furthermore, by integrating out the CQED gauge field in the corresponding partition function, we find that this gauge theory gives rise to a 1\u2009+\u20091-dimensional Thirring model22. We then demonstrate that the bosonized version of the interacting-fermion Hamiltonian describes exactly a HLL with a Luttinger parameter K and a renormalized Fermi velocity that depend on the value of the fine-structure constant \u03b1.In this work, we focus on the CQED because describes a massless mode along the whole edge and is dominant in the low-energy regime. It also preserves the dimensionality of both, the electric charge and the gauge field of the 3\u2009+\u20091-dimensional QED from which the CQED will be derived by using a dimensional reduction procedure. This method has been already used in studies of graphene2. They have a gapped bulk and topologically protected Dirac edge modes. These systems realize the quantum spin Hall effect, i.e. the chirality of the Dirac edge modes is locked to the spin, which is preserved due to the time-reversal symmetry. Thus, the dynamics of the edge modes can be described by a 1\u2009+\u20091-dimensional massless Dirac theory with a two-component Dirac spinor \u03c8\u2009=\u2009T, where \u03c8R and \u03c8L are the right-handed spin-up and left-handed spin-down chiral modes, respectively. It was theoretically proposed in refs13 and experimentally confirmed in ref.23 that these topological insulators can support HLLs on the boundary due to the presence of unavoidable electron-electron interactions. These non-Fermi liquid phases fully preserve the time-reversal symmetry and are formally described by the free Dirac theory plus suitable four-fermion interactions. We now show that this model and the corresponding HLL can be derived from a gauge theory by simply assuming that the electrically charged propagating Dirac fermions on the edge interact through a quantum dynamical electromagnetic field A\u03c1. The essential point of our approach is that the massless Dirac fermions are confined on the one-dimensional boundary, whereas the quantum excitations (i.e. photons) of the electromagnetic field are free to propagate in all the three spatial dimensions, as shown in Fig.\u00a0d2r\u2009=\u2009vdxdt and d4r\u2009=\u2009cdxdydzdt, with v and c the Fermi velocity and the speed of light, respectively. \u0127 is the Planck constant divided by 2\u03c0, e is the electric charge carried by each fermion, \u03b50 is the vacuum dielectric constant, \u03b3\u03bc are 2\u2009\u00d7\u20092 Dirac matrices with \u03bc\u2009=\u20090, 1 and {\u03b3\u03bd, \u03b3\u03bc}\u2009=\u20092g\u03bc\u03bd, where g\u03bc\u03bd\u2009=\u2009diag, F\u03c1\u03b2\u2009=\u2009\u2202\u03c1A\u03b2\u2009\u2212\u2009\u2202\u03b2A\u03c1 is the field-strength tensor, \u03c1, \u03b2\u2009=\u20090, 1, 2, 3. The effective interaction felt by the massless Dirac fermions due to the gauge field can be obtained by integrating out the A\u03c1-field in the partition function Seff\u2009=\u2009SD\u2009+\u2009Sint is the effective action, with SD the free Dirac action, given by the first term in Eq. \u03b4(x\u2009\u2212\u2009x\u2032) and \u03b4(t\u2009\u2212\u2009t\u2032) are two Dirac delta functions and 24, a finite-size regulator for the Dirac delta function in Eq. , and obtain22, whereas the Lagrangian for the 25. The pseudo-differential operator in the kinetic term of the e remains dimensionless, while The replacement of the terms in Eq.  in the e27. However, in the low-energy limit, i.e. It is known that the Schwinger-Thirring model leads to a massless and a massive bosonic mode29, i.e., a (2\u2009+\u20091)D QED with higher-order derivatives in the Maxwell term  even for the interacting phase by deriving the corresponding HLL in the following section. This CQED shares some properties with PQED. In fact, in both theories the electric charge e is a dimensionless parameter, as in usual (3\u2009+\u20091)D QED. The fact that the coupling constant remains dimensionless makes perturbative studies more reliable. Moreover, just like in the Luttinger-liquid case, in PQED and in CQED the excitations are collective modes and there are no quasi-particles because the Green\u2019s function has branch cuts instead of poles24.We want to emphasize that the dimensional reduction procedure performed here has been already employed in the study of two-dimensional materials, such as graphene. In this case, the corresponding effective field theory is the so-called Pseudo QED (PQED)., a 2\u2009+\u2009D QED wit22, with the coupling constant g\u2009=\u2009e2/4\u03c0\u03b50c. The corresponding Hamiltonian is then calculated by employing a Legendre transformation,\u03c8\u2009=\u2009T, with the fermion operators satisfying usual anti-commutation relations. The bosonization of Eq. , passing through non-interacting (K\u2009=\u20091), to attractive (K\u2009>\u20091)31. Nonetheless, how this parameter relates to fundamental properties of the materials was still unclear. In refs33, a formula that connects K with \u03b1 is derived by employing perturbation theory with either the Kondo or the backscattering interaction. Here, we have presented a gauge-principle derivation of the Luttinger parameter, which is found to depend on the strength of the electron-electron interaction \u03b1.The parameter 33, d is the distance from the quantum wells to a closeby metallic gate, and K on \u03b1 was obtained at the level of perturbation theory on the HLL Hamiltonian, i.e. additional interaction terms had to be taken into account, such as the Kondo or the backscattering interaction. Although our approach is non-perturbative, there are implicit approximations based on the theoretical description of the edge states in terms of QED. The presence of metallic gates in realistic experiments, for instance, could have crucial influence on the field lines of the virtual photons and would modify the effective action in a non-trivial way. Using the values of the parameters reported experimentally for HgTe quantum wells, v\u2009\u2248\u20095.5\u2009\u00d7\u2009105\u2009m/s34, \u03b5r\u2009=\u20091535, d\u2009=\u2009150\u2009nm and 23, the authors in ref.33 find K\u2009\u2248\u20090.8. Within our model, which depends only on \u03b1, we obtain K\u2009\u2248\u20090.84.Now, we compare our results with a prior theoretical prediction proposed in refsK, as seen in the case of InAs/GaSb quantum wells23. This implies that our theoretical prediction applies to materials that have weak backscattering and high Fermi velocities, such as HgTe36. Nevertheless, the backscattering term can be obtained within our approach upon considering the massive Thirring model. The corresponding bosonization is discussed in the supplemental material with the Klein factors defined as in ref.37. Other possible 2D topological insulators that would be good candidates to test our theoretical proposal are plumbene monolayers38 and germanene films39. The Fermi velocity in these materials has the same order of magnitude as that in HgTe, indicating that backscattering might not be so relevant.Notice that our approach does not involve the backscattering term, which induces further corrections to the parameter K in order to obtain different regimes of interaction. From Eq. , it would be possible to reach the value of K\u2009=\u20091. For smaller velocities v, the minimum value of the dielectric constant for which K becomes real increases, i.e., for v\u2009=\u20095\u2009\u00d7\u2009105\u2009m/s, e.g., v\u2009=\u2009106\u2009m/s. On the other hand, if we consider negative values of the dielectric constant by placing the topological insulator on top of a meta-material, then it is possible to switch from repulsive to attractive interactions, i.e., x\u2009=\u20092\u03b1/\u03c0. We illustrate this situation in Fig.\u00a040.Furthermore, we show how to tune From Eq. , we noti42, as done for topological insulators.In this paper, we derived a gauge theory on the boundary of two-dimensional time-reversal-invariant topological insulators. Our starting point was to assume that the interactions between the charged one-dimensional Dirac fermions at the edge are mediated by a quantum dynamical electromagnetic field, where the virtual photons are free to propagate in all the three spatial dimensions. By implementing a dimensional-reduction procedure, we derived the corresponding CQED, which describes the HLL. We emphasize that our approach is non-perturbative, and has a more vast applicability in condensed-matter physics. Indeed, the one-dimensional effective theory derived here also works in the case of nanowires deposited on a substrate, in which the HLL phase can be easily obtainedK by modifying the dielectric constant of the substrate on which the one-dimensional system might be deposited. Interestingly, we find that upon the use of a meta-material as a substrate, it is possible to change the interactions from repulsive into attractive. These results might have profound implications for transport properties in nanostructures in particular, and nanotechnology in general.In our work, we provide, to the best of our knowledge, a field-theory derivation of the Thirring model, which opens the path to the manipulation of the Luttinger parameter Supplemental Material"}
+{"text": "Single-cell analysis of the three-dimensional (3D) chromosome structure can reveal cell-to-cell variability in genome activities. Here, we propose to apply recurrence plots, a mathematical method of nonlinear time series analysis, to reconstruct the 3D chromosome structure of a single cell based on information of chromosomal contacts from genome-wide chromosome conformation capture (Hi-C) data. This recurrence plot-based reconstruction (RPR) method enables rapid reconstruction of a unique structure in single cells, even from incomplete Hi-C information. Through the development of measurement techniques, we are getting the glimpse that chromosomal structures in individual cells may be differentially organized to exhibit distinct genome and chromatin activities. Such cell-to-cell variability might be an important aspect of cell physiology during differentiation or cellular responses. Genome-wide chromosome conformation capture (Hi-C) analysis124ad hoc computational methods have been proposed6In a mathematical sense, reconstruction of the 3D chromosome structure from Hi-C data can be considered a problem of geometry. Therefore, many Here, to overcome such difficulties, we propose a new mathematical method using recurrence plots8A recurrence plot8xi is a state corresponding to time i, and \u03b5 is a predefined threshold. We plot a point at  when R\u2009=\u20091 and nothing there if R\u2009=\u20090 \u2009=\u20091} is a set of indices plotted in the ith column of the recurrence plot and thus the corresponding Hi-C data (see i and j when they are close to each other). Second, we obtain the shortest distance by the Dijkstra method\u03b5 for the recurrence plot is defined intrinsically by the experimental limits of detectable contacts by the sparse Hi-C method as well as the regular Hi-C method. When the coverage depth is too high, the regular Hi-C data may be pre-processed to reduce the number of counts. But, presumably this pre-processing will not be necessary because the proposed RPR method can be used even in the case where as high as 70% of elements for the binary contact map are 1 \u2009=\u2009R\u2009=\u20091 when the parts corresponding to i and (i\u2009+\u20091) are on the same chromosome. Using this technique, we can ensure that the proposed reconstruction is possible in most cases. If, instead, we modify d as a constant value when regions i and j have a contact or |i\u2212j|\u2009\u2264\u20091, the RPR method becomes more similar to the method of Paulsen et al.A necessary condition for our previous methodThus, as similar to reconstructing the three dimensional structure of strange attractors for deterministic chaos as shown in Single-cell Hi-C cannot report all the chromosomal interactions within a cell. In addition, sequencing data sometimes include errors. We therefore tested by toy models whether the RPR method is tolerant to the contamination of false positive noise and/or to the lack of information, as is often found in actual Hi-C data. Here we used the Lorenz modelH1 cells from Hi-C data for different single cells and from an ensemble (regular) Hi-C data .The Th1 ensemble Hi-C data and single-cell Hi-C data were acquired from the GEO database  the proposed method coverts a contact map to a distance matrix in a deterministic way, and (ii) the classical multidimensional scaling implemented in Matlab gives a unique configuration for a spatial arrangement of points given their distance matrix.et al.et al.et al.13In addition, the RPR method has other advantages in comparison with the conventional methods27172021222324252627How to cite this article: Hirata, Y. et al. Three-dimensional reconstruction of single-cell chromosome structure using recurrence plots. Sci. Rep.6, 34982; doi: 10.1038/srep34982 (2016)."}
+{"text": "Scientific Reports 10.1038/s41598-018-22914-5, published online 16 March 2018Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cavailability\u201d was incorrectly given as \u201cavailable\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying supplementary material."}
+{"text": "Genome median and genome halving are combinatorial optimization problems that aim at reconstruction of ancestral genomes by minimizing the number of evolutionary events between them and genomes of the extant species. While these problems have been widely studied in past decades, their solutions are often either not efficient or not biologically adequate. These shortcomings have been recently addressed by restricting the problems solution space.We show that the restricted variants of genome median and halving problems are, in fact, closely related. We demonstrate that these problems have a neat topological interpretation in terms of embedded graphs and polygon gluings. We illustrate how such interpretation can lead to solutions to these problems in particular cases.This study provides an unexpected link between comparative genomics and topology, and demonstrates advantages of solving genome median and halving problems within the topological framework. The basic case of three given genomes represents the genome median problem (GMP), which asks for reconstruction of a single ancestral genome, called median genome.One of the key computational problems in comparative genomics is the reconstruction of ancestral genomes based on gene species . Since mwhole genome duplication (WGD) events that simultaneously duplicate each chromosome of a genome. WGD events are known to happen in evolution of yeasts [doubled genomes, i.e., genomes immediately resulted from a WGD in the course of evolution. This problem is often posed for input genomes that have all genes present either in a single copy (ordinary genomes) or in two copies . In the simplest form, it is known as the genome halving problem (GHP), which asks for an ordinary genome for a given all-duplicated genome such that the distance between them is minimized. In the case of a given all-duplicated genome and an ordinary genome, the problem, called the guided genome halving problem (GGHP), asks for an ordinary genome at the minimal total distance from both given genomes.Since genome rearrangements preserve the gene content, it must be restricted to genes present in all input genomes with the same multiplicity. To account for genes appearing different number of times in different genomes, one need to consider other types of evolutionary events. One of important sources of duplicated genes in genomes are the f yeasts , fishes f yeasts , plants f yeasts , and evef yeasts , which iWhile the GHP admits a polynomial solution \u201311, its intermediate genome median problem (IGMP), restricts its solutions to the intermediate genomes, i.e., genomes appearing in a shortest rearrangement scenario between two of the three given genomes [restricted guided genome halving problem, RGGHP) that restricts the constructed doubled genomes to the GHP solution space [A recently introduced variant of the GMP, called the  genomes . Similaron space . It is won space , 15 to tIn this study, we show that the IGMP and RGGHP are, in fact, closely related, and put them into the framework of embedded graphs and polygon gluings . This frn genes as a graph cycle with n directed edges (encoding genes and their strands) alternating with n undirected edges (connecting the extremities of adjacent genes), called P-edges   operation breaks a genome at two positions and glue the resulting fragments in a new order, which model common types of genome rearrangements [P corresponds in P-edges with a different pair of P-edges2 on the same set of four vertices.A ngements , 24. A DP and Q composed of the same set of genes, the breakpoint graphP-edges and Q-edges, forming P-matching and Q-matching. Then P-edges and Q-edges, called PQ-cycles (or QP-cycles). Similarly, the breakpoint graph can be defined for three or more genomes [For genomes entclass1pt{minima genomes .Fig. 2ADCJ scenario between genomes P and Q is a sequence of DCJs transforming P into Q. A shortest such scenario has the following property:A P and Q, each DCJ splits some PQ-cycle in their breakpoint graph into two and thus increases the number of PQ-cycles by one.In a shortest DCJ scenario between genomes DCJ distance  between two genomes:From Lemma P and Q on n genes is given by the formula c is the number of PQ-cycles in the breakpoint graph The DCJ distance between genomes A be an all-duplicated genome and contracted genome graphA-edges form cycles (since each vertex is incident to two A-edges), called A-cycles. For a doubled genome 2R resulted from a WGD3 of an ordinary genome R, the contracted genome graph R-edges, called 2R-edges. It is clear that 2R-edges form a matching in R-edges with R-edges in The definition of breakpoint graph based on edge gluing can be easily extended to genomes with duplicated genes as follows. Let mentclass2pt{minimA and an ordinary genome R composed of the same genes, the contracted breakpoint graphA-edges and R-edges in A-cycles and R-matching, respectively.For an all-duplicated genome mentclass2pt{minimAR-cycles, called an AR-cycle decomposition. We remark that there exists an exponential number of AR-cycle decompositions of AR-cycle decompositions. One is maximalAR-cycle decompositions, which have the maximum possible number of AR-cycles, denoted AR-cycle decompositions is constructed as follows. For each A-cycle in A-edge becomes a directed edge. We decompose AR-cycles such that each R-edge in an AR-cycle connects the head of one A-edge and the tail of another. We call such AR-cycle decomposition an ht-decomposition of The graph mentclass2pt{minimLet us recall the formulation of the GHP and discuss the structure of its solutions.A, find an ordinary genome R minimizing dDCJ.For a given all-duplicated genome R maximizing In other words, the GHP asks for an ordinary genome AR, n is half the number of A-edges in A), and k is the number of even A-cycles in For any all-duplicated genome R such that R-noncrossing as defined below.It was shown in  that theR-edge connecting vertices of distinct A-cycles is called R-interedge. An R-edge connecting vertices of same A-cycles is called R-intraedge. We represent vertices and edges of each A-cycle in R-intraedges as straight chords inside these circles.For the graph A and an ordinary genome R, the contracted breakpoint graph R-noncrossing  and noncrossing R-intraedges (as chords within the corresponding circle); ora single even A-cycles  with single R-interedge and noncrossing R-intraedges.a pair of odd For a given all-doubled genome mentclass2pt{minimR-noncrossing guarantees that the genome R yields a solution to the GHP for an all-doubled genome A, this condition is not necessary, and there exist other genomes R solving the GHP .Given an all-duplicated genome intermediate genome from [We recall the definition of an ome from  Fig. 2)intermediI is intermediate between genomes P and Q iff dDCJ+dDCJ=dDCJ.An intermediate genome between two genomes is any genome appearing in a shortest DCJ scenario between them. In other words, a genome R-noncrossing contracted breakpoint graphs, for ordinary genomes P, Q, I, the breakpoint graph I-noncrossing if every its connected component is formed by a single PQ-cycle and noncrossing I-intraedges (as chords inside each PQ-cycle) .the total number of For ordinary genomes Similarly to the GHP, one can restrict the solution space of the GMP to intermediate genomes and pose the following problem:P, Q, and an outgroup genome R, find an intermediate genome I between genomes P and Q that minimizes dDCJ.Given genomes I plays in the IGMP a similar role to those of the ordinary genome R in the GHP. Indeed, let PQ be an artificial all-duplicated genome formed by the union of genomes P and Q. Then the breakpoint graph PQ-cycles. If I-noncrossing, then I-noncrossing, and k=c is the number of cycles in I such that I-noncrossing. Thus, the IGMP can be viewed as a particular case of the RGGHP, where all cycles are even. We remark that Lemma 5 for the IGMP can be refined as follows: the ht-decomposition with respect to any orientation of PQ-cycles in PQ-cycles are even), and each cycle in this decomposition is either a PI-cycle or a QI-cycle.From Theorem 7, one can observe that the intermediate genome Below we will show that both RGGHP and IGMP can be formulated within the framework of embedded graphs and polygon gluings.We recall the following definition from the topological graph theory:G\u03a3 is a graph whose vertices and edges are points and arcs on a surface4\u03a3 such that the edges do not intersect (except at the vertices);G\u03a3 in \u03a3 represents a collection of regions , and each face is a polygon.5the complement of A (2-cell) embedded connected graph m connected components is defined as the union m connected embedded graphs An embedded graph with G\u03a3 in \u03a3 can be viewed as the result of cutting \u03a3 along the edges of G\u03a3. Conversely, G\u03a3 can be obtained by gluing the sides of its faces, which are polygons. Let us denote this collection of polygons by G\u03a3 has two sides on \u03a3, the total number of sides in G\u03a3, and the edges of G\u03a3 define a (perfect) matching on the sides in \u03a3 is orientable, we can orient sides of each face clockwise. Then the matched sides of G\u03a3 head-to-tail.We remark that the complement of the connected embedded graph orientable gluing as the head-to-tail gluing of sides in each matched pair  matching on their sides Fig. a, we deair Fig. b. It ispartial. It results in an embedded graph G\u03a3 on a surface \u03a3with boundary. Connected components of the boundary are called holes. In this case, some edges of G\u03a3 represent glued pairs of sides, while the others represent non-glued sides and form holes.A polygon gluing according to a non-perfect matching is called G\u03a3 with v vertices, e edges, and f faces, the Euler formula states that For a connected embedded graph h(\u03a3) is the number of holes in \u03a3 and g(\u03a3) is the topological genus (number of handles) of \u03a3. Unless G\u03a3 is the result of a partial gluing, we have h(\u03a3)=0.where We start with establishing a correspondence between contracted breakpoint graphs and embedded graphs.A, the A-edges in A-cycles. Let us fix some orientation o of these A-cycles. For each A-cycle with k edges, we assign a k-gon whose sides correspond to the cycle vertices (such that adjacent sides correspond to adjacent vertices). Then the sides of each polygon inherit labels from the corresponding cycle vertices, and the polygon itself inherits the orientation from the cycle. We denote the collection of these labeled oriented polygons by Recall that for an all-duplicated genome R, the R-edges in R-matching on the vertices of A-cycles and thus on the sides of G=Go  Fig. a, b. It,R) Fig. d.Fig. A be an all-duplicated genome, R be an ordinary genome, and o be some orientation of the A-cycles. Then the vertices of Go are in one-to-one correspondence with the AR-cycles in the ht-decomposition of o.Let A-edges in G is an image of some vertices of A-edges belong to the same AR-cycle in the ht-decomposition of A-edge  in W1,V1), {V1,U1}, , {U2,V2},  in AR-cycle in the ht-decomposition of W1,V1), ,  are A-edges and {V1,U1}, {U2,V2} are (undirected) R-edges in Go the side V1 is glued with U1 and the side V2 is glued with U2 (in head-to-tail fashion), and so the vertex corresponding to , which is the head of the side U1 and the tail of the side U2, is glued with the vertices corresponding to  (the tail of V1), and  (the head of V2). Conversely, since every gluing of matched sides implies gluing of vertices that correspond to A-edges from the same AR-cycle, vertices that correspond to A-edges from distinct AR-cycles can not be glued. By transitivity we obtain the statement of the lemma. \u25a1Recall that the vertices of 2R) Fig. c, d. Cok polygons with an even number of sides (even-gons) and 2l polygons with an odd number of sides (odd-gons). Then the graph obtained by gluing the sides of n+k vertices, and this upper bound is achieved by the embedded graphs on k+l spheres.Let G, we get that the total number of vertices in G is n is half the number of sides in m is a number of connected components in G. We remark that in order to maximize v we need to maximize m and minimize m is k+l, and it is achieved iff each connected component of G is a result of gluing of either one even-gon or two odd-gons. The minimum value of g(\u03a3i) is achieved iff \u03a3i is a sphere (so that g(\u03a3i)=0).Let mentclass2pt{minimG has a maximal number of vertices  iff it has k+l connected components (each on a sphere). \u25a1So, We remark that Lemmas 9 and 10 provide a topological interpretation of the GHP and essentially give a new proof of Theorem 3, which is much simpler than previous ones , 26.A be an all-duplicated genome, R be an ordinary genome, and o be some orientation of the A-cycles. Then a DCJ on the genome R corresponds in the embedded graph Go to cutting two edges and gluing the resulting four sides in a new order .Let R\u2032 be the result of a DCJ on R. Then the R-matching and R\u2032-matching on the sides of Go cuts the two pairs of sides matched in R and glues the resulted four sides according to R\u2032. \u25a1Let Lemmas 9, 10, and 11 inspire us to pose the following problem:G, find a shortest sequence of DCJ-surgeries that results in an embedded graph G\u2032 on a maximum number of spheres.Given an embedded graph A and an ordinary genome B is equivalent to the GSP for Go, where o is some orientation of A-cycles.The RGGHP for an all-duplicated genome P, Q, and an outgroup genome T is equivalent to the GSP for Go, where o is any orientation of PQ-cycles.The IGMP for ordinary genomes R be a solution to the RGGHP for an all-duplicated genome A and an ordinary genome B. Let B and R. By Lemma 5, there exists an orientation o of A-cycles such that the ht-decomposition of Go is an embedded graph on a maximum number of spheres. By Lemma 11, the DCJ scenario Go into Go. Thus, the RGGHP for the genomes A and B is equivalent to the GSP for the embedded graph Go.(1) Let PQ-cycles in PR- and QR-cycles for any orientation o of PQ-cycles. Thus, the IGMP for genomes P, Q, T is equivalent to the GSP for Go with any orientation o of PQ-cycles. \u25a1(2) Since all A. For each solution R, there exists some orientation o such that Go is an embedded graph on the maximum number of spheres. This inspires us to define a maximal gluing as a polygon gluing that results in an embedded graph on the maximum number of spheres. By Lemma 10, each connected component of this graph has either one even-gon face or two odd-gon faces.Let us enumerate all the solutions to the GHP for a given all-duplicated genome We remark that there exists a method  that fork-gon equals the k-th Catalan number The number of ways to obtain a sphere by gluing the sides of a 2n+1)-gon and a (2m+1)-gon equals The number of ways to obtain a single sphere by gluing the sides of a -gon and a (2m+1)-gon. By Euler formula -gon and the (2m+1)-gon, respectively. So, any maximal gluing can be obtained in the following way: for some l, n\u2212l pairs of the (2n+1)-gon sides are glued and m\u2212l pairs of the (2m+1)-gon sides are glued (transforming each of these polygons into a sphere with one hole), and the remaining 2l+1 sides from one polygon are glued with the remaining 2l+1 sides from the other (resulting in a sphere).Let  of a 2n+-gon and n+1)-gon and a (2m+1)-gon. This is equivalent to enumeration of the pairs  and the ways to glue them into a sphere. Let 2l+1 be the length of the holes in G1 and G2. It is known [k+1)-gon by gluing k\u2212l pairs of its sides. Hence, for each l, there exist G1,G2). If l=0, then there is exactly one way to glue G1 and G2 together. If l>0, then there are 2(2l+1) ways to glue them into a single sphere (the factors 2l+1 and 2 account respectively for rotations and reflections of the holes in G1 and G2 with respect to each other). Combining these results together, we get that the number of maximal gluings of a (2n+1)-gon and a (2m+1)-gon equals Let us enumerate all the maximal gluings of a :P and Q, the number of intermediate genomes equals n1,\u2026,2nk are the lengths of the PQ-cycles in For given ordinary genomes A and ordinary genome B is equivalent to the GSP for G=Go, where o is some orientation of A-cycles. In this section, we show how one can solve the GSP in the case of G being an embedded graph with a single face on a torus .Consider a simple cycle of length 2y 2 Fig. a, b. Afl=1, we apply a DCJ-surgery that cuts the edges of this cycle, resulting in a sphere with two holes of length 2, and then glues each of these holes, resulting in a sphere. So, we have transformed G into an embedded graph on a sphere with l DCJ-surgeries. \u25a1If G be an embedded graph on a torus with one face. If G contains two simple odd cycles that have the total length 2l and share exactly one vertex, then G can be transformed into an embedded graph on a sphere with l DCJ-surgeries.Let l\u22121 DCJ-surgeries on G and obtain two loops (cycles of length 1) that share the vertex. We then apply a DCJ-surgery that cuts these loops, resulting in a sphere with a hole of length 4, and then glues this hole, resulting in a sphere. So, we have transformed G into an embedded graph on a sphere with l DCJ-surgeries. \u25a1Similarly to Lemma 17, we can apply G be an embedded graph on a surface with holes. g be the genus of the surface of G and G\u2032 be obtained from G by gluing a pair of sides from different holes. Then the surface of G\u2032 has genus g\u2032=g+1.Let G has one face and can be glued into an embedded graph on a sphere, then G is an embedded graph on a sphere with holes of even length. Furthermore, all simple cycles in G are holes.If Let G have v vertices, e edges, f faces and h holes. Let C1 and C2 be the holes that contain the pair of sides we are gluing. If at least one of the holes C1, C2 has length greater than 1, then G\u2032 has v\u2032=v\u22122 vertices, e\u2032=e\u22121 edges, f\u2032=f faces, and h\u2032=h\u22121 holes. If both C1 and C2 have length 1, then G\u2032 has v\u2032=v\u22121 vertices, e\u2032=e\u22121 edges, f\u2032=f faces, and h\u2032=h\u22122 holes. By the Euler formula (g\u2032=g+1 in both cases.1) Let  Let G haG has one face, it results from a partial gluing of a polygon. Obviously, any partial gluing resulting in a sphere with holes of even length can be extended to a gluing resulting in a sphere. Let us prove that any other gluing can not be extended in such a way. Let g the genus of the surface of G. Consider a gluing of G into an embedded graph on a sphere. If g>0, such gluing does not exist, since the genus cannot be decreased by such gluing. Hence, g=0 and thus G is on a sphere with holes. If there are holes of odd lengths, then some side from one of these holes has to be glued with a side from some other hole, which would increase the genus. So, all holes must be of even length.(2) Since G are holes. Let L be the total length of the holes, and v and e be the number of vertices and edges of G, respectively. Consider the embedded graph G\u2032 resulting from contraction of the edges belonging to holes in G. Then G\u2032 is an embedded graph on a sphere, which has v+h\u2212L vertices, e\u2212L edges, and one face. From the Euler formula  matching G\u2032 can be glued into each of G and G\u2032 is an embedded graph on a sphere with holes of even length. Let 2m be the total length of these holes. Note that every non-glued edge in G\u2032 represents a side of an edge in G that should be cut by some DCJ-surgery from Denote the face of b be a bridge  in G such that its sides s1, s2 are not glued in G\u2032. We will show that gluing of these sides into b in G\u2032 transforms this graph into another embedded graph b is a bridge, s1 and s2 cannot belong to distinct holes in G\u2032. Let C be a hole in G\u2032 that contains both sides s1 and s2. In C is transformed into two holes C1 and C2 (possibly empty) connected by the edge b. It is clear that the lengths of C1 and C2 have the same parity. It remains to show that both lengths are even. Assume that they are odd. Since b is a bridge, no side of C1 is glued with a side of C2 in G. Hence, at least one side from C1 is glued with a side from a hole different from C1 and C2. Similarly, at least one side from C2 is glued with a side from a hole different from C1 and C2. By Lemma 19, gluing of two sides from different holes creates a handle, implying that G should contain at least two handles, a contradiction to G being an embedded graph on a torus . Thus, both holes C1 and C2 in G\u2032. This proves that Let H\u2032 be an embedded graph obtained from G\u2032 by gluing all non-glued sides of bridges in G. Then H\u2032 is on a sphere with holes of even lengths. Note that any edge in G, whose sides are non-glued in H\u2032, is not a bridge and thus belongs to some simple cycle in G.Let H\u2032 into G. A handle in G can be created by gluing either two sides from distinct holes, say C1 and C2, or from one hole, say C, in H\u2032. In the former case, sides from C1 and C2 cannot be glued with sides from any other holes . The sides from Ci  cannot be glued with any other side from Ci, since this would result in a bridge missing in H\u2032. Thus, the sides from C1 and C2 are glued into edges that form a simple cycle in G of length 2l . Since |C1|+|C2|\u22642m, we have 4l\u22642m. In the latter case, we claim that the edges resulted from gluing of the sides of C form two simple cycles in G, which share a vertex. Indeed, let 2p be the length of C, and H\u2032 have V+2p vertices, E+2p edges, and h holes. After gluing the sides of C (as in G), we obtain a graph on a torus with V+v vertices, E+p edges, and h\u22121 holes, where v vertices and p edges are obtained from vertices and edges in C and form a (possibly non-simple) cycle G. By the Euler formula . 6 orientation o on its A-cycle.Construct o, construct the embedded graph Go.From Go, find a shortest even cycle C in Go.Using the breadth-first search (BFS) starting at each vertex in C|/2 DCJ-surgeries that cut the edges of C and transform Go into an embedded graph on a sphere.Construct a sequence of |B and return the resulting genome as a solution to the RGGHP.Apply the corresponding DCJs to the genome Theorem 20 inspires us to design the following algorithm for solving the RGGHP for given all-duplicated genome Go. Since in Go the number of edges equals n=|B|=|A|/2 and the number of vertices equals n\u22121, this step runs in O(n2) time.We remark that our algorithm runs in polynomial time. Indeed, the most time-consuming step is the BFS starting at each vertex of In the present study we establish a somewhat unexpected link between the restricted variants of genome median and halving problems and embedded graphs. We provide a new simple proof for existence of the GHP solutions as well as completely describe the structure of the GHP solution space and determine its cardinality. We also show how the topological framework can be applied for solving the restricted guided genome halving problem (and the intermediate genome median problem) in a particular case. In further development we plan to address the topological problem of an embedded graph surgery (GSP) on an arbitrary orientable surface , which may provide better heuristic solutions for the RGGHP and IGMP.double distance problem asking for a maximal cycle decomposition of the contracted breakpoint graph of a given all-duplicated genome and an ordinary genome. Also, embedded graphs on surfaces with boundaries (holes) can be related to models including genome rearrangements along with gene insertions and deletions [We remark that similar topological interpretations exist for other comparative genomics problems and can provide intuition for their solution. For example, analysis of non-orientable surfaces (such as Klein bottle) seems to be relevant to the eletions , 30.1 Some studies base their analysis on synteny blocks rather than genes. We will use the term \u201cgene\u201d to refer to an actual gene or a synteny block.2 Here we view genome P as being transformed and P-edges as changing.3 A WGD event can simultaneously duplicate each circular chromosome in genome Q either into a single circular chromosome or into two identical circular chromosomes, which have the same contracted genome graph [R may contain duplicated chromosomes of both types.me graph . We assu4 Under a surface we understand a 2-dimensional compact orientable manifold without boundary . We distinguish surfaces up to homeomorphisms.5 Under a polygon (n-gon) we understand a topological disc, whose boundary is formed by a collection of n sides.6 There exist two orientations of the A-cycle in"}
+{"text": "However, there are several areas that would benefit from a more stringent definition of \u201cunique\u201d, requiring that these sub-sequences of length W differ by more than k mismatches (i.e. a Hamming distance greater than k) from any other sub-sequence, which we term the k-disjoint problem. Examples include finding sequences unique to a pathogen for probe-based infection diagnostics; reducing off-target hits for re-sequencing or genome editing; detecting sequence  insertions; and multiple substitution mutations. Since both sensitivity and specificity are critical, an exhaustive, yet efficient solution is desirable.A common challenge in bioinformatics is to identify short sub-sequences that are unique in a set of genomes or reference sequences, which can efficiently be achieved by k-disjoint) sequences of up to 100 nucleotides in length. On a number of simulated and real data sets ranging from microbe- to mammalian-size genomes, we show that microTaboo is able to efficiently find all sub-sequences of a specified length W that do not occur within a threshold of k mismatches in any other sub-sequence. We exemplify that microTaboo has many practical applications, including point substitution detection, sequence insertion detection, padlock probe target search, and candidate CRISPR target mining.We present microTaboo, a method that allows for efficient and extensive sequence mining of unique  contains supplementary material, which is available to authorized users. There are several areas in bioinformatics and biomedical research that benefit from identifying short sub-sequences among a (large) pool of reference sequences that are as unique as possible, i.e. the next most similar sub-sequence differs by a given number of mismatches or more. For example, in infection diagnostics, pathogen strains can be identified via padlock probes , which aW that differ by at least k mismatches compared to any other sequence in a set, termed k-disjoint, is defined as follows: given two sets A and B containing sequences of length W, find all sequences X in A such that X is more than k mismatches away from any sequence Y in B. This formulation of the problem essentially finds the so-called k-disjoint set of A and B. An alternative formulation is: given two integer values W and k as well as two strings P and T with lengths n and m, respectively, the k-disjoint problem consists of finding all positions i (1\u2009\u2264\u2009i\u2009\u2264\u2009n) which have the property that a W length substring of P beginning at i is at a Hamming distance greater than k away from any W long substring of T. The complement of the k-disjoint is the k-intersection. The k-disjoint problem is closely related to the k-difference primer problem [Mathematically, the problem of identifying a set of sequences or strings of length  problem .k-disjoint is an extension of the exact-match problem, since for k\u2009=\u20090, the k-disjoint problem collapses into identifying truly unique sequences, even if they only differ by one single letter. For this much simpler problem, common solutions include the analysis of k-mers, short sub-sequences of a fixed size k. There, simple lookup, hash-tables, or suffix arrays provide efficient solutions, with a number of implementations available, among them bloom filter based methods and suffix array based programs, such as Jellyfish [k-mer spectra can thus be used to estimate repeat content or heterozygosity in a genome or sequence reads [Conceptually, ellyfish , and Talellyfish . The resce reads , 11. In ce reads ), which k-disjoint problem based on a mismatch matrix and a dictionary tree for fast lookup and search (see Implementation). The output of this method, all sequences that avoid \u201ctaboo\u201d, can either be used directly, or serve to pre-filter data for software for specific tasks, such as CRISPR-finder or SMS [ad hoc solution to a niche problem concerning the identification of unique sequences common amongst coagulase negative Staphylococci. Here, we have generalized, refined, and optimized the algorithm and data workflow, as well as packaged the solution into a fully functional software package, microTaboo.Here, we present microTaboo, a general, exhaustive, and efficient solution to the r or SMS . microTar or SMS . BrieflyA and targets B, each containing one or more FASTA files; ii) an integer value, W, indicating the sequence lengths to be found in A; iii) an integer value k representing the mismatch threshold; and iv) a parameter  specifying whether the results should present only the k-disjoint, the k-intersection, or both. microTaboo outputs a two column file for each FASTA file in the query directory, containing sequences satisfying the input parameters, together with their sequence-relative positions.microTaboo requires the following inputs: i) two directories representing queries i)N-coding first maps all sequences of size N onto unique numbers, and then pre-computes a mismatch matrix by calculating the number of mismatches between two N-sequences, allowing for fast look-up; N-coding converts all unique sequences of a fixed length, N, to a unique number , N is limited to 5. If W has multiple delimiters, microTaboo chooses the largest value for N. Next, a mismatch matrix M is constructed, the elements M being the number of mismatches between two N-code sequences. Both N-coding sequences and the mismatch matrix enable us to calculate mismatches between two sequences more efficiently, such that the mismatches between two W-long sequences can be calculated in W/N look-ups in the mismatch matrix.see Fig.\u00a0. This enii)Fragmentation extracts all sequences of length W (W is a multiple of N) in B, reverse complement strand included, and converts them into a list of vectors of length W/N using N-coding scheme. The output of this process is a list of N-coded sequences.iii)Partitioning divides the above list into sub-lists with respect to the first two elements of each vector, reducing comparisons. The output of this process is a hybrid dictionary-tree-list data structure, called here a Dictree, which is then fed into the filter engine module (see below). The Dictree can be viewed as being an indexed list, where all W-long sequences (in N-code format) from the B FASTA-files are stored and indexed with respect to their first two vector elements. For instance, all N-code vectors of the form <62, 3,\u2026\u2009>\u2009would be placed into the sub-list with the address: <62, 3\u2009>\u2009.iv)Filter engine search is the module that filters sequences in A against the Dictree of B through their respective W/N vectors. That is, the filter engine sequentially extracts all W long substrings in A, N-codes these and searches the Dictree of B for a match. Thus, querying a vector of the same form for k\u2009=\u20090 in the Dictree requires merely a comparison to the list with exact indices as an exact match to the query vector could theoretically only exist in that particular list address. For k\u2009>\u20090, microTaboo looks into multiple lists until either the number of mismatches exceeds k, or all sub-lists that could contain a match has been searched in and not found. Using the mismatch matrix, the addresses of all sub-lists that could possibly contain a sequence within k-mismatches of a given sequence in N-code format, X\u2009=\u2009{x1, x2, x3, x4, \u2026}, is obtained in the following way:The underlying algorithm that powers mircoTaboo involves several steps see Fig.\u00a0:Fig. 1Dai, such that: M\u2009\u2264\u2009kAddress 1\u2009=\u2009j, such that: M\u2009\u2264\u2009k\u2009\u2212\u2009MAddress 2\u2009=\u2009i and j that satisfies these conditions could possibly contain a sequence within k mismatch from the query sequence X.Thus, only the lists in the Dictree with addresses W), N-code size (N), genome length of query organism (LA) and genome length of \u201ctaboo\u201d organism (LB). Construction of the Dictree is done in two steps: extracting and converting all words of length W from the \u201ctaboo\u201d organism to N-code format and inserting the N-code vectors into the Dictree. The number of operations required to convert a single word into an N-code vector is:There are two computationally intensive procedures involved when running microTaboo, namely, constructing the Dictree, and searching the query organism in the Dictree. To evaluate their respective complexities, we define the following: word length  comes from the fact that microTaboo uses a five letter DNA alphabet and that we have (5N)2 leafs in the Dictree, each pointing to a sub-list with address i, j.The second computationally heavy procedure is searching the Dictree for all words of length W long sequence is first converted into a vector in N-code format, which takes 2 operations. Given that this sub-list contains Lb/5N2 elements, in the worst case, an equal number of vector-to-vector comparisons will be made. Each vector-to-vector comparison will consist of 3, the complete computational complexity for one word isSince any The computational operation burden to filter a query organism against a \u201ctaboo\u201d organism is:Combining the complexities for the search and the construction of the Dictree gives:A and LB are the dominating factors in terms of size. Therefore, the term involving the product of these would be the determining factor, making the theoretical complexity:In practice, LN5N2 gives a reduction in the number of computations needed resulting in vastly reduced runtimes, e.g. for any word that is divisible by 5, N becomes 5 which makes the denominator be 511. Taking into account k mismatches, we have empirically determined that microTaboo scales in the following fashion: O(10k).However in practice, the denominator Escherichia coli O157 Sakai [k\u2009=\u20095 mismatches of any W\u2009=\u200930\u00a0bp long sequence in 25 other bacteria, including four other E. coli strains , E. coli (~5.5Mbps), Saccharomyces cerevisiae [Candida albicans [k\u2009=\u20090 and W\u2009=\u200930, microTaboo successfully recovered all mutated sites albicans  , 1120 (TbLCJV), and three 60\u00a0bp long regions on chromosomes 1, 2, and 5 in S. cerevisiae. microTaboo detected all the sequences in and around the vicinity of the inverted regions. We repeated the experiment by introducing additional point substitutions and achieved identical results , following the pigeon hole principle. While the suffix array runs efficiently with larger values of S (20 and up), albeit slower than microTaboo in all but one case , performance dramatically drops with lower values  sequences and k ranging from 0 to 5. In a microbial genome, we show that the method is capable of quickly finding padlock probes that allow for uniquely identifying a specific strain, and in three simulated experiments, we demonstrate that microTaboo can identify mutations, inversions, and insertions, even in presence of single-point mutations. For pre-filtering regions that could serve as CRISPR targets at different stringencies of uniqueness, we applied microTaboo to a fungal, fly, and mammalian genome. While the genomic territory at three mismatches leaves only less than 1% of the genome accessible to genome editing at high stringency, examining this fraction as a function might be useful to predict the number of expected off-target hits.We present microTaboo, a fast, efficient, and general tool for directly solving the The software is available for the Windows, MAC OS and Linux operating systems and runs both on standard laptop computers for smaller tasks, as well as larger computer clusters for more profound tasks. We also demonstrate that microTaboo can be used for several applications and that it serves especially well as a powerful pre-filtering tool for further analysis of sequence data.Additional file 1: Table S1.Padlock Probe target search. (DOCX 119\u00a0kb)Additional file 2:Section 1 - Results, Section 2 - Runtime Comparisons. (DOCX 27\u00a0kb)Additional file 3: Table S2.Point mutation detection. (DOCX 39\u00a0kb)Additional file 4: Table S3.Inversion detection and virus incorporation. (DOCX 54\u00a0kb)Additional file 5:Table S4.Runtime comparisons -microTaboo vs. BLAST and a suffix array method. (DOCX 39\u00a0kb)Additional file 6: Table S5.Result coverage comparison \u2014 BLAST vs microTaboo. (DOCX 86\u00a0kb)Additional file 7: Table S6.Runtime comparisons for exact string matching algorithms. (DOCX 50\u00a0kb)"}
+{"text": "We have examined 35 pair-wise, sequence-specific hydrophobic interactions over the temperature range of 273\u2013333 K, based on data reported by Nemethy and Scheraga in 1962. A closer look at a single example, the pair-wise hydrophobic interaction of leucine-isoleucine, will demonstrate the significant differences when the data are analyzed using the Nemethy-Scheraga model or treated by the Planck-Benzinger methodology which we have developed. The change in inherent chemical bond energy at 0 K, \u0394H\u00b0(T0) is 7.53 kcal mol compared with 2.4 kcal mol, while \u2039ts\u203a is 365 K as compared with 355 K, for the Nemethy-Scheraga and Planck-Benzinger model, respectively. At \u2039tm\u203a, the thermal agitation energy is about five times greater than \u0394H\u00b0(T0) in the Planck-Benzinger model, that is 465 K compared to 497 K in the Nemethy-Scheraga model. The results imply that the negative Gibbs free energy minimum at a well-defined \u2039ts\u203a, where T\u0394S\u00b0 = 0 at about 355 K, has its origin in the sequence-specific hydrophobic interactions, which are highly dependent on details of molecular structure. The Nemethy-Scheraga model shows no evidence of the thermodynamic molecular switch that we have found to be a universal feature of biological interactions. The Planck-Benzinger method is the best known for evaluating the innate temperature-invariant enthalpy, \u0394H\u00b0(T0), and provides for better understanding of the heat of reaction for biological molecules.We have shown in our published work the existence of a thermodynamic switch in biological systems wherein a change of sign in \u0394Cp\u00b0(T)"}
+{"text": "Double-slit imaging is widely used for verifying the resolution of high-resolution and super-resolution microscopies. However, due to the fabrication limits, the slit width is generally non-negligible, which can affect the claimed resolution. In this paper we theoretically calculate the electromagnetic field distribution inside and near the metallic double slit using waveguide mode expansion method, and acquire the far-field image by vectorial Fourier optics. We find that the slit width has minimal influence when the illuminating light is polarized parallel to the slits. In this case, the claimed resolution should be based on the center-to-center distance of the double-slit. With the development of high-resolution and super-resolution microscopies, the resolution of optical microscopy can reach the sub-wavelength scale. In order to verify the resolving capability of a proposed microscope, it is very common to fabricate a sub-wavelength metallic double-slit sample to carry out imaging experiment12345678123567We theoretically investigate how the polarization of the illuminating light and the slit width will affect the imaging result. In traditional diffraction theory, the intensity distribution at the output port of a slit illuminated by a uniform plane wave is still considered as uniform. However, this approximation is not applicable for sub-wavelength structure. In this paper, we use waveguide mode expansion method to rigorously calculate the electric field inside and near the double-slit, and acquire the far-field image by vectorial Fourier optics. After the effect of slit width is revealed, we propose a criteria for resolution verification that can provide more consistent results in double-slit microscopic imaging experiments.The imaging system model is shown in In order to rigorously solve the electric field distribution inside and near the double-slit, we first expand the electric field inside the metallic slits into waveguide modes. The metal is regarded as perfect electric conductor.\u03b1\u2009=\u2009 is a four dimensional subscript, where \u03b11 indicates which slit the mode field is located in, \u03b12 indicates TE or TM mode, \u03b13 indicates the mode order, and \u03b14 indicated the forward or backward propagating direction. E\u03b1 is the electric field of mode \u03b1 inside the waveguide. The scattered field outside the double-slit can be expressed asHere, ETE is the TE-polarized plane wave outside the slits, and ETM is the TM-polarized plane wave outside the slits. FTM and FTE are the Fourier spectrum of TM-polarized and TE-polarized electric field, respectively. And kx is the x-component of the wave vector. Because the slits are assumed to be infinitely long, the diffracted field will not propagate in the direction where ky\u2009\u2260\u20090, thus there is an assumption in ky\u2009=\u20090. It is easy to acquire the boundary conditions at the input port and output port of the double-slit.Here, Ei is the incident field and Er is the reflected field when there is no slit on the metallic board. Subscript t represents the tangential component. \u03a3in and \u03a3out are the whole planes of the double-slit structure\u2019s input port and output port. Sin and Sout are the range of the slits in the planes of the input port and the output port.Here, a\u03b1. Thus we acquire the electric field inside the double-slit. Then we can acquire the electric field outside the double-slit by projecting the electric field inside the double-slit to ETE(kx) or ETM(kx) and matching the boundary conditions.According to the waveguide mode expansion method of ref. kx to be , where k0 is the wave number of the incident light. The calculation has been verified with Comsol simulation to ensure the validity of this method. The calculation result is shown in In our numerical calculation, we make the highest waveguide mode order to be 10, and make the range of E|2 in the x-z cross section. When the incident light is y-polarized, only TE modes can exist in the slits, and TE1 is dominant. The diffracted field is TE-polarized, i.e., only y-polarized electric field component exists in the free space behind the double-slit. E|2 in the x-z cross section. When the incident light is x-polarized, only TM modes can exist in the slits, and TM0 is dominant. The diffracted field is TM-polarized, i.e., both x-polarized and z-polarized electric field components exist in the free space behind the double-slit. Note that the profiles in Next, we use vectorial Fourier optics11kx) is a window function related to the NA of the objective lens. Note that in obtaining ky\u2009\u2260\u20090, FTE\u2009=\u2009FTM\u2009=\u20090, is utilized. If this condition is not satisfied, (e.g. finitely long double-slit), Here, \u03a0(F represents the Fourier transform.The tube lens transform this spectrum into image on the CCD. FTM(kx) at the output port is plotted in FTE(kx) is plotted in When the incident light is y-polarized, the scattered field is totally TE-polarized. The spectrum Ipit/Imax, where Ipit is the intensity at the pit between the two peaks in the image, and Imax is the maximum intensity in the image. Hence, the smaller this ratio is, the more likely the double-slit image can be resolved.Then we vary the spacing between two slits and their width. In order to evaluate the resolution of the image, we introduce a ratio dcc\u2009=\u20090.79\u03bb, dcc\u2009=\u20090.81\u03bb, dcc\u2009=\u20090.87\u03bb and dcc\u2009=\u20090.95\u03bb, and observe the change of Ipit/Imax when the slit width w varies from 0.05dcc to 0.95dcc. The result is shown in Ipit/Imax is insensitive to w/dcc; on the contrary, when the incident light is x-polarized, this ratio is very sensitive to slit width.In some researches, the resolution is claimed based on the center-to-center distance of the double-slit. Here we choose a fixed center-to-center distance from the following values: dss\u2009=\u2009dcc\u2009\u2212\u2009w. Here we choose a fixed side-to-side distance from the following values: dss\u2009=\u20090.45\u03bb, dss\u2009=\u20090.55\u03bb, dss\u2009=\u20090.65\u03bb and dss\u2009=\u20090.75\u03bb, and observe the change of Ipit/Imax when the slit width w varies from 0.05dss to 0.95dss. The result is plotted in Ipit/Imax is quite sensitive to w/dss.While in some other researches, the resolution is claimed based on the side-to-side distance of the double-slit, which is \u03bb/NA\u2009=\u20090.68\u03bb. This contradiction is because the Rayleigh\u2019s criteria is for incoherent systems. Generally, for a coherent system, if the two point sources are in phase, it has worse resolution than an incoherent systemIt is convenient to mark 0.735 as the critical condition when the two slits can just be discerneddcc\u2009=\u20090.95\u03bb and the blue curve of dcc\u2009=\u20090.81\u03bb. The energy distribution accounts for this phenomenon. dcc\u2009=\u20090.95\u03bb, where the slit width is w\u2009=\u20090.85dcc and w\u2009=\u20090.95dcc respectively. The energy distribution is concentrated at the edges of two slits. However, if the two slits are too close, the energy is more concentrated at the outer edges rather than the inner ones. dcc\u2009=\u20090.81\u03bb, where the slit width is w\u2009=\u20090.65dcc and w\u2009=\u20090.95dcc respectively. The energy distribution is concentrated at the center of each slit. If the two slits are too close, the peak of energy distribution profile will slightly shift outwards.The general tendency of the curves in dss\u2009=\u20090.75\u03bb for y-polarized illumination. This is because of a small bulge between the two well-separated main peaks. dss\u2009=\u20090.75\u03bb, where the slit width is w\u2009=\u20090.6dss and w\u2009=\u20090.9dss respectively. A bulge can be clearly seen between the two well-separated main peaks for w\u2009=\u20090.9dss.The general tendency of the curves in Ipit/Imax is insensitive to the slit width. That is to say, even though a pair of very thin slits are challenging for fabrication, using relatively wide slits in experiment can still well reproduce the result from thin slits, so long as the polarization of incident light is parallel to the direction of slits and the center-to-center distance is taken as the resolution criteria. These conditions can be adopted for more consistent resolution verification in similar high resolution microscopic experiments.An important observation we get from In practical experiment, if possible, the slit width has better to be greater than half a wavelength to enable a propagating TE mode within the slits. Another thing should be noticed is that there will be no TM light induced if the criteria are adopted, hence the proposed criteria is not suitable to some experiments where TM light is necessary.In conclusion, we rigorously study the scattering and imaging process in a double-slit microscopic imaging experiment and propose a criteria for more consistent resolution verification: The illuminating light polarization should be parallel to the extension direction of the slits, and the verified resolution should be based on the center-to-center distance of the double-slit.How to cite this article: You, S. et al. Resolution criteria in double-slit microscopic imaging experiments. Sci. Rep.6, 33764; doi: 10.1038/srep33764 (2016)."}
+{"text": "Nature Communications 10.1038/s41467-018-03154-7, published online: 02 Mar 2018Correction to: y-axis originally incorrectly went form \u20180\u2019 to \u20181.10\u22124\u2019. The correct scale goes from \u20180\u2019 to \u20180.4\u2019. In Fig.\u00a05f, the x-axis labels were incorrectly shifted to the right. The correct version of Fig. 5 is:The original version of this Article contained an error in Fig.\u00a05. In Fig.\u00a05e, the scale on the which replaces the previous:This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "We develop a heuristic called DOCKS to find a compact UHS, which works in two phases: The first phase is solved optimally, and for the second we propose several efficient heuristics, trading set size for speed and memory. The use of heuristics is motivated by showing the NP-hardness of a closely related problem. We show that DOCKS works well in practice and produces UHSs that are very close to a theoretical lower bound. We present results for various values of k and L and by applying them to real genomes show that UHSs indeed improve over minimizers. In particular, DOCKS uses less than 30% of the 10-mers needed to span the human genome compared to minimizers. The software and computed UHSs are freely available at github.com/Shamir-Lab/DOCKS/ and acgt.cs.tau.ac.il/docks/, respectively.With the rapidly increasing volume of deep sequencing data, more efficient algorithms and data structures are needed. Minimizers are a central recent paradigm that has improved various sequence analysis tasks, including hashing for faster read overlap detection, sparse suffix arrays for creating smaller indexes, and Bloom filters for speeding up sequence search. Here, we propose an alternative paradigm that can lead to substantial further improvement in these and other tasks. For integers  k-mer sets (DNA words of length k) to represent the sequences in a dataset. The runtime and memory usage of these highly depend on the size of the k-mer sets used. Thus, a minimum-size k-mer hitting set, namely, a set of k-mers that hit (have non-empty overlap with) all sequences, is desirable. In this work, we create universal k-mer hitting sets that hit any L-long sequence. We present several heuristic approaches for constructing such small sets; the approaches vary in the trade-off between the size of the produced set and runtime and memory usage. We show the benefit in practice of using the produced universal k-mer hitting sets compared to minimizers and randomly created hitting sets on the human genome.High-throughput sequencing data has been accumulating at an extreme pace. The need to efficiently analyze and process it has become a critical challenge of the field. Many of the data structures and algorithms for this task rely on  The pace of high-throughput sequencing keeps accelerating as it becomes cheaper and faster and with it the need for faster and more memory efficient genomic analysis methods grows. The NIH Sequence Read Archive, for example, currently contains over 12 petabases of sequence data and is growing at a fast pace. Increased use of sequence-based assays  in research and in clinical settings creates high computational processing burdens. Metagenomic studies generate even larger sequencing datasets. New fundamental computational ideas are essential to manage and analyze these data.L, its minimizer is the lexicographically smallest k-mer in it [S of any length its minimizer set is the set of minimizers of every L-long subsequence in S. Hence, every window of length L in S is represented in the set, and a minimizer set for a sequence S constitutes a succinct representation for it. As we discuss below, minimizers have had numerous applications in sequence analysis.The minimizer approach has been extremely successful in increasing the efficiency of several sequence analysis challenges. Given a sequence of length er in it , 2. For S, we introduce the notion of a universal hitting set. For integers k, L, a set Uk,L is called a universal hitting set of k-mers (UHS) if every possible sequence of length L must contain at least one k-mer from Uk,L. The set of all k-mers is a trivial UHS, but it does not provide any useful reduction in computational resources needed. Hence, our main computational problem is:Here, we generalize and improve on the minimizer idea. To avoid dependence on a particular sequence Problem 1. Given k and L, find a smallest universal hitting set of k-mers.A small UHS has a variety of applications in speeding up genomic analyses since it can be used where minimizers have been used in the past. For example:Hashing for read overlapping. A na\u00efve read overlapper must test O(n2) pairs of reads to see whether they overlap (where n is the number of reads). If we require an overlap of length L, any pair of reads with such an overlap must share a k-mer from set Uk,L in this overlapped region. By bucketing reads into bins according to the universal k-mers they contain, we need only test pairs of reads in the same bucket. The number of buckets is limited by |Uk,L|.Sparse suffix arrays. A sparse suffix array of a string S saves memory by storing an index for only every sth position in S [q, we perform at most s queries starting from indices 0, \u2026, s \u2212 1 in q; one of these queries will intersect a position stored in the suffix array. Using Uk,L, we can instead store only positions in S that start with a k-mer in Uk,L. Any query with |q| \u2265 L must contain one of these selected k-mers and will be matched when searching the suffix array. This approach has been applied with minimizers [ion in S . To quernimizers  to good Bloom filters to speed up sequence search. Bloom filters have been used to speed up sequence search by storing k-mers present in a read set for quick testing [k-mers present in a read set are stored in these filters. If, instead, only the set of k-mers in Uk,L is stored, any window of length \u2265 L is still guaranteed to contain one of these representative queries, potentially reducing the size of Bloom filters that must be maintained. testing , 6. In cet al. [et al. [k-mers by hashing them to their 4-mer minimizer to efficiently construct a de Bruijn graph for assembly. SparseAssembler [g-th k-mer in the sequence . Kraken [k-mers during metagenome sequence classification. KMC 2 [k-mer occurrences. The Locally Consistent Parsing (LCP) [Minimizers have been used for some of these and similar applications , 7\u20139. Thet al.  for geno [et al. . For exa [et al.  compressssembler  represen. Kraken  uses minn. KMC 2  uses minng (LCP)  algorithng (LCP)  uses corA small UHS, if it can be found, has a number of advantages over minimizers for these applications:k-mers , whereas we show that we can often generate UHSs smaller by a factor of nearly k. We also demonstrate on real genomic sequences that the number of UHS k-mers needed to process them is substantially smaller.The set of minimizers for a given collection of reads may be as dense as the complete set of k and L, a set of universal k-mers needs to be computed only once and not recomputed for every dataset.For any k-mers if they are sampled according to a UHS. This will enable easier comparison and integration of the datasets.The hash buckets, sparse suffix arrays, and Bloom filters created for different datasets will contain a comparable set of k-mers to use.One does not need to look at the reads or to build a dataset-specific de Bruijn graph in order to decide which k (see Definition 1 below). This is the viewpoint we take for most of this study:Problem 1 can be rephrased as a problem on the complete de Bruijn graph of order Problem 2. Given a de Bruijn graph Dk of order k and an integer L, find a smallest set of vertices Uk,L such that any path in Dk of length \u2113 = L \u2212 k passes through at least one vertex of Uk,L.edges in it. We show that the related problem of finding a minimum-size k-mer set that hits every string in a given set L-long strings is NP-hard. This problem differs from ours, in that the set k-mers that hits every sequence in a particular data set is hard further motivates the need for a universal set that can be computed once for any input sequence. Our main contribution is an algorithm called DOCKS that finds a compact set of k-mers that hits any L-long sequence. We also provide several variants of the algorithm, trading-off some solution quality for speed. We show empirically that the produced sets are often close to a theoretical lower bound, implying their near-optimality. Our use of a greedy heuristic is motivated by the fact that finding a minimum-size \u2113-long path cover in a graph G is NP-hard when G is a directed acyclic graph (DAG). We report on the size of the universal k-mer hitting set produced by DOCKS and demonstrate on genomic datasets that we can more uniformly cover sequences with a smaller set of k-mers than is possible using minimizers. For example, we show that the number of k-mers needed to cover the human genome using a UHS is less than one third of that required by minimizers.Here and throughout, the length of a path is the number of github.com/Shamir-Lab/DOCKS/. Universal sets of k-mers computed by DOCKS for a range of values of L and k are freely available at acgt.cs.tau.ac.il/docks/. A preliminary version of this study appeared in [The software to compute small UHSs is freely available at eared in .k denotes the length of a k-mer word, while L denotes the length of the long sequences.Throughout this paper, Definition 1 (de Bruijn Graph). A de Bruijn graph of order k over alphabet \u03a3 is a directed graph in which every vertex has an associated label (a string over \u03a3) of length k (k-mer) and every edge has an associated label of length k + 1. There are exactly |\u03a3|k vertices in a de Bruijn graph, each representing a unique k-mer. If an edge  has label l, then the label of u must be the k-prefix (prefix of length k) of l and the label of v must be the k-suffix (suffix of length k) of l. A complete de Bruijn graph contains all possible edges of this type, which represent together all (k + 1)-mers over \u03a3.v0, e0, v1, e1, v2, \u2026, vn of length n spells a sequence s of length n + k such that the label of vi occurs in s starting at position i for all 0 \u2264 i \u2264 n, and the label of ei occurs in s starting at position i for all 0 \u2264 i \u2264 n \u2212 1. Note that vertices and edges may repeat in a path.Every path in a de Bruijn graph represents a sequence. A path k-mers intersecting sequences over an alphabet \u03a3:We define terminology for Definition 2 (hits). We say that k-mer whits string S, denoted w \u2286 S, if w appears as a contiguous substring in S. k-mer set Xhits string S if there exists w \u2208 X s.t. w \u2286 S. Define hit = {S \u2208 \u03a3L \u2223 w \u2286 S} for k-mer w and length L, where \u03a3L is the set of all L-long substrings over alphabet \u03a3. Define k-mers from Problem 1 is then a set Uk,L which satisfies hit = \u03a3L.The universal set of hitting k, L)-hitting set. As we prove in the Appendix, the problem of finding a minimum  k-mer set that hits a given set of input sequences is NP-hard -HITTING SET in k-mer set. This algorithm works on the de Bruijn graph of order k in two steps: first it finds and removes a minimum-size k-mer set hitting all infinite sequences, and then it finds and removes additional k-mers in order to hit all remaining L-long sequences. We now describe these two steps in detail.It is not known how to efficiently find a minimum universal ), where M(k) is the size of the minimum unavoidable set. M(k) converges to |\u03a3|k/k (an exact formula is given in O(|\u03a3|k).The problem of finding a minimum-size t length . Note thput size . The oriput size . Its runk is equivalent to a set of vertices in a complete de Bruijn graph of order k whose removal turns it into a directed acyclic graph (DAG). Each k-mer in the set corresponds to a vertex, and the removal of vertices from every cycle guarantees that no infinite sequence is represented as a path in the graph. This set is known as a decycling set.An unavoidable set of constant length L-long sequences that avoid that set. Thus, we need additional k-mers to hit those. If we consider the graph formulation, after removal of a decycling set from the graph we are left with a DAG, which may contain (L \u2212 k)-long paths representing L-long sequences. We need to remove additional vertices, so that there is no path of length \u2113 = L \u2212 k. The problem of finding a minimum-size set of vertices that hit all \u2113-long paths in a general directed acyclic graph is known to be NP-hard, as we review in the Appendix  of a vertex v to be the number of paths of length \u2113 that contain v. The main observation is that we can calculate the hitting number of each vertex efficiently using dynamic programming. The solution is based on calculating the number of paths of length i that terminate at vertex v, and the number of paths of length i that start at vertex v, for all v \u2208 V and 0 \u2264 i \u2264 \u2113. Then, the number of \u2113-long paths through v is directly computable from these values by breaking any path into an i-long path ending at v and an (\u2113 \u2212 i)-long path starting at v, for all possible values of i. We set \u2113 = L \u2212 k to get the desired hitting number of each vertex.Our initial algorithm is based on the greedy algorithm for the minimum hitting set . We defiG\u2032 =  be the directed acyclic graph, after removal of the decycling set. Denote by D and F matrices of size |V\u2032| \u00d7 (\u2113 + 1) where D is the number of i-long paths in G\u2032 starting at vertex v and F is the number of i-long paths ending at vertex v.Specifically, let D and F is done recursively as follows:\u2113-long paths that vertex v participates in, we sum:E\u2032|)) times \u2113, giving a running time of O(|\u03a3|k+1 \u22c5 \u2113) for \u2113 = L \u2212 k.The calculation of k and remove it from the graph, obtaining a DAG. Then, we repeatedly remove a vertex v with the largest hitting number T until there are no \u2113-long paths, recomputing T for all remaining vertices u after each removal. This is summarized below (Algorithm 1).The full algorithm combines the two steps. First, we find a decycling set in a complete de Bruijn graph of order G of order k, set \u2113 = L \u2212 k.1: Generate a complete de Bruijn graph X using Mykkeltveit\u2019s algorithm.2: Find a decycling vertex set X from graph G, resulting in G\u2032.3: Remove all vertices in while there are still paths of length \u2113do4: D and F for each vertex v and 0 \u2264 i \u2264 \u2113.5: \u2003Calculate T for each vertex v.6: \u2003Calculate G\u2032, and add it to set X.7: \u2003Remove a vertex with maximum hitting number from end while8: X.9: Output set O(|\u03a3|k). In the second phase, each iteration calculates the hitting number of all vertices in time O(|\u03a3|k+1\u2113). The number of iterations is 1 + p, where p is the number of vertices removed. Thus, the total running time is dominated by steps 4\u20138 and is O((1 + p)|\u03a3|k+1\u2113).Finding the decycling set takes k limits the range of k to which it can be applied , can be calculated more quickly and serve as an estimate of T. We call this heuristic DOCKSany (Algorithm 2).In order to extend the range of v with maximum T(v) in each iteration. To compute T(v) for all v, the vertices in the current graph G\u2032 =  are first sorted in topological order v1 \u2264 \u2026 \u2264 vn. Define F(v) as the number of paths ending at v. The vertices are visited in topological order and the incoming edges into v are used to compute:D(v), the number of paths starting at v is computed by visiting the vertices in reverse topological order and computing.T(v) is then calculated for all vertices as:DOCKSany has the same structure as DOCKS, but with one difference: it removes a node v with maximum T(v) is removed, G\u2032 is updated, and the process is repeated until there are no paths of length \u2113 in the graph.A vertex G of order k, set \u2113 = L \u2212 k.1: Generate a complete de Bruijn graph X using Mykkeltveit\u2019s algorithm.2: Find a decycling vertex set X from graph G, resulting in G\u2032.3: Remove all vertices in while there are still paths of length \u2113do4: D(v) and F(v) at each vertex v.5: \u2003Calculate T(v) of paths passing through each vertex v.6: \u2003Calculate the number v with maximum T(v) from G\u2032, and add it to set X.7: \u2003Remove a vertex end while8: X.9: Output set D(v) for all v requires visiting each edge in the graph once, and hence takes O(|\u03a3|k+1). The time for computing F(v) for all v is the same. Hence, T is computable in O(|\u03a3|k+1) time. Computing the longest path in a DAG (step 4) also requires O(|\u03a3|k+1). If p vertices are removed, then the total runtime for this algorithm is O((1 + p)|\u03a3|k+1), a factor of \u0398(\u2113) faster than the DOCKS algorithm. The space complexity is also smaller, O(|\u03a3|k+1) vs. O(\u2113|\u03a3|k+1) for DOCKS.Computing L. The value of L only determines when the algorithm terminates. Thus, hitting sets for all values of L or larger can be computed in one run. This is in contrast with DOCKS, in which the hitting number of each vertex depends on L, and so DOCKS must be run for each desired value of L.In addition to shorter runtimes and decreased memory usage, this heuristic offers one more advantage over the original DOCKS algorithm. The vertex removal choice is independent of k, we can further speed up DOCKSany as follows. In the DOCKSanyX heuristic, the top X vertices, ranked by the hitting number T(v), are removed (in step 7) in each iteration. This can shorten the running time of each iteration by a factor of X, but may produce larger hitting set solutions.Finally, in order to calculate the hitting set for even larger k-mer hitting set as an integer linear program (ILP). In the ILP formulation there are |\u03a3|k binary variables xi representing whether vertex i is in the solution hitting set. There are also |\u03a3|k variables Li representing an upper bound on the number of edges in the longest path ending at vertex i. The constraints on Li guarantee that the vertices chosen remove all \u2113-long paths (\u2113 = L \u2212 k) from the graph. The ILP is defined as follows:To investigate whether optimal solutions can be found practically, we formulate the problem of the minimal universal E contains all |\u03a3|k+1 possible edges. The constraint on edge  requires that if v is not in the set then Lv \u2265 1 + Lu. The validity of this formulation is proven in the Appendix -mer hitting set, denote by S an (L + j)-long sequence. By definition, there must be at least one k-mer w \u2208 Uk, L that hits S\u2019s L-long prefix. Uk+j, L+j contains all (k + j)-mers w \u22c5 x, where x is any j-mer. Thus, it must contain a (k + j)-mer that hits S.The DOCKS variants described above have exponential dependence in U10,20 we obtain U20,30. The size of the set U10,20 is |U10,20| = c \u22c5 dec10, where k = 10 . Consequently, a minimum hitting set Uk, L has a size \u2265 C \u2265 |\u03a3|k/k.A decycling set necessarily contains a keltveit , states Lmax, the length of the longest sequence in a complete de Bruijn graph after a minimum decycling set computed using Mykkeltveit\u2019s algorithm is removed, for k = 2 to 14. For this range of k, the length of sequences avoiding the decycling set can theoretically be appropriate for long-read sequencing technologies, such as PacBio [L > 1000. Such long reads are all hit by a decycling set according to k \u2264 14 . However, many short reads can avoid the decycling set. Additional k-mers must be selected to obtain a hitting set for shorter sequences. Note that different minimum decycling sets may result in different lengths of the longest path in the remaining DAG. Mykkeltveit\u2019s approach is different from that of Champarnaud et al. (2004), and the former has an advantage in producing solutions with shorter longest paths [s PacBio  and Nanos PacBio , which pst paths .k and L: 5 \u2264 k \u2264 10 and 20 \u2264 L \u2264 200, in increments of 10. The values of k are typical lengths for minimizers, and the L values are typical lengths of short reads. Note that in some applications, like KMC 2 [k there) corresponds to our L parameter, and the length of the minimizers (m in KMC 2) corresponds to our k parameter.We implemented and ran DOCKS over a range of ke KMC 2  and Krakke KMC 2 , the lenk-mers included in the solution set decreases with L. It is easier to hit longer sequences as they contain more k-mers. In addition, running times and memory usage increase exponentially with k. For k = 10, DOCKS terminated after more than 2.5 hours and used more than 1 GB of memory. For k = 11 and L = 20 running time was 128 hours. Hence, DOCKS runtime would be prohibitively long for larger values of k. Running times were benchmarked on a single CPU of a 20-CPU Intel Xeon E5-2650 (2.3GHz) machine with 384GB 2133MHz RAM.The results are summarized in k. For k = 10 and L = 20 the number of added k-mers roughly equals the size of the decycling set, while for k = 5 and L = 20 it is only 20% larger. For all values of k, the ratio improves as L grows. We also compared DOCKS to a pure greedy algorithm that repeatedly removes a vertex with a maximum hitting number, without removing a decycling set first. For almost all combinations of  the size of the produced set, runtime and memory of the greedy algorithm were far greater than those of DOCKS , and it increased with L, as opposed to DOCKS\u2019s runtime, which decreased with L.k \u2264 11 and 20 \u2264 L \u2264 200. The results for k = 10 are shown in L, and that gap grows with k: from 10% for k = 5 to 60% larger for k = 10. Set sizes of DOCKS and DOCKSany are closer as L increases and both approach the size of the decycling set. In terms of running time, on the other hand, we see a great benefit in using DOCKSany as runtimes decrease to a small fraction of the DOCKS running times for the larger values of k. We also see reduced memory usage for larger values of k and L , so we turn to another heuristic to increase runtime on the expense of larger set sizes.We ran DOCKSany for 5 \u2264 k = 10, 20 \u2264 L \u2264 200 and X = 5i for 0 \u2264 i \u2264 5 . Remarkably, for k = 10, the size of the solution is similar to that of DOCKSany while there is a factor of > 100 \u00d7 speedup. The results, runtime and memory usage of DOCKSanyX are in We tested the performance of DOCKSanyX for Fig D in . As expeally see . Fig 2 ck \u2264 10 with 20 \u2264 L \u2264 200. To save time, we set the starting feasible solution to be the DOCKS solution. We let the solver run for up to one day for each k and L. This did not necessarily produce an optimal solution to the ILP, although the solver was often able to improve on the starting DOCKS solution. In k. Improvements diminish as L increases, since the set sizes approach the theoretical lower bound, i.e., the size of the minimum decycling set. Letting the ILP solver run for longer times may provide further improvements for small values of L.We solved the ILP using Gurobi 6.5.2  for 5 \u2264 k-mer in each window of w consecutive k-mers in order to reduce storage size for sequence comparison. We can improve the minimizers algorithm by choosing the lexicographically smallest k-mer that is in the DOCKS set for the corresponding k and L parameters (i.e. L = k + w \u2212 1). Such a k-mer is guaranteed to exist, as by construction, every window of length w contains a k-mer in the UHS. We ran the minimizer selection algorithm and DOCKS-based selection on four different genomes, using k = 10 and L = 30: the entire human reference genome (GRCh38), the bacteria A. tropicalis strain NBRC 16470, and C. crescentus strain CB15, the worm C. elegans assembly WBcel235. For comparison, we also included the results when using the minimizer according to a random ordering of the k-mers, instead of lexicographic. This random ordering typically improves over minimizers since it avoids the problem of always selecting the common poly-A homopolymer.The minimizer algorithm  selects k-mers and those k-mers are more widely spread apart in the sequence. The advantage of DOCKS grows as the sequence length increases, having a size \u2248 85% of the next-best method for the small bacterial genome, \u2248 50% for the larger C. elegans genome, and only \u2248 40% for the human genome.k-mers that together hit all L-long DNA sequences. Such compact sets have many applications in sequence analysis, including space efficient data structures and large-scale sequence analysis. We tested the sets produced by our algorithm in an application that requires finding a small set of 10-mers hitting all 30-long words in the input genomes. Compared to minimizers, the current state of the art, our sets were almost 2.5-3.5 times smaller for the human genome. We could produce sets for the range of k = 5 to 10 and L = 20 to 200, and the results show that for L > 100 the size of the solution is quite close to the theoretical lower bound. We expect the sets produced by our approach to be useful and improving a variety of biological applications that require complex analysis of numerous sequences.We presented the DOCKS algorithm, which generates a compact set of k-mer counting applications, such as KMC 2 [k-mer hitting sets. Analyses that rely on k-mer counting, such as metagenomic binning as implemented in Kraken [k-mers can typically be used as a drop-in replacement, improving computational performance.We see the benefit of our compact UHSs in many data structures and algorithms that analyze high-throughput sequencing data. For example, we expect that binning-based as KMC 2 , can redn Kraken , will alL-long sequences. In the second phase we greedily remove k-mers that hit remaining L-long sequences. Overall efficiency is primarily due to the first phase, which runs in time O(k) times the size of the output. In the second phase dynamic programming is used, providing running time polynomial in the output size.The good performance of the algorithms can be attributed to their two phase approach. In the first phase we optimally and rapidly remove a minimum-size set that hits all infinite sequences, which also takes care of many k = 10, DOCKSany for k = 11, and the fastest variant, DOCKSanyX for k = 13 (with X = 10000) with L = 200, within a day. Note that all heuristics are bound to hit a limit since their runtime depends exponentially on k. This is an inherent property of the problem and its output size. Still, we manage to increase k by one or two using each heuristic. In partial remedy, we also proposed a construction that can push that limit further at the expense of solution size.We developed two additional variants of DOCKS that reduce the runtime and memory usage at the price of increasing the size of the set created. DOCKS can provide a solution for k, L)-hitting set for a given set of sequences is NP-hard. Moreover, even after removing an optimal decycling set, one needs to solve the problem of finding a minimum vertex set that hits all L-long sequences in a directed acyclic graph, which is NP-hard. Hence, DOCKS usually produces sub-optimal solutions. For example, for k = 4 and L = 10 the optimal solution obtained by solving an ILP formulation had size 89, compared to 91 produced by DOCKS. In fact, our tests show that if further reduction to the hitting set size is needed, starting from the DOCKS solution and improving it using ILP is a good strategy, at least for small values of k.Our approaches are heuristic in nature. This is not surprising, since as we show, the problem of finding a minimum -hitting set similar to the characterization of decycling sets by Mykkeltveit [k and L that can check if a k-mer belongs to a particular universal -hitting set. The fact that MINIMUM -HITTING SET on a given set of input sequences is NP-hard still leaves the universal case open. A related question is whether one can find an algorithm that generates an optimal  -hitting set while requiring work polynomial in the output set size. This is particularly interesting for the universal case, where the input is only the values k and L and the output size is > |\u03a3|k/k. Second, is the problem of minimum \u2113-path cover in a DAG G polynomial when G is a subgraph of a de Bruijn graph? We know it is hard for a general DAG, but the specific structure of de Bruijn graphs may make the problem easier. Third, the bottleneck to DOCKS running time is the second phase, which currently re-calculates the vertex hitting numbers on each iteration. Can one find a dynamic algorithm that updates these numbers more efficiently after the removal of one vertex? Fourth, is there a tight upper bound on the number p of vertices that will be removed by the greedy heuristic? Fifth, can we give an upper bound or a tighter lower bound on the size of Uk, L?Our study raises several open problems. First, is there a characterization for a minimum universal  pair, but the sets for all longer L values are computed when computing the  set with DOCKSany or DOCKSanyX and the runtime can be amortized across all of these calculations.The table contains solution set size, time in seconds and memory in KB for DOCKS, DOCKSany, DOCKSanyX and the greedy approach algorithms. Note that the reported times are for individual runs of each ((XLSX)Click here for additional data file.S1 Text(PDF)Click here for additional data file."}
+{"text": "Scientific Reports 10.1038/s41598-017-18687-y, published online 18 January 2018Correction to: The original version of this Article contained an error in the title, where the phrase \u201cbet hedging\u201d was incorrectly given as \u201cbet -hedging\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "In this study, we present a novel model-based imaging method to enable high-resolution real-time PC-CMR with sparse sampling.Conventional phase-contrast cardiovascular magnetic resonance (PC-CMR) employs cine-based acquisitions to assess blood flow condition, in which electro-cardiogram (ECG) gating and respiration control are generally required. This often results in lower acquisition efficiency, and limited utility in the presence of cardiovascular pathology . Real-time PC-CMR, without ECG gating and respiration control, is a promising alternative that could overcome limitations of the conventional approach. But real-time PC-CMR involves image reconstruction from highly undersampled . Additionally, we performed a feasibility study of the proposed method on patients with cardiac arrhythmia.The proposed method achieves a spatial resolution of 1.8\u00a0mm and a temporal resolution of 18\u00a0ms for 2D real-time PC-CMR with one directional flow encoding. For the flow phantom experiments, both regular and irregular flow patterns were accurately captured. For the in vivo experiments with healthy subjects, flow dynamics obtained from the proposed method correlated well with those from the cine-based acquisitions. For the experiments with the arrhythmic patients, the proposed method demonstrated excellent capability of resolving the beat-by-beat flow variations, which cannot be obtained from the conventional cine-based method.The proposed method enables high-resolution real-time PC-CMR at 2D without ECG gating and respiration control. It accurately resolves beat-by-beat flow variations, which holds great promise for studying patients with irregular heartbeats.The online version of this article (doi:10.1186/s12968-017-0330-1) contains supplementary material, which is available to authorized users. Over the past few decades, phase-contrast cardiovascular magnetic resonance (PC-CMR) has been developed into a powerful tool for quantification and visualization of blood flow dynamics in the heart and large vessels \u20135. It haReal-time PC-CMR , 16 withIn this work, we present a new model-based method for real-time PC-CMR with sparse sampling. It is based on the integration of a novel low-rank model with parallel imaging. With temporal subspace modeling, the proposed method yields a convex optimization problem, thereby enabling efficient computation. The proposed method achieves real-time PC-CMR without ECG gating and respiration control, and well resolves the beat-by-beat flow variations that cannot be obtained from the conventional cine method. Compared with state-of-the-art real-time PC-CMR techniques, it provides higher temporal resolution. The effectiveness of the proposed method has been systematically evaluated in 2D real-time PC-CMR using both phantom experiments and in vivo experiments. A preliminary account of this work was presented in , 37.Ignoring flow during readout time, the imaging equation for real-time PC-CMR can be modeled as follows:\u03c1v denotes the dynamic image associated with either the flow-compensated  or flow-encoded image sequence , Si(r) the sensitivity map for the i th receiver coil , and dv,i and \u03b7v,i respectively the -space measured data and measurement noise. Here, the goal is to reconstruct \u03c1v from the undersampled data {dv,i}, and then calculate the velocity maps as \u0394\u03d5\u2009=\u2009\u2220\u2009\u03c1v\u2009\u2212\u2009\u2220\u2009\u03c11 denotes the phase difference between the flow-encoded and flow-compensated image sequences, and VENC the pre-specified encoding velocity. Since in real-time PC-CMR, there is no data sharing with ECG gating, -space data is often highly undersampled. Direct inversion of {dv,i} can incur significant aliasing artifacts and lead to inaccurate velocity measurements.where Cv admits a low-rank approximation due to strong spatiotemporal correlation of time-series images. Moreover, due to the nature of flow encoding, there is also strong spatial and temporal correlation among different flow image sequences. To exploit such correlation, the following joint Casorati matrix is introduced:Here we introduce a low-rank model-based reconstruction method with parallel imaging to address the problem. For convenience, we consider a discrete image model, in which each flow image sequence can be represented as a spatiotemporal Casorati matrix , i.e.,2\\ications \u201341, eachC)\u2009\u2264\u2009L. There are a number of ways of imposing low-rank constraints [C\u2009=\u2009UV, where U\u2009\u2208\u2009\u2102N\u2009\u00d7\u2009L and V\u2009\u2208\u2009\u2102L\u2009\u00d7\u2009M. In this low-rank representation, the columns of U and rows of V respectively span the spatial subspace and temporal subspace of C.on which we enforce the low-rank structure, i.e., rank..di denoV by acquiring training data with a specialized data acquisition scheme. Specifically, as shown in Fig.\u00a0, t)-space region with a random sampling scheme. With this sampling scheme, the two sets of data provide the complementary information for the low-rank model: the training data have high temporal resolution, while the imaging data have high spatial resolution. From the training data, we estimate the temporal subspace using the principal component analysis [U. To match the timing between the two sets of data, a proper temporal interpolation is performed, which interpolates the training data into those at the same time instants as the imaging data. Note that with such a scheme, the temporal resolution for the proposed method is 2\u2009\u00d7\u2009Nv\u2009\u00d7\u2009TR. Moreover, note that the coil sensitivities Si can be estimated from temporal averaged -space data from the flow-compensated image sequence.The image reconstruction problem can be further simplified. Extending the early work in cardiac imaging , 41, 46,analysis , 47. WitU by solving the following convex optimization problem:\u00db, the joint Casorati matrix can be reconstructed as With entclass1pt{minimaWe performed both phantom and in vivo studies to evaluate the performance of the proposed method for 2D real-time PC-CMR. The experiments were conducted on a 3.0\u00a0T whole body MR scanner , equipped with a 32-channel cardiovascular coil. A gradient-echo (GRE) based pulse sequence was adapted to implement the proposed real-time acquisition scheme as shown in Fig.\u00a0\u00d7\u2009120\u00a0mm, matrix size\u2009=\u2009182\u2009\u00d7\u2009100, spatial resolution\u2009=\u20091.20\u00a0mm\u2009\u00d7\u20091.20\u00a0mm, slice thickness\u2009=\u20095\u00a0mm, repetition time (TR)\u2009=\u20095.0\u00a0ms, echo time (TE)\u2009=\u20093.0\u00a0ms, flip angle\u2009=\u200910\u00b0, and VENC\u2009=\u2009100\u00a0cm/s. Notice that the temporal resolution for the real-time acquisition is 4\u2009\u00d7\u2009TR\u2009=\u200920\u00a0ms, while, for the cine acquisition, the temporal resolution is 56\u00a0ms (with 36 cardiac phases). The total acquisition time was around 42\u00a0s for both experiments.First, flow phantom experiments were performed to evaluate the capability of the proposed method in resolving various flow dynamics. Specifically, a 15-mm-diameter plastic tube simulating large vessel in the aorta was filled with blood-mimicking fluid , and plu\u00d7\u20091.80\u00a0mm, slice thickness\u2009=\u20095\u00a0mm, TR/TE\u2009=\u20094.5/2.8\u00a0ms, flip angle\u2009=\u200910\u00b0, and VENC\u2009=\u2009200\u00a0cm/s. For the real-time flow imaging, the temporal resolution is 4\u2009\u00d7\u2009TR\u2009=\u200918\u00a0ms, whereas for the cine imaging, the temporal resolution is around 36\u00a0ms (with 28 cardiac phases). The total acquisition time was around 94\u00a0s for both experiments.Second, in vivo experiments were performed to evaluate the proposed method. Ten healthy volunteers , who had no symptoms of cardiovascular diseases, were recruited. In addition, we performed a feasibility study of applying the proposed method for arrhythmia detection, and recruited two patients . This study was approved by the Institutional Review Board at Tsinghua University, and all the subjects gave written informed consent. Both the cine and real-time flow experiments were performed on the planes perpendicular to the ascending aorta (AAo) and descending aorta (DAo) during free breathing, and with one directional velocity encoding along the FH direction. For the cine acquisition, the retrospective ECG gating was set according to an estimate of each subject\u2019s heartbeat period, and three averages were performed to mitigate respiratory motion artifacts. For both the cine and real-time imaging experiments, the following imaging parameters were used: FOV\u2009=\u2009240\u00a0mm\u2009\u00d7\u2009225\u00a0mm, matrix size\u2009=\u2009132\u2009\u00d7\u2009124, spatial resolution\u2009=\u20091.80\u00a0mm\u2009V from the training data. We then estimated the coil sensitivity maps Si from the temporally averaged -space measurements. We further determined the spatial subspace U by solving Eq.  and 0.90 (P\u2009=\u20090.0002), respectively. This further confirms strong correlation between the two methods.We also performed a statistical analysis of the results from the two methods for all ten healthy subjects. Figure\u00a0Figure\u00a0Figure\u00a0L\u2009=\u200920. As can be seen, the proposed method reconstructs the spatial images and velocity maps with improved quality over the alternative formulation. This illustrates the benefits of imposing the low-rank constraint on the joint Casorati matrix.Figure\u00a0In this work, we introduced a new real-time flow imaging method and systematically demonstrated its effectiveness with both flow phantom experiments and in vivo experiments. Here, it is worth reiterating the key characteristics of the proposed method. First, the proposed method can be used as a viable alternative to the conventional cine flow imaging method in that it provides comparable (if not superior) image quality and flow information for healthy subjects. Second, the proposed method is able to resolve beat-by-beat physiological and/or pathological flow variations, which cannot be obtained from the conventional cine method based on ECG gating and respiration control. Such information is often clinically important .L). Generally, the selection of L needs to balance the model representational power, the number of measurements , and signal-to-noise ratio [L to trade off the above factors, and it consistently yielded good reconstruction performance, although it is worthwhile to investigate other principled model selection methods  in  in L). GThe proposed formulation results in a convex optimization problem, which enables efficient computation. For example, the runtime for reconstructing an in vivo dataset  takes around 10\u00a0min on a workstation with 64\u00a0GB RAM and 3.47\u00a0GHz CPU. The computational efficiency may be further improved by an implementation on graphical processing units. Such an investigation is beyond the scope of this paper, but is worthwhile to explore for future research.In addition to rank constraint, sparsity constraint can also be incorporated to accelerate PC-CMR. It has been demonstrated in , 43, 55 The flow-compensated and flow-encoded images share similar magnitude but different phase differences. We can extend the proposed method to exploit such information and impose a stronger constraint in the model-based reconstruction. However, the resulting formulation can involve a joint reconstruction of magnitude and phase images, which generally leads to a non-convex optimization problem. To solve such a problem, specialized algorithms and proper initialization are often needed. In contrast, the proposed method here employs a low-rank model to exploit the spatiotemporal correlation between flow images, which leads to a simple convex problem formulation and efficient computation. Given that the two models may have different trade-offs, comprehensively evaluating their advantages and drawbacks is a very interesting open problem to be explored in future work.In this work, we demonstrate the performance of the proposed method for 2D real-time flow imaging, in which through-plane flow was imaged. Considering the complex flow patterns and blood vessel geometry, it is highly desirable to perform 3D real-time flow imaging. However, 3D real-time flow imaging generally involves a more challenging trade-off between spatial resolution, temporal resolution, and imaging time, and a significantly more challenging computational problem. We are investigating an extension of the proposed method to 3D real-time flow imaging, and the results will be reported in future work.This paper is focused on the development of a novel real-time flow imaging technique, which should serve as a foundation for our subsequent clinical studies. Given that the proposed method well resolves beat-by-beat flow variations, it can provide more information on hemodynamics for patients with significant irregular heartbeats. In the future work, we plan to conduct systematic study of the proposed method for various potential clinical applications .It is also worthwhile to remark on the potential limitations of the proposed method. First, note that the aforementioned spatial and temporal resolution both refer to nominal resolution. For a linear shift-invariant reconstruction method , the resolution can be characterized through the point spread function. However, for a nonlinear reconstruction method -space data for real-time PC-CMR. The effectiveness and utilities of the proposed method have been demonstrated for 2D real-time PC-CMR with both phantom experiments and in vivo experiments. We expect that the proposed method will enhance the practical utility of real-time PC-CMR for various clinical applications.A new model-based method was introduced for high-resolution real-time PC-CMR without ECG gating and respiration control. It integrates the novel low-rank model with parallel imaging, which enables high-quality image reconstruction from highly undersampled (k"}
+{"text": "Scientific Reports 10.1038/s41598-017-17572-y, published online 12 December 2017Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cHeart\u201d was incorrectly given as \u201cHeat\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Information file."}
+{"text": "The ToyBox-intervention is a theory- and evidence-based intervention delivered in kindergartens to improve four- to six-year-old children\u2019s energy balance-related behaviours and prevent obesity. The current study aimed to (1) examine the effect of the ToyBox-intervention on increasing European four- to six-year-old children\u2019 steps per day, and (2) examine if a higher process evaluation score from teachers and parents was related to a more favourable effect on steps per day.A sample of 2438 four- to six-year-old children  from 6 European countries  wore a motion sensor (pedometer or accelerometer) for a minimum of two weekdays and one weekend day both at baseline and follow-up to objectively measure their steps per day. Kindergarten teachers implemented the physical activity component of the ToyBox-intervention for 6 weeks in total, with a focus on (1) environmental changes in the classroom, (2) the child performing the actual behaviour and (3) classroom activities. Children\u2019s parents received newsletters, tip cards and posters. To assess intervention effects, multilevel repeated measures analyses were conducted for the total sample and the six intervention countries separately. In addition, process evaluation questionnaires were used to calculate a total process evaluation score  for teachers and parents which was then linked with the physical activity outcomes.p\u00a0>\u00a00.05). In general, the intervention effects on steps per day were least favourable in four- to six-year-old children with a low teachers process evaluation score and most favourable in four- to six-year-old children with a high teachers process evaluation score. No differences in intervention effects were found for a low, medium or high parents\u2019 process evaluation score.No significant intervention effects on four- to six-year-old children\u2019 steps per weekday, steps per weekend day and steps per average day were found, both in the total sample and in the country-specific samples  contains supplementary material, which is available to authorized users. Sufficient levels of physical activity (PA) are associated with numerous positive mental and physical health outcomes, even at preschool age . In addiThe aim of the ToyBox-study was to develop, implement and evaluate a kindergarten-based, family-involved intervention to prevent overweight and obesity in four- to six-year-old preschool children from six European countries . One of the four behaviours on which the intervention focused, was PA  , 20. Thereach (level of participation in the intervention), fidelity , dose delivered (the amount of the intervention that was delivered by the implementers), dose received \u2013 exposure , dose received \u2013 satisfaction (the level of satisfaction of the implementer and the target group regarding the intervention) and context (within which the ToyBox-intervention was implemented) [A process evaluation should be guided by using a specific framework. The model used in the ToyBox-intervention is the model by Saunders et al. (2005) and is described in detail elsewhere , 26. Thiemented) .Thus, the aim of the current study was (1) to evaluate the effectiveness of the ToyBox-intervention on European preschoolers\u2019 objectively measured steps per day in the total sample and in the country-specific samples, and (2) to examine whether a higher level of intervention implementation and satisfaction of the PA-component of the ToyBox-intervention was related to more favourable effects on preschoolers\u2019 steps per day in the total sample.The kindergarten-based ToyBox-intervention with family involvement, targeting four- to six-year-old preschoolers, has a cluster randomised pre-test post-test design with intervention kindergartens and control kindergartens across six European countries: Belgium, Bulgaria, Germany, Greece, Poland, and Spain. Preschool children and their parents/caregivers were recruited at kindergartens, daycare centers or preschool settings, depending on the country regulations and legislation. In Germany, Bulgaria, Spain and Poland, children/families were recruited from kindergartens, in Greece from kindergartens and daycare centers, and in Belgium from preschool settings. In order to avoid confusion for the reader, all these settings  will be referred to as \u201ckindergartens\u201d in this paper. Additionally, to avoid confusion regarding the term \u201cpreschool children\u201d we will use the term \u201cfour- to six-year-old children\u201d throughout the manuscript.n\u00a0=\u00a016,798; age at baseline was 3.5\u20135.5\u00a0years old) received an information letter to take home in which the purpose of the study was explained to the parents/caregivers, and the child was invited to wear a pedometer or accelerometer for six consecutive days. Sample size calculations can be found elsewhere [Kindergartens were selected in the provinces of West- and Oost-Vlaanderen in Belgium, Varna in Bulgaria, Bavaria in Germany, Attica in Greece, Mazowiecki in Poland, and Zaragoza in Spain. Kindergartens were recruited from different SES backgrounds. Lists of all municipalities that exist within the selected provinces were collected and information on the SES variables was provided . Tertiles were created, based on the selected SES variables, and five municipalities were randomly selected from each tertile  in each country. Then, 1003 kindergartens within these randomly chosen municipalities across the six countries were randomly selected , and a personal visit was performed to inform the kindergarten staff about the ToyBox-study. In total, 309 kindergartens (30.8%) across the six countries agreed to participate in the study, and all four- to six-year-old children born in 2007 and 2008  to avoid contamination between kindergartens in the same municipality. This was done by by the project coordinator (Greece) with the use of a command in Excel, which means that the randomisation occurred automatically and electronically. Kindergartens allocated to the intervention condition received the intervention programme. Kindergartens allocated to the control condition continued with the normal kindergarten curriculum. The ToyBox-intervention was implemented within the school year 2012\u20132013.Before the start of the intervention, baseline measurements were performed on weekdays from May to June 2012. On those days, researchers visited intervention and control kindergartens and fitted those preschool children with an accelerometer (Belgium) or a pedometer (other countries) for whom written informed consent from their parents/caregivers had been obtained. One year later, from May to June 2013, follow-up measurements were performed and again, the same children with written informed consent from both intervention and control kindergartens received a pedometer or accelerometer to objectively measure their step counts.clinicaltrials.gov, ID: NCT02116296.The ToyBox-study was approved by the Ethical Committees in all European countries, in line with national regulations , and had a two-week \u2018repetition period\u2019 in weeks 19 and 20. Furthermore, some PA-components were also implemented throughout the whole school year, such as restructuring the classroom  in the classroom that stimulates moving such as balls, big sponge bricks,\u2026) and installing movement landscapes  in the classroom. The ToyBox-intervention was implemented by the kindergarten teachers, who had two 1-h teacher training sessions with the researchers to explain the goals and the material of the ToyBox-study, and to answer kindergarten teachers\u2019 questions, prior to the intervention. During the second training session, teachers were provided with the \u201cToyBox\u201d, i.e. a box containing material for the class , and material for the home . In the classroom activity guide for PA, three different themes were included, namely (1) setting environmental changes in the classroom , (2) the preschool child performing the actual behaviour , and (3) classroom activities . Teachers were asked to allocate a minimum of 1 h per week to use the ToyBox-materials and to implement the ToyBox-intervention in the classroom, while the environmental changes were conducted and retained throughout the project. The 1 h per week recommendation was chosen based on the focus groups that were held before the development of the intervention . Kindergwww.toybox-study.eu).To involve the parents/caregivers, four- to six-year-old children received two newsletters, two tip-cards and one poster (with key messages on PA that could be coloured at kindergarten or at home) to take home for their parents/caregivers. The newsletters and tip-cards contained tips and strategies to increase four- to six-year-old children\u2019 PA levels. The relevant materials can be found on the ToyBox-website   and ActiGraph  accelerometers with activated step count function (Belgium). Step counts from the pedometer and accelerometer are comparable and have been validated to measure PA in preschool children . The devFour- to six-year-old children wore a motion sensor (pedometer or accelerometer) for six full consecutive days, including two weekend days. Accelerometers were initialised to measure activity counts and step counts in 15-s epochs. Four- to six-year-old children\u2019s parents/caregivers received an information letter and were instructed to let their child wear the motion sensor during all waking hours and to remove it only during water-based activities. After data collection, data from pedometers were downloaded using Omron Health Management Software version E1.012, and data from accelerometers were downloaded using ActiLife version 5.5.5-software. Both the first (fitting day) and sixth day (collection day) were omitted, because these days did not have a full day of data and were therefore incomplete. All step counts below 1000 and above 30,000 steps per day were deleted and treated as missing data, which is according to the rules of Rowe et al. (2014) . Four- tTo investigate the intervention process and satisfaction, teachers had to fill in two logbooks with specific questions regarding the process and satisfaction of the PA component, which were based on the model of Saunders et al. (2005) , 26. TheThe specific questions per key element that were used from the monthly logbooks are depicted in Table Also parents/caregivers had to fill in a questionnaire regarding the process of the PA component of the intervention. These questions were also based on the model of Saunders et al. (2005) , 26. TheThe specific questions per key element that were used from the questionnaire are depicted in Table Steps per day were separately calculated for weekdays, weekend days and average days. To take into account that some four- to six-year-old children had more weekend days than others, outcome variables on an average day were calculated using the following formula: *5)\u00a0+\u00a0*2)/7. Prior to all analyses, all outcome measures were first checked for normal distribution (skewness <0.70) and appeared to be normally distributed. Descriptive statistics were computed to describe the characteristics  of the sample, and were reported as frequencies (%) or means and standard deviations or percentages.Multilevel repeated measures analyses were performed using MLwiN 2.31  to assess the effectiveness of the intervention on steps per weekday, weekend day and average day. Multilevel modeling  was used to take clustering of two measurements (baseline and follow-up) of four- to six-year-old children in kindergarten classes in kindergartens in countries into account. For the country-specific analyses, four levels were used . All analyses were adjusted for age and sex. Two \u00df-values will be reported in the results: (1) the \u00df-value for \u2018time\u2019 is the estimate for the time effect, and can be interpreted as the magnitude of change in the outcome variable going from follow-up to baseline for the reference category , and (2) the \u00df-value for \u2018time*condition\u2019 is the estimate for the intervention effect for all outcome variables, which describes the difference between the mean change in the intervention group and the mean change in the control group.p\u00a0<\u00a00.05.To study if the effect was different regarding the intervention process evaluation score four- to six-year old children\u2019s steps per weekday, steps per weekend day and steps per day, multilevel repeated measures analyses  were performed . All analyses were adjusted for children\u2019s age and sex. For all analyses, statistical significance level was set at t\u00a0=\u00a08.07, p\u00a0<\u00a00.001) and average days . There was no significant difference for steps at weekend days. In addition, 37.4%, 28.9%, and 32.1% of four- to six-year-old children complied with the PA guidelines of 11,500 steps per day [In total, 2438 children  provided valid step count data at baseline and follow-up (drop-out of 71.3%). At baseline, four- to six-year-old children took 10,739 (\u00b13258) steps per weekday, 9690 (\u00b13850) steps per weekend day, and 10,440 (\u00b12898) steps on an average day. At follow-up, they took 10,745 (\u00b13501) steps per weekday, 9028 (\u00b13924) steps per weekend day, and 10,254 (\u00b13059) steps on an average day. Descriptive analyses showed that four- to six-year-old children from the control group significantly took less steps at baseline compared to four- to six-year-old children from the control group, both at weekdays  did not fill in the logbook for PA during the first focus, and 23.3% (n\u00a0=\u00a0107) did not fill in the logbook for PA during the repetition period. The mean teachers\u2019 process evaluation score for all intervention kindergartens was 13.49 (\u00b12.56) on a total score of 26 . Kindergartens were divided into three groups, based on the teachers\u2019 process evaluation score: (1) kindergartens with the lowest teachers\u2019 process evaluation score , (2) kindergartens with a medium teachers\u2019 process evaluation score , and (3) kindergartens with the highest teachers\u2019 process evaluation score . Of all 312 teachers, 37.1% had a low, 29.7% had a medium and 33.2% had a high teachers\u2019 process evaluation score. Teachers scored best on dose received  and fidelity (6.23/11) and had the lowest scores for dose delivered (1.55/6). Detailed information on the scores for each component of the teachers\u2019 process evaluation score can be found in Table In total, a teachers\u2019 process evaluation score could be calculated for 1605 children (out of 2438), as not all teachers filled in the monthly logbooks. From the 460 teachers who participated in the intervention, 8.1% (p\u00a0=\u00a00.02). Four- to six-year-old children with a low teachers\u2019 process evaluation score significantly decreased their steps per weekday from baseline to follow-up , while children from the control group did not significantly change their steps per weekday from baseline to follow-up (p\u00a0=\u00a00.52). Furthermore, a significant interaction effect was found between children with a low teachers\u2019 process evaluation score and a medium and high teachers\u2019 process evaluation score, going from baseline to follow-up (\u03b2\u00a0=\u00a0558.57 (SE\u00a0=\u00a0250.95), p\u00a0=\u00a00.03 and \u03b2\u00a0=\u00a0682.16 (SE\u00a0=\u00a0264.62), p\u00a0=\u00a00.01). Four- to six-year-old children with a medium teachers\u2019 process evaluation score and a high teachers\u2019 process evaluation score did not significantly decrease their steps per weekday going from baseline to follow-up , while children with a low teachers\u2019 process evaluation score significantly decreased their steps per weekday .Regarding steps per weekday, a significant interaction effect was found between children from the control group and children with a low teachers\u2019 process evaluation score, going from baseline to follow-up (\u03b2\u00a0=\u00a0\u2212553.95 (SE\u00a0=\u00a0235.50); p\u00a0=\u00a00.003). Four- to six-year-old children from the control group significantly decreased their steps per weekend day from baseline to follow-up , while children with a high teachers\u2019 process evaluation score did not (p\u00a0=\u00a00.99). Furthermore, a significant interaction effect was found between children with a low and children with a medium teachers\u2019 process evaluation score (\u03b2\u00a0=\u00a0\u2212669.56 (SE\u00a0=\u00a0310.93), p\u00a0=\u00a00.03), and between children with a medium and children with a high teachers\u2019 process evaluation score (\u03b2\u00a0=\u00a01095.61 (SE\u00a0=\u00a0312.67), p\u00a0<\u00a00.001). Four- to six-year-old children with a medium teachers\u2019 process evaluation score significantly decreased their steps per weekend day from baseline to follow-up , while children with a low teachers\u2019 process evaluation score and children with a high teachers\u2019 process evaluation score did not show a significant change in their steps between the two time points .Regarding steps per weekend day, a significant interaction effect was found between children from the control group and children with a high teachers\u2019 process evaluation score, going from baseline to follow-up (\u03b2\u00a0=\u00a0866.35 (SE\u00a0=\u00a0293.65), p\u00a0=\u00a00.01). This means that children with a low teachers\u2019 process evaluation score significantly decreased their steps per day from baseline to follow-up , while children with a high teachers\u2019 process evaluation score did not change their steps per day from baseline to follow-up. No other interaction effects were found for steps per day. All interaction effects between time and teachers\u2019 process evaluation score for steps per weekday, steps per weekend day and steps per day can be found in Fig. Regarding steps per day, a significant interaction effect was found between four- to six-year-old children with a low teachers\u2019 process evaluation score and a high teachers\u2019 process evaluation score, going from baseline to follow-up (\u03b2\u00a0=\u00a0608.98 SE\u00a0=\u00a0234.10); 4.10; p\u00a0=four- to six-year-old children\u00a0=\u00a0464), (2) four- to six-year-old children with a medium parents\u2019/caregivers\u2019 process evaluation score , and (3) four- to six-year-old children with a high parents\u2019/caregivers\u2019 process evaluation score . Of all parents, 31.8% had a low, 34.7% had a medium, and 33.5% had a high parents\u2019/caregivers\u2019 process evaluation score. Parents/caregivers scored best on dose received - exposure (4.86/10) and had the lowest scores for dose received - satisfaction (1.88/6). Detailed information on the scores for each component of the parents\u2019/caregivers\u2019 process evaluation score can be found in Table In total, a parents\u2019/caregivers\u2019 process evaluation score could be calculated for 1420 children (drop-out of 11.5%). The mean parents\u2019/caregivers\u2019 process evaluation score for all intervention kindergartens was 6.90 (\u00b13.50) on a total score of 17 . Four- to six-year-old children were divided into three groups, based on the parents\u2019/caregivers\u2019 process evaluation score: (1) four- to six-year-old children with a low parents\u2019/caregivers\u2019 process evaluation score . This means that there is no difference between baseline and follow-up in steps per weekday, steps per weekend day or steps per day for four- to six-year-old children from the control group and four- to six-year-old children with a low, medium and high parents\u2019/caregivers\u2019 process evaluation score.For steps per weekday, steps per weekend day and steps per day, no significant interaction effects were found between time and parents\u2019/caregivers\u2019 process evaluation score . Second, we wanted to examine whether a higher teachers\u2019 or parents\u2019/caregivers\u2019 process evaluation score was related to more beneficial effects on four- to six-year-old children\u2019s steps per day.For the total sample, no intervention effects were found, which means that the intervention did not cause an effect on four- to six-year-old children\u2019s PA in terms of steps per day. Also country-specific analyses revealed no effects on European four- to six-year-old children\u2019s steps per day. The lack of effects on children\u2019s PA is in line with other published studies targeting four- to six-year-old children\u2019s PA levels , 17. OneThe results from the process evaluation showed a medium teachers\u2019 process evaluation score with a mean score of 13.5 on a total of 26. The higher score on fidelity can be explained by the fact that almost all kindergarten teachers handed out the newsletters and tip-cards for the parents/caregivers, based on the set time plan of the ToyBox-intervention. In addition, the higher score for dose received (satisfaction) shows us that kindergarten teachers in general might have enjoyed the intervention components and that they might be convinced about the clarity, appropriateness and the feasibility of the intervention components. The low score for dose delivered can be explained by the fact that the classroom activities were not implemented as intended. Although kindergarten teachers read the Kangaroo stories during the first weeks of intervention implementation, most of them did not implement the proposed excursions. In addition, during the repetition period, less than 25% of kindergarten teachers repeated using the Kangaroo stories and more than 90% of all teachers did not execute the excursions. This shows that excursions might be hard to implement in kindergarten classes, and that the Kangaroo stories can be used for a short period during the intervention, but not for longer implementation periods.The results in this paper show that there are some differences in effect between the control group and between kindergartens with different process evaluation scores (low to high). For example for steps per weekday, four- to six-year-old children with a medium and high process evaluation score did not decrease their steps from baseline to follow-up, while four- to six-year-old children with a low process evaluation score did. This shows that having teachers that do not implement the intervention as intended  and were not satisfied with the intervention, could have unfavourable effects compared to teachers that implement the intervention in a better way and were satisfied with the intervention or even compared to teachers that did not implement the intervention at all . This shows that not implementing an intervention  is better than implementing an intervention with low fidelity to the study protocol. The influence of teachers implementing the intervention as intended  was still present on weekend days, as children from the control group decreased their steps per weekend day from baseline to follow-up, while children with a high teachers\u2019 process evaluation score did not. This shows that teachers implementing the intervention with high fidelity to the study protocol can stop a possible decrease in steps per weekday or weekend day. These age-related declines in PA have been studied before  and coulA low parents\u2019/caregivers\u2019 process evaluation score was found with a mean score of 6.90 on a total score of 17. The results suggest that parents/caregivers read and were satisfied with the newsletters, tip-cards and posters for the PA component of the ToyBox-intervention, but that they were not satisfied with for example the usefulness, design and the amount of text of these tools. In addition, results showed that there was no difference in effect between four- to six-year-old children from the control group and four- to six-year-old children with a low, medium or high parents\u2019/caregivers\u2019 process evaluation score. This is comparable with the IDEFICS-intervention in which higher levels of parental exposure to the intervention was not related to more favourable effects in children\u2019s BMI z-scores, and parental exposure and involvement in the intervention was much less than aimed for . In the Based on the information received from both kindergarten teachers and parents/caregivers, the ToyBox-material and/or components could be adapted and revised to meet the comments. For example by providing active toys and/or activity videos for the teachers. In addition, qualitative research could be helpful to investigate kindergarten teachers\u2019 and parents\u2019/caregivers\u2019 perspectives on what worked and what did not work. The revised material and/or components could then be pilot tested to see whether teachers and parents/caregivers are more satisfied with the intervention components and implement the intervention as intended.Study strengths are the large sample of four- to six-year-old children that provided valid pedometer data, and the cluster randomised controlled trial with a pre-test post-test design. However, future studies could look into objectively measuring four- to six-year-olds\u2019 PA by using hip and wrist accelerometers simultaneously as wrist-worn accelerometers have shown to measure different PA intensities more accurately . AnotherStudy limitations include the fact that pedometers cannot distinguish between the different PA intensities and are only able to measure in steps per day. Missing data  were not imputed, which may have induced bias. Furthermore, there was a large drop-out of four- to six-year-old children due to a lack of valid pedometer data at both baseline and follow-up. Also, there was no objective measurement of intervention implementation as the data for the process evaluation scores were self-reported in both teachers and parents/caregivers. It is possible that both teachers and parents/caregivers overestimated their efforts, which might have introduced bias. In addition, as not all teachers filled in all logbooks and not all parents filled in the process evaluation questionnaire, this also might have induced bias. Future studies could try to incorporate objective methods  to study process evaluation. Furthermore, teachers\u2019 logbooks did not contain specific questions regarding the implementation of the environmental changes in the classroom, which means that valuable information was not recorded. This could however be taken into account by using observations. Another limitation that should be considered is that the differences by countries regarding the process evaluation score and sub-scores of each process evaluation component were not reported. However, this manuscript already gives a general image of the link between effect and process evaluation for all countries combined. Finally, it should be acknowledged that there is no standardised way to calculate process evaluation scores. Although it was based on a method used in previous studies , 49, 50,Overall, the ToyBox-intervention had no effect on European four- to six-year-old children\u2019s steps per day. Future European interventions with the aim to increase four- to six-year-old children\u2019s steps per day should incorporate country-specific adaptations to increase the effectiveness. The process evaluation scores showed that higher teachers\u2019 process evaluation score did not cause a decrease in steps per day, while four- to six-year-old children with a lower score or from the control group did. Therefore, future interventions should search for strategies to motivate the kindergarten teachers to induce larger effects, for instance by using a participatory approach in which kindergarten teachers are involved from the beginning of the study or by providing more active toys and exercise videos. However, this should be combined with actively involving children\u2019s parents."}
+{"text": "TATES is a so-called combination test: it tests a multivariate hypothesis by combining the m p-values obtained in the m univariate tests. Specifically, TATES is based on selection of the minimal p-value among m appropriately weighted p-values, and as such tests the hypothesis that at least one of the m phenotypes is associated to the particular SNP. TATES was inspired by the GATES procedure, a gene based test of association  given two phenotypes.We gratefully use this opportunity to comment on this work.m equaled 20, the number of simulations Nsim equaled 2000, and \u03b1 was set to 0.05. These simulation settings were deemed realistic in the context of questionnaire data , and tailored to this context, featuring various realistic models to account for the phenotypic covariance structure .In the original TATES paper, the authors showed in 20 scenarios (8 of which concerned the effect of missing data) that the Type I error rate of TATES is correct when the number of phenotypes m\u2009=\u20092 and m\u2009=\u20093 phenotypes in 10 correlational settings. In these simulations, 6 out of 10 (m\u2009=\u20092), and 21 out of 30 (m\u2009=\u20093) phenotypic correlations r\u2009>\u20090.70 . They then show that, given Nsim\u2009=\u2009100,000, the Type I error rate of TATES deviated significantly from 0.05 ) in 8 of the 10 scenarios when m\u2009=\u20092, with a maximal empirical rate of 0.0553 (when r\u2009=\u20090.9343) instead of expected 0.05. When m\u2009=\u20093, the Type I error rate of TATES deviated significantly from 0.05 in all 10 presented scenarios, with a maximal empirical rate of 0.0540 . Before we dwell on the statistical and practical significance of deviations of this magnitude, we first wish to gain a more comprehensive view of TATES\u2019s Type I error rate.Aliev et al. report simulations featuring m and the correlations r between the m phenotypes. Specifically, we simulated data for m\u2009=\u20092, 4, 8, and 16, and r\u2009=\u20090.1, 0.3, 0.5, 0.7, and 0.9, resulting in 20 simulation settings in total. Note that the resulting correlational structure is compound symmetric , which is consistent with a single  factor model. We simulated phenotypic and genotypic data for N\u2009=\u20092000 subjects. Like Aliev et al., we simulated a single diallelic variant , and ran Nsim\u2009=\u2009100,000 simulations for each setting.To investigate the empirical Type I error rate of TATES more extensively, we ran additional simulations in which we varied both the number of phenotypes m weighted p-values.To broaden the present scope of our simulations and to put the TATES results into perspective, we analyzed the simulated data using TATES and three other combination tests that, like TATES, are based on selection of the minimal p-value among Bonf; Simes m univariate analyses to regress m phenotypes on a SNP, the m p-values are all Bonferroni-corrected , and then the smallest Bonferroni-corrected p-value is selected. The second combination test, which we refer to as minPNS, is similar to minPBonf, except that one does not correct for the observed number of phenotypes m, but for the effective number of phenotypes Meff. As suggested by Nyholt  and the highest p-value is weighted with the smallest weight . The Simes p-value then corresponds to the smallest weighted p-value.The third combination test is the original Simes test that TATES is a variation on Simes . In Simem and j are replaced with the effective number of p-values me and mej. Specifically, TATES weights each jth p-value pj by me/mej, and mej is calculated asj is the number of top j p-values, \u03bbi denotes the ith eigenvalue of the correlation matrix between the j p-values (which can be approximated from the correlations between the j phenotypes), and I(x) is an indicator function taking on value 0 if \u03bbi\u2009\u2264\u20091 and 1 if \u03bbi\u2009>\u20091. That is, the effective number of p-values mej among the j p-values is calculated as the observed number of p-values j minus the sum of the difference between the eigenvalues \u03bbi and 1 for those eigenvalues \u03bbi\u2009>\u20091. The value of me is equal to mej for the case that j\u2009=\u2009m, i.e., when the selection of top p-values covers all p-values. The TATES p-value then corresponds to the smallest weighted p-value. Following this procedure, the smallest original p-value is always weighted by the largest weight, while the largest original p-value is weighted by me/me\u2009=\u20091 as in that case mej\u2009=\u2009me. As the weight me/mej is always\u2009\u2265\u20091, the weighted p-values are, like in the Simes test, always\u2009\u2265\u2009the original, unweighted p-values.TATES, which is based on GATES .All four combination tests test the hypothesis that at least 1 of the 95 given \u03b1\u2009=\u20090.05. The standard error of the ML estimator of the p-value is p denotes the percentage of significant tests expected given the chosen \u03b1 , and Nsim the total number of simulations. Given Nsim\u2009=\u2009100,000 and \u03b1\u2009=\u20090.05, the CI95 thus equals \u2009=\u2009. In Table\u00a095 given Nsim\u2009=\u2009100,000 are italicized, while values falling outside the CI95 given Nsim\u2009=\u200910,000 are italicized and bold.We ran the 20 simulation scenarios for all four methods, and then established the percentage of p-values per scenario smaller than 0.05. For all four methods, these observed Type I error rates are shown in Table\u00a0mentclass2pt{minimm is small, yet slightly conservative when m is large. Simes and minPBonf are almost always conservative, and becomes more so with increasing correlations and increasing m. In contrast, minPNS is generally liberal, and especially so when m is small and correlations are high. If we sum the absolute deviations from 0.05 across all 20 scenarios, we see that overall, TATES remains closest to 0.05, while minPBonf shows the largest overall deviation, entirely due to its conservativeness. Indeed, minPBonf shows the largest undershoot, while minPNS shows the largest overshoot.The Type I error results in Table\u00a0m- and r-dependent variation around 0.05, but these deviations are small, especially compared to the other considered combination tests. The deviations reported by Aliev et al. are associated with the special case of small m and (very) high r. However, regardless of the narrow scope of the simulations by Aliev et al., one may still ask whether the observed deviations are a reason to reject the TATES procedure.Overall, the Type I error rate of TATES does show Nsim\u2009=\u20092000 , Nsim\u2009=\u200910,000, and Nsim\u2009=\u2009100,000 , the CI95\u2019s of an unbiased p-value are 0.0404\u20130.0596, 0.0457\u20130.0543, and 0.0486\u20130.0514, respectively. The empirical Type I error rates of TATES, as displayed in Table\u00a0Nsim. Aliev et al. emphasized statistical significance in assessing the Type I error results. However, in this situation, we believe that it is more important to consider the practical relevance of deviations of 0.05, 0.005, or 0.001. We are convinced that deviations of this magnitude, while statistically significant given large Nsim, cannot justify the rejection of TATES, or any other method, and believe therefore that the TATES Type I error rates give little reason for concern.The larger the number of replications in a simulation study, the more power one has to demonstrate that the empirical Type I error rate of a method deviates from the expected Type I error rate. For instance, with Bonf, minPNS, and TATES work with these p-values. However, these combination tests themselves are based on selection of the minimal p-value among m weighted p-values. So while the p-values of the m univariate tests, on which these combination tests are based, should indeed generally be uniformly distributed, the relevant question here is whether the p-values resulting from combination tests\u2019 weighted-selection procedure should be uniformly distributed as well.Aliev et al. argued that the distribution of the TATES p-values should be uniform under the H0, and that the probability distribution function should at least not exceed 1\u00a0at the low end of the distribution, i.e., around 0. They consider this a condition for the Type I error rate of TATES to be correct. It is important to note that p-values may not be uniformly distributed under the H0 in special cases  in each of the 20 aforementioned simulation settings .Figure\u00a0m p-values that they are based on are. Specifically, when all p-values are weighted with the same weight , selection of the minimal weighted p-value results (as could be expected) in a p-value distribution with a right, positive skew. When smaller p-values are weighted more heavily, the deviation of uniformity increases with increasing m and increasing correlations, with the bulk of p-values at the high end of the distribution. Indeed, as both Simes and TATES weight the highest original p-value with the smallest weight , the Simes p-value and the TATES p-value very often equal the largest p-value before weighting.Clearly, p-value distributions of methods that are based on selection of the minimal weighted p-value are not uniformly distributed under H0, even if the or deflation, depending on the number of phenotypes m and the strength of their intercorrelations r. However, we consider the observed deviations of 0.05, whether or not statistically significant, to be too small to be considered of practical concern. Note that in this commentary, we addressed the Type I error rate given an expected rate of \u03b1\u2009=\u20090.05, like Aliev et al. did. We also considered \u03b1\u2009=\u20090.01 and \u03b1\u2009=\u20090.001  and found that Type I error rates of TATES were close to expectation . While again some values deviated statistically significantly from expectation , the deviations were small and, in our view, of little practical significance.Aliev et al. set out to show that the Type I error rate of TATES procedure is incorrect by presenting results of a simulation study and a mathematical proof concerning the non-uniformity of TATES\u2019s p-value distribution. With respect to the former, we believe that the simulation results of Aliev et al. as well as our own showed that TATES\u2019s Type I error rate indeed shows slight in- With respect to mathematical proof concerning the uniformity of the p-value distribution, we believe that the assumption that the distribution of p-values of a method that is based on p-value selection should be uniform, is based on misconception. The p-values that the combination tests are based on should be uniformly distributed, but the p-values of subsequent weighted-selection-based combination tests are not expected to be uniformly distributed.All in all, if one wishes to apply a combination test to tackle a multivariate problem, we believe that TATES represents a viable option.Below is the link to the electronic supplementary material.Supplementary material 1 (DOCX 19 KB)"}
+{"text": "Scientific Reports 10.1038/s41598-017-03116-x, published online 07 June 2017Correction to: The supplementary file \u201cBayesian phylogeographic recostruction.kmz\u201d was omitted from the original version of this Article. This has been corrected in the HTML version of the Article; the PDF version was correct at time of publication."}
+{"text": "Zhang  Zhang et al. proved that the three-term PRP method has global convergence under Armijo line search technique for general functions but this fails for the Wolfe line search. The reason may be the trust region feature of the search direction that cannot be satisfied for this method. In order to overcome this drawback, we will propose a modified three-term PRP formula that will have not only the sufficient descent property but also the trust region feature.We consider the optimization models defined byentclass1pt{minimae, e.g., ). The CGlas see \u201346) and  and 1.1\\e [e.g., \u201350), whee [e.g., , 51 defin et al.  proved tn et al. , Gilbertn et al. , Toouatin et al. , and Hu n et al.  hinted tIn the next section, a modified three-term PRP formula is given and the new algorithm is stated. The sufficient descent property, the trust region feature, and the global convergence of the new method are established in Section\u00a0Motivated by the above observation, the modified three-term PRP formula is between  and Step 0:Initial given parameters: Step 1:Step 2:Get stepsize Step 3:Let Step 4:Calculate the search direction }dk+1 by .Step 5:Set It has been proved that, even for the function ice  Equation  is the sk.(2) Equations  and 2.22.2 implymentclass2pt{minimTo establish the global convergence of Algorithm (i)The defined level set (ii)f has a lower bound and it is differentiable. The gradient g is Lipschitz continuousThe function Suppose that Assumptionholds and NTT-PRP-CG-A generates the sequenceThen there exists a constantsuch thatUsing  and 2.32.3 generows from . By , , 3.1), aet al. [Himmelblau rule: Set This section will report the numerical experiment of the NTT-PRP-CG-A and the algorithm of Zhang et al.  (called }dk+1 by . Since t}dk+1 by , we onlynt}\u03b1k in  and (2.3Table\u00a0No. the test problems number. Dimension: the variables number.Ni: the iteration number. Nfg: the function and the gradient value number. CPU time: the CPU time of operating system in seconds.A new tool was given by Dolan and Mor\u00e9  to analyIn this paper, based on the PRP formula for unconstrained optimization, a modified three-term PRP CG algorithm was presented. The proposed method possesses sufficient descent property also holds without any line search technique, and we have automatically the trust region property of the search direction. Under the Wolfe line search, the global convergence was proven. Numerical results showed that the new algorithm is more effective compared with the normal method."}
+{"text": "Feature selection is an important topic in bioinformatics. Defining informative features from complex high dimensional biological data is critical in disease study, drug development, etc. Support vector machine-recursive feature elimination (SVM-RFE) is an efficient feature selection technique that has shown its power in many applications. It ranks the features according to the recursive feature deletion sequence based on SVM. In this study, we propose a method, SVM-RFE-OA, which combines the classification accuracy rate and the average overlapping ratio of the samples to determine the number of features to be selected from the feature rank of SVM-RFE. Meanwhile, to measure the feature weights more accurately, we propose a modified SVM-RFE-OA (M-SVM-RFE-OA) algorithm that temporally screens out the samples lying in a heavy overlapping area in each iteration. The experiments on the eight public biological datasets show that the discriminative ability of the feature subset could be measured more accurately by combining the classification accuracy rate with the average overlapping degree of the samples compared with using the classification accuracy rate alone, and shielding the samples in the overlapping area made the calculation of the feature weights more stable and accurate. The methods proposed in this study can also be used with other RFE techniques to define potential biomarkers from big biological data. Feature selection is one of the main data analysis techniques in data mining, which has shown its power in many applications, such as insulator detection , medicinAlong with the quick development of the high throughput techniques, genomics, metabolomics, and proteomics have been widely applied in disease study, drug research, etc. One characteristic of omics data is summarized in the expression \u201dhigh dimensions, small samples\u201d, since omics data usually have a large number of features but few samples. As genomics data, metabolomics data and proteomics data usually contain many features, it has been critical to accurately measure the feature importance and select the most discriminative feature subset. Puthiyedth et al.  presenteSupport vector machine (SVM)  is a popBasically, SVM-RFE ranks the features according to the feature deletion order during the iterations. The top ranked features which are removed in the last iteration of SVM-RFE are the most important, while the bottom ranked ones are the least informative and removed in the first iteration. For a specific application, it is not enough to obtain a feature importance ranking; it needs to determine how many top ranked features (such as genes and metabolites) should be selected. Thus, based on the selected features, we can study the disease phenotype and disease mechanism. In some studies, the top ranked features were selected according to a predetermined number ,24. In oIt is not practical to specify the number of features to be selected in advance in some applications. However, it is well known that the feature subset selected should have a powerful discriminative ability. If a feature subset has a powerful discriminative ability, then the classifier based on it usually has a high prediction accuracy rate, and the different sample groups on the selected subspace should show different distributions with little overlapping areas. Hence, this study proposes a method, SVM-RFE-OA, which determines the number of features to be selected from the feature rank of SVM-RFE by combining the classification accuracy rate and the average overlapping ratio of the samples together. In addition, to weigh the features more accurately, this study also proposes a modified SVM-RFE-OA (M-SVM-RFE-OA) algorithm, which temporally screens out the samples lying in a heavily overlapping area in each iteration. The experiments on the eight public biological datasets show the validation of the two techniques proposed.X = {n samples, C be the class label set, Label \u2260 Label \u2260 Label represents the degree that sample x mixes with heterogeneous samples, and the average Nr(x) of all samples in the dataset reflects the mixing degree of the different class samples on the current subspace. If different classes show different distributions on the current feature subspace, then there is a clear separation among different classes, and the average Nr(x) of all samples is small. If different classes show almost the same distribution, they mix together on the subspace, and the average Nr(x) of all samples is large. Hence, the average Nr(x) can express how much discriminative information the current feature subset contains.Therefore, F contains all the input features. In each loop, an SVM learning model is built based on the current feature subset F, the weight (|w|) of each feature in F is calculated according to the support vectors on the hyper-plane of the SVM classifier. The features are then ranked based on |w|, and the bottom ranked features are removed from F. This procedure is repeated until F is empty. The feature removing sequence represents the feature importance rank [F, the more important the features are. The top ranked features are those that are removed from F in the last iteration of SVM-RFE.SVM-RFE ,12 is a nce rank ,12. The F. When the procedure terminates, the feature subset corresponding to the maximal accuracy rate is kept as the final selected feature subset [Thus, we can obtain a feature rank via SVM-RFE. However, for a certain data analysis, how many top ranked features should be selected from the feature rank of SVM-RFE is still to be considered. In some cases, the number of features to be selected is decided according to prior knowledge or is simply decided subjectively . In othee subset ,16.d-fold cross validation on the training dataset can be applied to determine which feature subset is selected during the backward feature deletion, i.e., the number of the selected features is determined by the classification accuracy rate on the training dataset. However, classification accuracy reflects the discriminative ability of the feature subset based on the classifier, and the distribution of the samples can also reflect the discriminative ability of the feature subset. If different class samples mix together on the current subspace, the overlapping degree of the samples is large, and the subspace has little discriminative information. Both the classification accuracy and the overlapping degree of the samples can tell us how much discriminative information the feature subset has. They evaluate the feature subset from two different aspects, respectively. The discriminative ability of the feature subset could be evaluated more comprehensively by combining these two terms. Hence, we propose SVM-RFE-OA (see Algorithm 1 SVM-RFE-OA), which measures the feature subset during the iterations of SVM-RFE by integrating the average overlapping degree of samples and the classification accuracy rate, and selects a feature subset that has a large accuracy rate and a small overlapping degree. In each iteration, SVM-RFE-OA calculates the average accuracy rate (T_c_acc) of d-fold cross validation and the average Nr(x) (T_c_oa) of all the samples in the training data, and the feature subset having the largest \u201cT_c_acc \u2212 T_c_oa\u201d is kept as the final selected feature subset.Algorithm 1 SVM-RFE-OAX, t.Input: training dataset FS.Output: selected feature subset Beginc_acc = 0;\u2003\u2003c_oa = \u221e;\u2003\u2003F = {all input features};\u2003\u2003F| > 0) Do\u2003\u2003While  of the samples in X based on F;\u2003\u2003\u2003F by |w| in descending order;\u2003\u2003\u2003Rank the features in T_c_acc \u2212 T_c_oa > c_acc \u2212 c_oa Then\u2003\u2003\u2003If \u00a0c_acc = T_c_acc;\u2003\u2003\u2003\u2003\u00a0c_oa = T_c_oa;\u00a0\u2003\u2003\u2003\u2003FS = F;\u2003\u2003\u2003\u2003\u00a0\u00a0\u2003\u2003\u2003Endif;F = F\u2212 {t \u00d7 |F| bottom ranked features in F};\u2003\u2003\u2003\u00a0\u00a0\u00a0\u2003\u2003Endwhile;FS;\u2003\u2003Return End.In biological data analysis, defining the most informative features (such as genes and metabolites) from the large complex data is of great importance to disease diagnosis and drug study. SVM-RFE is very efficient in analysis of large complex data. However, it is quite difficult to predetermine how many top ranked features should be selected from the feature rank of SVM-RFE. The classification accuracy rate of t (0 < t < 100%) is the filter factor. In each iteration of SVM-RFE, t \u00d7 |F| bottom ranked features are removed from the current feature subset F.Nr(x) of each sample in the training data is calculated based on the current subspace F; (2) the samples with Nr(x) > 0 are temporarily set aside and are not used in SVM training in this iteration. At most, one-third of the samples in each class in the training data are screened out to make sure that there are enough samples kept for the training. Since the samples in the heavy overlapping area are shielded in the training procedure, there is little chance that overfitting occurs, and the bias becomes small.Algorithm 2M-SVM-RFE-OAX, t.Input: training dataset FS.Output: selected feature subset Beginc_acc = 0; \u2003\u2003c_oa = \u221e;\u2003\u2003F = {all input features};\u2003\u2003F| > 0) Do\u2003\u2003While (|Nr(x) for each x \u2208 X based on F;\u2003\u2003\u2003Calculate t = XX;\u2003\u2003\u2003c \u2208 C Do\u2003\u2003\u2003For each cX = {x | x \u2208 X, Label(x) = c and Nr(x) > 0};\u2003\u2003\u2003\u2003\u03b8 = |{x | x \u2208 X, Label(x) = c}|;\u2003\u2003\u2003\u2003cX| > \u03b8/3 Then\u2003\u2003\u2003\u2003If |cX based on Nr(x) in descending order;\u2003\u2003\u2003\u2003\u2003Rank the samples in tX = tX \u2212 {\u03b8/3 top ranked samples in cX};\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003Else t = Xt \u2212 XcX;\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003End if;\u2003\u2003\u2003End for;tX and F;\u2003\u2003\u2003\u00a0\u00a0Construct an SVM based on T_c_acc = accuracy rate of SVM;\u2003\u2003\u2003\u00a0\u00a0T_c_oa = average Nr(x) of the samples in tX based on F;\u2003\u2003\u2003\u00a0\u00a0T_c_acc \u2212 T_c_oa > c_acc \u2212 c_oa Then\u2003\u2003\u2003\u00a0\u00a0If \u00a0\u00a0c_acc = T_c_acc;\u2003\u2003\u2003\u2003\u2003c_oa = T_c_oa;\u2003\u2003\u2003\u2003\u2003FS = F;\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003End if;F by |w| in descending order;\u2003\u2003\u2003\u2003Rank the features in F = F \u2212 {t \u00d7 |F| bottom ranked features in F};\u2003\u2003\u2003\u2003\u2003\u2003End while;FS;\u2003\u2003Return EndIn the calculation of feature weights, only the samples on the hyper-plane of the SVM learning model are considered ,12. The http://ligarto.org/rdiaz/Papers/rfVS/randomForestVarSel.html, and the last two datasets are from www.gems-system.org. Breast2 [To show the performance of the two techniques proposed, SVM-RFE-OA and M-SVM-RFE-OA were compared with SVM-RFE where the selected feature subset was determined by the classification accuracy rate. Eight public biological datasets were used in the comparison of the three algorithms, where Breast2, Colon, Lymphoma, Prostate, Brain_data, Srbct are from  Breast2 ,28 conta Breast2 ,29 datas Breast2  dataset  Breast2 ,31 datas Breast2 ,32 conta Breast2 ,33 conta Breast2  dataset  Breast2 ,34 datashttp://www.csie.ntu. edu.tw/~cjlin/libsvm/. Linear kernel was adopted in the SVM, and t was set to 5%. In SVM-RFE-OA and M-SVM-RFE-OA, k was set to 9. Five-fold cross validation was run 50 times for each method. The average classification accuracy rates and the average standard deviations are given in SVM-RFE, SVM-RFE-OA, and M-SVM-RFE-OA were implemented in C++. SVM was obtained from First, we compared SVM-RFE-OA with SVM-RFE to examine the performance of SVM-RFE-OA. Secondly, we compared M-SVM-RFE-OA with SVM-RFE-OA, thereby examining the performance of temporally screening out the poor samples lying in an overlapping area. Both M-SVM-RFE-OA and SVM-RFE-OA combine the classification accuracy rate and the average overlapping degree to calculate the discriminative ability of the feature subset and determine the number of top ranked features to be selected. To measure the feature importance more accurately, M-SVM-RFE-OA temporarily shields the samples in the overlapping area in each iteration. The comparison between M-SVM-RFE-OA and SVM-RFE-OA shows that temporarily screening out the samples mixed with heterogeneous samples in each iteration benefits the calculation of feature weights. The comparisons between SVM-RFE and SVM-RFE-OA and between SVM-RFE-OA and M-SVM-RFE-OA validate the two techniques proposed in this study. Finally, it can be seen that M-SVM-RFE-OA outperforms SVM-RFE for all eight datasets in terms of accuracy rate and outperforms SVM-RFE for all the four binary datasets in terms of sensitivity and specificity. Especially for Brain_data, the accuracy rate of M-SVM-RFE-OA is higher than that of SVM-RFE by 10.2%.Meanwhile, SVM-RFE-OA and M-SVM-RFE-OA are more stable than SVM-RFE. The standard deviations of M-SVM-RFE-OA on accuracy rate, sensitivity, and specificity are lower than those of SVM-RFE in most cases. Hence, from two different aspects, the classification accuracy rate and the average overlapping degree of samples, which reflects the sample distribution on the feature subspace (top ranked feature subset), we can obtain a more comprehensive measurement of the feature subset. Further, temporally shielding the samples with high overlapping ratios in each iteration could make the computation of feature importance more accurate.In systems biology, it is very significant to select the most meaningful features from large complex genomics, metabolomics, and proteomics data, which could help in classifying different disease samples, studying disease mechanisms, and developing new drugs. This paper proposes two techniques of selecting discriminative feature subsets based on SVM-RFE. One is measuring the feature subset by combining the classification accuracy rate with the average overlapping degree of samples, and the other is temporally screening out the samples in a heavily overlapping area in each loop of the SVM-RFE. Experiments on eight public biological datasets show the validation of these techniques and prove that filtering out the samples that lie in the heavily overlapping area could make the measurement of feature weights more accurate."}
+{"text": "There is an error in the 7th author\u2019s name. The correct name should be Antonio Condino-Neto. As a result, the name is indexed incorrectly. The name should be indexed as Condino-Neto A."}
+{"text": "In this paper, the authors study the boundedness of multilinear Calder\u00f3n-Zygmund singular integral operators and their commutators in generalized Morrey spaces. T be a multilinear operator initially defined on the m-fold product of Schwartz spaces and taking values into the space of tempered distributions, i.e.,K belongs to the class m-if  The operator T is said to be an m-linear Calder\u00f3n-Zygmund operator if there exists a function T extends to a bounded multilinear operator from Let mentclass2pt{minimm-linear Calder\u00f3n-Zygmund operator satisfiesIt was shown in  that if m-linear Calder\u00f3n-Zygmund operators was developed by Lerner et al. [B is the ball in The theory of multiple weight associated with r et al. . Let \\dom-linear Calder\u00f3n-Zygmund operator T and a b\u20d7 is defined byT in the jth entry of T, that is,Let entclass1pt{minimad Torres  proved tentclass1pt{minima\u03c9 be a weight. The space f satisfying Feuto  introducduced in . If \\docSimilarly, the weak space duced in .Feuto proved in  that CalIn this paper, we aim to study the boundedness of multilinear singular integral operators on the product of generalized Morrey spaces. Inspired by the above mentioned works, we state our main results as follows.LetTbe an m-linear Calder\u00f3n-Zygmund operator, andIfandthenIfand at least one ofthenLetbe a multilinear commutator, withandIfthenWhen \u03c9 belongs to p, i.e., B. If E of a ball B. Since the p, we use the following notation C is a positive constant independent of the main parameters. For \u03bbB for the ball with same center as B and radius \u03bb times radius of B.We first recall the definition of Now we give the definition of p. When Let Obviously, if LetThenif and only ifwhere the conditionis understood asin the caseAssume thatsatisfiescondition. Then there exists a finite constantsuch thatBMO. For B,k, we obtainIn order to prove the results for commutators, we need the following properties of E. For III. Since II, we just consider this case: (1) Let sides of , we get(2) For }\u03bb>0, by  and , , \\documesides of , we have"}
+{"text": "In this paper, we revisit the fractality of complex network by investigating three dimensions with respect to minimum box-covering, minimum ball-covering and average volume of balls. The first two dimensions are calculated through the minimum box-covering problem and minimum ball-covering problem. For minimum ball-covering problem, we prove its NP-completeness and propose several heuristic algorithms on its feasible solution, and we also compare the performance of these algorithms. For the third dimension, we introduce the random ball-volume algorithm. We introduce the notion of Ahlfors regularity of networks and prove that above three dimensions are the same if networks are Ahlfors regular. We also provide a class of networks satisfying Ahlfors regularity. Complex networks arise from natural and social phenomena such as the Internet, the protein interactions, the collaborations in research, and the social relationships. Readers are referred to Watts-Strogatz\u2019sdBdballdfCBB)8dB and dball respectively. However the minimum box-covering problem and minimum ball-covering problem are NP-complete, which are proved rigorously in Theorem 1 and Proposition 2 respectively. The NP-completeness implies that the CBB algorithm and the random ball-covering algorithm do not have high performance, then we suggest some algorithms to improve the random ball-covering algorithm. For the third dimension df, we obtain an efficient algorithm: the random ball-volume algorithm. When do the three dimensions coincide? To answer this question, we introduce the notion of Ahlfors regularity of networks and prove that dB\u2009=\u2009dball\u2009=\u2009df (Theorem 2) if networks are Ahlfors regular. Then for Ahlfors regular networks, the random ball-volume algorithm is efficient to obtain the above three fractal dimensions.In this paper, we revisit the fractality of complex network by investigating three dimensions minimum box-covering; Kim, Goh, Kahng and Kimminimum ball-covering approach to calculate the fractal dimension of complex networks.Song, Havlin and Makse8G\u2009=\u2009 equipped with geodesic distance d, we let an l-boxA denote a subset of V such that the geodesic distance of any two points in the subset is less than l, an l-ball centered at x0 the subset Nl be the smallest number of l-boxes needed to cover V, and Bl the smallest number of l-balls needed to cover V. Suppose thatRecall some notation. Considering a network as a graph dB is the fractal dimension defined by Song, Havlin and Maksedball is defined by Gao, Hu and Diwhere box-covering, Song, Gallos, Havlin and Maksel-box-covering problem is NP-complete for any l\u2009\u2265\u20092. On the other hand, for ball-covering, which is far from box-covering in graph theory, we haveFor Theorem 1. The minimum l-ball covering problem is NP-complete for any l\u2009\u2265\u20092.random ball-covering algorithm (RBC)l is fixed, in each time t, we randomly choose one node xt in the vertex set Vt\u22121 remained in time (t\u2009\u2212\u20091), and obtain Vt by cutting all nodes in Due to the NP-completeness, for finding the feasible solution of minimum ball-covering problem, we can apply the usual Vt\u22121 and take the first node. Moreover, given some function f.In the RBC algorithm we give a random sorting for nodes in f in nondecreasing order: If f is the degree function, we can obtain degree-order ball-covering algorithm (DOBC); If volume-order ball-covering algorithm (VOBC).Given a function g in nonincreasing order, we propose the following greedy algorithm:Assume that Vt inherits from V0\u2009=\u2009V.Set For a function volume-greedy ball-covering algorithm (VGBC). Let g(x)\u2009=\u2009deg(x), we have the degree-greedy ball-covering algorithm (DGBC).When Bl\u2009\u2264\u2009Nl\u2009\u2264\u2009Bl/2, hence l can be taken large enough, we haveIn the point of view on fractal geometry, the box dimension is independent of the geometric shapes of covering, such as ball or box. It is easy to check that Proposition 1. The fractal dimensions dBand dballw.r.t. the box covering and ball covering respectively are the same.l large enough, and the upper bound However, for real networks with small-world effect, we can not take Example 1. Through above 5 algorithms  be the average cardinality of nodes in a ball with radius l, suppose thatBased on Shanker\u2019s workdf the volume dimension. Please also see generalized volume dimensionet al.We call df related to average ball-volume and propose the random ball-volume algorithm for networks. Compared with the minimum box-covering algorithm and the minimum ball-covering algorithm, we have the following algorithm to calculate the average volume of ball with size l approximately.We will discuss the volume dimension Random ball-volume algorithm (RBV) (for fixed size l):x in the network.Randomly take a node \u03bd).Calculate the volume l-balls.Repeat the steps 1\u20132 and obtain average volume of random df\u2009=\u20095.833  measure supported on a compact subset E, denoted by spt \u03bc at point x be defined by H\u2009(\u00b7) isIn this paper, we try to find out the farther connection between the fractal networks and fractal geometry. Recall some classical result on fractal dimension. We find out that many dimension results have measure versions. Suppose P\u2009(\u00b7)25\u03bc such that Ahlfors regularity assumption on the measureThat means for Hausdorff dimension, we have the corresponding measure version. When replacing c is an independent constant.where natural measure on a graph G\u2009=\u2009. For \u03bd(\u03a9) be the cardinality of \u03a9, which is called the volume of \u03a9. We say that {Gt}t is a family of growing networks, i.e., Gt+1 contains node set of Gt, and neighbors of Gt are still neighbors of Gt+1. When {Gt}t is growing, we let \u03bdt(\u03a9) denote cardinality of Vt is the node set of Gt.We give a Remark 1. When takingas the sum of degrees of nodes in \u03a9, Wei et al.obtain the generalized volume dimension.Definition 1. Given s\u2009>\u20090, if we call the network an Ahlfors s-regular network. When {Gt}tis growing, we call {Gt}tAhlfors s-regular networks, if there is an independent constant c such that for allr\u2009<\u2009diam(Vt) and t,When the diameter of network is large enough, we haveTheorem 2. df\u2009=\u2009dball\u2009=\u2009dB\u2009=\u2009s if the network or growing networks are Ahlfors s-regular.When the networks are regular, we can use RBV algorithm to obtain their fractal dimensions efficiently.s-regular networks and growing trees in Now, we obtain a rule (rule 1) of generating Ahlfors Theorem 3. The growing self-similar trees defined above are Ahlfors s-regular with s\u2009=\u2009log\u20095/log\u20093. Therefore, we haveWe also have rule 2 and growing trees in t, we take rule 1 if xt\u2009=\u20091, else take rule 2. For example, if the sequence is G1, G2, G3 as in Fix an infinite sequence Moran tree with mixed rules. For this Moran tree without self-similarity, we have random growing networks, for each time t, we can choose rule 1 in probability p and rule 2 in probability 1\u2009\u2212\u2009p.Then we can generate a The rest of paper is organized as follows. Section 2 is devoted to the rigourous proofs on the NP-completeness of minimum ball-covering problem (Theorem 2) and minimum box-covering problem (Proposition 2). Section 3 is the preliminary on the Ahlfors regularity of fractal geometry, including covering inequality and self-similar fractal. In this section, we also recall the fact that the open set condition of self-similar fractal implies the Ahlfors regularity of fractal measure. Replacing the fractal measures by the cardinalities of subsets of networks, we obtain the Ahlfors regularity of networks. In Section 4, we prove Theorem 2 by using covering inequality shown in Section 2, and obtain Ahlfors regularity of a class of self-similar network (Theorem 3) by constructing bilipschitz mappings from a self-similar fractal, satisfying the open set condition, to self-similar networks, and estimating the cardinalities of balls of graph from the Ahlfors regularity of the fractal measure.Recall some notation of computer science. For an alphabet Definition 2. Let L and M be languages. ThenL is reduced to M) if there is a functionsuch thatWe say that some languageNP-complete, ifis for allBoolean satisfiability problem is NP-complete.The concept of NP-completeness was introduced in 1971 by CookClique covering problemG\u2009=\u2009, positive integer kInput: graph V is the union of k or fewer cliques, where a clique is a subset of vertices of G such that its induced subgraph is complete.Property: Set covering problemU and a family S of subsets of U, positive integer kInput: universe k or less, where a set covering is a subfamily U.Property: there is a set covering of size In 1992, KannDominating set problemG\u2009=\u2009, positive integer kInput: graph k or fewer nodes, where a dominating set is a subset D of V such that every vertex not in D is adjacent to at least one member of D.Property: there is a dominating set of In this section, we will show the following two problems are NP-completes.l-ball-covering problemG\u2009=\u2009, positive integer kInput: graph V is the union of k or fewer l-balls.Property: l-box-covering problemIn 1972, KarpG\u2009=\u2009, positive integer kInput: graph V is the union of k or fewer l-boxes.Property: l\u2009=\u20092, then l-ball-covering problem is exactly the dominating set problem, which is NP-complete.If l\u2009=\u20093, given a undirected graph G\u2009=\u2009 as in G.z (in red) in the edge x\u2009~\u2009z, z\u2009~\u2009y and x, y are not neighbors in For any We add a Hub (in blue) to connect all median points.Insert sub-median-point (in yellow) for every edge between one median point (in Step I) and Hub.We construct a leaf node (in pink) and the median point (in green) between leaf node and the Hub.If We have the followingClaim 1. There is a dominating set of k or fewer nodes in G if and only ifis the union of (k\u2009+\u20091) or fewer 3-balls.For any nodes V is a 3-ball centered at the Hub.The subset of all nodes not in V is 5, that means any 3-ball can not contain the pink node and any node of V simultaneously.The geodesic distance between the pink node and any node in D with u in For any 3-ball To verify this claim, we notice the following facts.G and there is a minimum 3-ball covering Suppose In fact, we have i\u2009\u2264\u2009s. Applying the fact (b), we see that there exists a 3-ball covering with (s\u2009+\u20091) balls. Hencefor any G, where On the other hand, considering the minimum 3-ball covering l\u2009=\u20093.Then (1) follows from (2) and (3). Then Theorem 1 is proved for l\u2009\u2265\u20094, we have the similar construction during reduction. In fact, we insert (l\u2009\u2212\u20092) median points into each edge of G, add a Hub to connect all median points, insert (l\u2009\u2212\u20092) sub-median-point for every edge between one median point and Hub. Finally, we construct the leaf node and connect it to the Hub, insert (l\u2009\u2212\u20092) the median point between leaf node and the Hub. See l\u2009=\u20094.For Remark 2. To prove one problem is NP-complete, we always find a reduction from a known NP-complete problem to our problem. On the other hand, we can always construct a reduction from our (NP) problem to a known NP-complete problem due to the definition of NP-completeness.We give a proof of the following fact which is pointed out by Song, Gallos, Havlin and MakseProposition 2. For any fixed size l, the l-box-covering problem is NP-complete.Proof. If l\u2009=\u20092, l-box-covering problem is exactly the clique covering problem, which is NP-complete.l\u2009=\u20093, given a undirected graph G\u2009=\u2009, as in G\u2032\u2009=\u2009 in polynomial time with respect to the size of G.z (in red) in the edge  with degree 2, i.e., x\u2009~\u2009z, z\u2009~\u2009y and x, y are not neighbors in G\u2032.For any We add a Hub (in blue) to connect all median points.We construct a leaf node (in pink) adjacent to the Hub.If We have the followingClaim 2. V is the union of k or fewer cliques if and only if V\u2032 is the union of (k\u2009+\u20091) or fewer 3-boxes.G\u2032 their geodesic distance For any nodes V is a 3-box.The subset of nodes not in V is 3.The geodesic distance between leaf node (in pink) and any node in To verify this claim, we notice the following facts.G such that s is minimal one. Suppose there is a minimum 3-box covering G\u2032. We only need to show thatSuppose Ai is a 3-box in G\u2032 for any i\u2009\u2264\u2009s. Applying the fact (ii), we see that there exists a 3-box covering with (s\u2009+\u20091) boxes. HenceIn fact, we have G where On the other hand, it follows from fact (i) that Then (4) follows from (5) and (6).l\u2009\u2265\u20094, we have the similar construction during reduction. See l\u2009=\u20094.\u25a1For X, d), let a \u03b4-ball centered at x0 be an open ball \u03b4-cube a cube of Euclidean space with side length \u03b4, a \u03b4-box B is a subspace of X such that its diameter less than \u03b4, i.e., d\u2009<\u2009\u03b4 for all x, Given a compact metric space \u2009\u2265\u2009d\u2009\u2212\u2009d\u2009\u2265\u20092\u03b4\u2009\u2212\u2009\u03b4\u2009=\u2009\u03b4. That means i. Now, we obtain a new packing family of P\u03b4\u2009\u2265\u2009B\u03b42.\u03b4-balls, then d\u2009\u2265\u2009\u03b4 for all xi, xj)\u2009\u2265\u20092\u03b4 for all \u03b4/2-balls \u03b4/2-ball contains at most one points in \u03b4/2-ball is less than \u03b4and d\u2009\u2265\u2009\u03b4 for all xi must be contained in some \u03b4/2-ball. Therefore, we obtain P\u03b4\u2009\u2264\u2009B\u03b4/2.\u25a1Assume We also haveBy the above inequalities, the classical result25In fact, in the above formula, we take upper box dimension Si is a similarity with ratio ri, i.e., x, Ri is orthogonal. That means any similarity is the compositions of homothety, translation and orthogonal transformation.Let OSC) holds if there exists a non-empty open set V such thatWe say that the open set condition (\u03bc (self-similar measure) satisfying H\u2009K\u2009=\u2009dimB\u2009K\u2009=\u2009s, and there is a constant C\u2009\u2265\u20091 such that for all r\u2009\u2264\u2009|K| (the diameter of K),Let E is said to be Ahlfors s-regular\u03bc supported on E satisfying (8). That means the self-similar set satisfying the OSC is Ahlfors regular.A compact set We introduce a special self-similar fractal on   and 15. where orthogonal. matrixes V be the interior of polygon with vertexes , , , ,  and . Then (7) holds for m\u2009=\u20095  and B\u2009=\u2009. Let Let Remark 3. One node may have distinct codingsandifWe also notice that each node has three codings at most.x, Two different nodes t be the geodesic distance on Gt.Let dd\u2009>\u20090 independent of the index i such that d\u22121bi\u2009\u2264\u2009ai\u2009\u2264\u2009dbi.We denote Now, we will prove the following importantLemma 2. There is a constant c\u2009>\u20090 independent of t such thatProof. Supposewhere where Case 1. If Then (9) follows in this case.\u25a1Case 2. If D\u2009=\u2009, let \u03b8\u2009\u2265\u2009\u03b80\u2009(>0). Now,For  exists   such thawhich impliesWe also have On the other hand,y1, D) and . By the self-similarity, now we only need to prove the case when by the tree structure. It follows from (10) and (11) that we only need to verify (9) for the pairs  follows.\u03bc with respect to the vector  is Ahlfors s-regular for s\u2009=\u2009log\u20095/log\u20093.Since the OSC holds, then the self-similar measure It follows from the above lemma and Remark 3 thatVt\u2009=\u20095t\u2009+\u20091. Therefore, we havewhere #t. Now, the growing networks {Gt}t are Ahlfors s-regular.Notice that the constant in (12) is independent of df and propose the random ball-volume algorithm, which has performance better than the above five minimum covering algorithms due to the NP-completeness. Applying the notion of Ahlfors regularity from fractal geometry, we prove that dB\u2009=\u2009dball\u2009=\u2009df\u2009=\u2009s if the network is Ahlfors s-regular. Finally, we investigate the Ahlfors regularity of a class of self-similar trees and random trees which come from the self-similar fractals and Moran fractals respectively. Although we only prove Theorem 3 for self-similar tree of model 1, but our approach can be applied to many self-similar trees, Moran tree and random trees. Essentially, our approach is to embed our networks into a self-similar (or Moran) fractal (on Euclidean space) satisfying the open set condition, using the Ahlfors regularity of corresponding self-similar (or Moran) measure, we can estimate the volume of balls in networks.We focus on the NP-completeness of minimum ball-covering problem, propose some heuristic ball-covering algorithms such as GOBC, GDBC, VOBC and VGBC, and compare these algorithms with usual RBC algorithm. Inspired by the notion of measure on fractal, a natural measure on the finite graph is obtained such that the measure of every subset is the cardinality of subset. Based on this measure, we revisit the volume dimension How to cite this article: Wang, L. et al. On the Fractality of Complex Networks: Covering Problem, Algorithms and Ahlfors Regularity. Sci. Rep.7, 41385; doi: 10.1038/srep41385 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "We generate the THz wave on the surface of an unbiased GaAs crystal by illuminating femtosecond laser pulses with a 45\u00b0 incidence angle, and investigate its propagation properties comprehensively both in a near-field and in a far-field zone by performing a knife-edge scan measurement. In the near-field zone, i.e. 540 \u03bcm away from the generation point, we found that the beam simply takes a Gaussian shape of which width follows well a behavior predicted by a paraxial wave equation. In the far-field zone, on the other hand, it takes a highly anisotropic shape; whereas the beam profile maintains a Gaussian shape along the normal to the plane of incidence, it takes satellite peak structures along the direction in parallel to the plane of incidence. From the comparison with simulation results obtained by using a dipole radiation model, we demonstrated that this irregular beam pattern is attributed to the combined effect of the position-dependent phase retardation of the THz waves and the diffraction-limited size of the initial beam which lead to the interference of the waves in the far-field zone. Also, we found that this consideration accounting for a crossover of THz beam profile to the anisotropic non-Gaussian beam in the far-field zone can be applied for a comprehensive understanding of several other THz beam profiles obtained previously in different configurations. Quantitative information such as absorption coefficient or optical conductivity can be retrieved through a well-established THz time-domain spectroscopy technique which is often combined with far-field or near-field microscopy11. To precisely extract quantitative optical information, by the way, it is important to have an accurate knowledge regarding the beam profile at the interaction points of light with optical elements including the sample specimen of interest, and accordingly there have been extensive experimental and theoretical investigations about the THz beam pattern depending on its generation mechanism14. For the THz wave generated by the optical rectification in a nonlinear optical medium, e.g., ZnTe, Lin et al.16 demonstrated that a Gaussian aperture model successfully accounts for THz amplitude profile in both near-field and far-field regions. For the THz wave generated by a surge current in semiconductors such as GaAs and InAs, there have been several studies to characterize the beam profile, to our surprise, with no clear consensus made until now. Jepsen et al.17 reported that the THz pulse generated from the GaAs-based photo-conductive antenna has the Gaussian radiation pattern in the far-field zone. Reiten et al.18 performed the similar beam characterization and claimed that the THz beam consists of not only the simple Gaussian mode but also higher-order Laguerre-Gauss modes which later they attributed to a coupling effect of the THz pulse to a focusing optic19. Meanwhile, Jin et al.20 reported that the THz pulse emitted from the photo-Dember effect in InAs has the non-Gaussian amplitude distribution of which details are strongly frequency-dependent.Over the last few decades, an electromagnetic wave at the THz frequency has received a significant attention as it can provide a useful spectroscopic access to unveil the collective behaviors of electrons entangled with other degrees of freedom, i.e., orbital, spin, and latticey-axis, i.e., normal to the plane of incidence, follow the Gaussian model in both the near-field and the far-field zone. On the other hands, along the x-axis, i.e., parallel to the plane of incidence, we find that the field pattern becomes strongly irregular as the beam propagates into the far-field zone. We discuss these anisotropic field distributions of the THz wave in terms of a numerical approach based on the dipole radiation model.In this paper, we examine the beam profile evolution of the THz wave as it is generated from the un-biased free-standing semi-insulating (SI) GaAs, and propagates into the near-field zone and also to the far-field zone. We find that field patterns along the 22. The model begins from spreading 1000 electric dipole moments with an interval of 1.2 \u03bcm along the x-axis as shown in Fig.\u00a0x-direction. Here, we assume that the THz generation by a transient dipole and the THz propagation occur with the same speed, and the position-dependent phase variations are determined mainly by a simple geometrical factor, i.e., incidence angle of the pumping beam. Therefore, we consider a linear variation of the oscillation phase of the dipole moment with a difference by 4\u2009ps for two dipoles located at each end  of SI-GaAs, a refraction of the beam can be clearly recognized from the color distribution. In particular, when we plot a line profile of the field magnitude along the x-direction  is employed as the THz light detector.In the actual experiment, THz wave is generated by illuminating a femtosecond laser pulse on to the un-biased freestanding GaAs (001) crystal with an incidence angle of 45 degrees. The pumping beam has a wavelength 800\u2009nm, and its photon energy 1.55\u2009eV is slightly larger than the band gap energy of SI-GaAs. The pumping power is 160\u2009mW, and the fluence is 0.25\u2009J/cm3. THz wave is generated at the top surface of the emitter and propagates into its inside. By sliding this assembly of the homogenous emitter and the knife edge, we can mimic the conventional knife-edge experiment24; the THz wave is largely reflected from the coated region, and it is detected in a reflection geometry. From this, we can investigate the beam profile at the back side of the emitter which is 540 \u03bcm (\u03b4) away from the generation point.Let us then examine the THz field pattern in the near-field zone. Since the near-field zone is still too close to put a conventional knife edge, we here introduce an alternative approach. Figure\u00a01) is the THz wave generated backwardly at the emitter surface, and the latter one (E2) is the THz wave generated forwardly and reflected backwardly at the backside of the emitter. Hence the temporal separation of about 12\u2009ps exactly corresponds to the traveling time of the THz wave inside of the medium with an effective thickness of 540 \u03bcm. With a variation of the position of the knife edge \u03c6x, whereas E1 remains the same, as expected, E2 exhibits dramatic changes; whereas E2 has an almost featureless waveform at \u03c6x\u2009=\u20090\u2009mm, E2 increases its magnitude with an increase of \u03c6x, and it reaches to have a maximal magnitude of about one-third of E1 at \u03c6x\u2009=\u20092.8\u2009mm. Actually, E2 at \u03c6x\u2009=\u20092.8\u2009mm can be well reproduced by considering a full reflection of the THz wave at the emitter-Al interface. And, a small electric field at \u03c6x\u2009=\u20090\u2009mm may originate from the tiny air-gap formed between two SI-GaAs layers.Figure\u00a02 with a variation of \u03c6x. We pick up the magnitude at 0.5\u2009THz from E2 spectra and display its \u03c6x-dependence in Fig.\u00a0M/d\u03c6x. Although it does not fully reflect the original beam shape, it helps us to get a rough idea about the beam shape without any model fitting; dM/d\u03c6x shows the Gaussian-like profile, and its width seems to have about 1.8\u2009mm, in accordance with the length scale of the THz beam waist at the generation point, i.e., Figure\u00a0\u03c6x. And, this is a typical feature of the simple Gaussian beam as demonstrated in Fig.\u00a0From these knife-edge experimental results obtained in the near-field zone, we examine THz beam profiles in more detail particularly with a variation of the frequency. Figure\u00a0mentclass2pt{minimM0 is the maximum magnitude at . To treat the anisotropic shape of the THz beam arising from a 45\u00b0 incidence angle, we set the x-axis is larger than that along the y-axis by a factor of We fit these results by adopting a Gaussian beam profile and display the full-width at half maximum as a function of the initial beam size and the light frequency in Fig.\u00a0THz Fig.\u00a0. To accoR\u2009=\u2009\u03c0n along both x- and y-directions to obtain the two-dimensional profile of the beam intensity. Figure\u00a0L\u2009=\u20093, 4, and 5\u2009cm. In each case, the magnitude and the corresponding derivation profiles dM/d\u03c6i=x,y are shown at two frequencies, i.e., at 0.3 and 0.5\u2009THz. For a guide to the eye, we also present solid lines following data points which are obtained by a simple polynomial fit. At L\u2009=\u20093\u2009cm, the magnitude changes smoothly with seemingly no discernible anomalies along both x- and y-directions. Accordingly, a global maximum appears in deviation profiles dM/d\u03c6i=x,y. Actually, such features evoke the Gaussian profile that we confirmed in the near-field zone. At L\u2009=\u20094\u2009cm, significant changes are observed particularly from dM/d\u03c6i=x,y; whereas the scan results along the y-axis look similar with the results at L=3\u2009cm, dM/d\u03c6i=x exhibits a highly off-centered global maximum with double local maxima  the THz beam profile is given anisotropically in the far-field zone, e.g., at L\u2009\u2265\u20094\u2009cm, (ii) its distribution along the x-direction strongly deviates from the simple Gaussian model, and (iii) details of the beam profile exhibit a large variation as the beam propagates. These observations at L\u2009\u2265\u20094\u2009cm cannot be explained by the Gaussian beam propagation theory, and suggest that some intriguing physical effects come into play when THz beam propagates from the near-field to the far-field zone.We now discuss how the THz wave evolves further during its propagation in the far-field zone. In this far-field characterization, we locate a conventional knife-edge at the distance int Fig.\u00a0, and varima Fig.\u00a0. Upon a x- and y-axes individually, and then multiply them to retrieve the two-dimensional magnitude profile. Figure\u00a0L\u2009\u2264\u200952\u2009mm. Here, the frequency is set to 0.5\u2009THz. To focus on the amplitude distribution, we normalize beam widths with respect to the width of the ideal Gaussian beams at the corresponding propagation distances. At L\u2009=\u20094\u2009mm, the THz beam shows an elliptical shape which simply reflects an initial beam shape at the source point. As L increases, the magnitude profile becomes inhomogeneous particularly along the x-axis; a major peak becomes more narrowly defined, and satellite peaks are clearly discernible being located nearby. Interestingly, the beam magnitudes along the y-axis do not seem to undergo significant changes, sharply contrasting to the x-axis case.To get an insight into the obtained results, we compute two-dimensional beam profiles in the far-field regime based on the electric dipole model as done for the generation point. Note that the basic details of the simulation are the same with those for the beam profile at the generation point demonstrated in the section 2. By the way, we obtain one-dimensional profiles along x- and y-directions. Figure\u00a0L\u2009=\u20094, 28, and 52\u2009mm. At L\u2009=\u20094\u2009mm, both quantities exhibit smooth position-dependent variations whereas the results along the x-axis reflect a broader profile as expected (Fig.\u00a0L increases, although the results along the y-axis remain with no discernible change, the profiles along the x-axis exhibit highly irregular position dependences; the derivative profiles become asymmetric and satellite peaks appear as expected from the amplitude distribution shown in Fig.\u00a0To make a more direct comparison with the experimental results, we estimate the magnitude profiles of the THz beam as in the knife-measurements along the ted Fig.\u00a0. As L inL\u2009<\u20094\u2009mm imply that the Gaussian magnitude distribution of the point dipoles plays an important role in determining the THz beam profile up to the certain distance in the far-field zone. To account for anisotropic non-Gaussian beam profiles observed at L\u2009>\u20094\u2009mm, on the other hand, it is clear that we have to consider the phase distribution as well as the amplitude distribution of the point dipoles. Along the x-axis, several satellite peaks appear. They are attributed to the position-dependent phase retardation of the THz waves generated from each dipole due to the grazing incidence of the pumping beam. As soon as the surge-current-induced electric dipole is created, the THz wave is radiated as an electric dipole radiation with its oscillation phase given uniformly irrespective of the generation point (Fig.\u00a0y-axis at the same value of L. Namely, along the y-axis, the phase of the point dipole or, equivalently, the THz wave is given homogeneously, and hence the THz beam profile is determined mainly by the magnitude distribution of the point dipoles following a propagation theory of the simple Gaussian beam (Fig.\u00a0Two-dimensional Gaussian profiles observed at int Fig.\u00a0. Since tint Fig.\u00a0. It shoueam Fig.\u00a0. As we i20, and we consider that each result could be attributed to the phase contribution for the normal19 and grazing incidence20, respectively. In the near-field zone, on the other hand, the THz profile is determined rather by the pumping beam profile leading to the Gaussian distribution as observed16.We examined how the beam profile of the surge-current-induced THz wave, generated at the surface of the unbiased GaAs, evolves as it propagates from the source point to the near-field zone, and also to the far-field zone. During its propagation, we observed a clear crossover behavior of the beam profile from the Gaussian shape in the near-field zone to the anisotropic non-Gaussian shape in the far-field zone. From the comparison with the simulation results based on the point-dipole radiation theory, we concluded that the THz wave properties are determined basically by the intensity profile of the pumping beam, incidence angle, and its size; the THz profile in the near-field zone is determined by the magnitude distribution of the point dipoles, i.e., the pumping beam intensity profile, and the THz profile in the far-field zone is influenced not only by the magnitude distribution but also by the phase distribution of point dipoles. As a result, we expect to observe a deviation from the Gaussian form more easily by increasing the incidence angle and also by reducing the pumping beam size particularly down to the diffraction-limit of the THz wave. We emphasize that this understanding can be applied to other experimental results characterizing beam profiles of THz waves. In the far-field zone, the THz wave has been reported to exhibit both the Gaussian and non-Gaussian shape"}
+{"text": "In this paper, we consider a size-dependent renewal risk model with stopping time claim-number process. In this model, we do not make any assumption on the dependence structure of claim sizes and inter-arrival times. We study large deviations of the aggregate amount of claims. For the subexponential heavy-tailed case, we obtain a precise large-deviation formula; our method substantially relies on a martingale for the structure of our models. G on X and \u03b8. The claim arrival times are Consider the following renewal risk model. Let F on n-fold convolution of F. Clearly, (F. See Embrechts et al. [We study large deviations of t}St\u2217 in . We onlymentclass2pt{minimOur main result is given now.Consider the aggregate amount of claimsin (assume thatandThen, for arbitrarily givenwe have uniformly for allt}St\u2217in , assume X and \u03b8, which was firstly proposed by Albrecher and Teugels [et al. [et al. [et al. [X given \u03b8; see also Li et al. [\u03b8\u0303 such thatx, they studied the large deviations of the aggregate amount of et al. [A non-standard renewal risk model with dependent components  Teugels  and furt [et al. , Cossett [et al. , Badescu [et al. , and amo [et al.  introduci et al. . In parti et al.  considermentclass2pt{minimX given \u03b8, e.g., Chen and Yuen [We now comment on the approaches used in this work. First, in Theorem\u00a0and Yuen  made theThe rest of the paper is organized as follows. Section\u00a0Throughout this paper, for two positive functions To obtain our desired results, we need to mention the following useful lemma.Consider the renewal counting processin (Under the assumptionThen, for anywe havet}Nt\u2217in . Under tu and t,First, for arbitrarily et al. [By }F\u2208S and , we needmentclass2pt{minimn,Therefore,By , therefoence, by  and (3.5As was remarked by a few researchers in the area, precise large-deviation results of size-dependent renewal risk models are particularly useful for evaluating some risk measures such as the conditional tail expectation of the aggregate amount of claims from a large insurance portfolio. Finally, we would like to point out that equation  agrees wfined by  does not"}
+{"text": "In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD\u2019s robustness and wide applicability. In many application domains, such as denoising, classification and compression of signals \u20133, it isdictionary matrix n < m) with columns di, i = 1,\u2026,m, called atoms, and a signal vector y as linear combination \u2211ixidi with as few as possible non-zero coefficients sparse approximation problem consists in finding y \u2212 Dx\u20162 under the constraint that its \u21130-norm \u2016x\u20160 \u2254 #{i: xi \u2260 0} be at most a threshold x is k-sparse. This problem is combinatorial in nature and hence NP-hard  \u2254 {1,\u2026,m} the set of first m positive integers and let I \u2282 [m] denote a set of indices for matrix columns or rows. Given any index set I of size s = |I|, let D formed by the columns indexed by I, that is DI = {di}i \u2208 I, and let X formed by the rows indexed by I; hence s is the size of atom group DI. In this setting, we can decompose the product DX into the sumDIXI dependent on the group I and a matrix DIcXIc dependent on the complement Ic = [m] \\ I. Therefore, the objective function in Basically, in the proposed method R-SVD, after splitting the dictionary DIXI in E \u2254 Y \u2212 DIcXIc, one can consider the optimization problemDI of unit \u21132-norm atoms.Now, after isolating the term R (i.e. RTR = I) applied on DI, namely R of order n, called orthogonal group O(n) (not to be confused with group of atoms), can be partitioned into the special orthogonal subgroup SO(n) formed by proper rotations, i.e. those with detR = 1, and the set O(n) \\ SO(n) of improper rotations (or rotoreflections), i.e. those with detR = \u22121. Therefore, the search for such an optimal transformation can be stated as the following minimization problemE and H we omit the dependence on I. The Orthogonal Procrustes problem  = I1 \u2294 I2 \u2294 \u2026 \u2294 IG into G subsets,at each dictionary update iteration (Step 2) partition the set of column indices  w.r.t. the usage of atom di, computable as \u21130-norm of the i-th row in X. For sake of simplicity we set uniformly the group size to s = |Ig| for all g, possibly except the last group (G = \u2308m/s\u2309) if m is not a multiple of s: |IG| = m \u2212 Gs. Regarding this choice, we have seen experimentally that our method is agnostic w.r.t. grouping criteria such as random balanced grouping, cumulative coherence based partitioning, and clustering by absolute cosine similarity.These updates can be carried out either in parallel or sequentially with some order. We have chosen the sequential update with ascending order of atom popularity, i.e. sorting the indices G groups, the method moves to the next iteration, and goes on until a stop condition is reached . The main steps can be summarized in Algorithm 1 .After processing all Algorithm 1 R-SVDInput:Output:YD picking m examples from Y at random1: Initialize dictionary repeat2: xi\u20160 \u2264 k for i = 1,\u2026,L3:\u2003Sparse coding: m] = I1 \u2294 I2 \u2294 \u2026 \u2294 IG sorting by atom popularity4:\u2003Partition indices [forg = 1,\u2026,Gdo5:\u2003J = Ig6:\u2003\u2003E = Y \u2212 DJcXJc7:\u2003\u2003H = DJXJ8:\u2003\u2003s SVD EHT = U\u03a3VT9:\u2003\u2003DJ = RDJ10:\u2003\u2003end for11:\u2003returnD, X12:\u2003until stop condition13: Notice that in our method the renormalization of atoms to unit length at each iteration is not necessary since they are inherently yielded with such a property from this Procrustes analysis, and hence in practice some large part of renormalizing computations as in ILS-DLA  and K-SVDI can be described as follows. Let us pre-compute EHT undergoing the SVD can be computed asDI and DIc come from previous update step, and the term XIYT is the submatrix formed by rows I of XYT, while XI(XT)Ic by rows I and columns Ic of XXT. With elementary matrix products this computation requires O(sn(n + m \u2212 s)) flops, which is lower than O(nmL) since s < n < m \u226a L.A useful computational speedup in the update of every group HET \u2264 rankH \u2264 s, it is not necessary to obtain the full SVD of HET, but rather truncate the decomposition to the first s singular vectors ui, vi: O(n2 log s) flops. The computation of HET and its SVD is repeated G = \u2308m/s\u2309 times. The computational time of R-SVD is dominated by the pre-computation of XYT and XXT, and therefore taking into account the sparsity of matrix X the asymptotic estimate for one iteration of R-SVD is TK-SVD = O((k2 + n)mL). Note that, when s = \u03a9(k) we have TR-SVD is lower than TK-SVD.Notice that, since rank rithm by  based ons defined above. Then we apply the method on synthetic data conducting extensive experiments on both R-SVD and K-SVD using OMP as sparsifier. A further investigation is conducted on two different sparse decomposition methods, namely k-Limaps and SL0, and alternative dictionary learning methods, namely ILS-DLA by Engan et al. [In this section we test the proposed R-SVD algorithm devoting at first an in-depth analysis to how to choose the group size n et al.  and OSDLn et al. .\u21132-norm. The training set L linear combinations of k dictionary atoms selected at random, and by adding white Gaussian noise matrix N with various signal-to-noise ratio (SNR), i.e. Y = DX + N. We measure the performances of the algorithms in terms of the reconstruction error  expressed as Following , the dics affects both reconstruction quality and running time. In order to give some insight on this parameter, we run R-SVD algorithm on synthetic training sets by setting L = 8000, k = 5 and SNR = 30 dB for noise N and letting s range in the interval 1 \u00f7 25. Notice that when s = 1, our method is similar to K-SVD [It is naturally expected that the group size to K-SVD  except iSNR (solid curve), and the computational times of both R-SVD (dashed curve) and K-SVD (dotted line), all averaged over 100 trials. It can be noticed that R-SVD method behaves better near the value s = 10. We thus choose this tradeoff setting for the experimental assessments of the method in the following sections.In L = 10000 and sparsity k = {5, 10}. The algorithms K-SVD and R-SVD are run for T = 200 dictionary update iterations, that turns out to be sufficient to achieve empirical convergence of the performance measure. For each experimental setting we report the average error over 100 trials.In order to test the R-SVD method and compare it to the K-SVD algorithm, we first run experiments on random training instances. We consider dictionaries of size 50 \u00d7 100 and 100 \u00d7 200, dataset of size up to SNR values on synthetic vectors Y = DX + N, varying the additive noise SNR = 10, 30, 50, \u221e (no noise) dB. It can be seen that, after an initial transient, the gap between R-SVD and K-SVD increases with the iteration count, establishing a final gap of 2 dB or more in conditions of middle-low noise power (SNR \u2265 30 dB).In T = 200) reconstruction error ESNR, varying L in 2000 \u00f7 10000, noise SNR in 0 \u00f7 60 dB, and in case of no noise. Dictionary sizes, sparsity and number of trials are set as above. When the additive noise power is very high (eg. SNR = 0 or 10 dB) the two methods are practically comparable, probably because the presence of significant noise would mislead any learning algorithm. On the other hand, when the noise is quite low the R-SVD algorithm outperforms K-SVD with a gap up to 3 dB.In order to explore the behavior of R-SVD and K-SVD in a fairly wide range of parameter values, we report in D from the noise-affected data Y. This is accomplished by maximizing the matching between atoms di of the original dictionary with atoms Moreover, it is useful to evaluate the number of correctly identified atoms in order to measure the ability of the learning algorithms in recovering the original dictionary is small , i.e. prIn k-Limaps [So far we have used OMP as sparsifier for both R-SVD and K-SVD methods. Here we investigate R-SVD\u2019s performances adopting the sparse decomposition techniques k-Limaps  and SL0 k-Limaps . The fork-Limaps ), while http://ee.sharif.edu/~SLzero/) is set up with scale parameter \u03bc0 = 2 and \u03c3 decrease factor equal to 4/5, while k-Limaps is initialized setting to 100 the maximum number of iterations. The experiments of R-SVD and K-SVD incorporating k-Limaps and SL0 were conducted under the same conditions of subsection 3.2. The resulting gap between final ESNR\u2019s is shown in Each method has been applied to compute line 3 of Alg. 1, R-SVD, and the corresponding operation in the K-SVD algorithm. The SL0  versus the iterative alternating scheme method ILS-DLA, and the on-line dictionary learning method OSDL by Sulam et al. .L = 5000, 10000, dictionaries of size 64 \u00d7 128 (where the atom size is a perfect square as required in OSDL), various levels of additive noise , and sparsity set to 10% of the atom size. The methods are run for 200 dictionary update iterations and the obtained results are averaged over 100 trials. In ESNR of R-SVD and each of ILS-DLA and OSDL, respectively. We can notice that R-SVD systematically demonstrates better performances than ILS-DLA and OSDL. More specifically, ILS-DLA shows a regular behavior, with a considerable rise of the gaps with the increase of additive noise\u2019s SNR. Concerning OSDL, we have even more significant gaps in favor of R-SVD, but with a less regular distribution, which is not easy to be interpreted. This may be in part due to OSDL having been originally conceived for learning of large dimension image patches.In these experiments we refer to random training sets of size In order to assess the applicability of the R-SVD method to various domains and tasks, we test it on ECG compression, EEG sparse representation, and image modeling. All the experiments are conducted on publicly available data, comparing the R-SVD and K-SVD performances, and adopting OMP as sparse decomposition method.Sparsity techniques have been already applied to the compression of electrocardiogram (ECG) signals , 32. To n-length normalized RR-segments. The second stage focuses on the dictionary learning where either R-SVD or K-SVD are used to train a dictionary on a group of RR-segments taken from an initial transient of the signal (train chunk). The latter stage concerns the encoding via sparse reconstruction of all RR-segments belonging to a broader interval of the signal (test chunk). This step is carried out referring to the learnt dictionaries, and applying the OMP algorithm. Naturally, in order to make the coding step easier, magnitudes and positions of non-null sparse coefficients are handled separately.In this experiment, the compression process is broken down into three stages. The former is a preprocessing step consisting in R-peak detection of the signal, and its normalization  so as to split it into y is composed of Nq-bit resolution samples forming M RR-segments, we havek is the sparsity level, m is the number of the atoms in the dictionary, and y, the overall reconstruction quality measure is here specialized for ECG signal as The compression level achieved by each method is measured as compression rate (CR), that is the ratio between the number of bits of the original signal and that of the compressed representation. Assuming that the test chunk fs = 250 Hz and q = 12-bit resolution. Performances are reported in SNR vs CR obtained from OMP, referring to dictionaries learnt by R-SVD or K-SVD, and to an untrained dictionary (i.e. randomly picking m RR-segments from the train chunk). Lower plots report the computational time spent by the two techniques in the learning stage. To make the experiment realistic, we set n = fs, m = 5n and L = 5000 RR-segments (about 120 minutes), while the test chunk is composed of M = 15000 RR-segments (about 4 hours). In order to analyze the methods at several rates, we varied k in the interval 5 \u00f7 80 with step size 1.We conducted the experiments on two ECG records taken from the Long-Term ST Database in PhysioNet . They arSuch experiments, besides confirming that trained dictionaries behave better than untrained one, prove the effectiveness of the R-SVD training method that outperforms K-SVD both in training ability and learning time.Electroencephalogram signals (EEG) are exploited in several Brain-Computer interfaces (BCI) mainly due to their high temporal resolution. An element of difficulty when dealing with this kind of signal is its non-stationary temporal behavior, an unwanted property that has negative consequences on common tasks such as classification. Several adaptive techniques and updating rules have been proposed to produce compelling dictionaries , 35. HerP of n-length normalized EEG chunks corresponding to a given motor imagery . The second stage concerns the dictionary learning in the strict sense: starting from a random dictionary Dinit of dimensions n \u00d7 2n, both the R-SVD and K-SVD methods are adopted to specialize Dinit on the basis of a pool of EEG chunks randomly taken from P. Finally, the quality of the learnt dictionaries, let\u2019s say DK-SVD, DR-SVD, is evaluated applying the OMP algorithm on a distinct pool of EEG chunks also taken from P.Operatively, we split the task into three stages. The former aims at producing a pool http://www.bbci.de/competition/iii/desc_IVa.html): EEG portions of signal corresponding to one motor imagery (either right foot or right hand) are extracted according to the given signal labelling, normalized to zero-mean signals and set into the pool P. The learning phase is carried out by setting the atom dimensions n = 150 or 300, the number of iterations T = 150, and expressing the sparsity k as various percentages of n. The cardinality of training set and test set is L = 2n and M = 4n respectively.We conducted the experiments referring to the dataset IVa from BCI competition III  . All results in the two phases are averaged on 50 trials. It is evident that the R-SVD method systematically exceeds K-SVD on both EEG chunk sizes. Moreover, the reconstruction quality increases with k, as well as the gap between the performances of K-SVD and R-SVD.In Sparse representation of images via learnt overcomplete dictionaries is a well-known topic in the fields of image processing and computer vision . In partP, a pre-processing is first applied aiming at both removing the patch mean intensity and reshaping all the patches to vectors in Given a pool of image patches k in 5 \u00f7 30. The initial dictionaries for the two algorithms have size n \u00d7 1.5n, while training and test sets have size L = 2n and M = 4n respectively; they are all made up of randomly selected patches from P.The learning phase is carried out by setting the number of iterations to 50, and varying the sparsity n = 81) and 16 \u00d7 16 (n = 256). In both cases we randomly extracted 100,000 patches from 500 images of Caltech 101 [SNR trends of the learning phase on the training sets. We can observe that, since the first iterations, R-SVD behaves better than K-SVD, maintaining a positive gap at convergence, especially in the cases of lower sparsity. In SNR attained in the test phase using the dictionaries learnt by K-SVD and R-SVD, and then applying OMP. All results in the two phases are averaged on 50 trials. As we can observe, the R-SVD method systematically exceeds K-SVD referring to both patch sizes and to several sparsity degrees. These results further confirm the effectiveness and generality of the R-SVD method.Experimentally, we considered patches of size 9 \u00d7 9 Click here for additional data file.S2 File(ZIP)Click here for additional data file.S3 File(ZIP)Click here for additional data file.S4 File(ZIP)Click here for additional data file."}
+{"text": "Streptomyces mediterranei (now Amycolatopsis rifamycinica)  was a 1955 French gangster film that was popular at the time and became the root of the name \u201crifamycin\u201d for this group of antimicrobial agents.  Rifampin  is the N-amino-N\u02b9-methylpiperazine (AMP) derivative of rifamycin.In 1957, Piero Sensi and colleagues isolated a new bacterium, ycinica) , from a"}
+{"text": "Several domains of cognitive function, including learning memory and executive function, are impaired in mood disorders. Also, the relationship between disturbances of these two cognitive domains has been suggested. In line with the recent initiative to establish a standard measure of cognitive decline in bipolar disorder, the present study was conducted to (1) test the criterion-related validity and test\u2013retest reliability of the California Verbal Learning Test (CVLT)-II Japanese version, and (2) determine if type of word learning tasks  affects severity of verbal memory deficits in patients with subsyndromal bipolar disorder.Thirty-six patients with bipolar disorder with mild symptoms and 42 healthy volunteers participated in the study. We first compared effect sizes for memory deficits in patients among the CVLT-II, Brief Assessment of Cognition in Schizophrenia (BACS), and Hopkins Verbal Memory Tests-Revised (HVLT-R). We next evaluated the correlations between scores of the CVLT-II vs. those of the BACS and HVLT-R. Bipolar patients were re-assessed with the same (standard) or alternate forms of the CVLT-II and HVLT-R 1\u2009month later.Scores on the CVLT-II 1\u20135 Free Recall and Long-delay Free Recall, as well as the HVLT-R Immediate Recall, but not the BACS List Learning were significantly lower for patients compared to control subjects. The effect sizes for cognitive decline due to the illness were comparable when measured by the CVLT-II and HVLT-R, ranging from 0.5 to 0.6. CVLT-II scores were significantly correlated with those of the HVLT-R and BACS. Test\u2013retest reliability of the CVLT-II was acceptable, and no significant practice effect was observed when the alternate form was used. There was no consistent relationship between mood symptoms and performance on the CVLT-II.These results suggest the CVLT-II Japanese version is able to discriminate between bipolar disorder patients and healthy controls with good sensitivity and validity. Data in this study also indicate that the degree of verbal memory deficits in bipolar disorder may be influenced by memory organizational strategy. Bipolar disorder is associated with poor psychosocial outcome not only in the manic or depressive state, but also in the subsyndromal state \u20133. PatieThere may be interactions in the disturbances of key cognitive domains in bipolar disorder. For example, the contribution of executive function to learning memory has been reported in patients with the disease . SpecifiTo evaluate verbal memory in subjects with bipolar disorder, several tasks, including the Brief Assessment of Cognition in Schizophrenia (BACS) , HopkinsThe effect size of cognitive decline in euthymic patients ranges from 0.66 to 0.90 . As verbThe main purpose of this study was to investigate the impact of memory organizational strategies on verbal (learning) memory, as measured by performance on word list tasks, in patients with bipolar disorder. For this aim, we sought to determine whether the CVLT-II and HVLT-R, but not the BACS would be able to discriminate between patients with subsyndromal bipolar disorder and normal control subjects. This is based on the assumption that only the former two tasks require subjects to use memory organization. Additionally, we investigated the validity and reliability of the Japanese version of CVLT-II using the BACS List Learning and HVLT-R as reference measures of verbal learning and memory. Preliminary analyses of the present data have been reported , 23.This was a multi-center collaborative study, whose design, characteristics of participants, and other information have been registered (UMIN ID: 000013623). The sample consisted of 78 participants; 36 individuals with bipolar disorder and 42 healthy control participants who were native Japanese and had no history of psychiatric disorders Table . The patWritten consent was obtained from all participants, according to ethics guidelines set out by each participating site. The study protocol was approved by the ethics committees of participating institutions.The subjects were administered three verbal learning tests twice with an interval of approximately 1\u2009month. Mood symptoms were also assessed each time using the MADRS and YMRS. The CVLT-II, BACS, and HVLT-R forms were switched to alternate forms in 43 subjects  at the follow-up (19 patients and 24 controls), whereas 35 subjects  were administered the same standard form at the follow-up (17 patients and 18 controls) as at the baseline. The same raters performed these cognitive tests at baseline and the 1-month follow-up assessments.To develop a Japanese version of the CVLT-II , one of The CVLT-II measures both recall and recognition abilities using two word lists. In the first five trials, immediately after presentation of List A, the subject is asked to recall the words of the list. List A contains 4 words from each of 4 semantic categories, for a total of 16 words. This procedure enables evaluation of semantic clustering ability, the most effective strategy for learning non-systemized verbal information. Subsequently, an interference list (List B) containing 16 words is presented, followed by a recall test. The interference test is followed by a short-delay free recall test and a short-delay cued recall test using List A. Then, following 20-min interval, a long-delay free recall test, long-delay cued recall test, and yes/no recognition test are administered using List A. After the yes/no recognition test, a new approximately 10-min forced-choice recognition test is arbitrarily administered. In the present study, data obtained in the immediate recall test after the first five trials of List A  and a long-delay free recall test were adopted for analyses, which were the candidate measures to be incorporated in the International Society for Bipolar Disorders-Battery for Assessment of Neurocognition .The BACS List Learning test consists of a word list, containing 15 words. The subject is asked to recall the words of the list immediately after presentation of the word list, which was repeated five times. The words in the list were not semantically organized unlike the case in the CVLT-II and HVLT-R. In the present study, a standardized measure in the immediate recall test after the first five trials was adopted for analyses. (The standardized measure was obtained by using the mean level of 49.2 and the standard deviation of 9.9.) .t-test was performed to explore between-group differences for CVLT-II 1\u20135 free recall scores and long-delay free recall scores, HVLT-R immediate recall scores, and BACS list learning scores at baseline. If a significant between-group difference in either measure was found, the effect size was calculated using a Cohen\u2019s d to explore its sensitivity. To examine the effect of mood symptoms, Spearman\u2019s rank correlation was performed between CVLT-II 1\u20135 free recall or long-delay free recall scores vs. MADRS and YMRS scores. Test\u2013retest reliability was evaluated using intraclass correlation coefficient (ICC) (Student\u2019s nt (ICC)  between To examine the criterion-related validity of the CVLT-II measures, Pearson\u2019s product-moment correlation among scores of the CVLT-II 1\u20135 Free Recall and Long-Delay Free Recall, HVLT-R Immediate Recall, and BACS List Learning was calculated for patients.t-test revealed a significant between-group difference for the CVLT-II 1\u20135 Free Recall  and Long-Delay Free Recall , and HVLT-R Immediate Recall , but not the BACS List Learning  , and Long-Delay Free Recall . On the other hand, performances on these CVLT measures were not correlated with YMRS scores .Student\u2019s The ICCs between the baseline and 1-month follow-up scores for the BACS List Learning, HVLT-R Immediate Recall, CVLT-II 1\u20135 Free Recall and Long-Delay Free Recall are summarized in Table F \u2009=\u20096.58, P\u2009=\u20090.012) and \u201ctime\u201d  and a significant \u201ctype\u201d\u2009\u00d7\u2009\u201ctime\u201d interaction  were found on scores of the BACS List Learning , but not type A-B . As for the HVLT-R, there was a significant main effect of \u201cgroup\u201d , while \u201ctime\u201d effect did not reach a significant level . A secondary analysis for each \u201cgroup\u201d revealed no significant main effect of \u201ctime\u201d or \u201ctime\u201d\u2009\u00d7\u2009\u201ctype\u201d interaction in either healthy controls  or bipolar disorder patients . Repeated measures ANOVA for CVLT-II 1\u20135 Free Recall revealed a significant effect of \u201cgroup\u201d  and \u201ctime\u201d . \u201cType\u201d\u2009\u00d7\u2009\u201ctime\u201d interaction was also significant . Therefore, secondary analysis for each \u201ctype\u201d was performed. There was a significant effect of \u201ctime\u201d in type A-A , but not type A-B . In addition, \u201cgroup\u201d\u2009\u00d7\u2009\u201ctime\u201d interaction was not significant in either \u201ctype\u201d . As for CVLT-II Long-Delay Free Recall, \u201cgroup\u201d effect  and \u201ctime\u201d effect , as well as \u201ctype\u201d\u2009\u00d7\u2009\u201ctime\u201d interaction  were significant. Also, \u201cgroup\u201d\u2009\u00d7\u2009\u201ctype\u201d\u2009\u00d7\u2009\u201ctime\u201d interaction was significant . A secondary analysis revealed a significant effect of \u201ctime\u201d in type A-A , but not type A-B . Moreover, \u201cgroup\u201d\u2009\u00d7\u2009\u201ctime\u201d interaction was not significant in either pattern .A significant main effect of \u201cgroup\u201d  was smaller than those previously reported using the CVLT (0.73\u20130.82) . Meanwhi17 the reliability coefficients ranged from 0.72 to 0.79 in a sample of 288 healthy subjects, with a median interval of 21\u2009days, similar to the ICC for the CVLT-II 1\u20135 free recall in healthy controls using an alternate form (0.70) in the present study /(four words per category) structure , while teuthymic state, although all met the subsyndromal state criterion. There is a possibility that the patient-control effect sizes may have been overestimated due to residual depressive symptoms. However, a positive correlation between rating with the MADRS vs. CVLT-II 1\u20135 Free Recall and Long-Delay Free Recall scores may argue against this view.Unlike previous studies, patients with bipolar disorder studied here were not necessarily in the The Japanese version of CVLT-II appeared to provide valid measures of verbal learning and memory function in bipolar disorder patients. The ability of the CVLT-II and HVLT-R, but not BACS List Learning, to discriminate between patients and control subjects may be related to the use of memory organization strategy specific to the CVLT-II and HVLT-R, which deserves further study.This study was carried out in accordance with the recommendations of \u201cname of guidelines, name of committee\u201d with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by ethics committees of the National Center of Neurology and Psychiatry Hospital, Fujita Health University Hospital, Nagoya University Hospital, and Hokkaido University Hospital.Contributions of each author are as follows: conception and design of the study (TS); acquisition of data ; analysis of data (KN and KS); and drafting of the manuscript (KN and TS).There are no conflicts of interest for any of the authors of this paper. No author has any possible financial gain for the findings presented here."}
+{"text": "A central concern of generative grammar is the relationship between hierarchy and word order, traditionally understood as two dimensions of a single syntactic representation. A related concern is directionality in the grammar. Traditional approaches posit process-neutral grammars, embodying knowledge of language, put to use with infinite facility both for production and comprehension. This has crystallized in the view of Merge as the central property of syntax, perhaps its only novel feature. A growing number of approaches explore grammars with different directionalities, often with more direct connections to performance mechanisms. This paper describes a novel model of universal grammar as a one-directional, universal parser. Mismatch between word order and interpretation order is pervasive in comprehension; in the present model, word order is language-particular and interpretation order  is universal. These orders are not two dimensions of a unified abstract object ; rather, both are temporal sequences, and UG is an invariant real-time procedure  transforming word order into hierarchical order. This shift in perspective has several desirable consequences. It collapses linearization, displacement, and composition into a single performance process. The architecture provides a novel source of brackets (labeled unambiguously and without search), which are understood not as part-whole constituency relations, but as storage and retrieval routines in parsing. It also explains why neutral word order within single syntactic cycles avoids 213-like permutations. The model identifies cycles as extended projections of lexical heads, grounding the notion of phase. This is achieved with a universal processor, dispensing with parameters. The empirical focus is word order in noun phrases. This domain provides some of the clearest evidence for 213-avoidance as a cross-linguistic word order generalization. Importantly, recursive phrase structure \u201cbottoms out\u201d in noun phrases, which are typically a single cycle . By contrast, a simple transitive clause plausibly involves two cycles (vP and CP), embedding further nominal cycles. In the present theory, recursion is fundamentally distinct from structure-building within a single cycle, and different word order restrictions might emerge in larger domains like clauses. One of the most significant recent developments for linguistic theory is the appearance of high-quality datasets on the full range of cross-linguistic variation. In the past, generative studies typically relied on detailed examination of one or several languages to illuminate syntactic mechanisms. While this approach is certainly fruitful, the accumulation of information about large numbers of languages opens new possibilities for sharpening understanding.the) fundamental property of language  of lexical items. The error inheres in thinking of lexical items as coherent units existing at a single level. This leads to thinking of sentences as single-level representations as well. Words, put simply, aren't This paper proposes a novel model of grammatical mechanisms, called ULTRA . Within local syntactic domains forming the extended projection of a lexical root (such as a verb or noun), ULTRA employs Knuth's  stack-soStack-sorting proves to be an effective procedure for linking word order and hierarchical interpretation, encompassing linearization, displacement, composition, and labeled brackets. The theory invites realization as a real-time performance process. Pursuing that realization significantly recasts the boundaries between performance and competence. Remarkably, ULTRA requires no language-particular parameters; an invariant algorithm serves as grammatical device for all languages. Put simply, I propose that Universal Grammar is a universal parser.Nevertheless, stack-sorting is too limited a mechanism to describe all the phenomena of human syntax. Three kinds of effects are left hanging: unbounded recursion, non-neutral orders, and the existence of apparently distinct languages. Moreover, understanding stack-sorting as a processing system encounters two obvious problems: it is a unidirectional parser, not trivially reversible for production; and it conflicts with strong evidence for word-by-word incrementality in comprehension.Although constructing a complete model of syntax and processing goes far beyond the scope of the paper, the problems that arise in basing a parser-as-grammar model on stack-sorting warrant consideration. I appeal to the distinction between reactive and predictive processes, casting stack-sorting as a universal reactive routine. A separate predictive module plays a crucial role in production, and in the appearance of distinct, relatively rigid word orders. Prediction also helps reconcile ULTRA with incremental interpretation. I appeal to properties of memory to resolve further problems, speculating that primacy memory (distinct from the recency memory underpinning stack-sorting) is the source of another cluster of syntactic properties, including long-distance movement, crossing dependencies, and the special syntax of the \u201cleft periphery.\u201d Finally, I suggest that episodic memory\u2014independently hierarchical in structure, in humans\u2014plays a key role in linguistic recursion.*213 in Neutral Word Order explores the generalization that 213-avoidance delimits information-neutral word order possibilities, across languages. Section Stack-Sorting as a Grammatical Mechanism proposes a stack-sorting procedure to capture 213-avoidance in word order. Section Stack-Sorting: Linearization, Displacement, Composition, and Labeled Brackets shows how further syntactic effects follow from stack-sorting. Section Comparison with Existing Accounts of Universal 20 compares ULTRA to existing accounts of 213-avoidance in word order, focusing on Universal 20. Section Universal Grammar as Universal Parser pursues the realization of stack-sorting in real-time performance. Section Possible Extensions to a More Complete Theory of Syntax addresses the challenges in taking stack-sorting as the core of Universal Grammar, sketching some possible extensions. Section Conclusion concludes.The structure of this paper is as follows. Section Linear Base argues that the \u201cbase\u201d structure within each local syntactic domain is a sequence. Section root, noting that in extended projections of nouns and verbs, the lexical noun or verb root is semantically dominant. The other sense of head concerns which element determines the combinatoric behavior of the composite; let us call this notion of head the label.Syntactic combination could take many forms. An emerging view is that combination largely keeps to head-complement relations Starke, . The terred books, would be represented as follows.In older theories of phrase structure, the two senses of head (root and label) converged on the same element; a noun, for example, combined with all its modifiers within a noun phrase. Headedness thus mapped to hierarchical dominance; the root projected its label above its dependents. To illustrate, a combination of adjective and noun, such as red books is represented as follows.This traditional conclusion about the relationship of dependency and hierarchy is overturned in modern syntactic cartography , which labels the composite, determining its combinatoric behavior. In cartographic representations heads are uniformly Questions arise about these representations, which postulate an abundance of unpronounced material. A curious observation is that functional heads and their specifiers seem not to occur together overtly, as formalized in Koopman's  Generalitokens of the same type, competing for a single position. Starke recasts the cartographic spine as an abstract functional sequence (fseq), whose positions can be discharged equally by lexical or phrasal material. Pursuing Starke's conception, the adjective-noun combination would be represented as below.Starke  takes Koits fseq.Again, we have reversed traditional conclusions about the hierarchy of heads and dependents. Nevertheless, the notion of root (picking out the noun) is still crucial, as the modifiers occur in the hierarchical order dictated by Syntactic combination of this sort is sequential, within each extended projection. These \u201cbase\u201d sequences encode bottom-up composition, so it is natural to order the sequence in the same way (bottom-up). The base  is widely taken to be uniform across languages, and to express \u201cthematic,\u201d information-neutral meaning (contrasted with discourse-information structure)A grammar, on anyone's theory, specifies a formal mapping linking sound and meaning . This specification could take many forms. Sequential representation of the base allows a remarkably simple formulation of the sound-meaning mapping. This reformulation yields a principled account of a class of word order universals. Moreover, while the interface objects  involved in the mapping are sequences, bracketed hierarchical structure arises as a dynamic effect.linearization, externalization, etc. This paper pursues a different view, where surface word orders are inputs to an algorithm that attempts to assemble the base as output. Significantly, the only inputs that converge on the uniform base under this process are 213-avoiding; all 213-containing word orders result in deviant output.There are various ways of conceptualizing the relationship between the base and surface word order. The usual view is that the base orders the input to a derivation, yielding surface word order as the output. That directionality is implicit in terms used to describe the hierarchy-order relation: b\u2026a\u2026c\u2026, for elements a \u226b b \u226b c, where \u226b indicates c-command in standard tree representations of the base . In other words, neutral word orders seem to avoid a mid-high-low (sub)sequence of elements from a single fseq. The elements forming this forbidden contour need not be adjacent, in surface order or in the base fseq.213-avoidance arguably captures information-neutral word order possibilities in a variety of syntactic domains, across languages. By 213-avoidance, I mean a ban on surface order \u2026213-avoidance is widely believed to delimit the ordering options for verb clusters, well-known in West Germanic  precede the noun, they are always found in that order. If they follow, the order is either the same or its exact opposite\u201d . What is forbidden is remnant movement.*Num Dem Adj N contains subsequences Num Dem Adj\u2026, and Num Dem \u2026 N, representing mid-high-low contours with respect to the fseq.Noun phrase orders obey a simple generalization: attested orders are all and only 213-avoiding permutations. All unattested orders have 213-like subsequences. For example, unattested There is a particularly simple procedure that maps 213-avoiding word(4) maps all and only 213-avoiding word orders to a 321-like hierarchy, corresponding to the base. 213-containing orders are mapped to a deviant output, distinct from the base. By hypothesis, that is why such orders are typologically unavailable: they are automatically mapped to an uninterpretable order of composition. This explains the Universal 20 pattern (Tables *Adj-Dem-Num.Let us illustrate how (4) parses some noun phrase orders: Dem-Adj-N, N-Dem-Adj, (5) Dem-Adj-N: PUSH(Dem), PUSH(Adj), PUSH(N), POP(N), POP(Adj), POP(Dem).(6) N-Dem-Adj: PUSH(N), POP(N), PUSH(Dem), PUSH(Adj), POP(Adj), POP(Dem).For attested orders, the nominal categories POP in the order < N, Adj, Dem>, matching their bottom-up hierarchy.*Adj-Dem-N: PUSH(Adj), POP(Adj), PUSH(Dem), PUSH(N), POP(N), POP(Dem).(7) * < Adj, N, Dem>, failing to construct the universal interpretation order.For the unattested 213-like order, items POP in the deviant order That's nice: (4) maps attested orders to their universal meaning, simultaneously ruling out unattested orders. But beyond such a mapping, an adequate grammar must explain other aspects of knowledge of language, including surface structure bracketing. If grammar treats surface orders and base structures as sequencesIn this section, I show that stack-sorting effectively encompasses linearization, displacement, and composition, as well as assigning brackets, labeled unambiguously and without search. Moreover, it does all of this without language-particular parameters.In the standard (\u201cY-model\u201d) view, linearization and composition are distinct interface operations, interpreting structures built in an autonomous syntactic module by Merge. In ULTRA, linearization goes in the other direction, loading surface word order item-by-item into memory, and reassembling it in order of compositional interpretation.Displacement is a natural feature of stack-sorting; from one point of view, it is the basic property of the system. In standard accounts, constituents that compose together in the interpretation should appear adjacent in surface order. This arrangement is forced by phrase structure grammars. Displacement, whereby elements that compose together are separated by intervening elements in surface order, has always seemed a surprising property, in need of explanation.every element in the surface order is \u201ctransformed,\u201d passing through memory before retrieval for interpretationThings work quite differently in ULTRA. A key assumption of the Merge-based view is discarded: there is no level of representation encompassing word order and the fseq within a unified higher-order object. Instead, word order and base hierarchy are disconnected sequences, related dynamically. Non-adjacent input elements can perfectly well end up adjacent in the output. Displacement, rather than being the exception, is the rule; The algorithm 4) implicitly assigns labeled bracketed structure implicitExamining these brackets, the sequence of pushes and pops  for each order implicitly defines a tree, as shown in Figure Setting aside the 321 tree(s) for the moment, the Dyck trees are systematic, loss-less compressions of Cinque's trees, with every subtree that is a right-branching comb in the Cinque tree replaced with a linear tree  is the most common noun phrase order; future research should illuminate the issueA key empirical question is whether 321 orders exhibit two distinct bracketed structures, as binary-branching treatments allow, or only the single, \u201cflat\u201d structure predicted here. The issue is even more acute for 4 elements, as in Universal 20, where there are up to 5 distinct Merge derivationsStack-sorting captures a surprising amount of syntactic machinery, normally divided among different modules. In the usual view, an autonomous generative engine builds constituent structures, interpreted at the interfaces by further processes of linearization and composition. In ULTRA, linearization and composition reflect a single procedure. Constituent structure is not primitive, but records the storage and retrieval steps by which stack-sorting assembles the interpretationThis section compares the stack-sorting account of Universal 20 to existing Merge-based accounts Cinque, . I argueCinque proposes a cross-linguistically uniform base hierarchy, reflecting a fixed order of External Merge. He proposes that movement  is uniformly leftward, while the base is right-branching, in line with Kayne's  LCA. He 0), below agreement phrases providing landing sites for movement. This structure, and his assumptions about movement, derives all and only the attested orders. The English-like order Dem-Num-Adj-N surfaces without movement; all other orders involve some sequence of movements of NP, or something containing it.The overt modifiers are specifiers of dedicated functional heads  a. N-L \u2013 Align\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Align NP's left edge with AgrWP's left edge.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0b. A-L \u2013 Align\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Align AP's left edge with AgrWP's left edge.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0c. NUM-L \u2013 Align\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Align NumP's left edge with AgrWP's left edge.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0d. DEM-L \u2013 Align\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Align DemP's left edge with AgrWP's left edge.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 a uniform base structure, (ii) syntactic movement, and (iii) principles of linearization. In all three accounts, (i) describes the order of External Merge. Details of (ii) and (iii) vary between the accounts. For Cinque  and StedNeeleman  require Neeleman  utilizesNeeleman  LCA; AbeNeeleman  have movNeeleman  have lanThese accounts all require different grammars for different orders. In Cinque  system, Finally, all these accounts have some measure of structural or grammatical ambiguity, for some orders. For Cinque , one kinThe stack-sorting account fares better with respect to these issues. Instead of postulating separate tiers of base, movement, and linearization principles, the relevant machinery is realized in one algorithmic process. The sorting algorithm is universal, eschewing language-particular features to drive movement, order sister nodes, or rank alignment constraints. Such a theory is ideally situated to account for the free word order phenomenonThis section develops the view that stack-sorting can form the basis for an invariant performance mechanism, realizing Universal Grammar as a universal parser. This modifies traditional conclusions about competence and performance, while providing a novel view of what a grammar is.what the system is doing, and why. Performance corresponds, rather loosely, to the lower, algorithmic level, describing how the computation is carried out, step-by-step.In generative accounts, a fundamental division exists between competence and performance Chomsky, . CompeteOf course, Marr's hierarchy applies to the information-processing in language, under the present theory as well as any other. However, the division of labor between these components is significantly redrawn here, with much more of the burden of explanation carried by performanceA novel claim of ULTRA is that there is a single parser for all languages. This departs from the nearly universal assumption that parsers interpret language-particular grammars. But even within that traditional view, the appeal of universal mechanisms has been recognized.\u201cThe key point to be made, however, is that the search should be a search for universals, even\u2014and perhaps especially\u2014in the processing domain. For it would seem that the strongest parsing theory is one which says that the grammar interpreter itself is a universal mechanism, i.e. that there is one highly constrained grammar interpreter which is the appropriate machine for parsing all natural languages\u201d Marcus,  p. 11.performance grammar only (PGO) view.The idea that \u201cthe parser is the grammar\u201d has a long history; see Phillips , 2003, K\u201cPGO theory enters the game with one powerful advantage: there must be psychological mechanisms for speaking and understanding, and simplicity considerations thus put the burden of proof on anyone who would claim that there is more than this\u201d Fodor,  p. 470.ibid., 472). This presupposes that movement is fundamentally difficult for parsing mechanisms . However, in ULTRA, displacement is not a complication over more basic mechanisms; displacement is the basic mechanism.However, while granting that this entails a simpler theory, Fodor rejects the idea, finding no motivation for movement outside an autonomous grammar  is essentially identical to the SYAIn fact, though the property is little used, the SYA is a sorting protocol; many input orders lead to the same internal calculation. As calculator users, we utilize one input scheme (infix notation), but others would do as well. The standardized input order for calculators has the same status as particular languages with respect to ULTRA: users may fall into narrow ordering habits, but the algorithm automatically processes many other orders.ungrammaticality. The former kind of knowledge is fundamentally about computing interpretations. But the invariant process interpreting one language's surface order can equally interpret the orders of other languages. From this point of view, there is only one I-language, and a single performance grammar that delivers it. While this conclusion is appealing, an important question remains: where do individual languages come from, with apparently different grammars?One of the central tasks ascribed to grammars is distinguishing grammatical sentences of a language from ungrammatical strings. In ULTRA, knowledge of grammaticality is very different from knowledge of This section addresses two kinds of problems that follow from interpreting stack-sorting as a performance device. The first concerns reconciling the theory with what is known about real-time language processing; the second concerns extending the model to properties of syntax that are left unexplained. Even discussing these problems in depth, much less justifying any solutions, is beyond the scope of this paper. The intent is merely to sketch the challenges, and indicate directions for further work.With respect to processing, one problem is that this approach seems to be contradicted by strong evidence for word-by-word incrementality in comprehension  memory. Primacy, on the other hand, is naturally described by queue  memory. Besides optimal order of access, there is another important difference between primacy and recency effects. Put simply, the first element in a sequence remains the first element, no matter how many more elements follow; the primacy signature of a given element is relatively stable over the time scale relevant to parsing. Recency is different: each element in a sequence is a new right edge, suppressing the accessibility to recency-based memory of everything that precedes it. Thus, we expect a kind of \u201cuse-it-or-lose-it\u201d pressure within recency memory, but not primacy memory.Tentatively, I would like to suggest that distinct primacy and recency memory codes underlie the Duality of Semantics, and the division between A-bar and A-syntax. Recency, associated with a stack, is the basis for information-neutral, local permutation, generally characterized by nesting dependenciesA final problem looming in the background is recursion. ULTRA operates within syntactic domains characterized by a single fseq. This requires some comment, as recursion is a fundamental property of syntax. For recursion as well, properties of memory, and intervention of a complementary predictive system, might be crucial. Intriguingly, human episodic memory appears to be independently hierarchical in structure, perhaps unlike related animals Tulving, . In the As discussed in section Comparison with Existing Accounts of Universal 20, in ULTRA, structural ambiguity does not arise without ambiguity of meaning, within single domains. However, structural ambiguity arises inevitably when multiple domains are present, in terms of which domain embeds in another, or where to attach an element that could discharge positions in two distinct domains. This is where the \u201cfast, stupid black box\u201d is helpless, and must call on other resources. One obvious source of help in stitching together multiple domains is a separate predictive system, with access to top-down knowledge of plausible meanings in context. The persistent problem of resolving embedding ambiguities also provides motivation for rigid word order, which sharply reduces attachment possibilities.An important point is that brackets are defined relative to a particular fseq. Recursive embedding of one domain in another  involves projection of a bracket corresponding to the entire embedded phrase, within the embedding domain(11) The dog chased a ball.There are three sorting domains here: two nominal projections, embedded in a third, verbal projection . Their ULTRA bracketing appears below.the [dog dog] the](12) NP1 = [a [ball ball] a]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0NP2 = [NP1 [chased chased] [NP2 NP2] NP1]\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0VP = [This example illustrates the ambiguity that accompanies embedding. The issue is how to link the nominal phrases to positions in the verb's fseq . As theta roles are not overtly expressed (case-marking is an unreliable guide), the reactive parser must draw on external means .A final point about recursion returns to the issue of how calculators work, via Dijkstra's Shunting Yard Algorithm. Such computations are recursive. But recursion isn't handled by the parsing algorithm; rather, it arises at the level of interpretation, where partial outputs of arithmetic operations feed into further calculations. A similar conclusion  is possible within the present framework, given the similarities between ULTRA and the SYA. Notably, both procedures compile input into Reverse Polish Notation, a so-called concatenative programming language, expressing recursive hierarchical operations unambiguously in serial format.this algorithm? Other sorting procedures are possible in principle, and would lead to different permutation-avoidance profiles. How do we justify selecting stack-sorting as the right procedure for syntactic mapping?I have shown how a particularly simple algorithm captures a range of syntactic phenomena. But the question is, why There are three crucial ingredients. The first is the orientation of the system as a parser, mapping sound to meaning. This is not logically necessary; it is simply one of the reasonable choices. The second factor is the linear nature of sound and meaning. This is straightforward for sound sequences, but much less so for interpretations, where it is simply a bold hypothesis. The third ingredient is the choice of stack memory. This can plausibly be tied to the Modality effect: intelligible speech input engenders unusually strong recency effects  itself comes from, a matter on which I will not speculate here.So far, stack-sorting has been implemented with an explicit algorithm. That may be unnecessary. Rather than thinking of stack-sorting as a set of explicit instructions, we might reframe it as an Summarizing, a simple algorithm (4) maps 213-avoiding word orders to a bottom-up compositional sequence, while mapping 213-containing orders to deviant sequences. While the input and output of the mapping are sequences, hierarchical structure is present: the algorithmic steps realize left and right brackets, almost exactly where standard accounts place them. The account differs from standard accounts in assigning unambiguous bracketing to all orders.This model improves on existing accounts of word order restrictions, which invoke additional stipulations , beyond core syntactic structure-building. In ULTRA, these effects fall out from a single real-time process. In turn, syntactic displacement, long seen as a curious complication, emerges as the fundamental grammatical mechanism. No learning of language-particular properties is required; one grammar interprets many orders.It should be clear that the system described here is only one part of syntactic cognition. This system builds one extended projection at a time; further mechanisms are required to embed one domain in another. However, that may be a virtue: it is tempting to identify the domains of operation for this architecture with phases, which are thus special for principled reasons.Moreover, stack-sorting only handles information-neutral structure. This ignores another important component of syntax, so-called discourse-information structure, associated with potentially long-distance A-bar dependencies. This deficiency, too, may be a virtue, suggesting a principled basis for the Duality of Semantics. I speculated that primacy memory plays a central role in these effects, potentially explaining several curious properties .Raising our sights, the larger conclusion is that much of the machinery of syntactic cognition might reduce to effects not specific to language. Needless to say, this is just a programmatic sketch; future research will determine whether and how ULTRA's stack-sorting might be integrated into a more complete model of language.The author confirms being the sole contributor of this work and approved it for publication.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Characterizing exposure-disease associations is a central issue in epidemiology, one which epidemiologists often approach by adopting the index of the odds ratio and presenting its point estimate, p-value and confidence interval. In this study, the parameter space of the odds ratio is partitioned into five mutually exclusive regions corresponding to \u2018strong protective factor\u2019, \u2018weak protective factor\u2019, \u2018no association\u2019, \u2018weak risk factor\u2019, and \u2018strong risk factor\u2019, respectively. The authors presented a suite of statistical methods tailored to such a five-region demarcation, including methods for hypothesis testing, confidence interval estimation and calculation of the sample size needed to obtain the desired level of statistical power. The authors show that the five-region methods can efficiently and informatively describe a putative exposure-disease association, including its presence or absence, as well as its direction and strength (if any association exists). Three published results were re-analyzed to demonstrate the methods. R code is provided for convenience as well. The five-region methods are recommended for routine use during the analysis of epidemiologic data. Epidemiologists often approach this issue by adopting the index of the odds ratio; presenting its point estimate, p-value and confidence interval; then declaring an exposure a risk factor for the disease if its odds ratio is statistically significantly greater than 1.0, or a protective factor if it is statistically significantly less than 1.00: OR\u2009=\u20091; H1: OR\u2009<\u20091 or OR\u2009>\u20091}, so can only be used to infer whether the exposure under study is a risk or protective factor for the disease. Further testing with regards to the cut-off points, such as {H0: OR\u2009\u2265\u20090.5; H1: OR\u2009<\u20090.5} or {H0: OR\u2009\u2264\u20092; H1: OR\u2009>\u20092}, incurs a multiple-testing penalty, and therefore, a power loss.Identifying a risk or protective factor for the disease may not be enough. We may also want to determine the strength of such an exposure-disease association. For example, we may want to know whether the odds ratio is statistically significantly greater than 2.0, indicating a strong risk factor; or between 0.5 and 1.0, indicating a weak protective factor. Conventional hypothesis testing for the odds ratio is for determining whether it is 1.0 or not: {Het al.2 proposed \u2018three-sided testing\u2019, a testing framework for simultaneous testing of \u2018inferiority\u2019, \u2018equivalence\u2019 and \u2018superiority\u2019 in clinical trials. A cardinal feature of Goeman et al.\u2019s method is that the three hypotheses can be simultaneously performed at a significance level of \u03b1, while the family-wise error rate remains within \u03b1. The approach was later adopted outside of clinical trial settings to compare two digital communication systems3. However, our intended, more informative characterization of an exposure-disease association requires partitioning the parameter space of the odds ratio into a total of five \u2018regions\u2019, which is more than the three \u2018sides\u2019 that Goeman et al.2 had considered.Goeman et al.\u2019s three-sided methods2 to the five-region characterization of exposure-disease associations. Our methods  are a reinterpretation of the results of the three-sided testing in terms of five regions. We will show that the \u2018five-region methods\u2019 are more statistically efficient than traditional methods in describing exposure-disease associations. Data from three published studies are re-analyzed to demonstrate the methods.In this paper, we expand the applicability of Goeman I, HII, \u2026, HV as shown below:i is OR \u2208Hi and the alternative hypothesis is OR\u2009\u2208\u2009i), for i\u2009=\u2009I, II, \u2026, V.Assuming that two cut-off points for the odds ratio are chosen: 0.5 and 2. (Proper choices of the cut-off points will be discussed later.) For the lower cut-off point, OR\u2009<\u20090.5 indicates a strong protective factor, and 0.5\u2009\u2264\u2009OR\u2009<\u20091 a weak protective factor. For the upper cut-off point, OR\u2009>\u20092 indicates a strong risk factor, and 1\u2009<\u2009OR\u2009\u2264\u20092 a weak risk factor. The parameter space of the odds ratio is thus partitioned into five regions: H4 thus applies here, dictating that all five hypotheses can be simultaneously performed at a level of \u03b1, while still keeping the family-wise error rate within \u03b1. See Web Appendix\u00a05 pointed out that the correction factor for a Bonferroni multiple testing procedure is not the total number of hypotheses tested, but the maximum number of hypotheses that can simultaneously be true. And in our case, the correction factor is 1. In other words, there is no need for multiple testing correction.Because the five regions are mutually exclusive, the true value of the odds ratio can lie in at most one of the regions, so that no two hypotheses can be simultaneously true. The \u2018partitioning principle\u2019\u03b1. Here, we propose to test HI with an \u03b1-level right-sided test , HII with one \u03b1/2-level left-sided test  and one \u03b1/2-level right-sided test  simultaneously; HIII with an \u03b1-level two-sided test , HIV with one \u03b1/2-level left-sided test  and one \u03b1/2-level right-sided test  simultaneously; and HV with an \u03b1-level left-sided test , respectively.The above partitioning principle says nothing about the types of the tests . For each hypothesis, any test can therefore be used as long as each of the five tests keeps its respective type I error rate within Zx is the x\u2019th quantile of the standard normal distribution. As explained earlier, such a five-region test should keep the family-wise error rate within \u03b1.Assuming normality for the log odds ratio, the \u2018five-region test\u2019 is detailed below:\u03b1/2-level one-sided tests simultaneously\u2019 that we used here for HII and HIV are very different from Schuirmann\u2019s procedure for equivalence6. For the HII test, the null hypothesis (0.5\u2009\u2264\u2009OR\u2009<\u20091) is to be rejected if either of the two null hypotheses  of the \u2018\u03b1/2\u2019-level one-sided tests is rejected. Similarly, for the HIV test, the null hypothesis (1\u2009<\u2009OR\u2009\u2264\u20092) is to be rejected if either of the two null hypotheses  of the \u2018\u03b1/2\u2019-level one-sided tests is rejected. By contrast, in Schuirmann\u2019s procedure, the null hypothesis  is to be rejected only if both null hypotheses  of the \u2018\u03b1\u2019-level one-sided tests are rejected.Note that the \u2018two \u03b1.Alternatively, one can calculate the \u2018five-region p-values\u2019:i in {I, II, \u2026, V}, the pi in (3) corresponds to the Hi test in (2), that is, an Hi will be rejected in (2) if and only if its pi\u2009\u2264\u2009\u03b1 in (3).Web Appendix\u00a0II, HIII, HIV, and HV, are rejected;(SP) a strong protective factor (the upper left non-shaded corner), if four hypotheses, HI, HIII, HIV, and HV, are rejected;(WP) a weak protective factor (the middle left non-shaded area), if four hypotheses, HIII, HIV, and HV, are rejected;(P) a protective factor without strength information (the non-shaded area nestled between the upper left non-shaded corner and the middle left non-shaded area), if three hypotheses, HI, HII, HIII, and HV, are rejected;(WR) a weak risk factor (the middle right non-shaded area), if four hypotheses, HI, HII, HIII, and HIV, are rejected;(SR) a strong risk factor (the upper right non-shaded corner), if four hypotheses, HI, HII, and HIII, are rejected;(R) a risk factor without strength information (the non-shaded area nestled between the middle right non-shaded area and the upper right non-shaded corner), if three hypotheses, HV, is rejected;(NSR) not a strong risk factor (the left lightly-shaded area), if one hypothesis, HI, is rejected;(NSP) not a strong protective factor (the right lightly-shaded area), if one hypothesis, HI and HV, are rejected.(NS) not a strong factor, risk or protective (the middle lightly-shaded area), if two hypotheses, HIf none of the five hypotheses are rejected, a five-region test is inconclusive  are possible. For example, it is not possible to have the middle three hypotheses, HII, HIII, and HIV, being rejected , we must also have III and HIV rejected) and V rejected), and if IV rejected), we must also have III and HII rejected) and 1\u2212\u03b1/2\u2009>\u2009Z1\u2212\u03b1 (HI rejected).Note that not all of the total 20: OR\u2009=\u20091; H1: OR\u2009<\u20091 or OR\u2009>\u20091}) leads to any conclusion at all , it only provides directional information about whether exposure is a protective or a risk factor , not a strong protective factor (HI rejected), or not a strong factor, risk or protective (both HI and HV rejected); at the same \u03b1 level, the classical test leads to none conclusion at all.By comparison, if a classical hypothesis test  confidence interval for the odds ratio.The well-known duality between confidence intervals and hypothesis tests dictates that an \u03b1-level right-sided test for an odd ratio in HI, an \u03b1-level two-sided test for an odds ratio in {HII, HIII, HIV}, and an \u03b1-level left-sided test for an odds ratio in HV. This is essentially Goeman et al.\u2019s three-sided testing2 . Therefore, the resulting \u2018five-region confidence interval\u2019 is also identical mathematically to Goeman et al.\u2019s three-sided confidence interval2.Here, we propose using an et al.\u2019s. Here, we explicitly check each and every one of the five regions, and reject a region if and only if none of its points fall within the confidence interval. Readers can verify that such use of the confidence interval leads to exactly the same conclusion of a five-region test in the previous section. For an example, see the solid lines  and the attached conclusions in a five-region test.However, our use of the confidence interval is different from Goeman Using the same principle that a region is rejected if none of its point fall within the confidence interval, a classical confidence interval can also be used to determine a five-region conclusion  We performed a total of 100,000 Monte-Carlo simulations to approximate the power for a given sample size and used the bisection method to calculate the sample size needed to reach the target power. For comparison, we used the same method to calculate the sample size needed for a classical confidence interval when used to make a five-region conclusion. Web Appendix\u00a0As pointed out earlier, when a five-region test  does reach a conclusion it can lead to one of 9 different conclusions. Here we calculate the required sample size to reach a target power of 80% at Figures\u00a0Figures\u00a0a priori information is available) or for all possible odds ratio values  should help researchers better plan their studies under time and cost constraints.As many researchers often do not have a very precise aim for their studies at the outset, calculating and comparing the required sample sizes for different conclusions and specific odds ratio values  to examine the association between Parkinson\u2019s disease and preceding nonfatal cancers. A conditional logistic regression was conducted for a matched-data analysis. Elbaz et al. reported an adjusted odds ratio of 0.22 [95%  confidence interval: 0.03\u20132.24] for bladder cancer occurring before the onset of Parkinson\u2019s disease. We calculated a standard error from the confidence interval presented (and likewise for the following two examples). The fact that the value 1 is within the classical confidence interval indicates that the observed negative association between bladder cancer and Parkinson\u2019s disease (OR\u2009=\u20090.22) is not statistically significant. The classical confidence interval itself is also inconclusive since it spans all five regions.Elbaz V\u2009=\u20090.031) of the HV region (a strong risk factor). Similarly, the 95% five-region confidence interval is 0.03\u20132.00, excluding the HV region entirely. In this example, while neither the classical test nor the classical confidence interval is conclusive about risk of exposure, the five-region test  at the same significance level of 0.05 can rule out the possibility that bladder cancer is a strong risk factor for Parkinson\u2019s disease; it can only be one of the following four possibilities: a strong protective factor, a weak protective factor, no association, or a weak risk factor.We then used the proposed method to reanalyze the data. The five-region test leads to a rejection . Parent et al. reported an adjusted odds ratio of 1.04 [95%  confidence interval: 0.49\u20132.22] for the association between night work and melanoma. The fact that the value 1 is within the classical confidence interval indicates that the association is not statistically significant. Again, the classical confidence interval itself, which spans all five regions, is also inconclusive.Parent I (a strong protective factor) and HV (a strong risk factor) . Similarly, the 95% five-region confidence interval is 0.50\u20132.00, excluding both the HI and HV regions. We see that while neither the classical test nor the classical confidence interval is conclusive about the risk of exposure, the five-region test  at the same significance level of 0.05 can rule out the possibility that night work is a strong factor, risk or protective, for melanoma; it can only be one of the following three possibilities: a weak protective factor, no association, or a weak risk factor.Using the proposed method to reanalyze the data, the five-region test rejects Het al.9 recruited a total of 610 cases and 837 controls to examine the association between indoor air pollution from coal combustion and the risk of neural tube defects. Logistic regression was conducted adjusting for the matching variables  and a number of other potential confounders . Li et al. reported an adjusted odds ratio of 1.50 [95%  confidence interval: 1.10\u20132.10] for the association between indoor air pollution from cooking and neural tube defects. The fact that the value 1 is not within the classical confidence interval indicates that the observed positive association between indoor air pollution from cooking and neural tube defects (OR\u2009=\u20091.50) is statistically significant. However, the classical confidence interval encompasses the HIV (weak risk factor) and the HV (strong risk factor) regions, so we cannot deduce the strength of this risk factor.Li IV region (weak risk factor), all other 4 regions  are rejected by the five-region test. The 95% five-region confidence interval is 1.10\u20132.00, which is fully embedded within the HIV region. In this example, the classical method can only label indoor air pollution from cooking as a risk factor for neural tube defects. But the five-region method at the same significance level of 0.05 can be more specific in stating that it is a weak risk factor with an odds ratio no greater than 2.Using the proposed method to reanalyze the data, we find that except for the HIII). We then chose two cut-off points, an upper cut-off (cupper\u2009>\u20091) and a lower one (clower\u2009<\u20091) which could have been values other than the \u20182\u2019 and \u20180.5\u2019 used in this paper, to mark the boundaries between strong and weak effects. We thus demarcated two regions (using cupper) for strong and weak risk factors (HV and HIV) to the right of the HIII region, and to the left of that we demarcated two regions (using clower) for strong and weak protective factors (HI and HII). Ideally, if we let clower\u2009=\u20091/cupper, then the testing framework of the five-region test is completely symmetrical in the two directions of an exposure-disease association. By imposing symmetry, we avoid all appearance of prejudice on whether the study exposure is a risk or a protective factor. Also, note that the five-region demarcation should be done beforehand since a data-snooping demarcation will incur bias. The required sample sizes will be different with different demarcations of the five regions as well.The proposed five-region methods hinge on a proper demarcation of the five regions. For the odds ratio index used in this paper, the value \u20181\u2019 was taken to be the center point, indicating no exposure-disease association. Therefore, we let a solitary {1} be a \u2018region\u2019  that should be performed in the region it belongs to. We pick one (or both) cut-off point(s), as appropriate, for the limit(s), if the previous step cannot find one or more suitable limit. Finally, we examine the span of this exact five-region confidence interval to make conclusions for the exact five-region test. Here, the coverage probability of the exact five-region confidence interval is at least (1\u2009\u2212\u2009\u03b1) and the type I error rate of the exact five-region test is at most \u03b1. Web Appendix\u00a0In this paper, we invoked the normality assumption for the log odds ratio (large sample theory). For small sample sizes exact methods will be needed. One can calculate the four limits  using the classical V) or very small (in HI), can a five-region/three-sided confidence interval be wider than a classical one  odds ratio can produce at most two open regions (where the precisions of the odds ratios can be traded off). The two open regions plus the remaining one closed region constitute a total of three \u2018sides\u2019, and thus no further performance improvement can be expected beyond Goeman et al.\u2019s three-sided confidence interval2.If a researcher opts for a more precise estimation, he/she will choose a method that produces a narrower confidence interval. In most circumstances, a five-region confidence interval  is at least as narrow as a classical one Fig.\u00a0. Only whTo characterize the association between an exposure and a disease, the current epidemiologic paradigm calls for a trio of inferential statistics to be presented for the odds ratio: a point estimate, a  p-value, and a  confidence interval, respectively. In this paper, we show that the five-region methods can describe a putative association more efficiently and informatively, including its presence or absence, as well as its direction and strength (if any association exists). The five-region methods are recommended for routine use during the analysis of epidemiologic data.Supplementary information."}
+{"text": "Although the Short Test of Functional Health Literacy in Adults (S-TOFHLA) is widely used, misidentification of individuals with low health literacy (HL) in specific HL dimensions, like numeracy, is a concern. We examined the degree to which individuals scored as \u201cadequate\u201d HL on the S-TOFHLA would be considered as having low HL by two additional numerical measures.English-speaking adults aged 45\u201375\u00a0years were recruited from a large, urban academic medical center and a community foodbank in the United States. Participants completed the S-TOFHLA, the Subjective Numeracy Scale (SNS), and the Graphical Literacy Measure (GL), an objective measure of a person\u2019s ability to interpret numeric information presented graphically. Established cut-points or a median split classified participants and having high and low numeracy.n\u00a0=\u2009187), on average were: aged 58\u00a0years; 63% female; 70% Black/African American; and 45% had a high school degree or less. Of those who scored \u201cadequate\u201d on the S-TOFHLA, 50% scored low on the SNS and 40% scored low on GL. Correlation between the S-TOFHLA and the SNS Total was moderate , while correlation between the S-TOFHLA and the GL Total was large .Participants . Health literacy (HL) represents a complex intersection of skills needed to \u201cobtain, process, understand, and communicate about health-related information needed to make informed health decisions.\u201d \u20133 The 20HL measures are useful for evaluating and classifying patient abilities so that information can be presented in a way to meet patients\u2019 skills and needs. Yet, existing measures of HL may lack the specificity to accurately assess patients\u2019 ability to comprehend numeric information, providing a limited view of patients\u2019 abilities , 12\u201314. The S-TOFHLA is the most frequently used measure of HL, used in over half of all published papers measuring HL , 11. Howclinicaltrials.gov: NCT02151032) designed to investigate the use of decision aids in colorectal cancer screening. Eligible participants were English-speaking, aged 45\u201375\u00a0years, and had no history of colorectal cancer. Participants were recruited in person between November 2012 and January 2013 in the Greater Houston Metropolitan area from: , 3210, 3Numeracy is a vital element of HL and is a priority for optimizing risk communication , 17. TheThe GL is a 13-item objective measure that assesses how individuals understand graphically-presented quantitative information . UnderstAs reported in the previous section, no optimal score cut-points exist for the SNS and the GL. Thus, we used three complementary scoring strategies. First, we used the median score from the total score to identify low and high literacy groups, based on a median split. This approach is justified based on the study setting, where more than half of the participants came from a community-based organization serving underserved groups. Second, a more conservative threshold was used, where the lowest quartile of participants from the total scores were classified as having low HL, an approach common in educational literature , 48. We Demographic characteristics, frequencies, and descriptive statistics were generated to summarize our participant population using IBM SPSS Version 23. The three S-TOFHLA HL categories  were used for scoring. For the other HL measures, we categorized the variables into high and low categories Table . These cOne hundred eighty-nine individuals enrolled in the study (67 from the cancer prevention center and 122 from the foodbank) and completed the questionnaires; however, two participants were excluded from the analyses due to missing data, for a total of 187 participants (Table\u00a0n\u00a0=\u2009134) scored \u201cadequate\u201d on the S-TOFHLA, while only 10.7% (n\u00a0=\u200920) scored in the \u201cmarginal\u201d category, and 17.6% (n\u00a0=\u200933) scored \u201cinadequate\u201d  of participants were in the bottom 25th percentile of the SNS Total score. Moreover, for the Ability and Preference Subscales, 30% (n\u00a0=\u200940) and 35% (n\u00a0=\u200947) of participants were categorized as \u201cadequate\u201d by the S-TOFHLA but in the bottom 25th percentile of their respective scale scores.Of those who scored \u201cadequate\u201d on the S-TOFHLA, 26% (n\u00a0=\u200953) of those classified as \u201cadequate\u201d on the S-TOFHLA were low on GL Total score. Furthermore, 18% (n\u00a0=\u200924) of those scoring in the bottom 25th percentile on GL Total, scored \u201cadequate\u201d on the S-TOFHLA. For the GL Subscales, 13% (n\u00a0=\u200918) of those classified as \u201cadequate\u201d on the S-TOFHLA were in the bottom 25th percentile of the GL1 Subscale. For the GL2 subscale, 21% (n\u00a0=\u200928) of those classified as \u201cadequate\u201d on the S-TOFHLA were in the bottom 25th percentile. Lastly, 30% (n\u2009=\u200940) were classified as \u201cadequate\u201d on the S-TOFHLA and in the bottom 25th percentile on the GL3 Subscale.Forty percent . The correlation between the S-TOFHLA and SNS Prefer scores was not significant . The S-TOFHLA and GL Total and GL 1 scores showed large, positive correlations . The correlation for the S-TOFHLA and GL3 was moderate in magnitude .Correlations between S-TOFHLA scores and SNS Total  to engage in these types of decisions. HL is a complex construct, and existing literature identifies and describes multiple ways of measuring it. For example, Duell et al. identified three levels for HL measurement: basic, communicative/interactive, and critical HL . These lThere are various approaches to help address the challenges associated with measuring HL. First, the assumption that a single HL measure is adequate may not be the case. The HL measures included in our investigation show the need for capturing the complex skills that make-up HL. While previous studies have provided evidence to push back against commonly-used measures, such as the S-TOFHLA and REALM, a continued effort to challenge the expected use of one of these tools as a way to definitively identify those with low HL is needed , 50. FurThis research study has potential limitations. This study was conducted in a large urban area using a convenience sample. Thus, the sample is diverse and matches the makeup of large urban centers, but rural patients may have not been well represented which may impact generalizability. Second, we used the 36-item S-TOFHLA measure, which does not assess numeracy. Although this measure is broadly accepted , includiThe S-TOFHLA is limited in its measure of HL. Though widely used, those with inadequate HL skills may be over-classified as having \u201cadequate\u201d HL, based on their S-TOFHLA scores. Use of HL measures that include numeracy, graphical, and preference questions is essential when considering measuring HL. Existing numeracy or graphical measures may be too cumbersome for the clinical setting but have higher utility when categorizing those with high and low numerical skills, which may be of particular interest to those developing decision support tools. Developing a brief tool with both subjective and objective quantitative questions may augment HL numeracy measurement."}
+{"text": "Scientific Reports 10.1038/s41598-017-09769-y, published online 30 August 2017Correction to: The original version of this Article contained an error in the title of the paper, where the family name \u201cCrassulaceae\u201d was incorrectly given as \u201cCrassulacaee\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Material."}
+{"text": "G that together cover all nodes, or edges, of G.Reconstructing the genome of a species from short fragments is one of the oldest bioinformatics problems. Metagenomic assembly is a variant of the problem asking to reconstruct the circular genomes of all bacterial species present in a sequencing sample. This problem can be naturally formulated as finding a collection of circular walks of a directed graph safe if it returns only those walks  that appear as subwalk in all metagenomic assembly solutions for G. A safe algorithm is called complete if it returns all safe walks of G.We address this problem with the \u201csafe and complete\u201d framework of Tomescu and Medvedev (Research in computational Molecular biology\u201420th annual conference, RECOMB 9649:152\u2013163, G, and a safe and complete algorithm finding all safe walks of G. In the node-covering case, our algorithm runs in time n and m denote the number of nodes and edges, respectively, of G. This algorithm constitutes the first theoretical tight upper bound on what can be safely assembled from metagenomic reads using this problem formulation.We give graph-theoretic characterizations of the safe walks of  In general, we do not know how many bacterial species are in the sample, so we cannot place any bound on the number of circular walks. Hence, in our above formulation they can be any arbitrary number. See the next section for formal definitions, and Fig. Because of the multiple genomes present in the sample, one can no longer formulate a solution for the metagenomic assembly problem as a It can be easily verified that the walks from\u00a0, 20\u201322\u2014wall walks w of a graph G such that for any metagenomic assembly solution R of G, w is a sub-walk of some circular walk in R. As opposed to the exhaustive search strategy from\u00a0 be the subgraph of G induced by the edges of C. Clearly, C is a node-covering circular walk of G[C], and thus G[C] is strongly connected. Moreover, we can argue that w is a node-omnitig in G[C], as follows. By taking the shortest proper circular sub-walk of C passing through x we obtain a cycle x. From (b), we get that w is a sub-walk of G[C], then also all edges of w appear in G[C] and thus w is a walk in G[C]. The two conditions from the definition of node-omnitigs are preserved under removing edges from G, thus w is a node-omnitig also in G[C]. By applying Theorem\u00a0G[C] we obtain that w is a sub-walk of all node-covering circular walks of G[C], and in particular, also of C. We have thus shown that for every node-covering metagenomic reconstruction R of G, there exists w is a sub-walk of C. Therefore, w is a node-safe walk for G. Otherwise, let mentclass2pt{minimThe following statement is a simple corollary of condition (b) from Theorem\u00a0LetG be a strongly connected graph, and letw be a safe walk inG. Then w is either a path or a cycle.We now give the analogous characterization of edge-safe walks. We first recall the analogous definition of edge-omnitigs from\u00a0. This isEdge-omnitig, [G be a graph and let G. We say that w is an edge-omnitig if for all  Let G bG that are sub-walks of all edge-covering circular walks of G. Our characterization of the edge-safe walks considered in this paper is:In\u00a0, it was LetG be a strongly connected graph. A walk inG is an edge-safe walk inG if and only if the following conditions hold:w is an edge-omnitig, andthere exists such thatw is a sub-walk of all cycles passing through\u00a0e.S(G) obtained from G by sub-dividing every edge once.Theorem\u00a0G, we let S(G) denote the graph obtained from G by subdividing each edge once. Namely, each edge  of G is replaced by two edges u, and exactly one out-neighbor, v. We can analogously define this operation for a walk w in G, and then consider the walk S(w) in S(G).Given a graph w is an edge-safe walk in G if and only if S(w) is a node-safe walk in S(G). Indeed, observe that the edge-covering metagenomic reconstructions of G are in bijection with the node-covering metagenomic reconstructions of S(G), the bijection being w is a sub-walk of a walk C in G if and only if S(w) is a sub-walk of S(C) in S(G). Therefore, w is an edge-safe walk in G if and only if S(w) is a node-safe walk in S(G).The proof follows the outline given in Fig.\u00a0w satisfies conditions (a) and (b) of Theorem\u00a0G if and only if S(w) satisfies conditions (a) and (b) of Theorem\u00a0S(G).It remains to show that Condition (a): It immediately follows from the definition that if S(w) is a node-omnitig in S(G) then w is an edge-omnitig in G. Assume now that w is an edge-omnitig in G. By the construction of S(G) and S(w), between any two consecutive nodes of S(w) there can be only one path in S(G) . Therefore, S(w) is a node-omnitig in S(G).Condition (b): Suppose that there exists an edge G passing through e contain w as sub-walk. Then by construction all cycles in S(G) passing through S(w) as sub-walk. Conversely, suppose that there exists a node S(G) passing through x contain S(w) as sub-walk. If x is a node of the type u,\u00a0v) of G, then it also holds that all cycles in G passing through w as sub-walk. Otherwise, if x,\u00a0y) be an arbitrary edge of G out-going from x; this exists because G is strongly connected. We claim that all cycles in G passing through w as sub-walk. Indeed, let S(G) corresponding to the edge . The set of cycles of S(G) passing through S(G) passing through x. Therefore, all cycles of S(G) passing through S(w) as sub-walk. We have now reduced this case to the previous one, when x is a node of the type u,\u00a0v) of G, and the claim follows. In this section we give an algorithm for finding all node-safe walks of a strongly connected graph. In the next section we show how to implement this algorithm to run in We begin with an easy lemma stating a simple condition when a maximum overlap of two node-omnitigs is a node-omnitig.LetG be a graph, and let be a walk of length at least two inG. We have thatw is a node-omnitig if and only if and are node-omnitigs and there is no path with first edge different than and last edge different thanw is a node-omnitig. The forward implication is trivial, as by definition sub-walks of node-omnitigs are node-omnitigs. For the backward implication, since both w can also be a single node.The following definition captures condition (b) from Theorem\u00a0Certificate) Let G be a graph and let w be a walk in G. A node w is a sub-walk of all cycles passing through x is called a certificate of w. The set of all certificates of w will be denoted  C first traverses C first traverses w is a node-omnitig and x-x path w is a node-omnitig.We now prove the reverse inclusion by induction on the length of w into the two walks x, once it passes through x passes also through w, and hence We now use the inductive hypothesis to show that if C the sub-walk of C starting at k, that is, Given a circular walk G (possibly with duplicates), but does not return each node-safe walk explicitly. Instead, it returns a node-covering circular walk C of G and the set of pairs  such that C is a node-safe walk.Algorithm\u00a01 finds all node-safe walks of a strongly connected graph C and checking whether each sub-walk of C starting at index i and of length k is a node-omnitig and has at least one certificate. If so, then it stores the index i in a set k. The algorithm first deals with the case C is a node-omnitig (Line\u00a07) and whether it has at least one certificate (Line\u00a08). The case C has at least one certificate (Line\u00a012).The algorithm works by scanning G and C to perform these verifications in constant time. This algorithm can be modified to output node-safe walks also without duplicates. For clarity, we explain this idea in the proof of Theorem\u00a0maximal node-safe walks, i.e., those that are not sub-walks of any other node-safe walk.In the next section we show how to pre-process Given a strongly connected graphG, Algorithm\u00a01 correctly computes all the node-safe walks ofG, possibly with duplicates.k that the set i for which C is a node-safe walk of length k. In the base case C is a node-omnitig (Line\u00a07). We also check if C has at least one certificate, by checking  is a node-safe walk  is a node-omnitig if and only if We will first prove by induction on entclass1pt{minimaG are paths or cycles, thus of length at most n. By the definition of node-safe, they are also sub-walks of C. Thus for each node-safe walk w of G of length By Corollary\u00a0In this section we describe the implementation of Algorithm\u00a01. We first show how to compute the certificates of all nodes.G be a strongly connected graph withn nodes andm edges. We can compute the sets for all, in timeO(mn).Let x . We then construct the graph G once. That is, we replace every node x of G with two nodes y,\u00a0z) of G, we add to We start by initializing O(m). We then iterate through all x belongs to all cycles of G passing through y, and thus we add y to O(mn) time. For every The following lemma shows how to check in constant time the first condition in the definition of node-omnitig.LetG be a graph withm edges. We can pre-processG in time  and space such that for every two distinct edges, we can answer inO(1) time if there is a path inG with first edge different than and last edge different thanWe show how to pre-compute a table G by removing z to compute how many of its in-neighbors are reachable from z, and for each in-neighbor w, we let w is reachable from z path in G with first edge different than w,\u00a0z) if and only if O(m), and then we process each edge of We iterate through all edges Using e.g., the result of\u00a0, we can LetG be a graph withm edges, we can pre-processG in timeO(m) such that for every edge we can answer inO(1) time whether  is the onlyx\u2013y path .strong bridge is an edge whose removal increases the number of strongly connected components of a graph  is a strong bridge. In\u00a0[A ee e.g.,\u00a0). It is idge. In\u00a0 it was si in C, the smallest  index C has a non-empty set of certificates if and only if k to i, that is, The following lemma shows how to check in constant time condition (b) from Theorem\u00a0LetG be a graph withn nodes andm edges, and let be a circular walk inG, with We can pre-processG and C in time , such that for every and, we can answer inO(1) time ifi, by n telling in how many of To simplify the notation, given an integer t as long as t reaches 0, then all sets O(n), and there are O(d) intersections to compute, giving a total of We begin by computing O(n) time.For O(n), by scanning the current intersection and removing the elements of d times, because for each i we start this scan from index Otherwise, we keep increasing We are now ready to combine these lemmas into the main theorem of this section.Algorithm\u00a01 can be implemented to run in time for any strongly connected graph withn nodes andm edges.G as G is strongly connected), and then continue from Any strongly connected graph admits a node-covering circular walk given in\u00a0.G and C as indicated in Lemmas\u00a0d. By Lemma\u00a0In the next section we discuss how to optimize Algorithm\u00a01 to start with a node-covering metagenomic reconstruction of minimum total length. However, there are graphs in which any node-covering metagenomic reconstruction has length maximal node-safe walks, that is, in node-safe walks that are not sub-walks of any other node-safe walk. A trivial way to obtain these is to take the output of Algorithm\u00a01, convert it into the set of all node-safe walks of G, and run a suffix-tree-based algorithm for removing the non-maximal ones, in time linear in their total length. However, given a node-covering circular walk C of length In a practical genome assembly setting we want to reconstruct fragments of the genomes as long as possible. As such, we are interested only in k is maximal if it is not extended into a node-safe walk of length C to check for previous occurrences of each walk of length k.In the next theorem we show how to reduce this time complexity to Given a strongly connected graphG withn nodes andm edges, Algorithm\u00a01 can be modified to output the maximal node-safe walks ofG explicitly and without duplicates, with a running time ofC of G, of length C there can start the occurrence of at most one maximal node-safe walk. By Corollary\u00a0n, thus the sum of the lengths of all maximal node-safe walks of G is C of all maximal node-safe walks without duplicates, then we can output all of them explicitly within the stated time bound.Let w of length k is maximal if no occurrence C of w in C was extended left or right at step w in C, as follows. Initially, we build the suffix tree T of the (linear) string C for a length T to the node C. In A node-safe walk nt}O(n2) . As we si to suffix-link in T to move to the node T to C with its first character removed). For a detailed discussion on the properties of the suffix tree, see e.g.,\u00a0[T such that the path from the root to C at step k are maximal, we traverse C again to output these node-safe walk.As we advance from ee e.g.,\u00a0. We thenAfter building the suffix tree using , the chierations . Thus, tmentclasspt{minimaIn this section we adapt Algorithm\u00a01 and its implementation to find edge-safe walks, as characterized by Theorem\u00a0LetG be a strongly connected graph withn nodes andm edges. In time we can output an edge-covering circular walk C, and the set of all pairs  such thatC is an edge-safe walk ofG.w consists of the edges e such that all cycles passing through e contain w as sub-walk. Analogously to Lemma\u00a0w equals the intersection of the sets of certificates of its individual edges. The algorithm for the edge-safe case is that same as Algorithm\u00a01, with the difference that we now start with an edge-covering circular walk C and we do not check anymore that each C is the only The proof is analogous to the node-safe case, and thus we briefly sketch the differences. In the edge-covering case, the set of certificates of a walk C has length at most mn and can be found in time O(mn). The certificates of all edges can be similarly computed in time C of length O(mn). The only difference in its proof is that the sets of certificates now have size at most m, thus their intersection takes time O(m). This implies that we can pre-compute G and C in time By the same argument given in the proof of Theorem\u00a0C has length O(mn). After this pre-processing phase, the algorithm itself works in time With a proof identical to the one of Theorem\u00a0Given a strongly connected graphG withn nodes andm edges, we can output the maximal edge-safe walks ofG explicitly and without duplicates, in time ofG has a node-covering circular walk of length n if and only if G is Hamiltonian. Observe though that instead of a single node-covering circular walk, we can start with a node-covering metagenomic reconstruction possibly consisting of multiple circular walks, and apply Algorithm\u00a01 to each walk in the reconstruction. This is correct by definition, since node-safe walks are sub-walks of some walk in any node-covering metagenomic reconstruction.A trivial way to optimize Algorithm\u00a01 is to start with a node-covering circular walk of minimum length. However, this is an NP-hard problem, since G, we construct the graph G once . In terms of real graph instances, the worst-case complexity of our algorithm may be prohibitive, and thus improving it is an important problem.We also leave for future work an idealized experimental study similar to what was done for the single genome case in . This coThe ultimate goal of a \u201csafe and complete\u201d approach is to be adapted to the peculiarities of real data, such as sequencing errors, insufficient sequencing coverage, reverse complements. However, our belief is that we first need a clean and solid theoretical foundation, which can later be extended, or weakened, to account for such features."}
+{"text": "An X-ray Talbot-Lau interferometer scanning setup consisting of three transmission gratings, a laboratory-based X-ray source that emits X-rays vertically, and an image detector on the top has been developed for the application of X-ray phase imaging to moving objects that cannot be tested clearly with conventional absorption contrast. The grating-based X-ray phase imaging method usually employs a phase-stepping (or fringe-scanning) technique by displacing one of the gratings step-by-step while the object stays still. Since this approach is not compatible with a scanner-type application for moving objects, we have developed a new algorithm for achieving the function of phase-stepping without grating displacement. By analyzing the movie of the moir\u00e9 pattern as the object moves across the field of view, we obtain the absorption, differential phase, and visibility images. The feasibility of the X-ray phase imaging scanner has been successfully demonstrated for a long sample moving at 5\u2009mm/s. This achievement is a breakthrough for the practical industrial application of X-ray phase imaging for screening objects carried on belt-conveyers such as those in factories. Among the methods of X-ray phase imaging reported so far, X-ray grating interferometry, such as X-ray Talbot interferometry5 and X-ray Talbot-Lau interferometry6, which is an advanced form of X-ray Talbot interferometry, is especially effective for practical X-ray phase imaging in clinical and industrial fields because they operate with conventional X-ray generators in hospitals and factories.X-ray phase imaging has been attracting attention because it produces significant contrast for weakly absorbing objects, such as polymers and soft biological tissues7, respectively. X-ray phase imaging separates these information quantitatively and generates absorption, refraction, and scattering  images.A Talbot or Talbot-Lau interferometer detects the slight X-ray refraction caused by an object. When the object is placed in the interferometer, the intensity change is detected through the gratings at each pixel of an image detector. This feature can be seen as a moir\u00e9 pattern. X-ray phase imaging with interferometers is normally performed by analyzing moir\u00e9 patterns acquired through a specific technique; that is, a fringe-scanning or phase-stepping technique by displacing one of the gratings. Moir\u00e9 fringes contain the information of attenuation, phase shift (refraction), and scattering by an object; they appear as the changes of fringe intensity, fringe position, and fringe visibilityIn the fringe-scanning procedure in combination with the grating displacement, the object is assumed to stay still in the field of view (FOV) during the entire scan, which is typically 30\u2009s in the clinical application of X-ray phase imaging reported in ref. This paper proposes an approach of a fringe-scanning method without any grating displacement for moving objects in the configuration of an X-ray Talbot-Lau interferometer. An apparatus (X-ray phase scanner) consisting of an X-ray source that emits X-rays vertically, X-ray transmission gratings, a sample stage that moves objects horizontally like a belt-conveyer, and a photon-counting image detector have been developed to demonstrate the approach. A pilot experiment of successful X-ray phase imaging for moving objects larger than the FOV of the apparatus is presented.An X-ray generator consisting of a tungsten rotating anode  was placed at the bottom of the scanner to generate cone-beam X-rays in the vertical direction. The generator can be operated at up to 60\u2009kV tube voltage and 90\u2009mA tube current (5.4\u2009kW maximum load). The focus size on the anode surface was 0.3\u2009mm\u2009\u00d7\u20093\u2009mm and the effective X-ray source size was 0.3\u2009mm\u2009\u00d7\u20090.3\u2009mm, taking into account the take-off angle (6\u00b0). The X-ray source size does not satisfy the requirement of spatial coherence for a Talbot interferometer, and therefore Talbot-Lau configuration with a source grating (G0), \u03c0/2-type phase grating (G1) and absorption grating (G2)  was employed. The gratings were mounted and aligned using mechanical stages, as shown in Fig.\u00a06\u2009cps/pixel with a readout speed up to 174 fps frame rate.An image detector  was mounted on the top of the scanner to capture a movie of the moir\u00e9 pattern while the sample is moved across the FOV. The detector is a photon-counting two-dimensional hybrid pixel array semiconductor detector having an active area of 77.5\u2009mm\u2009\u00d7\u200938.5\u2009mm with a pixel size of 100\u2009\u03bcm\u2009\u00d7\u2009100\u2009\u03bcm. The detector has an X-ray photon count rate of greater than 1011. However, the actual gratings used for a Talbot-Lau interferometer have slight deformations due to the fabrication process and mounting, and the degradation in resultant image quality is not negligible. It is not easy to fabricate an ideal grating, especially when a large area is required. In this study, we propose an algorithm that is applicable even when the gratings are deformed. Thus, the degradation of image quality is avoided, which leads to reduction in the cost of the apparatus.An approach for the fringe-scanning method without grating movement has been reported by generating artificial moir\u00e9 fringes with the assumption that the gratings are ideally fabricated and the spacing of the moir\u00e9 fringes is constantA, refraction \u03c6, and visibility V from a recorded moir\u00e9 movie of sample scanning. Here, p and q are the image coordinates fixed to the moving sample in the x- and y-directions, respectively, as shown in Fig.\u00a0p, q) on the detector plane, and therefore, the coordinates on the sample are calculated by considering the magnification due to a cone-beam projection. The movement of a sample is assumed to be parallel with the x-axis in this setup. Therefore, x\u2009=\u2009p\u2212vt and y\u2009=\u2009q, where v is the nominal sample speed on the detector plane and t is time.The purpose of the algorithm is to calculate three resultant images, namely, absorption 12 with grating displacement without a sample. Given the moir\u00e9 pattern observed at the j-th step of a fringe-scan is Ij0,d1 is the period of G1, z0 is the distance between G1 and G2 and M is the number of phase steps (M\u2009\u2265\u20093). A0 is illumination intensity, \u03c60 is the background differential phase caused by the deformation and alignment of gratings, and V0 is the visibility of moir\u00e9 fringes. Note that \u03c60 is wrapped between \u2212\u03c0 to \u03c0, and phase unwrapping is not needed here.As a pre-processing, the effect of the built-in moir\u00e9 pattern, which is normally observed without a sample because of incomplete grating alignment and slight grating deformation, was measured in advance as an instrumental function. For this purpose, we employed the conventional fringe-scanning technique or modified robust fringe-scanning technique explained elsewherep, q) of the sample must travel across at least one moir\u00e9 fringe along the x-axis. Therefore, \u03c60 must have values spanning from \u2212\u03c0 to \u03c0 at every y (Step 3). If this condition is not satisfied, gratings are re-aligned, for examply by inclining one of the gratings, so that more moir\u00e9 fringes are introduced, and steps 1 and 2 are repeated. After \u03c60 is thus defined, the FOV is divided into n regions, so that the pixel  having the value of \u03c60 between \u2212\u03c0\u2009+\u20092\u03c0(k\u2009\u2212\u20091)/n and \u2212\u03c0\u2009+\u20092\u03c0k/n belongs to the n-th region. Further, flag matrices Ak  (Step 5) are defined as,As explained later, this algorithm assumes that every coordinate point (Ak at every y is stored in Nk(y) (Step 6). The number n must be more than three and should be selected as large as possible, provided that sufficiently large values for Nk(y) are available.The number of flagged pixels in x-direction across the FOV (Step 7). Giving I as the movie frame at ti, where i indicates the frame number , Jk  is calculated (Step 8) byAfter this preparation, a movie is recorded while the sample moves linearly in the p, q) is fixed to the sample and relates to the coordinate  in the FOV with x\u2009=\u2009p\u2212vti and y\u2009=\u2009q. Thus, Jk , which corresponds to the k-th step of fringe-scanning, is obtained without moving gratings but rather by utilizing the movement of the sample. Next, the resultant images are calculated with conventional formulae (Step 9):y (q) direction due to cone-beam illumination. The raw images with moir\u00e9 fringes generated by the experimental setup and an example of the definition of Ak are shown in Fig.\u00a0As mentioned above, the coordinate . These parameters were chosen so that the nominal speed of the sample at the detector plane was one pixel per frame. The mean visibility of moir\u00e9 fringes  of the differential edge profile of the sample feature in the absorption image. The spatial resolution in the y-direction, which was independent of the motion blur, was evaluated by the FWHM of a sharp edge profile in the refraction image. They are shown as functions of v in Fig.\u00a0x-direction. Actually, the spatial resolution near the Nyquist limit was attained below 5\u2009mm/s, and clear degradation of the spatial resolution is found over that speed. Although the spatial resolution in the y-direction was almost constant as expected, the slight degradation shown in Fig.\u00a0The sample speed is crucial to the spatial resolution in terms of motion blur. The spatial resolution at the detector plane in the 13. Thus, it is feasible to improve the apparatus design for a high-energy phase-imaging scanner.The apparatus presented here was developed mainly to demonstrate the function of the proposed algorithm to realize phase imaging for moving objects. In order to translate this result into the development of practical apparatuses for use in factories, various improvements are needed, such as increasing the sample speed and expanding the FOV. The spatial resolution due to vibration at higher speed could be improved, for example, by equipping a rigid and X-ray transparent stage, to which belt-conveyers are adjacent and products moving on the belt-conveyers are transferred smoothly. In order to increase the sample speed, detector sensitivity is essentially important. The detector employed in this study (Hypix-3000) was dedicated originally for low-energy X-ray experiments, which can be replaced for example with a CdTe-based photon counting image detector suitable for high-energy X-rays used for non-destructive testing. Fabrication of gratings with a high-aspect-ratio is also needed to enable the use of higher energy X-rays. While the height of the gold pattern of G2 was about 100\u2009\u00b5m, a fabrication technique for realizing a height of 160\u2009\u00b5m has been utilized for an experiment with 183-keV X-raysy-direction, larger gratings and a larger image detector are necessary. Fabrication of a large grating is a challenging task, but gratings of a 10\u2009cm\u2009\u00d7\u200910\u2009cm area14 have been fabricated. However, when a larger grating is employed with a cone-beam illumination, a curved form is required for a high-aspect-ratio grating, which creates another technical challenge. Instead, it is also possible to align multiple flat gratings and detectors to cover an area larger than the FOV of each grating-detector set.In order to expand the FOV especially in the Although the scanner was developed for imaging continuously moving objects, the concept can be applied for the relative movement between objects and the Talbot-Lau interferometer system. Therefore, scanning the Talbot-Lau interferometer with an X-ray source and detector against a stable object is feasible with the same concept of image formation. As a result, this study can be expanded to the examination of big structures that cannot be moved easily and to the human body for medical diagnoses.An X-ray phase-sensitive scanner with the Talbot-Lau interferometer configuration and a laboratory-based X-ray source was demonstrated. While conventional phase imaging is performed for an object stable in the FOV with the fringe-scanning technique, a special algorithm was proposed and implemented in this study for an object moving across the FOV. It should be noted that this algorithm allows the use of slightly deformed gratings. X-ray phase imaging was successfully performed for a sample moving at 5\u2009mm/s with a spatial resolution of about 200\u2009\u00b5m, which corresponded to the Nyquist frequency of the detector. Thus, the presented X-ray scanning setup is promising for practical use of X-ray phase imaging at factories for quality control of products moving on a belt-conveyor system."}
+{"text": "In this work, we establish the maximal  A of an analytic semigroup on a Banach space X is said to have maximal u of the following parabolic differential equationX, every generator of a bounded analytic semigroup has maximal R-boundedness of a family of operators using the resolvent Maximal gularity , and Hilgularity . Beyond  by Weis  on UMD smentclass2pt{minimA-stable Runge\u2013Kutta methods. Kemmochi and Saito \u03b1\u03c4\u03b1.If  is satisestimate  in the fThe constant in condition  is sharphe model , and forition in . Hence, S(A) is the closed interval spanned by the largest and smallest eigenvalues, but in general, the numerical range S(A) has to be approximated [The condition  covers bR-boundedness of operator-valued analytic functions) If the function R-bounded on X, and its R-bound is at most, and R-bound of the set of operators Let e scheme  satisfieR-bounded. In fact, for R-bounded. It suffices to prove that the family of operators mentclass2pt{minimLet the function fined in , and \\doX be a UMD space, A be an R-sectorial operator on X of angle A), and R-bound of the set Let e scheme  satisfieR-bounded. Since R-bounded, by Lemma R-bounded for some R-bounded. However, C is some constant which may depend on A. By Lemma R-bounded and its R-bound is at mostR-bounded. If entclass1pt{minimaequation . Meanwhi\u03b8\u03c6)\u03c4\u03b1.If  is satisIn this section, we consider maximal adrature .We shall need the scaled X be a Banach space, A be a sectorial operator on X of angle N, A.Let E scheme  has the n, we haveK(z) is defined byzR is bounded for zR is also bounded for K(z)v is analytic in z in the region enclosed by v to the piecewise constant functionBy multiplying both sides of  by \\docuf, the maximal A, rather than the R-sectorial property. The general case  is a linear combination of  , for whiIn the proof of Theorem X be a Banach space, A be a sectorial operator on X of angle N, A.Let E scheme  has the In this section, we present a few examples of fractional evolution equations which possess the maximal Continuous problem) Consider the following time fractional parabolic equation in a bounded smooth domain R-sectorial operator in X with angle (Time discretization) Since the Dirichlet Laplacian R-sectorial of angle  Consider the following space\u2013time nonlocal parabolic equation in R-sectorial of angle  Consider the following time-fractional PDE with a complex coefficient in a bounded Lipschitz domain R-sectorial of angle (estimate  when \\doestimate  when \\doAs an application of the maximal E scheme , with th}Lp-norm . Other tR-sectorial operator of angle u of (Let ion u of  be suffiion u of  satisfieWe denote by \u2016En\u2016X\u2264c\u03c4 . By applu is smooth, and (If oth, and  gives thmentclass2pt{minimproblems . We will"}
+{"text": "L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the category CS can be embedded in the category SL-CS as a coreflective subcategory when L satisfying a multiplicative condition. By comparing the two functors and the well known Lowen functor , we exhibit the difference between (stratified L-)topological spaces and (stratified L-)convex spaces.Consider  Abstract convexity theory is an important branch of mathematics -convexity -convexity is precisely an M-fuzzifying convexity; when L,\u00a0M)-convexity is precisely an L-convexity; and when L,\u00a0M)-convexity is precisely a convexity. Similar to  topology, the categorical relationships between convexity and latticed-valued convexity is an important direction of research. When L being a completely distributive complete lattices with some additional conditions, Pang and Shi (L-convex spaces as a coreflective subcategory.It is easily seen that there is some similarity between convexity and topology (a family of subsets of a set closed for union and finite intersection). Thus, similar to lattice-valued topologies  to the category of stratified L-convex spaces (denoted by SL-CS). The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory when L being a continuous lattice. The second functor enables us to prove that the category CS can be embedded in the category SL-CS as a coreflective subcategory when the continuous lattice L satisfying a multiplicative condition. The second functor is an extension of Pang and Shi\u2019s functor topological spaces and (stratified L-)convex spaces from the categorical sense.In this paper, we shall continue to study the categorical relationships between convex spaces and stratified  functor  from theCS in the category SL-CS. In \u201cCS in the category SL-CS. Finally, we end this paper with a summary of conclusion.The contents are arranged as follows. In \u201ca is way below b (2)(3)such that(4)for some: Maruyama  A subsetL-convex spaces is called L-convexity-preserving  provided that L-convex spaces and whose morphisms are L-CP mappings will be denoted by SL-CS.A mapping Finally, we recall some categorical notions from Ad\u00e1mek et\u00a0al. .A and B are concrete categories; F,\u00a0G) is called a Galois correspondence if B-morphism; and A-morphism. is a Galois correspondence, then F is a left adjoint of G , hence F and G form an adjunction If . It is obvious.(LC2). It is easily seen that N is the set of all choice functions For any Let (LC3) Let 2.The set It is easily seen that 3.For any We have proved that for any By a combination of (1)\u2013(3), we have proved that Let be a convex space. Then iffThe sufficiency is obvious. We check the necessity. Let is CP iffisL-CP.L-CP. Let L-CP. Then for any Conversely, let It is easily seen that the correspondence Let be a stratifiedL-convex space. Then the setforms a convex structure onXand the correspondencedefines a concrete functor For any For any Let be directed. Thenfor anyLet L is called multiplicative  and (LC2) are obvious. We only check (LC3) below.C being closed for intersection and directed union. Let L-convex space. Then Pang and Shi convex space from (L-) topological spaces.At last, we give two interesting examples to distinguish \u2013(2), we can define (stratified) L-convex structure on M.Let L being a continuous lattice, an embedding functor from the category CS to SL-CS is introduced, then it is used to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. When L being a continuous lattice with a multiplicative condition, Pang and Shi\u2019s functor topological spaces and (stratified L-) convex spaces from categorical sense.When  functor  is gener"}
+{"text": "The results indicate that the band structure changes from semiconducting to metallic and a negative differential resistance effect occurs in the I-V curve. Interestingly, the current can be reduced to zero and this insulator-like state can be maintained as the bias increases. We find this unique property is originated from a peculiar band morphology, with only two subbands appearing around the Fermi level while others being far away. Furthermore the width and symmetry of the zigzag C2N-h2D nanoribbon can be used to tune the transport properties, such as cut-off bias and the maximum current. We also explore the electron transport property of an aperiodic model composed of two nanoribbons with different widths and obtain the same conclusion. This mechanism can be extended to other systems, e.g., hybrid BCN nanoribbons. Our discoveries suggest that the zigzag C2N-h2D nanoribbon has great potential in nanoelectronics applications.Motivated by the fabrication of layered two-dimensional material C Compared to graphene, its band opens a direct gap of 1.70\u2009eV, and the field-effect-transistor fabricated thereon has a high on/off ratio of 107, suggesting great potential in device application. In previous studies on fullerences, carbon nanotubes and graphene-based structures, researchers have found the negative differential resistance (NDR) effect which can be applied to logic operators, molecular switch, memory, oscillator, etc refs et al.et al.p+/p junction based on zigzag-edged graphene. Khoo et al.2N-h2D)-based model, and investigate the effect of width and symmetry on its electronic and transport properties. By performing first-principles calculations, we find C2N-h2D changes from semiconducting to metallic after been cut into a nanoribbon. In order to explore the physical mechanism, we first set up a periodic model. A NDR effect appears in this periodic system, surprisingly, the current can reduce to zero and then this state can be maintained as the bias increases. In a few nano-sized systems, this kind of phenomenon is rarely reported. In-depth study shows that this unique phenomenon stems from the peculiar band morphology where there are only two subbands near the Fermi level and others are far away. In addition, the width and symmetry of the zigzag C2N-h2D nanoribbon can tune the cut-off bias and the maximum current. We also show that similar electron transport occurs in a heterogeneous model and other materials. These transport properties are quite useful for future nanoelectronic device applications.Two-dimensional 2D) materials have attracted tremendous attention for applications in future nanoelectronics owing to their physical, electrical and chemical propertiesD materia4562N-h2D into a zigzag nanoribbon due to the presence of holes and nitrogen atoms. Classification can be carried out according to the atomic species of nanoribbon edges, e.g., carbon and nitrogen-edged or carbon-edged. In our research, we select the structure whose edge atoms are all carbon atoms. To show the nanoribbons more intuitively and clearly, here we use W to denote the width and choose W\u2009=\u20091.0 to 3.0 models to study. The schematic illustration of zigzag C2N-h2D nanoribbons with different widths is shown in 2N-h2D nanoribbon electrode, the central scattering region and the right semi-finite zigzag C2N-h2D nanoribbon electrode  characteristic of the two-probe system with W\u2009=\u20091.0. Apparently, a NDR peak appears in our model. The current firstly increases as the bias increases and reaches the maximum when the bias is 0.2\u2009V and then smoothly decreases to zero as the bias increases to 0.5\u2009V. We define 0.5\u2009V as the cut-off bias. Interestingly, as the bias continues to increase, the current maintains at zero. It indicates that the system is in an insulator-like state. This is contrary to its metallic state under a low bias. As far as we know, this phenomenon has not been reported in periodic systems with widths of several nanometers. A similar I-V characteristic can be seen in W\u2009=\u20091.5 model as shown in I-V characteristic of our models, we first calculate the transmission spectra of W\u2009=\u20091.5 model under different biases as shown in In order to investigate the physical mechanism of the peculiar 2N-h2D nanoribbon. For better illustration, we define the following variables, EAD\u2009=\u2009EA\u2009\u2212\u2009ED, EAB\u2009=\u2009EA\u2009\u2212\u2009EB and ECD\u2009=\u2009EC\u2009\u2212\u2009ED where EA, EB, EC and ED are respectively the energy values of the four subbands near the Fermi level at the \u0393-point. It should also be noted that EA is the minimum energy value of the second band above the Fermi level, ED is the maximum value of the second band below the Fermi level, EB is the maximum value of n\u2009=\u20091 subband and EC is the minimum value of n\u2009=\u20091\u2032 subband. Within the energy range of the EAD, only two subbands cross each other and pass through the Fermi level. Both the left and right electrodes are semi-infinite zigzag C2N-h2D nanoribbons, so they also have such a band structure. If we apply a bias on the electrodes, an electric potential difference will appear between the two electrodes, and their band structures will shift downward or upward relatively. In the middle and right panels of V+) of 0.125\u2009V on the left electrode and a negative bias (V\u2212) of \u22120.125\u2009V on the right electrode. As a result, there appears an energy window (the shadow region) due to the shift of the Fermi level. When the bias is low, the shadow region is small, and both n\u2009=\u20091 and n\u2009=\u20091\u2032 subbands exist in the V+ and V\u2212 regions, that is to say the n\u2009=\u20091 and n\u2009=\u20091\u2032 subbands in the V+ region overlaps those in the V\u2212 region. As the bias increases, the overlapping becomes smaller so that the transmission peak is getting lower. When the bias increases to 0.25\u2009V, in the energy window, the n\u2009=\u20091 subband in the V+ region is connected to the n\u2009=\u20091\u2032 subband in the V\u2212 region. Because the electrons can not hop from one subband to another, the transmission is forbidden. Interestingly, since there are sufficient gaps both in the EAB and ECD ranges, the tunneling channel does not exist and the insulator-like state can be maintained as the bias continues to increase. Meanwhile, we find that the insulator-like state will happen as long as EAB is greater than the absolute value of EC and ECD is greater than the value of EB. The greater EAB and ECD are, the greater bias range the insulator-like state can be kept in. 2N-h2D nanoribbon, whereas the same analysis is invalid for such models with an integer width. For example, the conduction should not be cut off at 0.5\u2009V, so this abnormal phenomenon is worthy of further investigation. 2N-h2D nanoribbon. It is clear that W\u2009=\u20091.0 model has the same band morphology as W\u2009=\u20091.5 model, except that the n\u2009=\u20091 and n\u2009=\u20091\u2032 subbands are more delocalized. \u03c3 mirror operation. Since these two subbands have opposite \u03c3 parity, an electron belonging to n\u2009=\u20091\u2032 subband (blue) can not hop to n\u2009=\u20091 (red) subband18V+ and V\u2212 region, but the electron transport only comes from the coupling between the same color subbands. When the bias increases to 0.5\u2009V, the n\u2009=\u20091 subbands in the V+ and V\u2212 region are connected in the energy window. However the n\u2009=\u20091 subband in the V+ region and the n\u2009=\u20091\u2032 subband in the V\u2212 region have different parity, and the tunneling between these two subbands is forbidden, so that the current is reduced to zero. This state is held as the bias continues to increase. When the bias is high, we can find the insulator-like state is still derived from the presence of band gaps in the range of EAB and ECD. Consequently, the phenomenons of NDR effect and insulator-like state of W\u2009=\u20091.0 model originate from the peculiar band morphology too, except that the different parity between the subbands near the Fermi level prevents the electron transport and promotes the insulation-like state to happen in lower bias.In 2N-h2D nanoribbon, we calculated the band structures of other models with different widths shown in 202N-h2D nanoribbon to tune the cut-off bias in future applications.To explore the effect of width on the electron property of zigzag CI-V) characteristic of the device W2-1. It can be seen that the morphology of the I-V curve is similar to that of W\u2009=\u20091.0 model which is shown in In the above analysis, we focus on the investigation of theoretical physical mechanism. Taking into account the possibility of experimental operation and practical application, a finite bias voltage could not be applied in a homogeneous situation with discrete translational symmetry, in order to avoid this problem we design the device of W2-1 as shown in El and Er regions. The electrons can hop between them, so the current firstly increases. When the bias is larger than 0.15\u2009V, n\u2009=\u20091 subbands do not overlap leaving only the n\u2009=\u20091\u2032 subbands to contribute to the transmission, so the current starts to decrease. When the bias increases to 0.35\u2009V, as show in El region is slightly far away from the n\u2009=\u20091\u2032 subband in the Er region. According to our previous analysis, the current should be zero when these two n\u2009=\u20091\u2032 subbands are connected under a bias less than 0.35\u2009V. It is noteworthy that some disturbance appears in the center of the scattering region after optimization, so the energy levels of the central part are a little different from the electrodes. That is why the current becomes zero at a higher bias. When the bias continues to increase, the current can be maintained at zero. This insulator-like state still derives from the peculiar band morphology which possesses a sufficient band gap between these two n\u2009=\u20091\u2032 subbands. The physics mechanism is consistent with what we discussed previously.It can be seen that when we apply a positive bias on the device, the band structures of the left and right electrodes will shift downward or upward relatively. If the bias is low, the shadow region becomes smaller, and there will be both n\u2009=\u20091 and n\u2009=\u20091\u2032 subbands in the et al.I-V curve here.In our research, we find that this mechanism can be extended to other systems, that is to say, as long as the structure has the similar band morphology, this phenomenon that the current in NDR effect can be reduced to zero and the insulator-like can be maintained will happen. For example, Kan 2N-h2D nanoribbons with different widths are studied using first-principles calculations. By cutting into nanoribbon, C2N-h2D changes from the original semiconductor to metallic structure owing to the introduced two edge states near the Fermi level. The band morphologies for all the nanoribbons have the same special characteristic, i.e., there are only two subbands near the Fermi level while other subbands are far away which leads to the emergence of gaps. To explore the physical mechanism, we give some homogeneous models. An obvious NDR effect and an insulator-like state occur in the I-V curve which has not been reported in such a nano-sized periodic structure in previous works. For asymmetric structures (W\u2009=\u20091.5 and 2.5), this phenomenon originates from the peculiar band morphology. For symmetric structures , besides the peculiar band morphology, the opposite parity of the two edge states is also a factor as it prevents some electron transport and promotes the insulation-like state to happen in lower bias. In addition, as the width increases, the two edge states become more localized, and the cut-off bias decreases. Therefore we can tune the electron transport by changing the width of the zigzag C2N-h2D nanoribbon. We also show a heterogeneous model composed of two zigzag C2N-h2D nanoribbons with different widths. It has a similar I-V curve, the peculiar band morphology still plays a decisive role and the disturbance in the center of the scattering region leads to the occurrence of the insulator-like in a little higher bias. We can also predict that for other materials, as long as they have similar band morphologies, the NDR and insulation-like state will happen.In summary, the electronic and transport properties of the zigzag Ck-point mesh is 1\u2009\u00d7\u20091\u2009\u00d7\u20091002N-h2D nanoribbon are terminated with hydrogen (H) atoms to remove the dangling bonds.To investigate the transport property of our system accurately, the Atomistix Toolkit (ATK) package which is based on the combination of density functional theory (DFT) and non-equilibrium Green\u2019s function (NEGF) technique is performedIn NEGF theory, the current of the two-probe system is calculated based on the Landauer-B\u00fcttiker formula\u03bcL(R) is the chemical potential of the left (right) electrode, f(E\u2009\u2212\u2009\u03bcL(R)) is the Fermi distribution of the left (right) electrode, and V\u2009=\u2009(\u03bcL\u2009\u2212\u2009\u03bcR)/e represents the bias window. T is the transmission coefficient obtained by using Green\u2019s function. Clearly, the current is determined by the area of the integral region in the bias window.where How to cite this article: He, J.-J. et al. Negative differential resistance and bias-modulated metal-to-insulator transition in zigzag C2N-h2D nanoribbon. Sci. Rep.7, 43922; doi: 10.1038/srep43922 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "D be a digraph on D. For any given sequence of pairs of integers k-arc strongly connected digraph D such that d is the degree sequence of D, then d is realizable and D is a realization of d. In this paper, characterizations for k-arc-connected realizable sequences and realizable sequences with arc-connectivity exactly k are given.Let  D is called a multiple digraph (or multi-digraph for short) if it has no loops. Furthermore, if D has parallel arcs neither, then D is strict. We follow ..D, if fodigraphic  if there exists a digraph  D with degree sequence d, where D is called a d-realization. Let d-realizations. Frank [d is required, then Hong et al. [A sequence of integer pairs entclass1pt{minimas. Frank   showed g et al.  gave theLetbe a sequence of non-negative integer pairs. Thendis multi-digraphic if and only if each of the following holds: (i)(ii)Furthermore, for a strict digraph, there is a similar result. The following theorem, which can be found in \u201310 among(Fulkerson-Ryser)Letbe a sequence of non-negative integer pairs withThendis strict digraphic if and only if each of the following holds: (i)(ii)(iii)D be a digraph and k be an integer. If for any arc set S of D with D is said to be k-arc strongly connected (or k-arc-connected for short). Clearly, 1-arc connected digraph is also a strongly connected digraph and vice versa. The arc-connectivity of D, denoted by k such that D is k-arc-connected. In [et al. characterized the sequence of pairs of integers d so that there is a strongly connected digraph k-arc-connected digraph in k-arc-connected multi-digraphs. Furthermore, we also give a characterization for multi-digraphs with arc-connectivity exactly k.Let cted. In , Hong etk-arc-connected realization. In Section\u00a0k. In Section\u00a0In the next section, we will give some tools and methods used in this paper. In Section\u00a0D be a digraph and D. The 2-switch of D is an operation to obtain a new digraph In this section, we give a special notation used in this paper that is also the main tool. Let k-arc-connected digraph or a digraph with arc-connectivity exactly k from an arbitrary digraph in Note that in the operation of 2-switch, the two arcs d to have a k-arc-connected realization  of D if D. An out-fragment  F is minimal if any proper subset of F is no longer an out-fragment . Let D and D. As a vertex set F is an out-fragment if and only if its complement F\u0305 is an in-fragment, D. This observation can be used to prove the following theorem.Let Letbe a sequence of integer pairs. Thendhas ak-arc-connected realization if and only if each of the following holds: (i)(ii)for each(iii)for eachd has a k-arc-connected realization, then by Theorem\u00a0k-arc-connectedness, (ii) holds. So, it suffices to prove the sufficiency. By (i), (iii) and by Theorem\u00a0D is k-arc-connected. Suppose this is not true. Then If D. Let D and By the definition, mentclass2pt{minimClaim 1. If F is an out-fragment of (i)(ii)(iii)(iv)(v)By the definition of Claim 2. F with F is also an out-fragment of D. Since D, which contradicts the minimality of By contradiction, we assume that D and by Claim\u00a02, F of D unless either F such that F is an out-fragment in D, then without loss of generality we may assume D. As D but not in D. Therefore, D is k-arc-connected, and this completes the proof.\u2003\u25a1By choice (a) of D D cannot exceed D is maximally arc-connected if the arc-connectivity of D equals By definition, the arc-connectivity of a digraph Letbe a multi-graphical sequence. Thendis also a degree sequence of some maximally arc-connected multi-digraph.k. Our method is to construct a new multi-digraph in k-arc-connected multi-digraph by reducing the arc-connectivity step by step. Moreover, by Corollary\u00a0In this section, we consider the degree sequence of multi-digraphs with connectivity exactly Letbe two integers andbe a sequence of pairs of integers. DenoteandThendis a degree sequence of some multi-digraph with connectivity exactlykif and only if each of the following hold. (i)(ii)(iii)forwhereifandifd is the degree sequence of some multi-digraph D with connectivity exactly k. By Theorem\u00a0D such that D has connectivity k, there exists First, we consider the necessity. Assume k-arc-connected multi-digraph D has arc-connectivity k, then we are done. So we may assume that k from D. First, we need some claims.Next, we consider the sufficiency. By Theorems Note thatClaim 1. Each of the following holds. (i)For any vertex disjoint two arcs (ii)For any (iii)For any  Denote byD. Now, by Theorem\u00a0D that meets our requirements.D, D is required. So we may assume that By the choice of Claim 2. For any two arcs D.Suppose, to the contrary, that o choice  of D.Claim 3. For any two arcs D. Claim\u00a03 is proved.Suppose, to the contrary, that X are incident with a vertex, say x. We only consider the case By Claim\u00a02 and Claim\u00a03, it is easy to see that all arcs leaving from or interring to Claim 4. We may assume that D.D. So X are incident with y. Let D. So Suppose, to the contrary, that there is an edge o choice  of D. Soo choice  of D. Som, all As k, then by Claim\u00a03 there exists i such that k, and we are done. So we may assume that If u, with an arc between If j, j such that Moreover, by (ii) and (iii), for any k. In other words, all digraphs in If Theorem\u00a0Letbe a sequence of integer pairs. DenoteandIf each of the following holds, then any digraphs inarek-arc-connected. (i)(ii)(iii)there exists somejsuch thatwhereifandifd to have a k-arc-connected realization by using some inequalities of these integers. As a consequence, we deduce a sufficient and necessary condition of d to have a max-arc-connected realization. Also, when d to have a realization D that has arc-connectivity exactly k. These results extend a similar result from undirect graphs into directed graphs.In this paper, sufficient and necessary conditions for a sequences of pairs of integers have been studied. For a sequence"}
+{"text": "Scientific Reports 10.1038/s41598-017-13236-z, published online 19 October 2017Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cPhylogenetic\u201d was incorrectly given as \u201cPhylogentic\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Information file."}
+{"text": "One of our main results is a characterization of permutations that k-commute with a given permutation. Using this characterization, we obtain formulas for the number of permutations that k-commute with a permutation We introduce and study  H the Hamming metric between permutations. Also, Gorenstein et\u00a0al. , and A053871 when In some cases, we need to know upper bounds for the number of permutations that almost commute with a given permutation, as in P\u0103unescu . With thf Sloane : A208529The relationship between the number , Rivera  showed mk-commute with a given permutation k-commute with any n-cycle. We present explicit formulas for the number We review our results. We present a characterization of permutations that points. We write cycle decomposition (Dummit and Foote has cyclea cycle ofa is a point in cycle cycle type of a permutation i in its cycle decomposition. The Hamming metric between permutations good commuting point (resp. bad commuting point) of g.c.p. (resp. b.c.p.). In this work, we use the convention m.We first give some definitions and notation used throughout the work. The elements in the set nd Huang  for moreblockA in a cycle m equivalent expressions of m). The length |A| of block A, and the points first and the last element of the block, respectively. A proper block (resp. improper block) of an m-cycle is a block of length A and B are disjoint if they do not have points in common. The productAB of two disjoint blocks, A and B, not necessarily from the same cycle of AB is not necessarily a block in a cycle of block partition of cycle k pairwise disjoint blocks, not necessarily from the same cycle of block permutationP, induced by Our definition of blocks was motivated by the definitions presented in the work of Christie  and in tLet m ways to write block notation  with Let The following result is the key to relate commutation and blocks in cycles.LetLetbe integers, withLetbe a cycle ofIfcommutes withon the blockthenis a block in a cycle ofi. The base case It is enough to prove that The following result is an easy exercise.Letbe anm-cycle ofThencommutes withonif and only iftransformsinto anm-cycle ofcommutes with r points in Let We now present one of our main results.Letbe anm-cycle ofandkan integer such thatThencommutes withif and only ifwhere the blockssatisfy the following:ifthenis a proper block in a cycle ofifthenarekpairwise disjoint blocks, from one or more cycles ofsuch that the stringis not a block in any cycle offor every(1) Suppose that Conversely, we can assume, without lost of generality, that (2) Suppose that k points in i, Conversely, if The function k-commute with Using Theorem\u00a01 we can characterize permutations that LetThenk-commutes withif and only if there existhcycles ofsaysuch thatcommutes withon each cycle ofnot inand for everywithwhere the blockssatisfy the following:if if Let As a first application of Theorem\u00a01, we obtain the following result, that is used in the proof of Theorem\u00a08Letbe a permutation whose maximum cycle length in its cycle decomposition ism. Ifcommutes withonpoints in anm-cycleofthencommutes withonP is a proper block in an l-cycle of m is the maximum cycle length of cycles in Suppose that Previous propositions is a generalization of Lemma 2(b) in Gorenstein et\u00a0al. . The folLetandbe two permutations thatk-commute, Suppose thatdoes not commute withon the cyclesof lengthsrespectively, and that commutes withon the rest of cycles of(if any). Then, there exists exactlyrcycles ofsayof lengthsrespectively, such thatmore, suppose thatdoes not commute withon exactlyi-cycles ofand that commutes withon the rest of thei-cycles of(if any). Then there exists exactlyi-cycles ofsuch that each of them contains at least one point that is the image underof one b.c.p. ofandLet i-cycles of i-cycles of i-cycles of By a similar argument, we can show that if If all the points in ani-cycle ofare images underof g.c.p., then there exists ani-cycle ofsuch thati-cycle l-cycle, say x and y in different cycles of x is a b.c.p. because t, then First, we prove, by contradiction, that if all the points in the With this claim, every cycle in We finish this subsection with the following resultLetIf one cycle ofhas exactly one b.c.p. ofandthen there exist a cycle ofthat contains at least two b.c.p. ofandl of cycle x, such that B a block of length Let r-cycles of l-cycles of s-cycle of l-cycle of l-cycle, say m-cycle, say r be an integer between 1 and l such that Case I. If Case II. If Now we consider the case k-commutes with m-cycle, say m-cycle, say canonical cycle notation of a permutation transition function of Let ion B\u00f3na ,\u00a0p.\u00a097.Let Step 1m-cycles, say Choose two Step 2k-subset Choose a Step 3k-cycle permutation Choose a Step 4Construct Step 5Construct m cycles of m-cycles of m-cycles of l-cycles of l-cycles of Let The following two propositions shows that Algorithm\u00a01 produces all the permutations with the desired properties.Any permutationconstructed with Algorithm\u00a01 does not commute withon all points inand commutes withon all points ink points in Let LetLetbe any permutation thatk-commutes withand such that all the b.c.p. ofandare in exactly onem-cycle ofThencan be obtained with Algorithm\u00a01.m cycle of m-cycle, k pairwise disjoint blocks in k, which is a contradiction.Let k expressions, choose the one that begins with block As k) is the greatest element in k-cycle in Now, we consider k-commute with In this section we present some results about the number Letbe a permutation of cycle typeThenandWhen k and any Now we show that for any nonnegative integer Ifthenfor anyFor The following result shows that LetSuppose thatis a non-empty set. ThenNow, let k-commutes with Let f(k) be the number of cyclic permutations (k-cycles) of Let Letbe a permutation of cycle typeLetkbe an integer, withThenf(k) ways to select the permutation t-cycles of t-cycles of As all the b.c.p. of T denote the number of n-permutations that k-commute with an n-cycle.Let Letnbe a positive integer andkand integer withThenT is now sequence A233440 in the OEIS database. With this corollary we can obtain, in an easy way, the binomial transform of sequence A000757. Let A. In Spivey and Steil .We have the following limit property for Letnbe a positive integer andmbe a fixed nonnegative integer withThenBy direct calculations we have thatLetn,\u00a0kbe positive integers withThenf(k) is independent of n we haveP to obtainLet  in Wilf ,\u00a0p.\u00a041 w in Wilf  to the sk, with k-commutes with h cycles, says k that consists of k ones.In this section we present formulas for the number Letbe anyn-permutation of cycle typeThenm-cycle), say m-cycle the strings The set of all points in the blocks From condition (a) to condition (c) we have that m ways to select the first point of block m ways to select the first point of block The number m-cycles m of m of t-cycles of t-cycles of m into cycles of length different than m. After summing over all possible values of m we have that There are In a similar way, but with many more cases to consider, we have obtained a formula for Letbe any permutation of cycle typeThenwhereIn this section we show formulas for Letand letthenIf The following theorem is a consequence of Proposition\u00a07, Theorem\u00a05, Theorem\u00a06 and Proposition\u00a011.Letbe a transposition. Thenn symbols, with Formulas (1), (2) and (3) in previous proposition coincide with the number of permutations of  Deutsch . Therefoa(n) be the \u201cnumber of deranged matchings of 2n people with partners (of either sex) other than their spouse\u201d (sequence A053871).Now we give a formula for Letbe a fixed-point free involution, Thenk and odd integer,m transpositions. From Proposition\u00a03 we have that if k odd. Now, if k-commutes with j transpositions, of j transpositions of j transpositions, j transpositions of X onto j! ways to arrange the blocks X onto a(j) ways. Finally, there are By hypothesis, the cycle decomposition of Letbe a fixed-point free involution. Thena(n) [see the formula section of sequence A053871 in Sloane (We use the well-known EGF for n Sloane ]\\documenk-commuting permutations. We present some formulas for the number of permutations that k-commute with n-cycle, or a fixed-point free involution, for any k. These results could be useful when we work in problems related with almost commuting permutations. Even more, these enumerative results could be useful to find relations between integer sequences in the OEIS database, as Rivera (In this paper we give some techniques to work with s Rivera  showed.The problem of computing in an exact way the number"}
+{"text": "Scientific Reports 10.1038/s41598-018-20591-y, published online 06 February 2018Correction to: In the original version of this Article, \u2018Neuroscience\u2019 was omitted from the category list.Additionally, in the original version of this Article, Figure\u00a03b contained an error in the labelling of \u2018Delay Walk Model\u2019.Finally, the original version of this Article contained an error in Figure\u00a04a, where the tau symbol was omitted from the legend.These errors have now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Neurobiological and molecular studies suggest a dichromatic colour vision in canine species, which appears to be similar to that of human red\u2013green colour blindness. Here, we show that dogs exhibit a behavioural response similar to that of red\u2013green blind human subjects when tested with a modified version of a test commonly used for the diagnosis of human deuteranopia (i.e. the Ishihara's test). Besides contributing to increasing the knowledge about the perceptual ability of dogs, the present work describes for the first time, to our knowledge, a method that can be used to assess colour vision in the animal kingdom. SpeciAlthough early behavioural studies on dogs' colour vision produced conflicting results (reviewed by ), recentet al. .The change between stimuli (stimuli presentation) was controlled by the experimenter and was dependent on the attention of the dog to the screen (inter-stimulus presentation time: 7\u2013120\u2009s). The stimulus presentation procedure was the same as described in \u00a72.3. The side of appearance of the \u2018moving cat\u2019 stimuli was randomized within each session. Owners were asked not to influence their dogs' behaviour (e.g. either to indicate the screen or to force looking behaviour). If the dog was distracted during the presentation of the stimuli or if it left the starting position (despite the beep sound) it was repositioned and the stimulus was then represented. Dogs visual angle was approximately of 2\u00b0 51\u2032 0.85The behaviour of the dogs was video recorded continuously during stimulus. Two trained observers who were blind to the testing paradigm subsequently analysed the video footage. The video was used to score any of the following listed behaviour: ears up-forward, scanning (dog turning head from left to right), eyes wide open, forward body orientation, eye/ear directed towards the target, gaze, head slightly lowered, paw lifted, freezing, alert position and head tilt. Each performed behaviour was allocated a score of 1, and the total for each dog was used to generate a reactivity index for the \u2018alerting\u2013targeting\u2019 behavioural category.In addition, looking time to different visual stimuli was measured, analysing dogs behaviour from the beginning of the target animation (soon after the \u2018beep\u2019 sound) until the stimuli disappeared  and calculated as percentage agreement .olorPro 5 colorimeter sensor and Sencore ColorPro 6000 software were used to calibrate the colours of the monitor to CIE Standard Illuminant D65 . The same apparatus was also used to measure the brightness of the white background and the average brightness of the tested stimuli  was tested with achromatic versions of RG-Cat stimuli in order to see if subjects use achromatic cues to perceive cat's moving animations.Two new animated cat targets were edited using eight frames (4\u2009\u00d7\u2009each animation) in which achromatic versions of red and green shades of Ishihara plate no. 22 were used .Figure In particular, the A-Cat-2 and the A-Cat-6 stimuli were edited using respectively the achromatic versions of the RG-Cat-2 and the RG-Cat-6 animations used during the red\u2013green colour-blind test.We predicted that if dogs use achromatic cues to perceive the cat animation most of the tested subjects should see and correctly interpret (showing orientation movements of the head and tip of predatory behaviour) more the movements of the cat obtained by using the achromatic version of the same colour shades employed to depict the number \u20182\u2019 on the Ishihara's plate no. 22 with respect to the movements of the cat edited by using the achromatic version of the same colour shades of the number \u20186\u2019 taken from the same plate (this prediction is based on the fact that achromatic contrasts are more apparent in the first condition than in the second).In addition, two different random achromatic animations (i.e. A-Background-1 and A-Background-2) were made using G-Background-1, and G-Background-2 stimuli without colour cues.owerPoint slideshows on a white background and were presented in pairs: the first slide showed two A-Background-1 (control animated plates), the second and the third presentation showed, respectively, the animations of A-Cat-6 versus A-Background-2 and A-Cat-2 versus A-Background-2; finally, the B-Cat animation was presented alone as a control on the same side of the A-Cat targets.Five stimuli were displayed during each trial by PThe testing procedure was identical to that described above for the red\u2013green colour blind test.The red\u2013green colour blind and the achromatic tests were presented separately  and the presentation order was alternated between subjects (i.e. five subjects performed the red\u2013green blindness test first and four dogs performed the achromatic test first).3.3.1.a,b.Results for the red\u2013green colour-blind test are shown in figure 4p\u2009<\u20090.001) (a). Dunn's post hoc test revealed that this main effect was owing to the time spent at looking both RG-Cat-2 and B-Cat being longer with respect to other stimuli: RG-Cat-2  versus G-Background-1 (0.09\u2009\u00b1\u20090.05 (s); m\u2009\u00b1\u2009s.e.m.) (p\u2009<\u20090.01); RG-Cat-2 versus G-Background-2 (0.31\u2009\u00b1\u20090.11 (s); m\u2009\u00b1\u2009s.e.m.) and versus RG-Cat-6 (0.63\u2009\u00b1\u20090.35 (s); m\u2009\u00b1\u2009s.e.m.) (p\u2009<\u20090.05); B-Cat (1.87\u2009\u00b1\u20090.22 (s); m\u2009\u00b1\u2009s.e.m.) versus G-Background-1 (p\u2009<\u20090.001); B-Cat versus G-Background-2 and RG-Cat-6 (p\u2009<\u20090.01). No statistical significant differences were found between the other pairwise comparisons .Friedman's ANOVA revealed a main effect of the type of visual stimulus on the mean looking time (<\u20090.001) a. Dunn'sp\u2009<\u20090.001; Friedman's ANOVA, figure 4b). Dunn's post hoc test revealed that the RG-Cat-2  elicited a higher alerting behavioural response with respect to the G-Background-1 , G-Background-2  (p\u2009<\u20090.01) and RG-Cat-6  (p\u2009<\u20090.05). Similarly, the analysis revealed higher alerting behavioural response between B-Cat and the other visual stimuli with the exception of RG-Cat-2: B-Cat  versus G-Background-1, G-Background-2 and RG-Cat-6 (p\u2009<\u20090.001). No other significant statistical differences were found .As to the behavioural score, the analysis revealed that there was a statistical significant difference in the score for alerting behavioural response between visual stimuli  (a). Dunn's post hoc test revealed that this main effect was owing to the time spent at looking the B-Cat being longer with respect to other stimuli: B-Cat (2.23\u2009\u00b1\u20090.13 (s); m\u2009\u00b1\u2009s.e.m.) versus A-Cat-2 (0.55\u2009\u00b1\u20090.18 (s); m\u2009\u00b1\u2009s.e.m.) and G-Background-1 (0.46\u2009\u00b1\u20090.13 (s); m\u2009\u00b1\u2009s.e.m.) (p\u2009<\u20090.01); B-Cat versus G-Background-2 (0.31\u2009\u00b1\u20090.11 (s); m\u2009\u00b1\u2009s.e.m.) and A-Cat-6 (0.66\u2009\u00b1\u20090.21 (s); m\u2009\u00b1\u2009s.e.m.) (p\u2009<\u20090.05). No statistical significant differences were found between the other pairwise comparisons .Friedman's ANOVA revealed a main effect of the type of visual stimulus on the mean looking time (=\u20090.001) a. Dunn'sp\u2009<\u20090.01; Friedman's ANOVA, figure 5b). Dunn's post hoc test revealed that this main effect was owing to the score for alerting behavioural response to the B-Cat stimulus being higher with respect to other stimuli: B-Cat (3.75\u2009\u00b1\u20090.16 (s); m\u2009\u00b1\u2009s.e.m.) versus G-Background-1 (0.44\u2009\u00b1\u20090.17 (s); m\u2009\u00b1\u2009s.e.m.) (p\u2009<\u20090.01); B-Cat versus G-Background-2 (0.66\u2009\u00b1\u20090.11 (s); m\u2009\u00b1\u2009s.e.m.), A-Cat-2 (0.62\u2009\u00b1\u20090.18 (s); m\u2009\u00b1\u2009s.e.m.) and A-Cat-6 (0.75\u2009\u00b1\u20090.25 (s); m\u2009\u00b1\u2009s.e.m.) (p\u2009<\u20090.05). No statistical significant differences were found between the other pairwise comparisons .As to the behavioural score, the analysis revealed a main effect of the type of visual stimulus on the score for alerting behavioural response between visual stimuli , most of the dogs exhibit an orienting response to the stimulus (both the eyes and the head oriented toward the animated cat silhouette) together with clear targeting behaviour. These results are similar to those reported in red\u2013green colour-blind humans who clearly recognize the red number \u20182\u2019 during inspection of Ishihara's plate no. 22 and the cat during presentation of the RG-Cat-2 animation.On the other hand, when dogs were presented with the red cat animation having the same red\u2013green colour shade of the number \u20186\u2019 of the Ishihara's plate no. 22, a significant lowering of both orienting and targeting behavioural response was observed, pointing to a considerable loss of subjects' capacities in perceiving the target.The above result is in accordance with the difficulty of the red\u2013green colour-blind humans to recognize the red-depicted number \u20186\u2019 of Ishihara's plate no. 22 and their inability to perceive the cat movements during presentation of the RG-Cat-6 animation.Furthermore, two aspects should be considered when the orienting response is used to evaluate visual discrimination: (i) habituation to the movements of the target  and (ii) aspecific head/eyes orienting response . Given that in the orienting response, habituation to the movements of the targets presented as the first could decrease the response to the next stimulus, we designed the experiment so that the two coloured targets were presented only once to each subject and the control stimulus (i.e. the black cat silhouette presented against a white back ground) was presented as the last during each session. In order to deal with the possibility of a \u2018false positive response\u2019, we scored during the experiment the targeting\u2013alerting dogs behavioural response towards the coloured cat animations which was then compared with the behavioural response towards the control cat animation (B-Cat). A statistical significant correlation between the alerting\u2013targeting behavioural response towards the coloured cat animation and the control ones make the hypothesis that dogs recognize the moving cat likely. In addition, in support to this hypothesis the behavioural score for alerting\u2013targeting towards the control cat animation was higher compared with that of the black square, indicating that the subjects were able to clearly distinguish the movements of the cat from those of the square.Regarding the dog\u2013owner dyads, the possibility that the owners influenced the dogs' orienting response during the test is very remote because, although the dyad was very close during the test (the dog sat or was laid between the owner's legs), the owners were asked to stare a fixed spot centrally located to the screen. In addition, given the results, it is reasonable to assume, that the owners did not influence the dogs, because they otherwise might have reacted to the animations that must have been visible to the owners .Another aspect to consider is that the luminance difference between stimulus colours and background could affect colour discrimination thresholds . DespiteThis finding supported previous results demonstrating that, in dogs, colour information may be predominant with respect to brightness .In addition, the observed difference between the red\u2013green blindness test and the achromatic one is consistent with reports of compelling evidence that colour can contribute to motion perception \u201318, but Overall, our results, together with the above-reported studies, confirm that dog colour vision is dichromatic in its nature, resembling that of human red\u2013green blindness. Besides contributing to increasing knowledge about the perceptual ability of dogs, the present work showed, to our knowledge, for the first time, directly canine red\u2013green blindness by using a modified test of colour vision in humans (Ishihara's test), thereby allowing direct comparison to colour vision (and colour blindness) in humans. Furthermore, the method used will open the door to the development of new techniques (e.g. coupling the modified version of the Ishihara's test with the use of eye-gaze detection and tracking systems) to assess colour vision in the animal kingdom."}
+{"text": "We wish to make the following corrections to their paper :The title of the paper \u2018Millimeter-Wave Chemical Sensor Using Substrate-Integrated-Waveguide Cavity\u2019 should be changed to \u2018Microwave Chemical Sensor Using Substrate-Integrated-Waveguide Cavity\u2019.In the second line of the abstract, on the fifth line of Section 3 (Simulation Results), and in Section 4  on Page 7, the phrase \u2018millimeter-wave frequency range\u2019, should be changed to \u2018microwave frequency range\u2019. Also, on the third line of the Conclusion Section, \u2018millimeter-wave\u2019, should be replaced with \u2018microwave\u2019. It is well-known that millimeter-wave corresponds to a frequency of over 30 GHz. As the proposed sensor functions at around 18 GHz, it should be called \u2018microwave\u2019. We apologize for any inconvenience these changes have caused to readers. The changes do not affect the scientific results. The manuscript will be updated and the original will remain online on the article webpage."}
+{"text": "N-representability of the pair density (PD) are needed for the development of the PD functional theory. We derive sufficient conditions for the N-representability of the PD that is calculated from the Jastrow wave function within the lowest order. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.Conditions for the  Therefore, the PD functional theory has been expected to be one of the promising schemes beyond the density functional theory28. We have proposed the PD functional theory that yields the best PD within the set of the Jastrow wave function PDs of the lowest-order (LO-Jastrow PDs)17. The search region for the ground-state PD is substantially extended as compared with the previous theory19. On the other hand, however, there remains a significant problem related to the N-representability of the LO-Jastrow PDs17. Concerning the N-representability of the PD or the second-order reduced density matrix, there are a lot of works39. But unfortunately, the necessary and sufficient conditions for the N-representability of the PD are not yet known in a practical form.The pair density (PD), which is defined as the diagonal element of the second-order reduced density matrix, has more information about the electron correlation than the electron densityN0-electron system. The Jastrow wave function is given byxi denotes the coordinates including the spatial coordinate ri and spin coordinate \u03b7i, and where 41Let us revisit the problem here. We shall consider an 17, we have confirmed that Eq.  in Eq. (N0\u2009\u2212\u20091) -electron SSDs that are defined as the minor determinants multiplied by In this section, we shall discuss the properties of the LO-Jastrow PD. To this aim, the properties of PDs that are calculated from SSDs are investigated. The cofactor expansion of N0\u2009\u2212\u20092)-electron SSDs, which are denoted by j\u2009\u2264\u2009N0\u2009\u2212\u20091). Then, each Likewise, the cofactor expansion of each where Multiplying both sides of Eq.  by \\docuN-representability of the LO-Jastrow PD.This relation is the starting point to examine the N-representability of We shall start with considering the N-representability of q, i.e.,where From Eq. , the PD 41. Therefore, if they are given, we can calculate N-representability of Eq. } (1\u2009\u2264\u2009\u03b1\u2009\u2264\u2009n\u2009+\u20091) that satisfy the conditions;\u03b1 \u2264 n + 1) denote the n-electron wave functions, and \u03c3 is a permutation operator upon the electron coordinates, and \u03c3.Proof. The left-hand side of Eq. -electron system as the whole system, and suppose that the wave function for such the (n + 1)-electron system is given by Eq. } (1 \u2264 \u03b1 \u2264 n + 1) that satisfy Eqs a\u03b1 that satisfy the following conditions:if there exists the set of functions q \u2264 3), i.e., Eqs (N-representability of Eq. (q \u2264 3) is obtained. Substitution of Eq. (p\u2009\u2264\u20094) that satisfy the following conditions:In addition to Eq. , the exi.e., Eqs  and 22)\\documentn of Eq.  into Eq.n of Eq.  leads top \u2264 4), i.e., Eqs (N-representability of Eq. (q \u2264 3) and p \u2264 4) belong to the set of sufficient conditions.The existence conditions for .e., Eqs  and 27)\\documenty of Eq.  and the i \u2264 N0), we eventually obtain sufficient conditions for the N-representability of Eq. -electron system, i.e., i \u2264 N0). Successively, each of the SSDs for the (N0\u2009\u2212\u20091)-electron system is expanded along the (N0\u2009\u2212\u20091)th row, and then the (N0\u2009\u2212\u20091) number of SSDs for the (N0\u2009\u2212\u20092)-electron system, i.e., j \u2264 N0\u2009\u2212\u20091), can be obtained for each i. After that and later, the cofactor expansions are likewise repeated, and we finally arrive at the SSDs for the two-electron system, i.e.,N0!/2, since q are integers such that 1 \u2264 i \u2264 N0, 1 \u2264 j \u2264 N0\u2009\u2212\u20091, 1 \u2264 k \u2264 N0\u2009\u2212\u20092, o \u2264 5, 1 \u2264 p \u2264 4 and 1 \u2264 q \u2264 3, respectively.Let us consider the SSD that consists of the resultant spin orbitals for the simultaneous equations. The SSD can generally be expanded using the cofactor. The SSD for the 41. We check whether all of q through Eq. (The two-electron SSD ough Eq. .p. If suitable p can be constructed from Eq. (By means of these d as Eq. . We willith Eqs.  and 22)\\documentfrom Eq. .o, the four-electron antisymmetric wave functions We successively proceed the case of four-electron wave functions that are defined as Eq. . In a si of Eqs.  and 27)\\documentfrom Eq. .n(\u2264N0\u2009\u2212\u20091), the LO-Jastrow PD of the N0-electron system becomes N-representable.Likewise, we further proceed the problem constructing the antisymmetric wave functions for more-electron systems. We search the set of ith Eqs.  and 12)\\documentith Eqs.  and (12)In the preceding section, the sufficient conditions for the N-representable may, in principle, be found along the above steps, though there is a possibility that the suitable correlation function may not exist in some system.As easily inferred, the above steps are feasible only for the small-electron systems from the practical viewpoint. However, it should be noted that the correlation function that makes the LO-Jastrow PD In the above-mentioned concrete steps, antisymmetric (n\u2009+\u20091)-electrons wave functions are built up from given antisymmetric n-electrons wave functions via Eq. . In thisInstead of Eq. , we can a\u03b1(xi) and b\u03b1(xn + 1) denotes functions that should be determined. If these functions satisfy the following conditions;a\u03b1(xi) and b\u03b1(xn + 1) that satisfy Eqs. a\u03b1(xi) \u03d5\u03bb(x), Similarly to the above, we can choose the other expression for d of Eq.  or 28)..\\documena\u03b1 denote a function that should be determined. If a\u03b1  satisfies the following conditions;where a\u03b1 that satisfy Eqs (then Eq.  becomes isfy Eqs  and 34)a\u03b1a\u03b1(xi, N-representable LO-Jastrow PD.Thus, various expressions for N-representability of the LO-Jastrow PD are discussed. Using the properties of the LO-Jastrow PD, we derive the sufficient conditions that are imposed on the correlation function of the Jastrow wave function. As shown in the previous section, additional steps to search the suitable correlation function, which satisfies the sufficient conditions, are attached to the computational scheme proposed previously17. Although the number of steps rapidly increases with that of electrons, the concrete steps that are presented in the previous section are feasible for a small-electron system. Of course, there is a possibility that the suitable correlation function cannot be found out. In this case, as mention in the previous section, we can adopt other expressions for N-representable in a sense that they satisfy four kinds of necessary conditions47.In this paper, the sufficient conditions for the"}
+{"text": "Using computational and theoretical approaches, we investigate the snap-through transition of buckled graphene membranes. Our main interest is related to the possibility of using the buckled membrane as a plate of capacitor with memory (memcapacitor). For this purpose, we performed molecular-dynamics (MD) simulations and elasticity theory calculations of the up-to-down and down-to-up snap-through transitions for membranes of several sizes. We have obtained expressions for the threshold switching forces for both up-to-down and down-to-up transitions. Moreover, the up-to-down threshold switching force was calculated using the density functional theory (DFT). Our DFT results are in general agreement with MD and analytical theory findings. Our systematic approach can be used for the description of other structures, including nanomechanical and biological ones, experiencing the snap-through transition. Such devices are prospective candidates for applications in information storage and processing3 technologies as their states can be manipulated by the applied voltages or charges and can store information for long intervals of time. Several possible realizations of memcapacitors were suggested by using micro-electro-mechanical systems4, ionic transport5, electronic effects6, superconducting qubits7, etc8.Memcapacitors1q(t) is the charge on the capacitor at time t, V(t) is the applied voltage, C is the memcapacitance (memory capacitance), x is a set of n internal state variables, and f is a continuous n-dimensional vector function. In some cases, it is more convenient to consider charge-controlled memcapacitors1 such that the charge instead of voltage is considered as input.Generally, voltage-controlled memcapacitive systems (memcapacitors) are described by4 are of significant interest as their geometry makes them intrinsically suitable for non-volatile storage of binary information. Indeed, the buckled membrane used as the top capacitor plate  Sec. \u201cMD Simulation Details\u201d. The standard elasticity theory is applied to the membrane switching in Subsec. \u201cBuckling and snapping-through within the theory of elasticity\u201d. A phenomenological analytical model of the snap-through transition is presented in Subsec. \u201cPhenomenological elasticity theory\u201d and in SI Sec. \u201cPhenomenological Elasticity Theory\u201d. Our DFT calculations are summarized in Sec. \u201cDensity Functional Theory\u201d. The results obtained within different approaches as well as their implications are discussed in Sec. \u201cDiscussion\u201d.In this paper, the following notations are used:q - the charge on capacitor (see Eq. ((see Eq. )V - the applied voltage (see Eqs ((see Eqs  and 2)))V - the C - the (memory) capacitance (see Eq. ((see Eq. )d - the distance between fixed sides of membrane \u03b6c - the maximum deflection of membrane (see Eq. ((see Eq. )\u03b8i(s) - the angle that the membrane makes with the horizontal (see Eqs ((see Eqs  and 17)\u03b8i(s) - ts - the internal coordinate that changes between \u22121/2 and 1/2 (see Eqs ((see Eqs  and 17)s - the iAi and ci - coefficients (see Eqs ((see Eqs  and 17)Ai and cizcm - the center of mass position (see Eq. ((see Eq. )Ub, Ustr, Uext - the bending, stretching and external potential contributions to the potential energy of membrane (see Eq. ((see Eq. )F\u2193 - the up-to-down threshold switching force , F\u2193 - the F\u2191 - the down-to-up threshold switching force (see Eqs ((see Eqs  and 28)F\u2191 - the \u03b50 - the vacuum permittivity36. We used classical MD simulations to investigate the dynamics of snap-through transition of buckled graphene membranes. Zigzag graphene nanoribbons (membranes) of two lengths were considered: the nanoribbon A, L\u2009=\u200954 \u00c5 (22 rings), and nanoribbon B, L\u2009=\u2009103 \u00c5 (42 rings). Both nanoribbons were of the same width (w\u2009=\u200941 \u00c5). In order to implement the clamped boundary conditions, the first two lines of carbon atoms at shorter sides were kept fixed. The buckling was realized by changing the distance between the fixed sides from L to d\u2009<\u2009L. The same external force was applied to each atom in the downward direction to simulate the attractive interaction between the plates.MD simulations are a well established modeling tool frequently employed in studies of nanoscale carbon-based materialsSee SI Sec. \u201cMD Simulation Details\u201d for the details of MD simulations.d/L and two membrane sizes. According to Fig.\u00a0L, the up-to-down threshold switching force  is larger for smaller values of d/L. Moreover, at fixed d/L, the threshold switching force is smaller for longer membranes. Additionally, some curves in Fig.\u00a0d/L\u2009=\u20090.8 and d/L\u2009=\u20090.98 in (a)), which can be related to thermal fluctuations of membranes. All these observations are intuitively reasonable.In order to simulate the up-to-down transition, the double-clamped graphene nanoribbon buckled upwards was subjected to the force in the downward direction. The final state of membrane was found using MD simulations as described in SI Sec. \u201cMD Simulation Details\u201d. Figure\u00a014 and involved in switching by smaller forces. Larger applied forces result in the switching through the symmetric profile. According to our observations and previous work14, in all cases, the membrane profile is symmetric at short times. If the force magnitude is sufficient to overcome the energy barrier for the symmetric profile, then, typically, the switching takes place through the symmetric path. Otherwise, a symmetry breaking occurs leading to the switching through the lower energy barrier associated with the non-symmetric membrane profile. Thermal fluctuations help the symmetry breaking.Depending on the force magnitude, the membrane switching occurs either through the symmetric or non-symmetric membrane profile see Fig.\u00a0. Figure\u00a04 that the memcapacitor membrane can be set into the buckled upwards state 0 38 disappear in the transition from flexible to rigid graphene. In agreement with this previous work37, our molecular dynamics simulations have shown the absence of ripples (spontaneous height fluctuations) in nanoribbons of reported sizes and their existence in larger nanoribbons. The latter, however, are not suitable for the memcapacitor application because of their flexibility. To summarize, while our simulation tools provide a means for ripples detection, we did not observe these in the reported structures that are mechanically rigid.In our work, we considered relatively small nanoribbons, which are mechanically rigid. This is an important requirement for the memcapacitor application as the mechanical nonvolatile information storage is not possible with flexible graphene. From some previous studies42. This allows us, on one hand, to obtain analytical expressions for the buckled membranes45 and, on the other hand, perform a comparison with MD simulations.Even though the graphene has a thickness of one atom, the graphene membranes are quantitatively good described by the theory of elasticity49). Such systems are frequently described in the framework of Euler-Bernoulli theory, which, however, leads to complex analytically unsolvable equations. Bubnov-Galerkin decomposition is a one of the best approaches to find the approximate analytical solution of these equations, although it still requires a complex phase-diagram analysis. In particular, using such analysis, the authors of refs49 investigated an electrostatically loaded double-clamped membrane above a rigid flat electrode and derived cumbersome conditions for the symmetric snap-through transition, symmetry breaking, existence of bifurcation and pull-in instability.There is a number of publications dealing with buckled beams and membranes under the transverse load  asT\u2009=\u2009T0\u2009+\u2009\u03b4T is the total tensile force, T0 is the force applied by the support and \u03b4T is the bending tension resulted from the extension,Consider a 2D membrane within the theory of elasticityS0\u2009=\u2009wL, and F is the external force density. The compression of membrane corresponds to T0\u2009<\u20090.\u03bc is the 2D mass density.Given the potential energy, one may also be interested in the dynamics of membrane, which is defined by the equationbn are the solutions of the equation cosh\u2009bncos\u2009bn\u2009=\u20091. One can find that bn\u2009\u2248\u20093\u03c0/2\u2009+\u2009n\u03c0 . The functions \u03b6n(x) are orthonormal.The spatial harmonics (eigenmodes) of clamped membranes can be written asn\u2009=\u20090 mode (taking \u03b6(x)\u2009=\u2009\u03b60(x) with \u03b6(d/2)\u2009\u2261\u2009\u03b6c) is\u03b1\u2009=\u2009\u03c02w(|T0|\u2009\u2212\u2009Tc)/(4d), \u03b2\u2009=\u20093\u03c04Dw/(4\u03b52d3), and f\u2009=\u2009\u03c0Fdw/6. Here, Tc\u2009=\u20094\u03c02D/d2 is the critical tension. At \u03b1\u2009>\u20090, that is at |T0|\u2009>\u2009Tc, the potential is the double-well potential with minima at symmetric deflections, \u03b4U\u2009=\u2009\u03b12/4\u03b2. 10) link \u03b6 in harmonics \u03b6n(x) (given by Eq. (qn(t) asn\u2009=\u20090,2 and n\u2009=\u20090,1 terms in Eq. (\u03b6m(x) and integrated taking into account the orthogonality of harmonics. Here we emphasize that for the harmonics (qn(t). Inserting the obtained functions qn(t) back into Eq. (tc\u2009=\u20091/\u03c9c)51 are analyzed for membrane B.Here we present a convenient method to describe the dynamics of membrane subjected to an external force and find the minimal force causing its snap-through transition. The main idea is to expand n by Eq. ) with ams in Eq. . Second,n\u2009=\u20090 and 2 harmonics. Next, we introduce a small asymmetry into the problem via a small non-symmetric modification of the force (of the order of 0.1%). This results in the non-symmetric dynamics of Fig.\u00a0n\u2009=\u20090 and 1 harmonics. We note that the force needed for the non-symmetric snap-through transition is smaller than that for the symmetric one, which will also be analyzed below in more detail. Finally, in Fig.\u00a014.Consider the results presented in Fig.\u00a0\u03b6c(tf), on the applied force F. At a certain value of force, F\u2009=\u2009F\u2193, the membrane switches from the buckled upwards state to the buckled downwards state. Our calculations show that the threshold force is proportional to the initial central-point deflection \u03b6c and is different for the symmetric (s) and non-symmetric (ns) dynamics. Namely, this force, being multiplied by the membrane area wL, readsFigure\u00a0qn(t) in the up-to-down transition. Importantly, the dynamics is well described by n\u2009=\u20090, 1, and 2 harmonics, while n\u2009=\u20093 and 4 harmonics amplitudes are negligibly small.Since the non-symmetric transition is energetically favorable, we expect that this value of force is the one to be used in the device design/experiment analysis. We note that estimations based on Eq.  are in aOur calculations (similar to the consideration of the up-to-down force above) demonstrate that the minimal force needed for the down-to-up transition is proportional to See also SI Subsec. \u201cDown-to-up transition\u201d, where the down-to-up transition is illustrated graphically.In this Section, in order to avoid all complications associated with the Bubnov-Galerkin decomposition, we elaborate a different approach describing the up-to-down and down-to-up transitions in a compact analytical form.Following our observation of the existence of the symmetric and non-symmetric membrane profiles in the snap-through transition see Fig.\u00a0, we intr\u03b8i(s) is the angle that the membrane makes with the horizontal, s is the internal coordinate that changes between \u22121/2 and 1/2, Ai and ci are coefficients, and i\u2009=\u2009{s, ns}. Clearly, Eqs (\u03b8i(\u00b11/2)\u2009=\u20090.Here rly, Eqs  and 17)\u03b8i(s) is Our goal here is to estimate the minimal force required for the snap-through transition. In this subsection, we assume that the snap-through transition is induced by a slowly increasing force such that the system always stays in the potential energy minimum. At zero applied force, there are two minima of the potential energy corresponding to the two stable states of membrane. The applied force modifies the potential energy landscape such that, starting at a certain force, the potential energy has a single minimum. Here, this value of force is found and considered as an estimation for the threshold switching force.F in the downward direction, the membrane potential energy is given byUb is the bending energy, Ustr is the stretching energy, Uext is the potential energy due to the applied force. Then, using Uext\u2009=\u2009Fzcm, where zcm is z coordinate of the center of mass, and neglecting Ustr term not important for the up-to-down transition , we get the following equation for the potential energy extrema:i\u2009=\u2009{0, 1} corresponds to {s, ns}, respectively. Equation (c0 and c1 for a given strength of the applied force.In the presence of a constant force F(zcm) and, for the transition through the symmetric shape, is given byc0\u2009=\u20090.3589 /L2. Performing the same calculations for the non-symmetric shape, one can find that the force needed to support the equilibrium non-symmetric shape decreases with the progress of switching. A zero force is reached at Ub,ns\u2009=\u200990Dw(L\u2009\u2212\u2009d)/L2. A possible (rough) estimation for the threshold switching force can be obtained taking the limit c1 \u2192 \u221e leading toUb,ns\u2009=\u200942Dw(L\u2009\u2212\u2009d)/L2.The minimal force needed for the snap-through transition corresponds to the maximum of F\u2009=\u20090 and slowly increase the force. The symmetry breaking occurs at a certain value of force, say, F\u2193. The dynamics of switching is a complex process significantly relying on thermal fluctuations. As the switching dynamics can not be reached within the framework of our model, for estimation purposes, we assume that F\u2193 corresponds to the point where the bending energies and applied forces for the symmetric and non-symmetric shapes are the same. One can find that both conditions are satisfied at c0\u2009=\u20090.4683 and c1\u2009=\u20090.6948, so that Ub\u2009=\u200947.8Dw(L\u2009\u2212\u2009d)/L2 andIn fact, a realistic scenario of the switching through the non-symmetric shape can be imaged as follows. We start with a symmetric membrane at F\u2009<\u2009F\u2193, the membrane keeps the symmetric shape and switches to the non-symmetric one as soon as F reaches F\u2193. As there is no barrier involved in the non-symmetric switching, no further increase in the applied force is required to complete the snap-through transition through the non-symmetric shape.Consequently, at Ustr  plays aMoreover, at equilibriumUnder the condition of small Using Eqs  and 27)27), Eq. We have verified that the threshold switching force for the down-to-up transition given by Eq.  is in ag14. In the present calculations, we focused on the effects of boundary conditions and buckling strength on the up-to-down threshold switching force. DFT computational details can be found in SI Sec. \u201cDFT Calculations\u201d.A DFT investigation of the up-to-down transition was performed following the previously reported study of the up-to-down switching of buckled graphene membraned/L\u2009=\u20090.96, Fig.\u00a0d/L\u2009=\u20090.78, and C3 with d/L\u2009=\u20090.63), and (2) clamped boundary conditions  hinged boundary conditions MD is widely used approach to describe the dynamics of nanoscale systems. In our work, MD clearly shows the possibility of 0 \u2192 1 and 1 \u2192 0 transitions of graphene membrane. We have also verified the occurrence of 1 \u2192 1 and 0 \u2192 0 transitions at the same values of forces required for 0 \u2192 1 and 1 \u2192 0 transitions, respectively.(ii)\u03b6. Expanding the function \u03b6 into membrane\u2019s harmonics allows reducing the integro-differential equation to a system of differential equations. This approach was utilized in Subsec. \u201cBuckling and snapping-through within the theory of elasticity\u201d. There it was shown that the up-to-down threshold switching force depends linearly on the initial central-point deflection, F\u2193\u2009\u221d\u2009\u03b6c, while the down-to-up snap-through force at low dissipation depends quadratically on the initial deflection, In the framework of elasticity theory, the membrane is described by means of an integro-differential equation for the deflection (iii)The phenomenological approach based on the theory of elasticity has allowed us to obtain analytical expressions for the up-to-down and down-to-up switching forces for buckled graphene membrane. The forces for 0 \u2192 1 and 1 \u2192 0 transitions are in a good agreement with MD simulations results.(iv)DFT is a non-standard method for studying mechanical properties of membranes. Similarly to other methods, DFT has shown that the non-symmetric switching pathway is the preferable one. This method also provides a consistent estimation for the up-to-down threshold switching force.52. For this purpose, it is desirable that both the distance between the fixed edge of membrane and second electrode ) are chosen (much) smaller than the membrane length. Moreover, the gap between electrodes should be larger than the maximal membrane deflection, h\u2009>\u2009zs(0) (see Eq. (zi(s)). For given capacitances C0 and C1 of the states 0 and 1  such that C1/C0\u2009<\u20093.01, one can find thatFrom the application point of view, the membrane memcapacitor should have a strong \u2018memory content\u2019, namely, the device characteristics in its two logic states should be sufficiently different so as to provide a significant influence on other elements of electronic circuitsV ))V  in Fig.\u00a0The threshold voltage can be estimated based on the energy conservation (Eq. ) and forfrom Eqs  and 27)\\documentAn additional aspect of membrane dynamics \u2013 an estimation of thermally-induced switching time \u2013 is considered in SI Sec. \u201cStability of Buckled Membrane\u201d.We have investigated the snap-through transition of a buckled graphene membrane using a variety of computational and theoretical tools. The main results of this paper are the expressions for the threshold switching forces Eqs  and 22 f f22 for supplementary\u00a0information"}
+{"text": "Protein motors, such as kinesins and dyneins, bind to a microtubule and travel along it in a specific direction. Previously, it was thought that the directionality for a given motor was constant in the absence of an external force. However, the directionality of the kinesin-5 Cin8 was recently found to change as the number of motors that bind to the same microtubule is increased. Here, we introduce a simple mechanical model of a microtubule-sliding assay in which multiple motors interact with the filament. We show that, due to the collective phenomenon, the directionality of the motor changes , depending on the number of motors. This is induced by a large diffusive component in the directional walk and by the subsequent frustrated motor configuration, in which multiple motors pull the filament in opposite directions, similar to a game of tug-of-war. A possible role of the dual-directional motors for the mitotic spindle formation is also discussed. Our framework provides a general mechanism to embed two conflicting tasks into a single molecular machine, which works context-dependently. Microtubule-based motors such as kinesins and dyneins are essential to a variety of processes, e.g., molecular transportation and mitotic spindle formation. The force generation is mediated by the walk of a unidirectional motor toward the plus/minus end of the microtubule (MT), following adenosine triphosphate (ATP) hydrolysis. Intuitively, highly processive and non-diffusive motor walks may be advantageous for efficient force generation. However, motors exhibiting a biased random walk toward a specific end with a large diffusion coefficient have also been reported123et al.8It was long believed that a given type of motor protein travels in a specific direction along an MT, and that this directionality remains constant in the absence of an external force. Quite recently, however, kinesin-5 Cin8, which is a tetrameric motor protein purified from budding yeast that can cross-link to two MTs, was found to exhibit directionality switching, depending on the number of motors bound to the same MTSimilarly, the emergence of a novel motility mode, other than the directionality transition, induced by team formation has also been reported in several experimental studies1011In this Paper, we introduce a mathematical model for a motor-filament system and demonstrate that directional collective motion contrary to the built-in directionality of a single motor can emerge in the absence of any external forces. This directionality transition emerges under a large diffusional component in the directional walk and asymmetry in the intra-molecular strain-dependent detachment. In addition, the collective directional motion of motors with non-biased diffusion is explained. The proposed model provides a representative example of a mechanism for embedding dual tasks into a single molecular machine, which will elucidate the role of a large diffusive component in the walk of a processive motor. The emergence of the collective motion demonstrated here is independent of, and fundamentally different from, that induced by the entropic force produced by a diffusible cross-linkeret al.N identical motors X1, X2, \u2026, XN can be attached to a single rigid rod. As shown in 9151617N increases, as illustrated in Because our study is motivated by the MT sliding assay reported in Roostalu xi  for the ith motor, whereas the filament coordinate is denoted by y, as illustrated in xi\u2009=\u20090 is assigned. The filament then slides along the surface, pulled by multiple bound motors with force k is a spring constant. The time evolution for the filament with the friction coefficient \u03b3y under over-damped conditions is given byThe displacement along the filament between the bound motor and the tethering point  is denoted by \u03bey(t) is the thermal random force applied to the filament as \u03b7i\u2009=\u2009\u03b7. For motors bound to the filament, it is natural to assume a no-slip condition: the relative distance between each bound motor xi and the filament y does not change unless \u03b7i causes the i-th motor\u2019s \u201cwalk\u201d on the filament.where \u03b3x is the friction coefficient of the motor with the surrounding medium, which is considered to be much smaller than that of filament \u03b3y. This indicates that the relative distance does not change if \u03b7i\u2009=\u20090. From where \u03ba\u2009=\u2009k/\u03b3y. The driving force of the walk \u03b7i is modeled as v0 represents the built-in walk velocity, Dx, and \u2329\u03bei(t)\u03bej(t\u2032)\u232a\u2009=\u2009\u03b4i,j\u03b4(t\u2009\u2212\u2009t\u2032). In addition, f(xi) represents how the motor\u2019s walk is biased depending on the intra-molecular strain xi. For example, the motor with xi\u2009>\u20090, which is pulled from the minus-end due to the intra-molecular strain, is more likely to proceed toward the minus-end in the next step of the motor\u2019s walk than the motor with xi\u2009<\u20090 does. Hereafter, we mainly take f(x) as a linear function: f(x)\u2009=\u2009a0x. The force-velocity relation of the single motor has been measured and discussed in several experimental papers19where x\u2009>\u2009\u0394+ or x\u2009<\u2009\u2212\u0394\u2212, with given positive parameters \u0394+ and \u0394\u2212, whereas for the force-independent detachment, every bound motor is detached at the rate xi. In x\u2009=\u20090 with rate r.The bound motor can be detached from the filament in either a force-dependent or a force-independent manner. For the force-dependent detachment, we assume that the motor becomes detached if v0\u2009<\u20090, which indicates that each individual motor takes a biased random walk toward a minus-end, whereas the case v0\u2009=\u20090 will be discussed later. Because of the walking direction asymmetry of each motor, the filament always moves toward the plus-end and a directionality transition is impossible unless some asymmetry is introduced. Indeed, a directionality transition is observed for increased N, under the presence of: (i) an asymmetric strain-dependent detachment \u0394+\u2009>\u2009\u0394\u2212 or (ii) an asymmetric dependency of the motor\u2019s velocity upon the intramolecular strain |f(x)|\u2009>\u2009|f(\u2212x)|. Here, we primarily address case (i). y for various N and the N\u2009\u2212\u2009N increases  is given by the Fokker-Planck equation , M1\u2009=\u2009v0\u2009\u2212\u2009f(x)\u2009\u2212\u2009\u03bax, and \u03b4(x) is the Dirac delta function. The stationary distribution of the above equation is given by P(x)\u2009=\u2009M0\u03c1(x), wherewhere N\u2009=\u20091 agree rather well with the results of the stochastic simulations, as shown in and N, the time evolution of P is given by an N-dimensional differential equation, which is very difficult to solve. As N goes to infinity, however, the time evolution of P is reduced to a one-body problem, which is governed by the same equation as D\u2009=\u2009Dx (see M1\u2009=\u2009v0\u2009\u2212\u2009f(x)\u2009\u2212\u2009\u03ba\u2329x\u232a. Here \u2329x\u232a is defined by M1 contains the term \u2329x\u232a, which cannot be determined without knowledge of P(x); thus, \u03c1(x) on the right hand side is given in x\u232a and \u03c1(x). The estimated analytical result agrees rather well with that of the stochastic simulations for sufficiently large N, as shown in For finite =\u2009Dx see  and M1\u2009=N\u2009=\u20091, the xi distribution has a significantly sharper profile than that for N\u2009=\u2009100, which indicates that the intra-molecular strain due to the extension of the motor is immediately released. That is, the filament can move immediately in the direction in which it is pulled by the motor, and x always remains close to zero. Thus, the asymmetry in \u0394+/\u0394\u2212 cannot manifest. The directionality is, therefore, determined according to the built-in walk direction, which is consistent with the slightly biased distribution in x\u232a: although the distribution seems to be almost symmetric, the non-zero value of P(x)\u2009\u2212\u2009P(\u2212x), as is shown in the inset of N and large Dx, the distribution of xi is significantly broader, which indicates that the multiple motors pull the filament in opposing directions, similar to a game of tug-of-war. Thus, the intra-molecular strain in each motor is released only a little. This \u201cfrustrated\u201d motor configuration causes the asymmetry in \u0394+/\u0394\u2212 to manifest. Specifically, in the case of \u0394+\u2009>\u2009\u0394\u2212, the backward force with respect to the walking direction  applied to the motors with x\u2009<\u20090 causes them to detach more easily than the forward force applied to the motors with x\u2009>\u20090. This asymmetry allows for a slightly longer tail at x\u2009>\u20090 compared to that at x\u2009<\u20090 in the distribution of x\u232a is positive and These analytical results illustrate the directionality transition mechanism. For Dx) in the walk, rather than a random thermal force \u03bey, is crucial for the emergence of the directionality transition. This is because large Dx leads to a broader x distribution, which reflects a highly frustrated \u201ctug-of-war\u201d situation of the motors. If Dx is small, the motors move with the built-in direction concurrently, yielding a sharper x distribution and smaller intra-molecular strains. Thus, the directionality transition is absent. This is also true even in the presence of a thermal force applied to the filament  much larger than v0, as this force does not change the relative distances between the motors.N discussed above, the phase diagram in \u03ba\u2009=\u2009k/\u03b3y . We have also confirmed this transition in the analytical calculation for N\u2009=\u20091, as shown by the red dot in \u03ba signifies low filament mobility and, thus, the strain in the stretching motor is not released by the filament movement, leading to a broader x distribution. As a result, the effect of the asymmetry in the strain-dependent detachment \u0394+/\u0394\u2212 becomes prominent, which allows for a slightly longer tail at x\u2009>\u20090 in the distribution; thus, the contribution of the tail to the mean \u2329x\u232a surpasses that of v0.In addition to the directionality transition with increased F(x), which results in N\u2009=\u20091, this F(x) is positive on average. That is, F(x) is required to immobilize the filament. This is despite the fact that the filament velocity is positive in the absence of F(x). This counterintuitive result can also be understood by noting that the increase in the strain ) through immobilization of the filament causes the asymmetry in \u0394+/\u0394\u2212 to manifest.In addition, we can also consider an extreme low-mobility situation, where the filament is fully immobilized through application of an external force N by introducing case (ii), the asymmetric dependency of the motor\u2019s velocity upon the intramolecular strain |f(x)|\u2009>\u2009|f(\u2212x)|, i.e., f(x)\u2009=\u2009a+x (if x\u2009\u2265\u20090) and a\u2212x (if x\u2009<\u20090), with a+\u2009<\u2009a\u2212. In this case, the same directionality transition as in case (i) \u0394+\u2009>\u2009\u0394\u2212 is obtained via the analytical estimates, as shown in Even without the asymmetry in the detachment process, directionality transitions can also be observed with increased v0\u2009=\u20090, we confirm that the filament moves via non-biased diffusion for N\u2009=\u20091, whereas collective directional motion of the filament toward the minus-end emerges for large N, as shown in P(x) is symmetric for N\u2009=\u20091 as illustrated by the inset in P(x) manifests for N\u2009=\u200950 in 1011Finally, by setting +/\u0394\u2212) or in the force-velocity relation (a+/a\u2212), the directionality in the filament movement can be reversed via an increase in the number of motors N. Although neither of these asymmetries has yet been measured for Cin8, asymmetry in the force-dependent detachment or the force-velocity relation have been reported for several motor proteins192021222324N, the intra-molecular strains in the motors are immediately released by the filament movement; thus, the motors walk in the built-in walk direction, i.e., towards the minus-end. On the other hand, when N increases, the diffusive nature of the processive motors leads to a frustrated motor configuration in which multiple motors pull the filament in opposite directions; thus, the intra-molecular strains in each motor are increased. These inter- and intra-molecular frustrations amplify the asymmetry in the strain-dependent properties of the motors and generate the opposite motility mode. Thus, the motors act as plus-end-directed motors, although their average movement is toward the minus-end. Similar to the several macroscopic models of motor-filament system262728In this Paper, we have investigated a mathematical model of a motor-filament system and shown that, with a large diffusivity in the motor\u2019s walk and asymmetry in the strain-dependent detachment  correspond to the changes in parameters in our model, and the consequent results by the changes are consistent to previous experimental observationset al.et al.Some references have reported changes in motility of Cin8 even in a single molecule assay; D\u00fcselder v0\u2009>\u20090 and \u0394+\u2009<\u2009\u0394\u2212. These experimental results are also explained by our model.Furthermore, quite recently, the directionality switch of another motor, kinesin-14 KlpA, due to collective binding of MT was reportedet al. reported the directionality switch in kinesin-5 Cut7In addition, an experimental study by Britto We have demonstrated that the number of molecules, rather than the density, can dramatically alter the motility mode. These findings are related to those reported in the growing literature on the small-number effect in chemical reaction systems32in vivo. In such a situation, the number of motors that can cross-link to the same MTs changes, depending on the configuration between the two MTs. Hence, the present mechanism provides a novel means of context-dependent regulation for a mechano-chemical coupling: plus- and minus-end directionality is used properly depending on the microtubule\u2019s configuration. For instance, a team of cross-linkers operating under the proposed mechanism can transport two MTs in an anti-parallel alignment with their minus-end leading for a long overlap region, as abundant motors can cross-link. In contrast, for a short overlap, the motors would transport the MTs with their plus-end leading via a change in the directionality. As a result, the overlap region between two plus-ends of the MTs would be stably maintained within a certain length by only a single type of motor, which is a possible functional role of the dual-directionality of Cin8. This is in contrast to the conventional view in which two different types of motors are required for the maintenance of the overlap region, which is important for the mitotic spindle formation2834Although we only considered a MT sliding assay here, the proposed mechanism is straightforwardly applicable to a situation where both ends of a motor can bind to two different MTs , as is commonly observed How to cite this article: Saito, N. and Kaneko, K. Embedding dual function into molecular motors through collective motion. Sci. Rep.7, 44288; doi: 10.1038/srep44288 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "Then we define the following real n-vector:x and a real number \u03bb such that\u03bb is called an H-eigenvalue of x is called an eigenvector of \u03bb [x and a real number \u03bb such that\u03bb is called a Z-eigenvalue of x is called an eigenvector of \u03bb. You can see more about the eigenvalues of tensors in [Let mentclass2pt{minimnsors in \u20137.k distinct vertices, then k-uniform hypergraph. The degree of a vertex i in i, denoted by Let udied in , 9.k distinct vertices kth order n-dimensional tensor with entries:Z-eigenvalues of the adjacency tensor Z-spectral radius of the adjacency tensor Let k-uniform hypergraph Z-eigenvalues For a nd Chang  presenteZ-spectral radius of hypergraphs, which improves the bound as shown in (Z-spectral radius of hypergraphs.In this paper, we give a new upper bounds in terms of degree mentclass2pt{minimSome basic definitions and useful results are listed as follows.The tensor Z-spectrum of Z-eigenvalues of Z-spectral radius of Let weakly symmetric was first introduced and used by Chang, Pearson, and Zhang [Z-eigenvalue of nonnegative tensors.The concept of nd Zhang  in orderLetbe a weakly symmetric nonnegative tensor, then the spectral radiusis a positiveZ-eigenvalue with a nonnegativeZ-eigenvectorx. Furthermore, ifis irreducible, xis positive.Letandbe two weakly symmetric and irreducible tensors of ordermand dimensionn. Ifandare nonnegative, theny be the eigenvector associated with \u03b2, where \u03b2 is a Z-eigenvalue of Let m\u00a04.7 of , we haveLetbe a sequence of nonnegative, weakly symmetric tensors of ordermand dimensionn, andbe nonnegative for each positive integerk. Then\u03bb is an eigenvalue of Let Z-spectral radius of tensors and hypergraphs.In this section, let Letbe weakly symmetric nonnegative tensors of ordermand dimension\u00a0n. ThenZ-eigenvalues Case 1. If entclass1pt{minima\u03f5. Now we substitute Case 2. If Z-spectral radius of a uniform hypergraph is obtained, we also compare the bound with the result in (By Theorem\u00a0esult in .Letbe ak-uniform hypergraph onnvertices with the degree sequenceThenCase 1. \u03f5. Now we substitute Case 2. If Obviously, we can getmentclass2pt{minimWe now show the efficiency of the new upper bound in Theorem\u00a0Consider 3-uniform hypergraph Consider 3-uniform hypergraph From Table\u00a0Z-spectral radius of tensors. As applications, in terms of the degree sequence Z-spectral radius of hypergraphs, which is always better than the bound in [In this paper, we get a new bound for the bound in . We list"}
+{"text": "Scientific Reports 10.1038/s41598-017-17044-3, published online 07 December 2017Correction to: Anabaena sp. PCC 7120\u201d was incorrectly given as \u201cAnabaena sp. PCC 7210\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Information file.The original version of this Article contained an error in the title of the paper, where \u201c"}
+{"text": "Nature Communications 10.1038/s41467-017-01896-4, published online: 13 Dec 2017Correction to: y-axes were incorrectly labelled from \u2018\u221240\u2019 to \u201840\u2019, rather than the correct \u2018-400\u2019 to \u2018400\u2019. The HTML has been updated to include a corrected version of the Supplementary Information.The original version of the Supplementary Information associated with this Article contained an error in Supplementary Figure 9e,f in which the"}
+{"text": "By measuring the Q factor with coupled power we find that the loss in the a-Si:H micro-rings scales linearly with power, and therefore cannot originate from two photon absorption. Theoretically comparing a-Si:H and c-Si micro-ring pair sources, we show that the high Kerr coefficient of this sample of a-Si:H is best utilized for microrings with Q factors below 103, but that for higher Q factor devices the photon pair rate is greatly suppressed due to the first order loss.We generate photon pairs in a-Si:H microrings using a CW pump, and find the Kerr coefficient of a-Si:H to be 3.73\u2009\u00b1\u20090.25\u2009\u00d7\u200910 Hydrogenated amorphous silicon (a-Si:H) has recently arisen as a photonics platform to contend with crystalline silicon (c-Si). a-Si:H can be deposited at low temperatures and so is easy to incorporate in the chip manufacturing processes, and retains many of the advantages of silicon based photonic structures - similar waveguide dimensions, CMOS compatibility and low loss guiding of telecom wavelengths. Additionally, the nonlinear properties of a-Si:H are known to be dependent on the manufacturing conditions, potentially giving a user freedom to design the material to his or her requirements. a-Si:H has quasi-bandgap of ~1.7\u2009eV, and experiences less two photon absorption (TPA) than c-Si, which has bandgap energy 1.1\u2009eV. Samples have been fabricated with Kerr coefficient several times larger than c-Si, overall giving a-Si:H a high nonlinear figure of merit12345678These properties make a-Si:H a potentially useful material for quantum optics applications, in particular photon pair generation via spontaneous four wave mixing (SFWM). In c-Si photon pairs can be generated by SFWM, but nonlinear losses such as TPA reduce the heralding efficiency of silicon sources for both microrings and waveguides. High heralding efficiency is a key requirement for a single photon source in linear optical quantum computing, and there are concerns that this inherent nonlinear loss in c-Si makes it unsuitable for large scale applications10121415In this work we study the performance of a-Si:H microring resonators, in comparison to c-Si. We find that a-Si:H has a Kerr coefficient ~8 times higher than c-Si, and that the main source of loss is linear with power, and so cannot originate from TPA. Instead, we model this loss by interband transitions facilitated by a mid-gap state, referred to here as sequential photon absorption (SPA)12\u03bcm, and waveguide effective area 0.3\u2009\u03bcm2. Light was coupled into the device using grating couplers with loss approximately 8\u2009dB each.The test structure was a a-Si:H micro-ring resonator coupled to a bus waveguide, illustrated in The ring resonator acts as a cavity, with a comb of resonances equally spaced in frequency. When light is is coupled into the ring and SFWM occurs, the signal and idler photons are generated at resonances either side of the pump wavelength, as shown 1621P is the power in the bus waveguide, L is the ring length, Q is the Quality factor of the ring, and vg is the group velocity. The nonlinear coefficient \u03c4 is equal to the self coupling t. The sign of \u03c4\u2009<\u2009t), and negative if the ring is under-coupled (\u03c4\u2009<\u2009t). SFWM is driven by the Kerr coefficient n2, and while we assume device dimensions and properties are fixed, the Q factor of the ring is dependent on the loss in the ring24The power dependent Q factor is given by\u03b1NL is the loss per metre in the ring due to nonlinear losses only. Q0 is the Q factor of ring when the coupled power is zero. The extinction ratio \u0393 also changes due to nonlinear losses, and can be described in terms of the Q factorwhere The extinction ratio \u0393 also gives information about the coupling of the device. If a ring is over-coupled, \u0393 will decrease with power, because the coupling condition becomes closer to critical coupling as the loss is increased. Conversely, if the ring is under coupled \u0393 will increase with power. In this work, a-Si:H rings B and C were under-coupled, and a-Si:H ring A was over-coupled.ns), and so we can neglect loss by TPA directlyWith a CW pump, the powers involved are generally too small for electronic state transitions via absorption of photons  to significantly influence the loss in the ring. However, these processes generate free electrons in the conduction band which can absorb photons via intraband transitions, known as free carrier absorption (FCA). The number of photons absorbed in the creation of a free carrier is much lower than the number of photons absorbed by the free carriers themselves, because the free carrier can absorb several photons during its lifetime  can be given by QSPA (P) or QTPA (P).Where The experimental set-up used to measure the Q factor with coupled pump power is shown in \u03c3\u03c4\u03b2SPA, giving 2.44\u2009\u00b1\u20090.223, 2.04\u2009\u00b1\u20090.200 and 2.13\u2009\u00b1\u20090.176\u2009\u00d7\u200910\u221227\u2009ms for rings A, B and C respectively. If there is any loss due to TPA generated free carriers present in the a-Si:H devices, it is negligible compared to the loss due to SPA generated free carriers, for the powers measured here. Since TPA is quadratic with power there exists a power threshold where TPA becomes dominant over SPA, so we cannot assume TPA is not present in this sample of a-Si:H, merely that we have not yet reached the power levels where it becomes important.The Q factor for the a-Si:H rings are shown in Q0\u2009=\u200911070,  and identical length to the a-Si:H devices, but where the main loss mechanism was due to TPA driven FCA, with TPA coefficient 8.4\u2009\u00d7\u200910\u221212\u2009W/m2\u2009To compare the behaviour of these rings to that expected for crystalline silicon, we modelled the power dependent Q factor for a c-Si device with To measure the rate of photon pairs generated via SFWM in the ring a CW laser was amplified and filtered to remove background noise from the amplifier and the wavelength tuned to the ring resonance wavelength. The signal and idler photons generated on resonance were separated from the residual pump light using a WDM after the chip and detected using super-conducting nanowire single photon detectors (SNSPDs). Coincidence counting hardware was used to obtain the rate of coincidence detections between the two SNSPDs, and accidental coincidence counts were removed. The rate of coincidences originating from photons generated in the waveguide was negligible in the devices.cm\u22121, corresponding to a wavelength shift of \u2248115\u2009nm for 1550\u2009nm photons, but the width of the peak is typically broader than in c-Si and tails off into lower wavenumbers due to the presence of hydrogen bonds2829The Raman spectrum of a-Si:H has a peak centred around 480\u2009Using the rate of the single counts at each detector, and the rate of coincidences, it is possible to remove the loss of each channel and obtain the absolute rate of photons generated in the ring, following the method outlined in ref. n2 to be 3.98\u2009\u00b1\u20090.03, 3.82\u2009\u00b1\u20090.07 and 3.39\u2009\u00b1\u20090.1\u2009\u00d7\u200910\u221218\u2009m2/W for rings A, B and C respectively, approximately 8 times larger than the literature value for c-Si. We measured the SPA parameter \u03c3\u03c4\u03b2SPA to be 0.87\u2009\u00b1\u20090.01, 0.55\u2009\u00b1\u20090.05 and 0.53\u2009\u00b1\u20090.06\u2009\u00d7\u200910\u221227\u2009ms for rings A, B and C. The discrepancy between these values and the previous section likely arise from the increased stability during the measurement  is not an issue. Another feature of SPA is that the process is non-instantaneous, since the mid-gap states have a non-negligible lifetime. In the CW regime this has no effect, but using a short pulsed pump could further reduce loss from SPA generated free carriers. It is advantageous to use a-Si:H for waveguide based sources, and low Q factor a-Si:H microrings could be useful for applications where short pulses with high peak power are required, although further study is required to determine whether operating in this regime we could achieve better heralding efficiencies than c-Si in general.How to cite this article: Hemsley, E. et al. Photon pair generation in hydrogenated amorphous silicon microring resonators. Sci. Rep.6, 38908; doi: 10.1038/srep38908 (2016).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "The extremely low loss of silica fibers has enabled the telecommunication revolution, but single-mode fiber-optic communication systems have been driven to their capacity limits. As a means to overcome this capacity crunch, space-division multiplexing (SDM) using few-mode fibers (FMF) has been proposed and demonstrated. In single-mode optical fibers, Rayleigh scattering serves as the dominant mechanism for optical loss. However, to date, the role of Rayleigh scattering in FMFs remains elusive. Here we establish and experimentally validate a general model for Rayleigh scattering in FMFs. Rayleigh backscattering not only sets the intrinsic loss limit for FMFs but also provides the theoretical foundation for few-mode optical time-domain reflectometry, which can be used to probe perturbation-induced mode-coupling dynamics in FMFs. We also show that forward inter-modal Rayleigh scattering ultimately sets a fundamental limit on inter-modal-crosstalk for FMFs. Therefore, this work not only has implications specifically for SDM systems but also broadly for few-mode fiber optics and its applications in amplifiers, lasers, and sensors in which inter-modal crosstalk imposes a fundamental performance limitation. N-mode optical fiber could permit N channels to transmit independent data and therefore increasing the transmission capacity by a factor of N, in comparison with a single-mode fiber. Rayleigh scattering is an inherent process that will affect signal propagation in these channels. Additionally, crosstalk among these channels due to random mode-coupling171817N2, optical fibers with a few modes, or, so-called few-mode fibers (FMFs), have been deployed for SDM systems.The discovery by Kao that the optical loss of silica fiber could be reduced to below 20\u2009dB/km34589101112131415Rayleigh scattering has been studied in single- and multi-mode optical fibers. And the relevant theories are well established. In particular, with regard to the Rayleigh scattering theory developed for MMFs01, LP11a, and LP11b modes, as an example to study Rayleigh scattering. The theory we developed here, however, can be extended to an arbitrary number of modes. The experiment, in principle, can also be trivially extended with the availability of efficient multiplexers/demultiplexers. In this work we didn\u2019t take polarizations into account and treated Rayleigh scattering as a scalar process.We used a three-mode optical fiber, containing the LP\u0394T and a constant power P0 was launched at z\u2009=\u20090 into mode i  of the three-mode fiber. In the main text of the paper, as well as in the 01, LP11a, and LP11b modes, respectively. The time-dependent power of Rayleigh back-scattering in mode j received at z\u2009=\u20090 can be calculated byWe derived the equation for mode-resolved time-dependent power of Rayleigh back-scattering received at the front end of the fiber. To develop the theory, we assumed that an optical pulse, with a temporal width of vig and vjg are the group velocities of modes i and j, respectively; \u03b1i and \u03b1j are the optical attenuation coefficients of modes i and j, respectively; \u03b1s(z) is the ratio of the total scattered power at z to the incident power at z; Bij(z) is the overall capture fraction, quantifying the ratio of the scattered power into mode j to the total scattered power at z. Detailed derivation of \u03b1s(z)\u2009=\u2009\u03b1s, Bij(z)\u2009=\u2009Bij, and where i\u2009=\u2009j\u2009=\u20091, vig\u2009=\u2009vjg\u2009=\u2009vg, and \u03b1i\u2009=\u2009\u03b1j\u2009=\u2009\u03b1.We note that Bij, can be calculated by averaging the local capture fraction, bj, over the near-field intensity distribution of the incident mode i:In where\u03c8jN and \u03c8jF represent the near and far fields  is modeled as the field of a dipole located at . Following derivations detailed in bj:in which elds see  of mode pole see . RayleigandR\u2032\u2009=\u2009R/a, a is the radius of the core of the optical fiber, Bij:where Bij satisfy the following relations . As expected [see bj across the cross-section of the fiber closely mimics the intensity distribution of the near field of mode j. Indeed, we calculated bj using Bij, as a function of normalized frequency V\u2009\u2261\u20092\u03c0aNA/\u03bb, where a is the core radius of the fiber, NA is the numerical aperture of the fiber, and \u03bb is the wavelength in free space. The dashed line shows the normalized cut-off frequency for the LP11a and LP11b modes, at V\u2009=\u20092.405. Our experiment was performed at V\u2009=\u20093.49.Bij in B11 is almost identical with the single-mode result reported in ref. The degeneracy and the relative magnitudes of Before we further discuss the case of forward scattering and its impact on inter-modal crosstalk, we first verify the newly-developed model via OTDR measurement of the backscattering. This is because the theories for forward- and backward-scattering share significant similarities. After we place the backward-scattering case on a solid ground, we can develop the forward case by analogy.We measured the time-dependent power of Rayleigh back-scattering using the experimental setup schematically shown in Lij. Lij in detail. For calculating the theoretical curves, we used the values obtained by fitting the experimental data of \u03b1i and \u03b1j; \u03b1s\u2009\u2248\u2009\u22120.039/km as in ref. vig\u2009\u2248\u2009vjg\u2009\u2248\u20092.067\u2009\u00d7\u2009105\u2009km/s. To quantify the relative difference between theoretical and experimental results, we compare the intercepts at z\u2009=\u20090 of the OTDR curves, as relative to Lij and Fij(z), the overall capture fraction for forward-scattering, are independent with z, i.e., \u03b1s(z)\u2009=\u2009\u03b1s and Fij(z)\u2009=\u2009Fij. Additionally, we assume that the incident light in mode i is continuous wave (CW) with a constant power Pi. Thus,We simplify Fij\u2009=\u2009Bij, i.e., the corresponding overall capture fraction of forward and backward scattering are identical. Therefore, the inter-modal crosstalk due to Rayleigh forward scattering isFrom symmetry consideration, 01 and LP11a(b) modes are stronger than that between the LP11a(b) and LP11b(a) modes. Inter-modal Rayleigh forward-scattering increases with z at the beginning because the scattered power from mode i keeps accumulating in mode j. At longer propagation distance, the coupled power decreases as z increases because the incident light in mode i attenuates due to propagating loss and the scattered light in mode j decreases in proportion to the local excitation. A maximum appears in between. \u03b11\u2009=\u20090.209\u2009dB/km, \u03b12\u2009=\u20090.210\u2009dB/km, and \u03b13\u2009=\u20090.233\u2009dB/km. We can use Tij is - 37\u2009dB, which is 7.51\u2009dB smaller than the minimum total crosstalk (\u221229.49\u2009dB for the case LP01\u2009\u2192\u2009LP11b) due, dominantly, to random mode-coupling and fiber imperfections that we measured in this three-mode optical fiber  of the fiber is 0.1259. The single-pass insertion loss between the first circulator and the last coupling lens of the mode multiplexer/de-multiplexer was 5.85\u2009dB, 9.83\u2009dB and 9.22\u2009dB for the LP01, LP11a, and LP11b channels, respectively. The coupling losses from free space to the fiber were 0.50\u2009dB, 2.51\u2009dB, and 2.89\u2009dB for the LP01, LP11a, and LP11b channels, respectively. 11b mode and the signal collected is in LP01 mode. We manually reconfigured the fiber connections for other combinations of excitation and collected channels.As shown in How to cite this article: Wang, Z. et al. Rayleigh scattering in few-mode optical fibers. Sci. Rep.6, 35844; doi: 10.1038/srep35844 (2016)."}
+{"text": "Print and television advertisements for e-cigarettes are currently legal in the United States. Given that e-cigarettes are a lower-risk alternative to cigarettes, these ads could have a positive public health impact if they motivate smokers to switch to e-cigarettes. However, the public health impact of e-cigarette ads could be negative if ads increase demand for both e-cigarettes and cigarettes. We use experimental auctions \u2013in which participants bid in real auctions and winners pay for the items they purchase \u2013 to study the effect of print and TV e-cigarettes ads on demand for the brand from the ad, for another e-cigarettes brand, and for cigarettes. We ran experiments with 288 Pennsylvania smokers in November 2014\u2013March 2015 and we found that in cases where an ad affects demand for e-cigarettes, the ad moves demand for cigarettes in the same direction. For example, the Blu print ad increases demand for Blu e-cigarettes and cigarettes among non-white participants. The Vuse TV ad reduces demand for both types of e-cigarettes and for cigarettes. We also find that non-white participants are willing to pay more for e-cigarettes in the absence of advertising, and that smokers who worry most about their health are willing to pay more for e-cigarettes. The results of this study point to the need for greater scrutiny of advertising for e-cigarette products such that they do not also induce demand for tobacco cigarettes. \u2022Print and television ads are currently legal in the United States.\u2022We use experimental auctions to assess how ads impact smokers demand for cigarettes and e-cigarettes.\u2022Examine ads for two major brands: Vuse and Blu\u2022Found that ads for e-cigarettes impact demand for cigarettes and e-cigarettes similarly Typically, this is accomplished through dissolving nicotine in a solution of propylene glycol and glycerin, and heating that solution to produce an aerosol that is inhaled by the user . While sIn April 2016, the Food and Drug Administration (FDA) released its final \u2018deeming\u2019 regulation, which extended its existing authorities over tobacco products to include e-cigarettes, hookah, cigars, and pipes . Among tUnderstanding the dynamics of e-cigarette use, and in particular, smoker demand for such products, is important for projecting their likely impact on public health. If large numbers of smokers were to abandon cigarettes in favor of e-cigarettes, the anticipated effects could be large and positive. However, if most smokers simply use them as a situational substitute, the effects could be substantially smaller, and even negative if such use patterns depressed attempts to quit, or encouraged those who otherwise would not have used tobacco to take up e-cigarettes.The same arguments apply to print and television advertisements for e-cigarettes, which are (as of this writing) legal in the United States. Intended use of e-cigarettes can be influenced by advertising, and e-cigarettes are unique in the US context in that advertising on television is currently permitted, a seeming advantage over other tobacco products. If these ads motivate smokers to switch from cigarettes to e-cigarettes, the public health impact is likely to be positive. But if e-cigarette ads increase demand for both cigarettes and e-cigarettes, the net public health effect may be negative.Experimental economics offers methods that are designed to examine demand for products in a nonhypothetical way, which may provide important insights into how much smokers truly value e-cigarettes as an alternative to cigarettes. Experimental auctions, first developed in the 1960s, have been used by economists for over 20\u00a0years to assess the demand for many products, including irradiated food products , food la22.1The study protocol was approved by the IRB at Susquehanna University. Tables were set up at grocery stores in Shamokin, PA and Williamsport, PA between November 2014 and March 2015. Eligible study participants were 18 and older, had smoked >\u00a0100 cigarettes in their lifetimes, had smoked at least one cigarette in the last month, and were not pregnant. Posted signs indicated that adult smokers could earn $20 for 15\u201320\u00a0min of their time. Auctions were conducted with one to eight participants at a time, and a total of 288 subjects participated.2.2https://youtu.be/k79Iutkwdcg and the Vuse TV ad can be viewed at https://youtu.be/J4XpPXzg8J8. The TV ads were shown on an iPad while the print ads were laminated.The study involved assessing how six advertising conditions along with a control group affected demand for two types of e-cigarettes and conventional cigarettes. Participants were randomly assigned to 1) a control group that saw no advertising; 2) a group given a print ad about Blu e-cigarettes; 3) a group given a TV ad about Blu e-cigarettes; 4) a group given both a print and a TV ad about Blu e-cigarettes; 5) a group given a print ad about Vuse e-cigarettes; 6) a group given a TV ad about Vuse e-cigarettes; and 7) a group given both a print and a TV ad about Vuse e-cigarettes. After surveying the companies' actual advertisements, we chose the ones we felt were most representative. Print ads can be found in the appendix while the Blu TV ad can be viewed at After seeing the ads , participants placed bids. Participants bid on a single-use Blu e-cigarette, a single-use Vuse e-cigarette, and a pack of Camel cigarettes. For both types of e-cigarettes, participants bid on the type of e-cigarette they preferred: menthol or full flavor. For the Camel cigarettes, participants also bid on the type they preferred: they had the option to bid on full-flavored, light, menthol, or menthol-light.2.3paying the selected price; a participant who bids less than the selected price does not purchase the product.For the current study, we used the Becker-DeGroot-Marschak (BDM) experimental auction mechanism . In thisThis BDM auction is \u201cdemand revealing\u201d because it is theoretically in a participant's best interest to bid his or her true value (demand) for the product. This has been shown to hold in practice in the laboratory  and the 2.4After screening for eligibility and signing consent forms, participants filled out a brief survey on smoking behavior and received a detailed explanation of the BDM auction. Participants were informed (1) that they would place a private, written bid for an item; (2) they would purchase the product if their bid was higher than the bid randomly drawn from a container; and (3) it was in their best interest to bid their true value for the products, no more and no less. Participants were told that while they would bid on more than one product in a series of auction rounds, only one auction for one product would actually be carried out, and that that product would be randomly chosen after participants had bid on all products. This was done to disincentivize participants from reducing bids in later rounds in anticipation of winning multiple products. Any questions they had were answered and a practice round was conducted in which participants bid separately on two candy bars.Participants then bid in the real auctions. The participants were presented with a single-use Blu e-cigarette and bid on it. Those bids were collected, and participants were then presented with a single-use Vuse e-cigarette and bid on it. Those bids were collected, and participants were presented with the pack of Camel cigarettes and bid on that pack. Once the three rounds of bidding were complete, the binding auction round  was randomly determined. The selected price was then randomly chosen from a uniform distribution, which ranged from $0.10 to $15.00 in increments of $0.10. If the participant bid equal to or more than this value, she paid the selected price and received the package. If the participant bid less, no purchase was made.3To control for demographic and smoking-related characteristics, we estimate different Tobit regression models for cigarettes, Blu e-cigarettes, and Vuse e-cigarettes. A Tobit model corrects for the fact that bids are censored at zero. Bids for each product are the dependent variables. Independent variables include demographic variables, smoking-related variables, and dummy variables to indicate the advertising treatments (the no-advertising control group is the omitted category). The full regression model is estimated as.Bidi\u00a0=\u00a0\u03b10\u00a0+\u00a0\u03b2\u2032Xi\u00a0+\u00a0\u03b3\u2032Si\u00a0+\u00a0\u03b4\u2032Ai\u00a0+\u00a0\u03bb\u2032Ni\u00a0+\u00a0\u03b5i,where Bidi is participant i's bid in for the product, \u03b1o is an intercept term, Xi is a vector of demographic variables and \u03b2\u2032 is the associated coefficient vector, Si is a vector of smoking-related variables and \u03b3\u2032 is the associated coefficient vector, Ai is a vector of advertising treatment dummy variables and \u03b4\u2032 is the associated coefficient vector, Ni is a vector of advertising treatment dummy variables interacted with the \u201cnonwhite or Hispanic\u201d dummy variable and \u03bb\u2032 is the associated coefficient vector, and \u03b5i is the error term.4The participants' average age was 39.6\u00a0years, and our sample was 56% female. Eighty-five percent of participants were white, and 60% had a household income of under $30,000 annually. Participants smoked an average of 18.5 cigarettes per day and 57% of participants had tried an e-cigarette. Non-white or Hispanic participants who were not presented with ads bid $9.46 more for Vuse e-cigarettes, a difference that was statistically significant. Participants who worried about their health bid a statistically significant $1.73 more for Blu e-cigarettes. Number of cigarettes smoked had a marginally statistically significant $0.06 negative effect on bids for Blu e-cigarettes.5E-cigarettes are another in a line of potentially reduced exposure products that have promised to reduce the risk of smoking. Our study examined smokers' preferences for two brands of e-cigarettes, Blu and Vuse, using an experimental auction. We found that smokers were willing to spend their money for e-cigarettes. In fact, given a single-use e-cigarette contains about two cigarette packs' worth of content, and that the bids for Vuse were double the bids for cigarettes, smokers had the same units/day bid for Vuse e-cigarettes as for cigarettes. At the same time, the units/day bid for Blu e-cigarettes was lower than for cigarettes. This difference in demand across brands reflects market conditions, as Vuse has recently overtaken Blu in terms of market share . The Vusboth cigarettes and Blu e-cigarettes. We found modest evidence that the Vuse TV ad decreased demand for cigarettes among nonwhite or Hispanic participants. Taken together, these results suggest that e-cigarette ads shift demand for cigarettes and e-cigarettes in the same direction. If true, this could have serious public health implications given that print and TV ads for e-cigarettes are currently legal in the United States. If effective e-cigarette ads coincidentally increase demand for cigarettes in some populations, this may offset the public health benefits from some smokers adopting lower risk e-cigarettes.We found that the Vuse TV ad decreased demand for cigarettes and Blu e-cigarettes among white, non-Hispanic smokers. One possible explanation is that smokers are cynical and turned off by pro-tobacco advertising. This would be consistent with evidence presented in Limitations of the current study include localization in North-central Pennsylvania, relatively low racial/ethnic diversity among participants, and limitation to two cartridge-based e-cigarette products. The latter limitation was driven by the need for paired print and TV advertising, since other forms of e-cigarettes  are not advertised in this way, but rather by word-of-mouth, in vape shops, or over the Internet . Future E-cigarettes hold potential to reduce smoking-associated disease burden . However"}
+{"text": "Scientific Reports7:2918; doi:10.1038/s41598-017-03112-1; Article published online 07 June 2017The original version of this Article contained an error in the title of the paper, where the word \u201cNoncanonical\u201d was incorrectly given as \u201cNoncanocial\u201d. This error has now been corrected in the HTML and PDF versions of this Article, and the Supplementary Information file that accompanies the Article."}
+{"text": "To evaluate the center of pressure (COP) progression similarity and its change during walking and jogging in Anterior Cruciate Ligament deficient (ACLD) patients.A study was performed in 64 unilateral ACLD subjects and 32 healthy volunteers who walked and jogged on footscan\u00ae system at a self-selected speed. COP trajectory during walking and jogging was calculated. The robustness and similarity scores of COP  were computed, and then the Analysis of Variance test was employed to compare among different conditions .(1) During the same motion status , SSCOP were higher than 0.885. However, SSCOP between walking and jogging were lower than 0.25 in both the healthy and ACLD group. SSCOP between the intrasubjects were statistically higher than those between the intersubjects (p<0.01). (2) SSCOP in the ACLD group were statistically significantly reduced to 0.885\u00b10.074 compared to 0.912\u00b10.057 in healthy volunteers during walking, and 0.903\u00b10.066 in the ACLD group compared to 0.919\u00b10.050 in the healthy group during jogging (p<0.01).SSCOP can distinguish walking from jogging, and SSCOP of ACLD patients would be different from that of healthy controls.The study protocol was approved by the Institutional Research Board of Peking University Third Hospital (IRB00006761-2012010). Anterior cruciate ligament (ACL) deficiency is a common sports injury that increases tibiofemoral laxity and leads to knee joint instability, which can affect the performance of daily activities. Several biomechanical studies ,2,3,4 reGait cycle of the walking and running consists of a stance phase and a swing phase. The percentage of the stance phase varies depending on gait speed\u2014about 60% with walking, 40% with running, and 22% with world class sprinters. The distinction of walking is that gait cycle involves a period of double limb support in which both feet are on the ground. However, there is a period of double float in which both feet are off the ground during jogging or running . The cenThe aim of this study was to describe and quantify the similarity of the COP displacement during walking and jogging in healthy volunteers and in unilateral ACL deficient patients. The similarity of the COP displacements during walking was further investigated whether differed from that during jogging, and if COP similarity in the unilateral ACL-deficient patients was different from that of healthy volunteers.Thirty-two healthy college students  and 64 symptomatically unilateral (33 left and 31 right side) ACL deficient subjects  participated in the study. The injured knee was verified with a physical examination by an orthopedic surgeon and with an MRI examination. Additionally, the status of each injured ACL was confirmed during an arthroscopy performed after the completion of this study. All ACL-deficient subjects included in this study had unilateral ACL rupture, accompanied with minimal other tissue injuries that do not need surgical intervention. There was no history of injury, surgery or disease in the contralateral knees. Regular intervention following ACL injury was done. Controlling the knee hemarthrosis and general inflammatory process was the first goal. The patients were given crutches and instructed in a pain-free partial weight-bearing gait. Motion exercises were started with concentration on passive extension to help prevent rapid scarring in the intercondylar notch. Weight bearing were increased as pain and joint effusion decreases, quadriceps control increases, and full active knee extension was achieved. The study protocol was approved by the Institutional Research Board of Peking University Third Hospital (IRB00006761-2012010). After explaining the aims and risks of the study, subjects gave written informed consent. During the test, all patients were free of knee joint swelling and were able to walk and jog without any subjective discomfort. However, they reported symptoms of giving-way during turning or twisting activities.The subjects walked or jogged barefoot on a two meter footscan\u00ae system , that was placed halfway on a 16.5 meter walkway. Before data collection, subjects warmed up and were asked to perform practice trials until they had familiarized themselves with barefoot walking and jogging. Subjects were asked to walk and jog at a constant (self chosen) speed.A trial was considered valid when the following criteria were met: (1) at least two complete footprints, (2) presence of a heel-strike pattern, (3) no visible adjustment in gait pattern when crossing the plate , (4) tot1) COP Trajectory GenerationCOPX and COPY, were the anterior-posterior, medio-lateral position of COP, respectively. Theoretically, they could be expressed according to following formula:F was the continuous pressure distribution in the supporting surface area. While in practice, pressure distribution was detected by pressure-sensor array, which just was a discrete case. To let the calculation of COPX and COPY be possible, formula  that satisfied the minimized process as characterized by the right side constraint of the formula. The vector  takes over all the activated sensors, and D, ) was the Euclidean distance between  and . The origin  of the coordinate system was set at the center of the heel.The coordinates of COP, noted as dxdywhere F Similarity ComputationS1 and S2 were two COP trajectories. Based on this definition, several statistics were defined to observe different aspects of human COP trajectory for a natural walking or jogging behavior. First, to observe the robustness of each person, an individual\u2019s similarity referring to intra-participant similarity was defined as in formula  and Si, Sj were two intra-participant COP trajectories. To observe the characteristics of COP trajectories of a specific group of participants, the average among all individual similarities within the group was taken according to formula , between intrasubject (within the same subject) or intersubjects (between different subjects), and between walking or jogging.In order to evaluate whether the COP similarity under Walking motion pattern (marked in \u201cW\u201d) was different from that of Jogging motion pattern (marked in \u201cJ\u201d) in Experiment I: On Different Motion Patterns, several groups corresponding to two motion patterns were setup under four conditions: Left side (marked in \u201cL\u201d), Right side (marked in \u201cR\u201d), Healthy volunteers (marked in \u201cH\u201d) and ACL-ruptured patients (marked in \u201cA\u201d). Thus, there was a total of four groups to investigate the difference between two motion patterns, noted as \u201cHL-WJ\u201d, \u201cHR-WJ\u201d, \u201cAL-WJ\u201d and \u201cAR-WJ\u201d respecitvely, where for example, the group labelled with \u201cHL-WJ\u201d referred that the observation were focused on Left side of Healthy subjects by calculating the similarity of COP trajectories between Walking and Jogging for a given subject. As a consequence, four similarity scores according to formula  were obtIn order to evaluate whether the COP similarity on the ipsilateral side (marked in \u201cI\u201d) was different from that on the contralateral sides (marked in \u201cC\u201d) in Experiment II: On ipsilateral and contralateral, similarity scores were calculated between the same sides and different sides  of the same subject during walking (marked in \u201cW\u201d) or jogging (marked in \u201cJ\u201d). Several groups corresponding to two motion patterns were setup under four conditions: Left side (marked in \u201cL\u201d), Right side (marked in \u201cR\u201d), Healthy volunteers (marked in \u201cH\u201d), and ACL-ruptured patients (marked in \u201cA\u201d). Thus, there was a total of four groups were formed to investigate the difference between the contralateral sides, respectively noted as \u201cHW-C\u201d, \u201cHJ-C\u201d, \u201cAW-C\u201d, and \u201cAJ-C\u201d, where for example, the group labelled with \u201cHJ-C\u201d referred to the observation that focused on the Contralateral sides of Healthy subjects by calculating the similarity of COP trajectories during Jogging. As a consequence, four similarity scores according to formula  were obtIn order to evaluate whether the COP similarity on the sides of intrasubjects (marked in \u201cIntra\u201d) was different from that of the intersubjects (marked in \u201cInter\u201d) in Experiment III: On intrasubject and intersubject, similarity scores were calculated between different sides of the same subject and those between different subjects during walking (marked in \u201cW\u201d) or jogging (marked in \u201cJ\u201d). Several groups corresponding to two motion patterns were setup under four conditions: Left side (marked in \u201cL\u201d), Right side (marked in \u201cR\u201d), Healthy volunteers (marked in \u201cH\u201d), and ACL-ruptured patients (marked in \u201cA\u201d). Thus, there were a total of eight groups formed to investigate the difference between the sides of different subjects, respectively noted as \u201cHWL-Inter\u201d, \u201cHWR-Inter\u201d, \u201cHJL-Inter\u201d, \u201cHJR-Inter\u201d, \u201cAWL-Inter\u201d, \u201cAWR-Inter\u201d, \u201cAJL-Inter\u201d and \u201cAJR-Inter\u201d. For example, the group labelled with \u201cHJR-Inter\u201d referred to the observation focused on the Right side of the Healthy Intersubjects by calculating the similarity of COP trajectories during Jogging. As a consequence, eight similarity scores according to formula  were obtIn order to investigate whether the COP similarity changed following ACL rupture, differences between normal and pathology subjects were studied in Experiment IV: The influences derived from ACL deficiency. Firstly, similarity scores were calculated according to formula  for ACL-To be clearly, all results from above experiments were re-exhibited in a new way, where similarity score of a healthy volunteers group under given observation condition was taken as a control group, while that of a ACL deficiency group under the same condition was taken as a studied group. Each group under some observation condition was labeled by same characters just as that used in experiments mentioned above, only with some slight position adjustment to let it lay out more clearly. Moreover, for all observation conditions that involve both left and right foot, they were combined together by simple averaging. As a consequence, totally 11 studied group were formed, respectively noted as \u201cA-W\u201d, \u201cA-J\u201d, \u201cA-WJ\u201d, \u201cA-W-I\u201d, \u201cA-W-C\u201d, \u201cA-J-I\u201d, \u201cA-J-C\u201d, \u201cA-W-Intra\u201d, \u201cA-W-Inter\u201d, \u201cA-J-Intra\u201d and \u201cA-J-Inter\u201d, together with corresponding 11 control groups, noted as \u201cH-W\u201d, \u201cH-J\u201d, \u201cH-WJ\u201d, \u201cH-W-I\u201d, \u201cH-W-C\u201d, \u201cH-J-I\u201d, \u201cH-J-C\u201d, \u201cH-W-Intra\u201d, \u201cH-W-Inter\u201d, \u201cH-J-Intra\u201d and \u201cH-J-Inter\u201d. For example, the group labelled with \u201cA-W\u201d referred that the observation were focused on the ACL rupture patients during Walking, its similarity score was obtained by simply averaging the scores of both \u201cAL-W\u201d and \u201cAR-W\u201d in Experiment I; the group labelled with \u201cA-J-C\u201d was right the \u201cAJ-C\u201d in Experiment II, referred to the observation focused on the Contralateral side of ACL rupture patients while Jogging; the group labelled with \u201cA-W-Intra\u201d referred to the observation focused on the same ACL rupture subject during Walking, its similarity value was obtained by simply averaging the scores of both \u201cAWL-Intra\u201d and \u201cAWR-Intra\u201d in Experiment III; the group labelled with \u201cA-J-Inter\u201d referred to the observation focused on the intersubjects of ACL deficiency during Jogging, its similarity score was obtained by simply averaging the scores of both \u201cJL-inter-A\u201d and \u201cJR-inter-A\u201d in Experiment IV.To detect whether the difference among studied conditions was significant or not, the Analysis of Variance (ANOVA) test was employed. All statistical tests were performed using SPSS 15.0 . The level of statistical significance was set at 0.05.Left side of Healthy subjects during Walking. \u201cHR-W\u201d referred to that the observation focused on Right side of Healthy subjects during Walking. \u201cHL-J\u201d referred to that the observation focused on Left side of Healthy subjects during Jogging. \u201cHR-J\u201d referred to that the observation focused on Right side of Healthy subjects during Jogging. \u201cHL-WJ\u201d referred that the observation were focused on Left side of Healthy subjects by calculating the similarity of COP trajectories between Walking and Jogging. \u201cHR-WJ\u201d referred that the observation were focused on Right side of Healthy subjects by calculating the similarity of COP trajectories between Walking and Jogging.\u201cHL-W\u201d referred to that the observation focused on \u201cHW-IL\u201d referred to the observation focused on the Ipsilateral Left side of Healthy subjects during Walking. \u201cHW-IR\u201d referred to the observation focused on the Ipsilateral Right side of Healthy subjects during Walking. \u201cHW-C\u201d referred to the observation that focused on the Contralateral sides of Healthy subjects by calculating the similarity of COP trajectories during Walking. \u201cHJ-IL\u201d referred to the observation focused on the Ipsilateral Left side of Healthy subjects during Jogging. \u201cHJ-IR\u201d referred to the observation focused on the Ipsilateral Right side of Healthy subjects during Jogging. \u201cHJ-C\u201d referred to the observation that focused on the Contralateral sides of Healthy subjects by calculating the similarity of COP trajectories during Jogging.\u201cHWL-Intra\u201d referred to the observation focused on the Left side of the same Healthy subjects during Walking. \u201cHWL-Inter\u201d referred to the observation focused on the Left side of the Healthy Intersubjects by calculating the similarity of COP trajectories during Walking. \u201cHWR-Intra\u201d referred to the observation focused on the Right side of the same Healthy subjects during Walking.\u201cHWR-Inter\u201d referred to the observation focused on the Right side of the Healthy Intersubjects by calculating the similarity of COP trajectories during Walking.\u201cHJL-Intra\u201d referred to the observation focused on the Left side of the same Healthy subjects during Jogging. \u201cHJL-Inter\u201d referred to the observation focused on the Left side of the Healthy Intersubjects by calculating the similarity of COP trajectories during Jogging. \u201cHJR-Intra\u201d referred to the observation focused on the Right side of the same Healthy subjects during Jogging.\u201cHJR-Inter\u201d referred to the observation focused on the Right side of the Healthy Intersubjects by calculating the similarity of COP trajectories during Jogging.\u201cWL-inter-H\u201d referred to the observation focused on the Left side of the Healthy subjects by calculating the similarity of COP trajectories during Walking. \u201cWL-inter-A\u201d referred to the observation focused on the Left side of the ACL-ruptured patients by calculating the similarity of COP trajectories during Walking. \u201cWL-HA\u201d referred to the observation focused on the Left side between Healthy volunteers and ACL-ruptured patients by calculating the similarity scores of COP trajectories during Walking.\u201cWR-inter-H\u201d referred to the observation focused on the Right side of the Healthy subjects by calculating the similarity of COP trajectories during Walking. \u201cWR-inter-A\u201d referred to the observation focused on the Right side of the ACL-ruptured patients by calculating the similarity of COP trajectories during Walking. \u201cWR-HA\u201d referred to the observation focused on the Right side between Healthy volunteers and ACL-ruptured patients by calculating the similarity scores of COP trajectories during Walking.\u201cJL-inter-H\u201d referred to the observation focused on the Left side of the Healthy subjects by calculating the similarity of COP trajectories during Jogging. \u201cJL-inter-A\u201d referred to the observation focused on the Left side of the ACL-ruptured patients by calculating the similarity of COP trajectories during Jogging. \u201cJL-HA\u201d referred to the observation focused on the Left side between Healthy volunteers and ACL-ruptured patients by calculating the similarity scores of COP trajectories during Jogging. \u201cJR-inter-H\u201d referred to the observation focused on the Right side of the Healthy subjects by calculating the similarity of COP trajectories during Jogging. \u201cJR-inter-A\u201d referred to the observation focused on the Right side of the ACL-ruptured patients by calculating the similarity of COP trajectories during Jogging. \u201cJR-HA\u201d referred to the observation focused on the Right side between Healthy volunteers and ACL-ruptured patients by calculating the similarity scores of COP trajectories during Jogging.From the re-exhibition of these results in , it can \u201cH-W\u201d referred that the observation were focused on the Healthy subjects during Walking, its similarity score was obtained by simply averaging the scores of both \u201cHL-W\u201d and \u201cHR-W\u201d in Experiment I; \u201cH-J-C\u201d referred to the observation focused on the Contralateral side of the Healthy subjects while Jogging; \u201cH-W-Intra\u201d referred to the observation focused on the same the Healthy subjects during Walking; \u201cH-J-Inter\u201d referred to the observation focused on the intersubjects of the Healthy subjects during Jogging.\u201cA-W\u201d referred that the observation were focused on the ACL rupture patients during Walking, its similarity score was obtained by simply averaging the scores of both \u201cAL-W\u201d and \u201cAR-W\u201d in Experiment I; the group labelled with \u201cA-J-C\u201d is right the \u201cAJ-C\u201d in Experiment II, referred to the observation focused on the Contralateral side of ACL rupture patients while Jogging; the group labelled with \u201cA-W-Intra\u201d referred to the observation focused on the same ACL rupture subject during Walking, its similarity value was obtained by simply averaging the scores of both \u201cAWL-Intra\u201d and \u201cAWR-Intra\u201d in Experiment III; the group labelled with \u201cA-J-Inter\u201d referred to the observation focused on the intersubjects of ACL deficiency during Jogging, its similarity score was obtained by simply averaging the scores of both \u201cJL-inter-A\u201d and \u201cJR-inter-A\u201d in Experiment IV.The purpose of this study was to examine the similarity of the COP and its change during walking and jogging following the ACL deficiency. In accordance with our hypotheses, COP similarity can distinguish walking from jogging. In addition, the COP similarity would be changed in ACL-ruptured patients compared with healthy volunteers. These findings provide a reliable dataset for COP characteristics during walking and jogging in healthy volunteers and ACL-ruptured patients.Walking and jogging are the most common activities that humans perform during activity of daily living, sports and rehabilitation. Given that an average adult takes more than 5,000 steps per day , even slSimilarity scores between walking and jogging COP trajectories were lower than 0.25 see  which inAlthough similarity scores between the COP trajectories in healthy volunteers were high , there was a significant difference between left and right sides not only during walking but also during jogging (p<0.0001). Our results showed that asymmetry and laterality (limb preference for a particular task) previously recognized not only in temporal and force parameters ,22,23 buACL deficiency would result in knee joint instability and increase internal rotation of the tibia during the gait cycle, which wIn summary, the present study showed that COP similarity from the dynamic pedobarography not only provides a practical and objective way to evaluate dynamic function of walking and jogging that was not studied exclusively before, but also helps in evaluating and guiding future rehabilitative and surgical techniques in ACL deficient patients. However, previous studies have established that ACL rupture induces variability in postural control and gait patterns. ACL deficiency adopts certain strategies to maintain dynamic stability and balance. The modulating mechanism for postural control is complex, possibly affecting the COP trajectory. Interpretations of these findings should not only generalize the effect of ACL rupture, but also consider the variation in dynamic postural control during motion. Further studies are needed to clarify the relationship between dynamic stability and ACL rupture. Furthermore, large-scale measurements of muscle activity and more detailed kinematic studies in both ACL-intact and deficient subjects are necessary to develop population reference values to improve our general clinical understanding of individual variations in the biomechanical coupling between foot and knee.This investigation showed the COP similarity during walking was significantly different from that during jogging. ACL deficiency tends to display a more variable COP curve compared to healthy adults. These findings regarding the COP similarity for ACL rupture provided more information for dynamic foot function and gait performance, potentially assisting in clinical intervention assessment for the ACL rupture.S1 Dataset(ZIP)Click here for additional data file."}
+{"text": "Cell-penetrating peptides (CPPs) are short peptides (5\u201330 amino acids) that can enter almost any cell without significant damage. On account of their high delivery efficiency, CPPs are promising candidates for gene therapy and cancer treatment. Accordingly, techniques that correctly predict CPPs are anticipated to accelerate CPP applications in future therapeutics. Recently, computational methods have been reportedly successful in predicting CPPs. Unfortunately, the predictive performance of existing methods is not satisfactory and reliable so as to accurately identify CPPs.In this study, we propose a novel computational predictor called SkipCPP-Pred to further improve the predictive performance. The novelty of the proposed predictor is that we present a sequence-based feature representation algorithm called adaptive k-skip-n-gram that sufficiently captures the intrinsic correlation information of residues. By fusing the proposed adaptive skip features with a random forest (RF) classifier, we successfully construct the prediction model of SkipCPP-Pred. The various jackknife results demonstrate that the proposed SkipCPP-Pred is 3.6% higher than state-of-the-art CPP predictors in terms of accuracy. Moreover, we construct a high-quality benchmark dataset by reducing the data redundancy and enhancing the similarity between the positive and negative classes. Using this dataset to build prediction models, we can successfully avoid the performance bias lying in existing methods and yield a promising predictive model.http://server.malab.cn/SkipCPP-Pred/Index.html).The proposed SkipCPP-Pred is a simple and fast sequence-based predictor featured with the adaptive k-skip-n-gram model for the improved prediction of CPPs. Currently, SkipCPP-Pred is publicly available from an online webserver (The online version of this article (10.1186/s12864-017-4128-1) contains supplementary material, which is available to authorized users. Cell-penetrating peptides (CPPs) are short peptides usually comprising 5\u201330 amino acid residues. Also known as protein transduction domains (PTDs), membrane translocating sequences (MTSs), and Trojan peptides, CPPs can directly enter cells without significantly damaging the cell membrane \u20133. This The first CPP, namely the Tat peptide, was derived from the transcription activator of human immunodeficiency virus type 1 in the late 1980s . Since tTwo factors , featureAs mentioned above, it is argued that the high predictive performance of existing computational methods seems doubtful \u201321. Firshttp://server.malab.cn/SkipCPP-Pred/Index.html), and is anticipated to become an efficient tool for researchers working with CPPs.In this study, we propose a high-quality dataset for predicting CPPs. The high-quality of the dataset lies in three aspects. First, the dataset shares relatively low sequence similarity, with no more than 80%, avoid the bias in the performance. Second, the new CPP dataset is sufficiently large to build prediction models. Third, the dataset considers the importance of negative samples on predictive performance . The colFigure\u00a0The k-skip-n-gram model, pioneered by Guthrie et al. , integraS as A1A2A3\u2026AL-1AL, where L represents the length of the sequence; and the indices denote the positions of the amino acids in the sequence . Ai\u00a0(1\u2009\u2264\u2009i\u2009\u2264\u2009L) belongs to a set of 20 different amino acids, alphabetically ordered as\u00a0\u03a9\u2009=\u2009{A,\u2009C,\u2009D,\u2009E,\u2009F,\u2009G,\u2009H,\u2009I,\u2009K,\u2009L,\u2009M,\u2009N,\u2009P,\u2009Q,\u2009R,\u2009S,\u2009V,\u2009W,\u2009Y}. An element of \u03a9 is denoted as i\u2032\u2009\u2264\u200920; for example, \u03a91 and \u03a92 denote the first and seconds elements of \u03a9, respectively.For convenience, we denote a given amino acid sequence AiAi\u00a0+\u00a01\u2026Ai\u00a0+\u00a0n-1) in the sequence S. To transform the variable sequence length into fixed length feature vectors, the traditional n-gram features are computed as follows:The traditional n-gram model provides the composition of n contiguous residues  denotes the total number of all elements in the set Tgrams. n possible residue combinations with length n. Tgrams. Accordingly, FVGrams measures the occurrence frequencies of S. The dimension of FVGrams is 20n.where S is short. To address this problem, the k-skip-n-gram model integrates the distance information into the n-gram model. The distance between any two residues Ai and Aj in a given sequence S is given by the interval length between the residues, calculated asClearly, the traditional n-gram model is sparse when the sequence A1 and A2 are contiguous, they are separated by an interval of zero length , and DT\u00a0=\u00a00, A1 and A3 are separated by one residue (A2), so the interval length DT\u00a0=\u00a01. Similarly, DT\u00a0=\u00a02 indicates that A1 and A4 are separated by two residues (A2 and A3).For example, if n residues with distances \u2264k in S. In other words, in addition to the n contiguous residues considered in the traditional n-gram model, this model considers the n residues with distances 1 to k in S. Similar to the n-gram features, the k-skip-n-gram features are calculated asThe k-skip-n-gram model provides the composition of N(TSkipGram) denotes the total number of all elements in the set TSkipGram, and TSkipGram, which is formulated aswhere Skip(DT\u2009=\u2009a)\u2009=\u2009{AiAi\u2009+\u2009a\u2009+\u20091\u2009\u2026\u2009Ai\u2009+\u2009a\u2009+\u2009n\u2009\u2212\u20091|\u00a01\u2009\u2264\u2009i\u2009\u2264\u2009L\u2009\u2212\u2009a\u2009,\u2009\u20021\u2009\u2264\u2009a\u2009\u2264\u2009k}.where n, leading to the overfitting problem, we limit our analysis to n<3 (<203-D). Moreover, when n\u00a0=\u00a01, the k-skip-n-gram model reduces to the traditional n-gram model. Thus, we analyze only the case for n\u00a0=\u00a02. The feature extraction procedure of the k-skip-2-g model is depicted in Fig.\u00a0Because the dimensions of the feature space exponentially expand with  to n<3 <03-D. Mork measures the distance between any two residues. The maximum value of k should be the minimum sequence length in the dataset. However, almost all CPP sequences are short (5\u201330 residues), implying that k should not exceed 5. In other words, the skip features consider only the local distance information with the interval length no more than 5 in all sequences in the dataset, which would not properly reflect the varying distances in the dataset. Therefore, we proposed a modified strategy in which k is the length of each sequence during the skip feature extraction. In this way, the proposed feature representation algorithm becomes parameter free. Additionally, the feature algorithm adapts to the different lengths of sequences in the dataset, and includes more distance information in the features. The k-skip-n-gram features extracted by this new strategy are referred to as adaptive k-skip-n-gram features.By definition of the k-skip-n-gram model, the parameter The RF classifier, introduced by Breiman et al. , has proAccording to machine learning theory, a well-established dataset is essential for building a robust and reliable prediction model. In this study, we carefully constructed an updated high-quality stringent dataset. The construction process of our dataset is described below.A CPP prediction dataset includes positive members  and negative members (non-CPPs). The initial positive dataset was constructed from 1855 experimentally validated CPPs downloaded from the CPPsite2.0 database. Among these are 1564 natural and 291 non-natural CPPs. Natural CPPs are natural amino acid sequences, whereas in non-natural CPPs, some of the amino acids are replaced by artificial characters. As these non-natural CPPs cannot be formulated into fixed length feature vectors, they are excluded from the positive dataset. Redundancy in the dataset is known to bias the predictive performance of a model. Therefore, to improve the quality of the positive dataset, we removed the redundancies using the CD-HIT program , which hTo construct the negative dataset, we randomly generated 2452 amino acid sequences with lengths between 5 and 50 as our initial negative pool. Such random generation of negative samples has been adopted in previous studies , 11. ForUltimately, we successfully constructed a high-quality dataset containing 462 CPPs (positive samples) and 462 non-CPPs (negative samples). For convenience, our dataset is designated as CPP924. To our knowledge, CPP924 has the lowest data redundancy and the highest between-class similarity among the reported datasets. By virtue of the latter quality, our dataset is highly representative of real CPPs.The quality of the predictor was evaluated by evaluation metrics and a validation method.Here, we employed four metrics commonly used in binary predictor evaluations ; sensitiTP, TN, FP and FN represent the numbers of true positives, true negatives, false positives and false negatives, respectively. The first two metrics, SE and SP, measure the ability of the predictor to predict the correct class [where ct class . Specifik-fold cross validation, the jackknife test [The effectiveness of a prediction model must be tested by a validation method. The three statistical validation methods are ife test , and an ife test \u201354. The Step 1. Go to the website  to see the homepage of the webserver. Click on the button About and you will see a brief introduction about how the proposed method SkipCPP-Pred is set up.Step 2. Enter the query protein sequences into the input box. The input sequences should be in the FASTA format. Examples of FASTA-formatted protein sequences can be seen by clicking on the button FASTA format above the input box. In particular, the webserver can receive an un-limited number of query sequences for every single run.Step 3. By clicking on the button Predict, you will get the predicted results on the screen of your computer. Take an actual cell-penetrating peptide, with an identifier of \u201ccpp_P7\u20134\u201d, as an example. After you enter the query sequence into the input box and click on the button Predict, you will see the predicted result showed on the screen: \u201cCell-penetrating\u201d with the prediction confidence of 98.8%.Step 4. Click on the button Clear to delete the query sequences you enter to the input box.Step 5. Click on the button Datasets to download the benchmark datasets used in this paper and the feature sets we proposed based on the datasets.An available webserver is important for researchers to access the proposed method to make predictions. Here, we have built a user-friendly webserver that implements the proposed method SkipCPP-Pred. The webserver is now freely accessible to the public. In this section, we give researchers a step-by-step guideline on how to use the webserver to get the predicted results they desire. The guideline is described as follows,This study proposes adaptive k-skip-2-g features as modifications of the traditional 2-g features. To investigate the impact of the adaptive k-skip-2-g features, we compared their performances with those of the traditional 2-g features. Classifier bias was avoided by employing two high-efficiency classifiers (RF and LibSVM). Table\u00a0We also analyzed the importance of the proposed k-skip-2-g features by calculating the information gain score . This met, which can be any integer higher than 1. Here, we investigated the impact of varying t from 10 to 500 in 10-step increments, and executing the RF classifier on the CPP924 dataset. The jackknife results for the various t values are illustrated in Fig.\u00a0t\u00a0=\u00a0150. Therefore, we set t\u00a0=\u00a0150 in our prediction model. The prediction results of the RF classifier for different values of t are detailed in Additional\u00a0file\u00a0Classifier parameter optimization is a potentially useful means of improving the predictive performance of machine learning methods \u201360. TherTable\u00a0To evaluate the effectiveness of the proposed computational predictor SkipCPP-Pred, we compared its performance with that of CellPPD, the best-performing predictor in the literature . In thisThe prediction results of the proposed SkipCPP-Pred and CellPPD, executed on the proposed high-quality dataset and evaluated by the jackknife test, are presented in Table\u00a0To intuitively compare the proposed method with the CellPPD predictor, we further conducted a graphic analysis by using the Receiver Operating Characteristic (ROC) curves . In the To identify known and potential novel CPPs, we developed a predictor, namely SkipCPP-Pred, by using a sequence-based feature representation approach (adaptive k-skip-n-gram model).To verify the effectiveness of the adaptive k-skip-n-gram model, we compared it with traditional n-gram model and found that the adaptive k-skip-n-gram model shows better performance than the traditional n-gram model. This is because that as compared with the tradition n-gram model, additional distanced correlation information embedded in the adaptive k-skip-n-gram model contributes to the performance improvement for CPP prediction.Moreover, due to the use of only sequential information for modeling, SkipCPP-Pred is capable to predict CPPs fast. We tested SkipCPP-Pred on the stringent CPP924 dataset with the jackknife test. The results indicated that SkipCPP-Pred has the strong capacity of classifying true CPPs from non-CPPs. And, we developed an online webserver that implements the proposed SkipCPP-Pred for researchers to predict CPPs conveniently. It is anticipated to be a useful tool to accelerate the research of CPP prediction. Importantly, the proposed feature representation method used in SkipCPP-Pred has the great potential to guide the sequence-based prediction of other special proteins (i.e. DNA-binding proteins).In this study, we proposed a novel computational method called SkipCPP-Pred, for accurate, fast and stable prediction of potential novel CPPs. Recognizing the importance of the dataset in model building, we also proposed a novel high-quality dataset for SkipCPP-Pred. The quality of this dataset is guaranteed by reducing the sequence redundancy, which alleviates the bias in the performance, and enhancing the similarity between the two classes (positive and negative CPPs). To our knowledge, we present the most stringent of the datasets reported in the literature. Thus, our high-quality dataset might become the benchmark dataset in the development of computational CPP prediction methods. As another contribution, we proposed the adaptive k-skip-n-gram model to CPP prediction. By the feature comparative analysis, the k-skip-n-gram feature model demonstrated greater discriminative power in CPP classification than the traditional n-gram model. Moreover, we compared the overall performance of the proposed SkipCPP-Pred and the state-of-the-art predictors in the literature. The jackknife results showed that the ACC and MCC performance measures on the CPP924 dataset were higher in SkipCPP-Pred than in the state-of-the-art predictors, demonstrating the superiority of SkipCPP-Pred. Accordingly, it is expected that the proposed predictor could become a useful tool in research of CPP prediction. At least, it could complement the existing predictors to improve the accuracy of CPP prediction by neural-like computing models \u201367, evolAdditional file 1: Table S1.a denotes information gain score. Higher IG for a feature means the feature is more discriminative. Table S2. Performance of the Random Forest classifier with different tree numbers on the benchmark dataset CPP924 with the jackknife validation test. Note that the tree number is changed from 10 to 500 with the incremental step of 10. (DOCX 61\u00a0kb)Feature ranking of the proposed adaptive k-skip-2-g features. IG"}
+{"text": "S-type eigenvalue localization set for a tensor is derived by dividing S and its complement. It is proved that this new set is sharper than those presented by Qi (J. Symb. Comput. 40:1302-1324, et al. (Numer. Linear Algebra Appl. 21:39-50, et al. (Linear Algebra Appl. 481:36-53, H-eigenvalue of strong M-tensors are established, and we prove that these bounds are tighter than those obtained by Li et al. (Numer. Linear Algebra Appl. 21:39-50, In this paper, a new  Eigenvalue problems of higher order tensors have become an important topic in the applied mathematics branch of numerical multilinear algebra, and they have a wide range of practical applications, such as best-rank one approximation in data analysis , higher H-eigenvalue of a tensor, consequently, one can identify the positive (semi-)definiteness of the multivariate homogeneous polynomial determined by this tensor; for details, see [One of many practical applications of eigenvalues of tensors is that one can identify the positive (semi-)definiteness for an even-order real symmetric tensor by using the smallest ils, see , 21, 22.H-eigenvalue of tensors when the order and dimension are very large, we always try to give a set including all eigenvalues in the complex. Some sets including all eigenvalues of tensors have been presented by some researchers [H-eigenvalue is positive, consequently, the corresponding tensor is positive definite. Therefore, the main aim of this paper is to study the new eigenvalue inclusion set for tensors called the new S-type eigenvalue inclusion set, which is sharper than some existing ones.However, as mentioned in , 23, 24,earchers \u20133, 21\u201324n, N denotes the set m dimension n, denoted by For a positive integer =1,2,\u2026,m .H-eigenpair, if both \u03bb and x are real [Let cument}A  if \\docu,xnm\u22121)T . Furtherm dimension n is called the unit tensor [A real tensor of order t tensor , denotedm-order n-dimensional tensor Z-tensor, if all of its off-diagonal entries are non-positive, which is equivalent to writing m-order and n-dimensional Z-tensors. A Z-tensor M-tensor if M-tensor if An negative , 14, 26,t}s>\u03c1(B) , 27.M-tensor m indices.The tensor educible . The speent}\u03c1(A)  of the tcument}A . A real mentclass2pt{minimymmetric , 22, 23 Let H-eigenvalue of nonsingular M-tensors. Wang and Wei [H-eigenvalue of nonsingular M-tensors, and they showed those are better than the ones in [S-type eigenvalue inclusion set, the other main results of this paper is to provide sharper bounds for the spectral radius of nonnegative tensors and the minimum H-eigenvalue of nonsingular M-tensors, which improve some existing ones.Recently, much literature has focused on the bounds of the spectral radius of nonnegative tensor in , 24, 28. and Wei  presenteBefore presenting our results, we review the existing results that relate to the eigenvalue inclusion sets for tensors. In 2005, Qi  generaliLetThenwhereis the set of all the eigenvalues ofandet al. [To get sharper eigenvalue inclusion sets than entclass1pt{minimai et al. , 30 and LetThenwhereet al. [S-type eigenvalue localization set by breaking N into disjoint subsets S and S\u0304, where S\u0304 is the complement of S in N.In addition, in order to reduce computations of determining the sets entclass1pt{minimaLetandSbe a nonempty proper subset of\u00a0N. Thenwhereoris defined as in Lemma\u00a0et al. [Based on the results of , in the et al.  exhibiteLetandSbe a nonempty proper subset of\u00a0N. ThenwhereS-type eigenvalue inclusion set for tensors. It is proved to be tighter than the tensor Ger\u0161gorin eigenvalue inclusion set S-type eigenvalue localization set H-eigenvalue of strong M-tensors. Numerical examples are implemented to illustrate this fact.In this paper, we continue this research on the eigenvalue inclusion sets for tensors; inspired by the ideas of , 3, we oS-type eigenvalue inclusion set for tensors is given, and proved to be tighter than the existing ones derived in Lemmas H-eigenvalue of strong M-tensors, which are proved to be sharper than the ones obtained by He and Huang [The remainder of this paper is organized as follows. In Section\u00a0nd Huang . FinallyIn this section, we start with some lemmas on tensors. They will be useful in the following proofs.Ifis irreducible nonnegative, thenis a positive eigenvalue with an entrywise positive eigenvectorx, i.e., corresponding to it.Letbe a nonnegative tensor. ThenSuppose thatThenLetbe a strongM-tensor and denoted bythe minimum value of the real part of all eigenvalues ofThenis an eigenvalue ofwith a nonnegative eigenvector. Moreover, ifis irreducible, thenis a unique eigenvalue with a positive eigenvector.Letbe an irreducible strongM-tensor. ThenA tensoris semi-positive if and only if there existssuch thatAZ-tensor is a nonsingularM-tensor if and only if it is semi-positive.Letassume thatis anM-tensor andThenis anM-tensor, andS-type eigenvalue set for tensors and establish the comparisons between this new set with those in Lemmas In this section, we propose a new LetwithAnd letSbe a nonempty proper subset ofN. Thenwhere\u03bb, i.e., For any i.e., (i) entclass1pt{minima(ii) entclass1pt{minimaS. If S to make Note that S-type eigenvalue inclusion set derived in this paper and those in Lemmas Next, we establish a comparison theorem for the new LetwithThenz satisfies According to Remark\u00a0entclass1pt{minimaBased on the results of Section\u00a0Letbe an irreducible nonnegative tensor withAnd letSbe a nonempty proper subset ofN. ThenwherewithSince i.e., (i) mentclasspt{minimai.e., (ii) Next, we extend the results of Theorem\u00a0Letbe a nonnegative tensor withAnd letSbe a nonempty proper subset ofN. Thenwherewith\u03b5 denotes the tensor with every entry being\u00a01. Then i.e., m and n are finite numbers, then by the properties of the sequence, it is easy to see that Let m\u00a02.3 in , we haveed bound .\u2003\u25a1Now, we compare the upper bound in Theorem\u00a0entclass1pt{minimaWe have showed that our bound is sharper than the existing one in . Now we Let entclass1pt{minimaentclass1pt{minimaH-eigenvalue of strong M-tensors and derive sharper bounds for that. This bounds are proved to be tighter than those in Theorem\u00a02.2 of [In this section, by making use of the results in Section\u00a0m\u00a02.2 of .Letbe an irreducible nonsingularM-tensor withAnd letSbe a nonempty proper subset ofN. ThenwhereandwithM-tensor, by Lemma\u00a0Since i.e., (i) ows from  that \\do(ii) ows from  that \\doWe next prove the bounds in Theorem\u00a0M-tensor: Consider the following irreducible nonsingular m\u00a02.1 of , we havem\u00a04.5 of , we get In the sequel, we extend the results of Theorem\u00a0Letbe a nonsingularM-tensor withAnd letSbe a nonempty proper subset ofN. ThenwhereandwithM-tensor, k is a positive integer, we see that the Z-tensor M-tensor if M-tensors satisfying i.e., \u03bb is an eigenvalue of M-tensor for Since S-type eigenvalue inclusion set for tensors is presented, which is proved to be sharper than the ones in [H-eigenvalue of strong M-tensors, these bounds improve some existing ones obtained by Li et al. [In this paper, a new  ones in , 3. As ai et al.  and He ai et al. . In addiS-type eigenvalue inclusion set and the derived bounds depend on the set S. How to choose S to make S.However, the new"}
+{"text": "The Need for Bayesian Hypothesis Testing in Psychological Scienceby Wagenmakers, E. J., Verhagen, J., Ly, A., Matzke, D., Steingroever, H., Rouder, J. N., et al. (2017). Psychological Science Under Scrutiny: Recent Challenges and Proposed Solutions, eds S. O. Lilienfeld and I. D. Waldman (Chichester: JohnWiley & Sons), 123\u2013138.A commentary on Psychological Science under Scrutiny. Their primary goal was to demonstrate the illogical nature of p-values, while, secondarily, they would also defend the philosophical consistency of the Bayesian alternative. In my opinion, they achieved their secondary goal but failed their primary one, thereby this contribution. I will, thus, comment on their interpretation of the logic underlying p-values without necessarily invalidating their Bayesian arguments.Wagenmakers et al.  argued tp-value itself, the statistic used by frequentists when testing research data.Historical criticisms . Therefore, their first premise proposes that, if H0 is true, the observed p-values cannot occur ; therefore not H0 \u00a0\u00a0\u00a0\u00a0\u00a0(1)If Hmodus tollens is rendered inconsistent when made probabilistic, as follows:Wagenmakers et al.'s If H0\u2014is unlikely. Therefore, the syllogism could be simplified as follows:There are, however, three problems with (2), problems which I would like to comment upon. One problem is stylistic: The first premise states a redundant probability; that is, that a significant result\u2014which already implies an unlikely or improbable event under H0, then p < sig; p < sig; therefore probably not H0 \u00a0\u00a0\u00a0\u00a0\u00a0(3)If Hmodus tollens  now highlights another of the problems: The second premise simply affirms that an unlikely result just happened If HModus tollens is in the form, If P, then Q; not Q; therefore not P. Thus, whenever the consequent (Q) gets denied in the second premise, it leads to denying the antecedent (P) in the conclusion. Such operation ought to prevail with probabilistic premises, as well  may be denied without its probability warranting transposition onto a non-probabilistic antecedent (P). For example, if all red cars (P) have a 95% chance of getting stolen (Q \u2265 0.95) and we learn of a Lamborghini with a lesser probability of so disappearing (not Q \u2265 0.95), it is logical to conclude that the Lamborghini is not red (not P).Correction (4) brings to light the most important problem: P > 0.2), yet he is not submitting his latest article (not Q), it is logical to conclude that he probably expects no publication (not P > 0.2).In comparison, Bayesian logic allows for the antecedent to be probable. For example, if John always submits to Nature (Q) whenever his subjective probability of getting published soars above 20% (modus tollens (1). Said otherwise, while Bayesian statistics allow for the antecedent to be probable (Pp), Fisher's and Neyman-Pearson's tests assume exact antecedents (P); therefore, a probabilistic conclusion does not hold with frequentist tests ] (Perezgonzalez, reductio ad absurdum argument may be informed by, but it is not dependent on, such p-value, the reductio being determined exclusively by the chosen level of significance. For \u201cit is open to the experimenter to be more or less exacting in respect of the smallness of the probability he would require before he would be willing to admit that his observations have demonstrated a positive result. It is obvious that an experiment would be useless of which no possible result would satisfy him\u201d (Fisher, It ought to be noted that the  Fisher, , p.13.modus tollens logically. Wagenmakers et al.'s criticism of the p-value is faulty in that they allow for a probability transposition not warranted either by modus tollens or by the technical apparatus of Fisher's and of Neyman-Pearson's tests. This critique, however, does not extend to their Bayesian argumentation, an approach much needed for testing hypotheses\u2014rather than just testing data\u2014in contemporary science.In conclusion, the technology of frequentist testing holds their The author confirms being the sole contributor of this work and approved it for publication.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Using the existence of solutions for equilibrium equations with a Neumann type boundary condition as developed by Shi and Liao (J. Inequal. Appl. 2015:363,  L on the space T, there exists a unique Borel regular measure \u03bc on T such that T; as an application, Shi and Liao , by Rad}Rn (see ), by Ban}Rn . He. HeL on aps .E be a Banach space and E and X and Y are subsets of E we shall denote by X is denoted by X is the function E. We endowed \u03b4 and the structures T be a non-empty set, let T and let T, endowed with the topology of uniform convergence. We denote by i.e. of the form A and \u03c3-algebra, then M is additive if A, B in M is said to be bounded if E. The semivariation of M is the map A defined byA; M will be called a set-valued measure of finite semivariation. We denote by m be a vector measure from E. We say that m is a bounded additive vector measure if its verifies similar conditions of bounded additive set-valued measures. We denote by m defined by A; L is an additive (resp. positively homogeneous) if for all f defined on T, we set Let ace  oLetbe the setand letbe a continuous linear map. Thenlis associated with an additive, positively homogeneous and continuous set-valued map if and only iffor allj is an isomorphism, more a homeomorphism \\documeLetLbe an additive, positively homogeneous and continuous set-valued map fromtoThen there is a unique bounded additive set-valued measureMfromtosuch thatfor allConversely for all bounded additive set-valued measurethe map: fromtois an additive, positively homogeneous and continuous set-valued map.M. Let l the unique extension of M from The second part follows from the definition of the integral with respect to The following corollary is partly known ."}
+{"text": "The LLOQ for AB-PINACA, AB-PINACA OH, and AB-PINACA pent is 0.10 ng/mL; the LLOQ for mitragynine is 1.0 ng/mL.\u201d The online version is correct.In the report \u201cSynthetic Cannabinoid and Mitragynine Exposure of Law Enforcement Agents During the Raid of an Illegal Laboratory \u2014 Nevada, 2014,\u201d on page 1292, the following footnote should have been included with the Table: \u201c"}
+{"text": "This \u201cnaive\u201d approach is, however, suboptimal in terms of statistical power, as it ignores information about the intra-subject variance. To address this issue, we review several approaches to deal with nested data, with a focus on methods that are easy to implement. With what we call the sufficient-summary-statistic approach, we highlight a computationally efficient technique that can improve statistical power by taking into account within-subject variances, and we provide step-by-step instructions on how to apply this approach to a number of frequently-used measures of effect size. The properties of the reviewed approaches and the potential benefits over a group-level t-test are quantitatively assessed on simulated data and demonstrated on EEG data from a simulated-driving experiment.Hierarchically-organized data arise naturally in many psychology and neuroscience studies. As the standard assumption of independent and identically distributed samples does not hold for such data, two important problems are to accurately estimate group-level effect sizes, and to obtain powerful statistical tests against group-level null hypotheses. A common approach is to summarize subject-level data by a single quantity per subject, which is often the mean or the difference between class means, and treat these as samples in a group-level  In psychology and neuroimaging, for example, multiple data points are often acquired for the same subject throughout the course of an experiment; thus, there exists a subject (lower) and a group (higher) level in the data hierarchy. Two important questions are how to obtain precise estimators for group-level effect sizes from nested data, and how to obtain powerful statistical tests for the presence of group-level effects. The main difficulty associated with such nested data is that the assumption of identically distributed observations is typically violated: while samples acquired from the same subject can be considered to be identically distributed, different distributions must be assumed for different subjects. Therefore, simply pooling the data of all subjects in order to apply a standard statistical test like a A flexible way to model nested data is to combine the data of all subjects in a single linear model, referred to as the nested linear model, hierarchical linear model, multi-level model or linear mixed model  literature, the use of suboptimal inference procedures is currently still widespread, as discussed in Mumford and Nichols  and Pernsufficient summary statistics of separate subject-level analyses. The resulting statistical methods are simple to implement, computationally efficient, and can be easily extended to settings with more than two nesting levels, which are common, e.g., in the analysis of functional magnetic resonance imaging (fMRI) data.Group-level statistical power can be improved by incorporating variances at the lower level in relatively simple ways. The problem of estimating group-level effect sizes and estimating their statistical significance can, moreover, be formulated in a compellingly simple framework, where group-level inference is conducted using the Sufficient summary statistics approaches are popular in the field of meta analysis  in relation to summary-statistic approaches.With this paper, we aim to fill this gap by providing a review of ways to estimate group-level effect sizes and to assess their statistical significance in the context of neuroimaging experiments. We first provide a reference for a number of popular parametric and non-parametric effect size measures (section 2.2), which may be skipped by readers who want to proceed directly to the nested setting. We then discuss the need to choose an appropriate group-level model, as between-subject variability differs depending on whether a \u201crandom effects\u201d or \u201cfixed effect\u201d model is assumed (section 2.3). We also demonstrate why the simple approach of ignoring the group structure by pooling the data of all subject is invalid (section 2.4). We then outline the popular \u201cnaive\u201d summary-statistic approach of computing effect sizes on the subject level and treating these effect sizes as single samples in a group-level test (section 2.5). With what we call the sufficient-summary-statistic approach, we then discuss a family of techniques capable to yield unbiased group-level effect size estimates and powerful statistical tests of group-level null hypotheses, and we highlight a particular approach that yields minimum-variance effect size estimates by weighting each effect with the inverse of its variance. In a tutorial style, we outline the steps that are required to apply this approach to different effect size measures (section 2.6). Lastly, we discuss the advantages and drawbacks of Stouffer's method of combining subject-level Using synthetic data representing a two-sample separation problem, we empirically assess the performance of the reviewed approaches (section 3). The properties of the various approaches and the advantages of the sufficient-summary-statistic approach are further highlighted in an application to EEG data acquired during simulated emergency braking in a driving simulator (section 4). All data are provided in Matlab format along with corresponding analysis codeThe paper ends with a discussion of nested linear models, of multivariate extensions, and a note on non-parametric (bootstrapping and surrogate data) approaches (section 5).effect size \u03b8 is any quantitative measure that reflects the magnitude of some phenomenon of interest . An estimatorunbiased, if its expected value is \u03b8.An statistical test is a procedure to decide, based on observed data, whether a hypothesis about a population is true. In this paper, our goal is to make inference about the presence or absence of an effect in the population. The null hypothesis is that no effect is present. The zero effect is denoted by \u03b80. The null hypothesis of no effect is denoted by H0 : \u03b8 = \u03b80. The alternative hypothesis that an effect is present is denoted by H1. A one-tailed alternative hypothesis assumes that either H1 : \u03b8 > \u03b80 or H1 : \u03b8 < \u03b80, while a two-tailed alternative hypothesis assumes that H1 : \u03b8 \u2260 \u03b80.A test statistic needs to be derived from the observed effect size, where its distribution under the null hypothesis is known or can be reasonably well approximated. The p-value denotes the probability of obtaining a result at least as strong as the observed test statistic under the assumption of the null hypothesis. Denoting the test statistic by T, its cumulative distribution function under the H0 by FT, and its observed value in a given sample by \u03c4, the p-values for a one-tailed alternative hypothesis are given byA Pr(\u00b7) denotes probability. The p-value for a two-tailed alternative hypothesis is given bywhere p-value falls below an alpha-level \u03b1. In the opposite case, no conclusion is drawn. The most commonly used alpha-levels are \u03b1 = 0.05 and \u03b1 = 0.01. If the null hypothesis is rejected, we speak of a statistically significant effect. The value of the test statistic that is required for a significant effect is called critical value. The power of a statistical test is the probability that the test correctly rejects the null hypothesis when the alternative hypothesis is true. Conversely, the false positive rate is the fraction of non-existent effects that are statistically significant.The null hypothesis is rejected if the Before introducing the nested data setting, we review a number of popular effect size measures. For each measure, we also present an analytic expression of its variance, which is a prerequisite for assessing its statistical significance. We will later need the variance for performing statistical inference in the nested setting, too.N independent samples x1, \u2026, xN \u2208 \u211d. The sample mean is denoted by A common measure of effect size is the mean of a sample. Consider a neuroimaging experiment, in which the participant is repeatedly exposed to the same stimulus. A common question to ask is whether this stimulus evokes a brain response that is significantly different from a baseline value. Assume that we observe independent and identically distributed (i.i.d.) samples, which are either normal (Gaussian) distributed or large enough, the null hypothesis Assuming N \u2212 1 degrees of freedom. This is the one-sample t-test.is approximately Student-t-distributed with yi could, for example, represent baseline activity that is measured in each repetition right before the presentation of the experimental stimulus. A natural null hypothesis is that the mean difference is zero, i.e., paired t-test, which replaces x by x \u2212 y in Equations (4), (5).A similar effect size is the mean difference x or y cannot be assumed to be normal distributed, a more appropriate test is the non-parametric Wilcoxon signed-ranked test which tests whether the mean population ranks differ  is a plot that visualizes the performance of such a binary classification system. It is obtained by plotting the true positive rate (TPR) against the false positive rate (FPR) when varying the threshold that divides the predicted condition into In many cases, one may be interested in quantifying the predictive accuracy of a binary classifier to separate experimental condition i et al.  for a coarea under the curve (AUC), and is equivalent to the probability that a classifier will correctly rank a randomly chosen pair of samples , where x is a sample from y is a sample from t-test discussed in section 2.2.2, if the data follow non-Gaussian distributions.A common way to reduce the ROC curve to a single quantity is to calculate the area beneath it Fawcett, . The resAssuming, without loss of generality, that higher values are indicative for class A = 0 and A = 1, while chance-level class separability is attained at A = 0.5. Thus, a common null hypothesis is H0 : A = 0.5.Perfect class separability is denoted by xn) the rank of xn  and VarH0(\u00b7) denote expected value and variance under the null hypothesis .A \u2260 0.5), the variances of U, W, and \u00c2 become data-dependent. The variance for general A can be approximated as  and U and W follow accordingly. A statistical test for the null hypothesis can be devised using thatwhere U and W).is approximately standard normal distributed for large sample sizes . Suppose that for each subject, we have N i.i.d. pairs of observations The H0 : \u03c1 = 0. Assessing the statistical significance of Pearson correlations can be done using the Fisher z-transformation  has a bivariate normal distribution, then If , \u03b21, \u2026, \u03b2K are corresponding regression coefficients, \u03b20 is an intercept parameter, and \u03b7n is zero-mean, uncorrelated noise. In a neuroimaging context, the samples yn could represent a neural feature such as the activity of a particular brain location measured at various times n, while the xn,k could represent multiple factors thought to collectively explain the variability of yn such as the type of experimental stimulus or behavioral variables. In some fields, such a model is called a neural encoding model. It is also conceivable to have the reverse situation, in which the xn,k represent multiple neural features, while the dependent variable yn is of non-neural origin. This situation would be called neural decoding.where the dependent variable xn,k could be either categorial  or continuous. The specific case in which all independent variables are categorial is called analysis of variance (ANOVA). Linear models therefore generalize a relatively broad class of effect size measures including differences between class-conditional means and linear correlations  regression. The resulting estimate is also the maximum-likelihood estimate under the assumption of Gaussian-distributed noise. Using the vector/matrix notations y = X\u03b2 + \u03b7. The OLS estimate is then given byThe most common way to estimate the regression coefficients \u03b2xn,k. The null hypothesis for factor k having no explanatory power is H0 : \u03b2k = 0. The estimated variance of The estimated coefficients where N \u2212 (K + 1) degrees of freedom. A similar procedure can be devised for regularized variants such as Ridge regression . Other quantities related to subject s are also indexed by the subscript s, while the same quantities without subject index denote corresponding group-level statistics.In the following, our goal is to combine the data of several subjects to estimate a population effect and to assess its statistical significance. We denote the number of subjects with Two different models may be formulated for the overall population effect.In the fixed-effect (FE) model, we assume that there is one (fixed) effect size \u03b8 that underlies each subject, that isThe observed effect s denotes the deviation of the subject's observed effect from the true effect \u03b8s = \u03b8. We assume that the noise terms \u03f5s are independent, zero-mean random variables with subject-specific variance where \u03f5H0 : \u03b8 = \u03b81 = \u2026 = \u03b8S = \u03b80, where \u03b80 denotes the zero effect.The null hypothesis tested by a fixed-effect model is that no effect is present in any of the subjects. Thus, In the random-effects (RE) model, the true effect sizes are allowed to vary over subjects. They are assumed to follow a common distribution of effects with mean \u03b8. The observed effect s denotes the deviation of the subject's observed effect from the true subject-specific effect \u03b8s, and where \u03bes denotes the deviation of the true subject-specific effect \u03b8s from the population effect \u03b8. \u03bes and \u03f5s are assumed to be zero-mean, independent quantities. The subject-specific variance of \u03f5s is s is where \u03f5H0 : \u03b8 = \u03b80), while each individual subject-specific effect \u03b8s may still be non-zero.The null hypothesis being tested is that the population effect is zero  relying only on a fixed-effect analysis: We may arrive at spurious results, as the underestimated variance leads to p-values that are too low  studies, this approach is sometimes pursued when computing \u201cgrand-average\u201d (group-level) waveforms of event-related potentials (ERP) that are elicited by the brain in response to a stimulus.p-values.Pooling the samples of all subjects may violate the assumption of identically distributed data underlying many statistical tests. Depending on the type of analysis, this may result in an over- or underestimation of the effect size, an over- or underestimation of the effect variance, and ultimately in over- or underestimated X and Y, are modeled for S = 4 subjects. N = 20 samples were independently drawn for each subject and variable from Gaussian distributions according to s = 1, \u2026, S, n = 1, \u2026, N, where the notation 2. The subject-specific offsets \u03bcs were independently drawn from another Gaussian: X and Y is correctly identified for each subject by Welch's two-sample t-test (p \u2264 0.02). Because of the substantial between-subject variance, this difference is, however, not significant in the pooled data of all subjects (p = 0.29). See Figure The following two examples illustrate the problem. In both cases, two variables, X and Y for each subject . However, the presence of subject-specific offsets \u03bcs causes a strong correlation of X and Y across the pooled data of all subjects , the test statisticwhich is an unbiased estimate of S \u2212 1 degrees of freedom. This is the standard one-sample t-test applied to the individual effect sizes \u03b81, \u2026, \u03b8S.is t-distributed with The naive summary-statistic approach is valid both under the fixed-effect and random-effects models  is valid regardless of the choice of the non-negative weights \u03b1s, s \u2208 {1, \u2026, S} as long as these weights are statistically independent of the corresponding effect size estimates. One popular choice is to assign equal weightsThe S data points on the group-level only. The equal-weighting approach instead uses the subject-level variances. That is, following Equation (35):to all subjects, such that S \u2212 1 degree of freedoms. This translates into a power gain, as illustrated in the simulation presented in section 3. However, estimating the between-subject variance for a random-effects model is not straightforward, and also may introduce biases and variability (see section 2.6.3).If the individual Interestingly, the choice of equal weights is suboptimal in terms of obtaining a group-level effect size estimate s should have a lower impact on the overall estimate than those that are estimated with high confidence. Inserting into Equation (35), we obtain the optimal valueThis result is consistent with the intuition that less precise \u03b8Note, however, that, by using data-dependent weights, the inverse-variance-weighting approach may not always result in unbiased group-level effect size estimates. The potential implications of correlations between individual subject-level effect sizes and their variances are demonstrated in section 3.3 and further discussed in section 5.1.To perform inverse-variance weighting under the random-effects model, the between-subjects variance the between-subject variance nd Laird  is estimwhere p-values may become too small when the number of subjects S is small  are generally over-estimated  or weights that are proportional to the subjects' sample sizes  or specific versions derived for equal and inverse-variance weighting schemes in Equations (38) and (40). Finally, the estimated mean effect is subjected to a z-test as introduced in Equation (36).The sufficient-summary-statistic approach is summarized in Algorithm 1. First, the subject-level effect sizes \u03b8Different effect sizes and their corresponding variances have been discussed in section 2.2. With the exception of the Pearson correlation coefficient, these measures can be directly subjected to the inverse-variance-weighting approach. That is, H0, 1, \u2026, HS0, , Stouffer's method aims to determine whether all individual null hypotheses are jointly to be accepted or rejected, or, in other words, if the global null hypothesis H0 :  is true. In general, the individual Hs0,  may not necessarily refer to the same effect size or even effect size measure, and the p-values for each individual hypothesis may be derived using different test procedures including non-parametric, bootstrap- or permutation-based tests. In the present context of nested data, Stouffer's method can be used to test group-level null hypotheses in the fixed-effect setting, i.e., the absence of an effect in all S subjects of the studied population.A general approach for combining the results of multiple statistical tests is Stouffer's method  and (46) into a group-level one-tailed p-value p1. The group-level two-tailed p-value is then obtained as p2 = 2\u00b7min (see Equations 1\u20133)  The data are generated either within a fixed-effect or a random-effects model. (2) The data are generated from either a Gaussian or a non-Gaussian distribution. In each scenario, we compare the methods' abilities to reject the null hypothesis when we vary the true class-conditional mean difference d.In the following, we present a set of simulations, in which we compare the statistical approaches reviewed above to test for a difference between two class-conditional means in artificial data. We consider two conditions S = 5 or S = 20 subjects s, s \u2208 {1, \u2026, S}, were generated as follows. First, subject-specific class-conditional mean differences ds were sampled according toData for rand = 0, while for the random-effects model, we set \u03c3rand = 0.2.where vs is uniformly distributed between 0.5 and 2, d, was varied across {0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3}.We then sampled H0rejection rate, which is the fraction of the test runs in which the null hypothesis was rejected. When the null hypothesis is true (d = 0), the H0 rejection rate is identical to the error or false positive rate of the statistical tests under study. In the converse case, in which the null hypothesis is false (d\u22600), the rejection rate determines the power of the test. All statistical tests were performed at significance level \u03b1 = 0.05. An ideal test would thus obtain a H0 rejection rate of 0.05 when the null hypothesis is true (d = 0), and a rejection rate of 1 otherwise. The higher the H0 rejection rate in the presence of an effect (d \u2260 0), the higher is the power of a test. However, if the null hypothesis is true, a H0 rejection rate greater than \u03b1 indicates the occurrence of spurious findings beyond the acceptable \u03b1-level.All experiments were repeated 1,000 times with different samples drawn from the same distributions. We report the S = 5 and S = 20 subjects. The \u201cpooling\u201d approach consists of pooling the samples of all subjects and performing one two-sample t-test (cf. section 2.4). \u201cNaive (paired t-test)\u201d refers the naive summary-statistic approach, in which each subject's mean difference is treated as an observation for a group-level paired t-test (cf. section 2.5). Four variants of the sufficient-summary-statistic approach are considered (cf. section 2.6). These variants differ in assuming either random effects (RE) or one fixed effect (FE), and in using either the inverse-variance-weighting scheme (Equation 39) or equal weights (Equation 37). \u201cStouffer\u201d finally refers to using Stouffer's method to combine p-values obtained from subject-level two-sample t-tests (cf. section 2.7). Note that all group-level tests are carried out two-tailed.Figure t-test.In line with our previous considerations, data pooling yielded very low power in the presence of an effect both under the fixed-effect and random-effects models. The highest power is achieved in both cases by the inverse-variance-weighted sufficient-summary-statistic approach, followed by Stouffer's method, the sufficient-summary-statistic approach using equal weights, and the paired Considerable differences are observed between the fixed-effect and random-effects settings. For data following the fixed-effect model, the fixed-effect variants of the sufficient-summary-statistic approach display only a negligible advantage over their random-effects counterparts, indicating that the latter succeed in estimating the between-subject variance to be zero. Moreover, in the case of equal class means, all approaches achieve a false positive rate close to the expected value of \u03b1 = 0.05.S = 5 subjects, the null hypothesis is still rejected too often (9% for inverse-variance weighting). This is due to the variability in the estimate of the between-subject variance S = 20 subjects are available, the expected false positive rate of \u03b1 = 0.05 is achieved.The situation is different for data following a random-effects model. Here, the fixed-effect variants of the sufficient-summary-statistic approach as well as Stouffer's method and the pooling approach display false positive rates that are between two and five times higher (26%) than what would acceptable under the null hypothesis. This problem is substantially alleviated by the random-effect variants of the sufficient-summary-statistic approach. Nevertheless, when data is only available from t-test of subject-wise means) achieves the expected false positive rate of 0.05 regardless of the number of subjects, and therefore represents a valid statistical test also in the random-effects setting.The naive summary-statistic approach (paired S = 20 subjects following either the fixed-effect model (top left panel) or the random-effects model (top right panel). For comparison, the results obtained on Gaussian-distributed data following a random-effects model are displayed in the bottom panel. Four different statistical tests are compared: (1) the random-effects inverse-variance-weighted sufficient-summary-statistic approach for the difference between class-conditional means, (2) the same test for the area under the non-parametric receiver-operating curve (AUC), (3) the naive summary-statistic approach in the form of a paired t-test between subject-wise means, and (4) its non-parametric equivalent, the Wilcoxon signed rank test. Note that for the naive summary-statistic approaches, the mean differences of each subject are treated as observations for a group-level paired t-test or Wilcoxon signed rank test, respectively.Figure The figure shows that, as for Gaussian-distributed data, the inverse-variance-weighted sufficient-summary-statistic approach achieves considerably higher statistical power than the corresponding naive summary-statistic approaches. Furthermore, non-parametric approaches achieve a higher power for non-Gaussian-distributed data than their parametric equivalents assuming Gaussian-distributed data. This difference is particularly pronounced for the better performing inverse-variance-weighted sufficient-summary-statistic approaches. The difference for the naive summary approaches is much smaller, because subject-level averages tend to be more Gaussian according to the central limit theorem. In contrast, parametric approaches have only a very minor advantage over non-parametric ones for Gaussian-distributed data. Note further that, when the Gaussianity assumption of the parametric approaches is violated, spurious results can, in theory, not be ruled out. However, such effects are very small here.H0-rejection rates for a negative correlation, implying that subjects with lower (negative) mean differences exhibit larger variability. In the inverse-variance-weighting approach, the influence of these subjects is down-weighted, which leads to an overestimation of the actual mean difference at the group-level. As a result, the number of false positive detections under the null hypothesis H0 : d = 0 dramatically increases. The right panel of Figure t-test are used.In the presence of dependencies between subject-level effect sizes and corresponding variances, the resulting group-level effect size may become biased if inverse-variance weighting is used. To demonstrate this adverse effect, we simulated data exhibiting a perfect correlation between the difference of the two group means and the standard deviation associated with this difference, represented by the square root of Equation (7). The between-subject variance was thereby kept at the same level as in the preceding random-effects simulations  by taking the subject-level variances into account.The bottom left panel of Figure t-tests and non-parametric AUC tests according to Equations (12) and (15). No substantial difference is found between the two except for a narrow time interval around 200 ms post-stimulus, in which the non-parametric test yields higher z-scores. Overall, this result suggests that the raw samples are approximately normal distributed, justifying the use of the parametric test.Finally, the bottom right panel of Figure t-test on subject-level effect sizes is valid, but has suboptimal statistical power. With the sufficient-summary-statistic approach and Stouffer's method, we discussed two general strategies that combine the simplicity and low complexity of \u201cnaive\u201d approaches with higher statistical power by using prior knowledge about the distributions and variances of the subject-level effect sizes. The benefit of these two strategies over the \u201cnaive\u201d approaches was demonstrated in a set of simulations. Note that the degree of improvement due to using sufficient summary statistics depends on the number of trials per subject vs. the number of subjects. Therefore, differing observations can be found in the literature  can be further combined into a higher-level average with known variance.Importantly, while we here only considered data with two nesting levels, both Stouffer's method and the sufficient-summary-statistic approach naturally extend to hierarchies with arbitrary numbers of levels. For example, t-test. An alternative is to use weights proportional to the subject-level sample sizes  may exhibit more variable activity representing their less constrained mental state. In practice, it is, therefore, advisable to test for monotonous relationships between effect size and variance, for example using Spearman's rank correlation. If no such relationship is found, the inverse-variance-weighted sufficient-summary-statistics approach can be used. In the opposite case, we recommend the use of the sufficient-summary-statistics approach using equal weights, which still improves upon the naive group-level The notions of \u201cfixed\u201d and \u201crandom\u201d effects are used differently in different branches of statistics. See, for example, Gelman  for a diHere we define a fixed effect (FE) to be constant across subjects, while a random effect (RE) is allowed to vary across subjects. The fundamental model underlying RE analysis is given by Equations (28) and (29), while the FE model is defined in Equation (27). These definitions are used in the meta-analysis literature Field, , which cIn parts of the neuroimaging literature, a different interpretation of the fixed-effect model is predominant . These models extend the multiple linear regression model discussed in section 2.2.5 to deal with nested data. Following Hox et al. , this isThe subject-specific coefficients are further expressed ass0,  is a subject-specific intercept, L known subject-resolved independent variables zl, s, k, s, and \u03b5k, s is group-level zero-mean noise. In this complete form, all coefficients are subject-specific. We therefore speak of a random-effects nested linear model. It is also conceivable that only some of the coefficients are subject-specific, while others are shared between subjects. For example, in some applications it may be reasonable to model subject-specific intercepts \u03b2s0, , but identical effects \u03b2k, 1 = \u2026 = \u03b2k, S = \u03b2k for all subjects. A resulting model would be called a mixed-effects nested linear model.where \u03b3Nested linear models are very general and allow for more complex statistical analysis than the procedures for estimating and testing group-level effects discussed here. On the downside, the estimation of nested linear models is difficult because no closed-form solution exists in the likely case that the variances of the subject- and group-level noise terms are unknown  are maintained except for the effect that is measured by \u03b8. As such, surrogate data can provide an empirical distribution for p-values, which can be subjected to Stouffer's method to test for population effects under the fixed-effect model. Originally introduced in the context of identifying nonlinearity in time series  statistical inference is performed jointly for multiple measurement channels, the resulting group-level e et al. , Nicholse et al. , and Pere et al. .Another way to perform inference for multivariate data is to use inherently multivariate effect size measures such as canonical correlations, coefficients of multivariate linear models, the accuracy of a classifier (e.g., Haxby et al., t-test. Because the true single-subject classification accuracies can never be below chance-level, the group-level null hypothesis being tested is the fixed-effect hypothesis of no effect in any subject. Another problem with \u201cinformation-like\u201d measures is that certain confounds are not appropriately controlled for, because confounding effects of different direction do not cancel each other out (Todd et al., A distinction is made in the neuroimaging literature between so-called \u201cactivation-like\u201d and \u201cinformation-like\u201d effect size measures. Allefeld et al.  argue thIn this paper, we have reviewed practical approaches to conduct statistical inference on group-level effects in nested data settings, and have demonstrated their properties on simulated and real neuroimaging data. With the sufficient-summary-statistic approach, we highlighted an approach that combines computational simplicity with favorable statistical properties. We have furthermore provided a practical guideline for using this approach in conjunction with some of the most popular measures of statistical effects.This work includes human EEG data from a previously published study (Haufe et al., Both authors contributed substantially to all aspects of the work including the conception and design of the work, the acquisition, analysis, and interpretation of data for the work, drafting of the work and revising it critically for important intellectual content. Both authors approved the final version to be published and agree to be accountable for the content of the work.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Biological networks consisting of molecular components and interactions are represented by a graph model. There have been some studies based on that model to analyze a relationship between structural characteristics and dynamical behaviors in signaling network. However, little attention has been paid to changes of modularity and robustness in mutant networks.In this paper, we investigated the changes of modularity and robustness by edge-removal mutations in three signaling networks. We first observed that both the modularity and robustness increased on average in the mutant network by the edge-removal mutations. However, the modularity change was negatively correlated with the robustness change. This implies that it is unlikely that both the modularity and the robustness values simultaneously increase by the edge-removal mutations. Another interesting finding is that the modularity change was positively correlated with the degree, the number of feedback loops, and the edge betweenness of the removed edges whereas the robustness change was negatively correlated with them. We note that these results were consistently observed in randomly structure networks. Additionally, we identified two groups of genes which are incident to the highly-modularity-increasing and the highly-robustness-decreasing edges with respect to the edge-removal mutations, respectively, and observed that they are likely to be central by forming a connected component of a considerably large size. The gene-ontology enrichment of each of these gene groups was significantly different from the rest of genes. Finally, we showed that the highly-robustness-decreasing edges can be promising edgetic drug-targets, which validates the usefulness of our analysis.Taken together, the analysis of changes of robustness and modularity against edge-removal mutations can be useful to unravel novel dynamical characteristics underlying in signaling networks.The online version of this article (10.1186/s12918-017-0505-2) contains supplementary material, which is available to authorized users. Robustness and modularity are key properties to understand complex dynamics in large-scale biological networks. The former means the capability of a network to maintain functioning against external and internal perturbations , and theIn this work, we tried to investigate the changes of the modularity and the robustness by edge-removal mutations in signaling networks. Through intensive simulations using a Boolean network model , 24, we G where V and A denote a set of nodes and a set of directed edges, respectively, we consider a partition P\u2009=\u2009{V1,\u2009\u2002V2,\u2009\u2026,\u2009\u2002VM} of V\u2009=\u2009maxP\u00a0M(P). Since it is difficult to optimize the partition, we computed the averaged modularity value of 30 trials of partitions optimized by an existing algorithm [In this study, we examined the modularity by using the method in a previous study  and it hlgorithm .G, V and A denote a set of Boolean variables and a set of ordered pairs of the Boolean variables called directed edges, respectively. A state of each vi\u2009\u2208\u2009V is 1 or 0 which represents on or off state of the gene, respectively. Then a state of a network G is defined as a vector of the states of all nodes. A directed edge \u2009\u2208\u2009A has a positive (activating) or negative (inhibiting) relationship from vj to\u00a0vi. Here, we used a nested canalyzing function (NCF) model [Ims and Oms between 0 and 1 uniformly at random.In this study, we employed a Boolean network model introduced in previous studies , 30 to iF) model  (see AddF) model  can be gF) model , and canF) model , 33. In G a Boolean network with a list of update-rules F\u2009=\u2009{f1,\u2009f2,\u2009\u2026,\u2009fN}. Every initial state converges to an attractor which can describe diverse network dynamics such as multi-stability, homeostasis, and oscillation [\u03b1 the attractor which the initial state s converged. The network is considered as robust against a perturbation at vi if the attractor is conserved and we herein considered an update-rule mutation which describes a scenario that F is changed to Im and Om are changed into 1\u2009\u2212\u2009Im and 1\u2009\u2212\u2009Om, respectively). This update-rule mutation may represent a deleterious change in the function of a protein or gene [\u03b3(G) is defined as follows:Let illation , 35. Let or gene , and hav or gene . Then thS is a set of initial states (i.e. S\u2009=\u20092N), and I(\u2219) is a function which outputs 1 or 0 if the condition is met or not, respectively. Because \u2223S\u2223 is a very large number, we used a sample subset S to calculate\u00a0\u03b3(G).where m1\u00a0and\u00a0r1 be the modularity and the robustness of the wild-type network, respectively. Given a removal rate parameter n (%), the mutant network is constructed by simultaneously removing approximately n\u00a0percent of a total number of edges from the wild-type network. Then let m2 and r2 be the modularity and the robustness of the mutant network. We defined the changes of the modularity and the robustness by the edge-removal mutations as (m2\u2009\u2212\u2009m1) and (r2\u2009\u2212\u2009r1), respectively. An illustrative example of the notion about the changes of modularity and robustness by edge-removal mutations is shown in Fig.\u00a0This study focuses on how the modularity and the robustness of a network are changed by edge-removal mutations. Let www.cellcollective.org) [To investigate real signaling networks, we used three datasets of signaling networks: a T-LGL survival network (T-LGL)  consistiive.org) .We need to extensively simulate randomly structure networks to verify that the new findings in real networks are generally conserved. In this study, we employed a shuffling model to generate random networks , 18. GivDEG) means the sum of the degrees of both end nodes of the edge.Degree of a node means the number of links incident to the node in a graph. On the other hand, the degree of an interaction (v0\u2009\u2192\u2009v1\u2009\u2192\u2009v2\u2009\u2192\u2009\u2026\u2009\u2192\u2009vL\u2009\u2212\u20091\u2009\u2192\u2009vL is an FBL of length L\u00a0(\u22651) if there exist links from vi\u2009\u2212\u20091 to vi\u00a0 with v0\u2009=\u2009vL and vj\u2009\u2260\u2009vk for j, k\u2009\u2208\u2009{0,\u20091,\u2009\u2026,\u2009L\u2009\u2212\u20091} and j\u2009\u2260\u2009k. The number of FBLs of a link e denoted by NuFBL(e) means the number of different FBLs involving e.An FBL is a circular chain where nodes are not revisited except the starting and the ending nodes . It playEBEW) is defined as the number of shortest paths between pairs of nodes that run along an edge [Edge Betweenness , and the results are shown in Fig.\u00a0In addition, the increase of the robustness was positively related to the removal rate. To examine the relationship between the changes of modularity and robustness values, we scattered them in the cases that the removal rate is 1% Fig.  and 2% . Intrigup-values\u2009<\u20090.001). That is to say, removing edges with a higher degree, EBEW, or NuFBL is more likely to increase the network modularity. These results can be relevant to previous results. For example, the edges with high betweenness values are most likely to lie between subgraphs [P-values\u2009<\u20090.0001 using t-test). In other words, the degree, the edge-betweenness and the number of FBLs were positively correlated with the change of the modularity whereas they were negatively correlated in the random networks. It means that those structural characteristics might be a vital factor in controlling both the changes of the modularity and the robustness.We showed that the changes of the modularity and the robustness are correlated when a network is subject to edge-removal mutations. To reveal structural characteristics to affect the changes of the modularity and the robustness, we investigated the correlations of each of the changes of the modularity and the robustness with each of three edge-based structural properties, DEG, NuFBL and EBEW (see Methods for the definitions) in T-LGL signaling network  order of the change of the modularity (resp. the robustness). Considering the distributions of the change of the modularity (resp. robustness), K was chosen to 20, 20, and 18  for T-LGL, STF, and HIV-1 networks, respectively. Then High-MI (resp. High-RD) denotes the union of the edges each of which was included in the modularity-increasing (resp. robustness-decreasing) top-K edges. Accordingly, we identified High-MI (High-RD) groups consisting of 22, 79, and 42 edges  in T-LGL, STF, and HIV-1 networks, respectively. Furthermore, we defined High-MI-incident (High-RD-incident) group which is a set of genes incident to an edge in the High-MI (resp. High-RD) edge group, and found the number of genes in the High-MI-incident (resp. High-RD-incident) were 29, 81, and 59  in T-LGL, STF, and HIV-1 networks, respectively. The topological distributions of High-MI and High-RD edge sets in T-LGL, STF, and HIV-1 networks are shown in Fig.\u00a0In the previous subsection, it was shown that the change of the modularity is positively correlated with the degree, the edge betweenness, and the number of involved FBLs with respect to the removed edges whereas the change of robustness is negatively correlated with them. From these results, we hypothesized that the edges whose removal will increase the modularity or decrease the robustness tend to be centrally located in signaling networks. To validate this hypothesis, we first specified \u201cHighly-modularity-increasing\u201d (High-MI) and \u201cHighly-robustness-decreasing\u201d (High-RD) sets of edges as follows: We examined the changes of the modularity and the robustness over 5000 trials of edge-removal mutations with 1% removal rate, and collected top-We conducted Gene Ontotlogy (GO) enrichment analysis  using ClueGO tool  to invesK edge sets ranked by a decreasing order of the robustness change among 5000 trials of edge-removal mutations with 1% removal rate. We found that (JAK\u2009\u2192\u2009STAT3), (IP3R1\u2009\u2192\u2009Ca), and (gp41\u2009\u2192\u2009CD28) showed the highest frequency in the T-LGL, STF, and HIV-1 networks, respectively. We hypothesized that these edges can be candidates of edgetic drug-targets, because they most frequently caused the highest decreasing robustness through removal mutations. To validate this, we surveyed some recent experimental studies. Regarding (JAK\u2009\u2192\u2009STAT3) interaction of T-LGL network  interaction of STF network  was found to be the highest frequency interaction . It is included in PI3K/Akt/mTOR pathway [JAK\u2009\u2192\u2009STAT3), (IP3R1\u2009\u2192\u2009Ca), and (PI3K\u2009\u2192\u2009PIP3) in T-LGL, STF, HIV-1, respectively . Considering that the number of involved FBLs was shown to be associated with the functional importance of a node or an interaction, it implies that the found interactions can be promising drug-targets.We performed a case study to show an application for edge-based drug discovery. For every interaction in High-RD group, we examined the inclusion frequency of the interaction in top-ork Fig.\u00a0, it was l cancer . Next, t pathway , which i pathway . AnotherThere have been many computational studies about the network robustness and modularity, whereas there are few studies on investigating the modularity change and the robustness change. Through extensive simulations, we found that both the modularity and the robustness increased on average in mutant networks by edge-removal mutations in this study. However, it was interesting that the changes of the modularity and the robustness were negatively correlated. Another interesting finding is that the changes of the modularity and the robustness are positively and negatively, respectively, correlated with each of the degree, the number of FBLs, and the edge betweenness of removed edges. These results were consistently observed in randomly structure networks. Additionally, we identified two sets of genes which are incident to the highly-modularity-increasing and the highly-robustness-decreasing edges, respectively, and observed that they are likely to be central by forming a large connected component. These two gene sets were enriched with different GO terms and the investigation on the reason why such GO terms are related to modularity and robustness will be a future study. Finally, we found that the highly-robustness-decreasing edge can be considered for promising edge-based drug-targets. Taken together, our results in this study can be useful to unravel novel dynamical characteristics of signaling networks."}
+{"text": "Research suggests that Black youth are less likely to use e-cigarettes than their white counterparts, yet little is known as to why. We examined perceptions of e-cigarettes among Black young adults (ages 18\u201325) to explore the meanings these youth ascribe to e-cigarettes and the role that identity plays in how these devices are viewed. Analysis of in-depth interviews with 36 Black smokers and non-smokers in the San Francisco Bay Area suggests that Black youth perceive e-cigarettes as serving distinct, yet overlapping roles: a utilitarian function, in that they are recognized as legitimate smoking cessation tools, and a social function, insofar as they serve to mark social identity, specifically a social identity from which our participants disassociated. Participants described e-cigarette users in highly racialized and classed terms and generally expressed disinterest in using e-cigarettes, due in part perhaps to the fact that use of these devices would signal alignment with a middle class, hipster identity. This analysis is discussed within a highly charged political and public health debate about the benefits and harms associated with e-cigarette use. Use of electronic nicotine delivery systems (ENDS), e.g., e-cigarettes, is increasing among youth in the United States . While tThough e-cigarettes appear to be increasing in popularity among youth and young adults generally, e-cigarette initiation and use nevertheless varies across youth groups. Similar to patterns of conventional cigarette use , Black aSimilar trends are present among young adults. McMillen and colleagues 2015) conducted nationally representative surveys each year between 2010 and 2013. Among young adults aged 18 to 24, current e-cigarette use increased in prevalence from 0% to 14% during this time 5 conduct. AnalysiFrom a public health perspective, lower e-cigarette uptake among Black youth may be regarded positively or negatively . Though To understand how Black youth perceive e-cigarettes, we draw on social science theories regarding social and cultural identity and the use of commodities to communicate those identities . Nearly Cultural attitudes towards products are shaped by the degree to which products are associated with utilitarian functions , as well as social identity functions  . In thisnon-helmet-wearing, superseded the unequivocally positive utilitarian function [Individuals may also choose not to use a product, or actively avoid certain objects or behaviors in order to disassociate with social groups . In thisfunction . Thus, dBetween April 2014 and July 2015, we conducted multiple method in-depth interviews with 46 Black (ages 18\u201325) smokers and non-smokers in the San Francisco Bay Area for a study designed to understand perceptions of tobacco control policies and the intersections of tobacco-related stigma with other social identity stigmas . Of the 46 participants in the study, 36 participants discussed these devices in their interviews, and 15 had used e-cigarettes at some point in the past.Participants were recruited on the street, through Facebook and Craigslist advertising, and by referrals. The interview guide was informed by (1) existing qualitative research on smoking among youth as well as by (2) exploratory focus groups we conducted with Black youth prior to data collection in an effort to identify potentially salient issues . E-cigarFollowing the interviews, the interviewer completed field notes to record preliminary analytical ideas emergent from interviews and to contextualize interviews with descriptive information not captured in audio recordings. Interviews were digitally recorded and professionally transcribed. Two research staff coded transcripts to distill data into manageable analytical segments, using ATLAS.ti , a qualitative data management system. During the coding process, researchers wrote memos to capture their analytical thinking about the data. Memos serve to contextualize coded narrative data with researchers\u2019 emergent interpretations that are based on the entire context of the interview. The code list was extensive to capture main study objectives, but for the purposes of the present analysis, only one relevant code was included  which indexed any narrative in interviews that either referenced e-cigarettes directly or was relevant to understanding perceptions of e-cigarettes. After the coding process, the lead author conducted a second more directed yet exploratory pattern-level analysis of all narrative segments coded as ENDS and all related memos. Patterns of emergent themes were identified primarily by examining the frequency and omission of topics across interviews . FrequenAnalysis of the patterns of participants\u2019 narratives illustrated that Black youth in this study perceive e-cigarettes as serving distinct, yet overlapping roles: a utilitarian function, in that they are recognized as legitimate smoking cessation tools, and a social function, insofar as they serve to mark social identity, specifically a social identity from which our participants disassociated. The majority of participants in this study were of low socio-economic status, with a household income of less than $35,000 USD, technically classified as living in poverty in the San Francisco Bay Area. Twenty-four young women and 22 young men comprised the sample. Twenty-five participants were current tobacco or nicotine users defined by past 30-day use. Among the 15 ever e-cigarette users, 12 had used e-cigarettes in the previous year, and among these, all reported smoking cigarettes in the previous 30 days. Among the 36 respondents whose interviews included discussion of e-cigarettes, 21 were current smokers  and 15 were non-smokers .\u201cA higher-income person, (someone) who goes to the doctor and feels guilty about smoking cigarettes and tobacco, and is into technology and (chuckles) maybe rides a bike.\u201dOverall, participants in our study described the stereotypical e-cigarette user as someone racially, socio-economically, and/or socially different from themselves. Participants emphasized that e-cigarettes \u201cweren\u2019t for them,\u201d ascribing social meanings to e-cigarette users from which participants in our study sought to disassociate. For example, \u201cZ\u201d, a 24-year-old non-smoking man, who has not used e-cigarettes, identified a \u201ctypical\u201d e-cigarette user as:\u201cI feel like a lot of hipsters use e-cigarettes. A hipster is someone who tries to fit in with a certain image because it looks cool. E-cigs are very trendy so they\u2019re like \u2018Ooh I look so cool with my e-cig.\u2019\u201dThe perception of a typical e-cigarette user as someone who is affluent was common among our participants, as was the concept of e-cigarettes being popular among \u201chipsters\u201d and \u201ctechies\u201d as is alluded to in the quote above and reinforced in other participants\u2019 narratives. For example, \u201cJazzy\u201d, an 18-year-old non-smoking woman, who does not use e-cigarettes, succinctly positioned e-cigarettes as a marker of social identity when describing them as products for people who are trying to look cool or trendy:\u201c\u2026non-Black people\u2026 So similarly with the cigarette smoking, actually having a cigarette, that is mostly White people. Then secondary, non-Black people, non-White people. But with the e-cigarettes, I suppose it would just be non-Blacks. I\u2019ve seen Asians smoking as well.\u201dAlthough hipster culture is notoriously difficult to define ,30, it i\u201cJane Doe\u201d, a 24-year-old woman who smokes, also stated that e-cigarettes are not something that she sees in the Black community:\u201cI sure don\u2019t see Black people smoking them\u2026 I see Black people smoking real cigarettes. I never see Black people with e-cigarettes or vapors\u2026\u201d She considered trying e-cigarettes but did not.\u201cWho do I see smoking e-cigarettes? Upper class individuals. I haven\u2019t seen a person of color smoking those e-cigarettes \u2018cause they\u2019re kind of expensive.\u2019\u201dMeanwhile \u201cDee\u201d, a 24-year-old woman who smokes, but does not use e-cigarettes, highlighted socioeconomic factors that may contribute to the association of e-cigarettes with the \u201ccommodification and consumption (that) is intrinsically connected to being a hipster\u201d .\u201cWho doShe went on to state that: \u201cUsually I see affluent people smoking those\u2026 I don\u2019t think they sell those in marginalized communities\u2026\u201d\u201cLet\u2019s just be straightforward. Particularly, I\u2019ve seen them in the hands of European Americans, white folks\u2026 I worked this tech show last week in San Francisco and I saw people with it.\u201d\u201cKeeno\u201d, a non-smoking, non-e-cigarette-using man aged 24, reinforces the notion that e-cigarettes signal membership in an external group (\u201ctech show\u201d participants) typically associated with a hipster style of consumption. Noting increasing e-cigarette use in Oakland and San Francisco, Keeno observes:\u201cI see a lot more business people with vape pens nowadays taking a\u2026 break outside instead of cigarettes. So that\u2019s a good thing, in my opinion\u2026 Maybe young black kids will prefer those over\u2026 cigarettes at some point in time.\u201dFrom a public health perspective, the disassociation of e-cigarettes among Black youth who smoke may be problematic due to the potential health benefits of switching from conventional smoking to e-cigarettes. One participant, \u201cLee\u201d, a non-smoking man aged 21, commented that he hoped e-cigarettes would become more than just a subcultural phenomenon, raising the possibility of harm reduction through e-cigarette use for Black youth who smoke. Lee had tried e-cigarettes in the past, but did not like them, and only occasionally \u201ctakes a few puffs\u201d from friends\u2019 devices.Lee\u2019s comment points to how e-cigarettes can be positively perceived for their utilitarian functions but still rejected when they are socially positioned as cultural commodities that signal membership in a group from which a particular youth group may be disassociated. In addition to the social identity signaling of e-cigarette use, analysis of the narrative data suggests that e-cigarettes were perceived to serve important utilitarian functions for some people\u2014i.e., for smoking reduction or cessation or for minimizing cravings when smoking is prohibited. According to \u201cLee\u201d, above, e-cigarettes are targeted \u201ctowards an older audience, you know, people that are trying to quit smoking or that are looking for an alternative for whatever reason\u201d. \u201cBlack Tar Rebellion\u201d, for example, a 21-year-old non-smoking woman, summarizes the typical e-cigarette user as: \u201cSomebody who wants to quit or somebody who doesn\u2019t want to smell like cigarettes.\u201d Black Tar Rebellion, who has never smoked, briefly used a nicotine-free vape pen as a way to look rebellious, but gave it up after experiencing negative health effects. \u201cSome people who actually had a habit of smoking cigarettes, who are trying to be better, they use them. I respect them way more.\u201dParticipants generally regarded people who used e-cigarettes for their utilitarian function as opposed to their social identity function more positively, and their perceptions of the typical utilitarian user did not tend to carry connotations of race and class. \u201cJazzy\u201d, for example, who mocked the typical e-cigarette user as a hipster who just wants to look \u201ccool\u201d, acknowledged a utilitarian role of e-cigarettes and stated that she has more respect for people who use e-cigarettes to quit smoking, as opposed to adopting a new trend:\u201cPeople who smoke e-cigarettes are trying to get off cigarettes and they just can\u2019t go cold-turkey, so that\u2019s like their in-between\u2026 But it\u2019s very ineffective on that in-between to get you off of it.\u201dThough participants in this study tended to disassociate from vapers and vaping, 15 participants nevertheless had experimented with e-cigarettes. In general, their initial motivation for trying the devices stemmed from health concerns about smoking, and they had heard that e-cigarettes might help to facilitate cessation. Notably, however, there was skepticism about the effectiveness of e-cigarettes as cessation tools, and not just among the participants who had tried the devices. For example, \u201cKaroline\u201d, a non-smoking woman aged 19, believed that e-cigarettes were primarily for individuals who cannot quit smoking, though she questioned the extent to which they work.\u201cHe had an e-cig, \u2018cause my mom bought it for him I think\u2018 cause she wanted to help him. She was happy that he was trying to be better, so in order to help him on his journey, she got him some e-cigs. He would charge it. Everything was cool. He stopped using cigarettes. Now he\u2019s just using his e-cig. Then after that, the next step would have been, \u2018Okay, now you\u2019re not even using an e-cig and you\u2019re good. You\u2019re fine. You don\u2019t even need it.\u2019\u2026 He ended up relapsing.\u201dSimilarly, \u201cJazzy\u201d described an acquaintance who used e-cigarettes to quit smoking, but who was ultimately unsuccessful.\u201cIt\u2019s just weird that they say it\u2019s not smoke, but then I learned that they about have the same, like, bad stuff as cigarettes. I thought it was healthier. That\u2019s why I was doing it. But there\u2019s no difference.\u201dIn addition to skepticism about the effectiveness of e-cigarettes for smoking cessation, participants in this study who smoked were generally not interested in switching to e-cigarettes due to questions about their safety. For example, \u201cMarley\u201d, a 22-year-old smoker who had tried e-cigarettes to quit smoking, believes that e-cigarettes are just as harmful as cigarettes.Similarly, \u201cJade,\u201d a 22-year-old smoker, questioned the point of switching from cigarettes to e-cigarettes: \u201cThis makes me wanna know a lot more about e-cigarettes, like what\u2019s in them, why it\u2019s okay to switch to e-cigarettes and it\u2019s okay to maintain that habit, but not regular tobacco cigarettes. So I wanna know what the differences are, but then also, why is the solution to stopping one habit starting another\u2026\u201d\u201cI smoke like two cigarettes a day. But I\u2019ll try the vape pen most of the time. Like today, I forgot my vape pen, so I\u2019m like, damn it, I\u2019m gonna have to go get a cigarette. I try to do as much of the vape pen as I can.\u201dNotably, however, among the few participants who reported regular use of e-cigarettes was \u201cNefarious,\u201d a 21-year-old woman who was using e-cigarettes to cut down on smoking and to minimize what she perceives to be negative consequences of smoking.\u201cThe smell (of cigarettes). That\u2019s why I got the vape pen\u2026 I don\u2019t smell like anything. It\u2019s all sweet and fruity. I still smoke like two cigarettes, but I\u2019ve been working since I was homeless to not smell like cigarettes. I was smelling like straight up cigarettes and God knows what else when I was homeless. I did not like that. My friends didn\u2019t like it.\u201dShe goes on to say that she originally purchased a vaping device because of:Here Nefarious\u2019 use of e-cigarettes in combination with cigarettes can be described as \u201cdual use,\u201d about which researchers in public health have expressed great concern due to the potential of dual use to exacerbate nicotine addiction and reinforce smoking ,32,33. HFew participants had adopted positions similar to Nefarious, however. Instead, participants in this study generally expressed safety concerns and/or skepticism about the effectiveness of e-cigarettes for cessation and few participants were using the devices. Research by Camenga and colleagues, who conducted focus groups with middle school, high school, and college students, also found that adolescents and young adults were skeptical about the efficacy of e-cigarettes in successful smoking cessation. Nevertheless, their participants generally perceived e-cigarettes to be less harmful than cigarettes . ConversFindings should be considered in light of the following limitations. Importantly, this exploratory analysis is based on the narratives of 36 Black women and men who were selected purposively for a study on perceptions of tobacco control strategies and experiences with multiple stigmas. Narrative surrounding e-cigarettes emerged occasionally throughout interviews, and after conducting 10 interviews for the study, we integrated a few open-ended questions about perceptions of e-cigarettes. As such, this study was not designed around understanding perceptions of e-cigarettes among Black youth, and, therefore, findings should be considered in light of this important limitation. Additionally, the study is limited in scope by the relatively small, non-random sample. Although this study is not necessarily a representative sample of Black youth in the San Francisco Bay Area, we did attempt to recruit a diverse range of participants  by using a multi-tiered recruitment strategy to reach participants from a variety of social contexts and networks. Notably, qualitative research does not aim for traditional conceptualizations of generalizability or representativeness. Instead, it aims to maximize the variation of perspectives among participants to develop theory that can be tested in future large-scale studies. A final limitation to note here is that the theoretical ideas discussed in this paper are based on our research team\u2019s interpretation of participants\u2019 narratives, and multiple interpretations of these narratives are possible. However, we integrate standard procedures into our study designs in an effort to reduce threats to the valid interpretation of data and enhance reliability to justify analytical generalizability, i.e., the likelihood that the theoretical contribution from our study is applicable to another situation. As Douglas and Isherwood wrote, \u201cGoods that minister to physical needs\u2026 are no less carriers of meaning than ballet or poetry\u201d  (p. 49).In particular, study participants offered clear individuating descriptions of a typical e-cigarette user, such as \u201chipster\u201d and \u201crides a bike\u201d. There is evidence of a hipster association with e-cigarettes in the literature. Tobacco companies have actively courted hipsters , and thenon-use of e-cigarettes also communicates meaning about social identities. It may be that our participants express disinterest in e-cigarettes for several reasons, but arguably an underlying context of this disassociation is related to social identity. We theorize that the rejection of e-cigarettes among our study participants who smoke is, in part, a function of dissociative signaling from a white, middle class, hipster social identity. Using e-cigarettes, even for their utilitarian function, would nevertheless signal membership in a racial, social, and socioeconomic status group that does not represent the identities of participants.Inasmuch as the use of e-cigarettes signals group membership, Research in consumer psychology has explored why consumers will refuse to use or cease to use a product when it is associated with an unfavorable group ,39. For In our study, participants clearly viewed e-cigarettes as a tool that could aid in smoking cessation. However, study participants who smoked, some of whom indicated an interest in quitting or reducing their smoking, nevertheless expressed disinterest in e-cigarettes due to their association with other youth cultural groups. As \u201cLee\u201d points out above, e-cigarettes may be inaccessible to some Black youth, which may harm them in the long run. This situation is problematic from a range of harm reductionist viewpoints, which may incorporate claims that continue to be a source of controversy among public health advocates , as Whether or not e-cigarettes are a viable long-term strategy for tobacco-related harm reduction has yet to be determined . Some puThough we are more cautious in our interpretation, we do acknowledge that studies among adults suggest that e-cigarettes can be an effective smoking cessation tool, and the majority of adult users are current or former smokers ,49. Stud"}
+{"text": "S-transform and chaotic analysis is proposed. There are BAFS , local spectral characteristics MSCC , and chaotic features (12). Finally, radar chart and F-score are proposed to optimize the features by the hierarchical visual fusion. The feature set could be optimized from 526 to 96 dimensions based on NKI-CCRT corpus and 104 dimensions based on SVD corpus. The experimental results denote that new features by support vector machine (SVM) have the best performance, with a recognition rate of 84.4% on NKI-CCRT corpus and 78.7% on SVD corpus. The proposed method is thus approved to be effective and reliable for pathological speech intelligibility evaluation.Pathological speech usually refers to speech distortion resulting from illness or other biological insults. The assessment of pathological speech plays an important role in assisting the experts, while automatic evaluation of speech intelligibility is difficult because it is usually nonstationary and mutational. In this paper, we carry out an independent innovation of feature extraction and reduction, and we describe a multigranularity combined feature scheme which is optimized by the hierarchical visual method. A novel method of generating feature set based on  S-transform in 1996, which can be regarded as the combination of wavelet transform and short time Fourier transform  can be expressed as x[n] = x(n\u0394T), n = 0,1, 2,\u2026, N \u2212 1. The x[n]\u2009\u2009S-transform can learn from discrete Fourier transform calculation. The x[n] Fourier transform isk = 0,1 \u2026, N \u2212 1.Let S-transform x[n] is computed by FFT:h, m = 0,1, 2,\u2026, N \u2212 1.The discrete x[n] of continuous signal x(t) is converted into the N\u2217N complex time-frequency matrix by S-transform from x[n] in FrameLen.Framing: framing (2)S-Transform: transform matrix S is got by S-transform (ransform .(3)Energy spectrum: energy spectra are obtained based on step (2).(4)Bandpass filter: the 26 filter banks are constructed.Log energy is calculated for each time in each filter bank:S is spectrum by S-transform in h\u0394T, x\u2032 is the m filter output in h\u0394T, and Hm(k) is the frequency response of triangle filters.where (5)L MSCC coefficients is got:Discrete cosine transform (DCT): discrete time mapping cepstrum domain in the MSCC extraction process is as follows; The chaotic-based features are presented in the previous sections, and anomalies in pathological voices stem from malfunctions of some parts of the voice production system. Speech signal has fractal characteristics; chaotic phenomena can occur during speech production when the vocal organ is within a lesion. Traditional acoustic parameters are very effective to analyze cycle speech signal, which have certain limitations on analyzing noncycle and chaotic signals. Chaotic features provide useful information on distinguishing normal and pathological voices. Therefore, three nonlinear chaotic features (CF) can be extracted, which are the largest Lyapunov exponent to measure the speech signal chaotic degree, approximate entropy to measure speech signal complexity, and Lempel-Ziv complexity which is another complexity index , 17, wheIn this article, the largest Lyapunov exponent extraction process as an example is introduced. In order to guarantee the largest Lyapunov exponent reliability, the classic small data set algorithm is used; we get 4 statistics , and the 526-dimensional feature set was composed of 4 statistics and the other 522 features.x(t) = {x1, x2, x3,\u2026, xN} is a one-dimensional time series, where N is the total number of time series; phase space is reconstructed as follows:m is embedding dimension, \u03c4 is delay, M is the total number of phase points, and M = N \u2212 (m \u2212 1)\u2217\u03c4.Pathological speech signal (1)p: the spectrum is obtained by the Fourier transform. The corresponding frequency is got in the maximum amplitude. This averaging period is the reciprocal of the frequency.Calculated time series averaging period (2)X(i), the nearest neighbor X(j) is found in the case of restrictions brief separation:In the phase space p is the average period of time series.where \u2016\u00b7\u2016 represents two-norm value and (3)dj(i) is the distance between X(j) and i discrete time:For each reference point, (4)\u03bb1 is got by the reference point Xj and the nearest neighbor The Lyapunov exponents represent the initial closed orbit exponential divergence of phase space; it is assumed that the exponential divergence Both sides of the equation were taken as the logarithm:i ~ ln\u2061dj(i) meet the linear relation of the slope \u03bb1\u0394t; thus,As can be seen above, q is the number of nonzero dj(i) and \u0394t is sample sampling period.where (5)\u03bb1 is the slope of this line:Linear regression is done using the least square, and the largest Lyapunov exponent The specific calculation steps of the small data set method are as follows:The 526-dimensional feature set is constructed by the above three features' extraction, which are BAFS (430), MSCC (84), and CF (12).F-score method to sort the features.A set of high-dimensional data is obtained after pathological speech signal feature extraction. Visual techniques and multi-information fusion idea are a high-dimensional data reduction approach; at the same time, they depict the internal structural relationship of features, which is beneficial to data classification. Radar chart has good interaction, which is able to reflect the trend of changes in a feature set and every dimensional situation. In order to express the structural characteristics among attributes, radar chart information visualization graphical feature is extracted. According to radar chart uniqueness theorem, radar chart must be unique if the input feature is restricted to a specified alignment. Therefore, the extraction of graph feature is closely related to the feature order; we introduce F-score is a measure to distinguish the two types of samples [xk \u2208 Rm,\u2009\u2009k = 1,2,\u2026, n, l\u2009\u2009(l \u2265 2), is the number of the sample category and nj is the sample number in the j class, j = 1,2,\u2026, l. The F-score of i is defined in the training samplesi feature of the whole training set, i feature of the j class, and xk,ij is the i feature of the first k sample data in j class. samples , given tRadar graphic information is called graphical feature , 18. GraM-dimensional radar chart is constructed by sample data r1, r2,\u2026, ri,\u2026, rM, M polygon  is composed of arbitrary continuous adjacent m-dimensional variables, and the center of M polygon by geometric algebra isw = 2\u03c0/M is the angle of the adjacent features, absim is the amplitude of M polygonal center , and\u2009\u2009anglei is angle direction of M polygonal center .An x1, x2,\u2026, xi,\u2026, xn), xi is the first i feature, and n is feature dimension; the features fusion and reduction algorithm are as follows: input is original feature . Output is feature Re_fea after reduction.(1)F-score value: Fi of xi\u2009\u2009F-score according to formula ( formula .(2)x1, x2,\u2026, xi,\u2026, xn) by the F-score value; then  is got, and sort the F-score value , where F1\u2032 \u2265 F2\u2032 \u2265 \u22ef\u2265Fi\u2032 \u2265 \u22ef\u2265Fn\u2032.Feature sort: sort all features ((3)F_Mean is F-score average; the first F_first is less than F_Mean, so F1\u2032 \u2265 F2\u2032 \u2265 \u22ef\u2265FF_first\u22121\u2032 \u2265 F_Mean, F_Mean < FF_first\u2032; the first lay is ; compute F_Mean2 of the average F-score from F_first to n; then F_second is less than F_mean2; the second level is ; the third level is .Slicing: (4)m = 2, to obtain the center of gravity when m = 2, m = 3, and m = 4, original feature set S\u2032 is constructed by three feature set fusions.Visual features fusion: specifically, in , if m = (5)S\u2032 is repeated to do steps (1), (2), and (3). Re_fea is got.In this work, we used the hierarchical visual technique for feature optimization. There are two hierarchical fusions in the process. In each level, firstly, the main aim is to sort the high-dimensional features. Secondly, the effecting features are got, which are grouped together as input to the next level, and the process is repeated to get fusion feature. Process is shown in F-score and radar chart. Finally, the speech intelligibility is evaluated by SVM classifier.In In the classification problems, SVM follows a certain procedure to find the separating hyperplane with the largest margin of two classes. Radial basis function (RBF), a kernel, is used in this article. The sensitivity, specificity, accuracy, and UA are an index. As a classification tool to evaluate the NKI-CCRT corpus by different feature sets, SVM algorithm constructs a set of reference vectors in role of boundaries that minimize the number of misclassifications. Therefore, it represents a low-cost, accurate, and automatic tool for pathological voice classification in contrast with other tools, such as Gaussian mixture model .Z, quantified as 16\u2009b. The corpus distribution is in The NKI-CCRT corpus  is recorrecordings of vowels /a/, /i/, and /u/ produced at normal, high, low, and low-high-low pitch;recordings of sentence \u201cGuten Morgen, wie geht es Ihnen?\u201d .SVD  is the fThat makes a total of 13 files per session. In addition, the electroglottogram (EGG) signal is also stored for each case in a separate file. The length of the files with sustained vowels is between 1 and 3 seconds. All recordings are sampled at 50\u2009kHz and their resolution is 16 bits. 71 different pathologies are contained, including both functional and organic. The corpus distribution is in Further analysis is required to study the effect of various features of each subsystem.S-transform is a time-frequency analysis method by Stock Well which combines the advantage of wavelet transform with short time Fourier transform [S-transform. MSCC is compared with the traditional MFCC in the NKI-CCRT and SVD corpus. Recognition results are shown in Tables ransform , which sransform . TherefoF-score values to evaluate MSCC and MFCC; MSCC shows better performance by F-score in x-axis represents feature dimension. y-axis represents F-score values. MFCC is generally less than 0.2; the average is at 0.09. The maximum F-score of MSCC is nearly 0.8, and the average is about 0.39. The results of F-score indicate that the MSCC feature is stronger in the pathology classification.For example, in NKI-CCRT corpus, each value index is improved, where UA is increased from 51.58% to 64.76% and accuracy is increased from 50.54% to 63.67%. Thus, MSCC contains more pathological information than MFCC. Meanwhile, in order to show the contrast that MSCC contains more information than MFCC directly, we use Firstly, MSCC is compared with basis acoustic features (430) by support vector machine (SVM). As it can be seen in Tables In our continued investigation, we design an automatic pathological speech intelligibility evaluation system by information visualization optimization method. Furthermore, this hierarchical method is experimented with in NKI-CCRT corpus. The classification accuracy of 84.44% can be achieved. Recognition results are shown in In our study, The signal characteristics of pathological speech have been studied widely in the literature. A previous study showed that changes from articulatory manner are associated with pathological speech, while variability in articulatory place occurs to both normal and pathological speech. Therefore, the results of this research show that MSCC acoustic features fed to other pathology common features can be used together with invasive methods as complementary tools for pathological speech intelligibility evaluation. Furthermore, results of classification demonstrated that optimized feature set has great capability for classification of pathological voices to normal ones compared with the other feature that is examined in this research. Therefore, efficient combination of this work is composed of acoustic long-time features, MSCC, chaotic features, and SVM, which yield sensitivity of 84.4%. This structure significantly improves the results of pathological speech recognition in comparison with the proposed algorithm found in the references .F-score. Further analysis is required to study the effect of fusion difference classifiers. In addition, we would also like to study the effectiveness of other features and reduction methods like particle swarm optimization. In a word, the proposed method has greatly improved the pathological speech intelligibility evaluation performance and can provide important theoretical bases of the clinical application of speech pathology, which can be applied to other areas.Feature extraction and pattern classification are a key of pathological speech recognition. This study proposes a new feature set and feature fusion method. The basis acoustic feature, precise time-frequency feature, and chaotic feature showed discriminating power for binary classification based fusion method . Featur"}
+{"text": "However, the sources of DDT in eastern China are mainly from historic application of technical DDTs and dicofol. The inverse dependence of o,p\u2019-DDT and p,p\u2019-DDE on temperature evidences the transformation of parent DDT to its metabolites. Initial usage, abiotic parameters and microbial communities are found to be the main factors influencing the migration and transformation of DDT isomers and their metabolites in soils. In addition, a prediction equation of DDT concentrations in soils based on stepwise multiple regression analysis is developed. Results from this study offer insights into the migration and transformation pathways of DDTs in Chinese arable soils, which will allow data-based risk assessment on their use.Due to the adverse impact of DDTs on ecosystems and humans, a full fate assessment deems a comprehensive study on their occurrence in soils over a large region. Through a sampling campaign across China, we measured the concentrations, enantiomeric fractions (EFs), compound-specific carbon isotope composition of DDT and its metabolites, and the microbial community in related arable soils. The geographically total DDT concentrations are higher in eastern than western China. The EFs and \u03b4 Dichlorodiphenyltrichloroethanes (DDTs) were widely used in the world as effective insecticides for vector-borne diseases control and for crop protectiono,p\u2019-DDT consists of one pair of enantiomers. The enantiomeric fraction (EF) can be changed during biodegradation and is a good indicator of past versus fresh chiral pollutant inputs8in situ biodegradation processes of organic pollutants10121114o,p\u2019-DDT is also rather limited, especially at a species level of bacteria. It is necessary to well understand their environmental behaviors under real complicated environment using the techniques mentioned above.Historical applications of technical DDTs and dicofol, which usually contains high levels of DDT compounds as impurities in the production process, are the two main sources of DDTs in the environment. DDTs can migrate from soils or transform to their metabolites via various mechanisms, including degradation, volatilization, leaching, run-off, adsorption and plant removal413C) of DDT and its main metabolites in arable soils. High-throughput techniques and network analysis were employed to characterize the microbial communities and explore their co-occurrence patterns with DDT and its metabolites in soils. The obtained data were used to estimate the migration and transformation of DDTs on a large scale and to explore the underlying influencing physicochemical and microbiological factors in arable soils after 30 years of DDT ban in China. Furthermore, results from this study would provide basic scientific data for the contamination management and risk avoidance of DDTs in Chinese soils.Therefore, in this study, we conducted a nationwide farmland sampling campaign across China and measured the concentrations, EFs and carbon isotope compositions  ranged from 0.025 to 211\u2009ng/g, with a mean value of 8.06\u2009ng/g. Among the six DDT components, p,p\u2019-DDE, which is the main metabolite of DDT, had the highest mean concentration (3.29\u2009ng/g). Regional variation of DDT concentrations and compositions in arable soils across China was mapped in p\u2009<\u20090.0001, p\u2009<\u20090.05) was also identified between the residual levels of DDTs and socioeconomic indicators (SIs), including gross regional product (GPR) and population (P)  17. Amongrn China . p,p\u2019-DDConsidering complex factors impacting on the residue levels of DDTs, stepwise multiple regression analysis was employed to explore the dominant factors and develop a prediction model. Based on the results of correlation analysis above, variables including organic matter, temperature, longitude and latitude were included. However, after significance and multicollinearity testing, temperature was excluded in the analysis. The significant prediction equation is as follows:where, C is the residue concentrations of \u2211DDTs in agricultural soils (ng/g); OM is the content of organic matter (%); LONG is the longitude of sampling site (\u00b0E); LAT is the latitude of sampling site (\u00b0N).p,p\u2019-DDT, 15% o,p\u2019-DDT, 5% p,p\u2019-DDE, <0.5% p,p\u2019-DDD, <0.5% o,p\u2019-DDD, <0.5% o,p\u2019-DDE and <0.5% unidentified compoundsp,p\u2019-DDE+ p,p\u2019-DDD)/p,p\u2019-DDT\u2009>\u20091 and of o,p\u2019-DDT/p,p\u2019-DDT\u2009<\u20090.2 /p,p\u2019-DDT was much higher in soils with higher organic matter contents (>2.3%) and higher temperatures (>14\u2009\u00b0C)  . In addi(>14\u2009\u00b0C) .o,p\u2019-DDT levels were selected for enantiomeric analysis. In general, the EF values of o,p\u2019-DDT in soils varied greatly, ranging from 0.066 to 1 as the initial stable carbon isotope composition of DDTs applied for agriculture. The \u03b413C of p,p\u2019-DDE ranged from \u221224.81\u2009\u00b1\u20090.12\u2030 to \u221230.26\u2009\u00b1\u20090.06\u2030 and deviated either positively or negatively from those of the initial product  but with a wider range  -o,p\u2019-DDT and o,p\u2019-DDT showed positive correlations with Devosia, Adhaeribacter and Cellulomonadaceae, but negative correlations with Gp3, Clostridium_sensu_stricto, Nitrospiraceae and Chloroflexi. The abundance of both o,p\u2019-DDT and its (\u2212)-enantiomer has negative correlations with Caedibacter_caryophilus and positive correlations with Skermanella_aerolata, Brevundimonas_alba, Cellvibrio, Brevundimonas, Devosia, Rhodobacteraceae, and Caulobacterales.Nineteen bacterial phyla were identified via Illumina sequencing from 28 samples across China. bacteria . Network\u2009<\u20090.01) . Bacterintiomers . Strong p,p\u2019-DDT, p,p\u2019-DDE is more persistent than other DDT componentsResidues of DDTs are found to be ubiquitous in agricultural soils across China even after 30-year ban of their application. Being the main metabolite of o,p\u2019-DDT/p,p\u2019-DDT in technical DDTs is 0.19, which is much lower than that in dicofol (7.0)p,p\u2019-DDT component with time compared to our previous study9o,p\u2019-DDT varied greatly in arable soils across China. Similar to previous studies919o,p\u2019-DDT in western China also deviated from that of the racemic compound. This might be due to long-range transport from other places and subsequent wet or dry deposition. The enantiomeric signatures of chiral chemicals may retain racemic or nearly racemic in the airo,p\u2019-DDT (mean\u2009=\u20090.016) compared to those at other sites further supports a significant DDT source from atmospheric deposition in western China. In addition, the different physiochemical and biological features of the soil environments might also contribute to the different EF values among the four geographic regions across China. Other studies also obtained EF values of o,p\u2019-DDT either > or <0.5, indicating a complex degradation preference91919o,p\u2019-DDT, but not on the enantiomer preference. It implies that the preferential degradation of o,p\u2019-DDT enantiomers may be modulated by the integrated effects of multiple environmental factors in soil environment. However, the absolute degree of the enantioselective degradation of o,p\u2019-DDT was found to be slightly elevated by temperature. It might be due to the higher enantioselective degradation rates related to higher microbial activities in sites with higher temperature.Historical usage is a crucial factor influencing the DDT concentrations in the environment. In this study, the spatial distribution pattern of \u2211DDTs in arable soils roughly overlaps with the usage inventory map of technical DDTs in 1951\u20131983 and dicofol in 1984\u20132003 in China dicofol .0p,p\u2019-DDin situ degradation of POPs in various environmentset al.13C difference of at least 2\u2030 for reliably interpreting the sources of different sites considering environmental complexity. Different \u03b413C of p,p\u2019-DDE and o,p\u2019-DDT were observed in different soils in this study  and its own dissipation (13C-enriched process). The fact that the Shanghai soil with an abnormally high concentration of p,p\u2019-DDT (15.9\u2009ng/g) bearing the lowest \u03b413C of p,p\u2019-DDE is consistent with this explanation . In addition, DDE residues in eastern China are mainly from the degradation of DDT. Their residues in colder western China, where less amount of DDTs were used than eastern China, are mostly from the long-range transport via air from eastern China13C is found for p,p\u2019-DDE in western China, which could partly account for the negative correlation between its \u03b413C and local temperature. This interpretation is also suitable for the positive correlation between the \u03b413C of o,p\u2019-DDT and temperature. All these hypotheses should be further tested with controlled experiments or additional sampling. Milosevic et al.13C of BTEX at contaminated landfill with lower concentrations, which was due to their microbial degradation and subsequent enrichment of 13C. Likewise, this trend was also observed for p,p\u2019-DDE in this study. However, the possible reason for our findings might be different due to the different initial usage amounts of DDTs across China. More technical DDTs and dicofol have been applied in eastern China than western China. Therefore, the relative newer and higher concentrations of DDT residues might be the main reason for the more negative \u03b413C of p,p\u2019-DDE in eastern China.Compound-specific isotope compositions can offer insights into the pathways of is study . o,p\u2019-DDlanation . The poso,p\u2019-DDT. Both the EF and \u03b413C values of o,p\u2019-DDT in the measured samples differentiated from those of racemic standard products, further suggesting active metabolism of DDTs in soils. Interestingly, the stable carbon isotope compositions of o,p\u2019-DDT showed different characteristics in soils with EF\u2009>\u20090.5 or <0.5. The \u03b413C of o,p\u2019-DDT in soils with EF\u2009>\u20090.5 displayed more negative values than those in soils with EF\u2009<\u20090.5. Bashir et al. observed higher stable carbon isotope fractionation for (+)- than (\u2212)-\u03b1-HCH during biodegradationo,p\u2019-DDT also have the similar carbon isotope fractionation, the observed different isotope fractionation patterns between EF\u2009>\u20090.5 -enantiomer) and <0.5 -enantiomer) could be explained. This prediction can be further tested using enantiomer-specifics table isotope analysis in future laboratory study.The combination of the enantiomer and stable carbon isotope fractionation, in a two-dimensional approach, may aid to further understand the degradation pathways of chiral et al.91619p,p\u2019-DDT to p,p\u2019-DDE and p,\u2019p-DDD by soil OM and temperature was observed in this study. It might be associated with the higher microbial activities in sites with higher soil OM and temperature. The R2 value of the prediction equation based on stepwise multiple regression analysis is 0.222. It means that 22% of the total variations in DDT concentrations are explained by OM, longitude and latitude. The content of OM is the principal factor among these variables. Although the prediction model is significantly developed, the R2 value is still a little small. The initial usage amounts of technical DDTs might be the most predominant factor influencing the distribution and residue levels of DDTs in agricultural soils across China.The initial use of chemicals can lead to a primary distribution pattern, which is controlled by the usage amount of chemicalsSerratia marcescens DT-1P, Pseudomonas fluorescens and Alcaligenes sp. KK, Sphingobacterium sp. D6 and Chryseobacterium sp. PYR2 and Bacillus sp. BHD-4, have been documented to be capable of converting DDTs to their metabolites3233343536Chloroflexi, Coriobacteriaceae (belong to Actinobacteria) and Syntrophobacter, Thermodesulfovibrio, Caedibacter_caryophilus (belong to Gammaproteobacteria), whose abundances correlate negatively with the fraction of p,p\u2019-DDT and positively with that of p,p\u2019-DDE, may be capable of biodegrading DDTs. The significant positive correlation between the degree of DDT degradation and the abundance of Actinobacteria and Gammaproteobacteria was also identified by Sun et al.3940Syntrophobacter and Thermodesulfovibrio, p,p\u2019-DDT but positively with that of its aerobic metabolite p,p\u2019-DDE. It suggests that these bacteria may have the potency to dechlorinate DDT to DDE in aerobic environments. Clostridia are obligate anaerobes and found to be affected by the pollution of metal and petroleum hydrocarbons42o,p\u2019-DDD-polluted soil across China as suggested by Guo et al.o,p\u2019-DDT with Alphaproteobacteria  and Sphingobacteria (Adhaeribacter found in this study) were also observed in Guo et al.26Peredibacter_starrii and Rhodobacteraceae correlate positively with both (+)-o,p\u2019-DDT and (\u2212)-o,p\u2019-DDT, indicating that different degradation rates by the same bacteria may be one possible explanation for the enantioselective dissipation of o,p\u2019-DDT in soils. This result is consistent with those reported by Lewis et al.Gp3, Clostridium_sensu_stricto, Nitrospiraceae, Chloroflexi and Caedibacter_caryophilus, are only capable of degrading (+)- or (\u2212)-enantiomer of o,p\u2019-DDT. Thus, different bacteria can degrade different enantiomers which could also result in the EF values deviating from 0.5. Generally, the taxa we found to correlate well with the stereoisomers and metabolites of DDTs in this study are mostly at genus and species level, not of higher levels. Our results demonstrate that DDT residues can influence the specific microbes and they could in turn impact the redistributions of DDTs in Chinese arable soils.Soil microbial communities, which are influenced by environmental conditions, play critical roles in the degradation of contaminants. Various bacteria, such as A total of 123 surface soils (0\u201320\u2009cm) were collected from agricultural fields covered 31 provinces across China in April and May 2013. Detailed information on sampling locations and strategy was described in our previous study and briefly presented in the o,p\u2019-DDE, p,p\u2019-DDE, o,p\u2019-DDD, p,p\u2019-DDD, o,p\u2019-DDT and p,p\u2019-DDT) (their molecular structures are listed in 2SO4), neutral silica gel, alumina, and florisil. Then, the target analytes eluted by hexane/DCM (7:3) were further concentrated for analysis.A mix of 6 DDT compounds . The determination of enantiomeric fractions (EFs) of chiral o,p\u2019-DDT were performed by a gas chromatograph-mass spectrometry (Agilent 7890A GC-5975C MS). A larger quantity of soils was used to obtain sufficient amounts of targets for isotope analysis. The stable carbon isotope composition (\u03b413C) of DDT and its metabolites was measured using an Agilent 7890A GC coupled to a GV Isoprime IRMS  (GC-C-IRMS) via a modified GC5 combustion interface at College of Environmental and Resource Sciences, Zhejiang University. Due to the limitation of concentration and the existence of interfering substances, only the \u03b413C of p,p\u2019-DDE and o,p\u2019-DDT were determined.The concentrations of DDT and its metabolites were measured on an Agilent 7890A gas chromatograph  equipped with BGB-172 chiral capillary column  based on the instructions of the manufacturer. 16S rRNA gene amplicons were pair-end sequenced at Shenzhen Huada Genomics Institute by using Illumina Miseq (300 bp-PE). The detailed procedures were described in Blank controls were ministered for every 15 soil samples to check potential cross-contaminations and interferences. The recoveries of DDTs were in the range of 82.8% to 105%. The mean recoveries of surrogates, including TCmX and PCB209 were 93.9\u2009\u00b1\u200912% and 89.2\u2009\u00b1\u200915%, respectively. Three times of signal-to-noise ratio were calculated as the limits of detection (LOD), which ranged from 0.003 to 0.005\u2009ng/g for target compounds. Potential thermal degradation of DDTs was checked daily and a ratio less than 6% was satisfied. Duplicate experiments were performed in the whole procedure.o,p\u2019-DDT are defined as the portion of the (+)-enantiomer to the sum of the (\u2212)- and (+)-enantiomers. Racemic standard of o,p\u2019-DDT with every 10 samples were injected and the mean EF value was 0.498\u2009\u00b1\u20090.005. Data was deemed acceptable only if the EF differences between the two monitored ions were within 0.05. The o,p\u2019-DDT in samples was considered to be racemic when the EF value was within the 95% confidence interval (CI) of the standard.The EF values of How to cite this article: Niu, L. et al. Enantiomer signature and carbon isotope evidence for the migration and transformation of DDTs in arable soils across China. Sci. Rep.6, 38475; doi: 10.1038/srep38475 (2016).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spaces. Furthermore, the p-adic weighted Hardy-Ces\u00e0ro operator is also obtained.In this paper, we introduce the  Howeveeader to \u20135. In rep, let p-adic numbers. It is defined as the completion of the field of rational numbers p-adic norm x is represented as \u03b3 is an integer and the integers m, n are indivisible by p, then (i)(ii)(iii)For a prime number p-adic analysis, we know that any non-zero element x of p-adic norm because p-adic integrals in It is well known that p-adic norm on The space Denote by dx on dx such thatSince f is a nonnegative integrable function on The most fundamental averaging operator is Hardy operator defined byto Hardy , states f is a nonnegative measurable function on For the multidimensional case ussed in \u201314. \\docn-dimensional spherical averaging operator, which was introduced by Christ and Grafakos in [The other definition is the fakos in  as folloet al. [n-dimensional p-adic Hardy operator:f is a nonnegative measurable function on p-adic Hardy operator on Lebesgue spaces with power weights.In 2012, Fu et al.  defined et al. [f is a nonnegative measurable function on In 2013, Lu et al.  gave thep-adic product spaces as follows and discuss the boundedness and best bound on the product of p-adic Lebesgue spaces.Next, we will introduce the definition of Hardy type operator on the higher-dimensional f be a nonnegative measurable function on p-adic Hardy type operator is defined byLet \u03c8. For Example, when In 1984, Carton-Lebrun and Fosset  defined p-adic Hardy operator \u03c8 is a nonnegative function defined on \u03c8 for which p-adic Hardy operator In 2006, Rim and Lee  defined et al. [\u03c8 defined on In 2013, Fu et al.  introducp-adic product spaces.Next, we will extend the operator f be a nonnegative measurable function on p-adic weighted Hardy type operator is defined by\u03c6 is a nonnegative measurable function on Let It follows from the Fubini theorem that we can easily formulate the dual operator of f be a nonnegative measurable function on p-adic weighted Hardy type operator is defined by\u03c6 is a nonnegative measurable function on Let In 2014, Chuong and Hung[f on Let p-adic analysisp-adic analog of the weighted Hardy-Ces\u00e0ro operator on weighted Lebesgue spaces and weighted BMO spaces. In each case, the corresponding operator norms are obtained. In 2016, Chuong et al. [p-adic weighted Hardy-Ces\u00e0ro operators and their commutators on weighted functional spaces of Morrey type, and the corresponding operator norms are also computed.In 2014, Hung  considerg et al.  considerp-adic weighted Hardy-Ces\u00e0ro operator.Motivated by these famous results, first we will give a higher-dimensional version of the f be a nonnegative measurable function on p-adic weighted Hardy-Ces\u00e0ro type operator is defined byLet p-adic Lebesgue product spaces with power weights. In Section\u00a0p-adic weighted Hardy-Ces\u00e0ro type operator also has the corresponding conclusion. In Section\u00a0The paper is organized as follows. Section\u00a0LetIfthen thep-adic Hardy type operatoris bounded onmoreover, the norm ofcan be obtained as follows:We provide the following weighted extension of this result.LetIfwhereandthen thep-adic Hardy type operatoris bounded onmoreover, the norm ofcan be obtained as follows:p-adic Hardy type operator will be easy to get on the p-adic Lebesgue product spaces, so we only provide the proof of Theorem\u00a0When Without loss of generality, we consider only the situation when p-adic Lebesgue product spaces with power weights. We haveIt is clear that f is a radial function, then we have f is a radial function.This implies the claim that if Substituting the variable f is a radial function, we have Using the generalized Minkowski\u2019s inequality and noting that Now let us prove that our estimate is sharp. For Let\u03c6is a nonnegative measurable function onIfthen thep-adic weighted Hardy type operatoris bounded onif and only ifSince the case We first prove the sufficiency of Theorem\u00a0This completes the proof of the sufficiency of Theorem\u00a0Next we prove the necessary of Theorem\u00a0Now, for any Obviously, k approach \u221e, then \u03b5 approaches 0 and Since the inequalitySince the operator Letand\u03c6be a nonnegative measurable function onIfthen thep-adic weighted Hardy type operatoris bounded onif and only ifUsing methods similar to Theorem\u00a0We note that in , the autp-adic Lebesgue product spaces.Inspired by the paper, we will consider sufficient and necessary conditions of the weighted Hardy-Ces\u00e0ro type operator SupposeLetbe a measurable function such thatfor some real\u03b2and almost everywhereIfthen thep-adic weighted Hardy-Ces\u00e0ro type operatoris bounded onif and only ifp-adic change of variables. It is worth pointing out that we need to make some appropriate modifications for the necessity. Applying this condition t, so it is easy to get the desired results by adopting the same method as Theorem\u00a0Noting that Theorem\u00a0p-adic Hardy type operator and considered the problem of finding a bound for the norm of it from p-adic Lebesgue product spaces with power weights to itself. Moreover, we characterized a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spaces. In addition, we also extended the results to the p-adic weighted Hardy-Ces\u00e0ro operator.In the present study, we introduced a class of"}
+{"text": "Inequal. Appl. 2013:514, The resolvent operator approach is applied to address a system of generalized ordered variational inclusions with \u2295 operator in real ordered Banach space. With the help of the resolvent operator technique, Li  This theory provides us with a framework to understand and solve many problems arising in the field of economics, optimization, transportation, elasticity and applied sciences. A lot of work considered with the ordered variational inequalities and ordered equations was done by Li al.; see , 6, 8, 9The fundamental goal in the theory of variational inequality is to develop a streamline algorithm for solving a variational inequality and its various forms. These methods include the projection method and its novel forms, approximation techniques, Newton\u2019s methods and the methods derived from the auxiliary principle techniques.H-accretivity [H-monotonicity [e.g., [It is widely known that the projection technique cannot be applied to solve variational inclusion problems and thus one has to use resolvent operator techniques to solve them. The beauty of the iterative methods involving the resolvent operator is that the resolvent step involves the maximal monotone operator only, while other parts facilitate the problem\u2019s decomposition. Most of the problems related to variational inclusions are solved by maximal monotone operators and their generalizations such as retivity , H-monottonicity  and manyy [e.g., \u201317 and tEssentially, using the resolvent technique, one can show that the variational inclusions are commensurate to the fixed point problems. This equivalent formation has played a great job in designing some exotic techniques for solving variational inclusions and related optimization problems.We initiate a study of a system of generalized ordered variational inclusions in real ordered Banach space. We design an iterative algorithm based on the resolvent operator for solving system of generalized ordered variational inclusions. We prove an existence as well as a convergence result for our problem. For more details of related work, we refer to , 18 and X be a real ordered Banach space endowed with norm \u03b8 and partial order \u2264 defined by the normal cone C with a normal constant In the paper, assume that The following well-known definitions and results are essential to achieve the goal of this paper.C (\u2260\u03d5) be a closed, convex subset of X. C is said to be a cone if (i)for (ii)p and if Let C is called a normal cone iff there exists a constant C.X. The real Banach space X endowed with the ordered relation \u2264 defined by C is called an ordered real Banach space.For arbitrary elements p and q are called comparable to each other and this is denoted by For arbitrary elements \u03b2-ordered comparison map, if it is a comparison mapping andA map Ifpandqare comparable to each other, thenandexist, andLetCbe a normal cone with normal constantinX, then for eachwe have the relations: (i)(ii)(iii)(iv)ifthen, 4\u20136Let \u2264 be a partial order relation defined by the coneCwith a normal constantinXin Definition\u00a0Then hereinafter relations survive: allow\u03bbto be real, thenifp, qandwcan be comparative to each other, thenpresumeexists, and ifandthenifp, q, r, wcan be compared with each other, thenifandthenifthenifthenifandandthenandfor allandA is called a \u03b3-order non-extended mapping if there exists a constant A is called a strongly comparison map if it is a comparison mapping and Allow M is called a weak-comparison map, if for M is called an \u03b1-weak-non-ordinary difference map associated with A, if it is weak comparison and for each M is called a \u03bb-order different weak-comparison map associated with A if \u2203 a M, a weak-comparison map, is called an ordered \u03b1-weak-non-ordinary difference map and a \u03bb-order different weak-comparison map associated with A, and Allow \u03b3-order non-extended map and an \u03b1-non-ordinary difference mapping with respect to A, respectively. The resolvent operator A and M is defined byLet I is the identity map on X.A map Ifandare an\u03b1-weak-non-ordinary difference map associated withAand a\u03b3-order non-extended map, respectively, withthenis an\u03b1-weak-non-ordinary difference map associated withAand the resolvent operatorofis a single-valued fori.e., ofholds.Letandbe aweak-ANODD set-valued map and a strongly comparison map associated withrespectively. Then the resolvent operatoris a comparison map.Letbe an orderedweak-ANODD map andbe a\u03b3-ordered non-extended map associated withforrespectively. Then the following relation holds:X to be a real ordered Banach space and C a normal cone having the normal constant Allow For some X), M and N are single-valued mappings and If  problem  reduces mentclass2pt{minimM is a single-valued mapping, then problem . Here, we discuss some special cases of SGIOVI . If \\docNow, we mention the fixed point formulation of SGIOVI .The set of elementsbecome a solution of SGIOVI , under some apt conditions.LetCbe a normal cone having a normal constantin a real ordered Banach spaceX. Letbe single-valued mappings such thatAis acompression mapping, is acompression andis acompression andare comparison mappings, respectively. Letbe single-valued mappings such thatis anrestricted-accretive mapping w.r.t. andis anrestricted-accretive mapping w.r.t. respectively. Supposeare the set-valued mappings such thatMis aweak-ANODD set-valued mapping andis aweak-ANODD set-valued mapping, respectively.In addition, ifand for allthe following conditions are satisfied:andThen the SGIOVI 17), we hnce from , 18) an an18\\docq2\u2225). By , we knowf SGIOVI .\u2003\u25a1This part of the article is associated with the construction of an iterative scheme as well as the strong convergence of the sequences achieved by the said scheme to the exact solution of SGIOVI .C to be a normal cone with the normal constant X. Let Allow For the initial guess Allowandto be sequences of nonnegative real numbers such that they satisfy(i)and(ii)Thenapproaches zero asnmoves to \u221e.AllowX, C, M, N, andto be as in Theorem\u00a0such that all the assertions of Theorem\u00a0are valid. Then the sequenceformulated by Algorithm (and (converges strongly to the unique solutionof SGIOVI (lgorithm  and 22)AllowX, f SGIOVI .By Theorem\u00a0By , 23) an an23) anBy using the same argument as in Theorem\u00a0ows from  and 24)26\\docume\u2212q\u2225). By , we knowSystem of generalized ordered variational inclusions can be viewed as natural and innovative generalizations of the system of generalized ordered variational inequalities. Two of the most difficult and important problems related to inclusions are the establishment of generalized inclusions and the development of an iterative algorithm. In this article, a system of generalized ordered variational inclusions is introduced and studied which is more general than many existing systems of ordered variational inclusions in the literature. An iterative algorithm is established with the \u2295 operator to approximate the solution of our system, and a convergence criterion is also discussed.We remark that our results are new and useful for further research and one can extend these results in higher dimensional spaces. Much more work is needed in all these areas to develop a sound basis for applications of the system of general ordered variational inclusions in engineering and physical sciences."}
+{"text": "Nature Communications 10.1038/s41467-017-01510-7, published online 27 November 2017Correction to: y-axis label in Fig. 2b was incorrectly labelled \u2018Snap-in force (\u03bcN)\u2019. In the correct version, the axis is labelled \u2018Snap-in force (nN)\u2019.The original version of this Article contained an error in Fig. 2b. The In the original version of this Article, the \u201cButterfly wings\u201d section of the Methods incorrectly stated the name of the butterfly as \u2018Golden bird\u2019. In the correct version, the name of the butterfly is \u2018Golden birdwing\u2019.These have now been corrected in both the PDF and HTML versions of the article."}
+{"text": "N can be \u201cunfolded\u201d to obtain a MUL-tree U(N) and, conversely, a MUL-tree T can in certain circumstances be \u201cfolded\u201d to obtain aphylogenetic network F(T) that exhibits T. In this paper, we study properties of the operations U and F in more detail. In particular, we introduce the class of stable networks, phylogenetic networks N for which F(U(N)) is isomorphic to N, characterise such networks, and show that they are related to the well-known class of tree-sibling networks. We also explore how the concept of displaying a tree in a network N can be related to displaying the tree in the MUL-tree U(N). To do this, we develop aphylogenetic analogue of graph fibrations. This allows us to view U(N) as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in U(N) and reconciling phylogenetic trees with networks.Phylogenetic networks are rooted, labelled directed acyclic graphswhich are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network  N to obtain a MUL-tree U(N) and that, conversely, a MUL-tree T can under certain conditions be \u201cfolded\u201d to obtain a phylogenetic network F(T) that exhibits T. We illustrate these operations in Fig.\u00a0T is a MUL-tree, and the network N is obtained by first inserting vertices into T and then folding up the resulting tree by identifying vertices in T to obtain F(T); the unfolding U(N) of N  is precisely T.Phylogenetic networks are rooted, directed acyclic graphs whose leaves are labelled by some set of species ) is isomorphic to T for any MUL-tree T (Huber and Moulton U and F operations are applied in the opposite order to some network as there are networks N for which F(U(N)) is not isomorphic to N ) is isomorphic to N. We call these stable networks. In Sect.\u00a0More specifically, although it is always the case that In Sect.\u00a0We then focus on the problem of displaying trees in networks. In Sect.\u00a0weakly displayed by a phylogenetic network N if it is displayed by the MUL-tree U(N). Using the concepts developed in Sect.\u00a0Finally, in Sect.\u00a0X denote a finite set of size at least two. In addition, all graphs that we consider are connected.Throughout this paper, we let G is a directed acyclic graph with vertex set V(G), arc set A(G) and a single root G, we denote the headv of a by tailu by a and G are parallel if v is a vertex of G, then the in-degree of v, denoted by indeg(v), is the number of incoming arcs of v, and the out-degree of v, denoted by outdeg(v), is the number of outgoing arcs of v. We say that a vertex below a vertex w to v in G. We call a vertex v of G a reticulation vertex of G, if v a tree vertex of G if v a leaf of G, or G by L(G) and the set of interior verticesv of G, that is, v is neither the root nor a leaf of G, by Suppose M is a multi-set onX if the set resulting from M by ignoring the multiplicities of the elements in M is X. Following Huber and Moulton for all (ii)for every leaf In addition, we call MUL-tree onX if the tree T does not have any vertices with in-degree one and out-degree one. If the map T rather than X is of no relevance to the discussion then we will call T a (pseudo) MUL-tree rather than a (pseudo) MUL-tree on X. For example, the tree T in Fig.\u00a0X that is not a MUL-tree on X. We say that two (pseudo) MUL-trees X are isomorphic if there is a digraph isomorphism We say that a multi-set  Moulton , we defimentclass2pt{minimT is a pseudo MUL-tree. For v a non-root vertex of T, we denote by T(v) the connected subgraph of T that contains v obtained by deleting the incoming arc of v. Clearly T(v) is a pseudo MUL-tree. We call a pseudo MUL-tree pseudo subMUL-tree of T if there exists a non-root vertex v of T such that T(v) and T a MUL-tree we say that a subMUL-tree T is inextendible if there exist distinct vertices v and T such that T(v) and T is inextendible if T contains more than one copy of that subMUL-tree. We say that a subMUL-tree T is maximal inextendible if T that contains Suppose T and its folding b are all inextendible subtrees of T and so are the two leaves labelled c. Each one of two subtrees of T of length two (ignoring the directions of the arcs of T) that have leaf label set To illustrate these definitions consider for example the MUL-tree mentclass2pt{minimX-networkN is a rooted directed acyclic graph, in which parallel arcs are allowed,An (i)N that has in-degree zero and out-degree at least two,there exists a unique root (ii)N except the root is either a reticulation vertex or a tree vertex,every vertex of (iii)there exists no vertex of in-degree one and out-degree one, and(iv)L(N) of leaves of N is X.the set A phylogenetic network ( onX) is an X-network that does not have parallel arcs. A phylogenetic tree onX is a phylogenetic network on X that has no reticulation vertices. We say that a phylogenetic network N is binary if the degree of every reticulation vertex and every non-leaf tree-vertex is three and X-networks N and isomorphic if there exists a bijection N with head u and tail v equals the number of arcs in X.such thatIn this section, we recall the unfolding and folding operations mentioned in the introduction that were first proposed in Huber and Moulton  , andthere is an arc from vertex x in X are labelled by x.the vertices in The MUL-tree obtained by suppressing all in-degree one and out-degree one vertices in U(N). In Huber and Moulton (U(N) is indeed a MUL-tree.We first describe the unfolding operation  Moulton  it is shv of an directed graph G as in Sect.\u00a0v by ch(v) and say that an X-network Nexhibits a MUL-tree T if the MUL-trees U(N) and T are isomorphic. In particular, any X-network N exhibits the MUL-tree U(N). Note that there exist MUL-trees T for which there is no phylogenetic network that exhibits T .We denote for all vertices F for constructing an X-network F(T) from a MUL-tree T introduced in  are isomorphic (as pseudo MUL-trees). The pseudo MUL-tree obtained once the last element in Now, to obtain F(T), we define an equivalence relation v,\u00a0w in F(T) be the X-network obtained by taking the quotient of G(T) denote the DAG with vertex set m. The X-network obtained from G(T) by suppressing all vertices of indegree one and outdegree one and defining the leaf labels in the natural way is F(T).Finally, to obtain T in Fig.\u00a0u in F(T), representing u. Similarly, the two vertices labelled w in F(T) in terms of w. Clearly F(T) from u to w.For example, consider the MUL-tree entclass1pt{minimaT is isomorphic with U(F(T)) (as MUL-trees) (Huber and Moulton T and U(F(T)). Also, note that if T is binary, then F(T) is semi-resolved, that is, every tree vertex in F(T) has out-degree 2. Moreover, in Huber and Moulton (F(T) is semi-resolved, then F(T) has the minimum number of reticulation vertices amongst all phylogenetic networks that exhibit T.Note that any MUL-tree  Moulton ,\u00a0ProposiX need not be a phylogenetic network. For example, consider the MUL-tree U(N) in Fig.\u00a0F(U(N)) is not a phylogenetic network as it contains parallel arcs. We now characterize those MUL-trees T for which F(T) is a phylogenetic network.In general, the folding of an arbitrary MUL-tree on T is a binary MUL-tree on X. Then F(T) is a phylogenetic network if and only if there is no pair of distinct vertices v,\u00a0w in T which share a parent in T and are such that T(v) and T(w) are isomorphic.Suppose F(T) is a phylogenetic network then there is no pair of distinct vertices in T with the stated property by establishing the contrapositive. Suppose T is a binary MUL-tree on X that contains two distinct vertices v and w which share a parent in T and are such that T(v) and T(w) are isomorphic. Without loss of generality, we may assume that v and w are such that there exist no two vertices T on the directed paths from the root of T to v and w, respectively, such that T(v) is inextendible. If T(v) is maximal inextendible then F(T) contains a parallel arc and so F(T) is not a phylogenetic network, as required. So, assume that T(v) is not maximal inextendible. Then there must exist some vertex T distinct from v and w such that T(v) is a subMUL-tree of We prove the claim that if v such that T. Then T(v) and T(w) as a subMUL-tree. Thus, T(v) is rendered maximal inextendible at some stage in the construction of F(T). Applying the operation F to T(v) introduces a parallel arc into F(T) and thus F(T) is not a phylogenetic network, as required.Let T is a binary MUL-tree on X such that there exist no two vertices v,\u00a0w in T which share a parent in T such that T(v) and T(w) are inextendible. Assume for contradiction that F(T) is not a phylogenetic network. Then F(T) must contain parallel arcs a and v is a tree vertex and w is a reticulation vertex of F(T). Let z denote the unique child of w in F(T). Note that since the folding operation implies that F(T) cannot contain an arc both of whose end vertices are reticulation vertices, z must in fact be a tree vertex in F(T).Conversely, suppose that F(T) to z which contain arcs a and U(F(T)) on X by v such that T. Thus, F(T) must be a phylogenetic network. Now, let F can be considered as the reverse of the operation U. However, there exist phylogenetic networks N such that F(U(N)) is not isomorphic to N ) and N are isomorphic.As mentioned above, the folding operation N for which F(U(N)) is isomorphic to N. We call such networks stable.In this section, we shall give a characterization of phylogenetic networks N is a phylogenetic network on X. We call two distinct tree vertices v and w in Nidentifiable if there exist directed paths N to v and w such that the subMUL-trees U(N) are isomorphic. In addition, we say that N is irreducible if it does not contain an identifiable pair of tree vertices. To illustrate, the network N depicted in Fig.\u00a0v and w are identifiable.We start by recalling the definition of an irreducible network (Huber and Moulton N is a phylogenetic network then let Ret(N) denote the set of reticulation vertices of N. We call Ncompressed if the child of each vertex in Ret(N) is a tree vertex. Note that in Cardona et\u00a0al. N is stable.(ii)N is compressed and irreducible.(iii)N is compressed and there does not exist a pair of distinct tree vertices v,\u00a0w in N such that Suppose that v,\u00a0w in N such that N is semi-resolved we have N is compressed the children a and b, respectively, are tree-vertices of N. Let N to v and w, respectively. Similarly, let N from v and w, respectively. Then the subMUL-trees U(N) are isomorphic and so are the subMUL-trees v. Similarly, let w. Then the MUL-tree obtained from v, w is an identifiable pair in N. Hence N is not irreducible which provides the required contradiction.(ii) N is not irreducible. Then N contains an identifiable pair of vertices v,\u00a0w. Without loss of generality, we may assume that v and w are such that there are no vertices v and w, respectively, that also form an identifiable pair.(iii) ch(v) and ch(w) are contained in Ret(N). Suppose that u of N let N to u. If s is a leaf of N then, since v and w are an identifiable pair, the MUL-trees X. Hence, s is a leaf of N.To obtain the required contradiction, we first claim that s is a non-leaf tree-vertex of N then, since z of N gives rise to a subset of vertices in the MUL-tree U(N), it follows that there exists a non-leaf tree vertex w such that v and w, we cannot have that s and s is assumed to be a tree vertex of N. Since every non-root vertex of N is either a tree-vertex or a reticulation vertex of N, it follows that If N is compressed, the child s must be a tree-vertex of N. Since r in N below w such that N which is impossible. Hence, r form an identifiable pair in N with v and r below w which is impossible in view of the choice of v and w. Thus, To complete the proof, assume for contradiction that there exists some (i)  Moulton ,\u00a0TheoremN is compressed and irreducible. Let N and F(U(N)), respectively. Since N is irreducible so is N exhibits U(N) so does N is compressed, it follows that N is stable. (ii)  Moulton ,\u00a0CorollaN is a phylogenetic network. A vertex w of N distinct from some vertex v of N is a sibling of v if v and w share the same parent, and a sibling that is a tree vertex is called a tree-sibling vertex. In addition, N is called a tree-child network if every non-leaf vertex of N has a child that is a tree vertex of N  such that X-morphism. We call the inverse image fibre over v. Informally, the fibre over v is the subset of V(T) that is mapped to v under f. For example, for the tree N depicted in Fig.\u00a0u, v and w in N are given by the vertices of Recall that the head of an arc mentclass2pt{minimmentclass2pt{minimU(N) of a network N. This result is an analogue of Boldi and Vigna  of a MUL-tree T can also give rise to a folding map. In analogy with Boldi and Vigna (V(T) of a pseudo MUL-tree T satisfies the local out-isomorphism property (LOIP) if the following holds for all LOIP: If T with tail v to the set of arcs in T with tail w such that a in T with tail v.We now use the LOIP-property to characterize when equivalence relations on MUL-trees give rise to folding maps (cf. Boldi and Vigna v in a rooted directed tree by pa(v).As we shall now show, the folding nd Vigna ,\u00a0p. 25, X, and V(T). Then the equivalence classes N on X) if and only if (i)LOIP,(ii)for all (iii)for all (iv)for all (v)v.for all Suppose that N is a phylogenetic network on X and f. For each a in T with tail v to the set of arcs in T with tail w by putting N is a phylogenetic network, it is straight-forward to check that (ii) must hold as no vertex in N can have in-degree and out-degree 1, (iii) must hold as every vertex of N that is not the root of N is either a reticulation vertex or a tree vertex (but not both), and that (iv) must hold as all elements in f to a vertex labeled by x which has in-degree 1. Finally, (v) follows from the fact that N does not contain parallel arcs.Assume first that V(T) that satisfies properties (i)\u2013(v). To simplify notation, put u in V(T). Let T by u],\u00a0[v]) an arc in u] in x in X with X.Conversely, assume that X-morphism that maps each vertex u in V(T) to its equivalence class [u], and each arc  in A(T) to the arc . It is straight-forward to check that f is a folding map as properties (i) and (iv) imply that f yields a well-defined surjective X-morphism from T to Now, define T, consider the equivalence relation F(T) is a phylogenetic network, we obtain a folding map Given a MUL-tree We now state a result that provides additional insight into unfoldings of networks, and that will also be useful in the last section. It can be regarded as a phylogenetic analogue of path lifting in topology ). By the comment following Theorem\u00a0F(U(N)). As N is isomorphic to F(U(N)), there also exists a folding map from N. By Corollary\u00a0Suppose entclass1pt{minimaN is isomorphic to Conversely, suppose entclass1pt{minimaF(U(N)) is isomorphic to N is isomorphic to F(U(N)), as required. Now, X-networks in general. We will not pursue this possibility further here, but it could be of interest to understand categorical properties of such maps , u to v). We illustrate this concept in Fig.\u00a0Following Iersel et\u00a0al. , we say In Kanj et\u00a0al.  it is shTreeDisplayingInstance: A binary stable phylogenetic network on X and a binary phylogenetic tree on X.Question: Is T displayed by N?N is a binary phylogenetic network on X and that R is a binary phylogenetic tree on X. Let N, let R, and let N and that R. Then the operation HangLeaves(v) adds the vertices N as well as the arcs R as well as the arcs To establish this fact, we show that this problem is NP-complete when restricted to compressed, binary tree-sibling networks and apply Corollary\u00a0TreeDisplaying is NP-complete, even when restricted to the class of binary, compressed tree-sibling networks.T be a binary phylogenetic tree on X and let N be a binary phylogenetic network on X. We will  modify N to a binary, compressed tree-sibling network X and, simultaneously, modify T to a binary phylogenetic tree T is displayed by N if and only if By Corollary\u00a0j et\u00a0al.  that it HangLeaves to transform N into a compressed tree-sibling network on some yet to be specified leaf set T to a binary phylogenetic tree on N a phylogenetic network e in N whose head is a reticulation vertex of N we subdivide e by a new vertex HangLeaves to X, every reticulation vertex of N has two siblings in The construction of v of N one of its two siblings. Let s denote that sibling. Let s and v in HangLeaves to v in X and all of the leaves added to N this way. Then it is easy to check that the resulting DAG Next, we follow the proof of Iersel et\u00a0al. ,\u00a0TheoremT is displayed by N if and only if T is displayed by N if and only if HangLeaves, to a vertex v of N.We now establish our claim that T is displayed by N. To see that N that is a subdivision of T. Combined with the fact that the subgraph of Assume first that N that is a subdivision of T. Thus, T is displayed by N which completes the proof of the claim. A repeated application of the last claim implies that T is displayed by N if and only if Conversely, assume that T and a network N on X, we say that T is weakly displayed by N if it is displayed by U(N)  that is a subdivision of T). For example, both of the trees in Fig.\u00a0N, but the tree in (ii) is not displayed by N. As we shall see, this concept is closely related to the problem of reconciling gene trees with species networks. In Sect.\u00a0T is displayed by a phylogenetic network N even if it is stable. In this section, we show that, in contrast, one can decide in polynomial time whether or not a tree is weakly displayed by any given phylogenetic network.Given a phylogenetic tree N on X, let V(N) together with the root on N. Following\u00a0Zhang et\u00a0al.  in A(T) is associated with a directed path N with initial vertex r(u) and terminal vertex r(v).Before presenting our algorithm, we first derive a characterization for when a tree is weakly displayed by a phylogenetic network in terms of so-called tree reconciliations. Given a phylogenetic network g et\u00a0al. , a reconr between T and Nlocally separated if for each pair of vertices T that have the same parent v, both We now give the aforementioned characterization for when a tree is weakly displayed by a phylogenetic network. We call a reconciliation N is a phylogenetic network on X. Then a phylogenetic tree T on X is weakly displayed by N if and only if there exists a locally separated reconciliation between T and N.Suppose that r between T and N, then T is weakly displayed by N. We illustrate the main idea of the proof in Fig.\u00a0r induces an X-morphism T into N, and so, using Theorem\u00a0X-morphism T is displayed by U(N).We first prove that if there is a locally separated reconciliation r is a locally separated reconciliation between T and N. Since each arc in T is associated with a directed path in N which contains at least one arc, it follows that r induces an X-morphism T to N. By Theorem\u00a0X-morphism from r is locally separated, it follows that the map More specifically, suppose that X-morphism, each vertex in T. Since U(N) does not contain any in-degree one and out-degree one vertices and U(N) it follows that T is displayed by U(N), and so T is weakly displayed by N, as required.Now, consider the set T is weakly displayed by N. Then there exists a subdivision T such that U(N). Since U(N), there exists a subdivision T) such that X-morphism from N given by Theorem\u00a0X-morphism N induces a map r from V(T) to V(N) defined by putting r(v) exists because V(U(N)) as X-morphism. Moreover, since X-morphisms it follows that r(v) is a tree vertex of N.Conversely, suppose that entclass1pt{minimau,\u00a0v) in T, denote the subdivision of  in u to v in r(u) to r(v) in N which contains at least one arc. Then it follows that r is a reconciliation between T and N. Moreover, to see that r is locally separated, consider an arbitrary pair of distinct vertices V(T) that have the same parent v. Denote the initial arcs of the two (necessarily distinct) directed paths a of U(N) put r is locally separated, as required. Now, for every arc  the phylogenetic network obtained from by N by first restricting N to v and all the vertices of N below v and then suppressing any resulting vertices with in-degree one and out-degree one. In addition, we define a function v is not a leaf in V(T), then we set u in N, and (ii) there exists a locally separated reconciliation between T(v) and v is a leaf with label x, then we set u is a leaf in N labeled with x or x is a leaf in N below u. We remark that u is below N.We now present a dynamic programming algorithm to solve this problem. Let T and N if and only if By definition, there exists a locally separated reconciliation between T be a binary phylogenetic tree on X, and N a phylogenetic network on X. Suppose that v is an interior vertex in T with two children u is an interior vertex in N with u, or there exist two distinct children u in N such that Let u then, by the previous remark, u is an interior vertex in N with two children N such that N such that for N obtained by combining the arc We begin by establishing the \u2018if\u2019 direction. Note that if v and f is a reconciliation between T(v) and N(u). Combined with the fact that f is also locally separated. Hence, Now consider the map v an interior vertex in T and u as otherwise the proposition clearly follows. Under this assumption, it follows that there exists a locally separated reconciliation f between T(v) and N(u) with Conversely, suppose that v and f is a locally separated reconciliation, it follows that u and that v but distinct initial arcs, it follows that there exist two distinct children u such that Now, let Proposition\u00a0k be the maximum number of children that any vertex in N may have. Note first that a topological ordering V(T)  such that T implies O(m) time. Similarly, we can compute a topological ordering V(N) in O(kn) time. Now, noting that i,\u00a0j)th entry is O(mnk) time to fill this matrix and, therefore, to compute T on X has Let entclass1pt{minimaT is a binary phylogenetic tree on X, and that N is a phylogenetic network on X. Then, using a dynamic programming algorithm, it can be decided inT is weakly displayed by N.Suppose that"}
+{"text": "Following this, Dresher type inequalities for the radial Blaschke-Minkowski homomorphisms with respect to p-radial Blaschke and p-harmonic Blaschke additions are established.In the paper, we first improve the radial Blaschke and harmonic Blaschke additions and introduce the  The surface of B is n-ball is denoted by n-dimensional volume of a body K. Associated with a compact subset K of K will be called a star body. Let \u03b4\u0303 denote the radial Hausdorff metric, i.e., if The setting for this paper is an n in the The radial Minkowski linear combination, mentclass2pt{minimith dual mixed volume of K and L, If entclass1pt{minimaIK whose radial function satisfies, for v is K. The volume of the intersection body of K is given by Ifandthenwith equality if and only ifKandLare dilates.K and L are dilates. In the following, we establish the Brunn-Minkowski inequality for the p-radial Blaschke addition.Taking t}i=0 in , we haveIfandthenwith equality if and only ifKandLare dilates.p-dual mixed quermassintegral p-radial Blaschke addition and together with inequality   \\document}i=0 in .\u2003\u25a1K and L are star bodies in K and L are dilates.Let us recall the concept of harmonic Blaschke addition defined by Lutwak . Supposehed (see ). If \\doIn the section, we give an improved concept of the harmonic Blaschke addition.p-harmonic Blaschke addition of star bodies K and L denoted by For p-harmonic Blaschke addition follows immediately from  a ap-harmoIfandthenwith equality if and only ifKandLare dilates.\u03a8 is continuous.For all n dimensions.For all A map K and L are star bodies in K and L are dilates.Radial Blaschke-Minkowski homomorphisms are important examples of star body valued valuations. Their natural duals, Blaschke-Minkowski homomorphisms, are an important notion in the theory of convex body valued valuations . In K and L are star bodies in K and L are dilates. The inequality is reversed when If e, e.g., )4.2\\docp<0 (see ).K and L are star bodies in K and L are dilates. Taking In 2013, an ished in : If K anent}p=1, .(see )Letbe a radial Blaschke-Minkowski homomorphism. There is a continuous operatorsymmetric in its arguments such that, forandi of K. K.Clearly, Theorem\u00a0etail in , 24. If (see )A mapis a radial Blaschke-Minkowski homomorphism if and only if there is a measuresuch thatwheredenotes the set of nonnegative zonal measures oni are integers. We now extend the integers i to real numbers, define the Blaschke-Minkowski homomorphism of order p of K.For the mixed radial Blaschke-Minkowski homomorphism induced by \u03a8, Schuster  proved tp of K, denoted by Let LetIfandthenwith equality if and only ifandare dilates.K and \u03a8L are dilates.Taking t}j=n in  and noti(u)=n\u03c9n,  becomes t}p=0 in , 5.1) b b\\documeLetIfandsatisfythenwith equality if and only ifandare dilates.Taking t}k=n in  and noti(u)=n\u03c9n,  becomes t}k=n in , we haveAn extension of Beckenbach\u2019s inequality  Ifand\u03d5is a distribution function, thenwith equality if and only if the functionsfandgare proportional.We are now in a position to prove Theorem\u00a0LetIfandsatisfythenwith equality if and only ifandare dilates.\u03bc is the generating measure of \u03a8 from Lemma\u00a0From , we obtafore, by , we haveTaking ment} in  and \\docWe are now in a position to prove Theorem\u00a0LetIfandsatisfythenwith equality if and only ifandare dilates.From , we obtace, from , we obtai(L). By , we haveTaking ment} in  and \\docp-radial addition and the p-harmonic Blaschke addition.In the present study, we first revised and improved the concepts of radial Blaschke addition and harmonic Blaschke addition in an"}
+{"text": "The DOT format was originally created in the early 2000s to represent graph topologies, layouts and formatting. DOT-encoded files are produced and consumed by a number of open-source graph applications, including Graphviz, Gephi, Tulip, and others. While DOT-based graph applications are popular, they emphasize general graph layout and styling over the topological and semantic analysis functions available in domain-focused applications such as Cytoscape. While domain-focused applications have easy access to large networks  and advanced analysis and formatting, they do not have as many styling options as the Graphviz software suite. dot-app enables the interchange of networks between Cytoscape and DOT-compatible applications so that users can benefit from the features of both. dot-app was first deployed to the Cytoscape App Store in August 2015, has since registered more than 1,200 downloads, and has been highly rated by more than 20 users. It enables users to discover and load curated and uncurated networks representing molecular and genomic interactions, load ad-hoc or custom networks, and share networks that others have created. Once networks are loaded, users can manually annotate a network or automatically integrate annotations using a number of algorithms and databases. Users can perform a number of graph-oriented and semantic-aware analyses ranging from graph statistics to motif and cluster discovery to upstream and downstream structural and functional inferences. Users can also perform a number of complex graph filtering and layout operations to drive and focus the semantic understanding of network interactions and structure.CytoscapeEven beyond analysis and layout, users commonly derive and demonstrate network meaning by using visual cues to distinguish relationships and attributes. For this, Cytoscape provides a visual style system that enables users to paint nodes and edges using color, border thickness, size, fonts, arrows, and other devices.http://apps.cytoscape.org). The store contains 319 apps (June 2017) that provide a range of functionality from file import/export to analysis to visualization and publishing. Based on the success of the combination of Cytoscape core and downloadable apps, Cytoscape is downloaded approximately 14,000 times per month worldwide and is started approximately 3,000 times each working day. As of 2015, Cytoscape has been cited in 700 academic peer-reviewed papers per year.Much of the power and functionality of Cytoscape is delivered as apps available in the Cytoscape App Store  and NNF (.nnf). Other file formats, such as GEXF (.gexf) and XGMML(.xgmml), include varying amounts of visual information. Our primary motivation for creating dot-app was to extend Cytoscape\u2019s interoperability to users that primarily use Graphviz software. Prior to dot-app, a user would either have to convert the network to a file format compatible with Cytoscape or attempt to manually reconstruct the network. Converting a DOT file into a Cytoscape network by use of an intermediary file format is an inherently bad process because each conversion results in a loss of some data. Furthermore, reconstructing a graph manually in Cytoscape might not be too difficult for a simple graph with few nodes and edges, but reconstruction would become more time consuming for larger networks which have nodes of distinct visual properties since each node would have to be created one at a time and these visual properties have to be set separately for each node if there is no underlying data to which the visual properties can be mapped. With dot-app, we minimize information loss by providing a direct conversion from DOT to a Cytoscape network and we reduce the time needed to reconstruct the DOT network in Cytoscape.While Cytoscape is the dominant network analysis and visualization platform in bioinformatics, it is not the only platform. To support interoperability with a number of network-oriented workflows and applications, Cytoscape offers a number of natively supported file import/export modules, and leverages a number of them that are available as apps in the App Store. Some of these file formats3 is a popular, well-established graph visualization software suite that produces DOT  files containing graph structure, layout, and styling information; and uses these files to output these networks in a variety of file formats. These files adhere to the DOT language syntax (http://www.graphviz.org/doc/info/lang.html). In this paper, we use \u201cDOT file/network\u201d and \u201cGraphviz file/network\u201d interchangeably. Due to Graphviz\u2019s continued usage, many graph visualization and analysis applications support the import and export of DOT files.Graphvizhttp://www.cs.rpi.edu/research/groups/pb/punin/public_html/XGMML/) and GEXF (http://www.gexf.net/format/index.html), which are two file formats that support visual information such as node shapes and line types. In comparison to GEXF and XGMML, the DOT format defines more node shapes, arrow shapes, and has unique features such as gradients for node colors and edges painted with multiple colors.As mentioned earlier, Cytoscape provides support for XGMML . While in the \u201cInstall Apps\u201d tab, type dot-app in the search bar. Make sure the download site isA Graphviz network can be imported in three ways: from the welcome screen (via the \u201cFrom Network File\u2026\u201d button), from the menu (\u201cFile->Import->Network->File\u2026\u201d), or from the toolbar (by clicking the \u201cImport Network from File\u201d button).https://marc.info/?l=graphviz-devel&m=129418103126092). From this point, importing a Graphviz network is the same as importing a network from any of Cytoscape's accepted file formats. Those steps are detailed in the Cytoscape User Manual .Users are presented with a file browser dialog titled \u201cNetwork file to load\u201d as in. The useTo export a Cytoscape network as a Graphviz network, use \u201cExport -> Network and View\u201d from the menu. Selecting \u201cGraphViz files \u201d in the Export dialog launches dot-app and prompts the user to choose from three options, as shown inPick edge style. Cytoscape provides edge-routing capabilities that cannot be conserved during the export process, so dot-app provides three edge routing options: \u201cStraight segments\u201d, \u201cCurved segments\u201d, and \u201cCurved segments routed around nodes\u201d. These options change the value of the \u201csplines\u201d attribute that appears in the exported Graphviz file. The Graphviz file for a network exported from Cytoscape is shown below, and the attribute modified by the \u201cPick Edge Style\u201d option is underlined and in bold.splines = \"false\"                                                    outputorder = \"edgesfirst\"esep = \"0\"pad = \"2\"node edge \"Node 1\u00a764\" \"Node 2\u00a766\" \"Node 3\u00a768\" \"Node 4\u00a770\" \"Node 1\u00a764\" -- \"Node 2\u00a766\"\"Node 2\u00a766\" -- \"Node 4\u00a770\"\"Node 1\u00a764\" -- \"Node 3\u00a768\"}graph example {bgcolor = \"#FFFFFFFF\"                        Pick node label location. Graphviz does not offer the flexible label placement that Cytoscape offers. As such, dot-app gives the options of \u201cCenter,\u201d \u201cTop,\u201d \u201cBottom,\u201d and \u201cExternal\u201d to allow the user to specify the label location applied to every node. In the output Graphviz file, the \u201cCenter\u201d, \u201cTop\u201d, and \u201cBottom\u201d options change the value of the \u201clabelloc\u201d attribute that appears in the node default attribute list. The options respectively change the value to \u201cc\u201d, \u201ct\u201d, and \u201cb\u201d. In contrast, the \u201cExternal\u201d option causes the node labels to set the \u201cxlabel\u201d attribute instead of the \u201clabel\u201d attribute in the output Graphviz file. The \u201cxlabel\u201d attribute causes the label to be placed in a location near its node that does not cause it to overlap with any other nodes or labels.Pick network label location. dot-app provides the options \u201cNo network label,\u201d \u201cTop,\u201d and \u201cBottom\u201d to allow the user to specify whether the network itself should be labeled and, if so, where the label is placed. The options \u201cTop\u201d and \u201cBottom\u201d cause the \u201clabelloc\u201d attribute and \u201clabel\u201d attribute for the graph to be written to the output Graphviz file. Furthermore, the \u201clabel\u201d attribute will be set to the network\u2019s name in Cytoscape. In contrast, the \u201cNo network label\u201d option omits both the \u201clabelloc\u201d attribute and the \u201clabel\u201d attribute.http://www.alexander-merz.com/graphviz/). We use JPGD to read the DOT file and create a JPGD data model of the graph or collection of graphs in the file. A JPGD Graph object is created for each graph in the file, a JPGD Node object for each node, and a JPGD Edge object for each edge. Each JPGD object contains the DOT attributes for the graph element they represent.http://www.alexander-merz.com/graphviz/doc.html).For the import function of dot-app, we used Java-based Parser for Graphviz Documents (JPGD), a Graphviz document parser made by Alexander Merz , but a few of the attributes either affect multiple visual properties at once  or a conversion needs to performed on their values  due to the fact that the information is stored differently between the DOT model and the Cytoscape model. If a DOT attribute is assigned a value that does not have an equivalent value for the corresponding Cytoscape visual property, then the DOT attribute is ignored. The \u201cweight\u201d DOT attribute is imported as an Edge table attribute  because no corresponding Cytoscape visual property exists. The DOT attributes listed in File 1 of the Supplementary Material are ignored and have no effect on the visualization in Cytoscape.Node DOT attributes.Edge DOT attributes.The \u201cstyle\u201d DOT attribute. The \u201cstyle\u201d DOT attribute applies to both nodes and edges. The attribute takes a comma-separated list of keywords as its value. These keywords directly affect which Cytoscape visual properties are modified.The \u201cweight\u201d DOT attribute. During the import of a network using dot-app, a weight column is added to the Cytoscape network\u2019s edge table. If the \u201cweight\u201d attribute is supplied for an edge, its value is assigned to the weight column entry for the edge.The The \u201cheight\u201d and \u201cwidth\u201d DOT attributes. In the DOT language, the height and width of nodes are specified in inches. However, the height and width of nodes are specified in points in Cytoscape. During both import and export we handle the necessary unit conversion (1 in = 72 pts) in order to maintain the correctness of the graph.Unsupported DOT features. The following features of Graphviz arenot supported in the import:1. HTML-like Labels2. not supportedexcept the following: triangle, diamond, ellipse, hexagon, octagon, parallelogram, rectangle, rect, box, and square. Msquare, Mcircle, and Mdiamond will be rendered the same as square, circle, and diamond respectively.All node shapes are3. not supportedexcept the following: vee, lvee, rvee, dot, normal, diamond, none, and tee. The arrow shapes odot, onormal, and odiamond will be rendered the same as dot, normal, and diamond respectively.All arrow shapes are4. Edge curves. The value of the \u201cpos\u201d attribute is ignored when it is used as an attribute for edges, so dot-app will render edges only as straight lines between nodes.5. The brewer colors chemes when using the \u201ccolorscheme\u201d attribute.6. The \u201ctapered\u201d and the \u201cbold\u201d edge style keywords7. The \u201cbold\u201d, \u201cdiagonals\u201d, \u201cstriped\u201d, and \u201cwedged\u201d node style keywords8. Default attribute values when grouping nodes with subgraphs. Only the default attribute values set within the root graph are considered.9. Record-based Nodes. The label will not cause the node to become sectioned10. Clusters11. Edges that are rendered as colored parallel lines: These are made by assigning a color list without weights to the \u201ccolor\u201d attribute.12. Edges that are rendered as colored segments in series. These are made by assigning a color list with weights to the \u201ccolor\u201d attribute.13. Gradients applied to the network backgroundUnsupported Cytoscape features. When exporting the network as a GraphViz file, some Cytoscape information is lost because it cannot be represented in DOT format. dot-app does not keep a log of the information that is not transferred to the Graphviz file. The following information is lost:Visual information1. Custom graphicsa. Images on nodesb. Charts on nodes2. Edge bends3. Nested network images contained in nodes4. Arrowhead colors (they will appear the same color as the edge itself)5. Certain line typesa. Dash dotb. Contiguous arrowc. Backward slashd. Separate arrowe. Sinewavef. Vertical slashg. Zigzagh. Forward slashi. Parallel lines6. Label positioninga. Edge labels only go on the midpoint of the edgesb. Node label positions are selected at export7. The V node shape8. Target arrow shapea. Target arrow shape does not appear if set as a default (this was a bug in Cytoscape v3.2 that has been fixed since v3.3)9. All annotationsNon-visual information1. Node group information 2. All table dataDetailed below are two cases for dot-app. The first use case describes how a DOT file can be imported into Cytoscape. The second use case describes how a Cytoscape network can be exported as a DOT file. The DOT file used for import, the Cytoscape session file of the network, and the DOT file generated by dot-app during export are contained in ZIP 1 of theOur first use case details how we would use dot-app to view a Graphviz-created network in Cytoscape. We used Graphviz\u2019s neato utility to create a DOT file with layout information and a PNG of the resulting network. The DOT file is shown below, andgraph toy_example {graph ;node ;   1     ;   2     ;   2 -- 1     ;   3     ;   3 -- 1     ;   3 -- 2     ;   4     ;   4 -- 2     ;   4 -- 3     ;}                                            In this second use case, we export the network ingraph toy_example {bgcolor = \"#FFFFFFFF\"splines = \"false\"outputorder = \"edgesfirst\"esep = \"0\"pad = \"2\"node  edge \"4\u00a762\" \"3\u00a763\" \"2\u00a764\" \"1\u00a765\" \"4\u00a762\" -- \"3\u00a763\" [color = \"#404040FF\"]\"4\u00a762\" -- \"2\u00a764\" [color = \"#404040FF\"]\"3\u00a763\" -- \"2\u00a764\" [color = \"#404040FF\"]\"3\u00a763\" -- \"1\u00a765\" [color = \"#404040FF\"]\"2\u00a764\" -- \"1\u00a765\" [color = \"#404040FF\"]}                                            https://docs.oracle.com/javase/tutorial/2d/text/fonts.html#logical-fonts). It is a font name that the Java Runtime Environment used and that maps to a physical font. When neato encounters the font name, it attempts to find an actual font named \u201cSerif.plain\u201d; if it cannot find one, it uses a default font.In order to prevent labels from appearing cut off, dot-app adds a padding of 2 inches to its output file. The difference in the labels\u2019 font is due to the font chosen in Cytoscape. In the output file shown above, we can see that the fontname attribute for the node default list is set to \u201cSerif.plain\u201d. This font is not an actual font family; rather, it is one of Java\u2019s logical fonts  and wrote our own DOT files. We then ran Graphviz\u2019s neato utility on these files to generate DOT files that contained layout information and PNG files to use as references. We then imported the DOT files to Cytoscape and visually compared the Graphviz-created PNG files to the Cytoscape display to validate the import process of dot-app.For import, we downloaded DOT files from Graphviz\u2019s gallery page (https://github.com/cytoscape/cytoscape-tests/blob/master/docs/Session-Files/Session%20Files.md) into Cytoscape and exported individual networks from these sessions to DOT files, and then used Graphviz\u2019s neato utility to create PNG files from these. We visually compared neato\u2019s PNG output to the Cytoscape display to determine the correctness and completeness of the Cytoscape-to-DOT translation.For export, we loaded Cytoscape test session files . If the test examples do not work with the app there will be issues with real world examples.\u00a0It is stated \"We verified the dot-app import and export functions separately.\u00a0All of the files we used in testing are found in ZIP 2 of the\u00a0Supplementary Material.\" This seems not to be the case. Please fix the issue https://github.com/idekerlab/dot-app/issues/15 [2] The app cannot be build from the provided repository after a clone. This is reported at https://github.com/idekerlab/dot-app/issues/14 Please fix this issue. This is related to my initial review where I reported this issue.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. We are satisfied that the authors have adequately addressed our comments in this new version.We have read this submission. We believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. The article introduces an app to import/export Graphviz (.gv-.dot) files to/from Cytoscape. Since the Graphviz format is of wide usage, the app is very useful to the community. The article is well-written and the user-guide is complete and easy to read.\u00a0 As minor comments I ask more details about which characteristics can be lost passing from a format to another. I tried some network choosing them randomly from internet, and sometimes I lost features that I didn't expect to lose. A table explaining which features are preserved and which not will be very useful in the paper. If there are problem of space maybe the implementation details can be described in supplementary materials and not in the main paper. The table should contains also short comments about the missing features that can be added in the future, and the problem that can be encountered implementing those characteristics that are not of immediate conversion. I think that with these updates the paper is suitable for indexing.I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Thank you Dr. Scardoni for your comment. We will take your valuable suggestions into consideration while we are refining the article. We appreciate your effort in examining the dot-app and the article for us in detail. dot-app is a Cytoscape App that\u00a0enables the inter-conversion of Graphviz and Cytoscape formatted files. As far as we are aware no similar application exists and this is therefore a potentially useful development. We found no problems with the usage of the app; it integrates well into Cytoscape, and can convert back and forth between formats without issue aside from the loss of information which is documented in the article. The code is readable and very well commented. We did have an issue when compiling from source, however. The\u00a0DOT\u00a0parsing\u00a0jar from Alex Merz\u00a0isn't being included properly when Maven builds the project. The major concern we had was that the concept for the application is really very straight-forward and following on from this, its functionality is therefore pretty limited. We wondered initially whether there was really a need for such an application, however, dot-app has been downloaded >1200 times so there is obviously a market for the tool. A remaining question, however, is whether the app justifies a 10-page paper? The paper itself reads a bit more like documentation and we would have preferred to have seen a more concise paper introducing the concepts together with more detailed documentation. We think that the paper could also benefit from a better discussion in the introduction of the motivation behind the development of dot-app. Can you give examples where one would want to create a network in one format and then convert it to another? How hard would it be to manually re-create the visualisation in Graphviz/Cytoscape? The application also appears very reliant on the parser developed by Alex Merz (this is not referenced properly). It would be good to clarify how much of the functionality is provided by this parser and how much is extended by dot-app. A key limitation of the app is that many of features of either format are lost when converting between them. This is because there isn\u2019t an equivalent feature in the other format. It is good that the authors are clear about which ones cannot be converted but this problem still means that manual intervention would likely be needed to customise the desired style. One thing that could be improved is how the implicit default values are handled by dot-app. Couldn\u2019t you set reasonable values for these if they are not specified in a particular visualisation to enable more faithful conversion of the visualisation style? One final concern is that it is very likely that the visual styles in both Graphviz and Cytoscape will continue to evolve over time. How will dot-app keep pace with these changes? Have the authors considered trying to get the Graphviz and Cytoscape communities to adopt at least the equivalent visual style features in both applications? Or at least to indicate in the Cytoscape and Graphviz documentation what is the equivalent feature (when there is one). Minor comment: Under Operation it would be good to start by explaining how to install the App (for novice Cytoscape users).We have read this submission. We believe that we have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however we have significant reservations, as outlined above. Thank you Dr. David Lynn and Dr. John Salamon for your comments. We completely agree with your suggestions, and we'll add those  to our article. Please expect to see the changes you recommended in the second version of our article. The article \"dot-app: a Graphviz-Cytoscape conversion plug-in\" is well written and describes background, implementation and use of the application in a comprehensible way. ## major comments \"The differences that arise between the Graphviz network and the Cytoscape network stem from how the two programs handle implicit default values. If a DOT attribute is omitted from the DOT file when using a Graphviz utility, an implicit default value for that attribute is used. The list of DOT attributes and their default values can be found on the Graphviz website (http://www.graphviz.org/content/attrs.html).\" -> The implicit dot default values should be used as default values in dot-app for the Cytoscape styles. Users of the dot language rely on the default values and expect rendering tools to use them. -> Especially, in combination with dot-app writing the Cytoscape default values in the exported dot this results in unnecessary changes of the graph rendering in the round trip (dot -> cytoscape -> dot). This round trip should introduce minimal changes to the rendering. Dot default values should be used and the respective text passage and figure be updated. ## minor comments >>> In the implementation all visual styles are hard coded in the visual mapping via bipasses. It would be better to create node attributes for the dot attributes and subsequently use them in visual styles. In this way users have access to the dot attributes, can use them in other visual mappings, create derived node attributes from them, or use them in analyses. >>> It is unclear how dot height and width are transformed to Cytoscape node height and width. There is some scaling factor, but how this is actually handled should be described in the manuscript. What information is lost in the roundtrip due to scaling. For instance height = \"0.486111\",width = \"1.041667\" result in height > 40 in Cytoscape. >>> The dot node font color is not rendered correctly. See: https://github.com/idekerlab/dot-app/issues/7 >>> Saving as *.gz always adds the .dot extension so that files are called *.gz.dot. If the user selects \"name.gz\" the file should be saved as 'name.gz', not as 'name.gz.dot'. >>> p5 \"For the import function of dot-app, we used Java-based Parser for Graphviz Documents (JPGD), a Graphviz document parser made by Alexander Merz(5)\" -> reference missing/wrong. There should be a reference for (5). >>> p5 \"After JPGD creates the model objects, dot-app creates a corresponding \" -> something wrong with first half-sentence, probably better: \"After JPGD has created the model objects, ... >>> p6 \"All other DOT attributes are ignored during the import process and have no effect on the visualization in Cytoscape.\" If the ignored DOT attributes can be listed, state them in the manuscript as list. This is very helpful to see what information should not be used in dot files if one wants full Cytoscape support of the file. If the unsupported attributes are only the features listed in \"Unsupported DOT features\" than this should be clearly stated. >>> p2 \"The store contains nearly 300 apps that ...\" At the state of review this is already >= 300. Add a date to the statement: -> The store contains nearly 300 apps (October 2016) that ... >>> Add reference for graphviz software/url see for instance http://www.graphviz.org/content/citing-graphviz-paper The preferred citation is @ARTICLE{Gansner00anopen, \u00a0\u00a0\u00a0 author = {Emden R. Gansner and Stephen C. North}, \u00a0\u00a0\u00a0 title = {An open graph visualization system and its applications to software engineering}, \u00a0\u00a0\u00a0 journal = {SOFTWARE - PRACTICE AND EXPERIENCE}, \u00a0\u00a0\u00a0 year = {2000}, \u00a0\u00a0\u00a0 volume = {30}, \u00a0\u00a0\u00a0 number = {11}, \u00a0\u00a0\u00a0 pages = {1203--1233} } and the URL is www.graphviz.org >>> p8 use cases Provide the *.gv files and Cytoscape files of the use cases in the supplement. This will provide the necessary materials to follow the provided examples. I tried to save the files from the pdf which did not work (due to line breaks in pdf), copying the examples from the HTML version of the manuscript worked. Adding the two example files to the supplementary information will improve this. >>> p9 testing Provide the url/repository for the test files and test results. There should be a page which shows all the comparison images with the respective dot files. In the article it is mentioned that this exists, but no resource is given for the test files and test results. >>> p9 conclusion \"This article describes the dot-app Cytoscape app, which enables a user to import a DOT-formatted **here** into Cytoscape\" -> word missing >>> p9 conclusion \"we recognize that future versions of Cytoscape may introduce new visual effects\" -> formulation. Better: 'visual shapes and styles\", visual effects are something else. >>> p9 conclusion \"we recognize that future versions\u00a0of Cytoscape may introduce new visual effects  that present opportunities for rendering DOT files more\u00a0truly or for the loss of formatting information if the DOT format\u00a0cannot represent them.\" -> second half of sentence does not make sense (... or for the loss of formating). Please reformulate to clarify what is meant. >>> The github release corresponding to the zenodo code is missing. The latest github release is 0.9.1 on 11.September, the zenodo was created in February. This makes it difficult to try to build the app from the mentioned source code, by checking out a corresponding tag. Which version is packed in zenodo? 0.9.2 ? Also the current app version in the app store is 0.9.3, but there is no 0.9.3 release on github. Please create a github release which is corresponding to the zenodo release and the mentioned code state of the publication. >>> I was unable to build the app from latest source code. The app is working via the app store, but in addition it should be possible to build the latest source code. https://github.com/idekerlab/dot-app/issues/8 git clone https://github.com/idekerlab/dot-app.git mvn clean install results in [INFO] Compiling 16 source files to /home/mkoenig/git/dot-app/target/classes [INFO] ------------------------------------------------------------------------ [INFO] BUILD FAILURE [INFO] ------------------------------------------------------------------------ [INFO] Total time: 7.250 s [INFO] Finished at: 2016-10-31T12:48:57+01:00 [INFO] Final Memory: 21M/238M [INFO] ------------------------------------------------------------------------ [ERROR] Failed to execute goal org.apache.maven.plugins:maven-compiler-plugin:2.0.2:compile (default-compile) on project dot-app: Compilation failure: Compilation failure: [ERROR] /home/mkoenig/git/dot-app/src/main/java/org/cytoscape/intern/read/reader/NodeReader.java: error: package com.alexmerz.graphviz.objects does not exist [ERROR] ... This should be fixed, I would recommend to setup some Continous Integration with travis to make sure the latest version always builds. see\u00a0https://github.com/idekerlab/dot-app/issues/8I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Thank you so much Dr. Matthias K\u00f6nig for your insightful comments. We really appreciate your efforts of carefully testing the dot-app features and throughly examining our article. We thank you for bringing the problems you found to our attention. While waiting for another referee's upcoming peer review report, we will take a close look into the issues and address them for our next version. This article describes a new Cytoscape plugin called \u201cdot-app\u201d designed for the import and export of Graphviz files conforming to the DOT format for representing graph topologies, layouts and formatting. Graphviz is a popular set of open source software tools initiated at the AT&T Labs Research that can generate or process DOT files. Many other software tools are using Graphviz to represent all kinds of graphs. The DOT language support visual features and attributes that are not currently included by Cytoscape network formats. There is currently no Cytoscape plugin for the import and export of networks to the DOT language. Therefore the dot-app plugin may be useful to convert and import biological networks, and might be very interesting for the large community of Cytoscape users. The article is globally clear, well-organized and logically structured. I particularly appreciated the efforts of the authors to explain the details of the conversion process and exactly what kind of visual properties are imported and exported, including the properties that are not supported.Add a table for at least some of the main visual features and attributes supported by the DOT format and indicate which ones are supported by XGMML/GraphML. The sentence mentioning the differences in the introduction section is too vague.Compile also in a small table some examples of applications (related to biology or not) that produces or consumes DOT files. Here also the paragraph discussing this in the introduction section is quite vague. I would suggest minor improvements to the article that could make it more precise and valuable for the readers.The reference to the JPGD parser do not appear in the bibliography.A few sentences on how to install the app in Cytoscape might be helpful. Minor comments:I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. Thank you Dr. Bonnet for your valuable comments. We will look into the possible improvements and minor issues you brought up, and fix them in our next version. Again, we really appreciate your \u00a0detailed observations!"}
+{"text": "A common goal in data-analysis is to sift through a large data-matrix and detect any significant submatrices  that have a low numerical rank. We present a simple algorithm for tackling this biclustering problem. Our algorithm accumulates information about 2-by-2 submatrices  within the data-matrix, and focuses on rows and columns of the data-matrix that participate in an abundance of low-rank loops. We demonstrate, through analysis and numerical-experiments, that this loop-counting method performs well in a variety of scenarios, outperforming simple spectral methods in many situations of interest. Another important feature of our method is that it can easily be modified to account for aspects of experimental design which commonly arise in practice. For example, our algorithm can be modified to correct for controls, categorical- and continuous-covariates, as well as sparsity within the data. We demonstrate these practical features with two examples; the first drawn from gene-expression analysis and the second drawn from a much larger genome-wide-association-study (GWAS). and subsets of patients\u2014a problem referred to as \u2018biclustering\u2019. In this paper we present a new biclustering method which can scale up efficiently to handle large genomic data sets, such as GWAS-data. Our method is quite accurate, outperforming current \u2018spectral\u2019 biclustering methods for many problems of interest. Perhaps most importantly, our method can be corrected for many features of experimental design, such as controls, covariates and sparsity\u2014all of which are especially important when analyzing real data sets.An important problem in genomics is how to detect the genetic signatures associated with disease. When a disease is caused by a single well-defined biological mechanism, the genetic signature often involves a handful of genes present across the majority of the diseased patients. On the other hand, when a disease is complicated or poorly understood there may be many possible biological mechanisms at play. Any genetic signatures associated with such a disease may involve multiple genes, and each signature might only manifest across a subset of the diseased patients. Finding the signatures responsible for this heterogeneity requires searching through subsets of genes  Many applications in data-analysis involve some form of \u2018biclustering\u2019\u2014also referred to as co-clustering, two-mode clustering, two-way clustering, block clustering, and coupled two-way clustering, to name a few . BroaIn this paper we\u2019ll present a simple method for biclustering which is well-suited for gene-expression and genome-wide-association-study (GWAS) data. We refer to our method as \u2018loop-counting\u2019, because it accumulates information about 2 \u00d7 2 submatrices within the data-array; we refer to these 2 \u00d7 2 submatrices as \u2018loops\u2019. We establish a connection between our loop-counting method and spectral methods, using both analysis and simulation-studies to describe the regimes where our method performs well. We demonstrate the efficacy of our loop-counting method by applying it to a gene-expression data-set and a GWAS data-set, using gene-enrichment analysis as a form of validation.One of our main goals is to ensure that our loop-counting method is practical and capable of accommodating the issues that arise when analyzing real experimental data. We emphasize that our method can be corrected for many features of experimental design, such as controls, covariates and sparsity\u2014all of which are especially important when analyzing GWAS data sets (which commonly aggregate batches of patients taken from across the world). With this goal in mind, we\u2019ll briefly delineate some features of our approach, contrasting them against some of the better-known methods for biclustering this kind of data.During our discussion below we\u2019ll often refer to the appendices in the Supporting Information see  Text, whM \u00d7 N data-array D comprising N genetic-measurements (which we\u2019ll refer to as \u2018genes\u2019) taken across M patients. Within this context, an m \u00d7 n \u2018bicluster\u2019 would correspond to a rectangular submatrix associated with m patients and n genes that\u2014together\u2014share a special structure.Within the field of bioinformatics there are a variety of approaches to biclustering, many of which differ in the types of structures they try and find, their assumptions regarding the \u2018noise\u2019 that might obscure these structured elements, and their goals in classifying the data Types of structure to search for: Several methods attempt to find biclusters containing mostly \u2018large\u2019 or \u2018small\u2019 values; i.e., comprising a subset of genes which are differentially-expressed relative to the rest of the patients in D , a, a19], aWhile appropriate for idealized situations such as the planted-bicluster problem, the simple loop-counting algorithm described above is not immediately applicable to real data. The reason is that the loop-scores in Eqs MD of the patients exhibit a certain disease, whereas the other MX patients do not . Instead of arranging our data into a single M \u00d7 N array, we will divide our data into an MD \u00d7 N array D describing the cases, and another MX \u00d7 N array X describing the controls. As is typical for gene-expression data, there will likely exist large subsets of genes which are correlated across large subsets of the population\u2014including both D and X\u2014without being particularly related to the disease. Such genes might include, e.g., genes related to development, or \u2018housekeeping\u2019 genes that are strongly coexpressed in most patients.To describe this strategy in more detail, we\u2019ll first focus on a situation involving cases and controls. Specifically, let\u2019s imagine that we are analyzing gene-expression data where largest biclusters, we would find these common genetic signatures, which are not related to the disease, and thus not of interest. Instead, we would like to search for biclusters which are restricted to a subset of the case-patient-population in D and which exhibit correlations which are not found in the control-population X. Such case-specific biclusters are more likely to be related to disease mechanisms.If we were to simply search for the D-only algorithm above. In Step-0 we now need to binarize both D and X. In Step-1 we need to calculate the loop-scores in a slightly different way. Given any fixed case-row j \u2208 D, there will be two types of loops that contribute to the score: (i) loops that are contained within D, and (ii) loops that travel through X. If row-j were part of a bicluster which was restricted to D, then we would expect row-j to participate in an abundance of rank-1 loops of type-(i), but not of type-(ii). Based on this intuition, we score the first type of loop positively if it is rank-1 and negatively if it is rank-2. In addition, we score the second type of loop the other way; negatively if it is rank-1 and positively if it is rank-2. This strategy produces control-corrected row- and column-scores of the form:We can achieve this goal by slightly modifying \u2018Step-0\u2019 and \u2018Step-1\u2019 of the These control-corrected loop-scores are designed so that biclusters which equally straddle both the cases and the controls will\u2014on average\u2014produce no signal, while biclusters which are significantly concentrated within the cases will still produce a signal. Biclusters which are fully case-specific will generate signals that are (on average) as large as they would have been using our original (uncorrected) loop-scores. A more detailed explanation of these control-corrected loop-scores, as well as corroborating numerical experiments, can be found in sections A similar principle can be used to correct for categorical-covariates, multidimensional continuous-covariates, as well as sparsity. We briefly discuss these corrections in the Methods section, deferring the details to sections In the following subsections we briefly present two examples drawn from genomics. These examples serve as proofs-of-principle for our method, and demonstrate that our method functions in practice.http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE48091). See \u2018Example-1b\u2019 in section Our first example is taken from the GSE48091 data-set available from the gene-expression-omnibus (found at N = 16738 gene-expression measurements (referred to later as \u2018genes\u2019 for simplicity) collected across 506 patients, each diagnosed with breast-cancer. Of these patients, MD = 340 were \u2018case\u2019-patients that developed distant metastatic disease. The remaining MX = 166 were \u2018control\u2019-patients that did not. The data-set is illustrated in The subset of data that we use comprises We\u2019ll use our control-corrected loop-counting algorithm to search this data-set for case-specific biclusters\u2014namely subsets of genes that are structured in some way across a significantly large subset of the case-patients, while not being similarly structured across the control-population. These case-specific biclusters will have the potential to pinpoint genes useful for diagnosis and discrimination between case and control status.m = 45 of the MD = 340 cases and n = 793 of the N = 16738 genes\u2014that was embedded in the case-matrix and discovered using our algorithm. This bicluster consists of genes that, taken individually, are neither significantly over-expressed nor under-expressed\u2014relative to the control population. Instead, these 793 genes are significantly co-expressed  across a significant fraction of the case population (in this case 45/340 \u223c 13% of the cases), without being as significantly co-expressed across a comparable fraction of the control population. While a little difficult to see in cj be the pearson\u2019s-correlation between the jth-patient in the bicluster and v. If we use the absolute value |cj| as a measure of \u2018alignment\u2019, most of the rows are aligned (with the stereotyped pattern) at a value of 90% or more.Some of our results are shown in cj| that is greater than 90%; most only exhibit an alignment around 0%\u221250%. This statement can be further quantified as follows: The distribution of alignments |cj| for the patients in the bicluster is significantly different than the distribution of alignments for the controls; the AUC  for these two distributions is 98%, meaning that there is a 98% chance that a randomly drawn patient from the bicluster will have a higher alignment than a randomly drawn control. Note that this AUC only implies a high prediction accuracy when discriminating cases within the bicluster from the controls; this AUC does not translate into high case/control prediction accuracy overall.To illustrate that this stereotyped co-expression pattern is indeed case-specific , we replot the bicluster at the top of Finally, we can ask: How significant is this bicluster? As described in more detail within the Methods, this bicluster has a P-value of \u2272 0.008. We obtain this P-value by comparing this bicluster against the distribution of biclusters obtained under a suitable \u2018label-shuffled\u2019 null-hypothesis\u2014i.e., formed from shuffling the case-vs-control labels , DNA-replication (3e-8), chromosome segregation (p = 2e-5) and many more; including several pathways that are likely to play a role in the development of cancer. See Supplementary-material If this were true, we would expect many of these genes to serve similar functions or affect the same pathway. This is indeed the case: a gene-enrichment analysis performed on these Our second example is a subset of a Genome-Wide-Association-Study used with permission from the Bipolar Disorders Working Group of the Psychiatric Genomics Consortium (PGC-BIP) Due to dN = 276768 alleles with varying minor-allele-frequency genotyped across 16577 patients. These patients fall into two phenotypic categories: 9752 are neurotypical, whereas the remaining 6825 exhibit a particular psychiatric disorder. For this example we\u2019ll try and find a signal within the neurotypical patients that is not shared by those with the disorder; We\u2019ll use the phenotypic information to divide the patients into MD = 9752 cases and MX = 6825 controls. Note that, within this example, our nomenclature is non-standard; neurotypical patients are typically referred to as \u2018controls\u2019 and not cases. The reason we deviate from this standard is because, below, we will try to find a bicluster within the neurotypical patients that does not extend to include the remaining patients. In order to remain consistent with our notation and equations throughout the rest of the manuscript .within the bicluster from the controls; this AUC does not translate into high case/control prediction accuracy overall. Nevertheless, as described in more detail in section If we calculate the distribution of alignments across individuals in this bicluster and compare them to the distribution of alignments across the controls , we obtain an AUC of > 99.75%. As in Example-A, this AUC by itself only implies that the pattern within the bicluster is significantly different than the pattern outside the bicluster; it does not imply that the bicluster itself is statistically significant. That is to say, this AUC only implies a high prediction accuracy when discriminating cases without correcting for the continuous-covariates, then we would find spurious biclusters involving patients that were highly concentrated in just a few regions of covariate-space , metal-ion transmembrane transport (p = 5.7e-4), calcium-ion binding (p = 1.2e-3), GTPase-activation (p = 2.2e-3), ion-gated channel activity (p = 3.3e-3), calcium-ion transport (p = 4.3e-3), voltage-gated channel activity (p = 1.0e-2), calcium-signaling (p = 1.1e-3), long-term-potentiation (p = 1.1e-3) and glutamatergic-synapses (p = 7e-3). See Below we\u2019ll briefly describe our approach to correcting for categorical- and continuous-covariates. In each situation we\u2019ll discuss the simplest possible case, involving case-patients only and disregarding controls. The full details of our method\u2014including how to combine the control-correction with covariate- and sparsity-corrections\u2014is given in section If the patients are drawn from different categories , then it is typically important to \u2018correct\u2019 for the effect of this categorical-covariate, and to find biclusters that are independent of covariate-category. In this section we discuss the simplest situation involving only two covariate-categories of equal size .Within the context of this scenario, we would like to ignore biclusters that include patients from only one gender, favoring instead biclusters that include a reasonable mixture of patients from both genders. Our strategy is to design a loop-score which tracks the loops associated with the different covariate-categories, comparing them against one another. This loop-score will demote the signal produced by any bicluster down to the signal that would be produced by that bicluster\u2019s \u2018balanced component\u2019 . As a result, \u2018imbalanced\u2019 biclusters that are concentrated in one gender will produce almost no signal. At the same time, \u2018balanced\u2019 biclusters that include an equal number of males and females will still produce a strong signal .j is given by:D into male-patients \u2018D1\u2019, and female-patients \u2018D2\u2019, and the fractions p = (MD1 \u2212 1)/(M \u2212 1) and q = (MD2)/(M \u2212 1) are the fraction of other males and females, respectively. The covariate-corrected loop-score for a female patient is defined analogously.In the simplest scenario (ignoring controls), the covariate-corrected loop-score for any male patient \u03b111, \u03b112, \u03b121, \u03b122 are defined to be Regarding the column-scores:A more detailed explanation of this construction, as well as an extension to the general case with three or more covariate-categories, is given in section all the covariate-categories. An example might be a data-set collecting patients across Icat separate studies. In such a scenario one might be interested in biclusters that include patients from at least Ireq < Icat of these individual studies. Our general method for categorical-covariate-correction requires the user to specify this required Ireq, which is used in defining our loop-scores. Details are given in section One of the important aspects of the general case is that, often, one is interested in biclusters that straddle many covariate-categories, even if they are not fully balanced across NT-dimensional vector of \u2018mds-components\u2019, serving as a proxy for the genetic similarity of those patients\u2019 ancestors [For certain applications each patient is associated with a high-dimensional continuous-covariate. For example, in genome-wide association studies, each patient is often equipped with an ncestors , 38. ConOur basic strategy for continuous-covariate correction will be similar to our strategy above. We\u2019ll design a loop-score which tracks the continuous-covariates associated with each loop, comparing them against one another. This loop-score will demote the signal of any imbalanced biclusters down to 0. At the same time, balanced biclusters will produce a signal that is\u2014on average\u2014as large as it would have been without covariate-correction.T the M \u00d7 NT matrix containing the continuous-covariates . The sum x\u230b = max, and \u03ba2 is a parameter that depends on NT .In the simplest scenario , the covariate-corrected loop-scores are given by:\u03ba2 along with corroborating numerical experiments, is given in section A more detailed explanation of this construction, including the calculation of Up to this point we\u2019ve assumed that\u2014after binarization\u2014each column of the data-matrix has a comparable number of positive and negative entries. This assumption is often valid when dealing with gene-expression data , but not when dealing with genotyped data. Indeed, single-nucleotide-polymorphisms (SNPs) can often involve minor-allele-frequencies (MAFs) that are quite small , giving rise to a large imbalance between \u00b11-entries in each column of the data-matrix.If a subset of columns in the data-matrix has a surplus of, say, negative entries, then that portion of the data-matrix will be \u2018sparse\u2019 . Such a sparse region is likely to contain large submatrices consisting of mostly negative entries, simply due to their abundance. The loop-counting algorithm we\u2019ve described so far will typically focus on these large submatrices, even though they are not statistically significant. The reason for this is that the loop-score above assumes that each loop carries the same weight, regardless of whether or not that loop comprises positive or negative entries.D; This normalization rescores each loop so that \u00b11-entries that are otherwise abundant do not add much to the score. Conversely, entries that are otherwise rare add more to the score.It is straightforward to correct for sparsity by \u2018normalizing\u2019 each column of k of the data-matrix D has sparsity coefficient pk, and setting qk = 1\u2212pk, we calculate the sparsity-corrected loop-scores as follows (ignoring controls and covariates for now):N \u00d7 1 vector of means \u03b1k = pk \u2212 qk, M \u00d7 1 vector of all ones. See section Assuming that column-In the previous sections we\u2019ve discussed modifications to our algorithm that correct for controls, covariates and sparsity. These can be combined in the following order to produce a single loop-score that corrects for all these features simultaneously:Correct for sparsity.Correct for continuous covariates.Correct for categorical covariates.Correct for cases versus controls.The motivation underlying these choices, as well as computational details and corroborating numerical experiments, are found in section DD\u22baDD\u22ba in the D-only situation. These trace-lists allow us to determine a p-value for our bicluster without applying a threshold to determine the \u2018boundary\u2019 of the bicluster.In addition to listing the rows and columns in the order that they were eliminated, our loop-counting algorithm also produces a list of the average row- and column-scores taken across the remaining data-matrix at each iteration. We refer to these average row- and column-scores as row- and column-traces, as they are both proportional to the trace of To describe this process, let\u2019s focus on Example-A . In this example we are comparing case-patients to control-patients. The row- and column-traces in this case can be rescaled to lie between \u22122 and +2 . These traces provide a measure of how tightly correlated the remaining data-matrix is at each iteration. More specifically: if, after sufficiently many iterations, the row- or column-traces become large , then the remaining rows and columns should form a highly correlated low-rank bicluster.Our typical hypothesis  is that there exists some disease-related structure in the case-patients that is not exhibited by the control-patients. This is in contrast to the null-hypothesis (H0) in which the case- and control-labels are actually arranged randomly and have no disease-related structure. Under this null-hypothesis the traces we observe after running our algorithm on the original data should be similar to the traces we would find if we were to shuffle the case-control labels randomly (across patients). To draw a sample from this null-hypothesis H0, we shuffle the case-control labels of the patients indiscriminantly while retaining the same number of cases and controls. If we were to correct for covariates, then we would restrict our null-hypothesis slightly (H0x) so that the random-shuffles respect the covariates. For example, if we were correcting for gender as a categorical-covariate, we would shuffle the labels of case-males only with control-males, and shuffle the labels of case-females only with control-females.For each label-shuffled trial we rerun our algorithm, and collect the output. Each trial does not depend on any of the other trials, and they can all be processed in parallel. This library of label-shuffled traces produces a distribution associated with H0 (or H0x). We use this label-shuffled distribution to calculate a p-value for the traces produced by the original data. An illustration along these lines is shown in Figs A full description of this procedure, as well as an analogous procedure used to find a p-value for Example-B, can be found in section This paper has focused so far on the detection of low-rank biclusters within a larger data-matrix. Our loop-counting method does a reasonable job of locating these low-rank biclusters , and even look for \u2018triclusters\u2019. The first two of these topics are explained in more detail in sections N measurements taken across M patients\u2014doesn\u2019t suffice. For example, in a clinical study there may be M patients, each of which are subjected to P different kinds of treatments . For each of these P treatments, N different variables may be measured for each patient. Within this paradigm, the data isn\u2019t best represented as a 2-dimensional array , but rather as a 3-dimensional array  comprising both rows and columns, as well as \u2018layers\u2019. In formal terms, we imagine our data arranged into an array D of dimension M \u00d7 N \u00d7 P, where Dj,k,l corresponds to the kth measurement of the jth-patient as they undergo therapy l.There are often situations where the data-paradigm we\u2019ve assumed\u2014involving Within this 3-dimensional array, it is often prudent to search for subsets of patients that exhibit some kind of simple structure across a subset of measurements as well as a subset of treatments. Such a \u2018tricluster\u2019 would correspond to a \u2018sub-cube\u2019 of the data, rather than simply a submatrix. The techniques we have discussed in the main text can readily be extended to search for these kinds of objects as well.D, sending each entry to either +1 or \u22121, depending on its sign. Once we binarize D, we can calculate the following scores:B with high probability as long as they are sufficiently large and sufficiently low-rank.In the simplest case , we first binarize the data-cube D. However, unlike the simpler situation discussed in the main text, D is a 3-dimensional array (and not merely a matrix). Consequently, there are 3 different kinds of loops within D, each traversing a different pair of array-dimensions .The reason this process works is that\u2014as before\u2014the scores accumulate the ranks of the various loops within ions see . Any looSlightly more detail, along with numerical experiments, can be found in section S1 DataThis spreadsheet contains the full list of pathways produced by a gene-enrichment analysis of the bicluster shown in the first example in the Supplementary-text (involving gene-expression data). To perform this gene-enrichment analysis we used \u2018Seek\u2019. Each page of this spreadsheet lists the enrichment results using one of the 11 different gene-ontology databases available within the \u2018Seek\u2019 software.(XLSX)Click here for additional data file.S2 DataThis spreadsheet contains the full list of pathways produced by a gene-enrichment analysis of the bicluster shown in Example-A in the Main text (involving gene-expression data). To perform this gene-enrichment analysis we used \u2018Seek\u2019. Each page of this spreadsheet lists the enrichment results using one of the 11 different gene-ontology databases available within the \u2018Seek\u2019 software.(XLSX)Click here for additional data file.S3 DataThis spreadsheet contains the full list of pathways produced by a gene-enrichment analysis of the bicluster shown in the Example-2 in the Supplementary-text (involving gene-expression data). To perform this gene-enrichment analysis we used \u2018Seek\u2019. Each page of this spreadsheet lists the enrichment results using one of the 11 different gene-ontology databases available within the \u2018Seek\u2019 software.(XLSX)Click here for additional data file.S4 DataThis spreadsheet contains the full list of pathways produced by a gene-enrichment analysis of the bicluster shown in Example-B in the main text (involving GWAS-data). To perform this gene-enrichment analysis we used \u2018Seek\u2019. Each page of this spreadsheet lists the enrichment results using one of the 11 different gene-ontology databases available within the \u2018Seek\u2019 software.(XLSX)Click here for additional data file.S1 TextThe first part of this 2-part document describes in more detail the examples shown in the main text. This document also contains a more detailed analysis of our method.(PDF)Click here for additional data file.S2 TextThe second part of this 2-part document describes in more detail the examples shown in the main text. This document also contains proofs of certain inequalities, and a comparison with a simple spectral method.(PDF)Click here for additional data file.S1 Source CodeThis archive contains Matlab source code for our loop-counting methods, along with a tutorial  which will guide users through our our first example (involving gene-expression data).(GZ)Click here for additional data file.S2 Source CodeThis archive contains C source code for our loop-counting methods, along with several drivers (written in Matlab) which allow users to replicate each of our numerical experiments (shown in the main text and supplementary information).(GZ)Click here for additional data file."}
+{"text": "In particular, a method for rapidly extracting pairs of l-mers is designed, which can be used not only for PairMotifChIP, but also for other DNA data mining tasks with the same demand. Experimental results on the simulated data show that the proposed algorithm can find motifs successfully and runs faster than the state-of-the-art motif discovery algorithms. Furthermore, the validity of the proposed algorithm has been verified on real data.Identifying conserved patterns in DNA sequences, namely, motif discovery, is an important and challenging computational task. With hundreds or more sequences contained, the high-throughput sequencing data set is helpful to improve the identification accuracy of motif discovery but requires an even higher computing performance. To efficiently identify motifs in large DNA data sets, a new algorithm called PairMotifChIP is proposed by extracting and combining pairs of  A DNA motif is a conserved pattern occurring in the regulatory region of DNA sequences with small mutations . All occThough very important, motif discovery is a challenging computational task. Given a set of DNA sequences, (i) the motif and its instances are unknown; (ii) each of the input DNA sequences is long with hundreds of bases, while the motif is short, generally 5 to 25 bases . In addiCurrently, there are a lot of motif discovery algorithms to deal with small-scale data sets, such as Weeder , PairMotThis paper mainly focuses on motif discovery algorithms for high-throughput sequencing data sets. According to motif representation, the algorithms can be divided into two categories. The algorithms in the first category represent motifs as words. Some of these algorithms, such as F-motif  and weedThe second category covers the discovery algorithms representing motifs as position weight matrixes (PWMs). A set of aligned sites of the same length in the input sequences can form a PWM. These algorithms often select some initial PWMs with certain means and then update each PWM iteratively until it reaches the maximum score. MEME-ChIP  is a well-mers in the input with relatively small Hamming distance. Comparisons with the state-of-the-art motif discovery algorithms show that the proposed algorithm can find motifs successfully with the shortest running time. Also, the validity of the proposed algorithm has been verified on real data.In order to efficiently identify motifs in large DNA data sets, we propose a new algorithm, which identifies motifs by extracting and combining pairs of l-mers, we are referring to two l-mers that come from two distinct sequences.The notations frequently used in this paper are summarized in the Notations. When we say a pair of Nmip. It is calculated by Almost all de novo motif discovery algorithms make identification based on the fact that the motif instances of the same motif are similar to each other. In other words, the motif information contained in the input sequences is presented by the similarity among motif instances. In addition to the degree of similarity among motif instances, the motif information also depends on the number of pairs of motif instances contained in the input sequences, denoted by t. The basic idea is to extract some pairs of l-mers in the input, making them contain at least one pair of motif instances, and then refine each pair of l-mers to get motifs. Because of the small value of Nmip, limited motif information can be obtained while retaining a large amount of disturbance information. Thus, in order to ensure good identification accuracy, exhaustive methods based on pattern-driven ideas are used for refinement, which has a poor time performance.In our previous work, PairMotif  and Pairl-mers in the input. Since the value of Nmip under large data sets is significantly greater than that under traditional promoter data sets, the advantages are as follows: (i) the extracted pairs of l-mers contain sufficient pairs of motif instances and (ii) it can be easier to filter out most of the random overrepresented pairs of l-mers; namely, we can distinguish most of the pairs of motif instances and random overrepresented pairs of l-mers by probabilistic analysis \u2013(4)), filtering pairs of l-mers (lines (5)\u2013(9)), and combining l-mers (lines (10)\u2013(13)). Next, the technical details of the three steps are described in detail.The overall algorithm of PairMotifChIP is shown in k so that we extract all pairs of l-mers x and x\u2032 in the input satisfying dH \u2264 k and design an efficient algorithm to extract pairs of l-mers.In this step, we need to determine the value of a threshold pi denote the probability that the Hamming distance between two random l-mers is no more than i. Let Ei denote the expectation of the number of pairs of l-mers x and x\u2032 in two n-length DNA sequences satisfying dH \u2264 i. Let k is determined by  \u2264 k, the simplest way is to traverse each pair of l-mers x and x\u2032 and calculate the Hamming distance dH separately. The time complexity of this method is O(n2l). Yu et al. , stores min \u2212 dH + 1 \u22ef i], s\u2032[j \u2212 min\u2061 + 1 \u22ef j]), where min is the smaller one of two integers. After calculating M, the Hamming distance between the two l-mers s[i \u2212 l + 1 \u22ef i] and s\u2032[j \u2212 l + 1 \u22ef j] can be obtained; namely, dH = l \u2212 .In order to handle large data sets efficiently, a good time performance of extracting pairs of u et al.  proposedl-mers with Hamming distance no more than k. That is, we do not need to calculate Hamming distance for all pairs of l-mers. If the Hamming distance between s[i \u2212 l + 1 \u22ef i] and s\u2032[j \u2212 l + 1 \u22ef j] is greater than k, it can be concluded that, for 0 \u2264 h < dH \u2212 k, the possibly smallest Hamming distance between s[i \u2212 l + 1 + h \u22ef i] and s\u2032[j \u2212 l + 1 + h \u22ef j] is still greater than k. Thus, after calculating the Hamming distance between s[i \u2212 l + 1 \u22ef i] and s\u2032[j \u2212 l + 1 \u22ef j], we can go directly to verify the Hamming distance between s[i \u2212 l + 1 + H \u22ef i] and s\u2032[j \u2212 l + 1 + H \u22ef j], where H is the skipped size calculated byIn this paper, we design a more efficient method. We only care about the pairs of s| = |s\u2032| = 20, \u2009l = 5, \u2009k = 1. First, convert the two DNA sequences s and s\u2032 into binary strings B and B\u2032. Then, fixing B, move B\u2032 from left to right gradually 2 bits each time and simultaneously do the exclusive OR for the overlapped substrings of B and B\u2032 with length equal to or greater than 2l; xor denotes the exclusive OR of the overlapped substrings of B and B\u2032 corresponding to s[i \u22ef j] and s\u2032[i\u2032 \u22ef j\u2032], where j \u2212 i = j\u2032 \u2212 i\u2032. Finally, extract pairs of l-mers with Hamming distance no more than k by traversing the exclusive OR xor for each overlapped part of B and B\u2032. Specifically, for each r\u2009(l \u2264 r \u2264 j), we look up a table [l-mers s[i + r \u2212 l \u22ef i + r \u2212 1] and s\u2032[i\u2032 + r \u2212 l \u22ef i\u2032 + r \u2212 1], which is equal to the number of 2 bits that is not 00 in xor. During the traversal, we use  denote the number of l-mers in the input sequences with Hamming distance no more than k from x in random case.For an arbitrary x, let occm(x) denote the number of motif instances in the input sequences with Hamming distance no more than k from x in random case.For an arbitrary motif instance x) denote the number of l-mers in the input sequences with Hamming distance no more than k from an l-mer x. In the process of extracting pairs of l-mers, we can easily record occ(x) for each l-mer x in the input sequences. For an extracted l-mer x, we filter it out if it does not satisfyWe perform filtration according to . Let occm(x). We calculate it by combining the methods , s[i + 2 \u22ef i + l + 1], and s[i + 5 \u22ef i + l + 4] in the sequence s, they are overlapped, and we merge them into a new substring s[i \u22ef i + l + 4].Merge the overlapped (ii)G by taking each substring as a vertex. For any two vertices v1 and v2, assume the corresponding substrings are str1 and str2, respectively. If there exist an l-mer x1 in str1 and an l-mer x2 in str2 such that dH \u2264 k, then we set the weight of the edge connected by v1 and v2 to 1, otherwise 0. Secondly, we cluster the vertices in the graph G using the MCL clustering algorithm [Cluster the substrings. At first, we build an undirected graph lgorithm . Finally(iii)For each obtained cluster, align the substrings in it and then fetch the fragment with high information content as an identified motif.The combining method is described in detail as follows:l-mers into one substring can help to reduce the elements to be clustered. Second, if the number of substrings is still large, we divide them into multiple groups with each group containing at most 1000 substrings. Then, we cluster substrings in each group separately and finally merge the obtained clusters.In the combining method, we control the number of elements to be clustered in order to ensure a good time performance. First, merging overlapped l-mers with relatively small Hamming distance for processing large DNA data sets. That is, given t DNA sequences, we verify whether the extracted pairs of l-mers with Hamming distance no more than k contain sufficient pairs of motif instances and whether the pairs of motif instances and the random overrepresented pairs of l-mers can be distinguished.We use probabilistic analysis to demonstrate the feasibility of motif discovery by extracting pairs of t, the sequence length n, the probability q that each input sequence contains a motif instance, and the motif conservation parameter g to 1000, 200, 0.8, and 0.8, respectively. For a fixed l, k is obtained by  and occm(x) are explained in the Notations.ained by , which iN1 and N2, it can be found that the extracted pairs of l-mers with Hamming distance no more than k contain sufficient pairs of motif instances and meanwhile many random overrepresented pairs of l-mers. For a given l-mer x, the l-mer in the input with Hamming distance no more than k from x is called a k-neighbor of x. From the values of occr(x) and occm(x), the number of k-neighbors of a motif instance is significantly larger than that of random overrepresented l-mers. Thus, we can distinguish the pairs of motif instances and the random overrepresented pairs of l-mers, so as to filter out most random overrepresented pairs of l-mers extracted in step 1. It should be noted that, for m(x) increases with the increase of the conservation degree, which makes it easier to distinguish the pairs of motif instances and the random overrepresented pairs of l-mers. In implementing PairMotifChIP, we fix the value of l to 15 because it corresponds to a large value of occm(x).From the values of We use both simulated and real data to make experiments. The simulated data are helpful for the comparison of different motif discovery algorithms, since the motifs and their locations are known exactly. The real data are mainly used to test whether the proposed algorithm can find motifs under the realistic biological situation.t\u2009\u2009n-length sequences and an l-length motif m randomly and then implant a random instance m\u2032 of m to each sequence with a probability q. Each instance m\u2032 differs from m in at most d positions; as shown in column 2 of d under a specific l is determined in terms of the challenging problem instance of planted motif search [m\u2032 from m, the specific Hamming distance i\u2009(0 \u2264 i \u2264 d) between m\u2032 and m is determined by  ChIP-seq data . Each mEm\u2032 is in a set of motif sites M, there exists a motif site m\u2032\u2032 in M such that m\u2032 overlaps m\u2032\u2032. Let K and P represent the published motif sites and the predicted motif sites, respectively. Then, site-level true positive (sTP), false negative (sFN), and false positive (sFP) are the number of motif sites in both K and P, in K but not in P, and not in K but in P, respectively. Based on this, sPC is calculated as follows:In the experiments, we compare the running time and identification accuracy of different motif discovery algorithms. For the site-level identification accuracy, we evaluate it by using the site-level performance coefficient sPC . When weK and P represent the nucleotide positions covered by the published motif sites and the predicated motif sites, respectively. Then, nucleotide-level true positive (nTP), false negative (nFN), false positive (nFP), and true negative (nTN) are the number of nucleotide positions in both K and P, in K but not in P, not in K but in P, and in neither K nor P, respectively. Based on this, nCC, nSn, and nSp are calculated as follows:For the nucleotide-level identification accuracy, we evaluate it by using the nucleotide-level correlation coefficient (nCC) , an inteWe select four compared algorithms: MEME-ChIP , F-motifhttp://meme-suite.org/tools/meme-chip), all the algorithms run on the same machine with a 2.67\u2009GHz\u2009CPU and a 4\u2009G memory. Each result is the average obtained on three randomly generated data sets with the same settings. Both PairMotifChIP and MEME-ChIP use the default parameters to identify motifs. In executing F-motif, the minimum motif length is set to 8, and the value of d is set to 2, 5, and 8 when the length of the identified motif is 9, 15, and 21, respectively. Both PairMotif+ and qPMS9 need specified l and d of the identified motif. When calculating identification accuracy, the predicated motif sites are needed. For MEME-ChIP, the predicated motif sites are returned by its web server; for other algorithms, the sites are obtained by searching the substring in each input sequence having the smallest Hamming distance from the predicted motif.All the algorithms are implemented in C or C++. Except for MEME-ChIP, whose results are produced by its web server  the running time of PairMotifChIP increases with the increase of data scale, but it does not depend on the motif length.For the second group of simulated data sets, whose data scales range from 500 to 3000 sequences, the comparison of different algorithms is shown in l-mers because it plays a key role in the time performance of the whole PairMotifChIP algorithm. l-mers with Hamming distance no more than k in two given n-length sequences, although the worst time complexity of the method in this paper is still O(n2), it has a better time performance in practice. Specifically, the method in this paper is 10 times faster than that in [Finally, it is necessary to test the method for extracting pairs of  that in , which ml = 13, \u200ad = 4, and k = 2 for each data set.We test PairMotifChIP's validity of motif discovery on the real ChIP-seq data . To better show the results, we take our previous algorithm PairMotif+ for comparison. For PairMotifChIP, we use default parameters without any prior information; for PairMotif+, we use the same setting l-mers and (ii) unlike PairMotif/PairMotif+, which obtains motifs by exhaustively verifying candidate motifs generated from extracted pairs of l-mers, PairMotifChIP obtains motifs by combining extracted l-mers based on clustering methods. The improvements of PairMotifChIP over PairMotif/PairMotif+ are that (i) PairMotifChIP runs much faster when identifying motifs in large data sets and (ii) PairMotifChIP can make motif discovery without any prior information . The executable program of PairMotifChIP is available at https://sites.google.com/site/feqond/pairmotifchip.In order to identify motifs in large DNA data sets, we propose a new algorithm, PairMotifChIP, which is a ChIP-tailored version of PairMotif/PairMotif+. The main difference between PairMotifChIP and PairMotif/PairMotif+ is that (i) PairMotifChIP designs a more efficient method for extracting pairs of It should be noted that, limited by the idea of combining overrepresented substrings, PairMotifChIP may not work well on the traditional promoter sequence data set containing dozens of sequences because of the lack of sufficient motif information."}
+{"text": "The e-CNF-PCP should be a very promising candidate as electrode material for CDI applications.Carbon nanofibers reinforced 3D porous carbon polyhedra network (e-CNF-PCP) was prepared through electrospinning and subsequent thermal treatment. The morphology, structure and electrochemical performance of the e-CNF-PCP were characterized using scanning electron microscopy, Raman spectra, nitrogen adsorption-desorption, cyclic voltammetry and electrochemical impedance spectroscopy, and their electrosorption performance in NaCl solution was studied. The results show that the e-CNF-PCP exhibits a high electrosorption capacity of 16.98\u2009mg g With an increasing human population combined with the over-exploitation of water resources for industrial and agricultural activities, water shortage has become the most serious problem in the 21th century1Capacitive deionization (CDI), also known as electrosorption, has entered in a rapid development period in the last ten years due to its minimum energy consumption and environmental friendliness compared to traditional desalination techniques56789101112131618212425\u22121 in 500\u2009mg l\u22121 NaCl solution. However, there are still some serious problems faced by the PCP electrode in previous work: (i) the surface pores  of PCP are mainly distributed in micropore range, which may cause the electrical double layer overlapping effect to hinder the CDI performance; (ii) the use of binder will increase the internal resistance and block some of the pores in the carbon materials, resulting in lower adsorption capacity.Recently, direct carbonization of metal-organic frameworks (MOFs) has been demonstrated to be a facile route to synthesize porous carbon materials283132Electrospinning, as a simple yet effective technique to fabricate continuous CNFs, has attracted much attention in the fields like energy storage351819371837\u22121 in 500\u2009mg l\u22121 NaCl solution, which shows great improvement compared to those of PCP and e-CNFs.In this work, CNFs reinforced 3D PCP network (e-CNF-PCP) was fabricated through electrospinning followed by thermal treatment and used as electrode materials for CDI for the first time. The e-CNF-PCP exhibits excellent performance with an EC of 16.98\u2009mg g\u22121, corresponding to D line and G line, respectively, which are signatures of graphitic carbon materials. The G line corresponds to the crystalline graphitic carbon and the D line is attributed to the defect and disordered structure. It is generally accepted that the relative intensity ratio of D peak to G peak (ID/IG) is the indication of disorder or defect in the carbon structure40D/IG values of e-CNFs, PCP and e-CNF-PCP are 0.89, 0.99 and 1.04, respectively, indicating that the synergistic effect of e-CNFs and PCP generates more defects in the e-CNF-PCP. The presence of defects can generate more accessible surface area and cause an increase in ability for the accumulation of charges, which is beneficial to the charge transfer in the adsorption process422 g\u22121. Clearly, the as-synthesized e-CNF-PCP displays a highly porous structure. The pore size distribution reveals that the e-CNFs and PCP are mainly composed of micropores and mesopores. However, the e-CNF-PCP exhibits a hierarchical pore structure consisting of not only micropores and mesopores but also macropores that are generated from the interconnected open channels between the nanofibers and the PCP. This 3D hierarchical pore structure can lower the resistance and shorten the ion transport pathway, which is beneficial to the electrosorption process.It is universally known that large accessible surface area and suitable pore size are crucial for the capacitive performance. Therefore, nitrogen adsorption-desorption and pore size distribution analysis of e-CNFs, PCP and e-CNF-PCP were performed and the results are presented in \u22121 within a potential range of \u22120.5\u20130.5\u2009V, respectively. All CV curves are nearly rectangular. The current increases and decreases steadily with the electric potential, indicating that no faradaic reaction happens and ions are adsorbed on the electrode surface by forming an electric double layer. The specific capacitances of e-CNFs, PCP and e-CNF-PCP electrodes are 217.13, 261.33 and 284.75 F g\u22121, respectively, as shown in dl) in parallel with the charge transfer resistance (Rct) at the contact interface between the electrode and the electrolyte solution. The inclined line, resulting from the Warburg impedance (ZW), corresponds to the ion-diffusion process in the electrolyte. The fitted Rct values for the electrodes are listed in ct, which is beneficial to the capacitive performance; (iii) compared to the PCP, the e-CNF-PCP is employed as free-standing electrode without the use of polymer binder.\u22121 during batch-mode experiments at four different applied voltages: 0.6, 0.8, 1.0 and 1.2\u2009V, respectively. All the charge processes were recorded until sorption equilibrium reached, and then the electrodes were shorted for regeneration. As expected, the ECs of these electrodes increase dramatically once the cell voltage is applied. High voltage results in high salt removal because of enhanced electrostatic force. The equilibrium ECs of e-CNFs, PCP and e-CNF-PCP electrodes at different voltages are listed in \u22121 at 1.2\u2009V, higher than those of e-CNFs (9.25\u2009mg g\u22121) and PCP (10.94\u2009mg g\u22121).Charge efficiency (\u039b) is a functional tool to gain insight into the EDL formed at the interface between the electrode and the solution27444546\u22121), \u0393 is the EC (mol g\u22121) and \u03a3  is obtained by integrating the corresponding current. The charge efficiencies of e-CNFs, PCP and e-CNF-PCP electrodes at 0.8\u20131.2\u2009V are shown in where F is the Faraday constant 96485\u2009C mol5\u2009C mol\u22121Adsorption kinetics, indicating the adsorption rate, is an important characteristic of adsorbents. It can be determined by using the pseudo-first-order adsorption kinetics and pseudo-second-order adsorption kinetics equations, which are often presented as:e (mg g\u22121) and qt (mg g\u22121) are the amounts of NaCl adsorbed at equilibrium and time t (min), respectively. k1 (mg g\u22121 min\u22121) and k2 (g mg\u22121 min\u22121) are the adsorption rate constants of pseudo-first-order and pseudo second order equations, respectively. 2 values of e-CNFs, PCP and e-CNF-PCP are 0.012, 0.014, 0.027, respectively. The higher rate constant of e-CNF-PCP indicates that its 3D hierarchical pore structure facilitates the quick access of ions onto its surface.where q\u22121 NaCl solutions are 10.03\u2009mg g\u22121/0.75, 12.56\u2009mg g\u22121/0.81 and 16.98\u2009mg g\u22121/0.80, which are higher than those of PCP  and e-CNFs . Obviously, e-CNF-PCP exhibits an improved CDI performance in all concentrations, which further confirms that e-CNF-PCP is an excellent electrode material for CDI application.To get a better understanding of the electrosorption behavior of e-CNF-PCP, the electrosorption experiments using e-CNF-PCP electrode in NaCl solution with different initial concentrations at 1.2\u2009V were carried out and the ECs and charge efficiencies were compared with those of PCP and e-CNFs, as shown in In order to further evaluate the electrosorption performance of e-CNF-PCP, the CDI performance and manufacturing difficulty of e-CNF-PCP is compared with those of other carbon electrode materials reported in the literatures, as shown in 18\u22121. The as-collected fibers were stabilized at 280\u2009\u00b0C for 2\u2009h in air at a heating rate of 2\u2009\u00b0C min\u22121.The e-CNFs were prepared in a typical process. 1\u2009g PAN  was dissolved in 8.8\u2009g N, N-dimethylformamide to form a homogeneous solution by stirring at 60\u2009\u00b0C for 10\u2009h. Then, the polymer solution was transferred into a 10\u2009ml syringe connected to a stainless steel needle. Electrospinning was carried out by applying a positive voltage of 22\u2009kV to the needle via an aluminum collector roller. The distance between the needle tip and the collector was 15\u2009cm and the flow rate of the solution was set at 1\u2009ml h2+.The as-prepared e-CNFs was firstly pre-treated using zinc nitrate solution through ultrasonic spray method at a frequency of 1.65\u2009MHz. Then the pre-treated e-CNFs cloth was immersed into a methanol solution containing 2.58\u2009g zinc nitrate and 2.63\u2009g 2-methylimidazole. After agitation the solution was aged at 25\u2009\u00b0C for 24\u2009h to get the e-CNFs-ZIF-8. After that, the as-synthesized e-CNFs-ZIF-8 was subsequently thermally treated at 1200\u2009\u00b0C in nitrogen for 2\u2009h with a heating rate of 2\u2009\u00b0C/min. Finally, the e-CNF-PCP was obtained by washing extensively by HCl to remove residual Znsp in F g\u22121) can be obtained from the CV process according to the equation:The surface morphology and structure of the as-synthesized e-CNF-PCP were examined by FESEM (JEOL JSM-LV5610), EDS (Oxford), and Raman spectroscopy (Renishaw inVia). Nitrogen adsorption-desorption isotherms were measured at 77\u2009K with an ASAP 2020 Accelerated Surface Area and Porosimetry System . The CV and EIS measurements were carried out in 1\u2009M NaCl solution by using Autolab PGSTAT 302N electrochemical workstation in a three-electrode mode, including a standard calomel electrode as reference electrode and a platinum foil as counter electrode. In EIS measurement, a frequency range of 0.1\u2009Hz to 100\u2009kHz and an AC amplitude of 5\u2009mV were applied. The specific capacitance (C\u22121) is the scan rate and m (g) is the total mass of electrodes.where \u22121. The volume and temperature of the solution were maintained at 50\u2009ml and 298\u2009K, respectively. Meanwhile, the variation of NaCl concentration was monitored and measured at the outlet of the unit cell by using a conductivity meter . The relationship between conductivity and concentration was obtained according to a calibration table made prior to the experiment, which has been described in our previous workThe e-CNF-PCP was used directly as free-standing CDI electrodes. Electrosorption experiments were conducted in a continuously recycling system including a unit cell495051In our experiment, the EC is defined as follows:0 (mg l\u22121) and \u03c1e (mg l\u22121) are initial and final NaCl concentrations, respectively. V (l) is the solution volume, and m (g) is the total mass of the electrodes.where \u03c1How to cite this article: Liu, Y. et al. Electrospun carbon nanofibers reinforced 3D porous carbon polyhedra network derived from metal-organic frameworks for capacitive deionization. Sci. Rep.6, 32784; doi: 10.1038/srep32784 (2016)."}
+{"text": "There are a limited number of studies on power analysis in multiple testing procedures. For some methods, the theoretical analysis is difficult and extensive numerical simulations are often needed, while other methods oversimplify the information under the alternative hypothesis. To this end, this paper aims to develop a new statistical model for power analysis in multiple testing procedures.Power analysis is a critical aspect of the design of experiments to detect an effect of a given size. When multiple hypotheses are tested simultaneously, multiplicity adjustments to p-value model under the alternative hypothesis, which is simple enough to perform power analysis without simulations, but not too simple to lose the information from the alternative hypothesis. The first step is to transform distributions of different test statistics  to distributions of corresponding p-values. We then use a step function to approximate each of the p-value\u2019s distributions by matching the mean and variance. Lastly, the step-function-based p-value model can be used for theoretical power analysis.We propose a step-function-based p-value model. Our model is then applied to the field of multiple testing procedures to explain the assumption of monotonicity of the critical constants. Lastly, we apply our model to a behavioral weight loss and maintenance study to select the optimal critical constants.The proposed model is applied to problems in multiple testing procedures. We first show how the most powerful critical constants can be chosen using the step-function-based The proposed model is easy to implement and preserves the information from the alternative hypothesis. A consequence of multiplicity adjustments is the loss of power . The probability density functions and the cumulative distribution functions of the normal-distribution-based and the step-function-based p-value models are compared in Fig. p-value models serve an approximation to the p-value models based on the original test statistics.with mean and variance mentclass2pt{minimp-value model has a density function Based on the univariate model, the corresponding multivariate hi(\u00b7)\u2019s may have different parameters fi\u2019s and gi\u2019s. In the following sections, the simplified step-function-based p-value model is applied to two problems in multiple testing procedures.where different n hypotheses p-values p-values as p(1)\u2264\u22ef\u2264pn),\u22ef,Hn)/n, and other choices of ci\u2019s were proposed by Rom [The global test compares d. Simes  proposedd by Rom , Cai andd by Rom , Gou andd by Rom .ci\u2019s, people usually run simulations [p-value model is an alternative choice to theoretically calculate the powers and make comparisons between different multiple testing procedures.Among different choices of critical constants ulations  or rely ulations  to make n hypotheses. For a global test with two single hypotheses, the control of type I error under independence requires c1\u2265c2. This equality is equivalent to In this section we first show how the most powerful critical constants can be chosen using our proposed method for a global test with two hypotheses, and then we can apply the successive recursion process to calculate the power for a global test with c2 decreases when c1 increases.From  we get \\p-value model, without loss of generality, we assume 1\u2264f1\u2264f2, the probability of rejecting the global hypothesis is By using the simplified step-function-based n=2), there are two configurations of true and non-true null hypotheses where the global null hypothesis is false: (1) one true null hypothesis (n0=1) and one false null hypothesis (m=1), and (2) two false null hypotheses (m=2).When the global hypothesis contains two single hypotheses \u03b1=1\u22122c2, therefore c2 decreases (c1 increases).When When f\u03b1c1\u22651, so power increases when c1 decreases (c2 increases).Note that f\u2019s. When we assume the alternative hypothesis has a small effect size, where c2=0 and c1=1/(f\u03b1) and c2=(f2\u03b1\u22121)/(2\u03b1f(f\u22121)), so when f increases, we can follow the strategy to decrease c1 (increase c2) to achieve the maximal power. When we assume the alternative hypothesis has a large effect size, where c2\u22651/(f\u03b1), so when f is large enough, different tests have similar power. We calculate the maximal power for different f1=f2=f, then the power is Second, assume that both null hypothesis are false with the same effect size, say, c1(c1\u22122c2)\u03b1=1\u22122c2, then c2 decreases (c1 increases).When f values. When we assume both hypotheses are false and with a small effect size, where c2=0 and c1\u22651/(f\u03b1). By taking both c2=0 is the uniformly best choice when both null hypotheses are false. We calculate the maximal power for different n single hypotheses, where m of them are true significances , define the probabilities as n,m indicates the probability for n hypotheses, where m is the number of the true significances, and n0=n\u2212m is the number of the true nulls.In general, for a global test with i=nSince i, since Similarly, for general iwe have the general recurrence relation for Bn,m,i for m=0 to calculate the type I error under the global null hypothesis. They proved a recurrence relationship among Bn,0,i\u2019s. We generalize this result to Bn,m,i\u2019s and have this recurrence relationship .So when m is relatively large , the bound c1,\u22ef,cn+1\u2212m and small cn+2\u2212m,\u22ef,cn tend to have large power. Similar observations were reported by Gou and Tamhane [Note that when  Tamhane  based onHi is false. For testing multiple hypothesis, powers can be of different types: individual, average, disjunctive, and conjunctive, and the appropriate power concept is determined on a case-by-case basis [p-value model.Note that in this application power is simply the probability of rejecting se basis . These pp-value model can be applied to various clinical trials, e.g., group sequential designs [Power analysis can be complex when multiple hierarchical objectives are involved. Alosh and Huque  discusse designs , graphic designs , 6.For multiple test procedures, critical constants are often required to satisfy , 12 13\\This requirement is called the monotonicity assumption of critical constants.Suppose that we have a set of critical constants \u03b1, then another test with critical constants \u03b1, and has the same power with the previous test which does not satisfy the monotonicity assumption. Hence, only the set of critical constants which satisfies the monotonicity assumption needs to be considered.So if a test with critical constants Many multiple tests have critical constants which satisfy a strict monotonicity assumption , 22, 25 p-value models can explain that this assumption is necessary because the corresponding tests are generally more powerful than other tests which do not satisfy this assumption.Some multiple tests satisfy the monotonicity assumption , but do p-value model, we have several observations: (1) when there is one true null hypothesis and one false null hypothesis, only if f values. In general, on the parameter space of the effect size , the tests which do not satisfy  whe satisfy  is less  satisfy  for all  satisfy  have mor satisfy  only at  satisfy , because satisfy .2, and randomly assigned the participants to a comparison treatment with a print manual and telephone follow-ups, or an experimental treatment of the coach approach exercise-support protocol. The self-efficacy for controlled eating (SE-eating) is one of the psychological predictors of behavioral changes. Annesi et al. [t=2.88, and there was no significant between-group difference during the weight-loss maintenance phase (month 6-24) with t=\u22120.48.Annesi et al.  evaluatep-value model because it is easy to implement and preserves the information from the alternative hypothesis. If we take the weight-loss study by Annesi et al. [\u03b4=2.88 and variance 1, and the increase during the weight-loss maintenance phase is normally distributed with mean \u03b4=0 and variance 1. To match the mean for the normal-distribution-based p-value model with parameter \u03b4=2.88, the parameter f of the simplified step-function-based p-value model is 23.979. From /(2f)=62 %, and the optimal choice of critical constants is =(1/(f\u03b1),(f2\u03b1\u22121)/(2\u03b1f(f\u22121)))=. So the larger p-value is compared with 0.8341\u03b1 and the smaller p-value is compared with 0.5036\u03b1, and if any p-value is less than the corresponding critical value, the global null hypothesis will be rejected.The increases of the self-efficacy for controlled eating were evaluated both during the weight-loss phase and during the weight-loss maintenance phase, so the multiplicity adjustment is advised to apply. To choose the optimal multiplicity correction based on the estimated effect size from the pilot study, we recommend our proposed step-function-based i et al.  as a pilp-value models for power analysis simplify the theoretical analysis that is difficult in many situations. At the same time, information of loss remains at an acceptable level. Finner and Gontscharuk [p-values under the false null hypotheses follow a Dirac distribution with point mass at 0. When the Dirac-uniform configuration is applied to Annesi et al.\u2019s [\u03b4 is lost, and any choice of positive critical constants  will result a claim of significance. Under the p-value model based on Dirac function, all choices of critical constants have the same power, and the optimal choice is unable to be located.The step-function-based tscharuk  and Sarktscharuk  used a tet al.\u2019s  study, tp-value model based on normal distribution. By using Annesi et al.\u2019s [N, and the other test statistic is N. The probability of rejecting the global null hypothesis is The Dirac-uniform configuration is too brief to include necessary information to choose the optimal critical constants. Hung et al.  discusseet al.\u2019s  researchThe optimal choice of critical constants is followed by solving \u03b4=2.88 and \u03b1=0.05, the optimal solution is =. While the step-function based p-value model and the normal-distribution based p-value model produce similar choices of critical constants , the model based on step function has an explicit solution of critical constants and requires little computational effort.This optimization problem has no explicit solution. When p-value model and its simplified version. These p-value models are simple and concise to perform theoretical power analysis. In addition, different test statistics, for example, t, chi-square or F, can be transformed to the p-value scale. These models can be applied to the field of multiple testing procedures to explain the assumption of monotonicity of the critical constants. We also use these p-value models to choose suitable sets of critical constants with more power. In this paper, we consider the independent p-values for the multivariate cases. Dependence structures can be brought into these p-value models, like Sarkar et al. [p-value models in a separate paper. Finally, there are many applications of the step-function-based p-value models, and multiple testing procedure is an example in point.We have given a step-function-based r et al.  or Gou ar et al. , and we"}
+{"text": "We employ this similarity metric to improve the accuracy of the alignments. The experimental results on the KEGG database show that when compared with other state-of-the-art methods, in most cases, our method obtains better performance in the node correctness and edge correctness, and the number of the edges of the largest common connected subgraph for one-to-one reaction mappings, and the number of correct one-to-many reaction mappings. Our method is scalable in finding more reaction mappings with better biological relevance in large metabolic pathways.Metabolic pathway alignment has been widely used to find one-to-one and/or one-to-many reaction mappings to identify the alternative pathways that have similar functions through different sets of reactions, which has important applications in reconstructing phylogeny and understanding metabolic functions. The existing alignment methods exhaustively search reaction sets, which may become infeasible for large pathways. To address this problem, we present an effective alignment method for accurately extracting reaction mappings between two metabolic pathways. We show that connected relation between reactions can be formalized as binary relation of reactions in metabolic pathways, and the multiplications of zero-one matrices for binary relations of reactions can be accomplished in finite steps. By utilizing the multiplications of zero-one matrices for binary relation of reactions, we efficiently obtain reaction sets in a small number of steps without exhaustive search, and accurately uncover biologically relevant reaction mappings. Furthermore, we introduce a measure of topological similarity of nodes (reactions) by comparing the structural similarity of the  In the last few decades, the quantity and quality of metabolic data in biological databases such as KEGG (Kyoto Encyclopedia of Genes and Genomes)  and MetaIn the metabolic pathway alignment problem, metabolic pathways are usually represented as directed graphs, where a node denotes a molecule which can be specified as reaction, enzyme, or compound and an edge represents the interactions between molecules. A one-to-one mapping between nodes in two metabolic pathways maps a node from one pathway to a node in the other. A one-to-many mapping between the nodes in two metabolic pathways maps a node from one pathway to a connected subgraph of many nodes in the other . The sizAccordingly, we can categorize existing literature on metabolic pathway alignment into two types. The first type finds one-to-one mappings between molecules of metabolic pathways to identify similar parts in different pathways , 11\u201320. et al.  = 1 when reaction ri is connected to reaction rj, and Mp = 0 when ri is not connected to rj, i = 1,2,\u2026,N and j = 1,2,\u2026,M. Mpn can be computed recursively by Mp1 = Mp and n\u22652. Mp2.In this work, we represent binary relation of reactions in metabolic pathway by zero-one matrix In the following section, we present our method MPBR.Gp =  and Gp\u2032 = , the goal of MPBR is to find the reaction mappings between Gp and Gp\u2032. Without loss of generality, we assume that |Vp|\u2264|Vp\u2032|, reaction sets RS\u2286Vp and RS\u2032\u2286Vp\u2032. MPBR consists of three main stages ; (2) Construct a similarity matrix BM by computing the similarity between the reactions in Gp and Gp\u2032 (as detailed in Subsection \u2018Second Stage\u2019); (3) Find mapping  such that the similarity score of mapping  is maximized (as detailed in Subsection \u2018Third Stage\u2019). A set RSmap of mappings  is the result for aligning Gp and Gp\u2032. For a pair of metabolic pathways RSn = {RS1, RS2,\u2026, RSN} in Gp, and the set RSm\u2032 = {RS1\u2032, RS2\u2032,\u2026, RSM\u2032} in Gp\u2032 respectively. For metabolic pathway Gp, there is a path from r1 to rn if there is a sequence of reactions r1,r2,\u2026,rn with edges , ,\u2026, and  in Gp. Accordingly, we derive theorem 1.In this subsection, we discuss how to exploit the multiplications of zero-one matrices for binary relation of reactions to create the set ri and rj, there is a path of length n from ri to rj in Gp if and only if Mpn = 1, where n is a positive integer, i = 1,2,\u2026,n and j = 1,2,\u2026,n.Theorem 1: For reactions ri to rj in Gp if and only if Mp = 1, so the theorem is true when n = 1.Proof: We will use mathematical induction. There is a path of length one from n. There is a path of length n+1 from ri to rj if and only if there is a reaction rk in Gp such that there is a path of length one from ri to rk in Gp, so Mp = 1, and a path of length n from rk to rj in Gp, that is, Mpn = 1. Consequently, by the induction hypothesis, there is a path of length n+1 from ri to rj in Gp if and only if there is a reaction rk with Mp = 1 and Mpn = 1. But there is such a reaction if and only if Mpn+1 = 1. Therefore, there is a path of length n+1 from ri to rj in Gp if and only if Mpn+1 = 1, i = 1,2,\u2026,n and j = 1,2,\u2026,n. \u03b3Assume that the theorem is true for a positive integer RS of size n for Gp.Following from theorem 1, we introduce how to find reaction set Mpn-1. Then we create a reaction pair set NS and iteratively extend NS with the reaction pair  where Mpn-1 = 1. According to theorem 1, for reactions ri and rj with Mpn-1 = 1, there is a path of length n-1 from ri to rj in Gp if and only if Mpn-1 = 1. That is, there are n reactions in this path. Thus, we can construct reaction set RS of size n containing these n reactions. Finally, we search every path of length n between two reactions in each reaction pair of NS in Gp, and create each reaction set RS of size n containing the reactions in each path to construct the set RSn = {RS1, RS2,\u2026, RSN} in Gp. Similarly, we can find each reaction set RS\u2032 of size m and construct the set RSm\u2032 = {RS1\u2032, RS2\u2032,\u2026, RSM\u2032} in Gp\u2032.First, we compute ri, rj) with Mp2 = 1, i = 1,2,3 and j = 1,2,3,4,5. These reaction pairs are , , ,  and . Next we create a reaction pair set NS = {, , , , } by these reaction pairs. Then, we search the paths of length 2 between two reactions in each reaction pair of NS. These paths are Path 1(r1\u2192r2\u2192r3), Path 2 (r2\u2192r3\u2192r1), Path 3 (r3\u2192r1\u2192r2), Path 4 (r2\u2192r3\u2192r4) and Path 5 (r3\u2192r4\u2192r5) respectively. Finally we create reaction sets RS1 = {r1,r2,r3}, RS2 = {r2,r3,r1}, RS3 = {r3, r1, r2}, RS4 = {r2, r3, r4} and RS5 = {r3, r4, r5} with the reactions in Path 1, Path 2, Path 3, Path 4, and Path 5 respectively.Gp, we drive the following property.Based on theorem 1 and the above searching procedure of reaction sets in RS of size n+1 in Gp can be found through performing Mpn.Property 1: Reaction set Gp.Property 1 illustrates the relationship between the search of reaction sets and the multiplications of zero-one matrices for binary relation of reactions in Mpn, we have the following theorem.For t and s with t>s such that Mpt = Mps, then for any positive integer n, it holds that Mpn\u2208S = {Mp, Mp2, \u2026, Mpt-1}.Theorem 2: If there exist positive integers Proof:n, when n\u2264t-1, we have Mpn\u2208S. We want to prove Mpn\u2208S when n>t-1. When n>t-1, it holds n>s. For n, s and t, there exist positive integers q and r such that n-s = (t-s)q+r . Therefore, n = s+(t-s)q+r and Mpn = Mps+(t-s)q+r. Since 0<r\u2264t-s-1, so s+r\u2264t-1 and Mps+r\u2208S. Since Mpn = Mps+(t-s)q+r, if we can prove Mps+(t-s)q+r = Mps+r, then it follows Mpn = Mps+r\u2208S. In the following, we will use mathematical induction to prove Mps+(t-s)q+r = Mps+r.For any q = 1, it yields Mps+(t-s)q+r = Mps+(t-s)+r = Mpt+r = Mps+r. Assume that for any q\u2264k, Mps+(t-s)q+r = Mps+r holds. When q = k+1, we have Mps+(t-s)(k+1)+r = Mps+(t-s)k+r+(t-s) = Mps+(t-s)k+rMpt-s)q+r = Mps+r also holds for q = k+1. By induction, we have proven that Mps+(t-s)q+r = Mps+r for all q>0. Consequently, since Mpn = Mps+(t-s)q+r, Mps+(t-s)q+r = Mps+r and Mps+r\u2208S, hence Mpn = Mps+r\u2208S.\u03d2When Gp and theorem 2 leads to the following corollary.The discussion regarding the search of reaction sets in s and t with s<t such that Mps = Mpt, then the reaction set RS of size n\u2265t in Gp can be found through performing at most Mpt-1.Corollary 1: If there exist positive integers Proof:S = {Mp, Mp2,\u2026,Mpt-1}. When there exist positive integers s and t with s<t such that Mps = Mpt, according to theorem 2, for any positive integer n, it holds that Mpn\u2208S = {Mp, Mp2,\u2026,Mpt-1}. In other words, when n-1\u2265t-1, there is a positive integer v\u2264t-1 such that Mpv = Mpn-1\u2208S. According to property 1, we need to perform Mpn-1 to find reaction set RS of size n in Gp. Because Mpv = Mpn-1 when n-1\u2265t-1, so we only need to perform Mpv to find the reaction set RS of size n in Gp instead of performing Mpn-1, where v\u2264t-1. \u03d2Let RS of size n through performing Mpn-1. Furthermore, corollary 1 implies that, in order to find reaction set RS of size n, when n\u2265t, we only need to try at most Mpt-1. Therefore, we can find reaction set RS of size greater than t in metabolic pathway through performing at most Mpt-1.Property 1 implies that we can find reaction set Mpn-1. Secondly, MPBR creates a reaction pair set NS and iteratively extends NS with the reaction pair  where Mpn-1 = 1. Finally, through finding the paths of length n-1 between two reactions in each reaction pair of NS in Gp, MPBR obtains the set RSn = {RS1, RS2,\u2026, RSN} in Gp and the set RSm\u2032 = {RS1\u2032, RS2\u2032,\u2026, RSM\u2032} in Gp\u2032. Thus, in this way, we avoid the exhaustive search of reaction sets, and produce candidate reaction sets in finite steps.In the first stage, MPBR first computes Gp and Gp\u2032, which combines topological and homological similarities of reactions, and construct a |Vp|\u00d7|Vp\u2032| similarity matrix BM, where BM  is the similarity value between nodes (reactions) u and v, u\u2208Vp, v\u2208Vp\u2032.The second stage aims to compute the similarity values between any two reactions in u is mapped to node v, then their neighbors in the corresponding graphs should also be similar. From this observation, we measure topological similarity of nodes by comparing the structural similarity of the k-neighborhood subgraphs of nodes. Next, we discuss how to compare the k-neighborhood subgraphs of nodes to compute topological similarity of nodes. Nk(u) is defined as the k-neighborhood node set of u in Gp and Nk(u) is a subset of Vp, u\u2209Nk(u), where k is an integer and k\u22650. The shortest distance between u and x\u2208Nk(u) is defined as the number of edges of the shortest path between u and x, which is not exceeding k. Similarly, Nk(v) is defined as the k-neighborhood node set of v in Gp\u2032.We first introduce how to compute topological similarity of nodes (reactions) in metabolic pathways. Our computation of topological similarity of nodes is based on the following observation. If node u\u2208Vp and v\u2208Vp\u2032, the k-neighborhood subgraph of u in Gp is denoted by Ek(u) is defined as the edge set of Nk(u)\u222a{u} in Gp. The k-neighborhood subgraph of v in Gp\u2032 is denoted by Nk(v)\u222a{v} in Gp\u2032. Let d(u) be the degree of u in Gp and d(v) be the degree of v in Gp\u2032. Suppose that the degree sequence of the nodes in Nk(u) is d(x1), d(x2),\u2026,d(xi),\u2026,and Nk(v) is d(y1), d(y2),\u2026,d(yj),\u2026,and k-neighborhood subgraph of u with the k-neighborhood subgraph of v to compute the topological similarity T between u and v:Km is the maximal value of k and is determined by the user, Nk(u) and Nk(v) respectively. The impact of edges on the topological similarity T is evaluated by k = 0, Nk(u) = u and Nk(v) = v.For Bsim between u and v is computed by the following equation:ue is the enzyme catalyzing reaction u, ve is the enzyme catalyzing reaction v, Esim is the similarity score between enzyme ue and enzyme ve. We employ the enzyme similarity score defined in 21], we met al.  reportedet al. . On the 5CR-1tomany is the ratio of the number of correct one-to-many reaction mappings to the total number of mappings produced by the alignment [CR-1tomany can be used to investigate the percentage of the correct one-to-many reaction mappings in the alignment. Higher values for CR-1tomany indicate that the alignments for one-to-many reaction mapping are of high quality [lignment . CR-1tom quality .6C-manytomany is the number of correct many-to-many reaction mappings between the first pathway and the second one. By reference to C-1tomany, let  be a many-to-many mapping from an alignment of GX and GX\u2032 where RS = {r1, r2,\u2026,rx}, RS\u2032 = {r1\u2032, r2\u2032,\u2026,ry\u2032}, and P1,\u2026,Pi,\u2026,Px be the pathways that include a reaction in RS and are associated with metabolism 1.m in the species X. Similar to C-1tomany, a many-to-many reaction mapping  is called correct if it satisfies the following two conditions: (1) The start reactions in RS and RS\u2032 share at least one input compound and the end reactions in RS and RS\u2032 share at least one output compound. (2) Every reaction in RS\u2032 is included in at least one of the pathways P1\u2032,\u2026,Pi\u2032,\u2026,Px\u2032 where each Pi\u2032 is a pathway in metabolism 1.m of species X\u2032 and corresponds to Pi of X.MPBR, CAMPways and SubMAP provide the options of one-to-one alignment and one-to-many alignment. We can perform one-to-one alignment of two pathways to find one-to-one reaction mappings between these two pathways. Similarly, we can perform one-to-many alignment of two pathways to find one-to-many reaction mappings between these two pathways. In the experiments, the one-to-many reaction mappings include 1-to-2 and 1-to-3 reaction mappings.EC, NC and ELCCS to measure the quality of one-to-one alignment, and use C-1tomany and CR-1tomany to measure the quality of one-to-many alignment. In addition, we use C-manytomany to evaluate the capability of MPBR for searching many-to-many reaction mappings.In this paper, we use k = 3 and \u03c3 = 0.6, and CAMPways and SubMAP were run using their default parameter settings. MPBR, CAMPways and SubMAP were run on the Sugon 5000A computer system of cluster architecture at Guangxi University, using a single computing node with a quad-core Intel(R) Xeon(R) CPU E5620 @ 2.40GHz and 40GB RAM. The operating system is Linux.In the experiments, MPBR was run using The following five subsections will provide our experimental evaluations on the qualities of the alignment results computed by MPBR, CAMPways and SubMAP respectively. Subsections \u2018Same-domain One-to-one Alignments\u2019 and \u2018Same-domain One-to-many Alignments\u2019 focus on one-to-one alignment and one-to-many alignment between the species within the same domain respectively. Subsections \u2018Across-domains One-to-one Alignments\u2019 and \u2018Across-domains One-to-many Alignments\u2019 focus on one-to-one alignment and one-to-many alignment between the species from different domains respectively. Subsection \u2018Running time and memory requirements\u2019 discusses the performance of each method in terms of the running time and memory requirements. Subsection \u2018Many-to-many Alignments\u2019 discusses the experimental results of many-to-many alignments of the pathways. Subsection \u2018Case study\u2019 introduces three sample alignments to show how MPBR, CAMPways and SubMAP can be used to analyze metabolic pathways.NC of the alignment results of MPBR, CAMPways and SubMAP for the fifth level of the FGC hierarchy are shown in Tables NC for the first four levels of the FGC hierarchy are shown in The values of In this subsection, we discuss the quality of the same-domain one-to-one alignments produced by MPBR and other comparative methods. Tables EC, NC and ELCCS for 19, 18 and 18 instances respectively, whereas all three methods obtain equal values of EC, NC and ELCCS for 5, 6 and 7 instances respectively. Additionally, MPBR and CAMPways obtain equal values of EC, NC and ELCCS for 4, 4 and 3 instances respectively. These experimental results emphasize that, for the same-domain one-to-one alignment, in most cases, our MPBR method outperforms other comparative methods not only in topological accuracy but also in biological relevance of the results. Thanks to the use of structural similarity among the neighbors of reactions, MPBR is able to improve the topological and biological accuracy of the alignments.As shown in Tables C-1tomany and CR-1tomany of the one-to-many alignment results for the same domain species are shown in Tables In this subsection, we compare the quality of the same-domain one-to-many alignments produced by MPBR and other comparative methods. The values of C-1tomany and CR-1tomany in 22 and 15 out of all 28 instances respectively. For 4 instances, all three methods obtained the same values of C-1tomany and CR-1tomany, while the value of C-1tomany of MPBR is lower than CAMPways for 2 instances and is lower than SubMAP for 1 instance. The value of CR-1tomany of MPBR is lower than SubMAP for 4 instances, and some values of CR-1tomany of MPBR are lower than CAMPways for 7 instances. This means that, in most cases, MPBR is able to return more correct one-to-many reaction mappings than CAMPways and SubMAP in the same-domain one-to-many alignment. On the other hand, when the size of the pathway becomes large, SubMAP is unable to generate a result for 9 instances under the current computing environment while MPBR and CAMPways are not restricted to the size of the pathway in the same-domain one-to-many alignment.From Tables This subsection discusses the quality of the across-domains one-to-one alignments produced by MPBR and other comparative methods. Tables EC, NC and ELCCS for 47, 42 and 51 instances respectively. Some values of EC and NC of MPBR are a bit lower than those of CAMPways for 4 and 3 instances respectively. This demonstrates that, in most cases, MPBR is also capable of achieving better topological accuracy and biological relevance of the alignment results than other two comparative methods in across-domains one-to-one alignment.As can be seen from Tables EC, NC and ELCCS of the same-domain alignments are obviously higher than those values of across-domains alignments. This is also consistent with the analysis that the biological relevance of the species within the same domain is much stronger [In addition, from Tables stronger . Thus, wC-1tomany and CR-1tomany of the one-to-many alignment results for different domain species are shown in Tables In this subsection, we compare the quality of the across-domains one-to-many alignments produced by MPBR and other comparative methods. The values of C-1tomany and CR-1tomany compared to other comparative methods in 44 and 32 out of 56 instances respectively. For only 10 out of 56 instances MPBR fails to be the best. On the other hand, combining Tables C-1tomany and CR-1tomany of MPBR are still high enough without being affected by the size of pathway. While the comparative methods suffer from the size of large-scale pathway, MPBR overcomes this problem and returns more correct one-to-many reaction mappings.From Tables C-1tomany and CR-1tomany shows that, in most instances, MPBR also performs better than the other two methods in across-domains one-to-many alignment. In conclusion, the results from subsection \u2018Same-domain One-to-many Alignments\u2019 and subsection \u2018Across-domains One-to-many Alignments\u2019 demonstrate that MPBR is an effective method in retrieving one-to-many reaction mappings in the alignment of metabolic pathways.The above analysis of PSI represents the percentage of the solved instances of each method, in one-to-one alignment, ART1 denotes the average running time for the 64 instances solved by all three methods and ART2 represents the average running time for the 84 instances solved by MPBR and CAMPWays, and in one-to-many alignment, ART3 denotes the average running time for the 41 instances solved by all three methods, and ART4 represents the average running time for the 80 instances solved by MPBR and CAMPWays.In the experiments of one-to-one and one-to-many alignments, we have tested a total of 168 instances. In some cases, SubMAP and CAMPWays consumed an unusually long time until running out of memory, As can be seen from For the one-to-many alignment, we can observe from C-manytomany of many-to-many alignment results of MPBR.In addition to one-to-many alignments, we can also reveal alternative pathways that have similar functions by finding many-to-many reaction mappings between different pathways. This subsection discusses whether MPBR can accurately find such mappings in the alignment of metabolic pathways. The many-to-many reaction mappings include 2-to-2, 2-to-3 and 3-to-3 reaction mappings. Both CAMPways and SubMAP do not implement the functionality of many-to-many alignment. Escherichia coli (eco) and Agrobacterium tumefaciens (atc) are single-cell microorganisms, Homo sapiens (hsa) and Mus musculus (mmu) are complex organisms with cell membranes. Both atc and eco. The result is shown in atc and eco. This implies a common ancestral pathway, which is consistent with the theory that pathways for synthesis of proteinogenic amino acids were established before ancient organisms diverged into archaea, bacteria, and eucarya [In this subsection, we present three cases  terms or sequence information, to compute homological similarity of reactions. Another interesting issue is to exploit binary relation of reactions to identify functional motifs in metabolic pathways.S1 Table(DOC)Click here for additional data file.S2 Table(DOC)Click here for additional data file.S3 Table(DOC)Click here for additional data file.S4 Table(DOC)Click here for additional data file.S5 Table(DOC)Click here for additional data file."}
+{"text": "Scientific Reports 10.1038/s41598-017-07589-8, published online 04 August 2017Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201csources\u201d was incorrectly given as \u201csoruces\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "P-values are being scrutinized as representing the most widely applied and abused practices. One line of critique is that P-values are inherently unfit to fulfill their ostensible role as measures of credibility for scientific hypotheses. It has also been suggested that while P-values may have their role as summary measures of effect, researchers underappreciate the degree of randomness in the P-value. High variability of P-values would suggest that having obtained a small P-value in one study, one is, ne vertheless, still likely to obtain a much larger P-value in a similarly powered replication study. Thus, \u201creplicability of P-value\u201d is in itself questionable. To characterize P-value variability, one can use prediction intervals whose endpoints reflect the likely spread of P-values that could have been obtained by a replication study. Unfortunately, the intervals currently in use, the frequentist P-intervals, are based on unrealistic implicit assumptions. Namely, P-intervals are constructed with the assumptions that imply substantial chances of encountering large values of effect size in an observational study, which leads to bias. The long-run frequentist probability provided by P-intervals is similar in interpretation to that of the classical confidence intervals, but the endpoints of any particular interval lack interpretation as probabilistic bounds for the possible spread of future P-values that may have been obtained in replication studies. Along with classical frequentist intervals, there exists a Bayesian viewpoint toward interval construction in which the endpoints of an interval have a meaningful probabilistic interpretation. We propose Bayesian intervals for prediction of P-value variability in prospective replication studies. Contingent upon approximate prior knowledge of the effect size distribution, our proposed Bayesian intervals have endpoints that are directly interpretable as probabilistic bounds for replication P-values, and they are resistant to selection bias. We showcase our approach by its application to P-values reported for five psychiatric disorders by the Psychiatric Genomics Consortium group.Increased availability of data and accessibility of computational tools in recent years have created an unprecedented upsurge of scientific studies driven by statistical analysis. Limitations inherent to statistics impose constraints on the reliability of conclusions drawn from data, so misuse of statistical methods is a growing concern. Hypothesis and significance testing, and the accompanying  P-values are often singled out as major culprits, not only because these concepts are easy to misinterpret, but for purported inherent flaws. Variability of P-values appears to be underappreciated in the sense that when a small P-value is obtained by a given study, researchers commonly suppose that a similarly designed independent replication study is likely to yield a similarly small P-value. We will use the term \u201creplication P-values\u201d, introduced by Killeen1, to mean the P-value obtained from subsequent, replicate experiments with the same sample size, taken from the same population. Great variability of replication P-values casts doubt on validity of conclusions derived by a study at hand and implies lack of confidence in possible outcomes of any follow-up studies. In reality, one should expect a greater uncertainty in what a replication P-value will be. Special prediction intervals for P-values, named \u201cP-intervals\u201d, have been employed to characterize that uncertainty6. P-intervals have been presented as an objective measure of P-value variability, as opposed to subjective judgments reported by researchers in surveys, with the conclusion that the subjective estimates are too narrow and, therefore, researchers tend to underestimate randomness of replication P-values3. While P-intervals have been used mainly as a tool to elucidate flaws of P-values, they have also been defended as important additions to P-values themselves in publications supportive of P-values as universal measures that provide useful summary of statistical tests6. It has been suggested that P-intervals may serve the purpose of improving P-value interpretability, especially in large-scale genomic studies with many tests or in other studies utilizing modern high-throughput technologies6. For example, in their discussion of P-values and their prediction intervals, Lazzeroni and colleagues6 argued that the P-values \u201cwill continue to have an important role in research\u201d and that \u201cno other statistic fills this particular niche.\u201d They present P-intervals not as a way to expose alleged weaknesses of P-values but rather as a tool for assessing the real uncertainty inherent in P-values.Poor replicability has been plaguing observational studies. The \u201creplicability crisis\u201d is largely statistical and while there are limits to what statistics can do, a serious concern is misapplication of statistical methods. Significance testing and P-intervals for prediction of uncertainty in replication P-values is the lack of clear interpretation of their endpoints due to their frequentist construction. Classical prediction intervals, also known as \u201cprediction confidence intervals\u201d, have statistical properties that are similar to the regular confidence intervals (CI\u2019s). Both types of intervals are random and are constructed to cover the replication value (1\u2009\u2212\u2009\u03b1)% of the time, referred to as the coverage property % represents the desired confidence level). As Lazzeroni and colleagues5 noted while discussing results of their simulation experiments, \u201cBy definition, the coverage rate is an average across the distribution\u201d [of P-values]. This statement can be expanded as follows: given a large number of original studies with different P-values, if (1\u2009\u2212\u2009\u03b1)% P-intervals were to be constructed in each of these original studies regardless of statistical significance of the obtained P-value, then the average number of replication P-values covered by respective P-intervals is expected to be (1\u2009\u2212\u2009\u03b1)%. In this model, there are multiple original studies with a single replication P-value for each prediction interval, and it either falls into the interval or it does not. The average is taken over the proportion of times the replication P-value falls into the prediction interval. Caveating Lazzeroni et al.\u2019s5 discussion, the endpoints of an interval constructed around a P-value obtained in any particular study cannot be interpreted in a probabilistic way with regard to a replication P-value, because it is either captured by the interval or not and the endpoints of the interval do not represent the range of possible values.In our view, the major difficulty with the applications of P-interval interpretation arises when it is constructed for a specific P-value. The coverage property of P-intervals as a long-run average is well-defined for random P-values, and the resulting intervals are themselves random. On the other hand, a P-interval constructed for a given P-value, P-values (0 to 1) to a narrow interval around \u03b5. We can think of a process that generates these P-values as being the same as in the unrestricted case, but then we would discard any P-value outside the \u03b5 interval and evaluate coverage only for the intervals around P-values that are similar to P-values restricted to a specific range could be much smaller than the nominal (1\u2009\u2212\u2009\u03b1)% level expected across all possible values of the P-value5. Thus, the endpoints of any particular P-interval constructed around an obtained P-value are not readily interpreted in terms related to the P-value at hand or any future values in replication studies.Another difficulty with 8. Neyman starts by approaching the interval estimation from a Bayesian perspective, and describes a posterior distribution of the parameter \u03b8, given the data x . Neyman writes that this distribution, Pr(\u03bc|x), \u201cpermits the calculation of the most probable values of the \u03bc and also of the probability that \u03bc will fall in any given interval,\u201d7 for example, \u03bcL\u2009\u2264\u2009\u03bc\u2009\u2264\u2009\u03bcU. Neyman notes that the calculation of such a posterior interval requires placing a prior probability distribution on \u03bc, something he seeks to avoid through the development of CIs. In the Bayesian set-up, the endpoints \u03bcL and \u03bcU are fixed numbers, while \u03bc is random. To derive the CI endpoints as functions of random data, L(x)\u2009\u2264\u2009\u03bc\u2009\u2264\u2009U(x), Neyman instead proceeds by working with the probability of the data x given the parameter value \u03bc: Pr(x|\u03bc). In contrast with posterior intervals, the value \u03bc is unknown but constant and the interval endpoints L(x) and U(x) are random.It is illustrative to follow the reasoning of Neyman, who developed the theory of CI's\u03bc is contained in every interval computed based on the data x, the scientist will be correct (1\u2009\u2212\u2009\u03b1)% of the time in the long-run. He writes that the use of the intervals in practice would consist of collecting data x, calculating the endpoints, and \u201c stating that the true value of \u03bc lies between [the interval endpoints]\u201d. He stresses that the word \u2018\u2018stating\u2019\u2019 \u201cis put in italics to emphasize that it is not suggested that we can \u2018\u2018conclude\u2019\u2019 that we can \u2018\u2018conclude\u2019\u2019 that [the true value of \u03bc\u2009=\u2009\u03bc*] is L(x) \u2264 \u03bc* \u2264 U(x) nor that we should \u2018\u2018'believe\u2019' 'that \u03bc*is actually between L(x) and U(x)\u201d and continues: \u201cthe probability statements refer to the problems of estimation with which the statistician will be concerned in the future\u201d, but \u201conce the sample is drawn and the values of L(x), U(x) determined, the calculus of probability adopted here is helpless to provide answer to the question of what is the true value of \u03bc\u201d.Neyman describes unequivocally the operational usage of CI's as \u201cbehavioral\u201d: when a scientist consistently adheres to the rule of deciding to accept that after observing the values of the x\u2019s [\u2026] we may decide to behave as if we actually knew that the true value [of the parameter \u03bc] were between [L(x) and U(x)]. This is done as a result of our decision and has nothing to do with \u2018\u2018reasoning\u2019' or \u2018\u2018conclusion'\u2019 [\u2026] The above process is also devoid of any \u2018'belief\u2019' concerning the [true value of \u03bc]\u201d'.Neyman\u2019s description excludes any probabilistic meaning attached to the endpoints of a particular interval: \u201cP-value in the case of P-intervals, and \u201c0\u201d indicates that the replication P-value is outside that interval. Properly constructed intervals applied repeatedly to independent data sets will result in 1\u2019s occurring with (1\u2009\u2212\u2009\u03b1) frequency. Although it is desirable to have the shortest possible intervals with this property, there is generally no information provided by the interval endpoints about a possible spread of replication P-values. However, interpretation of the classical interval endpoints in a meaningful way is warranted from a Bayesian viewpoint. A Bayesian derivation of a classical interval may reveal the tacitly assumed data generating mechanism. We will refer to that mechanism conventionally as an implicit prior distribution. It allows one to interpret the endpoints of a replication P-interval as (1\u2009\u2212\u2009\u03b1) probability of capturing the replication P-value. The endpoints of a P-interval are typically interpreted in a probabilistic fashion without specifying implicit prior assumptions. The following quote from Cumming2 gets to the heart of the matter succinctly: \u201cThis article shows that, if an initial experiment results in two-tailed P\u2009=\u20090.05, there is an 80% chance the one-tailed P-value from a replication will fall in the interval  [\u2026] Remarkably, the interval\u2014termed a P interval\u2014is this wide however large the sample size.\u201d An equivalent statement appears in a Nature Methods letter by Halsey and colleagues: \u201cregardless of the statistical power of an experiment, if a single replicate returns a P-value of 0.05, there is an 80% chance that a repeat experiment would return a P-value between 0 and 0.44.\u201d4 Both statements make use of a specific value, P-values.An important point in the preceding discussion of confidence and prediction intervals is that their coverage property is defined as a long-run average of zeros and ones, where \u201c1\u201d indicates an event that a random interval covers the quantity of interest, i.e., a replication P-interval coverage due to restrictions on the P-value range, consider the following example. Suppose one performs a test for the mean difference between two populations and predicts variability of P-values in a replication study by constructing the corresponding 80% P-interval. If multiple samples are drawn from these populations and 80% P-intervals are constructed each time regardless of whether the observed P-value was significant or not, the results of these multiple experiments can be summarized graphically by Fig.\u00a0P-value in the original study. The underlying effect size and sample sizes across studies are kept constant so replication values of the test statistic ranges from about negative two to positive two across all simulated experiments. Pink color highlights P-intervals that failed to capture the future value of statistic. Given these results, one can calculate an empirical binomial probability, i.e., the proportion of times a parameter was captured by the interval, which should be close to the stated nominal level. For instance, in Fig.\u00a0To further illustrate possible issues with P-intervals are constructed only if the experiment returns a P-value close to 0.05, Pobt\u2009\u2248\u20090.05. That is, all experiments with P-values that did not reach statistical significance are discarded and a particular P-interval is constructed only if the obtained P-value is close to 0.05. Would about 80% of the P-intervals constructed around the respective Pobt still capture the future value of statistic? An intuitive way to think about this scenario is in connection to the publication bias phenomenon, where the actual relationships tend to be weaker in reality than what was claimed in publications, and we may suspect that P-intervals should be similarly biased when constructed around non-random, selected subsets of P-values.Now, consider a bit different scenario, in which P-interval is constructed for a particular Pobt, how can one interpret its bounds? If it is constructed based on an 80% classical prediction interval for a normal test statistic as originally suggested by Cumming2, with no regard to prior distribution assumptions, by definition it guarantees that 80% of P-intervals will capture a replication P-value. That is, the lower and the upper bounds of a P-interval do not provide bounds on the range of possible values of a replication P-value.Further, once a P-values based on the Mixture Bayes approach whose endpoints have a clear probability interpretation for any specific interval constructed based on a given data set. Unlike the classical coverage property, Bayesian intervals based on a posterior P-value distribution have the interval endpoints that are directly interpreted as defining a target range to contain a replication P-value with probability (1\u2009\u2212\u2009\u03b1).Our main goal in this work is to derive prediction intervals for P-values can be viewed as random variables, reflecting variability due to random sampling. This notion goes back to Fisher, whose method of aggregating information from several independent P-values is based on recognizing the fact that their product is itself a random variable (and twice the negative logarithm of that product has a chi-square distribution)9. The distribution of P-value and thus its variability are easily characterized analytically for the basic test statistics and depend on a measure of effect size, such as the value of odds ratio (OR) of disease given exposure vs. nonexposure to a pollutant. The nature of P-value randomness may be viewed from a number of angles12, but the randomness of P-value reflects randomness of the respective test statistic. When the effect size is zero, P-value of a continuous test statistic is uniformly distributed between zero and one, and as the departure from the null hypothesis increases, the shape of the P-value distribution becomes increasingly skewed toward zero (suppl. section\u00a013) in which case the P-value distribution becomes a weighted average, i.e., a marginal distribution over all possible values of the effect with their respective probabilities as weights.P-intervals is that without specifying any prior knowledge on possible values of the effect size, one can take at face value the magnitude of an obtained P-value (Pobt). In other words, there is information about the magnitude of the effect size contained in the magnitude of Pobt, and that information alone can be used to make predictions about a P-value obtained in a replication study, denoted as Prep. As we illustrate with quotes from Cumming2 and Hasley4, practical applications of P-intervals are often factually Bayesian, defaulting to some interpretation about a possible spread of replication P-values. Our next goal is to explore relationships between P-intervals and Bayesian intervals. These relations are important because not explicitly stating a prior distribution amounts to sweeping a potentially unrealistic prior under the rug. In this work, we give explicit expressions for how the influence of the prior on the P-interval diminishes as more data is collected. Eventually, as the sample size increases, the P-interval endpoints approach those of the Bayesian intervals, but the sample size requirements depend on the variance of the prior distribution. In observational research, and especially in genetic association studies, where majority of tested hypotheses are effectually false, we find that sample sizes need to be very large.The idea behind the P-intervals can be viewed as a special case of the intervals that we develop: they correspond to the assumption that the product of the sample size N and the variance of the prior distribution \u03b4) is a \u201clarge\u201d number, in the sense that if we consider a normal random variable whose variance is \u03b4\u2009=\u2009\u03bc/\u03c3). Flat priors are sometimes described as \u201cnoninformative,\u201d reflecting lack of researcher\u2019s knowledge or preference about a possible effect size. Yet, far from being uninformative, the flat prior places equal weighting on tiny as well as on large deviations from the null hypothesis. For example, correlation (being the standardized covariance) cannot be outside -1 to 1 interval, so simply acknowledging this range in a prior is already an improvement over an unrestricted prior. If part of the replicability problem lies with the preponderance of tiny effects in reality, the a priori assumption of a flat distribution for the effect size implicit in P-intervals would tend to result in intervals with the left endpoint that is unrealistically close to zero and thus promote false findings.Further, we show that \u03b4\u2009=\u2009(\u03bc1\u2009\u2212\u2009\u03bc2)/\u03c3 for a given value of log(OR) cannot exceed \u03b4 values is unrealistic. To re-iterate this point, the effect size, for example, as measured by log(OR) can be quite large, but the standardized effect size \u2009\u2248\u20091/2. Such large ORs are rarely encountered in observational studies14, suggesting that realistic variance values \u03b4 for any OR, no matter how large, cannot exceed \u2248\u20090.663. This bound places further restrictions on realistic and maximum possible values of the prior variance 15 and cancers16 translates into the values of the order 10\u22126\u201310\u22125 for How large can P-intervals unfit as a prediction interval for a replication value\u2019s (Prep) variability and provide a generalization based on the Mixture Bayes approach, which is not constrained to the conjugate model only and provides researchers with the flexibility to specify any desired prior effect size distribution. Our results reveal immunity of the Mixture Bayes intervals to multiple-testing phenomena and to selection bias. When an interval is constructed for a particular value of Prep, its endpoints can be interpreted as a likely range of the Prep values. We contrast the performance of the traditional P-intervals relative to the Bayesian-based prediction intervals using results from the Psychiatric Genomics Consortium (PGS)5 and conclude with a discussion of the implications of our findings.In the next sections, we show how small values of P-interval can be obtained as a classical prediction interval for the normally distributed test statistics, (Z-statistics). The classical interval prediction problem is to probabilistically predict possible values of a future random observation, Xn+1, based on a sample of n values that have been already obtained, X1,\u2026,Xn. In the case of the Z-statistic, the information about the effect  is summarized by the sample average, Zrep is based on a single obtained test statistic, Zobt, that statistic, as well as its corresponding P-value, Pobt, depend on all n sample observations. Moreover, in cases such as this, P-value as the only summary of data, it is possible, at least for standardized effect sizes, to obtain the full Bayesian posterior distribution and to characterize uncertainty about the effect size values. This conversion of statistics or P-values to posterior distributions requires one to augment information contained in P-values with a prior distribution on the standardized effect size. This approach is quite general, because while effect size may be measured by different types of statistics, such as the difference of two-sample means, or the logarithm of the OR, the summary of the effect present in the data is captured by the same Z-statistic, and it is the type of the test statistic that determines the interval properties, rather than a particular measure of the effect size.The Zrep relates to one-sided P-value as Prep\u2009=\u20091\u2212\u03a6(Zrep) and has a normal distribution, \u03a6, where \u03a6(\u22c5) is the standard normal cumulative distribution function (CDF). Thus, the classical P-interval is constructed as:z\u03b1/2), whereZrep is \u03a6. Therefore, the P-interval based on the distribution \u03a6 is a Bayesian interval that implicitly assumes that s2|Zobt\u2009=\u20091 and the prediction distribution for Zrep equal to \u03a6. We refer to the resulting intervals as the Conjugate Bayes intervals. The endpoints of these intervals are given byThe prediction distribution for the statistic P-interval in Eq. . However, the conjugate model is restrictive in that a specific prior distribution has to be assumed, which may not provide an adequate representation of external knowledge about the effect size distribution. It also limits construction of the intervals to P-values derived from statistics for which there are known conjugate priors. Here, we introduce a more flexible approach, the Mixture Bayes, without these restrictions. The Mixture Bayes intervals can be constructed for P-values derived from statistics whose distribution is governed by a parameter \u03b3 that captures deviation from the usual point null hypothesis, H0, and has the form N\u2009\u00d7\u2009\u03b42. This includes normal, chi-squared, Student\u2019s t and F-statistics. We partition the prior distribution of \u03b41, \u03b42,\u2026, \u03b4B with the corresponding prior probabilities, Pr(\u03b4i). As an example, let P-value be derived from an F-test for comparison of two-sample means, with the corresponding sample sizes n1 and n2. Let N\u2009=\u20091/(1/n1\u2009+\u20091/n2). For i-th prior value of effect, a statistic based on sampling values of 1\u2009=\u20091, df2\u2009=\u2009n1\u2009+\u2009n2\u2009\u2212\u20092:f is the density of the noncentral F-distribution. The posterior distribution is a mixture,Derived as a Bayesian prediction interval through the conjugate model, the endpoints of a l in Eq.  can now Trep, asNext, we obtain the CDF of the prediction distribution for the replication statistic, Then, the Mixture Bayes interval endpoints are derived from the quantiles of this CDF that are given by https://github.com/dmitri-zaykin/bayesian-PValue-Prediction-Intervals. The software allows users to construct a Mixture Bayes prediction interval for a P-value from the standard normal, Student\u2019s t, chi-square or an F-statistic. For a P-value based on the standard normal or a t distribution, users have a choice between the conjugate normal model and the tabulated prior effect size distribution. For the F and the chi-squared test, no conjugate model exists, but prior values can be specified in a tabulated manner.We have developed a user-friendly software tool for implementation of our Mixture Bayes approach, available at p1 and p2, in the case of binary variables) as P-values for commonly used test statistics depends on the product of the sample size, , i.e. \u03b4\u2009=\u2009\u03bc/\u03c3. For example, when the outcome is a case/control classification and the predictor is also binary, the standardized effect size can be expressed in terms of the correlation (R) times the sample size as follows:v is the proportion of cases in the sample. In terms of the logarithm of the odds ratio, OR,Genetic epidemiology and other observational studies routinely test hypotheses conceptually related to a comparison of two-sample means. Effect size is often measured by the log of OR, which can be related to the difference in means  that we obtained by maximizing the right hand side of Eq. (13) as:For a given value of OR, the standardized effect size Pr(OR \u2265 x)\u2009=\u2009\u03b2 and assuming a symmetric distribution of the effect size around zero, i.e., m0\u2009=\u20090, we can relate the value \u03b4max to the prior variance of the conjugate model in the following way:Let The maximum spread for the conjugate prior distribution is, therefore, obtained when its variance is equal to\u03b4 value for a given value of OR, however, it is not monotone in OR. The maximum possible value of \u03b4max(OR) can be found to be at OR \u2248 121.35. Curiously, this value of OR implies \u03b4max(OR) value equal to the Laplace Limit constant, 0.662743\u2026It should be noted that Eq.  gives thP-interval is equivalent to a Bayesian prediction interval if 16 reported distribution of effect sizes for breast, prostate and colorectal (BPC) cancers in terms of a table, giving the numbers of different loci (Li) with the corresponding values of ORi. Using the same approach, Chen et al.15 provided the effect size distribution for the BP risk loci. Assuming the total number of independent variants to be M\u2009=\u2009300,000, proportions of associated loci are wi\u2009=\u2009Li/M. We assumed the average OR among non-associated loci to be 1.005 (or its inverse for the negative part of the log(OR) distribution). The variance \u22126 for both cancer and the BP disorder risk loci. Thus, N needs to be about 50,000 for In Eq. , we showP-interval and Mixture Bayes interval performance for the different values of prior variance P-values would be commonly selected. One may also select results with the largest effect sizes as tentatively most promising for a follow-up. This selection induces a \u201cselection bias\u201d, for example, the largest estimated effect size in the original study would tend to be smaller once re-evaluated in a replication experiment, a phenomenon also known as the winner\u2019s curse17. This would reflect the fact that the actual population effect size would tend to be over-estimated due to selection of the best outcome from the original study. An intuitive way of seeing why a selection bias would be present is to imagine a multiple-testing experiment where none of the tested predictors have any relation to the outcome. When one selects a predictor that showed the maximum estimated effect size, there will obviously be a bias, because the true effect size is zero. But this type of bias would also be present if the underlying effect sizes are non-zero for some or all of the predictors. Selection bias is difficult to correct for in the frequentist setting, but Bayesian analysis can be robust to this bias18. It is expected that the performance of frequentist-based P-intervals may suffer under selection while Bayesian-based intervals may not be affected by it. Thus, we investigated several types of selection and the resulting potential bias, measured by the proportion of times an interval captures Prep relative to the stated nominal level .In the next section, we explore P-value selection (simulation study set-up is detailed in Supplementary Information). The observed P-value was based on a two-sample Z-test and was thresholded according to the following selection rules: (i) no selection, i.e., a prediction interval is constructed for a randomly observed P-value; (ii) selection of P-values around a value, e.g., P-values that were close to the 5% significance level; (iii) selection of P-values that are smaller than a threshold, e.g., P-interval proposed by Cumming2.Table\u00a0\u03c30/8 for every component and truncated the normal prior at 10\u22126 and 1\u221210\u22126 quantiles. This provided us with sufficient accuracy and resulted in the number of mixture components, B, equal to 76 for all values of Mixture Bayes intervals were included in these simulations to check how well they approximate a continuous prior distribution assumed by the conjugate intervals. We used mixture components with the length P-value \u2208. However, selection and small prior variance both impair performance of P-intervals. For instance, if an interval is constructed for a P-value <\u20090.001 and P-interval may be as low as 17%. This poor coverage is due to a combination of both the selection bias and the implicit assumption that prior variance of P-interval endpoint being too close to zero. However, even for large values of prior P-interval has poor coverage when constructed for P-values around genome-wide significance levels . On the other hand, for large P-values the coverage of P-intervals becomes greater than the nominal (1\u2009\u2212\u2009\u03b1)% value. This is a consequence of the fact that P-interval\u2019s width depends on the magnitude of P-values and as P-values become larger, the width of the interval increases as well. For example, given the prior variance P-intervals and the Bayesian intervals coincides at P-value\u2009=\u20090.446 . The P-interval around P\u2009\u2264\u20090.995, while the Bayesian interval is 0.110 \u2264 P \u2264 0.958.Table\u00a0P-interval coverage for P-values less than 0.05, we replicated Fig.\u00a0P-interval is constructed only for P-values close to 0.05, P-intervals are becoming increasingly likely to miss Prep values altogether. The underlying effect size was kept the same in both figures and blue dots that represent values of zrep have similar range. Restricting P-values to be close to 0.05 induces selection bias, causing overestimation of the underlying effect size  and a vertical shift in P-intervals. Bias in coverage can be potentially removed by extending the interval endpoints by a correct amount, but the appropriate size of the interval appears difficult to determine analytically in a general way.To illustrate implications of decrease in entclass1pt{minimaP-value out of L tests  for attention deficit-hyperactivity disorder (ADHD), autism spectrum disorder (ASD), bipolar disorder (BPD), major depressive disorder (MDD), and schizophrenia. The consortium reported four single-nucleotide polymorphisms (SNPs) associated with these psychiatric disorders but, for illustrative purposes, we constructed prediction intervals only for a single SNP, rs2535629. We used four different methods to calculate prediction intervals: (i) the conjugate Bayesian model with the estimated prior variance, 15 (see Methods section); (ii) Mixture Bayes approximation to this continuous conjugate normal prior, using the same variance, P-intervals for one-sided P-values). We note that prediction intervals given in Table\u00a0P-value) scale. However, follow-up studies target replication of the directional effects. For example, if a study reports a risk allele for a phenotype of interest and a replicatioin study finds the effect to be protective, one can not conclude that the follow-up study replicated the original report. Thus, one-sided tests would be more appropriate in follow-up studies and prediction intervals for one-sided P-values should be of interest. To transform prediction intervals for a two-sided P-value in Table\u00a0P-value, one needs to subtract logarithm based ten of two  scale to P-value scale by raising ten to the negative logarithm based ten of the bounds power.To illustrate the interpretation of the prediction intervals and contrast the performance of the Bayesian-based intervals to the classical mentclass2pt{minimmentclass2pt{minimP-values based on the approach suggested by Lazzeroni et al.5 are smaller than the ones from the Bayesian-based methods. For instance, Lazzeroni and colleagues concluded that in a similarly powered replication of the original PGC design, a P-value for an association between rs2535629 and ADHD could be as low as P-value of 0.1005. Our interval results portray a less optimistic picture with the P-value lower bound for ADHD equal to 0.023. Similar observations hold for psychiatric disorders with significant observed P-values. For example, in Lazzeroni et al. the BP is concluded to be likely to yield a P-value between 1.69\u2009\u00d7\u200910\u221213 and 0.04 and thus could reach genome-wide significance  at a replication study. Mixture Bayes prediction interval based on the reported effect size distribution15 suggests a higher lower bound for BP replication P-value of 6.92\u2009\u00d7\u200910\u22127, concluding that a second, identical implementation of the original PGC design would be unlikely to yield any P-values <10\u22128. This difference in the spread of possible replication P-values highlights the implicit prior assumption built into the P-intervals that large effect sizes are as likely to be observed as small ones.Table\u00a0P-interval: /\u03c3, are readily extractable from P-values that originate from many basic and widely used test statistics, including the normal Z-statistics, Student\u2019s t-test statistics, chi-square and F-statistics.Despite their pitfalls, we believe that P-intervals, a careful construction of the prior distribution may be difficult\u2014a common issue in Bayesian analysis that is not unique to our particular method. Among other problems are assumptions of the model used to compute P-values themselves and including possibilities of confounding unaccounted for by the model. Keeping these limitations in mind, our results show that while classical P-intervals are derived without the explicit assumption that all effect sizes are equally likely, such a \u201cflat\u201d prior is assumed implicitly, whenever the endpoints of any given interval are interpreted as related to the range of replication P-values, which may lead to bias. For instance, bias will be present if a P-interval is constructed for a particular value, such as Pobt\u2009=\u20090.05. It should be recognized that in some experimental fields, statistical comparisons can be carefully targeted to investigate only those effects that are very likely to be real. A large probability of nearly zero effect size in the prior is inappropriate in this case. Still, one can argue that the prior should reflect some degree of skepticism toward a proposed hypothesis. On the other hand, under the flat prior assumption, all possible effect sizes are equally likely and hence a classical P-interval neither contemplates \u201ca degree of doubt and caution and modesty\u201d21 toward the hypothesis that the effect is present and substantial, nor acknowledges implausibility for the standardized effect size to take large values. When the effect size distribution is modeled in such a way that allows a proportionally small chance to encounter a large effect size and assumes that the majority of effect sizes would be close to zero, the Mixture Bayes approach would explicitly incorporate higher chances of what may be deemed \u201ca false positive result\u201d and it would adjust prediction interval bounds accordingly. Similarly, the flat prior assumption will lead to an invalid P-interval if it is constructed for a range of P-values . The (1\u2009\u2212\u2009\u03b1)% nominal coverage of P-intervals can be Bonferroni-adjusted5 for L tests as (1\u2009\u2212\u2009\u03b1/L)%. While that procedure can restore the long-run coverage property, i.e., (1\u2009\u2212\u2009\u03b1/L)% empirical binomial probabilities for P-intervals presented in Table\u00a0P-value. Further, we showed that a flat prior effect size distribution may be incompatible with the bounded nature of the standardized effect size distribution and once again may lead to biased P-intervals. For example, many observational studies are seeking for associations between health outcomes and environmental exposures and can be viewed conceptually as a comparison of two-sample means, \u03b4\u2009=\u2009\u03bc1\u2212\u03bc2. Presence of a true association in such studies implies a certain difference in mean values of exposure between subjects with and without disease. In such examples, the prior variance reflects the prior spread of the mean of a test statistic, which usually can be related to the spread of the standardized mean difference. The prior spread in units of standard deviation cannot be very large, especially in the fields of observational sciences, that are currently at the focus of the replicability crisis. For example, assuming that effect sizes with the OR greater than three are relatively rare (1% occurrence rate), the prior variance for \u03b4 can not exceed approximately \u22120.66 < \u03b4 < 0.66 for any value of OR.Here, we focus on one of many aspects of statistical assessment of replicability; moreover, there are limitations to our approach. While we believe that due to the limited range of possible values for standardized effect size, it is difficult to do worse in terms of mis-specification of the prior distribution than to assume the prior implicit in lue (Eq. ) and wouP-values is present. Reanalysis of the intervals reported by Lazzeroni and colleagues5 shows that P-intervals can be substantially different from Bayesian prediction intervals, even when sample sizes are very large  are deemed to be statistically significant , where F(Z) is the tail area of the normal curve from\u2014\u221e to Z. The probability of the null hypothesis given the P-value takes a very similar form, N is the half of the harmonic mean of the sample sizes n1, n2, and \u03d1 is the variance of a zero-centered prior distribution for the standardized mean. Clearly, the one-sided P-value approaches this posterior probability as N increases.It is notable that a major part of P-values, or some modifications of them can be useful. Rather than adopting the view that P-values should be abandoned because they are poorly suited for what they are used for in practice, we advocate development of statistical methods for extracting information from them in such a way that when augmented with the external (prior) information about the effect size distribution, P-value can be transformed into a complete posterior distribution for a standardized effect size. How small a particular P-value is (its magnitude) does not inform us what to expect in a replication study25. Nevertheless, P-values, as transformations of statistics (such as the Z-statistic) contain summary information about the standardized effect size. Conditional on that information, one can predict a possible spread of future P-values and the respective statistics in replication studies. As part of addressing the multifaceted replicability crisis, researchers would benefit from availability of tools for prediction of variability inherent in commonly used statistics and P-values. In particular, prediction intervals equip researchers with quantitative assessment of what they may expect if they would have repeated their statistical analysis using an independent confirmatory sample.Overall, we share the viewpoint of Lazzeroni et al. that Supplementary Material"}
+{"text": "Reaching toward a point target has been intensively studied in human motor control. However, little is known about reaching toward a redundant target, such as grasping a bar, in which the grasping point is irrelevant to the achievement of a task. We examined whether humans could solve the target-redundancy and control problems in a serial fashion or control their body without solving the target-redundancy problem. We equalized the target ranges between two reaching tasks: a point-to-point reaching task without target-redundancy and a point-to-bar reaching task with target-redundancy. In the both tasks, we measured hand viscoelasticity at movement end as parameters that reflect the adopted control strategy. As a result, the hand viscoelasticity in the point-to-bar reaching task was smaller than that in the point-to-point reaching task, even under the same kinematics. These results indicate that the hand viscoelasticity was modulated depending on the target-redundancy. Moreover, it is suggested that a human reaches toward a redundant target by effectively utilizing information of target redundancy rather than explicitly solving the target-redundancy problem. When we move our hand to some specific target, we plan how to reach it before performing a hand movement24We hypothesized two types of strategies adopted by the CNS to deal with the target redundancy in the point-to-bar reaching task. One is a strategy that explicitly solves the target redundancy problem. In this strategy, the CNS explicitly determines a specific target point on the bar to transform the point-to-bar reaching problem to the point-to-point one. After solving the redundancy problem, the CNS can use the same control strategy in both point-to-bar and point-to-point reaching movements. An alternative type is a strategy that does not explicitly solve the target redundancy problem. In this case, the CNS temporarily holds information of a target redundancy and utilizes it for the planning and execution of a point-to-bar reaching movement. Therefore, the CNS adopts different strategies to perform the point-to-bar and point-to-point reaching tasks. This implies that the CNS utilizes the information of target redundancy to generate a motor command. In this study, we investigated which type of strategy the CNS adopts to perform the point-to-bar reaching task. In other words, this study investigated whether the CNS explicitly solves the target redundancy problem during movement planning.et al. reported that the limb stiffness was modulated when the shape of the target changedWe have to control movement conditions to compare the difference in control strategies from the kinematics. In this study, we controlled experimental environment, start position of movement, target position, required movement precision, and movement duration between two reaching tasks and equalize kinematics between the tasks. Previous studies have indicated that humans voluntarily control their viscoelasticities  according to the goal of the given task678t-test showed no significant difference in the X-direction: t(9)\u2009=\u20090.26, P\u2009=\u20090.80 or the Y-direction: t(9)\u2009=\u2009\u22121.74, P\u2009=\u20090.12). These results indicate that we could properly control the movement kinematics in both reaching tasks.To properly compare control strategies from motor outputs, we controlled the movement kinematics. First we check the movement kinematics in both reaching tasks. The subjects showed similar amplitude of variability of hand position at movement end in both reaching tasks (n\u2009=\u200910), the stiffness component along the X-axis in the point-to-bar task was significantly smaller than that in the point-to-point task (t-test: t(9)\u2009=\u2009\u22123.59, P\u2009=\u20090.0058\u2009<\u20090.01). However, the stiffness component along the Y-axis was not significantly different between the two tasks (t(9)\u2009=\u20091.50, P\u2009=\u20090.17). Moreover, the hand viscosity showed similar results for hand stiffness (n\u2009=\u200910), the viscosity component along the X-axis in the point-to-bar task was significantly smaller than that in the point-to-point task (t-test: t(9)\u2009=\u2009\u22123.10, P\u2009=\u20090.013\u2009<\u20090.05). However, the viscosity component along the Y-axis was not significantly different between the two tasks (t(9)\u2009=\u20090.84, P\u2009=\u20090.42\u2009>\u20090.05). These results indicate that subjects modulated hand viscoelastic properties along only the X-axis, which is switched from the redundant direction to the control direction depending on the task.Next we check the movement dynamics. tiffness . Specifitiffness . AccordiIn this study, we examined how the CNS deals with the target redundancy, i.e., the target redundancy problem is explicitly solved or not. In the point-to-point reaching, the CNS deals with the hand trajectory redundancyet al. reported that the shape of the target, i.e., the required movement precision, affects the limb stiffnessX-direction, the variability of hand position at movement end in the point-to-point task would be smaller than that in the point-to-bar task due to the small size of the target. However, there was no significant difference in the standard deviation of hand position at movement end between the two tasks  the response to the external perturbation was not modulated based on target redundancy, and (2) no directional modulation of hand stiffness was observed5119Tagliabue, Ten healthy right-handed males participated in the experiments. Their average age was 25.8 (20\u201333 years). Their dominant hand was assessed by the Edinburgh handedness inventoryWe used a manipulandum system named \u201ctwin visuomotor and haptic interface system (TVINS)\u201d to record force and movement kinematics of both hands at 2000\u2009Hz . SubjectY-direction was fed back. Thus, subjects needed to control only the Y-directional movement. The target bar and subject\u2019s hand were displayed by a 1.5\u2009cm\u2009\u00d7\u200919\u2009cm rectangle and a 2\u2009mm\u2009\u00d7\u200919\u2009cm rectangle (line), respectively. In the point-to-point reaching task, the hand positions in both directions were fed back. Thus, subjects had to control both directional movements. To equalize the target ranges between the two reaching tasks, we determine a target length in the X-direction in the point-to-point task as the standard deviation of hand position at movement end in the point-to-bar task. This enabled us to control the kinematic properties of movements in the point-to-point task to those in the point-to-bar task. Specifically, the target point width along the Y-axis was 1.5\u2009cm, as with the point-to-bar reaching task, but the target length along the X-axis was\u2009\u00b1\u20092 standard deviation of hand position at movement end in the point-to-bar task (mean\u2009\u00b1\u2009SD: 3.13\u2009\u00b1\u20090.75\u2009cm). The position of the subject\u2019s hand was displayed by a 4-mm-diameter circle. The start position was displayed by a 1-cm-diameter circle placed 37\u2009cm ahead of the center of gyration of the shoulder. The center of the target in the point-to-bar task was 16\u2009cm ahead of the start position. The center in the point-to-point task was mean hand position at movement end in the point-to-bar task. We defined the times at movement start and end as the points when the tangential hand velocity was above and below 0.02\u2009m/s, respectively.Subjects performed the point-to-bar reaching task with the one-dimensional target for 80 trials first, then the point-to-point reaching task with the two-dimensional target for 80 trials . In the X-direction. They were not explicitly instructed where they should move the hand on the bar. In the point-to-point task, they were instructed to move the point within the box and to apply control of movements in both directions.Under both task conditions, subjects were instructed to move their hand 16\u2009cm toward the target in 0.55\u2009\u00b1\u20090.1\u2009s. In the point-to-bar task, they were instructed to move the line within the box and not to give attention to hand movements in the To estimate the hand viscoelasticity, we applied a positional perturbation to the subjects\u2019 hands by using the TVINS at movement end  and measured reactive force. The position of the manipulandum handle automatically shifted toward eight directions in a pseudo-random order. Each perturbation had small amplitude (7\u2009mm) and short duration (0.4\u2009s) with ramp-up, hold and ramp-down profiles . To miniP\u0394, velocity V\u0394, acceleration A\u0394, and force F\u0394 from perturbation onset. Using mean values of P\u0394and F\u0394 across a stable constant phase  phase, i.e., at a time when the first peak of hand force appears after perturbation onset .Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "The differences between \u03b2- and \u03b3-actin are deeper than those between the amino acid sequences of these two proteins. Related research article Vedula P, Kurosaka S, Leu NA, Wolf YI, Shabalina SA, Wang J, Sterling S, Dong D, Kashina A. 2017. Diverse functions of homologous actin isoforms are defined by their nucleotide, rather than their amino acid sequence. eLife6:e31661. doi: 10.7554/eLife.31661Protein isoforms \u2013 proteins that are similar to each other and perform similar roles within cells \u2013 have played an important role in the generation of biological diversity throughout evolution. In some cases a single gene can encode two or more isoforms by exploiting a process called alternative splicing. In other cases two or more closely related genes are responsible for the isoforms. At its simplest, isoform generation provides a mechanism to specialize the properties of a gene or protein at one of three levels \u2013 DNA, messenger RNA (mRNA) or the sequence of amino acids in the protein itself . DependiActins are proteins that are essential for a number of fundamental cellular processes such as cell division and muscle contraction. In mammals, there are six actin isoforms, and two of these \u2013 \u03b2-actin and \u03b3-actin \u2013\u00a0have been\u00a0the focus of much research over the past 40 years. It is not in dispute that \u03b2-actin and \u03b3-actin perform different functions in mammalian cells, and engage in distinct biological processes . MoreoveThe fact that \u03b2-actin and \u03b3-actin are both conserved across birds and mammals is clear evidence for selective pressure to maintain certain features of these two proteins. However, it is not clear why birds and mammals have evolved to use two near-identical proteins to build cell architecture . The nucNow, in eLife, Anna Kashina and co-workers at the University of Pennsylvania and the National Institutes of Health \u2013 including Pavan Vedula and Satoshi Kurosaka as joint first authors \u2013 report that the differences between \u03b2-actin and \u03b3-actin at the level of nucleotides may be as important as the differences at the level of amino acids . In a elBased on current knowledge, one might expect one of these roles to be localizing molecules of \u03b2-actin mRNA (but not \u03b3-actin mRNA) to the periphery of cells. However, Vedula et al. draw attention to another feature unique to the \u03b2-actin mRNAs: they have a much higher density of ribosomes than \u03b3-actin mRNAs. This does not relate to the relative amounts of the two proteins in cells, but to a large difference in the capacity of cells to make\u00a0these proteins at any point in time. The fact that a cell can produce a large amount of \u03b2-actin protein in a short burst, whereas it would take a longer time to produce the same amount of \u03b3-actin, could be significant. They also report differences in ribosome density between other actin isoforms and isoforms of histones and tubulins.In the mid-1970s the Nobel Prize-winning biologist Francois Jacob eloquently argued that much of evolution is 'tinkering' . But wou"}
+{"text": "We obtain some conditions for real-valued functions to be a (edge)  BCK-algebras and BCI-algebras were introduced by Is\u00e9ki and Is\u00e9ki and Tanaka  selective d-algebras and pre-d-algebras, and they showed that the squared algebra d-algebra d-algebra if and only if d\u00a0/\u00a0BCK-algebras. Using such deformations, d-algebras were constructed from BCK-algebras. Kim et\u00a0al.  d-algebra  (Neggers and Kim X with a constant 0 and a binary operation \"(I)(II)(III)For brevity we also call X a d-algebra. In X we can define a binary relation \"\u2264\" by A strong d-algebra (V)A d-algebra which is not a BCK-algebra. polynomial real algebras by using the real functions. In \"d-algebras. In \"d-algebra. We may apply the analytic method discussed here to several algebraic structures, and it may useful for find suitable conditions to construct several algebraic structures and many examples.We constructed some algebras on the set of real numbers by using elementary functions. The notions of (edge)"}
+{"text": "Nature Communications 10.1038/s41467-018-03540-1, published online: 19 March 2018.Correction to: The original version of this Article contained an error in the first sentence of the Acknowledgements section, which incorrectly referred to the Estonian Research Council grant identifier as \u201cPUTJD618\u201d. The correct version replaces the grant identifier with \u201cPUTJD619\u201d. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "In this note, we give an elaboration of a basic problem on convergence theorem of  The rapid development of q-calculus has led to the discovery of various generalizations of Bernstein polynomials involving q-integers. A detailed review of the results on q-Bernstein polynomials along with an extensive bibliography is given in [q-Bernstein polynomials are shown to be closely related to the q-deformed binomial distribution [q-boson theory giving a q-deformation of the quantum harmonic formalism [q-analogue of the boson operator calculus has proved to be a powerful tool in theoretical physics. It provides explicit expressions for the representations of the quantum group q-oscillator algebras well known in the earlier physics literature related to the representation theory of single parameter quantum algebras [During the last decades, the applications of given in . The q-Bribution . It playormalism . The q-at}SUq(2) . Meanwhialgebras .p and q versus single parameter q-Bernstein-type operators [Recently, ursaleen . BesidesMirakyan , BaskakoMirakyan  and KantMirakyan  operatormentclasspt{minimaMirakyan . For furMirakyan , 16\u201318. perators , 20. Theperators ).k and k, n with For example, consider the posed in . Given \\p and q with n. We then choose a sequence In general, we expect The convergence theorems for ers . For exers (ii)Since Set We assert that the inverse proposition of (ii) also holds. Indeed, for each sufficiently large Next, we infer that as . \u2018\u21d0\u2019 of , we knowTherefore, (low from  and (2.1low from .\u2003\u25a1(If In general, from  we have (If (If Similarly, from (n, there exists In Case (Now we utilize Theorem For n\u2192\u221e. See , Theoremn\u2192\u221e. See , formulaIn this note, we mainly obtain the sufficient and necessary conditions for"}
+{"text": "Fully gapped d-wave superconducting states have, however, been proposed in several cuprate systems thanks to subdominant order parameters producing d\u2009+\u2009is- or d\u2009+\u2009id\u2032-wave superconducting states. Here we study both magnetic and potential impurities in these fully gapped d-wave superconductors. Using analytical T-matrix and complementary numerical tight-binding lattice calculations, we show that magnetic and potential impurities behave fundamentally different in d\u2009+\u2009is- and d\u2009+\u2009id\u2032-wave superconductors. In a d\u2009+\u2009is-wave superconductor, there are no bound states for potential impurities, while a magnetic impurity produces one pair of bound states, with a zero-energy level crossing at a finite scattering strength. On the other hand, a d\u2009+\u2009id\u2032-wave symmetry always gives rise to two pairs of bound states and only produce a reachable zero-energy level crossing if the normal state has a strong particle-hole asymmetry.Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure  The cuprate superconductors with their much high transition temperatures would here be a tantalizing option, if it were not for their d-wave order parameter symmetry which enforces a nodal energy spectrumd-wave superconductor can only host virtual bound states72Cu3O\u03b47\u2212 a fully gapped spectrum has recently been discovered and attributed to the existence of subdominant order parameters, with the superconducting symmetry likely being either d\u2009+\u2009id\u2032)22\u03c0/2-phase shift relative to the dominant order. The d\u2009+\u2009id\u2032-wave state is also a chiral state with its non-trivial topology classified by a Chern number N\u2009=\u20092d\u2009+\u2009is- or d\u2009+\u2009id\u2032-wave symmetry.One severely limiting factor in all these studies is the low superconducting transition temperature accompanied by the small energy gap associated with conventional d-wave superconductors. More specifically, we investigate the intra-gap bound states due to potential and magnetic impurities using both an analytic continuum T-matrix formulation and numerical tight-binding lattice calculations. We show that impurities create entirely different bound states in d\u2009+\u2009is-wave and chiral d\u2009+\u2009id\u2032-wave superconductors, despite both being fully gapped and with a dominant parent d-wave state. For a d\u2009+\u2009is-wave superconductor we find that a potential impurity does not induce any bound states, while a magnetic impurity gives rise to a pair of bound states, which behaves very similar to the YSR bound states in conventional s-wave superconductors. This includes the behaviour of the energy spectrum when tuning the scattering strength Umag of the magnetic impurity. Since the d\u2009+\u2009is-wave state is topologically trivial and with a low-energy s-wave gap, this resemblance with a conventional s-wave superconductor is very plausible. More specifically, we find that the magnetic impurity bound states have a zero-energy level crossing at a finite critical scattering d-wave to the subdominant s-wave order parameter. Moreover, through self-consistent tight-binding calculations we find a first-order quantum phase transition at \u03c0-phase shift for the s-wave component of the order parameter.In this work we establish the properties of both potential and magnetic impurities in these two fully gapped d\u2009+\u2009id\u2032-wave state we find a very different behaviour. Here both potential and magnetic impurities induce two pairs of bound states. For superconductors with a particle-hole symmetric normal state, the bound states are two-fold degenerate and there is no level crossings for any finite coupling. Instead, it is only in the unitary scattering limit (Uc\u2009\u2192\u2009\u221e) that the bound states approach the middle of the gap. Doping the normal state away from particle-hole symmetry, the degeneracy is lifted for a magnetic impurity but not for a potential impurity. Moreover, for finite doping there is now a zero-energy level crossing, but for low doping it occurs only at very large scattering strengths. Self-consistent calculations for a single impurity in a d\u2009+\u2009id\u2032-wave superconductor finds a first-order phase transition at the level crossing, but no local phase shifts in either the dominant or subdominant order parameters. Considering that recent experiments have demonstrated access to adjustable magnetic scattering strengths Umagd\u2009+\u2009id\u2032-wave state and the likewise time-reversal symmetry breaking but topologically trivial d\u2009+\u2009is-wave state.For the chiral d-wave state, which persist even above the superconducting transition temperature and consequently, can not be considered to be a good probe of the symmetry of the superconducting stated-wave superconductors offer a tantalizing alternative due to potentially much higher superconducting transition temperatures. Our results show that magnetic impurities in both d\u2009+\u2009is- and d\u2009+\u2009id\u2032-wave superconductors are interesting systems in this regard, as they generate zero-energy impurity states with no band degeneracies.These results have several important consequences. In spite of impurities only generating localized imperfections to the lattice structure, we find that they are very suitable for probing and differentiating the symmetry of the superconducting state. Our results show that the symmetry of the order parameter can even be probed by simply counting the number of induced subgap states. This is in sharp contrast to the virtual bound states in the pure d-wave superconductors with a fully gapped energy spectrum. Introducing a subdominant superconducting order parameter will achieve this, since it very generally align with a complex \u03c0/2 phase relative to the dominant d-wave state. Here we consider a two-dimensional (2D) Impurity-induced bound states only exist in \u0127\u2009=\u20091)The Hamiltonian in the presence of a single impurity  reads . The exact form of \u03be(k) is unimportant as we can linearise the spectrum around the Fermi level, setting k| for the order parameter. The dominant order parameter is \u03941(k), while \u03942(k) represents the subdominant order parameter. We assume that the magnetic moment is large enough to ignore quantum fluctuations and thus we treat the impurity as a classical spin. The local moment of the impurity is directed along the z easy axis, but it is straightforward to show that the results are not affected by this assumption, since the electrons pair in the spin-singlet channel. This is different from magnetic impurities in p-wave superconductors, where the direction of the impurity generally affects the bound state energy\u03c4i and \u03c3i are the Pauli matrices acting in particle-hole and spin spaces, respectively, while \u03c40 and \u03c30 are unit matrices. The bare Green\u2019s function for the superconductor iswhere we use the Nambu space spinor magnitude of the wave vector k, but only on its direction with the energy spectrum Fi(\u03c9) asLet us first consider a fully particle-hole symmetric spectrum for the normal state, which imposes \u03c1\u2009=\u2009kF/(2\u03c0\u03bdF) is the density of states of the 2D free electron gas at the Fermi level. The above result is for a particle-hole symmetric normal state, but this symmetry is often broken in reality. We use the chemical potential \u03bc to measure the degree of particle-hole symmetry breaking in the energy spectrum, thus leaving the case \u03bc\u2009=\u20090 to represent full particle-hole symmetry. Considering a small deviation from particle-hole symmetry, such that F3\u03c43\u03c30. Up to first order in F0, F1, and F2 remain unchanged from the particle-hole symmetric case.Here F1(\u03c9)\u2009=\u20090, due to the periodicity of the cosine function and the subdominant order parameter \u0394s not depending on \u03d5. Then, in the limit of \u03bc\u2009=\u20090, the bound states can be found as the solutions toFirst, we consider the Umag. In order to find the bound state energies for a magnetic impurity we rephrase F0(\u03c9) and F2(\u03c9) in terms of the complete elliptic integral of the first kind KSince we are interested in real bound states, we only look for solutions s-wave superconductor: d\u2009+\u2009is-wave superconductor comes as the solution of s-wave superconductor, where the level crossing signals a quantum phase transition between two different ground states. For a magnetic impurity stronger than d\u2009+\u2009is-wave superconductor. Interestingly, for a d\u2009+\u2009is-wave superconductor, the critical coupling depends only on d and \u0394s separately. By setting s-wave parameter is small compared to the d-wave order.where we have defined If we now break the electron-hole symmetry of the normal state, i.e. assume d\u2009+\u2009is-wave superconductor. Moreover, the modifications of the bound state spectrum induced by a magnetic impurity is of the order It is clear that also in this case, for a purely potential impurity there are no real roots and consequently, potential impurities never induce any bound states in a d-wave or \u03d5) and sin(2\u03d5), all off-diagonal terms in the summation of the bare Green\u2019s function, i.e. Fi with \u03bc\u2009=\u20090) is then onlyNext, we turn to the impurity bound state formation inside the gap of a chiral In this case the bound states are found as the solutions tod-wave superconductor lead to exactly the same pairs of intra-gap bound states, these states are explicitly shown in \u03bc\u2009=\u20090 we find that for a potential impurity the negative energy branch (those occupied at zero temperature) consist of one spin-up and one spin-down state, and there is thus a Kramers degeneracy of the states. However, for a magnetic impurity the bound states with negative energy are both spin-down quasiparticles. For an impurity with both potential and magnetic scattering effects on the charge carriers (Upot and Umag both non-zero), four non-degenerate bound states are generally present in a chiral d-wave superconductor, such that the two-fold degeneracy in Very interestingly, pure potential or pure magnetic impurities in a chiral F3\u03c43\u03c30, where, up to first order in d-wave state compared to the d\u2009+\u2009is-wave state. For a potential impurity the bound states energies are still two-fold degenerate, but a non-zero \u03bc shifts the energy of the bound states in the unitary limit, as is illustrated in \u03bc\u2009>\u20090, a level crossing now appears for repulsive impurity scattering (Upot\u2009>\u20090), while for a hole doped system, \u03bc\u2009<\u20090, the level crossing instead occurs for an attractive impurity (Upot\u2009<\u20090). Thus doping can be used as a simple means to control the level crossing for potential impurities. A local chemical potential induced by a tunneling probe could even offer in-situ tunability of the level crossingIf the particle-hole symmetry of the normal states is broken, here by setting \u03bc, as illustrated in Umag. In this case, one pair of bound states move away from the middle of the gap (thick red lines). For these states no zero modes are thus expected even in the unitary scattering limit for any positive scattering Umag\u2009>\u20090. The other pair of bound states (thin blue lines) move toward the middle of the gap and consequently a level crossing appears at some Umag, the bound states also do not depend on the sign of \u03bc. Remarkably, the dimensionless critical coupling for reaching a zero-energy state for both magnetic and potential scatterers is the same \u03bc|.For a magnetic impurity the bound state degeneracy is lifted for finite s-wave superconductivity to the chiral d-wave. More precisely, if the order parameter takes the form s\u2032 is k-independent, the energy degeneracy for magnetic impurity bound states is lifted, while the bound states remain degenerate for a potential impurity. Therefore, the degeneracy of the bound states in the presence of a magnetic impurity in a chiral d-wave superconductor is very fragile and can easily be lifted.For the purpose of the forthcoming self-consistent numerical calculation, we mention already here that even at half-filling, the energy degeneracy can still be lifted by adding a small amount of extended d\u2009+\u2009is- and chiral d\u2009+\u2009id\u2032-wave superconductor. The effective Hamiltonian for the 2D superconducting host with an impurity with both potential and magnetic scattering elements located at R is refs 31We now turn to discuss the results obtained from tight-binding lattice calculations. In all calculations we use a generic finite-size square lattice in which we consider a single impurity located at the middle site. Again we consider both a i\u2009=\u2009 represents a site in the square lattice, with the lattice spacing a set to be 1. The dominant d-wave order exists on nearest neighbour bonds, while the subdominant s-wave order is an on-site parameter and the d\u2032-wave order reigns on next nearest neighbour bonds. For the self-consistent calculations (see below) we do not a priori assume any symmetries or conditions for any of these three order parameters. However, in calculations with constant order parameters throughout the sample, i.e. non-self-consistent calculations, we enforce the d-wave order by setting y-directed bonds is equal in magnitude but with opposite sign compared to the order parameter on x-directed bonds. Likewise, the d\u2032-wave state has opposite signs on bonds in the \u00b1(x\u2009+\u2009y) direction compared to bonds in the \u00b1(x\u2009\u2212\u2009y) direction. We also enforce the subdominant order parameter (s or d\u2032) to be purely imaginary in the non-self-consistent calculations.Here We solve 3233d-wave superconductor at finite doping, for both the numeric tight-binding method and an analytic T-matrix calculation. In order to be able to do this comparison, we evaluate the summations appearing in the T-matrix formalism for a discrete mesh over the first Brillouin zone of the square lattice using the same form of the kinetic energy. The main difference between the continuum and discrete calculation is that in the former we neglect the radial dependence of the order parameter in reciprocal space while in the latter, we keep both the radial and angular dependence. Therefore, the discrete summation over the full tight-binding model gives us a more relevant solution to compare with the finite-size numerical calculations. We also find an excellent agreement in the unitary scattering limit (Umag\u2009\u2192\u2009\u221e), which in the tight-binding lattice calculation can be implemented by simply removing the impurity site, thus creating a vacancy.We find that the tight-binding calculations fit exactly to the analytical T-matrix results. For instance, in V in each pairing channel and calculate the order parameter(s) explicitly everywhere in the lattice. For a d-wave state we use the self-consistent condition i, j are nearest neighbour sites. In the self-consistent calculation we start by guessing a value for \u0394d on each bond, solve d on each bond using the self-consistent condition, and repeat until \u0394d does not change between two subsequent iterations. For the d\u2009+\u2009is-wave state we also assume a finite Vs in addition to Vd and calculate separately d\u2009+\u2009id\u2032-wave state i, j are next nearest neighbour sites.Above we simply assumed constant order parameters and enforced the correct condensate symmetries. Now we allow the condensate to appropriately respond to the impurity through a proper self-consistent calculation. Since the superconductor symmetry is important for the properties of the bound states, this is the most accurate way to ensure a correct solution. In these self-consistent calculations we only assume a finite and constant pair potential d on x- and y-directed bonds are treated fully independent and the same applies to the d\u2032-wave state. Thus, we have not a priori assumed any symmetry for any of the pairing states. In the calculations we use Vd/t\u2009=\u20091.7, Vs/t\u2009=\u20091.7 for d\u2009+\u2009is-wave state and Vd/t\u2009=\u20091.8, Vd\u2032/t\u2009=\u20091.7 for chiral d-wave state, but the results are not sensitive to these particular values. We also set \u03bc/t\u2009=\u2009\u22121 for the most general case and to avoid the van Hove singularity at half-filling. We mainly use a 51\u2009\u00d7\u200951 lattice, with similar results obtained with a 31\u2009\u00d7\u200931 lattice, which guarantees that the results are not sensitive to the lattice size.We take the initial guess for the subdominant order parameter to be purely imaginary but through the self-consistency loop it is free to acquire a real component as well. Likewise, we emphasize that \u0394d\u2009+\u2009is- and d\u2009+\u2009id\u2032-wave states in the presence of either magnetic or potential impurities. The self-consistent tight-binding lattice calculations reveal that the results obtained for fixed order parameters are still largely valid. However, important effects appear around the critical scattering strength in the self-consistent calculations. Starting with the d\u2009+\u2009is-wave state, the self-consistent results show that the intra-gap localized bound states from a magnetic impurity behave largely in a similar way to their non-self-consistent counterpart as seen in s-wave superconductorUsing the self-consistently calculated order parameters, we extract the LDOS at and close to the impurity site for both s-wave and s-wave order parameter. This extended s-wave order resides on the nearest neighbour bonds and appears only very close to the impurity. It is thus a direct consequence of the impurity weakening the d-wave character in favour of the more disorder-robust s-wave symmetry. At the quantum critical point this extended s-wave state even becomes the dominant order parameter but notably only at the impurity site, farther away the d-wave order parameter is still dominant. In addition, both the s-wave and extended s-wave order parameters develop a \u03c0-phase shift on the impurity site across the critical coupling. This is in line with previous calculations for pure s-wave superconductors where the s-wave state undergoes a local \u03c0-shift1530d-wave state stays constant.The order parameter at the impurity site shed more light on this transition as can be seen in d-wave superconductor, there is only a level crossing for one pair of bound states as seen in d\u2009+\u2009is case. Considering the order parameter, the self-consistent calculation reveals that the dominant dxy-wave state, as seen in in s-wave components appear on nearest and next-nearest neighbour bonds, defined here as \u0394s and \u0394s\u2032, respectively. Interestingly, this means that for a chiral d-wave superconductor, the impurity does not disturb the dominant d-wave orders nearly as much as in the d\u2009+\u2009is-wave case. Despite the smallness of the s-wave components generated in the self-consistent calculations, we find that they are still responsible for lifting of the degeneracy of the impurity bands in the half-filled lattice case (\u03bc\u2009=\u20090).For the case of a magnetic impurity in a chiral d-wave superconductors. The main results are summarized in d\u2009+\u2009id\u2032-wave superconductor, while for a d\u2009+\u2009is-wave superconductor, there is only one (zero) pair of bound states for a magnetic  impurity. As a result, the number of intra-gap bound states becomes a powerful means for establishing the symmetry of the superconducting state in a fully gapped d-wave superconductor, such as that recently established in cuprate nanoislands or at certain cuprate surfaces22In this work we have investigated impurity-induced bound states in fully gapped d\u2009+\u2009is-wave and chiral d-wave superconductors is the behaviour of the zero-energy level crossings for the impurity-induced states. For a d\u2009+\u2009is-wave superconductor, increasing the magnetic scattering strength Umag leads to a level crossing of the bound states, which means there always exists a critical coupling d\u2009+\u2009id\u2032-wave superconductor there is no level crossing for a particle-hole symmetric normal band structure (here indicated by \u03bc\u2009=\u20090) at any finite scattering strength, for either potential or magnetic impurities. Only at significant doping away from \u03bc\u2009=\u20090 there is a zero-energy level crossing at an experimentally achievable scattering strength. It is also important to notice that the impurity bound states in a chiral d\u2009+\u2009id\u2032-wave superconductor are often twofold degenerate for both potential and magnetic impurities. For a magnetic impurity the degeneracy is lifted by either a finite \u03bc or by ever-present subdominant extended s-wave components, as we find in our self-consistent calculations, nonetheless, there are often two nearly degenerate states.Another important difference between d\u2009+\u2009is- and d\u2009+\u2009id\u2032-wave superconductors, have the potential for hosting Majorana fermions. However, in the case of a single impurity, the two zero energy states at s-wave456d\u2009+\u2009id\u2032-wave31d\u2009+\u2009id\u2032-wave superconductor the near degeneracy of the impurity bands however possess additional complications for Majorana fermions in an impurity wire. An even number of positive (or negative) near zero-energy states in the single impurity limit will result in two putative Majorana end modes for a wire, which then hybridize and split off from zero energy, losing their Majorana character. Thus, in terms of the potential for generating Majorana modes, our results directly shows that only magnetic impurity wires in a d\u2009+\u2009is-wave superconductor or in a heavily doped d\u2009+\u2009id\u2032-wave state are promising systems.The systems with zero energy states and no impurity band degeneracies, i.e. magnetic impurities in both d\u2009+\u2009is and d\u2009+\u2009id\u2032-wave superconductors, these are first-order quantum phase transitions, with clear discontinuities in both energy levels and order parameters. For the d\u2009+\u2009is-wave state we even find a local \u03c0-shift at the phase transition for all subdominant order parameters, consistent with the behaviour in conventional s-wave superconductors30d\u2009+\u2009id\u2032-wave superconductor we, however, do not find any \u03c0-shifts.Finally, we emphasize that our self-consistent calculations confirm our analytical results where we have assumed constant order parameters uninfluenced by the impurities. In addition, the self-consistent calculations shed more light on the nature of the zero-energy level crossings and show that for both How to cite this article: Mashkoori, M. et al. Impurity bound states in fully gapped d-wave superconductors with subdominant order parameters. Sci. Rep.7, 44107; doi: 10.1038/srep44107 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations."}
+{"text": "N = 207 older adults (age 45\u201360) working full-time (>30-h/week) were randomly assigned to SLE questions framed as either \u2018Live-to\u2019 or \u2018Die-by\u2019 to evaluate competing predictions for FTP. Results indicate general support for decreasing age-change in FTP, indicated by independent-sample t-tests showing lower FTP in the \u2018Die-by\u2019 framing condition. Further general-linear model analyses were conducted to test for interaction effects of retirement planning with experimental framings on FTP and intended retirement; While retirement planning buffered FTP\u2019s decrease, simple-effects also revealed that retirement planning increased intentions for sooner retirement, but lack of planning increased intentions for later retirement. Discussion centers on practical implications of our findings and consequences validity evidence in future empirical research of FTP in both workplace and retirement domains.Future time perspective (FTP) is defined as \u201cperceptions of the future as being limited or open-ended\u201d ; p. 125. On the other hand, retirement scholars regard FTP as mediating age effects for retirement planning  converge to yield static domain structures. That is, conditioning predictions on age for meaningful interpretation of relevant criteria across workplace and retirement domains, requires independence assumptions between work and retirement contexts. Independence of work \u2013 retirement domains is intuitively flawed, given the dependence of retirement from a previous worklife. Consequently, age is limitedly meaningful for the growing complexity and overlap of work and retirement contexts. This practical disconnect evidences in probabilistically opposing  age-predictions for FTP concerning the focal criteria of interest (delaying intentions/advancing preparations for retirement).Table 1).In contrast to age effects on employment and retirement, much less research attention has been given to its counterpoint, that is, subjective life expectancy SLE; . EmpiricTaken together, current empirical findings suggest that RetirPlan (accelerator) and FTP (delayer) may operate as competing mechanisms on retirement decisions Empirical support for the first mechanism, RetirPlan as-accelerator of workforce withdrawal is well-illustrated by the design of r = -0.45  work vs. non-work valuation (affect), and (2) short vs. long time horizons (cognitive), as two mechanisms linking work and retirement has not yet been evaluated in a single study. The goal of the current experiment, therefore, is to pit these competing mechanisms in an evaluative framework by manipulating SLE via attribute-framing conditions. The results are expected to clarify competing age-predictions for FTP across workplace and retirement research domains. Next, we will introduce our SLE manipulation for subsequently deriving our research hypotheses.live-to\u2019/\u2018die-by\u2019 95-years of age? The \u2018Die-by\u2019 frame has been found to lower SLE compared to \u2018Live-to\u2019 framings.The current study evaluates the competing predictions for age-FTP with an attribute-framing manipulation of SLE and simultaneous estimation of FTP and RetirIntent. Recent findings indicate that the framing of SLE questions, as either \u2018Live-to\u2019 or \u2018Die-by,\u2019 results in an SLE difference of approximately 7\u201310 years . ExampleConceptually, we may re-interpret this SLE manipulation as a \u2018subjective age\u2019 manipulation. In this case, if the \u2018Die-by\u2019 frame is successfully replicated so that it lowers SLE, we may interpret this as inducing \u2018older subjective age.\u2019 Consequently, the randomization of participants and comparison on FTP enables us to infer how FTP covaries with different perceptions of one\u2019s remaining lifetime/SLE. Restated in the context of formal hypothesis-testing, we hypothesize that the \u2018Die-by\u2019 SLE frame will reduce FTP compared to the \u2018Live-to\u2019 frame.H1: The \u2018Die-by\u2019 frame will decrease FTP compared to the \u2018Live-to\u2019 frame.Additionally, we include the variable \u2018retirement intention\u2019 in order to assess the consistency of directional effects across \u2018work\u2019 and \u2018retirement\u2019 domains. Specifically, if we accept retirement to be subsumed by overall age, then it follows that older workers (lower SLE from \u2018die-by\u2019 frame) should report closer proximity to retirement (sooner retirement). Thus, we also hypothesize that the \u2018Die-by\u2019 SLE frame will reduce retirement intentions compared to the \u2018Live-to\u2019 frame.H2: The \u2018Die-by\u2019 frame will decrease RetirIntent compared to \u2018Live-to\u2019 frame.Finally, \u2018retirement planning\u2019 is purposefully assessed before randomized treatment assignment (live-to/die-by). Therefore, because \u2018retirement planning\u2019 is domain-specific to \u2018life after retirement,\u2019 we assume that greater planning for this post-work time will reduce the negative effect of lowered SLE on FTP as a \u2018global\u2019 construct. That is, we hypothesize that RetirPlan will operate by interacting with the \u2018Die-by\u2019 frame by buffering its negative effect on FTP.H3: RetirPlan will interact with the \u2018Die-by\u2019 frame on FTP, such that high RetirPlan will reduce the negative effect.In contrast, we expect that the domain-specificity of \u2018retirement planning\u2019 and \u2018retirement intention\u2019 to conjoin, so that the hypothesized main-effect of \u2018sooner retirement\u2019 will be strengthened by more retirement planning . That is, we hypothesize that RetirPlan will operate by interacting with the \u2018Die-by\u2019 frame by strengthening its negative effect on retirement intentions.H4: RetirPlan will interact with the \u2018Die-by\u2019 frame on RetirIntent, such that high RetirPlan will strengthen the negative effect.In addition to hypothesizing SLE-manipulation effects via response processes, that is, on mean-level changes of our focal outcomes, we further explore the nomological pattern of correlates with relevant external variables, in particular, the association between RetirPlan and RetirIntent.N = 207 participated in \u20182 \u00d7 1\u2019 between-subjects experimental design. SLE served as between-subjects factor via the framing manipulation (\u2018Live-to\u2019 vs. \u2018Die-by\u2019). Inclusion criteria required that participants be presently working full-time (>30-h/week) for appropriate study of focal retirement variables. Amazon\u2019s Mechanical Turks crowdsourcing labor market was used for participant recruitment. Participants received nominal compensation ($1.50) for completion of the online experiment-questionnaire, with an additional incentive offered via a $100 lottery drawing.A sample of Figure 2 below.This study was carried out in accordance with the recommendations of \u2018international-ethical human study guidelines\u2019 in accordance with the Declaration of Helsinki. The protocol was approved by the authors\u2019 academic institutional review board (Georgia Institute of Technology). All subjects were given written, informed consent prior to participating in the online questionnaire. Additional educational materials on retirement preparation was provided for interested participants on completion of the questionnaire. See, Subjective life expectancy was assessed on a slider-scale with probabilities ranging from 0 to 100. Participants were instructed to use the slider to indicate their probability of living to ages 65, 75, 85, and 95-years old. Instructions varied with experimental condition, so that participants assigned to the \u2018live-to\u2019/\u2018die-by\u2019 condition read, \u201cUsing the slider scale below, please indicate the likelihood you currently believe you will \u2018live-to\u2019/\u2018die-by\u2019 65 / 75 / 85 / 95-years of age. Cronbach\u2019s internal reliability was estimated at \u03b1 = 0.83.2. Participants indicated their agreement with how \u201ctrue\u201d each item described themselves using a 7-point Likert-type scale from 1 (Very untrue) to 7 (Very true). A sample item is, \u201c(1) Many opportunities await me in the future.\u201d Cronbach\u2019s internal reliability was estimated at \u03b1 = 0.91.Carstensen and Lang\u2019s  original 10-item instrument was administered to assess FTPRetirIntent was assessed as a four-item composite of intended retirement age across four domains: \u2018current employer,\u2019 \u2018career,\u2019 \u2018occupation,\u2019 and \u2018general workforce.\u2019 Responses were recorded on a continuous scale. A sample item is, \u201cI intend to retire at age 66\u201395.\u201d Cronbach\u2019s internal reliability was estimated at \u03b1 = 0.89.RetirPlan was assessed with t-tests were conducted to compare means on FTP and RetireIntent. High- and low-RetirPlan groups were generated with median-splits on the RetirPlan variable in order to test interaction-hypotheses in our experimental design. In order to test for interaction-effect hypotheses, SPSS\u2019s univariate-general linear model procedures were implemented with SLE-experimental condition (Live-to vs. Die-by) and RetPlan groups (high vs. low) entered in a full-factorial model. Type III sums-of-squares were utilized in parameter estimate calculations. Significant-interactions were further inspected with simple pairwise-comparisons of experimental conditions within each level of the data-driven moderator (low/high RetirPlan). Bonferroni\u2019s corrections were implemented for managing Type-1 error rates from multiple-comparison tests. The observed-score general linear model was selected over latent-variable approaches3 due to its parsimony, including lower sample size requirements and our focus on competing predictions between specific relations/localized pathways .Preliminary response-quality screening, missing-data assessment, and hypotheses testing was conducted in SPSS v23. To test main-effects across our randomly allocated experimental groups, independent-sample Table 2 below. SLE-manipulation effects were successfully replicated, such that participants in the \u2018Live-to\u2019 condition reported a 10.02% greater chance of living to age 80 compared to the \u2018Die-by\u2019 condition . Notably, we observed a differential correlation between SLE-FTP that is consistent with theoretically competing age-predictions for FTP, r = 0.40(Live)/-0.30(Die). That is, the directional discrepancy may be retraced to \u2018younger\u2019 and \u2018older\u2019 populations that were the foci for early-child development and gerontological theories predating the lifespan framework\u2019s practical integration.Summary sample characteristics are reported in M = 44.74, SD = 11.15) compared to the \u2018Live-to\u2019 condition ; t(205) = 3.44, p = 0.03, Cohen\u2019s d = 0.48.Main effect hypotheses received mixed-support. Supporting H1, participants assigned to the \u2018Die-by\u2019 condition reported significantly lower FTP  compared to the \u2018Live-to\u2019 condition , but the effect was not significant; t(205) = 0.52, p = 0.31, Cohen\u2019s d = 0.07. Main effect results are summarized in Figure 3 below as standardized reductions of the \u2018Die-by\u2019 frame compared to the \u2018Live-to\u2019 frame.For H2, participants assigned to the \u2018Die-by\u2019 condition also reported lower RetirIntent  = 3.01, p = 0.044. A simple-contrast estimate indicated significance in the hypothesized direction, such that the \u2018Die-by\u2019 frame\u2019s negative effect on FTP was limited to low RetirPlan . In contrast, for high RetirPlan, the \u2018Die-by\u2019 frame had no effect on FTP . FTP\u2019s marginal-means used for simple-contrasts are illustrated in the left-panel of Figure 4.Interaction hypotheses for RetirPlan were generally supported. Specifically, regarding H3 for RetirPlan\u2019s buffering effect of the \u2018Die-by\u2019 frame on FTP, results indicated a significant interaction, F = 3.40, p = 0.03. A simple-contrast estimate indicated significance in the hypothesized direction, such that the \u2018Die-by\u2019 frame\u2019s negative effect on RetirIntent was significant for high RetirPlan . For low RetirPlan, an unexpected increase in RetirIntent was also observed, although it was only marginally significant . This unexpected cross-over interaction helps to explain the unobservable main-effect for RetirIntent, which would seem to-have been obscured. RetirIntent\u2019s marginal means used for these calculations are illustrated in the right-panel of Figure 4.Regarding H4 for RetirPlan\u2019s enhancing effect of the \u2018Die-by\u2019 frame on RetirIntent, results indicated a significant interaction, Table 3 below summarizes descriptive statistics for all simple-pairwise comparisons. Specifically, each row of Table 3 lists the mean differences of all 2 \u00d7 2 combinations of low/high RetirPlan for FTP and RetirIntent with Bonferroni-adjusted 95% confidence intervals [CIs] reported.Finally, r = 0.19, p = 0.04. In contrast, for the \u2018Die-by\u2019 condition, a significant negative correlation was observed, r = -0.22, p = 0.03. The latter finding supports views of RetirPlan as a mechanism that accelerates workforce withdrawal (earlier retirement).In addition to mean-level effects on focal outcomes, the patterning of external correlates was different across \u2018Live-to\u2019 and \u2018Die-by\u2019 conditions. Specifically, for the \u2018Live-to\u2019 condition, a significant positive correlation was observed between RetirPlan-RetirIntent, t-test was re-conducted, excluding the j = 3 reverse-scored FTP items. There remained a significant difference for the FTP subscore in the hypothesized direction across \u2018Live-to\u2019  and \u2018Die-by\u2019  conditions; t(205) = 3.84, p = 0.03, Cohen\u2019s d = 0.54. The pattern of interactions also remained unchanged in terms of direction and statistical significance.Given the patterning of external correlates, we considered additional explanatory causes for our experimental findings to support substantive interpretation of RetirPlan\u2019s moderation effects. First, we considered if the FTP main effect may be attributable to its sensitivity to \u2018careless responding\u2019 based on mix-scored items (positive- / reverse-scored). An independent-samples t-test was re-conducted separately for the low-Time and high-Time groups. The non-significant difference for RetirIntent remained for both the low-Time  and high-Time  groups. The pattern of interactions also remained unchanged in terms of direction and statistical significance. We summarize our findings and briefly elaborate their implications for future work-retirement integrative research in the section \u201cDiscussion\u201d below.Because our RetirIntent outcome comprised no reverse-scored items, we examined if the non-significant main effect would hold across a median-split on survey duration . An independent-samples The current study identified a construct, FTP, with disproportionate external validity evidence in a shifting applied context, specifically, workers and retirees. The mono-operation bias inherent to two contrarian theoretical origins of FTP across functionally dissimilar populations (workers and retirees), thus, vesseled weak validity evidence and poor verisimilitude . We evalr = 0.40) and negative in the \u2018Die-by\u2019 condition (r = -0.30). For hypotheses, H1 was supported with a significant negative effect of the \u2018Die-by\u2019 condition on FTP. The finding generally support inveterate lifespan theories that postulate age-related decline in FTP . Furthermore, we received support for FTP\u2019s hypothesized interaction with RetirPlan, such that participants reporting more RetirPlan were unaffected by the \u2018Die-by\u2019 framing\u2019s negative impact on FTP.Summarizing our findings, first, we successfully replicated the SLE-framing manipulation and observed the opposing relations between SLE-FTP, which was positive in the \u2018Live-to\u2019 condition  revealed an unexpected cross-over effect, providing some indication for obscuring the hypothesized main effect. Contrast analyses supported our hypothesis for RetirPlan\u2019s strengthening of the negative \u2018Die-by\u2019 effect. On the other hand, we also observed an unanticipated positive effect of the \u2018Die-by\u2019 condition on RetirIntent for low-RetirPlan. The cross-over effect could be interpreted as a delay of RetirIntent when shorter SLE is combined with inadequate preparation. This interpretation is consistent with recent empirical findings that indicate FTP\u2019s dual-mechanism of prompting planning and inducing sunk-cost biases/escalations of commitment with current conditions. That is, in the same way that job characteristics may enhance occupational FTP, contracted lifespans may induce avoidance of retirement\u2019s unknown, if ill-prepared, event space.Taken together, we hope that the current findings hold practical import for bettering the practice of career counseling and job crafting amid longer working lives. For example, practical implications of this experimental study intersect the age-integration of social institutions and domain-integration of work-life balance. To this end, results should inform ongoing areas of research on related lifespan concepts \u2013 For example, \u2018active aging\u2019 , \u2018aging-later RetirIntent. Although exploratory analyses were conducted to increase substantive inference from our findings, important limitations are noteworthy for cautious interpretation. For example, from a response-modeling perspective, our focus on latent-structural relations limited our examination of potential response biases to classical approaches, such as conditioning on standard- and reverse-scored items . The current authors concur with MK designed the experiment, recruited and ran participants, and conducted primary analyses. SE provided advanced-methodological consultancy and conducted expository write-up.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Scientific Reports 10.1038/s41598-017-03497-z, published online 16 June 2017Correction to: The original version of this Article contained a typographical error in the spelling of the author Zoran Jak\u0161i\u0107, which was incorrectly given as Zoran Ja\u0161i\u0107. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "An underestimated FDR can lead to unexpected false discoveries in the follow-up validation experiments. This issue has not been well addressed in literature, especially in the situation when the permutation procedure is necessary for p-value calculation.q-value. In practice, it is usually necessary to calculate p-value by a permutation procedure. This was also considered in our adjustment method. We used simulation data as well as experimental microarray or sequencing data to illustrate the usefulness of our method.We proposed a statistical method for the conservative adjustment of q-value, particularly in the situation that the proportion of differentially expressed genes is small or the overall differential expression signal is weak.The conservativeness of our approach has been mathematically confirmed in this study. We have demonstrated the importance of conservative adjustment of  Since the introduction of microarray technology, the concept of false discovery rate (FDR) and its related statistical methods have been well developed [q-value is a statistical method for the estimation of FDRs [Microarray and sequencing technologies have been widely used in genome-wide expression experimental for biological and medical studies \u20135. Aftereveloped , 7. q-va of FDRs . It has q-value is an estimation method, it is possible that it underestimates true FDRs. Then, an undesirable consequence is that many genes detected with low q-value cannot be validated in a follow-up experiment. Therefore, it is important to avoid underestimations of FDRs. However, there is a lack of statistical method to address this important issue. Furthermore, in many situations, q-values are calculated based on p-values that are evaluated based on a permutation procedure . Then, these p-values are also estimated. This increases the complexity of FDR underestimations. It is necessary to adjust the underestimation of FDRs in a comprehensive approach.Since q-value, which is one of the most frequently used procedure for estimating FDRs. We first reviewed the concepts of multiple hypothesis testing, FDR and q-value. Then, we introduced a concept of conservative adjustment. Based on the theory of rank-based quantiles, we described a non-parametric approach and we conducted simulation and application studies to illustrate its usefulness.In this study, we proposed a statistical method for the conservative adjustment of m total hypotheses, with a threshold for declaring significance, we have R hypotheses rejected (claimed positives). If we know the underlying nature of each variable, then its related hypothesis can be classified as either a true null or a false null (termed gold standard). If this information is provided, then we know the numbers U, V, W and S in Table U, V, W and S represent the numbers of true negatives, false positives, false negatives and true positives, respectively. However, in practice, the gold standard information (or the underlying nature) is usually unknown. Therefore, it is statistically interesting to evaluate U, V, W or S (or their combinations).When a large number of variables are simultaneously screened, it is usually a situation that a mixture of true and false null hypotheses is presented. . Statistically, this is a situation of multiple hypothesis testing (MHT). An illustrative summary is shown in Table V [p-value threshold), it is usually difficult to claim statistical significance. The false discovery rate (FDR) has been proposed to empirically evaluate the proportion of false positives among the claimed positives: V/R [q-value [The traditional family-wise error rate (FWER) provides a strong control on V . Since Fves: V/R . The con[q-value  is one oq-value method that is a statistical procedure for FDR evaluation. Suppose T is the test statistic and genes with test scores greater than or equal to t will be claimed significant. Let \u03b1 be the p-value at t, and let f(t) and s(t) be the expected numbers of false positives and significant genes, respectively. Storey and Tibshirani [T=t could be approximated by the proportion of false positives: Storey and Tibshirani  proposedbshirani  proposedm is the total number of genes and \u03c00 is the proportion of true null hypotheses  estimates mPr(T\u2265t).where p-value of t. Therefore, a permutation based p-value \u03b1. Then, the permutation version of q-value is In practice, it can be difficult to obtain the theoretical p-values, it is possible to obtain underestimated results. We have proposed a conservative adjustment of permutation p-values to address this issue [When the permutation method  is used is issue .q-value is actually a combination of three estimates: \u03c00,\u03b1,#{T\u2265t}) for mPr(T\u2265t). must still be empirically estimated even when \u03b1 can be theoretically determined. To address the underestimation of FDR , our solution is to consider a conservative adjustment of q(t).From above, notice that q-value for T=t can be defined as: \u03b1(t)=Pr(T\u2265t|H0) and \u03b3(t)=Pr(T\u2265t).According to Eq. , the thea)% conservative adjustment of q(t) as an estimator We define the 100(1\u2212Our solution for a0)(1\u2212a1)(1\u2212a2)\u22651\u2212a, then we claim that \u03c00,\u03b1(t)>0 and If , it is difficult to calculate a lower confidence limit of \u03c00 (the proportion of true null hypotheses) is usually conservatively estimated in practice [\u03c00 [convest [\u03c00. . According to our experience, it is reasonable to assume that Due to the identifiability issue, practice . Many stice [\u03c00 . Among t[convest  is a welconvest method (or other similar methods). Then, we discuss When q-values associated with observed test scores can be evaluated, and it is difficult to accurately evaluate the q-values for unobserved test scores. Here are the mathematical details. With a test statistic T, we can obtain m observed test scores {T1,T2,\u2026,Tm} for m variables (genes). An empirical estimate of \u03b3(t)=Pr(T\u2265t) is \u03b4(TRUE)=1 and \u03b4(FALSE)=0. If we sort these m test scores in an increasing order: T(1)\u2264T(2)\u2264\u2026\u2264Tm) can also be considered as the results from a particular permutation, they are generally included in the pool of permuted test scores. Based on r permuted test scores: \u03b1(t)=Pr(T\u2265t|H0) is If the theoretical distribution of rocedure  for evalr permuted test scores in an increasing order: If we sort these p-value of T=t will be t. Therefore, the permutation p-value of T=t can also be considered as a rank-based quantile estimator.Note that, if the observed test scores are not included in the pool of permuted test scores, then the permutation Since atistics , we haveatistics . Such anq-value method underestimates the true false discovery rate, we conducted a simulation study. We choose the normal distributions for simulating expression data and the Student\u2019s t for differential expression. In this way, we could evaluate the true false discovery rate theoretically.To understand how likely the N for both groups. Then, we considered four scenarios. For the first simulation scenario, the proportion of differentially expressed genes was 10%; the expression data for differentially expressed genes were simulated from N and N for the first and the second sample groups, respectively (\u0394=1). For the second simulation scenario, the proportion of differentially expressed genes was 10%; the expression data for differentially expressed genes were simulated from N and N for the first and the second sample groups, respectively (\u0394=2). For the third simulation scenario, the proportion of differentially expressed genes was 20%; the expression data for differentially expressed genes were simulated from N and N for the first and the second sample groups, respectively (\u0394=1). For the last simulation scenario, the proportion of differentially expressed genes was 20%; the expression data for differentially expressed genes were simulated from N and N for the first and the second sample groups, respectively (\u0394=2).Ten thousand genes were simulated for two sample groups with sample size 5 for each group . For non-differentially expressed genes, the expression data were simulated from t-test was used for differential expression analysis. To evaluate p-values, we performed all possible (126) permutations for each simulated gene and pooled all 1,260,000 permuted test scores together as the empirical null distribution.  For each scenario, we conducted 100 repetitions to understand the variations in the simulation results.For all different scenarios, the Student\u2019s q-values). In summary, when the proportion of differentially expressed genes (1\u2212\u03c00) becomes smaller (from 20 to 10%), it is more likely to obtain underestimated FDRs; when the signal of differential expression (\u0394) becomes weaker, it is more likely to obtain underestimated FDRs. Figure \u03c00=15%) and overall moderate differential expression signals (\u0394=1.5). Each curve is a comparison between the empirical FDRs  vs. theoretical FDRs (based on one repetition of simulation). Below 0.05 theoretical FDR, some curves can be observed under the diagonal line, which indicate that these empirical FDRs  are underestimated. Furthermore, among 100 repetitions, there is a considerable portion of empirical FDRs underestimated .The simulation results are shown in Fig. ler from 0 to 10%,q-value less than 10%. However, it may be surprising that much less genes can be confirmed after the RT-PCR validation.  This hypothetical situation would be an example of under-estimation of FDR.A conservative adjustment of false discovery rate (FDR) can be useful in practice, especially before the experimental validation of genes identified from a genome-wide expression study. For example, based on a microarray or RNA-seq study, one may want to validate a few genes with N and N for the first and the second sample groups, respectively. The expression profiles of non-differentially expressed genes were simulated from N for both groups. The Student\u2019s t-test was used for differential expression analysis. To evaluate p-values, we performed all possible (126) permutations for each simulated gene and pooled all 1,260,000 permuted test scores together as the empirical null distribution.  The convest method proposed by Langaas et al. [\u03c00, which was used in the q-value estimation procedure [q-value. Then, we considered a conservative adjustment. We set a0=0 , a=0.05). Figure q-values.To demonstrate the above situation, we conducted a simple simulation study. 10,000 genes were simulated for two sample groups. The sample size was 5 for each group. The proportion of differentially expressed genes was 10%. The expression profiles of differentially expression genes were simulated from s et al.  was usedrocedure . In thisWe applied our method to two genome-wide expression data sets. The first one was a microarray data set and it was collected for a diabetes study. It is well-known that differential expression signals are usually weak in diabetes studies. When the sample size is not relatively large, it is usually difficult to detect true differentially expressed genes. . It is interesting to understand the adjustment effects from our method for this scenario. The second one was a RNA sequencing (RNA-seq) data set and it was collected for a prostate cancer study. It is also well-known that differential expression signals are usually strong in cancer studies. Genome-wide expression data for different types of cancer have been increasingly collected in The Cancer Genome Atlas project . The cury-value is a specific FDR and the x-value is the related number of genes with the specific FDR). Our application results can also be summarized in term of this type of curve.In practice, it is not feasible to calculate the theoretical true FDRs. The curve of estimated FDR vs. number of identified genes is widely used to for a summary of differential expression analysis. . We set a0=0 . Figure q-values (estimated FDRs) can only be as low as slightly less than 0.2. There were only several genes with q-values around 0.2. However, after our conservative adjustment, Fig. q-values are greater than 0.8. This comparison implies that most genes were very likely noise genes and the detections of differentially expressed genes by low q-values could be very unreliable. The only gene with q-value less than 0.2 is a mRNA for CD20-like precursor. However, no literature was found to support its association with diabetes diseases.For the first microarray genome-wide expression data set for a type 2 diabetes study , there wt method ), \\docump-values calculation. Therefore, there was no need for an adjustment of p-values (i.e. a1=0). Then, we set a0=0 . Figure q-values (estimated FDRs) can be extremely low and lots of genes can be detected. After our conservative adjustment, Fig. q-values almost overlaps with the curve of original q-values. This comparison implies that many genes were truly differentially expressed genes and the detection of these genes by low q-values could be highly confident. After checking literature for top ranked genes, many of them have been studied to be either directly or indirectly related to prostate cancer or general cancer diseases (details not shown).For the second RNA-seq genome-wide expression data set for a prostate cancer study , there wt method ) and a2t-test calculations. We set a0=0 . Figure q-values (estimated FDRs) can only be as low as approximately 0.4 (about 20 genes). However, after our conservative adjustment, Fig. q-values are greater than 0.5. This comparison implies that more top ranked genes were likely noise genes. The only two genes with q-value less than 0.4 are mRNAs for ARNT and APCDD1. Although ARNT has been widely studied for its association with diabetes diseases, no literature was found to support the association between APCDD1 and diabetes diseases.For the third microarray genome-wide expression data set for a pancreatic-islet study , there wt method ), \\docum\u03c00 estimation. Since the estimators for \u03c00 are usually conservative , we do q-value could be achieved. Furthermore, an independence assumption is required. It is well-known that genes work with each other during molecular and cellular processes. It would be an interesting future research topic to address the dependence among genes. Therefore, it will be our future research topics to investigate possible better upper/lower bounds for the conservative adjustment of q-value, as well as the impact of dependence on the conservative adjustment of q-value.A clear advantage of our approach is that there are rigorous mathematical theories to support it. Furthermore, no distribution assumptions are required for our conservative adjustment. However, the adjustment may be over-conservative. If we could further improve the control of upper/lower bounds , then less conservative adjustment of q-value, which is widely used to estimate false discovery rate (FDR) in practice. We provided a mathematical proof to confirm the conservativeness of our approach. We conducted simulation studies to understand how likely the q-value method would underestimate FDRs. From our simulation results, both the proportion of differentially expressed genes and the overall differential expression signal were two important factors. When both of them were relatively small/weak, it was likely to identify genes with underestimated FDRs. Our first application was based on a microarray diabetes study data set with relatively small sample size . Our third application was based on a microarray pancreatic islet study data set with relatively small sample size . The results were consistent with the conclusion from our simulation studies. Our second application was based on a RNA-seq prostate cancer study data set with relatively large sample size . According to the results, the conservatively adjusted q-values were close to the originally unadjusted q-values.In this study, we proposed a statistical method for the conservative adjustment of Mathematical Proof:X, Y and a constant c, Pr(XY\u2265c|X\u22651)\u2265Pr(Y\u2265c) since Y\u2265c\u21d2XY\u2265c given X\u22651 ({Y\u2265c} is a subset of {XY\u2265c} when X\u22651).For any random variable q-values.R-functions for calculating conservatively adjusted \u03c00; pvals is a list of permutation p-values based on r permutations; m is the number of permutation p-values .Notice that pi0est is a conservative estimate of"}
+{"text": "Titanium (Ti) has been used for long in dentistry and medicine for implant purpose. During the years, not only the commercially pure Ti but also some alloys such as binary and tertiary Ti alloys were used. The aim of this review is to describe and compare the current literature on binary Ti alloys, including Ti\u2013Zr, Ti\u2013In, Ti\u2013Ag, Ti\u2013Cu, Ti\u2013Au, Ti\u2013Pd, Ti\u2013Nb, Ti\u2013Mn, Ti\u2013Mo, Ti\u2013Cr, Ti\u2013Co, Ti\u2013Sn, Ti\u2013Ge and Ti\u2013Ga, in particular to mechanical, chemical and biological parameters related to implant application. Literature was searched using the PubMed and Web of Science databases, as well as google without limiting the year, but with principle key terms such as \u2018 Ti alloy\u2019, \u2018binary Ti \u2019, \u2018Ti-X\u2019 , \u2018dental implant\u2019 and \u2018medical implant\u2019. Only laboratory studies that intentionally for implant or biomedical applications were included. According to available literatures, we might conclude that most of the binary Ti alloys with alloying <20% elements of Zr, In, Ag, Cu, Au, Pd, Nb, Mn, Cr, Mo, Sn and Co have high potential as implant materials, due to good mechanical performance without compromising the biocompatibility and biological behaviour compare to cp-Ti. Titanium (Ti) is a transition metal and element with the atomic number of 22. Ti has a lustrous finishing and characterized with silver colour, low density and high strength. It has a high ability to resist corrosion in various media such as sea water, aqua regia and chlorine . Ti is a\u22121/2. For \u03b2-Ti, beta phase was observed at room temperature after quenching, or sometimes even upon air cooling. Thus, it is ready for cold working (forming), and could be solution-treated, quenched and aged to give higher strength together with low ductility. However, its fatigue performance is poor. The tensile strength is about 1220\u20131450\u2009MPa and fracture toughness of >50\u2009MPa m\u22121/2.Ti is a dimorphic metal with two phase, \u03b1 and \u03b2 phase. \u03b1-Ti is hexagonal close-packed (hcp) crystal lattice, and \u03b2-Ti is body-centered cubic (bcc) lattice. During the processing, Ti exists as \u03b1-Ti when the temperature is lower than 883\u2009\u00b0C. When Ti is heated exceeding 883\u2009\u00b0C, the atoms in the hcp crystal lattice packed closer with each other and become \u03b2-Ti . \u03b1-Ti isIndeed, the commercially pure Ti (cp-Ti) is divided into four Grades from 1 to 4, according to the purity and the processing oxygen content . These dIn order to replace a missing tooth, a lot of materials, such as cobalt\u2013chromium  and stainless steel, had been attempted to make an implant. The development of materials science and technology improved the materials for implant application. Nowadays, Ti becomes the most popular implant material due to its advantages.x) as film, is very stable and could separate the bulk Ti material from its surrounding. Thus, Ti has a high ability to resist the corrosion. The TiOx layer is typically around 3\u201310\u2009nm thick that stably stayed onto the Ti surface, and the oxide film on the surface \u2212 + H3O+\u2212) which incur negative charge on the surface, and the acidic type [Ti-OH2]+ incur positive charge for 2]+. Thus, surface treatment methods such as the acid etching could not only roughen the surface that provide a harbouring site for negatively charged osteoblast [2]+, which is hydrophilic and documented for biological activity enhancement [2]+ on Ti surface could be a good strategy for Ti-osteoblast bonding without the addition of bi-positively charged growth factors/proteins +, a storage of acidic medium is recommended which might be a tactic in the commercial product \u2018SLActive\u2019  that use an acidified saline  to preserve effectively the hydrophilicity and nanostructure [However, during the storage and the equilibrium nature of the oxide, the nano-oxide layer will become thicker due to the time and quality of exposed storage atmosphere . In suchtructure .In general, titanium is a good choice for intraosseous applications not only due to the biocompatibility, but also mechanically titanium could be processed and machined in a rapid manner such that the shapes and sizes could be easily controlled. Nevertheless, one of the disadvantages of the titanium could be the aesthetic problem since Ti is grey in colour, such that the dark colour would be seen through the thin mucosa if the soft tissue situation is not optimal. Ti also proceeded with some other drawbacks, e.g. low deformability and wear resistance, and high reactivity with the surrounding impurities (such as oxygen and nitrogen) at elevated temperatures , 27. MorOne of the tactics\u2014alloying Ti with a variety of elements\u2014might become viable to enhance some of these properties, such as increase the corrosion resistance, lower the modulus of elasticity, and improve the machinability. This is because the Ti-alloys properties are related to their respective phases/crystalline structures, such that by adding some alloying elements could stabilize certain phases. In addition, some metal substrates could combine with this oxide layer in order to prevent absorption and disintegration of coating , 31. ThuCommonly, alloy could broadly defined as \u2018a mixture of a metal and another element(s) which has metallic bonding character\u2019. In titanium, a lot of attempts, such as using Silver (Ag), Aluminium (Al), Copper (Cu), Iron (Fe), Vanadium (V) and Zinc (Zn), have been done in order to improve the material.In fact, as aforementioned, the titanium has three forms: \u03b1, \u03b2 and \u03b1-\u03b2. With the addition of the alloying elements, the phase compositions could be adjusted and thus change the bulk Ti-alloy properties. For example, Al acts as \u03b1-phase stabilizers which could improve the strength and lower the weight of the alloy. V is \u03b2-phase stabilizer that could improve the ductility and formability. Thus, by adding of the Al and V, the temperature for \u03b1-phase transform to \u03b2-phase has also been changed to a range, i.e. both \u03b1 and \u03b2 phases exist in the temperature range. The most commonly used Ti-alloy in dental implant , 32 is T2O3 ceramic ball heads. However, Ti-6Al\u20134 V alloy has the disadvantage of low wear resistance [Ti\u20136Al\u20134V  is one of the most commonly used tertiary titanium alloy, that is usable as a biomedical implant. As the symbol implies, Ti\u20136Al-4V has the composition of 6\u2009wt% aluminium and 4\u2009wt% vanadium. In particular, Ti\u20136Al\u20134V alloy has a higher strength that could be used in various applications, such as for anchorage stems of femoral components, together with Co\u2013Cr\u2013Mo alloy or Alsistance , high elsistance  , is a neutral element when dissolved in Ti. Zirconium belongs to Group 4 (according to new IUPAC name) in the periodic table, which is the same as titanium and hafnium, have similar chemical structure and properties. Thus, they have been recognized as non-toxic and non-allergic. Zirconium is a transition metal with atomic number 40 and atomic weight of 91.22\u2009amu. Being as a greyish-white lustrous metal, Zirconium has extremely high melting (1857\u2009\u00b0C) and boiling (4409\u2009\u00b0C) points. Zirconium has a great resistance to corrosion, which is similar to Titanium, and is therefore highly biocompatible  since th2), has started to use in dentistry, due to its biocompatibility and possesses the capacity to osseointegrate [et al. [et al. [Start from 1990s, the oxide form of zirconium, Zirconia  is lowered by increasing the amount of Zr  regardless \u03b1-Ti or \u03b2-Ti. Thus, the casting process could be easily facilitated. In addition, from the knowledge of casting titanium , reducinet al. [Recently, due to their good corrosion resistance and biocompatibility, binary Ti\u2013Zr alloys have been developed for dental applications  which clet al.  demonstret al. , which iet al. [et al. [Kobayashi et al.  investig [et al.  has claiFor a long time, Indium (In) has been used in Pd- and Ag-based porcelain-fused-metal (PFM) applications. In fact, during the firing process of porcelain, the indium oxides film would formed on the metal surface, which could be served as a \u2018bonding agent\u2019 between metal and porcelain , 75. In Several studies on experimental Ti-In alloys has shown that Ti-In alloys were biocompatible. Further, with the addition of indium to Ti could improve clinical performance in terms of mechanical properties, corrosion resistance, and biocompatibility  of dentaet al. [For binary Ti-In alloys, Wang  found thet al.  has showet al. [et al. [Han et al.  has furt [et al.  that the [et al.  showed aet al. [et al. [in vitro cytotoxicity test which showed Ti\u2013Ag alloys and cp-Ti alloys seem to be cytocompatible with each other. They recommend that, for dental application, Ti\u20135Ag and Ti\u201320Ag might be more suitable according to the surface passive film and cytotoxicity viewpoints.Oh et al.  reported [et al.  confirme2Cu was found. Thus, Ti\u2013Cu alloys that have a nearly eutectoid composition was expected to have higher strength and less ductility than cp-Ti.Copper has been used for long time as dental casting alloys. Study  has showStudies , 81 reveMoreover, in terms of grindability, some Ti\u2013Cu and Ti\u2013Ag alloys had shown a better outcome than cp-Ti , 82. At per se belongs to Group 11 in the periodic table, same as silver and copper. Gold, similar to silver and copper, stabilizes \u03b2-phase of titanium to a lower temperature according to the binary equilibrium phase diagrams.Gold (Au), has been mainly used for dental prostheses in dentistry for a long time, particularly for casting, since gold has good corrosion resistance, suitable melting point, and could achieve appropriate mechanical properties by alloying . Gold pe3Au forms. Therefore, gold, as an alloying element for titanium, might be expected to positively affect on the mechanical properties and grindability of titanium, similar to silver and copper.According to the phase diagram, similar to the Ti-Cu and Ti-Ag alloys, the Ti-Au alloy has the eutectoid point with titanium. At the gold concentration of 15.3% the intermetallic compound Tiet al. [Hwang et al. [et al. [et al. [ca. 1 at% Ag, Au, Pd and Pt) vs. commercial Ti-6Al-7Nb in the fluoridated artificial saliva. Takahashi et al. [Moser et al.  reported [et al.  utilized [et al.  utilizedi et al. , 88 alsoet al. [et al. [Lee et al.  studied  [et al. , they exet al. [Manganese (Mn), is one of the trace elements that could be found in human body which has lower toxicity than Al and V. Mn can be added to tri-calcium phosphate by doping and become a bioceramic which showed a good cell compatibility . In a reet al.  has inveet al. [\u2212, the Ti\u201320Cr alloy had a greater corrosion resistant than cp-Ti. In addition, according to phase diagram, alloying high Cr content (46%) to Ti could reduce the liquidus temperature from the high melting point of cp-Ti (1670\u2009\u00b0C) to a minimum (1410\u2009\u00b0C), similar to Ti\u2013Zr as previously discussed.Chromium (Cr), is well-known in dentistry due to the Co\u2013Cr application that could control the anodic activity of the alloy, and could passivate Ti . Takemotet al.  reportedet al. [Hsu et al.  reportedet al. [et al. also studied the fractography of the specimen, and fractographs of SEM showed that the Ti\u201310Cr alloy has: (i) coarse cleavage facets in the fractured surface; and (ii) some terrace-type morphology. In addition, the Ti\u201320Cr has shown to be ductile, such that it has even 460% more elastic recovery capability than cp-Ti, whereas other composition of Ti\u2013Cr alloys did not exhibit such properties. As shown in their unetched optical micrographs, large number of slip bands was observed on the surfaces of the Ti\u201320Cr alloy. That said, slippage dislocations are the reasons of the Ti\u201320Cr alloy deformation. Therefore, if Ti\u2013Cr alloys are needed to be use for prosthetic dental applications, many properties such as mechanical properties and deformation behaviour should be further studied.Ho et al.  investiget al. [According to Bania  and Ho eet al. , a minimet al. , and eveet al. , due to et al. . Indeed,et al.  at low cV) of the Ti\u2013Sn alloys, e.g. 30\u2009wt% Sn showed a high hardness value of 357\u2009HV. To illustrate the CAD/CAM processability, grindability of the alloys was also studied [Ti\u2013Sn has been found nontoxic and nonallergic . Thus, T studied . In factCobalt (Co), is a widely accepted biocompatible element  might haet al. [et al. [6Ge5 and subsequently TiGe2 would be preferentially nucleated and crystalized [Lin et al.  has stud [et al.  has repo [et al. , for thestalized . For Ti\u2013stalized  i.e. coret al. and Song et al. [Titanium and its alloys has the properties of attracting cells, including osteoblasts and bacteria, due to various properties such as surface charge , existeng et al. , 108 evag et al.  and biomg et al.  could beg et al.  and Ti\u20136g et al.  have beeBinary Ti alloys, in particular to Ti\u2013\u2013Zr, Ti\u2013In, Ti\u2013Ag, Ti\u2013Cu, Ti\u2013Au, Ti\u2013Pd, Ti\u2013Nb, Ti\u2013Mn, Ti\u2013Cr, Ti\u2013Mo, Ti\u2013Sn and Ti\u2013Co, with the alloying components <20% has a high potential as implant materials due to good mechanical performance without compromising the biological behaviour compare to cp-Ti. Further investigation on the inherent anti-biofilm properties could be a future topic for these alloys.Conflict of interest statement. None declared."}
+{"text": "Compressed sensing (CS) has been applied to accelerate magnetic resonance imaging (MRI) for many years. Due to the lack of translation invariance of the wavelet basis, undersampled MRI reconstruction based on discrete wavelet transform may result in serious artifacts. In this paper, we propose a CS-based reconstruction scheme, which combines complex double-density dual-tree discrete wavelet transform (CDDDT-DWT) with fast iterative shrinkage/soft thresholding algorithm (FISTA) to efficiently reduce such visual artifacts. The CDDDT-DWT has the characteristics of shift invariance, high degree, and a good directional selectivity. In addition, FISTA has an excellent convergence rate, and the design of FISTA is simple. Compared with conventional CS-based reconstruction methods, the experimental results demonstrate that this novel approach achieves higher peak signal-to-noise ratio (PSNR), larger signal-to-noise ratio (SNR), better structural similarity index (SSIM), and lower relative error. MRI prok-space sampling [k-space sampling pattern to shorten the sampling time, increase the imaging speed, and reduce the motion artifacts. However, aliasing artifacts may occur in these sampling methods. The high-frequency part contains less image information than the low-frequency part. Hence, by using undersampling patterns, the information about details is lost in the reconstructed images. Besides, the substantial aliasing artifacts appear incoherent. In case that the sampling ratio is extremely low, it is almost impossible to remove the significant aliasing artifacts from real signals [k-space data. The discrete wavelet transform (DWT) is widely applied in CS-MRI, but it is sensitive to shift, lacks information about phase, and has poor directionality [\u21131-norm regularization. These approaches, such as conjugate gradient [O(1/k2), where k is the number of iterations.In recent years, a variety of techniques have been proposed to enhance the quality of MRI, which can be roughly classified into three categories : incohersampling , spiralssampling , radial sampling , and Gausampling ) takes a signals , 8, 9. Fionality . Waveletionality . The staionality . Similarionality , 19. Thegradient , two-stegradient , 22, andgradient , have begradient  can be eTo enhance the image reconstruction quality and reduce the reconstruction artifacts, in this paper, we propose a novel reconstruction scheme, which combines CDDDT-DWT with FISTA. Although dual-tree complex wavelet transform has also been exploited in the literature , its dirThe remainder of this paper is organized as follows. \u03c6h(t) and \u03c6g(t) and four distinct wavelets \u03c6h,i(t) and \u03c6g,i(t), where \u03c6h,1(t) is an offset from \u03c6h,2(t) by one-half and \u03c6g,1(t) is an offset from \u03c6g,2(t) by one-half. One pair of wavelets \u03c6h,i(t) and \u03c6g,i(t) form an approximation of the Hilbert transform pair [\u03c6g,1(t) \u2248 \u210b{\u03c6h,1(t)}, \u03c6g,2(t) \u2248 \u210b{\u03c6h,2(t)}.The CDDDT-DWT is an overcompleted discrete wavelet transform that combines double-density DWT  with duaorm pair ; namely,L0L0, H0H0) and 16 high-frequency subbands  to describe the details of the recovered image.Two-dimensional (2D) double-density dual-tree DWT includes 2D real double-density dual-tree DWT and 2D complex double-density dual-tree DWT. The former is constructed from two oversampled 2D double-density DWT in parallel, which is redundant by a factor of two. Lp and Hp make up the filter banks of the first-level decomposition, where Lp represents a scale filter and Hp depicts eight wavelet filters, while Lw and Hg denote the filter bank structures of the second-level decomposition. Each level generates four low-frequency subbands  and 32 high-frequency subbands  through 2D CDDDT-DWT transform. Similar to other wavelet transforms, the redundant transform is achieved by recursively applying low-frequency subbands to complete the decomposition of each level. For each pair of subbands, CDDDT-DWT takes their summation and difference to produce the 32 oriented wavelets, describing a total of 16 main directions. Besides, each main direction contains two distinct wavelet representations, which indicate the real part of a complex-valued 2D wavelet function and the imaginary part, respectively [The latter is formed by utilizing four oversampled 2D double-density DWT in parallel to the input image. The filter bank structure of this transform can be obtained by extending the one illustrated in ectively .x denotes the fully sampled image, y is the k-space data acquired from a MR scanner, and \u03be (\u03be > 0) is a parameter appropriately chosen based on the noise level, which controls the difference between the object image and the reconstructed one. Fu is the undersampled Fourier transform in MRI. \u03d5(\u00b7) is called the regularization function in the transform domain, which is generally nonsmooth. This optimization problem can be potentially solved by total variation- (TV-) based approaches [\u03c4 is a positive regularization parameter. To solve (\u21130 \u201cnorm\u201d (\u2016x\u20160 = |{i : \u22600}|) is chosen as the regularization function. \u03d5(x) = \u2016x\u20160 especially provides the simplest way to enforce the sparsity:x can be sparsely represented in this selected domain \u03a6. Here, \u03a6i  is the 16 high-frequency subbands of CDDDT-DWT, which serves as a new sparse basis. However, the solution of  = (1/2)\u2016Fux \u2212 y\u201622 represents the quadratic term, which is a convex function with Lipschitz continuous gradient, and g(x) = \u03c4\u2016\u03a6ix\u20161, i = 1,2,\u2026, 16 is a nonsmooth convex regularizer.Since  convex,  can be c convex,  to effec convex, , f(x) = zk, we can get the gradient of f(x) at zk byFuT(Fuzk \u2212 y) denotes the gradient of f(x) at the given point zk, which is a specific combination of the previous estimate values xk, xk\u22121. The original FISTA based on wavelet transform has been well studied in the literature with a backtracking step size or a constant step size \u03c1, both of which can provide an improved global convergence rate of O(1/k2) [The FISTA algorithm is applied to solve the optimization problem of . For a g O(1/k2) . For simxg, we can getwh is the new wavelet coefficients, which can be adjusted by the proximal forward-backward iterative scheme [\u21131-norm is nonsmooth, it is separable and CDDDT-DWT has the characteristics of tight frame. It is known that the shrinkage thresholding function with threshold T is utilized to obtain the modified wavelet coefficients wh\u2032:Applying the sparsity transform CDDDT-DWT to a local optimal image e scheme  to catchxk is updated byThe recovered image i\u22121, \u2009i = 1,2,\u2026, 16) is applied by the synthesis filter bank structure, constituted by inverse order of the analysis filter bank [\u03b2 is a threshold relaxation factor to adjust T, which optimizes T and reduces the calculation time. When the stop condition T \u2264 \u03f5 is satisfied, we obtain the optimal solution of  for solving  is depick-space data of the axial brain are acquired by a 3T GE MR750 scanner using fast spin echo sequence . The spine MR data are a fully sampled k-space data obtained by a 3T GE MR750 system with FRFSE sequence . For the sake of brevity, the size of all testing images is scaled to 256 \u00d7 256. All experiments are performed using MATLAB 2014b on a desktop computer with a 3.2\u2009GHz Intel core i5-4460 CPU.To evaluate the performance of the proposed reconstruction algorithm, we implement the complex double-density dual-tree wavelet and conventional wavelet using the software in , 29. Thek-space pattern and radial undersampling pattern are used to undersample the fully sampled k-space raw data. For most of MR images, the k-space signal with a large magnitude is generally localized in the central part. k-space and less high-frequency signals in the peripheral region of k-space. The radial undersampling pattern displayed in Gaussian random In this work, FISTA based on three different sparsity transforms is utilized to solve the optimization problem of . These tk-space data. In the axial brain experiment, we set the optimal parameters \u03f5 = 0.001, \u03c1 = 1, \u03b2 = 0.9, and T = 0.0095, while parameters in the spine experiment are set as \u03f5 = 0.0001, \u03c1 = 1, \u03b2 = 0.9, and T = 0.01. For different testing datasets, the tuning parameter \u03c4 is set to different values and the total number of iterations in all the cases is set to 120. Additionally, in both simulation and experiments on in vivo data, we add Gaussian white noise to simulate a realistic environment. For simplicity, the same standard derivation \u03c3 = 0.01 is used.We first conduct the experiment on the Shepp-Logan phantom image shown in x denotes images reconstructed from fully sampled data, M and N are the number of rows and columns in the input image, respectively. MAX means the maximum possible pixel value in the input image data, and The peak signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), structural similarity (SSIM) index, and relative error (Rel.Err) are used to evaluate the FISTA-CDDDT recovery performance. The PSNR is calculated using the following equation:The SNR is defined asp and q are the various local windows from the same local window in the two different images to be compared. \u03bcp and \u03bcq are the mean of p and q, respectively, while \u03b8p and \u03b8q represent their variance. \u03b8pq is the covariance of p and q. c1, c2, and c3 are three variables used to increase the stability of the results. Both SSIM index and SNR have the same criterion as PSNR; that is, the reconstruction quality is directly proportional to the value of the metrics.The definition of the SSIM index is given byThe Rel.Err is defined asNote that, for all the figures in this part, various approaches are labeled by different colors below the images. The green dotted lines mean FISTA-DWT, the pink dotted lines denote FISTA-CDT, and the blue lines represent the proposed FISTA-CDDDT.\u21131-norm based CS techniques may result in poor performance with substantial artifacts. Consequently, CS methods cannot guarantee the quality of the reconstructed image at low sampling ratios.For further analysis, the PSNRs of the reconstructed images using different methods are plotted at various sampling ratios. It is clear from k-space data. The k-space data from each coil are reconstructed separately, and the final image is generated by the sum-of-square method [Figures e method .Note that the PSNRs of reconstructed axial brain images using radial sampling mask by FISTA-DWT, FISTA-CDT, and FISTA-CDDDT are 33.99\u2009dB, 37.58\u2009dB, and 38.87\u2009dB, respectively. The magnified images are shown in Figures \u03c3 = 0.01. These results further demonstrate that the proposed FISTA-CDDDT is superior to the other two methods, because it exhibits the highest SNR, best SSIM index, and lowest Rel.Err.Figures Considering the superiority of CDDDT-DWT in preserving edges and maintaining higher directional selectivity, the proposed reconstruction approach combines the CDDDT-DWT with FISTA to produce better recovery results with a faster convergence rate. Although the ISTA and TwIST can be integrated with CDDDT-DWT as well, both of them were designed for simple regularization problems. Besides, they have some drawbacks that cannot be ignored. ISTA based on the operator-splitting strategy is a promising method, which has been successfully used in signal recovery. However, it belongs to the first-order algorithm that converges quite slow. As a variant of ISTA, TwIST is also an iterative thresholding algorithm, which is not guaranteed to converge globally. In contrast, FISTA has a faster convergence rate and better reconstruction accuracy, as proved in .l1-norm regularization is studied in this work. Furthermore, FISTA-CDDDT first uses proximal forward-back optimization to approximate the linearized function f(x), then applies shrinkage thresholding function to solve the minimization problem due to the separable characteristics of l1-norm, and finally adopts the specific linear combination of xk and xk\u22121 to smartly select the search points. Besides, the threshold relaxation technique can further reduce the computational cost. Consequently, our method can gain a more accurate solution with a dramatically improved complexity of O(1/k2).It is worth noting that Zhu et al.  designedIn this paper, we develop a new image reconstruction method for CS-MRI based on complex double-density dual-tree wavelet transform. The filter bank structure of the CDDDT-DWT is explored. This novel approach has been applied to Shepp-Logan phantom and axial brain and spine image reconstruction and compared with two popular methods, namely, FISTA-DWT and FISTA-CDT. The reconstructed results demonstrate that our scheme improves the PSNR and SNR as well as SSIM index and reduces the reconstructed artifacts significantly. In both simulation and experiments on in vivo data, we use the FISTA as the reconstruction algorithm. However, it can only solve the unconstrained minimization problems. An algorithm that can solve both unconstrained and constrained convex optimization problems will be studied in the future work."}
+{"text": "B-matrix. The proposed error bounds are better than some existing results. The advantages of the results obtained are illustrated by numerical examples.In this paper, new error bounds for the linear complementarity problem are obtained when the involved matrix is a weakly chained diagonally dominant  LCP) is to find a vector LCP has various applications in the free boundary problems for journal bearing, the contact problem, and the Nash equilibrium point of a bimatrix game [A linear complementarity problem  matrix if A is diagonally dominant, i.e.,A of the form A matrix wcdd) B-matrix if it can be written in the form wcdd matrix whose diagonal entries are all positive.A matrix et al. [M is a B-matrix: Let B-matrix with the formGarc\u00eda-Esnaola et al.  gave theet al. [B-matrix with the form To improve the bound in , Li et aet al.  presentementclass2pt{minimM is a weakly chained diagonally dominant (wcdd) B-matrix, Li et al. [wcddB-matrix with the form Recently, when i et al.  gave a bmentclass2pt{minimM is a B-matrix since a B-matrix is a weakly chained diagonally dominant B-matrix [This bound in  holds whB-matrix .Now, some notation is given, which will be used in the sequel. Let M is a wcddB-matrix. Numerical examples are given to verify the corresponding results in Section\u00a0The rest of this paper is organized as follows: In Section\u00a0M is a wcddB-matrix. Firstly, several lemmas, which will be used later, are given.In this section, some new upper bounds for Letbe a wcddB-matrix with the formwhereis defined as , an, an8), aesult in  holds frB-matrix is also a wcddB-matrix, then by Theorem\u00a0Since a Letbe aB-matrix with the formwhereis defined as (Thenwhereis defined as in Theorem\u00a0mentclass2pt{minimmentclass2pt{minimWe next give a comparison of the bounds in  and 5)  5) as foLetbe a wcddB-matrix with the formwhereis defined as , an, anLet\\ in Theorem\u00a0(ii)n is very large, one needs more computations to obtain these upper bounds by (When ounds by  than by ounds by .In this section, we present numerical examples to illustrate the advantages of our derived results.B-matrices in [Consider the family of rices in :\\documeentclass1pt{minimaentclass1pt{minimawcddB-matrix in [Consider the atrix in :\\documeM is a weakly chained diagonally dominant B-matrix, which improve some existing results. A numerical example shows that the given bounds are efficient.In this paper, we present some new upper bounds for"}
+{"text": "Nature Communications 10.1038/s41467-017-02269-7; published online 28 February 2018Correction to: The original PDF version of this Article had an incorrect volume number of \u20188\u2019; it should have been \u20189\u2019. This has been corrected in the PDF version of the Article. The HTML version was correct from the time of publication."}
+{"text": "The paradigm of the rubber hand illusion was applied to a shadow to determine whether the body-shadow is a good candidate for the alternative belonging to our body. Three kinds of shadows, a physical hand, a hand-shaped cloth, and a rectangle cloth, were tested for this purpose. The questionnaire results showed that both anatomical similarity and visuo-proprioception correlation were effective in enhancing illusory ownership of the shadow. According to the proprioceptive drift measurement, whether the shadow purely originated from the physical body was a critical factor in yielding the significantly positive drift. Thus, results demonstrated that the shadow can distort illusory ownership with the rubber hand illusion paradigm, but the proprioception was clearly distorted only when the body-shadow was purely applied. This implies the presence of special cognitive processing to discriminate the self-body shadow from the others. There is a well-known and old game for children called \u201cka-ge-fu-mi\u201d in Japan wherein a chaser (tagger) tries to step on the shadow of the others (resulting in switching of roles in the game). In this imaginary world, touching the body-shadow is identical to touching the physical body. Similar beliefs, such that an attack to the body-shadow is equivalent to physical body, have been found in various parts of the world, suggesting a special involvement with the body-shadows in cognitive processing.Although seeing a shadow of an object is found to have a positive effect on recognizing the object accurately in many studies e.g.,  or even Therefore, it is probable that the body-shadow is processed as a substitution or extension of the physical body casting that shadow, but it is so difficult to assume that the participants in the related experiments felt their shadow just as a part of the body amid the relevant perceptual distortion. In other words, the related studies have demonstrated that the body-shadow can affect the cognitive processing in a level of body-schema but not in a level of body image . This seAn obvious feeling we naturally have for each part of the self-body is called body ownership. Rubber hand illusion (RHI) can provide body ownership to a fake hand based on spatio-temporal correlation between visual and tactile stimulation . AnotherIn this research, four shadow environments were designed for illusion induction to examine the effect of body-shadow in RHI . Specifishadow type , hand movements , and statement type (illusion vs. control). The results \u2009=\u200920.40, p\u2009<\u2009.001, and statement type, F\u2009=\u200951.84, p\u2009<\u2009.001, in addition to a significant interaction among the three factors, F\u2009=\u200914.03, p\u2009<\u2009.001. Hand movement did not yield any significant effect, F\u2009=\u20090.00, p\u2009=\u2009.98, n.s. A follow-up test with simple effects analysis revealed that the static trial was accompanied by a significant predominance of the average rating for the ownership illusion statements over that of the ownership control statements for the three shadows, Hand\u2009+\u2009: F\u2009=\u200952.65, p\u2009<\u2009.001; Handshape\u2212: F\u2009=\u200921.41, p\u2009<\u2009.001; Rectangle\u2009+\u2009: F\u2009=\u20094.88, p\u2009<\u2009.03; Rectangle\u2009\u2212\u2009: F\u2009=2.83, p\u2009=\u2009.10, n.s., whereas such a significant trend was only shown in the active shadows in the active trial, Hand+: F\u2009=\u2009104.05, p\u2009<\u2009.001; Handshape\u2212: F\u2009=\u20090.62, p\u2009=\u2009.43, n.s.; Rectangle+: F\u2009=\u200935.93, p\u2009<\u2009.001; Rectangle\u2212: F\u2009=\u20090.04, p\u2009=\u2009.84, n.s. In addition, multiple comparisons using Ryan\u2019s method (p\u2009<\u2009.001 for Hand+ vs. Rectangle+ and Handshape\u2212 vs. Rectangle\u2212). Finally, the active trial provided significantly higher ratings for the illusion ownership statements as compared with the static trial for the active shadows, F\u2009=\u200911.80, p\u2009<\u2009.001 for Hand+; F\u2009=\u200927.55, p\u2009<\u2009.001 for Rectangle+), whereas a significant trend toward the opposite direction was found for the static shadows, F\u2009=\u200928.24, p\u2009<\u2009.001 for Handshape\u2212; F\u2009=\u20097.41, p\u2009<\u2009.008 for Rectangle\u2212.First, ownership statements for both static and active trials were analyzed using a three-way ANOVA with within-subject factors: s method  revealedshadow type and statement type and revealed a significant main effect of shadow type, F\u2009=\u200920.4, p\u2009<\u2009.001, and statement type, F\u2009=\u200951.84, p\u2009<\u2009.001, in addition to significant interaction, F\u2009=\u200914.37, p\u2009<\u2009.001. Simple effects analysis revealed that the active trial was accompanied by a significant predominance of the average rating for the agency statements over that of the agency control statements only for active shadows, F\u2009=\u200919.58, p\u2009<\u20090.001 for Hand\u2009+\u2009; F\u2009=\u200928.87, p\u2009<\u2009.001 for Rectangle+.Next, agency statements for the active trial were analyzed using a two-way ANOVA with within-subject factors shadow type, hand movement, and sight type (eyes-open vs. eyes-closed). The results \u2009=\u20095.56, p\u2009<\u2009.003, and sight type, F\u2009=\u20096.95, p\u2009<\u2009.019, whereas hand movement did not yield a significant effect, F\u2009=\u20090.57, p\u2009=\u2009.46, n.s. In addition, the multiple comparisons (Ryan\u2019s method) under the eyes-open measurement demonstrated that the drift for Hand+ was significantly higher than that of the three other shadows . Finally, one-tailed Welch\u2019s t-test comparison with zeroes showed that Hand+ had a significant positive drift in both the static and active trials with the eyes-open measurement but not with the eyes-closed measurement, t(15)\u2009=\u20094.01, p\u2009<\u2009.002 for static trial; t(15)\u2009=\u20093.55, p\u2009<\u2009.003 for active trial, whereas the other shadows did not have any significant effect.Finally, we analyzed proprioception change. Prior to the analysis, the proprioceptive drift of each participant was calculated for each sight condition (eyes-open and eyes-closed) using a common pre-illusion proprioception of the right hand (baseline), which was pooled and averaged per sight condition to restrain dispersion. The obtained proprioceptive drifts (post-illusion proprioceptive height minus pre-illusion proprioceptive height) were analyzed using a three-way ANOVA with within-subject factors The questionnaire analysis revealed that both the anatomic similarity to the body-part and the visuo-proprioception correlation were effective in enhancing illusory ownership. This demonstrates that the shadow could distort illusory ownership with the RHI paradigm. In contrast, these effects on the proprioceptive drift were uncertain. In fact, there was no significant difference in the drift between the static and active trials, regardless of the type of the shadow shape. In addition, the hand-shaped cloth\u2019s shadow (Handshape\u2212) did not yield a significantly greater drift than the rectangle cloth\u2019s shadows in any situations. Thus, the proprioceptive drift was less sensitive to both the anatomic similarity and the visuo-proprioception correlation as compared with the illusory ownership. These points support the recent view that the proprioceptive distortion does not have a causal link with a feeling of limb ownership .As is unusual for the study of RHI, we tested the proprioceptive drift measurement not only in the eyes-closed situation but also with eyes open toward the shadow (eyes-open measurement) to probe the effect of seeing the shadow in detail. Contrary to the former reports with the other artificial hands, all the shadows, including the body-shadow, did not yield the significant positive drift in the eyes-closed measurement, even for the active trial. Although we do not have a convincing explanation for this disagreement, it is invalid to suppose that this is consistently reproducible considering that we found the opposite trend for the body-shadow in some preliminary experiments. With the eyes-open measurement, the physical hand\u2019s shadow (Hand+) was the only shadow that provided with the significant positive drift; notably, its drift was also significantly greater than for the hand-shaped shadow. Thus, the proprioceptive drift did not occur merely because the subjects see the hand-shaped shadow; the shadow should be the innocent body-shadow. Here, it is also remarkable that even the static trial yielded the significant positive drift toward the body-shadow. As the static trial did not involve the physical hand movement, the results indicate that just seeing the body-shadow results in visuo-proprioceptive recalibration. In the study of RHI, a few studies have reported that changes in hand proprioception can occur even without visuo-tactile correlation e.g., . ConsideIn total, 16 students  participated in the experiment. All participants were recruited from the Faculty of Design and Architecture, Nagoya City University, and signed informed consent prior to their participation. All participants received a book of tokens as compensation (1000 Yen). All experiments were conducted in accordance with the Declaration of Helsinki. The study protocols were approved by the ethics committee of the Nagoya City University.We set up three acrylic transparent plates vertically at a suitable interval, where the participant could see a shadow from any of the three kinds of objects . They could be viewed on the screen of the top plate via a light source installed on the floor, with the palm of the right hand on the middle plate, 12\u2009cm below the top plate. The shadow on the top screen approximately magnified the objects below by 5% to 10%. Four shadow environments were designed for illusion induction: first, an active hand shadow (Hand+) where the top plate shows the right hand\u2019s shadow in a straightforward manner; second, a static, hand-shaped shadow (Handshape\u2212) showing the shadow of the hand-shaped cloth (on the bottom panel) that remained stable regardless of the hand movement; third, an active rectangle shadow (Rectangle+) showing the shadow of a rectangle cloth (clinging to the right hand) that moved in sync with the hand movement; and fourth, a static rectangle shadow (Rectangle\u2212) showing the shadow of the rectangle cloth (on the bottom panel) that remained stable regardless of the hand movement .hand movement \u2014is independent from the classification of static or active shadows. Thus, the illusion induction was accompanied by the shadow\u2019s movement only when the active trial was applied for the active shadows (Hand+ and Rectangle+); the static trial did not involve the shadow\u2019s movement for not only the static shadows but also the active shadows. Subsequent to this illusion induction, they were asked again to localize the right hand with the sight condition that was applied at the pre-illusion stage. Notably, the eyes-open measurement was done without the participants taking their eyes off the shadow to measure proprioceptive height during the prior illusion induction as accurately as possible. Quickly after they answered four- or six-item questions (see lower right of"}
+{"text": "Viruses are key players in ocean ecology and biogeochemistry, not only because of their functional roles but also partially due to their sheer abundance Fuhrman, . BecauseV, mL\u22121) and microbial cells  are approximately proportional. A rule-of-thumb \u201cvirus-to-microbe\u201d ratio of 10 has been used  regression on log-transformed V and M data, to our knowledge none have tested the linear model V = aM+b. Unlike V = \u03b1M, the linear model V = aM+b has the same number of parameters as the nonlinear model V = \u03b1M\u03b2, is consistent with a decreasing V/M as M increases, and is not a special case of the nonlinear model. We interpret V = aM+b to consider V as the sum of two pools\u2014a pool of viruses whose abundance is proportional to microbial abundance (aM), and a background pool of other viruses and virus-like particles whose abundance is unrelated to microbial abundance (b). Because this model is simple and its parameters are comparatively straightforward to interpret and possibly predict, its ability to explain observations should be evaluated before concluding that V and M are nonlinearly related.While several studies  and subsurface  samples, totaling 27 datasets. We repeated their OLS regression of log10-transformed V and M data . We also fit the model V = aM+b after log-transformation:We first reanalyzed the datasets considered in Wigington et al. . They anV = b as M \u2192 0 and to V = aM as M \u2192 \u221e. We analyzed log-transformed data to be consistent with Wigington et al.  we found n = 18) we found Knowles et al.  and Paria et al.  (n = 221ls Table .V-M relationship. Maranger and Bird (n = 149), and Danovaro et al.  represent burst size, virus-microbe interactions, viral decay, and microbial growth respectively , novel experiments with model systems, or other types of data that improve upon the indiscriminant measure of virus-like particles may help answer this question (Baran et al., b. For now, we contest that a linear model remains plausible.These analyses highlight the need for alternative methods to quantify viruses in the environment relative to their hosts. Measurements from marine environments with extremely low microbial densities (because the two models diverge for low values of BC conceived the research, performed the analyses, and wrote the paper. MC, CF, and MF assisted in the writing process and revised the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "In this paper, we first present a new lattice-based PKE scheme on SIS, proving that it achieves CPA-security under DBi-ISIS assumption. Compared to some lattice-based schemes, ours has some advantages and is quite efficient as well as great simplicity. Similarly, we give a lattice-based PKE with multiple bits which is CPA secure under DBi-ISIS assumption. We hope that our contributions help to pave the way for the development of lattice-based PKEs in the future work. Nowadays, with the development of technologies, such as cloud computing and quantum information technology, quantum computing power becomes stronger and stronger. As a result, traditional cryptosystems, e.g number-theoretic cryptosystems, could be almost broken by quantum computers. To handle this case, lattice has come up as a powerful technique to resist quantum computers and been gradually used to construct cryptography primitives which can be against quantum attack. Maybe lattice-based cryptography will be a replacement to number-theoretic cryptography in cryptography field.the shortest independent vectors problem SIVP (one variant of SVP)   factors, because they remain secure even against quantum computers.Over the last decades, lattice has emerged as a very attractive foundation for cryptography. The appeal of lattice-based primitives stems from the fact that their security can often be based on worst-case hard problems such as shortest vector problem (SVP)  was one of the most fundamental primitives in cryptography. The first security notion for PKE was indistinguishability of encryptions under chosen-plaintext attacks (indistinguishability against chosen-plaintext attacks) (IND-CPA or CPA) Stinson , also knIn 2008, Gentry et\u00a0al.  was at lIn 2014, Wang et\u00a0al. . We takeThis paper is organized as follows. \u201cNotations\u00a0Assume that n is the the main security parameter in this paper. Bold lower-case letters denote vectors in the column form, e.g. x. Bold capital letters denote matrix, e.g. A, and the transposition of A is X uniformly at random is denoted by Here mainly describe some definitions and properties on lattice Regev , 2009.k linearly independent column vectors n-dimensional lattice n dimensional real space Bx is the usual matrix-vector multiplication.Regev  Given k Regev \u00a0For inteThe most well-known basic hard computational lattice problems are SVP  minimizing the quantity (SIVP) (Micciancio The approximation variants of these problems: B of a full-rank (SVP (Decision Version): nd Regev .n-dimensional lattice basis B. The goal is to output a set of n linearly independent lattice vectors (The hard-on-average problem first proposed by Ajtai  was the A) Regev .q, a uniformly random  \u00a0=\u00a0n. Let A, and A, such that for S and Given security parameters (DBi-ISIS problem)   if for all PPT adversaries negl such that:. The challenger gives pk as well as oracle access to sk private.Queries phase 1m where message m must be in the plaintext space associated with pk. The challenger responds with Encrypt  . Then computex secretly  and output ciphertext C.Decrypt follows by the form of We utilize the \u201cGame hopping\u201d Dent  to proveIfDBi-ISISproblem is hard for a PPT algorithmthen the lattice-based PKE scheme in \u201csection has indistinguishable encryptions under CPA. Namely, our PKE shcheme is CPA secure underDBi-ISISassumption.Suppose there exists an adversary GenKey is the same as in Let m\u00a0from\u00a0Although the receiver cannot calculate the plaintext\u00a0m being encrypted. Virtually, when m. Obviously, the first element m. Taken together, the ciphertext in m and hence contains no information about m. Thus we getNow we discuss that the ciphertext in Setup The adversary m.)Queries phase 1 The adversary m, where m is an alleged plaintext.Challenge The adversary b, constructs the challenge ciphertext C is a valid encryption of C is independent of b in the We note that Queries phase 2 Same as phase 1. But the adversary is not allowed to query the Guess Then b. If C is completely random. Because C is a valid ciphertext. DBi-ISIS game, DBi-ISIS problem is hard, there must exist a negligible function negl(n) such thatS has advantage at most negl(n) in solving DBi-ISIS problem). It follows that our PKE in \u201chas indistinguishable encryptions under CPA. By Definition\u00a014, we haveWe see that if Pub.size) and computation complexity (e.g Enc.comp.) of PKEs. Pub.size means the size of the public key, others are so; Comput.Comp. means the computation complexity and is estimated by the number of the multiplications in n is the security parameter, q is a polynomial function of n.For the comparison to be meaningful, we consider the latticed-based PKEs. Table\u00a0mentclass2pt{minimpriv.size in our system is nearly the same as that of Regev .X secretly.Then computeDecrypt Upon receiving M.Correctness If the system is run honestly, the message M is obtained correctly.M by computingTo show the correctness of our scheme, Theorem\u00a016 indicates that our extended PKE of matrix form in \u201cIf DBi-ISIS problem is hard for a PPT algorithmthen the lattice-based PKE in \u201csection is security against CPA under DBi-ISISassumption.The proof of Theorem\u00a016 is similar to that of Theorem\u00a015, omit it here.In this paper, we present a simple PKE scheme that achieves CPA security under the DBi-ISIS assumption. We build it on previous works of Wang et\u00a0al.  and RegeIn addition, we extend the lattice-based PKE in \u201cNote that our PKE schemes in both \u201c"}
+{"text": "Immunoglobulin genes are generated during differentiation of B lymphocytes by joininggene segments. A mouse pre-B cell contains a functional immunoglobulin heavy-chain gene,but no light-chain gene. Although there is only one heavy-chain locus, there are two lightchainloci: \u03ba and \u03bb.It has been reported that \u03ba loci in the germ-line configuration are never(in man) or very rarely (in the mouse) present in cells with functionally rearranged \u03bb-chaingenes. Two explanations have been proposed to explain this: (a) the ordered rearrangementtheory, which postulates that light-chain gene rearrangement in the pre-B cell is firstattempted at the \u03ba locus, and that only upon failure to produce a functional \u03ba chain is therean attempt to rearrange the \u03bb locus; and (b) the stochastic theory, which postulates thatrearrangement at the \u03bb locus proceeds at a rate that is intrinsically much slower than that atthe \u03ba locus. We show here that \u03bb-chain genes are generated whether or not the \u03ba locus haslost its germ-line arrangement, a result that is compatible only with the stochastic theory."}
+{"text": "We present a numerical spectroscopic study of visible and infrared laser radiation in a biological tissue. We derive a solution of a general two-dimensional time dependent radiative transfer equation in a tissue-like medium. The used model is suitable for many situations especially when the external source is time-dependent or continuous. We use a control volume-discrete ordinate method associated with an implicit three-level second-order time differencing scheme. We consider a very thin rectangular biological-tissue-like medium submitted to a visible or a near infrared light sources. The RTE is solved for a set of different wavelength source. All sources are assumed to be monochromatic and collimated. The energetic fluence rate is computed at a set of detector points on the boundaries. According to the source type, we investigate either the steady-state or transient response of the medium. The used model is validated in the case of a heterogeneous tissue-like medium using referencing experimental results from the literature. Also, the developed model is used to study changes on transmitted light in a rat-liver tissue-like medium. Optical properties depend on the source wavelength and they are taken from the literature. In particular, light-transmission in the medium is studied for continuous wave and for short pulse. Diffuse light imaging and spectroscopy aims to investigate tissue physiology in subsurface. There is a spectral window existing within tissues in the near-infrared. The absorption of hemoglobin and water is small in the near-infrared, but elastic scattering from organelles and other microscopic interfaces is large. In tissue optics, any measuring is devoted for either spectroscopy or imaging. Spectroscopy is useful for measurement of time-dependent variations in the absorption and scattering of large tissue volumes. Many spectroscopic methods involving laser interactions in scattering media were employed to study different types of biological tissue \u20133. PhotoSPN equation provides accurate solutions for a time-independent RTE. Boulanger and Charette [The purpose of this paper is to produce a computational Laser spectroscopic study in a biological tissue. We aim to examine light-transmission through a biological tissue for different wavelength sources. Our concern is with modeling light propagation using the radiative transfer theory. We derive a model that unifies the basic applications of diffuse optical tomography which differ essentially by the time behavior of the external source. In particular, we will work with two choices for the external source, continuous wave and short-pulse. The simplest and easiest source to use is the continuous wave (CW). In this case, the source amplitude is constant, and the transmitted amplitude is measured as a function of source-detector separation or wavelength. The second type is a short-time-pulse. In this scheme, a short pulse is launched into the medium, and the temporal point spread function of the transmitted pulse is measured. First, we must say a few words about another way to model propagation of visible and near-infrared light in biological media which is the diffusion equation \u201311. It iCharette  have useCharette , 22 wherCharette , 24. SucCharette  investigIn this work, we derive a control volume discrete-ordinate method associated with an implicit three-level second-order time differencing scheme to solve a two-dimensional time-dependent radiative transfer equation in a general biological tissue medium. We investigate many cases concerning the properties of the medium and the characteristics of the source. We will prove that the used model suits for all these applications. First, the proposed model is tested in the case of a heterogeneous tissue-like phantom illuminated by a continuous wave source. Experimental results are taken from . NumericLight propagation in a human biological tissue is modeled by using a general time-dependent RTE :I\u03bb\u2009\u2009is the monochromatic directional energetic radiance at the spatial position-vector r = . When used in a dimensional form, the radiance I\u03bb\u2009\u2009is often expressed in units of W\u00b7cm\u22122sr\u22121. The photon direction is described using a unitary direction vector\u2009\u2009\u03a9;\u03bca(r)\u2009\u2009and\u2009\u2009\u03bcs(r) are the absorption and the scattering coefficients, respectively. They are both given in units of cm\u22121. c is the speed of light in vacuum. n is the medium's refractive index. Also we make use of reduced scattering coefficient:S\u03bb\u2009\u2009is an injected monochromatic radiance at the medium boundary; The source term p\u2009\u2009describes the probability that during a scattering event a photon with direction\u2009\u2009\u03a9\u2032 is scattered into the direction\u2009\u2009\u03a9. In this paper, we use a commonly-applied phase function in tissue optics. It is the Henyey-Greenstein phase function [The phase function function , 28: g is the anisotropy factor and \u03b8 is the angle between \u03a9 and\u2009\u2009\u03a9\u2032. The integral of radiance over all angles \u03a9 at one point r yields the fluence rate: \u03bb will be omitted in all the rest of this paper.The radiance in the boundary is the sum of the external source contribution and the partly reflected radiance due to the refractive index mismatch. This givesrb is a vector position on the boundary and n is the unit outer normal vector. The reflectivity R is given for each direction using a Fresnel's relationship:\u03c6ref\u2009\u2009and \u03c6tra are the reflection and the transmission angle respectively. In the air, the transmission angles, is calculated through the following Snell's law: nm depends on the tissue and n0 is taken as unity. The critical angle is determined by the following equation:d will be called detected fluence rate and we will take AP = 45\u00b0 in all our investigations.V. The spatial calculus domain is divided into a set of I \u00d7 J elementary uniform volumes \u2206V with unitary depth. This yields a calculus domain subdivided in I \u2217 J rectangular cells. Each -cell is \u0394x\u2206y-sized. So, we can write. In this paper, we use a control volume discrete-ordinate method , 30 asso\u03bem = cos(\u03a9m \u00b7 xn) and \u03b7m = cos(\u03a9m \u00b7 yn) with nx\u2009\u2009and\u2009\u2009ny being two normal vectors to the -plane and the -plane, respectively. wm is a weighting factor depending on the chosen quadrature formula. In this work, we use a constant weight quadrature. After angular discretisation, the phase function term becomes W and S and they are unknown on the faces E and N of the -cell and also in the centre P. Therefore, we need two complementary relations to eliminate IE,m and IN,m.These relations can be obtained by using interpolation formula:\u03b1 is an interpolation parameter. Using the above formulae, -cell, we can obtain results over the cells  and  by using the boundary conditions and the following relations:\u03bem > 0\u2009\u2009and\u2009\u2009\u03b7m > 0), then we get the following equation: Ii,j,mn+1Ii,j,mn = ISi,j,mn = S.n \u2265 1,To solve , we use Ii,j,mn)updatedk+1 becomes a linear combination of the iterated value k+1 and the previously computed value k asechnique . So the \u03c1 being a relaxation parameter whose value is usually between 1 and 2. In most of our calculus, we have used: \u03c1 = 1.1. The solution is obtained when the relative discrepancy value, \u03f5 = |k+1 \u2212 k/k|, is smaller than a tolerance value tol. In that case, we take k as a solution. It will be noted \u22128 and for initial condition, we take x = \u0394y and a uniform time step \u0394t = 10\u221213s. Also it is important to mention that when a continuous source is injected, another iterating process is implemented to attempt the steady-state solution. This is obtained by iterating the solution \u03a9m)\u2009\u2009is divided into four subsets depending on the sign of \u03bem and \u03b7m. By the use of direction cosine sign, all cases can be given through the following general equation:It is worth noting that, in all our simulations, we take a tolerance value: tol = 10In all our investigations, the power laser-source is assumed to be equivalent to a forward collimated radiance injected at a pinpoint on the bottom side of the boundary. We use two types of source:\u22122sr\u22121.a continuous wave source with a uniform equivalent intensity value of 20\u2009mWcm\u22122sr\u22121,a short-Laser-pulse source, applied only at the first instant of calculus. It is a 100fs-pulse having an equivalent radiance value of 200\u2009mWcmIn our presented results on the boundary, we use either calculated detected fluence rate or normalized detected fluence rate:\u03d5d\u2009\u2009is the computed detected fluence rate at a detector point d, D is the number of the detector points on the concerned side of the boundary, and wd is a weighting factor from the generalized trapezoidal integration rule [n\u0394t, as:ion rule . Also, dx < 1/(\u03bca + \u03bcs\u2032). In these calculations, we have used \u0394x = \u0394y = 0.05\u2009cm.To test our model, we have considered a case of 678\u2009nm-light punctual continuous wave source. Our Model is tested by comparing obtained results with phantom experimental data reported in . Figure \u03b1 = 0.5) shows the closest results to the experimental measurements. In the rest of investigations, the interpolation parameter value will be putted 0.5. Also In this investigation, we consider a rat liver tissue-like medium as it is shown in  In this investigation, we study the same medium as in the just precedent paragraph but we use a short-pulsed source. In all cases, it is a 100fs-laser pulse injected in the medium through a point on the middle of the bottom side of the boundary.This paper investigated situations concerning biological tissue interaction with Laser radiation by using radiative transfer theory. More precisely, a computational radiative transfer model is used to establish a numerical Laser spectroscopic study in a rat-liver-tissue-like medium. The response of the medium to both time-dependent and time-independent sources is explored. Obtained Results are tested by using experimental measurements from the literature and by using Monte Carlo simulations. The maximal transmission from the tissue is observed in the red and the near infrared part of radiation spectrum. Also multiple scattering is prevailing in 488\u2009nm while more and more absorption is observed in 2100\u2009nm."}
+{"text": "Brain structures important for \u201ctiming\u201d are also discussed to be critical for the deterioration of movements in Huntington's disease (HD). Changes in \u201ctiming processes\u201d are found in HD, but no study has varied the degree of motor demands in timing functions in parallel in HD. It may be hypothesized that timing functions may be deteriorated to a different extent in motor and non-motor timing, because in motor timing the underlying brain structures may be more demanding than in non-motor timing.We assessed timing in two different experiments: a time-estimation (TE) and a time-discrimination (TD) task. The demand on motor functions is high in the TE-task and low in the TD-task. Furthermore, general motor ability was assessed at different complexity levels. A presymptomatic (pHD), a symptomatic (HD) and a control group were investigated. We found a decline in timing functions when demands on the motor system were high (TE-task), in HD and even in pHD, compared to controls. In non-motor timing (TD task) and in the assessment of general motor ability, performance in the pHD-group was comparable to the controls and better than in the symptomatic group. Performance in both timing tasks was related to the duration until the estimated age of onset in pHDs.The study shows a selective deterioration of time-estimation processes in symptomatic and even presymptomatic Huntington's disease. Time-discrimination processes were not affected in both patient groups. The relation of timing performance to the duration until the estimated age of onset in pHD is of clinical importance. Huntington's disease (HD) is an autosomal dominant, monogentic neurological disorder causing a degeneration of the neostriatum. The disease is genetically expressed by an extension of the CAG-repeat length at the 4th chromosome Optimal motor functioning requires a highly precise timing of the coordination of muscles involved in a movement. If timing functions are crucial, it may be speculated that deficits in cognitive timing functions may underly the voluntary movement disturbances in HD. This seems likely, since \u201ctime processing\u201d is mediated via brain systems that are affected in HD and important for movement execution: i.e. cortico-striatal circuits, especially the MSPs, the SMA and the dopamine system In summary, the study aimed at assessing timing processes with varying demands on the motor system in presymptomatic (pHD), symptomatic HD (HD) and healthy controls. Furthermore the relation of possible timing dysfunctions to voluntary movement dysfunctions in HD will be investigated. Finally we want to explore the value of the assessment of timing for the diagnosis of HD.The results show a selective deterioration of time-estimation processes in presymptomatic Huntington's disease. Time-discrimination processes, as well as general motor performance were not dysfunctional, compared to healthy controls. In the pHD-group performance in the TE and TD-task was related to the estimated age of onset (eAO). In the HD-group, performance was poor in all tasks.The aim of this study was to assess to assess timing processes with varying demands on the motor system in presymptomatic (pHD), symptomatic HD (HD) and healthy controls to estimate if the assessment of timing of timing functions may be of clinical value in the diagnosis of HD.A group of twelve right-handed presymptomatic gene mutation carriers defined by a positive gene test and absence of clinical symptoms  from 22 to 52 years of age  were recruited. The mean CAG-length was 42.58 . Calculation of the estimated age of onset (eAO) Additionally, a group of ten unmedicated symptomatic gene mutation carries  from 21 to 57 years of age  were recruited. The mean CAG-length was 47.10 . The mean age of onset (AO) was 34.20 . All patients  agreed to be videotaped to document their neurological status. Scores for each group  of the UHDRS-motor score, UHDRS cognitive score, TFC, IS, MMSE, BDI and YMRS are given in In this study four different tasks were performened. Two tasks were designed to assess timing functions (time estimation (TE); time discrimination (TD), two tasks were designed to assess general motor functions (continuous reaction task (CRT); tapping (TA). The tasks are described in detail, below. The sequence of conducted tests  was counterbalanced in all groups. All four tasks were trained by the subjects until stable performance was reached.In this task subjects were presented with a white square (2.5\u00d72.5 cm size) on a black computer screen. Subjects were required to press a response key as exactly as possible at 1200 ms after onset of a stimulus (a square). This time, which includes the estimated time for the motor response, had to be estimated by the subjects, i. e. the motor response defines the length of the time interval. Feedback was given if the response was made in a time range from 1000\u20131400 ms or not. If the response was made within that time range, positive feedback was given. If not, negative feedback was given; 120 trials were conducted.after the stimulus was presented. Thus the time interval is not defined by a precise motor response, making timing not as heavily dependent on precise motor function as in the TE-task.Time discrimination was assessed using a two-alternative-forced-choice paradigm. At the beginning of this task white letters \u201cS\u201d and \u201cL\u201d (2.5\u00d72.5 cm size) were presented on a black computer screen. The stimuli differed in their duration of presentation. \u201cS\u201d was presented for 1000 ms and \u201cL\u201d was presented for 1200 ms. The subjects had to react with the left hand on \u201cS\u201d-presentations and with the right hand on \u201cL\u201d-presentations. After the subjects were familiar with the different presentation times of \u201cS\u201d and \u201cL\u201d they underwent 120 trials, in which the letter \u201cH\u201d was presented instead of \u201cS\u201d and \u201cL\u201d. The presentation times of \u201cH\u201d randomly changed between 1000 ms and 1200 ms  and the subjects had to decide using the appropriate response, if the presentation of the letter \u201cH\u201d was presented for a short (i.e. 1000 ms) or long period (i.e. 1200 ms). This decision had to be carried out In this task subjects were presented with white arrowheads , either pointing to the left or to the right. The subjects were required to react with the left hand when the arrowhead pointed to the left and with the right hand when the arrowhead pointed to the right. 60 arrowheads pointed in the left and 60 pointed to the right direction. The subjects were required to respond as fast as possible.This task assesses simple movements Asymptomatic gene carriers as well as symptomatic patients were recruited from the local Huntington Centre of the Neurological Clinic of the University of Bochum. They were selected on the basis of pre-clinical counselling in the case of asymptomatic gene mutation carries or on the basis of routine clinical counselling in the case of symptomatic patients. Healthy controls were recruited by newspaper announcements. All participants gave written informed consent. For the symptomatic individuals, a family member was aware of the recruitement for the study and was involved in the consent procedure. The study was approved by the ethics committee of the University of Bochum.P >.425; one-tailed). The TE- and TD-task were analyzed in a repeated-measures ANOVA using the within-subject factor \u201cexperiment\u201d (TE vs. TD) and the between-subject factor group . Both the CRT- as well as the tapping task (TA) were analyzed using separate univariate ANOVAs with the between-subject factor group . The degrees of freedom were adjusted using the Greenhouse-Geisser-Correction when appropriate. Significances are given one-tailed, due to higher test-power. In addition effect sizes (\u03b7) are reported. The mean and standard deviation (\u00b1SD) are given. Post-hoc tests were calculated using the Bonferroni-correction. Due to higher test power, one-sided tests were performed. For statistical analysis SPSS 11.0 was used.Data from twelve presymptomatic gene mutation carriers (pHD) (N\u200a=\u200a12), ten symptomatic subjects (HD) (N\u200a=\u200a10) and twelve healthy controls (N\u200a=\u200a12) was analyzed. There were no drop-outs. For the TE- and TD-task the number of error trials was analyzed. For the CRT-task the mean reaction time across all trials was analyzed. For the tapping task (TA) the mean number of performed taps as well as the intertap-interval was analyzed. Tests of normal distribution within each group using the Kolmogorov-Smirnov test revealed that each variable included to the ANOVAs and correlational analysis was normal distributed  showed that the number of errors increased from controls (36.58\u00b116.23) to pHD (50.58\u00b127.08) and HD (79.05\u00b111.20). The main-effect \u201cexperiment\u201d \u200a=\u200a166.29; p<.001; \u03b7\u200a=\u200a.84), showed poorer performance (i.e. more errors) in the TE-task (68.48\u00b117.60) than in the TD-task (40.26\u00b126.02). Both effects interacted with each other \u200a=\u200a37.05; p<.001; \u03b7\u200a=\u200a.70). Subsequent univariate ANOVAS revealed a group-effect in both tasks \u200a=\u200a20.83; p<.001; \u03b7\u200a=\u200a.57; TD: \u200a=\u200a128.01; p<.001; \u03b7\u200a=\u200a.89). Post-hoc tests for the TE-task showed that controls (50.33\u00b18.02) performed better than both HD-groups  (p<.001), which did not differ from each other (p\u200a=\u200a.637) (p\u200a=\u200a.461), and both performed better than the HD-group (77.30\u00b16.65) (P<.001) .Results of the performance in each test are given in \u200a=\u200a.637) . For the(P<.001) . For thep<.001; \u03b7\u200a=\u200a.58) with the pHDs and controls not differing from each other  (p>.9), but performing better than the HD-group (518.6\u00b144.21) (p<.001)  with pHDs and controls not differing from each other  (p >.9), and performing better than the HD-group (137\u00b127.2) (p<.001). For the calculated inter-tap interval there was the same effect than for absolute frequencies \u200a=\u200a19.45; p<.001) with the pHDs and controls not differing from each other  (p>.9) and performing better than the HD-group (480.43\u00b116.55) (p<.001).The CRT-task also revealed a group-effect \u200a=\u200a21.59; (p<.001) . The sam(p<.001)  P\u200a=\u200a.007; TD: r\u200a=\u200a\u2212.502, p\u200a=\u200a.048) (refer: p\u200a=\u200a.391), tapping  was not.In pHDs performance in the TE and the TD tasks was related to the duration until the eAO in the pHDs ) refer: , while pIn sum, both HD-groups showed comparable performance in motor embedded timing (TE) and performed more poorly than the control group, while in TD controls and pHDs showed comparable performance The results suggest that in presymptomatic gene mutations carriers (pHD) performance in the TE-task is deteriorated, while performance in the TD-, CRT- and TA-task is still normal. Additionally, performance in the timing tasks (i.e. TE- and TD-task) was related to the estimated age of onset (eAO) in pHD. For the symptomatic group (HD) performance was generally poor.The result found for the TD-task is in line with the findings by Paulsen et al. Regarding the \u201cneuroanatomy of timing\u201d striatal medium spiny neurons (MSPs), the dopamine system and the SMA play a central role in a network mediating time control Despite performance in all tasks being poor in HD, only performance in timing-tasks was inversely related to the duration until the estimated age of onset (eAO) in pHDs Future studies may incorporate larger sample sizes in order to increase generalizability of results. What may also be critical in the current study is, that CAG-repeat sizes differed between the presymptomatic (pHD) and symptomatic group (HD), since different CAG-repeat size may be accompanied by different strengths of pathogenic processes. Yet, this was side effect of matching the groups with respect to their age, since tasks assessing cognitive timing functions are known to be age-sensitive. Since this study was restricted to behavioural data, the precise brain mechanisms underlying the observed pattern of results must remain hypothetical.In summary, the study shows a selective deterioration of time-estimation processes in presymptomatic Huntington's disease. Time-discrimination processes were not affected. It may be inferred that under special circumstances voluntary movements can be deteriorated even in the preclinical stage of HD. These may depend on the time-scale in which the movement takes place. Furthermore, performance in the TE- and TD-task is related to the duration until the likely onset of motor symptoms in HD. Future studies may be done in a longitudinal manner to better document the time course of preclinical disease progression and strengthen clinical importance. This may also be an important step in order to estimate if these easy and fast applicable tasks may be implemented in large clinical trials."}
+{"text": "The algorithm outputs the minimum free energy structure.The analysis of sequence-structure relations of RNA is based on a specific notion and folding of RNA structure. The notion of coarse grained structure employed here is that of canonical RNA pseudoknot contact-structures with at most two mutually crossing bonds (3-noncrossing). These structures are folded by a novel, After giving some background on RNA pseudoknot structures and providing an outline of the folding algorithm being employed, we present in this paper various, statistical results on the mapping from RNA sequences into 3-noncrossing RNA pseudoknot structures. We study properties, like the fraction of pseudoknot structures, the dominant pseudoknot-shapes, neutral walks, neutral neighbors and local connectivity. We then put our results into context of molecular evolution of RNA.Our results imply that, in analogy to RNA secondary structures, 3-noncrossing pseudoknot RNA represents a molecular phenotype that is well suited for molecular and in particular neutral evolution. We can conclude that extended, percolating neutral networks of pseudoknot RNA exist. It is represented by drawing the vertices in a horizontal line and its arcs , where i <j, in the upper half-plane. The vertices and arcs correspond to nucleotides and Watson-Crick  and (U-G) base pairs, respectively. A diagram is k-noncrossing if it contains at most k - 1 mutually crossing arcs. Diagrams have the following three key parameters: the maximum number of mutually crossing arcs, k - 1, the minimum arc-length, \u03bb, and minimum stack-length, \u03c4, The length of an arc  is j - i and a stack of length \u03c4 is a sequence of \"parallel\" arcs of the formWe will show that the notion of diagrams  allows u\u03bb a \u03bb-arc. Biophysical constraints on the base pairings imply that in all RNA structures \u03bb is greater than or equal to four. We call diagrams with a minimum stack-length \u03c4, \u03c4-canonical and if \u03bb \u2265 4 we refer to diagrams as structures. To reiterate, in the simplest case we have 2-noncrossing RNA structures, i.e. the secondary structures in which no two arcs cross, see Figure O(n3)-time and O(n2)-space.see Figure ViennaRNA , having the following propertiesA \u27e8(M1) it has a nonnesting core\u03c4 = 3 and length \u03bb = 4.(M2) all its arcs are contained in stacks of length exactly m-shadow is a k-noncrossing diagram obtained by successively increasing the stacks of m from top to bottom, see Figure A The key observation about motifs is that they can, despite the fact that they exhibit cross-serial dependencies, be generated inductively .ISi,j, over . ISi,j is a skeleton which has no nested arcs, see Figure Skeleta represent the non-inductive \"frames\" of pseudoknot RNA, i.e. skeleta entail exactly the cross-serial dependencies, that need to be considered exhaustively. A skeleton, S, is a 3-noncrossing structure, whose core has a connected L-graph. An L-graph is a diagram whose arcs are the vertices and two being adjacent if their corresponding arcs cross . An irreGiven a skeleton, cross saturates or \"fills\" via context-sensitive DP routines the skeleton-intervals. Note that, while the inserted substructures cannot cross any arc of the skeleton, they will in general contain crossing arcs within themselves.To summarize, first cross inductively constructs all roots of the skeleta-trees, second cross generates the skeleta-trees themselves and third it saturates the skeleta.\u03b1 be an arc in the 3-noncrossing RNA structure, S and denote by AS(\u03b2) the set of S-arcs that cross \u03b2. Clearly, we have \u03b2 \u2208 AS(\u03b1) if and only if \u03b1 \u2208 AS(\u03b2). An arc \u03b1 \u2208 AS(\u03b2) is called a minimal, \u03b2-crossing arc if there exists no \u03b1' \u2208 AS(\u03b2) such that \u03b1' \u227a \u03b1.We next discuss loops of 3-noncrossing RNA structures. Loops are not only the basic building blocks for the mfe-evaluation but also of importance for the coarse grained notion of pseudoknot-shapes, discussed in Subsection. Let i, j] denote the sequenceLet the interval  ) and subject to the following condition: if all \u03c9h, \u03c4h), i.e. all substructures are simply arcs, for all h, then h = 2.where (4) a pseudoknot, see Figure (P1) a set of arcsi1 = min{is} and jt = max{js}, such thatwhere P is irreducible, i.e. the line-graph of P is connected and(i) the diagram induced by the arc-set is, js) \u2208 P there exists some arc \u03b2 (not necessarily contained in P) such that  is minimal \u03b2-crossing.(ii) for each  all vertices k.We now show that each 3-noncrossing RNA structure can uniquely be constructed by simpler substructures . FurtherTheorem. Suppose k \u2265 2,\u03c4 \u2265 3.Any k-noncrossing, t-canonical RNA structure corresponds to an unique sequence of shadows.(a) Any \u27e83. \u03c4\u27e9-structure has an unique loop-decomposition.(b) In Figure Our results are organized in two sections. First we describe our findings with respect to the statistics of pseudoknot RNA structures and second we present our data with respect to the particular organization of the sequences in neutral networks.3, which generates 3-noncrossing, 3-canonical mfe-structures and second, cross4, which produces 3-noncrossing, 4-canonical mfe-structures.In this section we present some key statistics on pseudoknotted RNA structures. In order to put our findings into context we consider two variants of cross: first, cross3 and cross4. Figure n = 100, approximately 50% of the structures folded by both versions of cross contain pseudoknots.We next compute the fraction of RNA structures with pseudoknots within all structures for crossk-noncrossing cores  denote the set of S-compatible sequences, consisting of all sequences that have at any two paired positions one of the 6 nucleotide pairsLet us consider a fixed RNA structure, S motivates to consider a new adjacency relation within C [S]. Indeed, we may reorganize a sequence  into the pairThe structure uj denote the unpaired nucleotides and the pj =  all base pairs, respectively, see Figure vu =  \u21a6 )) or Hamming distance two  \u21a6 )). We call a u- or a p-neighbor, y, a compatible neighbor. If y is contained in the neutral network we refer to y as a neutral neighbor. This gives rise to consider the compatible- and neutral distance, denoted by C and N. These are the minimum length of a C[S]-path and path in the neutral network between v and v', respectively.Accordingly, there are two types of compatible neighbors in sequence space: u- and p-neighbors: a u-neighbor has Hamming distance one and differs exactly by a point mutation at an unpaired position. Analogously a p-neighbor differs by a compatible base pair-mutation, see Figure S(v). We then proceed inductively: assume vi is constructed. We randomly select some neutral (compatible) neighbor of vi, denoted by vi+1, subject to the condition dH > dH, where dH denotes the Hamming distance. If no such neighbor exists we choose some vi+1 \u2260 vi with the property dH = dH. If all neutral vi-neighbors satisfy dH <dH we stop and output the integer dH. In Figure H-pseudoknot loop structure (a), second a hairpin-loop structure (b), third an interior-loop structure (c) and finally the phenylalanine tRNA structure (d), see Figure Our basic experiment is as follows: We select a (random) sequence, v and fold it into the structure v with respect to the structure S = S(v) is a u- or a p-neighbor, y, contained in the neutral network of S. It has Hamming distance one or two, depending on whether it is induced by a point or base pair mutation, see Figure S. The data presented here, are obtained in the course of the neutral walk experiments, displayed in Figure 4.Complementing the analysis of neutral walks, we study now the distribution of neutral neighbors. Recall that a neutral neighbor of a sequence n, of an n-cube alone does not imply that a small Hamming distance implies a small distance in \u0393n. For neutral sequences this means that two neutral sequences with Hamming distance less than four, are possibly connected via a neutral path of much greater length. Evidently, for molecular evolution it is therefore not connectivity but the existence of these short paths what matters. Local connectivity is a property which guarantees the existence of these short paths. If \u0393n is locally connected then a small Hamming distance does imply a \u0393n-distance scaled by at most a factor of \u0394 > 0. We shall begin by studying local connectivity for random induced subgraphs of n-cubes, i.e. where we select sequences with independent probability \u03bbn. Then we transfer the derived concepts to neutral networks of RNA pseudoknot structures.Connectivity of a subgraph, \u0393n is locally connected if and only if almost surely (a.s.)We call \u0393v, v' are in \u0393n. We immediately observe that, trivially, for any finite n such \u0394 exists. However, the key point is that (\u2020) employs the notion \"almost surely\", i.e. it holds for arbitrary n.provided \u03bbn smaller than n\u03b4/\u03b4 > 0 is arbitrarily small, there exists a.s. no finite \u0394 satisfying (\u2020). On the other hand, for \u03bbn larger than or equal to n\u03b4/n-cubes have giant components for \u03bbn = (1 + \u03b5)/n, where \u03b5 > 0 [n-cubes.Random graph theory  shows thre \u03b5 > 0  we can cS and sequence v, contained in its neutral network. By construction, local connectivity refers to the two n-cubes S, see Figure Suppose we are given a structure S at v is given bybe the cardinality of the set of sequences in compatible distance two. Then the degree of local connectivity of DS(v) is the fraction of locally connected vertices of the compatible distance two neighbors of v, that can be obtained via a neutral path of length at most four.In other words, DS(vi) and the total number of locally connected sequences. Our findings are presented in Figure We perform the following experiment: we consider neutral walks for the UTR-pseudoknot structure of the mouse hepatitis virus displayed in Figure k-noncrossing canonical RNA structures and the resulting sequence to structure map employed for our experiments is new and represents a natural generalization of RNA secondary and bi-secondary structures. To be precise, bi-secondary structures are exactly planar 3-noncrossing RNA structures [RNA pseudoknot structures-in particular their statistical properties-are a fascinating and new territory. To our knowledge the only statistical data beyond RNA secondary structures were derived for bi-secondary structures in ,54. The ructures .n = 80 we have approximately 35% structures with nontrivial pseudoknots. In addition it is striking that basically all folded structures are irreducible, i.e. only a very small fraction can be decomposed into several independent substructures. This is of interest since decomposable structures can be folded much faster. It is known, [x-axis, decompose on average into three irreducible parts. This is of relevance, since a slight generalization of Dyck-path, the Motzkin-paths, having additional horizontal steps, correspond to secondary structures. Our findings suggest, that while secondary structures, decompose nontrivially, higher and higher crossing numbers change the picture. This complicates the computation of mfe-pseudoknot RNA due to their imminent irreducibility.It is clear, that for sequence-length less than or equal to 100 we only encounter pseudoknots of limited complexity. Our findings presented in Figure s known,  that Dyc3 exhibits more structural variety due to the fact that its minimum stack-length is only three. The ratio of pseudoknot structures shifts significantly from n = 80 to n = 100 to approximately 50%. We can conclude from this that pseudoknots cannot be ignored, they evidently become the dominant structure class for n greater than or equal to 100. Figure 3 and cross4 coincide, decreases linearly as a function of sequence length. This indicates that larger and larger sequences will exhibit more subtle structural elements whose emergence is facilitated by stabilizing large stacks.Both versions of cross produce analogous findings, confirming the generality of our results. The vast majority of pseudoknot-shapes is of a single type. As expected, crossk-noncrossing canonical RNA structures, given in Table 4 and cross5, have for n = 76 two stacks less than random 3-noncrossing structures with minimum stack-length greater than four and five, respectively. This deviation is significant and indicates that mfe-pseudoknot structures are far from \"typical\" random structures. We remark that, while it is straightforward to generate random RNA secondary structures, it is nontrivial to obtain random pseudoknot structures. In particular, at present time, no polynomial time algorithm is known which generates a random 3-noncrossing RNA structure with uniform probability.Furthermore, the mfe-pseudoknot structures generated by cross are far from being random. The central limit theorems for random The organization of the sequences contained in neutral networks of RNA pseudoknot structures seems to be very analogous to the neutral networks of RNA secondary structures . Figure n. However, the high neutrality degrees of RNA pseudoknot structures of Figure We discussed in Subsection local connectivity, a property of neutral networks which implies the existence of short, neutral paths. It is apparent that local connectivity is of central importance for molecular evolution and any type of evolutionary optimization. It has been shown in  that locUTR: Untranslated Region; HDV: Hepatitis Delta Virus; DP:dynamic program; lhs: left hand side; rhs: right hand side.The authors declare that they have no competing interests.All authors contributed equally to this paper."}
+{"text": "To maximize the time-integrated X-ray flux from multiple X-ray sources and shorten the data acquisition process, a promising way is to allow overlapped projections from multiple sources being simultaneously on without involving the source multiplexing technology. The most challenging task in this configuration is to perform image reconstruction effectively and efficiently from overlapped projections. Inspired by the single-source simultaneous algebraic reconstruction technique (SART), we hereby develop a multisource SART-type reconstruction algorithm regularized by a sparsity-oriented constraint in the soft-threshold filtering framework to reconstruct images from overlapped projections. Our numerical simulation results verify the correctness of the proposed algorithm and demonstrate the advantage of image reconstruction from overlapped projections. Since the first computed tomography (CT) scanner was made , all the Interestingly, the technology of field-emission X-ray sources based on carbon nanotubes (CNT) is a recent invention with several intrinsic advantages over conventional X-ray tubes. To maximize the time-integrated X-ray flux from multiple sources and improve the signal-to-noise ratio (SNR), multiplexing was used, where multi-source are excited with different temporal modulations . If two  Here, we consider how to reconstruct an image from overlapped projections. Previously, our group developed a generalized simultaneous algebraic reconstruction technique (SART) algorithm to reconstruct an image from data collected with an X-ray line source . Assumin The paper is organized as follows. In the next section, we will formulate the overlapped projection model, which is not a sum of line integrals and quite different from that in the single-source case. In the third section, we will design a SART-type reconstruction algorithm for image reconstruction from overlapped projections. In the fourth section, we will report numerical results. In the last section, we will discuss related issues and conclude the paper. f =  \u2208 \u211dI \u00d7 \u211dJ, where the index 1 \u2264 i \u2264 I and 1 \u2264 j \u2264 J are integers. DefineFor CT reconstruction, a two-dimensional digital image can be expressed as n \u2264 N and N = I \u00d7 J, we have the image in a vector representation f = T \u2208 \u211dN. In this paper, we will use both the signs fi,j and fn for convenience. Let g = T \u2208 \u211dM be a measured vector with M being the product of the number of projections and the number of detector elements. They are linked by the following linear system: A =  \u2208 \u211dM \u00d7 \u211dN is a measurement matrix. In a typical fan-beam geometry, the nth pixel can be viewed as a rectangular region with a constant value fn, the mth measured datum gm as an integral of partially covered pixel areas by a narrow beam from an X-ray source to a detector element which are weighted by the corresponding X-ray linear attenuation coefficients. Thus, the component am,n in  or ordered-subset (OS) version of a general Landweber scheme , of whicAm is the mth row of A, k the iteration index, and 0 < \u03bbk < 2 a free relaxation parameter. Let \u039bN+ \u2208 \u211dN \u00d7 \u211dN be a diagonal matrix with \u039bn,nN+ = 1/an+ and \u039bM+ \u2208 \u211dM \u00d7 \u211dM be a diagonal matrix with \u039bm,mM+ = 1/am+, \u03bbk for k : = 0; initialize (S.2.)N,k+ and \u039bM+,k; compute (S.3.) initialize the error image (S.4.)q = 1 to Q backproject the projection error;  for (S.4.1.) weight the projection error (S.4.2.)M+,k; weight the projection error (S.4.3.)qth X-ray source; backproject the weighted projection error towards the (S.4.4.)N,k+; weight the backprojected error image by \u039b(S.4.5.) add the backprojected image to (S.5.) update the current estimated image by(S.6.)k : = k + 1;  set (S.7.) go to (S.2) until the convergence criteria are satisfied;(S.8.) scale the reconstructed image k, the relax parameter \u03bb, and the initial image \u03bbk = 1 and k. (S.3)-(S.4) computes the current error image for one step iteration according to  initializes the iteration index rding to . BecauseThe conventional data acquisition is based on the Nyquist sampling theory, which states that for accurate reconstruction of a band-limited signal or image the sampling rate must be at least twice the highest frequency of the signal or image. However, the recently developed CS theory shows that a high-quality signal or image can be reconstructed from far fewer measurements than what is usually required by the Nyquist sampling theorem , 8. In l(SS.5.) perform a soft-threshold filtering operation for (SS.5.1.) compute the sparse transform;(SS.5.2.) estimate the optimal threshold;(SS.5.3.)perform the soft-threshold filtering;(SS.5.4.)perform the inverse sparse transform. In the above pseudo-code, the sparse transform in (SS.5.1) can be either any invertible lossless compressible transform such as wavelet transform  and FourTo verify the proposed SART-type algorithm for image reconstruction from overlapped projections, we implemented it in Matlab on a PC, with the computationally intensive segments coded in C and linked via the MEX mechanism. As illustrated in \u03bbk in the SART formula (I0 = 5 \u00d7 104 photons per detector element [ For each of our selected numbers of projections over a full-scan range, we first equiangularly acquired the corresponding projection dataset based on the aforementioned projection model in the single, dual, and triple source cases, respectively. Then, we reconstructed the images using our algorithm described in  formula  was set  element . The res In the CT field, the line integral model along an X-ray path has been widely used in consistency with Beer's law. However, it does not reflect the divergence due to the combination of the finite detector size and the source focal spot. As shown in  As far as the convergence of the proposed algorithm is concerned, it should converge to the least square solution in the cases of either noise-free and noisy projections. The reason is that the proposed method is in the framework of the general Landweber scheme, whose convergence has been well studied under quite general conditions , 13. Whe In conclusion, we have developed a SART-type algorithm for image reconstruction from overlapped projections. The algorithm has been verified and demonstrated in the numerical simulation. Our methodology has a potential to support more flexible designs of multi-source CT/micro-CT systems for better contrast and temporal resolution."}
+{"text": "Eukaryotic cell cycle is a complex process and is precisely regulated at many levels. Many genes specific to the cell cycle are regulated transcriptionally and are expressed just before they are needed. To understand the cell cycle process, it is important to identify the cell cycle transcription factors (TFs) that regulate the expression of cell cycle-regulated genes.We developed a method to identify cell cycle TFs in yeast by integrating current ChIP-chip, mutant, transcription factor binding site (TFBS), and cell cycle gene expression data. We identified 17 cell cycle TFs, 12 of which are known cell cycle TFs, while the remaining five  are putative novel cell cycle TFs. For each cell cycle TF, we assigned specific cell cycle phases in which the TF functions and identified the time lag for the TF to exert regulatory effects on its target genes. We also identified 178 novel cell cycle-regulated genes, among which 59 have unknown functions, but they may now be annotated as cell cycle-regulated genes. Most of our predictions are supported by previous experimental or computational studies. Furthermore, a high confidence TF-gene regulatory matrix is derived as a byproduct of our method. Each TF-gene regulatory relationship in this matrix is supported by at least three data sources: gene expression, TFBS, and ChIP-chip or/and mutant data. We show that our method performs better than four existing methods for identifying yeast cell cycle TFs. Finally, an application of our method to different cell cycle gene expression datasets suggests that our method is robust.Our method is effective for identifying yeast cell cycle TFs and cell cycle-regulated genes. Many of our predictions are validated by the literature. Our study shows that integrating multiple data sources is a powerful approach to studying complex biological systems. Eukaryotic cell cycle is a complex process and is precisely regulated at many levels. One important aspect of this regulation is at the transcriptional level. That is, many genes specific to the cell cycle are transcribed just before they are needed . To haveet al. , where bi,j = 1 if (1) the p-value for TF j to bind the promoter of gene i is \u2264 0.01 in the ChIP-chip data and the promoter of gene i contains one or more binding sites of TF j or (2) the disruption of TF j results in a significant change of the expression of gene i and the promoter of gene i contains one or more binding sites of TF j. Otherwise, bi,j = 0.Using three data sources , we can construct a high-confidence TF-promoter binding matrix However, binding of a TF to the promoter of a gene does not necessarily imply regulation. Hence, additional information is required to solve this ambiguity inherent in the TF-promoter binding matrix. Using a time-lagged dynamic model of gene regulation, we can refine the TF-promoter binding matrix into a high-confidence TF-gene regulatory matrix. We consider the transcriptional regulatory mechanism of a target gene as a system with the regulatory profiles of several TFs as the inputs and the gene expression profile of the target gene as the output. The transcriptional regulation of a target gene is described by the following time-lagged dynamic system model -45y[t] represents the target gene's expression profile at time point t, k represents the target gene's basal expression level induced by RNA polymerase II, N denotes the number of TFs that bind to the promoter of the target gene (inferred from the TF-promoter binding matrix B), di indicates the regulatory ability of TF i, xi[t] represents the regulatory profile of TF i at time point t, \u03c4i indicates the time lag for TF i to exert a regulatory effect on the target gene's expression, \u03bb indicates the degrading effect of the target gene's expression value y [t - 1] at time point t - 1 on the target gene's expression value y [t] at time point t and \u03b5[t] denotes the stochastic noise due to the modeling error and the measuring error of the target gene's expression profile. \u03b5[t] is assumed to be a Gaussian noise with mean zero and unknown standard deviation \u03c3 The biological meaning of Equation (1) is that y [t]  is determined by i at time point t - \u03c4i, where i = 1,..., N) and -\u03bb\u00b7y[t - 1] (the degradation effect of the target gene at time point t - 1).where xi[t] (the regulatory profile of TF i at time point t) is defined as a sigmoid function of zi[t] (the gene expression profile of TF i at time point t) , y [v]} for i \u2208 {1, 2, ..., N}, v \u2208 {1, 2, ..., M}. Equation (2) at different time points can be put together as followsUsing the yeast cell cycle gene expression data from Spellman et al. , we can Y, \u03a6, \u03b8 and e to represent Equation (3) as followswhere Y = [y[w] ... y [M]]T, \u03a6 is the system matrix, \u03b8 = [d1 ... dN k \u03bb]T is the unknown parameter vector, and e is the error vector, The parameter vector \u03b8 can be estimated by the maximum likelihood (ML) method as follows ) [p-value computed by the t-distribution is then adjusted by the Bonferroni correction to represent the true alpha level in the multiple hypotheses testing [i is said to be a true regulator of the target gene if the adjusted p-value padjusted \u2264 0.05.Since se \u03b5[t]) . The p-v testing . FinallyB =  into a TF-gene regulatory matrix C = . In this matrix, ci,j = 1 if bi,j = 1 and if TF j is shown by the time-lagged dynamic system model to exert a significant regulatory effect on the expression of gene i. Otherwise, ci,j = 0.From the above analysis, we can refine the TF-promoter binding matrix et al. [j is a cell cycle TF is as follows. Let S be the set of cell cycle-regulated genes identified by Spellman et al. [G be the set of genes that are regulated by TF j (inferred from the TF-gene regulatory matrix), T = S \u2229 G be the set of cell cycle-regulated genes that are also regulated by TF j, and F be the set of all genes in the yeast genome. Then the p-value for rejecting the null hypothesis (H0: TF j is not a cell cycle TF) is calculated asFrom the high-confidence TF-gene regulatory matrix, the regulatory targets of each of the 203 TFs in yeast can be inferred. Then a TF is said to be a cell cycle TF if a statistically significant portion of its regulatory targets are in the set of 800 cell cycle-regulated genes identified by Spellman et al. ,47. The G| means the number of genes in set G. This p-value is then adjusted by the Bonferroni correction to represent the true alpha level in the multiple hypotheses testing [j is said to be a cell cycle TF if the adjusted p-value padjusted \u2264 0.05. This procedure is applied to each of the 203 TFs under study.where | testing . TF j isX phase  if a statistically significant portion of its regulatory targets belong to the X phase cell cycle-regulated genes identified by Spellman et al. [G and F are defined as before, S now denotes the set of X phase cell cycle-regulated genes identified by Spellman et al. [T = S \u2229 G now denotes the set of X phase cell cycle-regulated genes that are also regulated by the cell cycle TF under study. The p-value computed by Equation (4) is then adjusted by the Bonferroni correction to represent the true alpha level in the multiple hypotheses testing. We say that a cell cycle TF functions in the X phase  if the adjusted p-value padjusted \u2264 0.05.For each of the 17 identified cell cycle TFs, we want to determine in which cell cycle phases it functions. We regard that a cell cycle TF functions in the WSW developed the algorithm, performed the simulation and wrote the manuscript. WHL conceived the research topic, provided essential guidance and revised the manuscript. All authors read and approved the final manuscript.Supplementary Table 1 contains the detailed information of the 17 identified cell cycle TFs, the 178 novel cell cycle-regulated gene (including 59 uncharacterized genes), the results of using different cell cycle gene expression datasets, and performance comparison between our method and four existing methods.Click here for file"}
+{"text": "Knowledge of the subcellular localization is also essential for genome annotation and drug discovery. Supervised machine learning methods for predicting the localization of a protein in a cell rely on the availability of large amounts of labeled data. However, because of the high cost and effort involved in labeling the data, the amount of labeled data is quite small compared to the amount of unlabeled data. Hence, there is a growing interest in developing unlabeled data. We compare semi-supervised AAMMs with: (i) Markov models (MMs) (which do not take advantage of unlabeled data); (ii) an expectation maximization (EM); and (iii) a co-training based approaches to semi-supervised training of MMs (that make use of unlabeled data).In this paper, we present an Abstraction Augmented Markov Model (AAMM) based approach to semi-supervised protein subcellular localization prediction problem. We investigate the effectiveness of AAMMs in exploiting The results of our experiments on three protein subcellular localization data sets show that semi-supervised AAMMs: (i) can effectively exploit unlabeled data; (ii) are more accurate than both the MMs and the EM based semi-supervised MMs; and (iii) are comparable in performance, and in some cases outperform, the co-training based semi-supervised MMs. The problem of predicting subcellular protein localization is important in cell biology, because it can provide valuable information for predicting protein function and protein-protein interactions. Furthermore, the location of proteins in their designated subcellular compartments is essential for the proper functioning of the cell. Abnormal subcellular localization has been correlated with diseases such as cancer .thk order Markov chain models, with k ranging from 1 to 8, and used an approximation technique to estimate the probability of each element in a sequence given the k contiguous previous elements.Many supervised machine learning methods have been successfully applied to the problem of predicting the subcellular localization of a protein, which can be formulated as a sequence classification problem , where tunlabeled data can provide valuable information, i.e., they contain information about the joint probability distribution over sequence elements. Consequently, there is a significant interest in semi-supervised algorithms ..abstractlabeled sequences LD using Equations (3), (4), and (5) . The current model is used to assign probabilistic labels to the  unlabeled sequences UD  using Equation (6) (E-step). Next, a new model is learned from originally labeled sequences EM applied to MMs (EM-MMs) involves an iterative process of E- and M-steps. Specifically, an initial Markov model is learned only from  another .LD be a set of labeled examples, and UD a set of unlabeled examples. A set U\u2032D is obtained by sampling u examples from UD (we used u = 75 examples in experiments). Each example x has two views, i.e., can be encoded with two different sets of features, x(1) and x(2). First, use LD and the x(1) encoding to train a classifier h1, and LD and the x(2) encoding to train another classifier h2. Second, classify the examples in U\u2032D using h1 and h2 separately. Select h1\u2019s and h2\u2019s top (jk)j=1,\u2026,|C| most confident predictions from each class (corresponding to the underlying data distribution), add them to LD, and remove them from U\u2032D. Sample 2 UD and move them to U\u2032D. This process is repeated for a fixed number of iterations, or until all unlabeled data are used up   are clustered together if they induce similar conditional distributions of the next node, independent of the class. When the data are scarce, the estimates of joint probabilities are not reliable. However, the unlabeled data contain information about the joint probability distribution over sequence elements, and can help improve the statistical estimates of parameters. The abstraction hierarchy is subsequently used to learn a Markov model with abstract values of the parents.Our abstraction-based approach to learning classifiers for the protein subcellular localization prediction task exploits large amounts of m of an m-cut that defines an AAMM, an array of indices of size equal to the number of unique k-grams specifies the mapping between k-grams and abstractions . However, the number of parameters of AAMM (for a given class) based on such an abstraction hierarchy and an m-cut is m|X|, as opposed to |X|k|X| in the case of MMs, where m \u226a |X|k.It is worth mentioning that part of the AAMM is the representation of the clustering. Specifically, after the abstraction hierarchy is learned, for a given choice of the size abstraction. It is of interest to incorporate into AAMMs some means of gracefully trading off the complexity of the model against its predictive accuracy. One way to do this is to augment the algorithm, e.g., by designing an MDL-based scoring function to guide a top-down search for an optimal cut  is the number of times the symbol \u03c3 \u201cfollows\u201d the k-gram s in the sequence xl, and p(ly =j c|xl) \u2208 {0,1} is obtained based on the sequence label.where # is the number of times s occurs in xl.where # and # represent the number of times the symbol \u03c3 \u201cfollows\u201d the k-gram s in the sequence xl, and xu, respectively.where #[k-grams, the context of an abstraction a = {s1,\u2026, s|a|} is obtained by a weighted aggregation of the contexts of its k-grams. That is,Since an abstraction is a set of where a\u2032 and a\u2033 in D as follows:We identify the most \u201csimilar\u201d abstractions as those that have the smallest weighted Jensen-Shannon divergence between their contexts. JS divergence  provideswhere  labeled training set \u03b8 from LD, denoted by k-gram s \u2208 S . The estimates a = {s1,\u2026,s|a|}, are a weighted aggregation of the estimates of a\u2019s constituent k-grams, i.e.,Given awhere x0,\u2026,nx\u22121 and an m-cut \u03b3m through T, k-gram ix\u2212k\u2026ix\u22121 find the abstractionw a \u2208 \u03b3m it belongs to and retrieve the parameters associated withw a. Successively multiply i = k,\u2026, n \u2212 1 to obtain Given a new sequence x = As in MMs, apply Bayes rule to obtain The authors declare that they have no competing interests.All authors read and approved the final manuscript."}
+{"text": "In this paper, the PI polynomial of the phenylenic nanotubes and nanotori are computed. Several open questions are also included.The PI polynomial of a molecular graph is defined to be the sum X G be a simple molecular graph without loops, directed and multiple edges. The vertex and edge sets of G are represented by V(G) and E(G), respectively. A topological index is a numeric quantity derived from the structural graph of a molecule. Usage of topological indices in chemistry began in 1947, when Harold Wiener developed the most widely known topological descriptor, the Wiener index, and used it to determine physical properties of the type of alkanes known as paraffins , see [Let G)], see  and 4]..G be a cet al. defined a new polynomial which they named the Padmakar-Ivan polynomial. They abbreviated this new polynomial as PI, for a molecular graph G. We define PI = \u2211uv\u2208 V(G) XN where for an edge e = uv, N = neu(e|G) + nev(e|G) and zero otherwise. This polynomial is very important in computing the PI index. This newly proposed polynomial, PI, does not coincide with the Wiener polynomial ) for acyclic molecules.In a series of papers , 6 Ashraet al. investigated the structure and computed the Hosoya polynomial of some nanotubes and nanotori. Gutman et al.   et al. iAlso, in  and 12]et al. inn,2m]. We also denote a V-Phenylenic nanotorus by H=VPHY. Let G be an arbitrary graph. For every edge e, we definee), for every edge e \u2208 E(G). From above the argument and mn\u20132n, |E(H)|=36mn and |V(T)| =24mn, |V(H)| =24mn. In the following theorem we compute the PI polynomial of the molecular graphT in Proof: To compute the PI polynomial of T, it is enough to calculate N(e). To do this, we consider three cases: that e is vertical, horizontal or oblique. If e is horizontal. a similar proof as Lemma 1 in [e)=8m. Also, if e is a vertical edge in one hexagon or octagon then N(e) = 4n, 2n, respectively.The novel phenylenic and naphthylenic lattices proposed can be contructed from a square net embedded on the toroidal surface. In this section, the PI polynomial of a V-Phenylenic nanotube and nanotorus are computed. Following Diudea  we denotrem 1 in  we have:e in A(T), we have two cases:We consider the set A(T) of oblique edges in T. For every Case 1:n.A similar argument as Lemma 2 in  gives thCase 2:th row of oblique edges in A(T) by Ai , by computations, we have N(e)=4n+2i-2, also if 2(m-|n-m|)+1 \u2264 i \u22642m, then N(e)=8n-2. If m>n, then N(e)=8m. For n>m because of symmetry computations are similar to u er part of graph. So we have:We denote the iy Ai see . It is eAlso:Thus:Which completes the proof.H and calculate its Padmakar-Ivan polynomial, PI, In our next theorem we consider a V-Phenylenic nanotorus Proof: To prove the theorem, we apply a similar method as in Theorem 1. It is easily seen that N(e)=8n for each vertical edge in hexagons, that is two times more twice the tube case by horizontal symmetry. A vertical edge in an octagon has 2n parallels, as in Theorem 1. Also N(e) =8m for each horizontal edge. Let z = min{m,n}, for each oblique edge e we have N(e) = 6z \u2212 2. So:We conclude our paper with the following open questions:Question 1: Let n. Is there a V-phenylenic nanotube or nanotorus T such that PI  = F(x)?Question 2: Is it true that for every polynomial F(x) with positive coefficients and of degree n, there exists a V-phenylenic nanotube or nanotorus T, such that PI  = F(x)?Question 3: What is the relation between the Hosoya polynomial and PI polynomial of a V-phenylenic nanotube or nanotorus?"}
+{"text": "We thank Tarone for his letter, as it provides an opportunity to elaborate on analytic strategies for the study of DDT associations with breast cancer.p,p\u2032-DDT  is the primary ingredient of commercial grade DDT. p,p\u2032-DDE , the most persistent DDT-related compound, is a metabolite of p,p\u2032-DDT that is both made by humans during active exposure, and also ingested directly from food sources where it can be stored for long periods in fat -2-(o-chlorophenyl)ethane] is a low-concentration contaminant of commercial DDT that is eliminated by humans most quickly, making it a marker of recent exposure  of their exposure was only  Table 1 ]. Hence, Table 1 , suggestp,p\u2032-DDT, p,p\u2032-DDE, and o,p\u2032-DDT allow evaluation of potential differences in the effects of these compounds. Other studies have also observed differing associations with cancer risk for p,p\u2032-DDT and its metabolite, p,p\u2032-DDE. p,p\u2032-DDT association with risk of liver cancer was enhanced when p,p\u2032-DDE was low. We also reported that a higher proportion of p,p\u2032-DDT to p,p\u2032-DDE in maternal serum samples was associated with longer time to pregnancy in their daughters 30 years after exposure in utero (p,p\u2032-DDE\u2014after adjustment for p,p\u2032-DDT\u2014for predicting breast cancer, particularly in postmenopausal women. We believe that simultaneous adjustment for DDT-related compounds is a strength of our study.Concurrent measurements of in utero . In anota priori and were a primary objective of our study. In this setting, subgroup analyses are a strength that enabled us to examine whether age at DDT exposure may be of importance in human breast cancer.Tarone suggests that subgroup analyses weaken the results of our article . Howeverin situ disease and its successful treatment, which would reduce incidence of invasive disease and mortality.The trends in breast cancer incidence in young women previously presented by Tarone in Table 1 of his article  do not r"}
+{"text": "Self-consistent field theory is used to study the self-assembly of a triblock copolymer melt. Two different external factors (temperature and solvent) are shown to affect the self-assembly. Either one or two-step self-assembly can be found as a function of temperature in the case of a neat triblock melt, or as a function of increasing solvent content (for non-selective solvents) in the case of a triblock-solvent mixture. For selective solvents, it is shown that increasing the solvent content leads to more complicated self-assembly mechanisms, including a reversed transition where order is found to increase instead of decreasing as expected, and re-entrant behavior where order is found to increase at first, and then decrease to a previous state of disorder. These molecules are much less studied than the less complicated diblock copolymers, because the addition of a third chemically distinct block greatly complicates the microphase separation properties of these self-assembling molecules. It is this increased morphological richness however that makes triblocks appealing, as they can form structures inaccessible to diblocks. It is not just a question of which structures will self-assemble, but also the manner in which the self-assembly takes place. Diblocks can only be in an ordered state or a disordered state, whereas triblock copolymers are the simplest possible copolymer than can be also in a \u201csemi-ordered\u201d state, where two of the blocks are mixed while the third alone is segregated. Triblock copolymers can therefore go from a completely disordered state to a completely ordered state through a multi-step process that holds promise for technological applications if it can be sufficiently understood and predicted.Triblock copolymers are linear polymers composed of three separate regions, or \u201cblocks\u201d, of monomers. Triblocks with three different chemical blocks are usually labeled as block-poly (D8-styrene)-block-poly(vinyl methyl ether) (PI-b-PDS-b-PVME) triblock terpolymers and found that ordering may proceed via a two-phase mechanism. These authors [Experimental studies of complex ordering in triblock systems were undertaken by Yamauchi , 2 who e authors  that seg authors  used sel authors , 2.Here, we build on the previous theoretical results  and show2.N, N, N, Af, Cf, Aa/Ca and Ba/Ca. These are, respectively, the segregation parameters between A and B segments, B and C segments, A and C segments, the volume fraction of A segments, the volume fraction of C segments, the ratio of the A statistical segment length to the C statistical segment length and the ratio of the B statistical segment length to the C statistical segment length. The segregation energies are standardly defined in terms of N, which is the product of the Flory-Huggins parameters N in a single triblock molecule, based on a reference segment volume Af and Cf need to be specified since through incompressibility Bf is not independent. For the current work, we will simplify the system further by restricting our attention to cases where Af C= f \u2261 A/Cf = 0.25 (fB = 1 \u2212 Af \u2212 Cf = 0.5), in keeping with the previous work [Aa = Ba = Ca \u2261 a. These restrictions will impose certain symmetries on the system, but should still allow the predominant structures and mechanisms to emerge as previously demonstrated for diblock systems [N = N = 50, but more general values will be considered here. In addition, we will also allow for the presence of solvent.Equilibrium morphologies for a neat, incompressible melt of monodisperse triblock copolymers can be calculated from the free energy functional given in ref. . The parous work . Similar systems . In our \u03c6, with the volume fraction of the solvent being \u03c6s = 1 \u2212 \u03c6. The second is the molecular volume ratio \u03b1, which is the ratio of the volume of a solvent molecule to the volume of a polymer molecule. This will be held fixed (\u03b1 = 0.01) in this work. The third set is the interaction of the solvent with the polymer, which is determined by the three parameters N,N and N. The modified SCFT equations then areq = 1. s is the normalized contour length (0 \u2264 s \u2264 1) of a polymer chain, and the field \u03c9(r) is equal toq\u2020  is also defined by the equation\u03c9(r) and the Lagrange multiplier \u03be(r) (which is introduced to force incompressibility)j = A, B, C, and S. The single chain partition function and the monomer densities are thenF is given byIn order to introduce the effect of the solvent in the SCFT, we need to introduce more variables . The firare thenQ\u00a0\u00a0=\u00a0\u222bdr\u00a0\u00a0\u00a0q\u03c6A(r)\u00a0\u00a0=\u00a0d2F/d\u03c62 > 0 for all \u03c6; the mixture will macrophase separate if the curvature is negative [d2F/d\u03c62 is always positive so that macrophase separation is absent. Overall we have an eight dimensional parameter space: N, N, N, N, N, N, fa/c, \u03c6. Obviously it is difficult to explore the whole space, so we will choose representative points that illustrate the wide variety of self-assembly mechanisms available to the triblock-solvent system. In particular, we wish to explicitly examine temperature dependence, and the effects of both non-selective and selective solvents in order to more closely parallel the experimental methods of Yamauchi et al. [The free energy curvature must be checked to ensure that negative . In the i et al. , 23.3.1.N = N fixed, and varying N. Although this shows in principle the possibility of engineering one or two-step self-assembly, it is not amenable to experiment nor is it the approach used by Yamauchi et al. [N) and temperature [A and B are constants related to the chemical interactions between species. Ignoring solvent (setting \u03c6 = 1), we drop B for qualitative analysis and we vary all A\u2019s equally with temperature such that N = N = N \u221d T\u22121. This results in one-step self-assembly as shown in N = N = N \u2272 35.5 self-assembly is absent and the melt remains in a disordered state. At N = N = N \u2243 35.5 (marked as TP in N < 35.5 is the disordered phase where the free energy follows the expected linear dependence of N. Above TP (N > 35.5) the lowest free energy is realized by the hexagonal morphology illustrated in In Ref. , it was i et al. ,2. Here,perature , 10(13)A and B in ABA = BCA \u2260 ACA in N, N and N to have temperature dependent and independent terms, but with N having a different temperature dependence factor. Since the relative values of the Flory-Huggins parameters vary with a different rate, the separation of different polymer components will occur at different temperatures and a two-step self-assembly will be observed. N = N = N. At high temperatures (low N) no phase separation occurs as all three components are able to mix. Lowering the temperature (increasing N) the A and C components becomes sufficiently immiscible with the B component to induce phase segregation (TP2 in TP1) to form the structure shown in If this symmetry in the interaction is now broken for any reason, then the transition will take place in two separate steps. There are many possible ways of lifting this symmetry as there are no known constraints on the values of n TP2 in , and the3.2.without using the dilution approximation. We fix N = N = N and N = N = N and vary the solvent volume fraction (1 \u2212 \u03c6). The qualitative behavior of the melt with the solvent is found to be the same for a large range of the parameters describing the solvent-polymer interaction  all three components segregate into spatially iseparated domains. This scenario persists as small amounts of solvent is added to the mixture. Since the solvent is non-selective it distributes roughly uniformly throughout the system (see < 5 % above average solvent concentration) at the domain interfaces. This excess phenomena is known to be an energetic effect [ABA = BCA \u2260 ACA and select any corresponding N, N and N  then upon adding non-selective solvent while holding these parameters fixed, we can induce two-step self-assembly just as if temperature were varied for components with an unequal temperature response. This is again consistent with dilution arguments. Thus either one or two-step self-assembly may be achieved through the use of non-selective solvent rather than through varying temperature.Similarly, if we choose 3.3.A and C components of the polymer than it is with the B component. Selecting N \u2243 N < N, and keeping N = N = N we expect the presence of the selective solvent to produce a two-step self-assembly upon increasing solvent content. As the selective solvent is added to the polymer melt, it builds up primarily in the A and C rich domains (see \u03c6 \u2243 0.68 (TP1 in \u03c6 \u2243 0.64 causes a complete loss of structure as the order-disorder transition occurs (TP2).The symmetry in the interaction can also be broken by using a selective solvent. The selective solvent will have different concentration in regions occupied by different polymer components. This will affect the interactions between polymer components and break the symmetry. To demonstrate this effect we choose a solvent that is more miscible with the ains see , which i8 TP1 in  where thet al. [In general, the phase behavior of a triblock melt with solvent is very complicated. The complete phase diagram is embedded into a 6 + 2 dimensional parameter space (6 for the Flory-Huggins parameters plus two for the triblock composition and the volume fraction of polymer). So far we have dealt with simple transitions, which are straightforward extrapolations from a diblock to a triblock copolymer. Using polymers consisting of different components, and different types of solvent (which leads to different Flory-Huggins parameters) one might expect more complicated transitions. In the experiments by Yamauchi A and C component of our polymer should be mixed. To achieve miscibility of the A and C polymer components at low/no solvent density we have to chose a polymer with a weak interaction between these two components therefore we have to reduce the N parameter. Since we expect these two components to separate by adding solvent, this parameter cannot be much lower than the critical transition value. A selective solvent with a strong attractive interaction with the A component will tend to concentrate in the A rich domains. If at the same time this solvent strongly repels the C polymer component, it will cause an effective immiscibility of the A and C polymer components.Although it is very difficult to explore the full parameter space, we can determine a physical mechanism that explains this reverse transition. We assume that initially the N \u2272 N \u2272 N with N less than but very close to the order-disorder transition between A and C, and take \u03c6 = 1. A semi-ordered structure, results  induces re-entrant behavior in that the system becomes semi-ordered once again \u2013 A and C mix again as illustrated in A and C internal morphologies have reversed their patterns so that A now forms the cores in the mixed domains; this is similar to the reversal of morphologies seen in diblock solutions with strongly selective solvents [B-C interaction becoming increasingly diluted whereas both B and C interaction with the solvent remains very unfavorable. It therefore becomes attractive for the system to use the C monomers\u2019 weak interactions with the A monomers to minimize the interaction with the solvent.Further increasing the solvent content  triblock melt, we find that one or two-step ordering is possible, the former occurring when N = N = N with all segregation being varied with temperature equally, and the latter occurring when N is lower than N or N.We have illustrated ordering mechanisms in a triblock copolymer system as they appear as a function temperature and (non-selective and selective) solvent content. For temperature dependent N values of A, B and C triblock constituents are held fixed at equal, or unequal values. For N = N = N, one-step ordering occurred, but for N = N \u2260 N, two-step ordering resulted.The addition of non-selective solvent may also induce either one or two-step ordering processes depending on whether the Adding selective solvent causes two-step self-assembly when the solvent is sufficiently selective, and for certain choices of system parameters, a much more complicated route of self-assembly was found."}
+{"text": "Their article should be interpreted with caution, particularly the estimated 5-fold increase in risk for women born after 1931 the authors reported without qualification in the \u201cAbstract\u201d; this value was repeated in the news article by p,p\u2032-DDT, o,p\u2032-DDT , and p,p\u2032-DDE \u2014by various categories of year of birth, yet they found no significantly increased risk estimates for any of the three DDT congeners in multiple comparisons that were not adjusted for the other DDT-related chemicals either in all women or in women born after 1931. The estimated 5-fold increase in risk for the upper tertile of p,p\u2032-DDT serum levels was only observed in subgroup analyses that were both restricted to women born after 1931 and adjusted for serum level of o,p\u2032-DDT. The impact of the adjustment for o,p\u2032-DDT on the risk estimate for p,p\u2032-DDT is remarkable in view of the low o,p\u2032-DDT levels observed (35% were below the limit of detection). A significant inverse association between o,p\u2032-DDT level and breast cancer risk, which was interpreted by Cohn et al. in terms of length of time since DDT exposure, became stronger after adjustment for p,p\u2032-DDT levels; presumably this does not indicate a protective effect of recent DDT exposure.In a recent article, p,p\u2032-DDE levels and breast cancer risk (In view of the absence of evidence for an association between cer risk , it seemcer risk . Women bcer risk , but thecer risk ; yet the"}
+{"text": "Several approaches, including metabolic control analysis (MCA), flux balance analysis (FBA), correlation metric construction (CMC), and biochemical circuit theory (BCT), have been developed for the quantitative analysis of complex biochemical networks. Here, we present a comprehensive theory of linear analysis for nonequilibrium steady-state (NESS) biochemical reaction networks that unites these disparate approaches in a common mathematical framework and thermodynamic basis.A obtained in the standard, linear-dynamic-stability analysis of the steady-state can be decomposed as A = SRT where R and S are directly related to the elasticity-coefficient matrix for the fluxes and chemical potentials in MCA, respectively; the control-coefficients for the fluxes and chemical potentials can be written in terms of RTBS and STBS respectively where matrix B is the inverse of A; the matrix S is precisely the stoichiometric matrix in FBA; and the matrix eAt plays a central role in CMC.In this theory a number of relationships between key matrices are introduced: the matrix One key finding that emerges from this analysis is that the well-known summation theorems in MCA take different forms depending on whether metabolic steady-state is maintained by flux injection or concentration clamping. We demonstrate that if rate-limiting steps exist in a biochemical pathway, they are the steps with smallest biochemical conductances and largest flux control-coefficients. We hypothesize that biochemical networks for cellular signaling have a different strategy for minimizing energy waste and being efficient than do biochemical networks for biosynthesis. We also discuss the intimate relationship between MCA and biochemical systems analysis (BSA). Developing methodologies for quantitative analysis, both experimental and mathematical, of complex biochemical networks has become one of the central themes of post-genomic biochemistry and mathematical biology. Several disparate approaches, including metabolic control analysis (MCA) ,2, flux The physical concept of a NESS  applies to that of a driven system, such as a living organism, with a constant flow of matter (transforming nutrients to waste) through the system and a corresponding dissipation of free energy . Even thA obtained in linear stability analysis, the flux control-coefficient matrix C in MCA, the stoichiometric matrix S of FBA, and the correlation matrix R from CMC are intimately related. We develop the relationships in the context of complex biochemical networks and their NESS thermodynamics. We show that all the key matrices in MCA and CMC can be computed if one knows the fluxes, chemical potential differences, and the stoichiometric matrix.We distinguish between two types of linear analysis: (i) linear stability analysis , and , fluxes (currents), and resistances. It becomes immediately clear that the resistances are related to reaction effectors, such as the expression levels of enzymes, that affect both the forward and backward fluxes of a given reaction, but do not change the chemical potential difference. It is this thermodynamic perspective of a NESS that can be used to develop a comprehensive theory that unites these approaches.J of each metabolic reaction in a NESS metabolic network is decomposed into J = \u03c6+ - \u03c6- and the chemical potential difference of the reaction in the NESS is \u0394\u03bc = kBT ln(\u03c6-/\u03c6+), where kB is Boltzmann's constant and T is absolute temperature. Therefore, knowing the chemical potential difference and the flux of a reaction givesIn the context of the newly developed biochemical circuit theory (BCT) ,16, the \u03bco is known from equilibrium thermodynamics, then Furthermore, if the standard-state free energy of reaction \u0394\u03b2-cells and ketogenesis in hepatocytes, where cellular organelles, such as mitochondria, play a key role in the handshake between metabolism and signaling. Ultimately, our goal is to understand how these cellular systems behave in response to stress and disease [In many theoretical approaches, metabolic networks and signaling pathways are often separated into disparate mechanisms with only peripheral interactions. This is far from reality, however, as these mechanisms are intimately intertwined and often indistinguishable. For example, in whole-body metabolism, glucose and fatty acids serve as the fuel for cellular metabolism, but also as signals for insulin secretion in pancreatic  disease . It is iS, and measures the correlation matrix, R, to obtain the control coefficients, and vice versa . The jth biochemical reaction  is characterized by a set of stoichiometric coefficients Let us consider a network of \u03bd's and \u03ba's can be zero. The N \u00d7 M matrix S = \u03ba - \u03bd is known as the stoichiometric matrix. Eq. (2) assumes that the forward and backward reaction kinetics are characterized by the constants Some of the integer s. Segel , for exaFor the reaction system (2), kinetic equations of the time-dependent concentration changes for each biochemical species can be written according to the law of mass action as ,20x\u2113to denote the concentration of respective X\u2113, and i = 1, 2, ..., N) are external injection fluxes to species i . We use the convention that subscripts index species and superscripts index reactions. To further simplify the notation, we introduce forward and backward fluxes where we use j=\u03c6+j\u2212\u03c6\u2212j:dx/dt = SJ + Je, in which x and Je are N-dimensional column vectors, and J is an M-dimensional column vector.Then Eq. (3) becomes closed reaction system, Je = 0. In this case, it can be shown that thermodynamic equilibrium is the only positive stationary solution to Eq. (3): the internal fluxes J = \u03c6+ - \u03c6- = 0 for each and every reaction. For a closed biochemical reaction system, since all the fluxes are necessarily zero in its unique equilibrium , all the control coefficients are necessarily zero. Therefore, in a NESS, at least one injection flux and one effux are nonzero , i.e., there is no unique stationary solution for different initial conditions.same NESS. We use the notations For an open system that approaches a NESS, the stationary solution is not usually degenerate. If we assume {In the linear regime near the NESS ,\u03b4xj = xj - in which A = {Aij} is called the linear stability matrix. We introduce the N \u00d7 M matrix R = A = SRT. We also denote A-1 = B.S does not have full rank and A is singular [A into a nonsingular matrix by replacing its linearly dependent rows with vectors in its left null space (see Ref. 18 of [A is understood to be the transformed nonsingular matrix.If the nonlinear dynamics scheme of Eq. (3) conserves certain quantities, such as total element, motif, or enzyme concentrations, singular ,19,20. IEq. (3) is a general scheme for biochemical reaction networks. For metabolic reactions involving enzymes, the enzyme and the enzyme-substrate complexes are treated as additional \"species.\" In this section, however, we study MCA, and assume that every reaction involves an enzyme which is not explicitly expressed as a species. Rather, we assume enzyme activity is absorbed into the rate constants for the forward and backward reactions. This is clearly not an accurate approximation for many enzymatic reaction mechanisms. Nevertheless, it provides a first-order approximation for treating a metabolic network. More complex rate laws for enzymatic reactions have been discussed for biochemical systems analysis ,22.th reaction or the Nth  species.MCA focuses on how the NESS {N is changed: XN. The immediate, local change is characterized byFirst, we consider the case where the concentration of external species \u03b5 = (dg J)-1 RT. Here, we use the same notation used by Heinrich and Schuster [v) denotes the diagonal matrix containing the components of the vector v along its diagonal. The unscaled, local, elasticity-coefficient matrix is given by \u03b5' = (dg J) \u03b5 (dg x)-1 = RT (dg x)-1. The prime symbol is used to distinguish unscaled coefficients from scaled coefficients, both here and in what is to follow.which is called the scaled, local elasticity-coefficient . These cSchuster , where  satisfyThe coefficient response . When a BiN is the Nth column vector of the matrix A-1. The new NESS established near {Jm + \u03b4Jm, are given bySolving Eq. (6), we have Hence, the scaled, steady-state elasticity-coefficient is \u03b5 = (dg J)-1 RTB (dg B)-1. Here, (dg B) denotes the diagonal matrix containing only the diagonal components of the matrix B along its diagonal. The unscaled, steady-state, elasticity-coefficient matrix is given by \u03b5' = (dg J) \u03b5 (dg x)-1 = RTB (dg B)-1 (dg x)-1.which may also be known as a response coefficient ,25. Thes\u03b5 and \u03b5 are different. In principle, the \u03b5 can be experimentally measured as a system response, but obtaining \u03b5 can be more difficult since it is a transient response that must be measured individually.As we shall show, some connectivity theorems for the two quantities th reaction EM is changed: EM \u2192 EM + \u03b4EM. Since we have assumed that the rate constants for reaction M, M, EM, we haveNext, we consider the case where the enzyme for the MEM \u2192 EM + \u03b4EM, the new NESS satisfies [When atisfies \u03b4xj/j = 1, 2, ..., N), we haveSolving for From Eq. (10), we get the scaled, concentration control-coefficient ,BS(dg J). The unscaled, concentration, control-coefficient matrix is x) J)-1 = -(dg x)BS.which is an element of the scaled, concentration, control-coefficient matrix given by Combining Eqs. (7) and 10), we get the scaled, flux control-coefficient [0, we get\u03b4mM is the Kronecker delta function. These coefficients are elements of the scaled, flux, control-coefficient matrix given by C = I - (dg J)-1 RTBS (dg J). The unscaled, flux, control-coefficient matrix is C' = (dg J) C (dg J)-1 = I - RTBS.where \u03b5, \u03b5, C, and Among between the scaled coefficients, and similarly,between the unscaled coefficients.SJ = -Je = 0, we haveSecond, from Eqs. (13)\u2013(16), it is straightforward to show that if there is no injection flux, i.e., in NESS 1i \u00d7 j and 0i \u00d7 j denote the i \u00d7 j matrices of ones and zeros, respectively. Eqs. (17) and (18) are known as the summation theorems for the scaled control-coefficients. For the unscaled control-coefficients, we have the generalized summation theorems, C'K = K and K is the M \u00d7 (M - N) loop (or nullspace) matrix, i.e., its columns form a basis of the nullspace of S so that SK = 0N \u00d7 (M - N) [where  (M - N) ,16.Euler's theorem on homogeneous functions can be used to understand the significance of the injection fluxes ,26. If tBSRT = I \u21d2 (RTBS)(RTB) = RTB, which yields the connectivity theorems for the scaled coefficients:Third, and the generalized connectivity theorems for the unscaled coefficients :Finally, by combining the generalized summation and connectivity theorems, we getK \u03b5') has been proved to be invertible [which is the central equation in MCA . The matvertible ,27. TherUsing the steady-state elasticity-coefficients, we haveK \u03b5') is also invertible (see Methods). Therefore, if the steady-state elasticity-coefficients are known, the control-coefficients can be calculated. This is an important result because \u03b5 can be experimentally measured as a system response, but obtaining \u03b5 can be more difficult since it is a transient response and must be measured individually.The matrix , and vice versa. In general, the flux J and the chemical potential difference \u0394\u03bc are nonlinearly related [Both  related :J and \u0394\u03bc are linearly related with the biochemical conductance being \u03c6+/kBT (= \u03c6-/kBT) [\u03c6- is relatively unperturbed. Then we have \u03b4J/\u03b4\u0394\u03bc = -\u03c6+/kBT. Similarly, if the reaction is perturbed from its downstream, then \u03b4J/\u03b4\u0394\u03bc = -\u03c6-/kBT.In the linear regime with small flux and chemical potential difference,  \u03c6-/kBT) ,16. In tscaled, local elasticity-coefficients for chemical potentials [Combining BCT and MCA, we can define the tentials \u03b5\u03bc \u0394= kBT (dg \u0394\u03bc)-1 ST, the scaled, steady-state elasticity-coefficients for chemical potentialsas elements of the matrix \u03b5\u03bc \u0394= kBT (dg \u0394\u03bc)-1 STB (dg B)-1, and the scaled, potential control-coefficients [as elements of the matrix ficients C\u03bc \u0394= -kBT (dg \u0394\u03bc)-1 STBS (dg J), where reaction potentials and substrate concentrations in the reference state are used for normalization. The corresponding unscaled coefficients are given in matrix form asas elements of the matrix ST, STB, and STBS in the local and steady-state elasticity-coefficients and the control-coefficient for the potentials, as compared to the matricies RT, RTB, and RTBS in the coefficients for the fluxes. Furthermore, note the relationshipsNote the appearance of the matrices Eqs. (19) and (29) in combination yield the summation  and connEq. (31) can also be derived using the homogeneous function theory (discussed above with flux and concentration control-coefficients). For the unscaled coefficients, we get the generalized summation and connectivity theorems by combining Eqs. (21) and (30) so thatEq. (33) is a manifestation of Kirchhoff's loop law ,16.By combining the generalized summation and connectivity theorems, we getK \u03b5') has been proved to be invertible [The matrix  has an inverse (see Methods). Therefore, if the steady-state elasticity-coefficients are known, the control-coefficients can be calculated.The matrix (xN \u2208 Correlation metric construction (CMC) focuses on how the NESS {If the random perturbation has a sufficiently long correlation time compared to the relaxations of all the reactions in the system, then we are dealing with a shift in the NESS where, according to Eq. (6),\u03b4xi} with an uncorrelated perturbation on \u03b4xN, we haveFrom the time series of {i, j = 1, 2, ..., N.for \u03b4xN is a Markov process characterized byCMC extracts information from reaction systems by using perturbations with insufficiently long correlation times. kd controls the relaxation time of the perturbation, a is its random amplitude with Gaussian distribution, and \u03be(t) is a uncorrelated noise. \u03b4xN in Eq. (38) is called an Ornstein-Uhlenbeck (OU) process with auto-covariance functionwhere With this type of random perturbation, the temporal correlations between the concentration fluctuations give information on the connectivity of a network following the kinetic equation (4)i = 1, 2, ...,(N - 1). More precisely , instead of Eq. (40) CMC follows an autoregressive (AR) process, the discrete version of an OU process, with discrete time T, 2T, ...,for in which A matrix into a (N - 1) \u00d7 (N - 1) matrix Let's rewrite the which leads tog(\u03c4) in Eq. (39) is \u226b all the relaxation times of Two limits of Eq. (42) are particularly interesting. If the correlation time of Rij(t) is the response curve, as a function of t, for the ith species to an impulse of the jth species at time 0. The relation between the correlation matrix and the fundamental solution is expected for a linear system. For directly connected species i and j, the i and j are not directly connected, The matrix analyzed .Both flux control-coefficients and biochemical conductances can be used as indicators for rate-limiting steps in a biochemical network . TraditiLet's consider the linear pathwayx0 and xn for X0 and Xn, respectively. Analogous to a continuous energy landscape, we have the discrete energy functionunder NESS with clamped concentrations j = 1, 2,..., n. If there is a rate-limiting step, say for example that reaction j is nearly irreversible, then Ej is maximal and that is where the highest energy barrier is located. We now show that it is also where the largest flux control-coefficient and the smallest conductance are.for The NESS flux of reaction system (44) can be solved for analytically to yield ,32Therefore, the flux control-coefficient isEj. The biochemical conductance, on the other hand, iswhich reaches its maximum at maximal Ej where concentration x\u2113is the lowest.which is at its minimum when J given, the smallest conductance also corresponds to the largest |\u0394\u03bc|. In general, the rate-limiting step is not necessarily where the k's are smallest. The most efficient situation for reaction system (44) is when all the conductances are equal. This result is analogous to the constant torque principle suggested for molecular motors [Note that with r motors ,13,33.The analysis provided in the present paper poses the following biological question. When is a NESS of a biochemical network controlled by a constant flux injection and when is it controlled by a clamped concentration ? Clearly in real biological systems, the appropriate answer is a combination of both. Just as a real battery, having both finite internal resistance and conductance, in an electrical circuit is a combination of constant-current  and constant-voltage  ideal batteries, so too would a real biological system be a combination of constant flux injections and clamped concentrations . NeverthJ to a simple unimolecular reaction in a NESS, we have the heat dissipation rate (hdr)First, let's see what are the respective consequences of these two different types of \"forcing\" to a biochemical system. For a constant flux injection J a reaction with larger \u03c6-  dissipates a smaller amount of heat. For a constant clamped chemical potential \u0394\u03bc, we haveThis indicates that for the same injection flux hdr increases with \u03c6- for the constant potential difference (concentration clamping) case. These results are analogous to an electric circuit in which the heat dissipation equals I2R and U2/R, respectively.We note that This observation leads us to the following hypothesis. In a biochemical network for biosynthesis, the fluxes are essential for supply and demand. Hence, such networks will in general have large conductances in order to minimize the energy waste and be efficient. On the other hand, in a biochemical network for cellular signaling, the concentrations are the essential signal. Thus, in this case the conductances are generally small in order to minimize the energy waste.J in the enzymatic reaction as a rational function of the concentration of a substrate x [MCA shares an intimate relationship with the biochemical systems analysis (BSA) originally proposed by M.A. Savageau . A critistrate x , such thK \u2264 L due to substrate saturation or effector inhibition. The coefficients ai, bi, \u03b10, and \u03b20 contain the concentrations of all the other substrates. BSA provides insight to the properties of ai and bj. The network of metabolic reactions is then modeled [where  modeled  by a sysJ can be written asIn terms of Eq. (49) the local elasticity-coefficient for the flux which also has the standard form of a Pade approximation . Furtherwhich is essentially the integral form of the definition of local elasticity-coefficients.In contrast, MCA assumes no specific rate laws for an enzymatic reaction except that the rate is linearly proportional to the enzyme concentration. This assumption is certainly valid for most biochemical reactions except when a substrate concentration is significantly less than that of an enzyme.K \u03b5'), that appears in the central, control-analysis equations, i.e., Eqs. (24) and (36), is invertible, we note that since we are dealing with systems without conserved quantities, rank(S) = N. Furthermore, we note that the matrix KTK is invertible because K contains linearly independent columns, and because all columns of K are in the right nullspace of S, the matrixTo demonstrate that the matrix,  loop (or nullspace) matrix (SK = 0); R: N \u00d7 M correlation matrix defined such that A = SRT; S: N \u00d7 M stoichiometric matrix; x:N-dimensional vector of species' concentrations; J: M-dimensional vector of reaction fluxes; \u0394\u03bc: M-dimensional vector of reaction potentials; \u03b5:M \u00d7 N local, elasticity-coefficient matrix; \u03b5: M \u00d7 N steady-state, elasticity-coefficient matrix; N \u00d7 M concentration, control-coefficient matrix; C: M \u00d7 M flux, control-coefficient matrix; C\u03bc\u0394: M \u00d7 M biochemical potential, control-coefficient matrix; (dg v): If v is a vector, (dg v) denotes the diagonal matrix with the components of v along its diagonal. If v is a matrix, (dg v) denotes the diagonal matrix with only the diagonal components of v along its diagonal; *: Denotes steady-state; ': Distinguishes unscaled coefficients from scaled coefficients.BCT: Biochemical Circuit Theory; BSA: Biochemical Systems Analysis; CMC: Correlation Metric Construction; FBA: Flux Balance Analysis; MCA: Metabolic Control Analysis; NESS: Nonequilibrium Steady-State; HQ initiated this work. All authors contributed to and wrote the manuscript together. All authors read and approved the final manuscript."}
+{"text": "With the abundant information produced by microarray technology, various approaches have been proposed to infer transcriptional regulatory networks. However, few approaches have studied subtle and indirect interaction such as genetic compensation, the existence of which is widely recognized although its mechanism has yet to be clarified. Furthermore, when inferring gene networks most models include only observed variables whereas latent factors, such as proteins and mRNA degradation that are not measured by microarrays, do participate in networks in reality.Motivated by inferring transcriptional compensation (TC) interactions in yeast, a stepwise structural equation modeling algorithm (SSEM) is developed. In addition to observed variables, SSEM also incorporates hidden variables to capture interactions (or regulations) from latent factors. Simulated gene networks are used to determine with which of six possible model selection criteria (MSC) SSEM works best. SSEM with Bayesian information criterion (BIC) results in the highest true positive rates, the largest percentage of correctly predicted interactions from all existing interactions, and the highest true negative (non-existing interactions) rates. Next, we apply SSEM using real microarray data to infer TC interactions among (1) small groups of genes that are synthetic sick or lethal (SSL) to SGS1, and (2) a group of SSL pairs of 51 yeast genes involved in DNA synthesis and repair that are of interest. For (1), SSEM with BIC is shown to outperform three Bayesian network algorithms and a multivariate autoregressive model, checked against the results of qRT-PCR experiments. The predictions for (2) are shown to coincide with several known pathways of Sgs1 and its partners that are involved in DNA replication, recombination and repair. In addition, experimentally testable interactions of Rad27 are predicted.SSEM is a useful tool for inferring genetic networks, and the results reinforce the possibility of predicting pathways of protein complexes via genetic interactions. While the existence of genetic compensation is widely accepted, the mechanism is largely unknown but important ,2. The pGraph models  depict Although each class of models has been shown to be informative for understanding genetic interactions, most of the models, except some Bayesian networks, have the estimation bias problem due to model mis-specification. The model mis-specification arises from the fact that microarrays measure the mRNA expressions only, while genetic interactions may be influenced by enzymes or proteins, for instance transcriptional factors. Furthermore, most genetic networks reconstructed in previous studies considered only a subset of the whole genome. Consequently, those genes that were left out may be regarded as latent factors influencing the genes of interest. Thus, ignoring latent factors in the models may cause bias when inferring the genetic interactions. Although a Bayesian network can also incorporate latent factors ,12, the et al. , where c \u2265 3. A large sample size can inflate a small difference between S and \u03c72 statistic. Numerous indices were proposed to remedy the bias, among them four have been assessed in our pilot studies, namely, \u03c72/df, \u03c72 - df [df denotes degree of freedom. The former two were found to be more effective than the latter two for network (model) selection.Among the six MSC's studied, the od ratio . Assumin \u03c72 - df , TLI [43 \u03c72 - df , where dT is the number of time points in the gene expression data. AIC [L/24.MSE between the observed and the predicted gene expressions is defined as ata. AIC  and BIC ata. AIC  are two  Schwarz  proposed, Sclove  suggestex(t), \u039b and w. The significance of each link (\u03bbij and Wkl) is tested by its associated t-statistic. Let ti-window , respectively.A genetic network inferred from LDFM can be built by latent factor-gene and gene-gene interactions. A correct network is essential for estimation of gene-gene interactions using SEM. However, learning the optimal network from data subject to a goodness-of-fit index is NP-hard. Although global optimization techniques, such as simulated annealing and genetic algorithms, may be applied, the required computation time is not feasible. To make the learning process practical, we propose a stepwise approach. The key idea is to generate a set of candidate networks and retain plausible links by both using SEM and iteratively filtering with a moving window as follows. For any network generated in the iteration, we apply SEM to estimate Sc, Sp and Sf denote the sets of c-links, p-links and f-links, respectively. Suppose that EFA suggests k factors for a given data set. Given fixed k - 1, k or k + 1 factors, EFA is applied again to learn the associated latent (factor-gene) structures. SSEM begins with the aforementioned latent structure and a fully connected gene structure, namely, each gene is regulated by all genes and k - 1, k or k + 1 latent factors. To start the stepwise search, SEM is applied to the initial networks to estimate x(t), \u039b and w. For a given initial network, first let the initial t0-window be 0 can be generated as follows. Checking the t-statistics of all links against the t0-window f-links, and retain all c-links, while considering all 0\u20131 combinations of p-links. Suppose there are l p-links in an initial model, then there are 2l combinations of each p-link being included in a model or not. Models including all c-links and each aforementioned combination are considered, and these 2l models can be viewed as generated by the t-window filtering. That is, the t-window serves as a filter to eliminate insignificant (the less-likely-to-exist) links. Specifically, \u03a60 = {\u03c6|\u03c6 \u2208 Sc \u222a Lp, \u2200 Lp \u2208 P(Sp)}, where P(Sp) = {Lp|Lp \u2286 Sp} is the power set of Sp and Lp is a subset of Sp. Furthermore, we apply SEM to each candidate network in \u03a60 to obtain the pre-specified goodness-of-fit index. To save computation time and to ensure that the superior networks are kept for the next iteration, only the top m networks (denoted by \u03a90) are retained for the next iteration.Let i \u2265 1, SSEM generates a set of candidate networks by t-window filtering all networks generated by the top m networks from iteration(i-1), i.e., \u03a9i-1, with k - 1, k or k + 1 factors, respectively, to form \u03a6i. So in total, there are 3 m seed models to generate networks. Among the networks in \u03a6i \u222a \u03a9i-1, only the top m networks (\u03a9i) are retained by the specified goodness-of-fit index for iteration (i + 1). First, we let the ti-window equal to the ti-1-window +c. We use c = 0.1, but c can be other small constants. Again, given the ti-window, each link in the jth network in \u03a9i-1 can be discarded, retained or considered according to its t-statistic value. We denote the collection of these f-links, c-links, and p-links by Sjf, Sjc, and Sjp, respectively. A set of candidate networks is generated by retaining all c-links and considering all 0\u20131 combinations of p-links with k - 1, k or k + 1 factors in the model, and this set is denoted by \u03c6|\u03c6 \u2208 Sjc \u222a Lp, \u2200 Lp \u2208 P(Sjp)}. We combine all the generated sets to result in the ith set of networks Similar to the initial iteration, for each iteration i, we obtain the top m scored networks from \u03a6i \u222a \u03a9i-1, which form \u03a6i, to go to iteration (i + 1). The iteration terminates if the specified goodness-of-fit index can not be further improved.Evaluating the specified goodness-of-fit index for every network in \u03a6k.Fit EFA to a given data set to determine the number of factors, say k - 1, k or k + 1 latent factors, respectively.\u2022 Apply EFA to generate three initial networks by estimating the latent structures with \u2022 For given k factors, obtain the latent structure by eliminating the links with factor loading less than a constant .\u2022 Specify an MSC.\u2022 For each initial network:i = 0, run SEM on the data set. Specify the t0-window = c-links and one of all the 0\u20131 combinations of p-links. Compute the MSC of all networks and select the top m models to form the candidate set \u03a90.Step 1. Set iteration i = i + 1. Specify the ti-window Step 2. Set i-1, generate a set of networks, and form \u03a6iStep 3. Similarly to Step 1, for each network in \u03a9i, and choose the best m networks from \u03a6i \u222a \u03a9i-1 to form the ith candidate set \u03a9i.Step 4. Evaluate the MSC for all networks in \u03a6ith top 1 MSC = the (i-1)th top 1 MSC, stop ; Otherwise, go to Step 2.Step 5. If the m networks from the union of all networks generated by different initial guesses.\u2022 Select the best Project home page is in . SSEM alGS and CC conceived the study, devised the method, and supervised methodology and implementation. CY carried out the method and part of simulation, and wrote an early draft of Shieh et al. in . JH wrotSSEM-TR. Technical Report of SSEM \u2013 Shieh et al. (2005).Click here for fileqRT-PCR. Description of the design of qRT-PCR experiments and how the experiments were conducted to confirm the predicted TC and TD interactions.Click here for fileSimulation. The description of the 6- and 10-gene networks, and the results of EBVM applied to the two networks.Click here for fileBayesianNW. The 6-gene network predicted by the three Bayesian network algorithms in Beal et al. (2005), Rangel et al. (2004) and Perrin et al. (2003).Click here for fileMulti-AR(1). The result of fitting multivariate AR(1) straightforwardly to the real data for the 6-gene network.Click here for fileSSL-TCNW. TC networks of SSL gene pairs. Description of how TC and TD interactions of SGS1 and RAD27 SSL gene pairs were predicted by SSEM.Click here for fileSSEM-algorithm. The zipped file consists of the standalone executable (.exe) file of SSEM.Click here for file"}
+{"text": "Yet TEs play a substantial role in genome evolution and are themselves an important subject of study. Repeat annotation, based on counting occurrences of k-mer counting and indexing of large sequence sets. Unlike previous methods, Tallymer is based on enhanced suffix arrays. This gives a much larger flexibility concerning the choice of the k-mer size. Tallymer can process large data sizes of several billion bases. We used it in a variety of applications to study the genomes of maize and other plant species. In particular, Tallymer was used to index a set of whole genome shotgun sequences from maize (B73) . We analyzed k-mer frequencies for a wide range of k. At this low genome coverage (\u2248 0.45\u00d7) highly repetitive 20-mers constituted 44% of the genome but represented only 1% of all possible k-mers. Similar low-complexity was seen in the repeat fractions of sorghum and rice. When applying our method to other maize data sets, High-C0t derived sequences showed the greatest enrichment for low-copy sequences. Among annotated TEs, the most highly repetitive were of the Ty3/gypsy class of retrotransposons, followed by the Ty1/copia class, and DNA transposons. Among expressed sequence tags (EST), a notable fraction contained high-copy k-mers, suggesting that transposons are still active in maize. Retrotransposons in Mo17 and McC cultivars were readily detected using the B73 20-mer frequency index, indicating their conservation despite extensive rearrangement across cultivars. Among one hundred annotated bacterial artificial chromosomes (BACs), k-mer frequency could be used to detect transposon-encoded genes with 92% sensitivity, compared to 96% using alignment-based repeat masking, while both methods showed 92% specificity.Here we introduce the Tallymer software, a flexible and memory-efficient collection of programs for .The Tallymer software was effective in a variety of applications to aid genome annotation in maize, despite limitations imposed by the relatively low coverage of sequence available. For more information on the software, see  Repetitive elements abound in the genomes of higher organisms. Tandem repeats, simple sequence repeats, long terminal repeats (LTRs), segmental duplications, and transposable elements (TEs) are among those types commonly found in eukaryotic species. The biological role of these entities in genome evolution has been documented ,2, but fFor anticipated plant genome projects and those currently underway, effective and rapid annotation of their many repeats has acquired a new urgency. For example, the maize genome is estimated to be 60\u201370% repetitive, mainly in the form of retrotransposons that proliferated in the last 2 to 6 million years -5. ExtenRepeat identification strategies fall under two broad categories: de novo detection and similarity-based detection. RepeatMasker , one of De novo methods address many of these concerns. RECON  currentlk-mers. K-mer frequency based methods were originally used in whole genome shotgun assemblers , ZMMBBb0284N04 [Genbank: AC157977], ZMMBBb0614J24 [Genbank: AC157487], and ZMMBBb0448F23 [Genbank: AC160211]. A polymerase chain reaction was used on template ZMMBBb0382K21 to give a unique 1864 bp sequence [Genbank: AC163004] that served to fill a physical gap between ZMMBBb0483G05 and ZMMBBb0284N04. Overlap between clone sequences allowed assembly of a complete supercontig of 453,421 bp.This study used publicly available datasets, including expressed sequence tags (ESTs), gene-enriched genome fractions, representative whole genome sequences, and repeat libraries, as summarized in Table Zea mays L. ssp. mays), generated by the Joint Genome Institute were downloaded from the NCBI Trace Archive on February 13, 2006 and clipped to remove vector sequences using cross match  into equal sized non-overlapping subintervals at some suitable distance \u0394. We obtain the intervalsbe the minimum and maximum possible \u03bbmin = -m\u0394 and (n - 1)\u0394 \u2264 \u03bbmax <n\u0394. Then for each integer j \u2208  we computesuch that \u03bb = j\u0394. That is, \u03a9k, M is the fraction of sequences in M falling into the jth subinterval. \u03a9k, M is called \u03bb-distribution ratio for M.where k-mers in S. That is, it is derived from the distribution of occ for all k-mers w in S. Now let \u03b4S, k be a table such that for all i \u2265 1, \u03b4S, k[i] is the number of different k-mers occurring exactly i times in S. For example, \u03b4S, k by one.According to these equations we can efficiently compute k-mers are computed by hashing methods. However, these only work, if the number 4k of possible k-mers is considerably smaller than n. This does not hold for our application, where k ranges from 10 to 500. We have developed a different approach based on enhanced suffix arrays  for a range of values of k. This is useful when determining the optimal value for k.Traditionally, occurrence counts for x arrays . The spaTo explain our approach we begin with the concept of enhanced suffix arrays, as introduced in .S consists of r sequences. To process S we concatenate all sequences in S into a long string denoted 1,...,$r-1 between the r sequences. Additionally we add a sentinel character $r following the last sequence in the concatenation. Obviously, k-mers as S. That is, we can compute k-mer counts based on Suppose n + 1. i] denotes the character at position i in i \u2264 n - 1. For i \u2264 j, i..j] denotes the substring of S starting with the character at position i and ending with the character at position j. For i > j, i..j] denotes the empty string. A substring of h, 0 \u2264 h \u2264 n, h = h..n - 1] denotes the h-th non-empty suffix of h in Suppose that 1 < ... <$r. This character order induces an order on all nonempty suffixes of n, specifying the lexicographic order of the n + 1 non-empty suffixes of The key to our method is to lexicographically sort the suffixes of n. For each h, 1 \u2264 h \u2264 n, lcp[h] is the length of the longest common prefix of r is the largest suffix in the lexicographic order, r. Hence we always have lcp[n] = 0. In the following, the combination of the suffix array and the lcp-table is called enhanced suffix array.The lcp-table lcp is an array of integers in the range 0 to k-mers. An interval [i..j], 0 \u2264 i <j \u2264 n, is an lcp-interval of lcp-value \u2113 ifThe notion of lcp-intervals, introduced in  is centri] < \u2113,1. lcp[h] \u2265 \u2113 for all h, i + 1 \u2264 h \u2264 j,2. lcp[h = 0 or lcp[h] = \u2113 for at least one h satisfying i + 1 \u2264 h \u2264 j,3. j = n or lcp[j + 1] < \u2113.4. i..j] of lcp-value \u2113. We say that an \u2113-interval [i..j] represents the substring i]..suf[i] + \u2113 - 1] of We will also use the shorthand \u2113-interval for an lcp-interval [i..i], 0 \u2264 i \u2264 n is a singleton interval. We say that a singleton interval [i..i] represents the suffix i]..n - 1] of m-interval [l..r] is said to be embedded in an \u2113-interval [i..j] if it is a subinterval of [i..j]  and m > \u2113. Note that we cannot have both i = l and r = j because m > \u2113. A singleton interval [l..l] is said to be embedded in an \u2113-interval [i..j], if i \u2264 l \u2264 j. If an interval [l..r] is embedded in [i..j], then [i..j] is the interval enclosing [l..r]. If [i..j] encloses [l..r] and there is no interval embedded in [i..j] that also encloses [l..r], then [l..r] is called a child interval of [i..j].An interval [n]. An important property of the lcp-interval tree is the fact that it implicitly stores the number of occurrences of all substrings of i..j] represents a string occurring j - i + 1 times in The parent-child relationship of the intervals constitutes a conceptual  tree which we call the lcp-interval tree of the suffix array. The leaves of the tree are the singleton intervals and the internal nodes of the tree are the lcp-intervals. In particular, the root of this tree is the 0-interval  as follows: Let d be the lcp-value of the parent node of [i..i]. Then i]..suf[i] + k - 1] is a k-mer occurring exactly once in \u2022 We process a singleton interval  + k \u2264 n,2. suf[i]+d..suf[i] + k - 1] does not contain the symbol N.3. k, max{d + 1, kmin} \u2264 k \u2264 min{k' - 1, kmax}, we increment \u03b4S, k[k' is the minimum value greater than d such that either suf[i] + k' = n or i] + k'] = N.As a consequence, for all i..j] different from [0..n] as follows: Let d be the lcp-value of the parent of [i..j]. Then j]..suf[j] + k - 1] is a k-mer occurring j - i + 1 times in d <k \u2264 \u2113. As a consequence, for all k, max{d + 1, kmin} \u2264 k \u2264 min{\u2113, kmax}, we increment \u03b4S, k[j - i + 1] by one.\u2022 We process an \u2113-interval  + d..suf[i] + k - 1] does not contain the symbol N. Rather than checking this condition character by character, we use information about ranges of Ns, preprocessed from the input sequence. That is, we store, in sorted order, the first position of each run of consecutive Ns in i, 0 \u2264 i \u2264 n - 1, i] \u2260 N, we can determine the smallest position i' > i such that i' = n or i'] = N using a binary search. Let q be the number of these runs. Then this method takes on the order of log2q time and requires extra space proportional to q.The algorithm to enumerate the lcp-intervals and singleton intervals, given the enhanced suffix array, runs in linear time, see  for detakmax occurring more than once as substrings in kmax, which results in a space requirement proportional to kmax.Due to property (4), the enhanced suffix array does not need to be represented in main memory. At any time, we only need to store two consecutive entries of table suf and lcp. Hence the space requirement is dominated by the stack needed for the bottom-up traversal of the  lcp-interval tree. Our specific application only requires to store nodes representing strings of length shorter than \u03c4 be the number of values i satisfying \u03b4S, k[i] > 0 for some k \u2208 . Then this data structure (e.g. hash table) requires space proportional to \u03c4 \u2264 n.Besides random access to the sequence, we also need random access to a data structure for accumulating the occurrence counts. Let n + kmax + q and the running time is proportional to n log2q. While the running time does not depend on kmax, the space requirement is linearly dependent on kmax. Since kmax and q are both much smaller than n, they can be neglected. As a result, we obtain an algorithm that is linear in running time and space requirement. In contrast, the hashing methods run in time proportional to n + 4k time and space proportional to 4k for some fixed value of k. That is, their running time and space requirement grows exponentially with k. As a consequence, these methods can only be applied for small values of k. These values are fixed, in contrast to our method which allows the computation for a range of values of k.The overall space requirement of the algorithm is proportional to k-mer counts  is dominated by the suffix array construction. This is especially true for the space requirement. To get an idea of whether our method can be applied to large sequence sets, we have to consider the space requirement of the suffix array constructions in more detail. The most space efficient suffix array construction requires (n\u2308log2 n\u2309)/8 bytes per input symbol plus 2n/8 bytes for representing the sequence. Given a 32-bit computer with 4 gigabytes (232 - 1 bytes) of main memory, n has to satisfy the inequality (2n + n\u2308log2 n\u2309)/8 \u2264 232 - 1. That is, the sequence length is limited to 1 gigabyte. Since we want to process considerably larger sequences, we developed a divide-and-conquer approach. This cuts the sequence The analysis above shows that the running time and space requirement of our algorithm for computing occ, pos) where pos is a position in the corresponding section and occ is the number of occurrences of pos..pos + k - 1] in this section. Thus each pair encodes a k-mer, and the pairs are stored on a file in the order they are delivered by the algorithm, namely in lexicographic order with respect to the k-mer. This property allows to combine the appropriate values in a merging process, which works as follows: Suppose we are given, say m, files storing the occurrence counts for the m sections of m - 1 pairwise merge-operations. The merging steps only require to have the entire sequence n/4 bytes suffices for representing the sequence. That is, the merging procedure allows to process sequences of length up to 16 gigabytes on a 32-bit computer.Processing each section by the algorithm described above results in occurrence counts for each section. More precisely, for each section we enumerate pairs  of a sequence v is determined relative to the k-mer content of S. Since we want to compute \u03bb for a fixed set S and many different sequences v, it makes sense to preprocess S into a k-mer frequency index S, occmin, occmax) storing all k-mers occurring between occmin and occmax times in S. Here occmin and occmax are user defined positive numbers. Constraining the indexed k-mers by user specified values occmin and occmax is relevant in applications where we are interested in k-mers occurring rarely  or frequently . Given the index S, occmin, occmax), we want to solve the following tasks:In contrast to the occurrence ratios, the average frequency w of length k, determine if it occurs in the index.(1) For each possible sequence k-mer occurring in the index, determine the number of its occurrences in the index.(2) For each k-mers. Instead of deriving occurrence ratios by incrementing some table \u03b4S, k, the same enumeration process can determine the k-mers w satisfying the constraint occmin \u2264 occ \u2264 occmax. If this is satisfied, the k-mer is stored on a file. As the k-mers are enumerated in lexicographic order, the index S, occmin, occmax) is simply a sequence of lexico-graphically ordered k-mers stored on a file. Whenever this is needed it can be mapped into main memory.In the previous section we have shown how to compute occurrence ratios by enumerating S, occmin, occmax), we directly store each k-mer together with the occurrence count, if this is required. As a k-mer is a string over an alphabet of size 4, it can be stored in k log2 4 = 2k bits. This, of course restricts the choice of k to small values. But since the optimal values for k are rather small  and (2) can be solved by a binary search over the index. Each step of the binary search requires to compare 2k bits. As these are represented by integers of the machine word size \u03c9, a single comparison takes time proportional to 2 r comparisons to determine if a k-mer occurs in the index. If it occurs, then the occurrence count can be determined in constant time by a single table lookup. Altogether, the search for a k-mer takes time proportional to 2 r. For example, on a 32-bit computer, it takes on the order of 2 log2 r steps to perform the binary search when k = 20.Let To put it together, our index differs in several aspects from other indexing approaches employed in sequence analysis . As a consequence, the querying times for our index are extremely short.\u2022 Second, we directly store each tallymer-occratio), for generating a k-mer index , and for searching a k-mer index . The software-distribution is complemented by a program to construct enhanced suffix arrays. The 32-bit version of this program can handle sequences of size about 150 million bp per gigabytes of main memory. For example, to handle the 0.45 \u00d7 WGS data set  in this amount of main memory, we have to split it into eight sections each of approximately 136 million bp. The program tallymer-occratio provides flexible options to specify the range of k-mer sizes considered and to tailor the values output. For example, one can specify that values are output as ratios instead of absolute counts. Comparison of k-mer frequencies of two sequence sets is not directly supported by the software, but can easily be done as follows: create an index of the first sequence set and query it with the second, and vice versa.The Tallymer software  providestallymer-search takes multiple fasta files as input. It generates all k-mers not containing any N from the given files, and matches them against the index in forward and/or reverse direction. Currently only exact matches are supported. An extension to degenerate matches would require a combination of index traversal and dynamic programming techniques, as, for example, implemented in Vmatch [The program n Vmatch  for the k-mer frequencies for large values of k, we have a wide latitude for selection of a k-mer size. Figure k-mer uniqueness ratio for the 0.45 \u00d7 WGS for k in the range 10 to 500. As k approaches 500, the curve reaches unity. The information content of the k-mer set increases at a very fast rate from k = 10 to k = 20. Beyond this point, increasing k does not significantly increase the number of unique k-mers, but does decrease the overall resolution of the k-mer set. The inflection point on this curve is likely to change for other genomes and other sources of survey sequence, but for our WGS reference, k = 20 is optimal.Because our method allows us to compute k-mer frequencies is premised on the availability of an unbiased sequence set reflecting the overall repeat character of the genome in question. To test whether the 0.45 \u00d7 WGS meets this criterion, we computed the corresponding 20-mer frequency index, i.e. S is the 0.45 \u00d7 WGS set and k = 20. It contains 456,445,768 different 20-mers. There are 1,041,350,089 positions at which a 20-mer occurs. We screened seven publicly available maize sequence sets  maize whole genome sequences, (B) maize repeats, and (c) maize gene enrichment sequences. The seven sequence sets are known to have differing degrees of repetitiveness and should therefore provide a means to verify our method. For example, we expect gene enriched sequence to be less repetitive than RepII sequences (DNA transposons), and RepII sequences to be less repetitive than RepI sequences (TEs).-57)). Though the \u03bb-distribution for RepII also appears to be bimodal, we were unable to find significantly different repeat populations among the DNA transposon derivatives and superfamilies.The results of this analysis are shown in Figure C0t method succeeds in concentrating unique sequence without much leakage of the highly repetitive content evident to some extent in the ESTs, and to a far greater extent in the methyl-filtered library. This difference observed between the High-C0t and methyl-filtered libraries was previously observed in [The three sequence sets delivered by gene enrichment methods shown in Figure erved in .i, in a BAC was masked if the logarithm of the absolute frequency of the 20-mer starting at position i achieves some threshold. Figure We used a previously published set of 100 maize BAC sequences that had been chosen at random to be representative of the whole genome . A positWe compared these results to masking based on the curated MIPS REcat repeat library. This library includes repeats from many sources including annotated TEs from the BACs used in this analysis. Thus application of this library can be regarded as a 'gold-standard' for detection of TEs within these BACs. Indeed, masking using the MIPS REcat library, resulted in a total repeat coverage of 80.8% . This exceeds the masking rate of 67% originally reported for this set , suggestIn contrast, 81% of the MIPS REcat-masked positions are also masked by our method. This was achieved at the absolute frequency threshold of 0.3 Figure . At the We next compared the two repeat detection methods for their ability to discriminate TEs at the level of predicted genes. The set of 100 BACs were annotated using FGENESH and resulting predictions were classified as presumptive genes or as TEs using a similarity-based search (see Section \"Methods\"). Of the 2504 predicted genes, 359 (14%) were screened out as showing no evidence of homology to NCBI GenPept peptides. Of the remainder, 1842 (86%) were classified as TE while the remaining 303 (14%) were classified as presumptive genes. For these latter two classes the percent of coding sequence masked was calculated based on either RepeatMasker data or on constituent 20-mer frequencies at various thresholds. For each method of masking, receiver operating characteristic (ROC) curves were used to define a threshold of masking that best discriminated TEs from presumptive genes. Area under the curve (AUC), sensitivity, and specificity were used to compare efficacies .k-mers depends on which absolute frequency threshold is used, we first optimized the threshold by comparing all ROC curves for absolute frequency thresholds between 0 and 4.0 at 0.1 increments. The threshold of 0.8 gave the maximum area under the curve (AUC), with a value of 0.961 . For masking using REcat the AUC was only slightly higher, 0.962 . Comparison of these two ROC curves, shown in Figure Because percent masking using k-mer frequencies as found within a low coverage whole genome shotgun sequence. Furthermore, the two methods showed a similar false-positive rate, each having specificity near 92%.Table While both RepeatMasker and our method masked the majority of RepI retroelements, some low copy TEs escaped masking under our method based on average frequencies. As shown in our analysis of the 100 pilot BACs, low-copy DNA transposons, may be annotated as such by curated repeat databases, but missed by the counting approach used here. In the context of directed sequence finishing, low-copy repeats are often as in need of characterization as protein coding genes. Leaving them unmasked in maize is actually in the best interests of the project. But the average frequency threshold must be chosen carefully: more permissive thresholds will lead to finishing TE-like elements, and more strict thresholds may mask high-copy gene families. To use this method optimally, a balance must be struck with respect to the genome in question, and the thresholds need to be adjusted according to the annotation requirements.k-mer frequencies. In another set of experiments, we analyzed a 453 kb portion of maize chromosome 8 (assembled in-house as described in Section \"Sequence data sets\") and display a portion of its annotation from position 67,000 to 165,000 in Figure ab initio gene predictions classified as either putative protein-coding genes (blue) or transposable elements (red). The Global k-mer Frequency (GKF) track visualizes the absolute frequency across the region. Frequencies in this histogram were generated by querying each overlapping 20-mer in a 5' to 3' direction against the WGS index. Note that some regions contain k-mers occurring on the order of 1000 times in the maize WGS set. In the GKF track, TE-like genes often correspond to regions of high absolute frequency, while genes similar to known proteins reside in regions of smaller absolute frequencies.The validated WGS index can be used to annotate any portion of the genome with respect to its component k-mer frequencies are computed with respect to the region itself, independent of the WGS index, a significantly different picture emerges. The Local k-mer Frequency (LKF) track represents a self-analysis: the frequencies of overlapping 20-mers in the query are determined relative to the 453 kb region alone. Even in a local context many TEs are present at high copy number . But the LKF highlights local features in a way GKF cannot. This region contains four locally duplicated genes related to Selenium-binding proteins. Figure If the scope of the experiment is narrowed, however, and the k-mer frequencies to annotate sequence with copy-number information, we have found that the frequency information contained therein are themselves biologically informative, illuminating cross species differences in repetitive content. For example, Figure \u03c1S, k, 100\u00b7\u03c1S, k, 100\u00b7\u03c1S, k, 100\u00b7\u03c1S, k, 100\u00b7\u03c1S, k  is the ratio of k-mers occurring between q and q' times in S. The multiple occurrence ratio q, q') is similarly defined, but takes the number of occurrences of a k-mer into account. See section \"Methods\" for details.Beyond employing ) Figure  and 100\u00b7) Figure , where kFor example, in the case of maize, there are 1,041,350,089 positions at which a 20 mer occurs. There are 456,445,768 different 20-mers of which 378,556,535 are found only once, while the most highly represented sequences exists 47,933 times.k-mers. Maize demonstrates the most substantial growth in repetitive content, a finding attributable to its known TE expansion [k-mer frequency method provides a novel way of quantifying this important evolutionary event.The multiple occurrence ratios represented in Figure xpansion -5. Thus,k-mer sizes greater than 50 base pairs impractical. However, genome assemblies obviously do not suffer from these read length restrictions. Currently, there are very few plant assemblies. Though a number of projects are underway, only four genomes have been published: arabidopsis [k-mer uniqueness ratio for these genomes, as a function of k. We tested k-mer sizes from k = 10 to k = 500. With k approaching 500, the uniqueness ratio converges to 1. More repetitive genomes such as rice and poplar converge at a much slower rate than arabidopsis.Read lengths in whole genome shotgun sequencing projects limit this sort of analysis. Since Sanger reads average around 700 base pairs in length, most repetitive elements will be truncated at the 5' and 3' ends, making experiments with bidopsis , rice [3bidopsis ,40, poplbidopsis , and grabidopsis . In Figuk-mer frequencies cannot be used to annotate repeats across species (data not shown) owing to divergent TE families. But within a species, our method seems to work across cultivars regardless of which subtype is considered. For maize, our standard 0.45 \u00d7 WGS sequence set is derived from B73, the cultivar currently being sequenced. Figure k-mers in these TEs have undergone little divergence.We performed a number of experiments demonstrating that k-mer frequencies allowing for annotating large repetitive plant genomes. As we have demonstrated, our method is useful as an alternative or supplementary form of repeat annotation in novel genomes. The novelty of genomes being sequenced is precisely the reason why this approach has value. By definition, new genomes lack comprehensive repeat libraries, and the construction of de novo libraries is often hampered by the paucity of sequence available at a project's outset. In the absence of such libraries, survey sequences in the form of Sanger WGS, 454 [k-mer frequency indices for use across multiple subtypes.We have described a method based on WGS, 454 , Solexa WGS, 454 , or SOLIWGS, 454  reads cak-mer frequency approach to be completely independent of any manual annotation, we apply a binary decision framework: given a numerical threshold, sequence is designated as either repeat or non-repeat. Though binary designations are sufficient for sequence masking, we believe that the k-mer frequencies (and measures we derive from it) are best used in combination with other methods designed for careful repeat annotation as demonstrated in the accompanying publication [In designing the lication .k-mers, and to retrieve their occurrence counts from the index. The algorithms are implemented in the Tallymer software. A distribution of the software and the Perl-scripts post processing the output is available from the Tallymer website [To apply our methods to large sequence sets, we have developed fast and memory efficient algorithms to compute occurrence ratios, to index  website .SK developed the algorithms and implemented the Tallymer software. AN analyzed sequence data sets with respect to Tallymer output. JS performed annotation of maize BACs, their visualization, and ROC analysis. DW conceived this study. All authors contributed to writing the article."}
+{"text": "Correction to: npj Digital Medicine 10.1038/s41746-018-0031-7, Published online: 27 June 2018\u03c72, two-sided, p\u2009>\u20090.05)\u201d. This has been changed to \u201cThe 18\u201324 year old are over-represented in the all user treatment population, while the 50\u201364 year old are underrepresented in both tracked and all user population, p-values were <0.05 for age groups and gender.\u201d This has been corrected in the HTML and PDF version of the Article.In the original version of the published Article, there was an error in the caption to Table 1 which stated \u201cNone of the differences are statistically significant ("}
+{"text": "Medicine, Tong Yu's degree appeared incorrectly and should be Master of Law (ML), not PhD.In the article, \u201cSocioeconomic status and self-rated health in China: Findings from a cross-sectional study\u201d,"}
+{"text": "Correction to:npj Digital Medicine 10.1038/s41746-019-0079-z, Published online 29 January 2019In the original version of the published Article, there was a sentence fragment prior to the last sentence under the subheading \u201cReproducibility and digital medicine\u201d which stated \u201cSome journals, such as PLOS ONE, have made an early\u201d. To improve clarity, the sentence fragment has been removed. This has been corrected in the HTML and PDF version of the Article."}
+{"text": "We prove among other things that every m-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly m-subharmonic, and has bounded m-Hessian measure.We study the geometry of  In this paper, we shall study the geometric properties of these domains. Let us now give a thorough background on the motivation behind this paper. It all starts with the following theorem:The geometry of the underlying space is usually essential when studying a given problem in analysis. The starting point of this paper is the model presented by Caffarelli et al.\u00a0 in 1985 Assume that regular at every boundary point strong barrier at every point weak barrier at every point exhaustion function that is negative and subharmonic, i.e., there exists a non-constant function Jensen boundary w.r.t. the Jensen measures generated by the cone of functions that are continuous on entclass1pt{minimaThe idea of a regular boundary point can be traced back to 1911 and 1912 with the works of Zaremba\u00a0\\documentJensen measure with barycenterw.r.t.Jensen boundary w.r.t. Let The Jensen boundary is another name for the Choquet boundary w.r.t. a given class of Jensen measures. For further information see e.g.,\u00a0, 48.There are many different spaces of Jensen measures introduced throughout the literature. Caution is advised.The most important tool in working with Jensen measures is the Edwards\u2019 duality theorem that origins from\u00a0. We onlyg be a real-valued lower semicontinuous function defined on (Edwards\u2019 Theorem). Let We end this section with a convergence result.n, let Assume that The Banach\u2013Alaoglu theorem says that the space of probability measures defined on m-hyperconvex domains , but itIn Example\u00a0m-subharmonic function if, and only if, k-hyperconvex, sincek-subharmonic exhaustion function. In particular, we get that for For a given integer 11.13 in\u00a0). FurtheWe shall need the following elementary lemma. For completeness we include a proof.Let For The aim of this section is to prove the following theorem, especially property (3).m-hyperconvex domains in m-hyperconvex in If m-hyperconvex in The domain m-subharmonic on The domain m-hyperconvex, then m-hyperconvex.If Assume that Part (1) For each m-hyperconvex domain m-hyperconvex in Part (2) This part is concluded by defining a negative exhaustion function byPart (3) The proof of this part is inspired by\u00a0[pired by\u00a0. First,  Theorem\u00a0 we have strictlym-subharmonic exhaustion function for m-subharmonic functions on defined M-test. To see that m-subharmonic, note that if m-subharmonic, we have that m-subharmonic on j.Next, we shall construct a continuous Part (4) The idea of the proof of this part is from\u00a0[m-hyperconvex. Let m-subharmonic exhaustion function for j, take a smooth function m-subharmonic for c such thatm-subharmonic function defined on m-subharmonic, and  is from\u00a0. By the A2.4. in\u00a0). Hence,m-hyperconvex domain, and To see that (1) holds, first note that it is clear that m-hyperconvex domain it can be proved as in part (3) of Theorem\u00a0Assume that B-regular and hyperconvex domains within the Caffarelli\u2013Nirenberg\u2013Spruck model. More precisely, in Theorem\u00a0In this section, we shall investigate the geometry of the corresponding notions of m-hyperconvex in the sense of Definition\u00a0m-subharmonic;m-subharmonic; andFor every Assume that The implications z that is m-subharmonic. Since there exists a constant  Theorem\u00a0, we knowm-hyperconvex, and that z, andm-hyperconvex.  Theorem , it folla 2.3 in , impliesBefore we can start with the proof of Theorem\u00a0m-hyperconvex domain in Let f to a continuous function on f. Since m-hyperconvex domain then by Theorem\u00a0j, we have thatAssume that  Theorem\u00a0 gives usm-hyperconvex, then we have a similar result as in Corollary f to If We end this section by proving Theorem\u00a0m-subharmonic;m-subharmonic, and such that Assume that f be a continuous function on z.m-subharmonic, and by the generalized Walsh theorem .g defined on a neighborhood of  Theorem\u00a0. \\documeAn immediate consequence of Theorem\u00a0Let z, and let z, that is m-subharmonic, and defined in some neighborhood of z, that is m-subharmonic:Let The purpose of this section is to prove the implication m-Hessian measure of u is defined byAssume that m-Hessian measure is well-defined for much more general functions than needed in this section. For further information see e.g.,\u00a0[The ee e.g.,\u00a0.m-hyperconvex domain in m-hyperconvex domain admits an exhaustion function that is smooth, and strictly m-subharmonic. Our method is that of approximation. Therefore, we first need to prove a suitable approximation theorem. Theorem\u00a0m. In connection with Theorem\u00a0m-subharmonic. Thereafter, they prove that approximation is possible. Whereas we prove that smooth approximation is always possible on an m-hyperconvex domain, i.e., there should only exist a negative exhaustion function. Thereafter, we prove the existence of a negative and smooth exhaustion function that is strictly m-subharmonic, and has bounded m-Hessian measure. We believe that Theorem\u00a0For a bounded  Cegrell\u00a0. If the m-hyperconvex domain in m-subharmonic function u defined on Assume that Before proving Theorem\u00a0u,\u00a0v be smooth m-subharmonic functions in m-subharmonic function Let Now to the proof of Theorem\u00a0m-subharmonic.By Theorem\u00a0We want to prove that for any Step 1. Fix a constant m-subharmonic functions decreasing to bu. Out of this sequence pick one function, h is the unique harmonic function on h can be obtain as (see\u00a0[ as (see\u00a0)\\documen Theorem\u00a0, we haveStep 2. Let We start by taking m-subharmonic functions decreasing to W such thatW and Step 1, it follows that Take an open set Step 3. Now if proof of .u is a negative m-subharmonic function defined on To finish the proof of this theorem, assume that 1.7.1 in\u00a0 implies  Then by\u00a0, there eWe shall end this paper by proving the implication m-hyperconvex domain in m-subharmonic, and has bounded m-Hessian measure.Assume that m-subharmonic, and belongs to n, we arrive atm-subharmonic. Let Theorem"}
+{"text": "In the original version of the article \u201cA network-based conditional genetic association analysis of the human metabolome\u201d by Y.A. Tsepilov et al. , there w"}
+{"text": "This research proposes the first one-out-of-two quantum oblivious transfer (QOT) scheme that does not have a two-level structure and is not subject to Lo\u2019s no-go theorem. Instead, the proposed scheme is a simple and efficient approach based on nonorthogonal states. The nonorthogonality causes one of a pair of messages to be unable to be measured to achieve the irreversible goal of discarding a message, resulting in a one-out-of-two selection effect. The proposed QOT protocol is therefore built directly on quantum resources rather than on a two-level structure in which two classical keys must first be created using quantum resources  and then a one-out-of-two protocol is built from there. Furthermore, the proposed protocol allows Alice and Bob to test each other\u2019s loyalty by comparing measurement results. In addition, the relationship with the no-go theorem is discussed in detail; this relationship is often overlooked in other studies. A security analysis demonstrates that the proposed protocol is secure against both external and internal attacks. In addition, an efficiency analysis shows that the proposed protocol is more efficient than other, two-level-structured protocols. In the all-or-nothing OT protocol, a sender Alice wants to send a secret message, m\u2009\u2208\u2009{0, 1}, to a receiver Bob who has only a 50% probability of receiving m. He will either learn the message m with 100% reliability or learn nothing about m. At the end of all-or-nothing OT, Alice remains oblivious as to whether Bob received the message m. Following the proposal of this protocol, Even et al.2 presented one-out-of-two OT (or it can be abbreviated as 1\u20132 OT), in which Alice transfers two messages, m0 and m1, to Bob, and he can choose only one of them and will have no idea what the other message is. When the one-out-of-two OT protocol is complete, Alice learns nothing about which message Bob selected. In 1988, Cr\u00e9peau3 presented a method for building a one-out-of-two OT protocol by using p-all-or-nothing OT, in which the receiver has a probability p of receiving the message m, called Cr\u00e9peau\u2019s reduction. The receiver builds two key sets to represent his choice, key0 and key1, one of which he learns with 100% certainty and the other of which he learns with 0% certainty. Based on Bob\u2019s choice j\u2009\u2208\u2009{0, 1}, he asks Alice to encrypt her messages m0 and m1 using keyj and mj under this two-level-structured method.Oblivious transfer (OT) is an important branch of cryptography with many useful and important applications, such as secure computation, bit commitment, remote coin-flipping, and digital contract signing, for which OT protocols are the cryptographic primitives. The two most commonly used OT protocols are the all-or-nothing protocol and the one-out-of-two protocol. All-or-nothing OT was first introduced by Rabin4. However, Shor showed that a quantum algorithm5 can be used to break the RSA cryptosystem in polynomial time, which means that such protocols may be unsafe against quantum algorithms. In 1984, Bennett and Brassard proposed the first quantum key distribution protocol6, called BB84, thereby initiating the study of quantum cryptography. Researchers later showed that BB84 is unconditionally secure10 both in theory and in implementation by achieving a one-time pad. The security of quantum cryptography is based on physical laws, unlike that of classical cryptography, which is based on mathematical complexity. This physical basis allows quantum cryptography to easily achieve many goals that were difficult or unthinkable in the past, including unconditional security.Classical OT protocols are almost all based on the RSA cryptosystem6, researchers have been designing quantum oblivious transfer (QOT) protocols using quantum properties. Cr\u00e9peau and Kilian11 proposed the first all-or-nothing QOT scheme in 1988, and Bennett et al.12 proposed the first one-out-of-two QOT scheme protected by a quantum error-correcting code in 1992. In 1994, Cr\u00e9peau13 presented a one-out-of-two QOT scheme based on quantum bit commitment (QBC), which guarantees security under the assumption that Bob cannot delay the quantum measurement. In 1995, Yao14 further proved that this protocol is secure against coherent measurement if QBC is secure. However, in 1997, Lo15 doubted that all one-sided two-party computations  but only one of the two parties is allowed to learn the result) may be insecure, including one-out-of-two QOT (the function f in one-out-of-two QOT is a selector). This was called Lo\u2019s no-go theorem, and because of the computational equivalent12 to two OTs, this theorem has caused extreme difficulties in the development of QOT research.Since the proposal of BB8416 presented an interesting communication method analogous to one-out-of-two QOT with a 50% probability of completing the communication. They17 then improved the security of their protocol against entangled pair attacks in 2003. Moreover, in 2006, He and Wang18 proposed a secure all-or-nothing QOT scheme using four entangled states, which, as a result, was no longer subject to Lo\u2019s no-go theorem15. Consequently, He claimed that Lo\u2019s no-go theorem15 did not truly cover all QOT conditions. Thereafter, He19 demonstrated that a one-out-of-two QOT scheme built on all-or-nothing QOT protocol using Cr\u00e9peau\u2019s reduction3 also is not subject to Lo\u2019s no-go theorem15. The key is that the receiver inputs his choice before the sender inputs her messages m0 and m1, causing the functions f of the one-out-of-two protocol and Lo\u2019s no-go theorem15 to be different.Recent studies have, however, proposed various methods of avoiding Lo\u2019s no-go theorem. In 2002, Shimizu and Imoto19, researchers have been designing new one-out-of-two QOT schemes19. In 2007, Wei Yang et al.20 presented a one-out-of-two QOT scheme using tripartite entangled states based on He\u2019s proof19 and also showed that this scheme is not covered by the cheating strategy of Lo\u2019s no-go theorem15. Li Yang21 presented an all-or-nothing QOT scheme using nonorthogonal states, similar to B9222, and used it as a basis for constructing a one-out-of-two QOT scheme in 2013. Subsequently, Yu-Guang Yang and his research team, as part of a research effort that began in 2014, have proposed several QOT protocols. They have been testing various schemes for building one-out-of-two QOT protocols using He\u2019s proof19. In 2014, they23 proposed all-or-nothing and one-out-of-two QOT protocols based on an untrusted third party. In 2015, they24 developed an all-or-nothing QOT protocol by analyzing the probability of the qubit state distribution, which led them to propose a method of testing the loyalty of the sender and then to build a one-out-of-two QOT protocol on this basis. They25 also designed a one-out-of-two QOT scheme with a two-level structure using BB846 and reduced it to B9222 for an all-or-nothing QOT scheme. In addition, they26 attempted to use Bell states to achieve the same effect as B9222 for one-out-of-two QOT. Furthermore, in 2017, they27 proposed a method of using any two nonorthogonal states by cooperatively measuring the qubit sequence and then built a one-out-of-n QOT scheme using this method.Following He\u2019s proof27 all have two-level structures, in which two classical keys are created using an all-or-nothing QOT protocol and then a one-out-of-two QOT protocol is built on top. The two-level structure is clearly inefficient, because many quantum resources are consumed for all-or-nothing QOT instead of being used to transfer the message. In addition, this structure reduces the elasticity and diversity of protocol design because such designs can only follow He\u2019s proof19 with minor revisions to the details of the all-or-nothing QOT scheme. In our opinion, He\u2019s proof19 not only revealed a different function f, which is not subject to Lo\u2019s no-go theorem15, based on a two-level structure but also provided a new approach in the sense that if any protocol can achieve the same effect as that of f in He\u2019s proof19, then it is also covered by He\u2019s proof19. In this work, the first one-out-of-two QOT protocol is proposed that is directly based only on the properties of quantum resources, namely, nonorthogonal states, rather than a two-level structure, while also being covered by He\u2019s proof19. The key to our protocol is that Bob\u2019s choice is made before Alice inputs her messages m0 and m1. The property of nonorthogonality ensures that one of the two messages cannot be measured and thus maintains obliviousness, thereby achieving the same effect as that of f in He\u2019s proof19. Therefore, our protocol is not only secure (and not subject to Lo\u2019s no-go theorem) but can achieve greater efficiency than protocols27 that are based on a two-level structure.However, these protocols15 and He\u2019s proof19, and its security and efficiency analyses. The preliminaries introduce the properties of quantum machines and define some notation. Then, the basic idea of the proposed protocol is introduced before the details of the protocol itself, which are described in the subsequent section. Moreover, the relationship among Lo\u2019s no-go theorem15, He\u2019s proof19 and the proposed protocol is discussed in the subsection titled \u201cResisting Lo\u2019s cheating strategy15\u201d. Finally, security and efficiency analyses are presented in the last two subsections.This section consists of six subsections, including the preliminaries, the basic idea of our protocol, the proposed protocol itself, its relationship with Lo\u2019s no-go theoremThis subsection introduces the basic definitions of concepts relevant to quantum machines, such as quantum bits, superposition, entanglement, gates, and operations, as well as some properties of quantum machines.The classical information carrier is called a \u201cbit\u201d. The quantum information carrier is called a \u201cquantum bit\u201d, or a \u201cqubit\u201d. A qubit collapses to certain states of a basis when it is measured. Two bases are commonly used: the Z-basis and the X-basis. The Z-basis is defined as \u03d5\u232a will collapse to |0\u232a and |1\u232a with probabilities of Superposition refers to the phenomenon that a qubit can simultaneously exist in both the |0\u232a and |1\u232a states; i.e., +\u232a is measured, as in Eq.\u00a012 or |11\u232a12, where the subscript indicates the qubit order. As a result, in this case, it is possible to immediately learn the states of two qubits when only one is measured. Einstein referred to this as \u201cspooky action at a distance\u201d.Another important property, entanglement is the phenomenon that qubits cannot exist singly. There are four common entangled states, called Bell states, as shown in Eq.\u00a0UU*\u2009=\u2009U*U\u2009=\u2009I) are regarded as gates in quantum computers. There are four common operations, represented by operators called Pauli matrices, which are denoted by {I, X, Y, Z}, as shown in Eq.\u00a0I and Z cannot be distinguished in the Z-basis, and Y and Z cannot be distinguished in the X-basis. A single qubit cannot be observed using all four operations, which means that some information is ignored; this is a key element of the proposed protocol. For example, after a Y gate, the state |0\u232a becomes \u2212|1\u232a; i.e., a result of |1\u232a will be obtained when the qubit is measured. This negative amplitude is called a global phase and cannot be measured. Another important gate is the Hadamard gate, as described in Eq.\u00a0H gate. The H gate can be used to convert between two different bases (the Z-basis and the X-basis). For example, after an H gate, the state |0\u232a (|+\u232a) H becomes |+\u232a (|0\u232a). Table\u00a0I, X, Y, Z}.Moreover, unitary operations , he learns m0 unambiguously , M is the number of channel checking qubits, and K is the number of loyalty testing qubits, then the total length of the QOT sequence is N\u2009+\u2009M\u2009+\u20092K. Bob randomly prepares M qubits from {|0\u232a, |1\u232a, |+\u232a, |\u2212\u232a} (each qubit is independent) and inserts them into his sequence. Subsequently, he also inserts his N and 2K candidate choice intentions  into his sequence and then sends the sequence to Alice. Let us give a simple example to describe the proposed one-out-of-two QOT protocol without channel checking, suppose that Bob prepares two qubits in |0+\u232a12 (N) to represent his choices and an additional two qubits in |0+\u232a34 (2K) for loyalty testing. He then sends these four qubits to Alice.Step 2. Once she receives the sequence from Bob, Alice first checks the channel for an eavesdropper (Eve) and then tests Bob\u2019s loyalty. First, she asks Bob to publish the bases and states that he has created. If the error rate is higher than a given threshold, then an Eve is present on the channel, and Alice and Bob abort their communication; otherwise, Alice goes on to test Bob\u2019s loyalty. She discards the qubits for channel checking and then randomly selects several positions and requests that Bob publish his bases. If different results, i.e., \u2209\u2009{|0\u232a, |+\u232a}, are measured and the error rate is higher than the given error rate, then Bob is considered dishonest, and she aborts this communication; otherwise, she proceeds to the next step. Following the above example, once Alice receives the ordered sequence |0+0+\u232a1234, she randomly chooses a qubit for loyalty testing. Suppose that Alice\u2019s random choice is qubit 4; then, she asks Bob to publish the basis of qubit 4, measures it, and compares the published and measured results. If the error rate is higher than the threshold, then Bob is considered as dishonest; after that, qubit 4 is discarded.Step 3. Since the loyalty test may disturb the order of Bob\u2019s choice intentions, Bob must ask Alice to reorder the qubits. It is for this purpose that 2K additional qubits are initially provided to prevent vacancies in the list of choice intentions. In this step, the sequence after reordering represents Bob\u2019s real choices. Following the above example, after the loyalty test, Bob asks Alice to reorder the remaining qubits in the order 21, and the states become |+0\u232a21, with qubit 3 discarded. The resulting state |+0\u232a21 represents Bob\u2019s choices, j1 and j0, respectively.Step 4. Alice now inputs her secret messages m0 and m1 through the I, X, Y and Z operations, corresponding to the combinations \u201c00\u201d, \u201c10\u201d, \u201c11\u201d and \u201c01\u201d, respectively. Following the above example, Alice performs Z and X in accordance with her messages \u201c0112\u201d and \u201c1034\u201d, where the subscripts indicate Alice\u2019s classical bit order, on qubits 2 and 1, respectively. This converts the state |+0\u232a21 into |\u22121\u232a21.Step 5. Alice then randomly inserts decoy qubits from {|0\u232a, |1\u232a, |+\u232a, |\u2212\u232a} into the sequence for channel checking and sends the sequence to Bob.Step 6. When Bob receives the sequence from Alice, he asks Alice to publish the positions and states of the decoy qubits. If the error rate is higher than the channel error rate, they abort this communication and return to step 1. Otherwise, Bob learns the contents of the classical messages by measuring the qubits with the bases he prepared. Following the above example, Bob performs X- and Z-basis measurements to learn the second and first classical messages, \u201c1\u201d and \u201c1\u201d , respectively.Step 7. At the end of this protocol, where Bob has to test Alice\u2019s loyalty to prevent Alice from cheating, she can learn Bob\u2019s choice with the probability 25%, or 29.3% by POVM. Bob chooses some random positions and asks Alice to publish her operations. Bob performs the operations according to Alice\u2019s announcement, in order to recover those qubits into {|0\u232a, |+\u232a}. If the error rate of loyalty testing is higher than the threshold, then Alice is considered as dishonest. Following the above example, Bob asks Alice to publish operation (X), which performs on qubit 1; then, Bob performs X on qubit 1 to recover the state into |0\u232a.15 provides a cheating strategy for learning all messages in a one-sided two-party secure computation, which doubts that one-out-of-two QOT is insecure. The key to Lo\u2019s cheating strategy15 is requirement (A-i), namely, that \u201cBob learns f, j) unambiguously\u201d  represents a pair of messages in a one-out-of-two QOT scenario), which leads to a probability of 100% that the selected state will collapse. In addition, the result is obtained after reversible operations. As a result, choices can be made repeatedly to learn all messages, as shown in Eq.\u00a0G and |\u03d5\u232a represent two different selected operations, any unitary operation for inputting two messages and any quantum state, respectively. Therefore, once Bob learns the content of a message, he can recover the state G\u2009\u00d7\u2009|\u03d5\u232a, which is the state after Alice\u2019s input, by applying the selected operation k\u2009\u2208\u2009{|0\u232a, |1\u232a}. In this way, Bob can change his choice and learn the contents of all messages by repeating the above process.Lo\u2019s no-go theorem15. Obviously, definition B is a special case of definition A. Definition B describes the case in which Alice inputs her messages first and then Bob inputs his choices. The important point here is that if Bob inputs his choices first and Alice subsequently input her messages, as in definition C (the proposed protocol), this scenario is not equivalent to the function considered in Lo\u2019s proof15. This is because the function becomes f, j) when Bob inputs his choices first, and f, j1) is meaningless with respect to f, j). Therefore, Bob cannot change i from i to i without Alice\u2019s help. Following from the above relation, in the proposed protocol (definition C), the result after Bob\u2019s and Alice\u2019s actions can be expressed asDefinition B corresponds to the one-out-of-two QOT scenario covered by Lo\u2019s proofG\u2009\u2208\u2009{I, X, Y, Z}. Eq.\u00a0G. Therefore, Bob cannot perform Lo\u2019s cheating strategy15. As a result, Bob cannot reverse the effects of his inputs without Alice\u2019s help. The condition of Equation\u00a0f, j) is similar to that of He\u2019s proof30. This proof shows that the order of input of the choices and messages may change the function f, which means that this protocol is not subject to Lo\u2019s no-go theorem. In addition, He30 has extended the concept of his proof19 to the general case; if Alice and Bob interact with each other and Bob cannot eliminate the effects of his operations independently, then the interaction is covered by He\u2019s proof19 and resists Lo\u2019s cheating strategy15.Definition A: ideal one-sided two-party secure computation(A-i) Bob learns f unambiguously.(A-ii) Alice learns nothing about j and f.(A-iii) Bob learns nothing about i more than what logically follows from the values of j and f.Definition B: one-out-of-two OT (Lo\u2019s no-go theorem15)(B-i) Alice inputs i, which is a pair of messages .(B-ii) Bob inputs j\u2009=\u20090 or 1.(B-iii) At the end of the protocol, Bob learns the content of message mj but not of the other message f\u2009=\u2009m0 and f\u2009=\u2009m1.(B-iv) Alice does not know which mj Bob received.Definition C: the proposed protocol(C-i) Bob inputs j\u2009=\u20090 or 1 to change the qubit state to {|0\u232a, |+\u232a} (Z- or X-basis) in accordance with his choice intention.(C-ii) Alice inputs her messages m0 and m1 using {I, X, Y, Z}.(C-iii) Bob learns the content of either m0 or m1 using the basis (Z- or X-basis) he prepared.Here, Two security conditions are considered in this study: security against external and internal attacks. External attacks involve an eavesdropper, Eve, attempting to steal messages without being detected. Internal attacks involve either Alice or Bob attempting to steal the other\u2019s secret information; i.e., Alice wants to learn Bob\u2019s choices, or Bob wants to learn the contents of both of Alice\u2019s messages.31, Eve will be able to illicitly eavesdrop on their messages. In the proposed protocol, several single qubits \u2208\u2009{|0\u232a, |1\u232a, |+\u232a, |\u2212\u232a} are randomly inserted into the transmitted sequence as decoy qubits for channel checking, as described in steps 1 and 5 of the protocol. The positions and states of these qubits are then published and measured to check whether an Eve is present. If the measured results obtained with the same bases are different and the error rate is higher than the channel error rate, then an Eve is present. Two common external attack strategies are the intercept-and-resend attack and the entangling attack. They are discussed below.Alice and Bob must ensure that the communication channel between them is secure, because without channel checking or reduced frequency6, each qubit has a probability of M. As a result, the security level can be assessed based on the detection rate by legal agents, \u03be1, as expressed in Eq.\u00a0Eve intercepts all qubits during transmission when the sender sends the qubit sequence to the receiver, measures them to obtain the message contents, and then resends those qubits to the receiver. This action should disturb the states of the qubits, including the decoy qubits, because Eve does not know which bases have been prepared by Alice and Bob. According to the detection rate of BB84E\u232a, and performs a unitary operation Ue on the intercepted qubit to entangle it with her qubit |E\u232a during transmission. The unitary operation Ue is defined as shown in Eq.\u00a0e00\u232a, |e01\u232a, |e10\u232a, and |e11\u232a are four states determined by the unitary operation Ue, Ue must satisfy a\u2009=\u2009d\u2009=\u20091, b\u2009=\u2009c\u2009=\u20090, and |e00\u232a\u2009=\u2009|e11\u232a, and as a result, the proposed protocol ensures that no information can be obtained in this way.Eve may instead use a different method that does not disturb the qubit states, namely, the entangling attack. In this attack, she intercepts the transmitted sequence, prepares an ancillary qubit |Internal attacks involve the legal agents Alice and Bob attempting to steal each other\u2019s secret information; i.e., Alice wants to learn Bob\u2019s choices, or Bob wants to learn the contents of all messages sent by Alice. Therefore, two conditions must be discussed, namely, Alice\u2019s and Bob\u2019s cheating strategies.I, X, Y, Z, H} etc., and she has 25% or 29.3% chance to learn Bob\u2019s choices; however, this kind of attack can be always detected in our protocol. The second condition is that Alice has the ability of entanglement. In this condition, Alice has the ability to perform two or more qubit gates, which leads to diverse attacks. However, Bob is also required to have the ability of entanglement to resist attacks from Alice, and a dishonest Alice will be detected by the discussion below.There are two conditions to be discussed. The first condition is that Alice has no ability of entanglement. In this condition, Alice only has the ability to perform a single qubit gate such as {22, because a measurement in the incorrect basis can yield incorrect measurement results that nevertheless help Alice to determine Bob\u2019s initial state. For example, if Bob sends the state 0 to Alice, she has a probability of E1, E2, I\u2009\u2212\u2009E1\u2009\u2212\u2009E2} on Bob\u2019s qubit, whereA dishonest Alice can learn 25% of Bob\u2019s choices, as in B92Then, she can unambiguously distinguish states {|0\u232a, |+\u232a} with probability\u03be2 can be decided by the user through the number of qubit D for loyalty testing. Therefore, Bob can detect that Alice is cheating. If Alice does not use POVM, the total detection rate is In other word, the remaining 70.7% of Bob\u2019s choices will be unknown, which means that Alice should randomly create several state \u2208\u2009{|0\u232a, |1\u232a, |+\u232a, |\u2212\u232a} to send to Bob. However, she cannot know Bob\u2019s final measurement results, as he does not publish any information about the bases. In other words, for each bit, he will be unable to correctly decrypt with a probability of I, Z} to escape this testing, and there are two branches: 1. Bob uses Z-basis as his choice; in this case, Alice can always escape the testing; 2. Bob uses X-basis as his choice; in this case, Bob has a 50% to get |+\u232a or |\u2212\u232a. When he gets |+\u232a, the operation Z cannot restore the state |+\u232a to |+\u232a. Otherwise, when he gets |\u2212\u232a, operation I cannot restore the state |\u2212\u232a to |+\u232a. Therefore, Bob always has a probability to detect Alice\u2019s dishonesty.For a simple example regarding the detection rate with a remaining qubit, which Alice randomly prepared, Alice prepares a qubit in state |0\u232a and guesses Bob\u2019s choice. In this case, she can only publish operation {+\u232aAB to perform a teleportation attack. In this way, she can pass Alice\u2019s loyalty testing, and then, learn Bob\u2019s choices with 25% or 29.3% chance without being detected. For a simple example to explain the teleportation attack, in step 3, the qubit from Bob after Bob\u2019s loyalty testing is called |\u03c6\u232aC. In step 4, instead of inputting her secret message into qubit C, Alice creates a Bell state in B to Bob to replace qubit C, and holds qubit A. After that, Alice performs a Bell measurement , BM for short, on qubit C and A, and publishes one of four operations I, X, Y or Z as her secret message according to BM results |00\u232aCA, |01\u232aCA, |11\u232aCA and |10\u232aCA, respectively. Bob can then perform one of four operations I, Z, X or Y to recover state |0\u232aB or |+\u232aB according to a result that Alice published. As shown in Eqs\u00a0B or |+\u232aB, because the BM results |00\u232aCA, |10\u232aCA, |01\u232aCA and |11\u232aCA can always match operations I, Z, X and Y, respectively.A dishonest Alice can prepare Bell states in |\u03a6A1 to Alice. Under normal conditions, we can know that Alice will do honest behavior. After Alice performs an operation in {I, X, Y, Z} on qubit A1, the entangled state will be Eq.\u00a0A1 and B1 with one of two bases {IY, XZ} according to Alice\u2019s operations to check Alice\u2019s loyalty.However, without loss of generality, Bob should also have the same entanglement ability as Alice. He can prepare an entangled state in mentclasspt{minimaB to Bob for the teleportation attack. Alice will perform the BM on qubit A1 and A, which leads the entire system to be Eq.\u00a0\u03be3 is as given in Eq.\u00a0F is the number of detected entangled qubit pairs. Therefore, Alice and Bob can decide security level \u03be3, and whether they will continue the protocol according to the detection result.\u00a0In summary, if the dishonest Alice only has the ability to perform single-qubit operations, then follow this protocol Bob can always have a probability to detect dishonesty one. Moreover, if the dishonest Alice can prepare Bell states or perform teleportation attacks, Alice\u2019s cheating becomes more and more difficult because she has to have the technology to store the qubits received from Bob. However, such a long-term quantum storage technology is still a technical challenge and an open issue today. Even though when the long-term quantum storage technology can be built, the protocol still can intentionally delay the operation time between step 4 and step 7 to prevent these attacks.However, Alice may be dishonest and perform a teleportation attack. Alice creates an entangled state in +\u232a, as given in Eq.\u00a0K positions and asks Bob to publish the bases he prepared in step 2. If different measurement results are given, i.e., \u2209\u2009{|0\u232a, |+\u232a}, Bob is dishonest. The detection rate by legal agents, or the security level \u03be4, is as given in Eq.\u00a0A dishonest Bob can prepare entangled qubits of the form |\u03a625 based on Cr\u00e9peau\u2019s reduction3. The protocols of Wei Yang et al.20 and Yu-Guang Yang et al.27 are not considered because that of Wei Yang et al. may not work, whereas the first protocol of Yu-Guang Yang et al.23 involves an untrusted third party, and the second27 is a one-out-of-n QOT protocol for which the resource consumption for one-out-of-two QOT is similar to that of Li Yang\u2019s protocol21. The three protocols considered for comparison25 have two-level structures in which one-out-of-two OT is built on all-or-nothing QOT. However, the probability p of all-or-nothing QOT (where p is the probability of the unambiguous key) is not always 50%. Significant quantum resources are required to build two classical keys (one unambiguous and the other unknown) using all-or-nothing QOT for one-out-of-two OT. In addition, every transmission should include decoy qubits for channel checking. Some protocols may need many transmissions, and many decoy qubits, to complete all-or-nothing QOT. For fairness, the security level \u03be1 is ensured to be at least 99.9999% by using 50 decoy qubits for each transmission. Then, the most important indicators are the conversion efficiency between two OT protocols and the number of transmissions (which indirectly affects the number of decoy qubits). The total cost of each protocol, as calculated under the requirement that R message bits are received, is given in Table\u00a024 do not consider any loyalty testing, which means that the sender and receiver may not truly trust each other, whereas the loyalty testing of the third protocol24 requires the consumption of a large number of qubits, making the quantum cost difficult to calculate. Detailed descriptions of the protocols considered for comparison25 are given below.This section presents a performance comparison of the proposed protocol with three modern two-level-structured one-out-of-two QOT protocols21 uses the B9222 protocol as the all-or-nothing QOT protocol on which it is based. Therefore, it requires four qubits on average to obtain an unambiguous key and only one transmission. However, the cited study focused more on the bit-commitment protocol than on the OT protocol, with no further security analysis of the QOT protocol or strategies for detecting eavesdroppers. Therefore, no strategy was provided for loyalty testing between Alice and Bob. In addition, the number of decoy qubits is computed as described above because the original detection strategy of B9222 is less efficient. Therefore, the same detection strategy with decoy qubits is used. As a result, the total quantum cost is 4\u2009\u00d7\u2009R\u2009+\u200950.This protocol24 also requires at least four qubits on average to obtain an unambiguous key using its all-or-nothing QOT strategy, i.e., R\u2009+\u20092\u2009\u00d7\u200950.This protocol25 reduces BB846 to B9222. It uses the BB846 strategy and the publication of additional state information to allow Bob to generate unambiguous keys as in B9222. It also requires four qubits for the generation of an unambiguous key. In addition, it requires one transmission to complete all-or-nothing QOT. However, it does not include a loyalty testing method for the all-or-nothing QOT stage. Errors may be detected at the application level. The overall cost of the protocol is 4\u2009\u00d7\u2009R\u2009+\u200950.This protocol25, with a probability p of R\u2009+\u20092\u2009\u00d7\u200950.The proposed protocol is based directly on quantum resources and consumes one qubit for each received bit. The proposed protocol is more efficient than the others25; this is also shown in Fig.\u00a03, which requires a two-level structure.As seen from Table\u00a015. A simple and efficient one-out-of-two QOT protocol with single nonorthogonal qubits, in which one of the two messages is discarded automatically, has been successfully developed based on the most basic properties of quantum machines. Second, the proposed protocol can effectively prevent both external and internal attacks, as proven by a detailed security analysis. Regarding internal attacks, an important feature of the proposed protocol is that loyalty testing is applied to provide security against internal attacks by a dishonest Alice or Bob; the dishonest one can always be detected at the loyalty testing stages with safety parameters \u03be2, \u03be3 and \u03be4, respectively. Finally, the proposed protocol has a lower cost and is more efficient than many traditional protocols based on a two-level structure. In addition, as this protocol uses only a single qubit, it is easily implemented.In conclusion, there three important contributions of the proposed method. First, to the best of our knowledge, the proposed protocol is the first one-out-of-two QOT protocol to be designed directly based on quantum properties without relying on all-or-nothing QOT, and it has been proven to be secure and not subject to Lo\u2019s no-go theorem"}
+{"text": "Ron,sp) lateral double-diffused metal-oxide-semiconductor transistor (LDMOS) with enhanced dual-gate and partial P-buried layer is proposed and investigated in this paper. On-resistance analytical model for the proposed LDMOS is built to provide an in-depth insight into the relationship between the drift region resistance and the channel region resistance. N-buried layer is introduced under P-well to provide a low-resistance conduction path and reduce the resistance of the channel region significantly. Enhanced dual-gate structure is formed by N-buried layer while avoiding the vertical punch-through breakdown in off-state. Partial P-buried layer with optimized length is adopted under the N-drift region to extend vertical depletion region and relax the electric field peak in off-state, which enhances breakdown voltage (BV) with low drift region resistance. For the LDMOS with enhanced dual-gate and partial P-buried layer, the result shows that Ron,sp is 8.5\u00a0m\u03a9\u00b7mm2 while BV is 43\u2009V.An ultra-low specific on-resistance ( Ron,sp) and maximizing off-state breakdown voltage (BV) [Ron,sp vs. BV for LDMOS devices [Ron,sp and the contribution of the channel region cannot be ignored.With the increase of demand for more complex and faster logic function in analog power IC, it is significant to improve the performance of the lateral double-diffused metal-oxide-semiconductor transistor (LDMOS), specially minimizing specific on-resistance (age (BV) \u20139. Most  devices \u201320. In o devices . The depRon,sp and high BV.In this work, a novel ultra-low specific on-resistance LDMOS with enhanced dual-gate and partial P-buried layer is investigated. The physical models IMPACT.I, BGN, CONMOB, FLDMOB, SRH, and SRFMOB are used in numerical simulation. On-resistance analytical model is proposed to provide an in-depth insight into the relationship between the drift region resistance and the channel region resistance. Based on the model, N-buried layer and partial P-buried layer are optimized to achieve low Ron,sp and enhance BV, respectively. In the channel region, the enhanced dual-gate is formed by trench gate and highly doped N-buried layer. Compare to conventional dual-gate structure, N-buried layer significantly reduce the resistance of the channel region by provide a low on-resistance conduction path under P-well in the on-state. In the drift region, the partial P-buried layer with high doping concentration is introduced under the N-drift region to enhance BV while maintaining low Ron,sp. The partial P-buried layer helps to reduce the vertical electric field in the off-state without breaking charge balance in the drift region. The key size of the novel device is listed in Table\u00a0Figure\u00a0Rd) and the resistance of the channel region (Rc) in series. In the channel region, surface channel conduction path parallels the trench channel conduction path. Thus, Rc is equal to (Rchs\u2009+\u2009Racc)//(Rcht\u2009+\u2009Rnb), where Rchs, Racc, Rcht, and Rnb are the resistances of the surface-gate channel, the accumulation region, the trench gate channel, and the N-buried layer, respectively. Based on the proposed on-resistance model, the reduction of Rc would achieve by decreasing Rnb without affecting the other performances, because the other resistances are mainly determinate by the process technology, operation voltage, and threshold voltage. The Rd has been reduced by introducing P-buried layer under N-drift region to enhance the Reduce Surface-field (RESURF) effect in our previous work. In this work, the partial P-buried layer is adopted to improve the BV while maintaining the low Rd.Figure\u00a0Rc, the N-buried layer with high doping concentration is introduced under P-well. Figure\u00a0Rc as functions of the doping concentration of the N-buried layer (Nnb) with single-gate and dual-gate. It is indicated that the dual-gate structure helps to reduce Rc compared with the single-gate. When Nnb\u2009=\u2009Nd\u2009=\u20095.5\u2009\u00d7\u20091016\u2009cm\u22123, Rc is 110\u00a0m\u03a9. According to the on-resistance model, Rnb is the main contributor to Rc. And then, the Rnb is desired to decrease with the aim of smaller Rc. As shown in Fig.\u00a0Rc is reduced with Nnb increasing. When Nnb\u2009=\u20091.35\u2009\u00d7\u20091017\u2009cm\u22123, Rc is reduced to 85\u00a0m\u03a9. However, Fig.\u00a0Nnb would be limited by punch-through breakdown. Because of adding trench gate, Rc is decreased firstly by 34% with Nnb\u2009=\u2009Nd\u2009=\u20095.5\u2009\u00d7\u20091016\u2009cm\u22123. As Nnb increases, Rc continuously decreases. With optimized Nnb\u2009=\u20091.05\u2009\u00d7\u20091017\u2009cm\u22123, Rc is decreased by 45% at last. When Nnb\u2009>\u20091.05\u2009\u00d7\u20091017\u2009cm\u22123, punch-through breakdown will happen in P-well. The analytical result of Ron,sp shown in Fig.\u00a0Aiming at the reduction of Nnb with different doping concentration of P-well (Npwell). Nnb has an effect on not only the Rc, but also the BV. For a given Npwell, BV keeps unchanged at small Nnb, and then decreases with Nnb increasing. When Nnb increases to 1.2\u2009\u00d7\u20091017\u2009cm\u22123, BV starts to drop with Npwell\u2009=\u20092\u2009\u00d7\u20091017\u2009cm\u22123. The drop of BV is ascribed to punch-through breakdown in the P-well region as shown in Fig.\u00a0Npwell, the depletion mainly extends to the drift region, and the punch-through breakdown is avoided without degrading the BV. Although P-well with high doping concentration benefits to avoid the punch-through breakdown, it would enhance the threshold voltage. Thus, Npwell of 2\u2009\u00d7\u20091017\u2009cm\u22123 is chosen with consideration to threshold voltage and the trade-off between the BV and Ron,sp.Figure\u00a0Rd and high BV, partial P-buried layer is introduced under the N-drift region. Figure\u00a0Lpb with different Npb. For a given Npb, as \u0394Lpb increases, BV increases and then decreases slightly. When \u0394Lpb\u2009=\u20090.1\u2009\u03bcm, Npb\u2009=\u20091\u2009\u00d7\u20091017\u2009cm\u22123, BV reaches the maximum value 43\u2009V. The insert shows the equipotential contour profile with Npb\u2009=\u20091\u2009\u00d7\u20091017\u2009cm\u22123. It is indicated that the equipotential contour in the partial P-buried layer structure extends more to substrate with comparison to full P-buried layer. Figure\u00a0Rd.In order to achieve low Ron,sp as functions of the doping concentration of the P-buried (Npb) for different Nd. For a given Nd, BV has a maximum value with varied Npb, and the maximum of BV increases with the decrease of Nd. However, Ron,sp can be increased as the Nd decreasing. Due to BV required higher than 40\u2009V, the Nd\u2009=\u20095.5\u2009\u00d7\u20091016\u2009cm\u22123 and Npb\u2009=\u20091\u2009\u00d7\u20091017\u2009cm\u22123 are chosen. Figure\u00a0Ron,sp as functions of the thickness of the STI layer (Tsti). Tsti has strong impact on BV and Ron,sp, and it should be designed and optimized carefully as well as our previous work [Tsti\u2009<\u20090.3\u2009\u03bcm, the breakdown point under the edge of poly field plate has a high electric field peak. As Tsti increases, the electric field peak is relaxed, and then BV increases. For Tsti\u2009=\u20090.3\u2009\u03bcm, BV of 43\u2009V is obtained. For Tsti\u2009\u2265\u20090.3\u2009\u03bcm, the electric field peak under the edge of poly field plate is enough low, as a result, the breakdown point transfers to P/N junction under the drain side. As Tsti increases, BV increases and then saturates.Charge balance between N-drift and partial P-buried layer is required to achieve high BV. Figure\u00a0ous work . For TstRon,sp is 8.5\u00a0m\u03a9\u00b7mm2 while BV\u2009=\u200943\u2009V, which is reduced by about 37% compared with our previous work.Figure\u00a0Rc. Partial P-buried layer is introduced under the N-drift region to enhance BV with keeping charge balance. The fabrication process of the LDMOS in this work is compatible with the existing BCD technology reported in our previous work. The result shows that the Ron,sp of the proposed LDMOS is reduced by 37% at BV of 43\u2009V compared with previous work. With the semiconductor processing technology going to nanometer level, the Ron,sp can reduce further with channel length decrease.A novel ultra-low specific on-resistance LDMOS with enhanced dual-gate and partial P-buried layer is proposed and investigated by numerical simulation in this paper. N-buried layer with high doping concentration is utilized to achieve enhanced dual-gate with reducing"}
+{"text": "Nature Communications 10.1038/s41467-018-07613-z; published online 05 December 2018.Correction to: The original version of this Article contained an error in Fig.\u00a04a, in which the \u201c=\u201d sign of the equation was inadvertently replaced with a \u201c-\u201c sign. This has been corrected in the PDF and HTML versions of the Article."}
+{"text": "Scientific Reports 10.1038/s41598-017-08007-9, published online 09 August 2017Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cmycorrhizal\u201d was incorrectly given as \u201cmychorrizal\u201d. This has now been corrected in the PDF and HTML versions of the Article, as well as the Supplementary Information that accompanies the Article."}
+{"text": "Numerical results validate the efficiency of the proposed schemes by showing a received data-rate fairness among UEs and an improvement in the UE\u2019s minimum received data rate.Future-generation radio access networks (RAN) are projected to fulfill the diverse requirements of user equipment (UE) by adopting a heterogeneous network (HetNet) environment. Necessary integration of different radio access technologies (RAT), such as 2G, 3G, 4G, wireless local area network (WLAN), and visible light communication (VLC) is inevitable. Moreover, UEs equipped with diverse requirements will be capable of accessing some or all the RATs. The complex HetNet environment with diverse requirements of UEs will present many challenges. The HetNet is likely to suffer severely from load imbalance among the base stations (BSs) from inheriting the traditional user association scheme such as max-SINR /max-RSSI , unless some sophisticated schemes are invented. In this paper, a novel scheme is devised for a joint-user association for load balancing, where BSs are densely deployed and UEs typically have a certain degree of mobility. Unlike most of the present works, a dynamic network is considered where the position and channel condition of the UEs are not fixed. We develop two complex and distributed association schemes based on  The\u00a0traffic demand in wireless communication systems has surged over the past few years. This\u00a0trend will continue in the future because of the growing popularity and heavy usage of wireless devices . Accordiuser association, power control, and resource allocation that need to be addressed [To boost areal spectral efficiency, reuse of radio resources is indispensable. However, the deployment of more macro BSs, forming a dense homogeneous network, is an unattractive solution as the deployment costs, along with the operational and maintenance costs, are very high. An\u00a0alternative to this homogeneous deployment is to have a heterogeneous one, where many low-powered small cells are deployed within the coverage area of a macro BS. A HetNet cellular network consists of randomly located BSs forming a multi-tier cellular network. Here, each tier differs in the average transmitting power, data rate, and deployment density. The\u00a0HetNet provides big capacity, high performance, ease of operation, and fast deployment, but with the cost of additional revenue, interference, resource management, and backhaul management . HetNet ddressed . The\u00a0traddressed , used byddressed . This\u00a0isddressed , and\u00a0biaddressed  schemes.ddressed . The\u00a0UE ddressed , where tThe\u00a0definition of \u201cload\u201d in a cellular network changes according to the environment. The authors in Refs. ,17,19 coIn\u00a0this paper, we propose low-complexity online distributed algorithms for cell selection in a HetNet environment, while considering two types of load definitions. The\u00a0BSs and UEs are treated as bidders and objects, respectively, such as that in online combinatorial auctions. We present an analytical model to show the near-optimal performance of our proposed solutions.The\u00a0remainder of this paper is organized as follows. Recent surveys ,21 show In\u00a0the offline user association scheme, a static network environment is provided where the complete setup is assumed to be known previously. In\u00a0general, a throughput optimization problem is formulated for the user association problem. Authors in Refs. ,41,42,43probabilistic and d-choices-based user association schemes. D-choices-based distributed load-balancing algorithms have been successfully applied to various server selection and channel allocation problems [d number of servers uniformly at random and associates with that server, which has a minimum load. A solution to balls into non-uniform bins was investigated in Ref. [n is the number of bins and d is the number of choices for a ball. A more realistic environment was considered in Ref. [d-choices-based scheme has not been applied to the user association problem in a cellular network.The\u00a0low complexity and dynamic nature of the distributed algorithm is well-suited for the cell selection problem. In\u00a0this paper, we proposed two types of online distributed algorithms for load-balancing in a heterogeneous cellular network, such as problems , where a in Ref. , where a in Ref. ,where a K-tier HetNet, and denote the set of tiers as U arrives last. The\u00a0maximum capacity, as well as maximum transmission power varies from one tier to another. Each BS has a positive integer capacity, also termed the size of a BS. We denote j at tier k, where j \u2208 k \u2208 j at tier k, i, and BS j at tier k. We consider a  in Ref. ; hence,  in Ref. . The\u00a0avej of tier k. If the BS schedules for equal resources for each UE in an OFDMA-based MAC protocol [j at tier k. Note that if a scheme can evenly distribute UEs among the BSs, then the minimum data rate will also increase as the per-user resource sharing rate will be high.In\u00a0a conventional network, the UE will associate with that BS whose protocol ,19,27,39i depends on the total number of UEs attached to and sharing the same BS [We assume that equal time-sharing will be used to schedule the UE, in case a BS is associated with multiple UEs. Hence, the throughput of an UE  same BS ,19,39. WSimilarly, while considering the average data rate of a BS as Note that both Equations  and 5)  5) repreBefore the problem statement is formally defined, we highlight the trade-off problem between throughput and fairness. The authors in Ref.  presentein Refs. ,52 proviin Refs. .i obtains utility i is connected to the BS j of tier k and 0 otherwise. We formulate the user association problem for Q1):Q1 is an integer program, it is generally difficult to find the optimal solution. The\u00a0problem Q1 can easily be converted to a convex optimization problem by simply making the utility function as a logarithmic utility and relaxing the constraint in Equation  as follows:Taking a utility function perspective, we assume that UE ,j\u2208B,k\u2208Kxi,j,k\u2208{0Q2 maximizes the average UE throughput, which ensures fairness in the network. The\u00a0problem Q2 has same set of constraints as that of Q1.The\u00a0problem In\u00a0the following, we consider a static environment and implement a centralized solution, and later compare with our proposed schemes to show the novelty. j. ith UE. The\u00a0UE obtains the Algorithm 1 Centralized solution1:Assign UEs to the BSs which have 2:Find the BS with a \u2003\u20033:4:L,Find a BS which has a \u2003\u20035:ifthen6:\u2003\u20037:ifthen\u2003\u20038:\u2003\u2003\u2003\u2003Do not consider this base station in future processing9:\u2003\u2003\u2003\u2003Go to Row 210:end if\u2003\u200311:\u2003\u2003Go to Row 412:else13:\u2003\u200314:i whose A\u2003\u2003Select an UE 15:ifthen\u2003\u200316:\u2003\u2003\u2003\u200317:\u2003\u2003\u2003\u2003Go to Row 1418:end if\u2003\u200319:\u2003\u2003Assign the Selected UE to BS 20:end if21:Update the 22:Goto Row 2d-choices-based selection, which try to balance the load over the whole network.The\u00a0above-mentioned scheme works well in a static, idealistic environment where there is no mobility and the channel quality remains intact. A slight change in the j at tier k. Higher values of j. The\u00a0intuition behind this scheme is that higher i arrives at the system, it checks for the BSs in range and calculates the b be the set of BSs the UE can associate with. For each BS that satisfies the SINR constraint i calculates the following association parameter In\u00a0this probability scheme, the UE selects a BS in a probabilistic manner upon arrival at the network. Actually, the UE considers two parameters, i then calculates the probability of association. The\u00a0probability of association with a BS is given by:The\u00a0value of The\u00a0UE now has information regarding the probability of association with each BS. Equipped with this information, the UE then selects one BS in a probabilistic way. Note that the BS having higher Algorithm 2 Probability scheme1:i \u2208 j \u2208 k \u2208 Initialize 2:for each UE i in the network do3:\u2003\u20034:\u2003\u2003Calculate 5:i with BS j of tier k with probability \u2003\u2003Associate UE 6:end forEach UE executes the Algorithm 2 at their respective end. In\u00a0Step 1, all the UEs in the network initialize their association probability to 0. Cell selection begins at Step 2 and in Step 3, the UE collects the BS information, which satisfies the SINR threshold. These are the potential BSs the UE can attach to. As the BS broadcasts their load information periodically, the UE is able to calculate Equation , is diffd number of bins to associate with, and\u00a0the expected maximum load is given by Equation  load-balancing in different tiers, and (2) load-balancing in each BS in a particular tier. The\u00a0network traffic for different RATs must flow through the corresponding service gateway, so care must also be taken to balance the load in the service gateway level. We assumed that all BSs broadcasted their load information periodically. The\u00a0macro BS, having the highest coverage area, has a special task, in\u00a0that it accumulates all the load parameters of BSs of different tiers, adds them up tier-wise, and then broadcasts the load value. The\u00a0broadcast signal by macro BS will have the load value of all tiers in the\u00a0network.The d tiers uniformly at random, and then chooses a tier from the d number of tiers which has a minimum load. The\u00a0next step is to choose a BS from the already chosen tier. The\u00a0UE repeats the above procedure for selecting a BS from the chosen tier. The\u00a0UE chooses d number of BSs uniformly at random, and\u00a0selects a BS from the d number of BSs which has a minimum load. This\u00a0procedure ensures load balancing at two levels: (1) tier-level load-balancing, and (2) BS-level load-balancing. Note that tier-level load-balancing is required to shift the load from a heavily loaded tier to a lightly loaded tier. Algorithm 3, d-choices, depicts the above distributed d-choices scheme by considering The\u00a0UE performs the load-balancing task in two levels. Algorithm 3 Two-level d-choices scheme.1:ith UE | 2:for all UEs, ido3:\u2003\u2003Independently choose a set 4:\u2003\u20035:\u2003\u2003find 6:\u2003\u20037:\u2003\u2003Independently choose a set 8:\u2003\u20039:\u2003\u2003find 10:i with \u2003\u00a0\u00a0Associate UE 11:end for12:13:14:15:d-choices schemes in two levels. The UE begins its user association procedure by accumulating the BSs which satisfy the d-choices scheme. The same procedure is applied to choose a BS from the chosen tier in Steps 6\u20139. Then in Step 10, the UE associates with the chosen BS. As the two load parameters, Algorithm 3 executes the d-choices, we consider a hypothetical scenario where there are four tiers and each tier has 10 servers. 1000 UEs arrive at the system one by one to attach with a server. First, the UE randomly picks d-choices, average Jain\u2019s fairness index, and the total probes made by a UE are given in To evaluate the effect of different d chosen tiers and allocate the UE to the minimum loaded BS, then the scenario will be totally different. This strategy may not ensure a load-balancing scenario. Think of a situation where all the servers of a tier have an equal number of UEs, but the total UE number is less than another unbalanced tier. The balanced tier will never be selected, even though the total number of UEs are less than other tiers. The final outcome will be an unbalanced allocation; hence, this method is not desirable.Apart from selecting the tier with a minimum load, a new scheme could be considered for the evaluation. If we select the most unbalanced tier from the In this section, we give an analytic model of the performance for the online algorithms by considering mong UEs . The utiDefinition\u00a01.The UE utility function Lemma\u00a01.Proof.\u00a0Our proof is, in essence, similar to the proof given in Ref. . Here, wFor every For N = \u2205, we need to show that submodular and monotone.The function i\u2019s utility for BS j belongs to tier k is given as Now, we prove the fact that the UE utility function, Now, we establish the similarity between Equations 15) and (17). Equation ( and (17)The expression Equation  exhibitsEquation , we concTheorem\u00a01.Under the submodularity and monotonicity of Proof.\u00a0The submodularity and monotonocity of  in Ref. , we can C, where the time complexity for Algorithm 2 will then be of k, in the first level and a BS, j, from that tier in the second level. Both selections of the tier and BS are performed on the number of choices In this section, we compute the time complexity of the different proposed algorithms. The time complexity of Algorithm 2 depends on the number of UEs and BSs. Each UE calculates the D), where D is in kilometers. The path-loss model for pico and femto BS is taken as 37 + 30*logD), where D is in meters. We assume log-normal shadowing with a standard deviation d values in Algorithm 3, we restrict the choices to only two, as the probability for higher d decreases in a real environment [Here, we consider a three-tier HetNet environment consisting of macro, pico, and femto BSs. We develop the HetNet environment and run the simulation on the MATLAB platform. The BSs are uniformly and independently distributed in a 2000 \u00d7 2000 mironment . We perf(a) Cumulative distribution function (CDF) of spectrum efficiency(b) Normalized minimum user rate  R be the minimum data rate experienced by the UE(s) in the network. The value R will vary from one scheme to other. Let there be N schemes, so the normalized user rate, The minimum user rate is normalized with the optimum value. The optimum value is the maximum among the minimum user rate on each scheme. Let (c) Normalized sum user rate  S be the sum user rate of the network. The value S will vary from one scheme to other. The normalized sum user rate, The sum user rate of the network is normalized with the optimum value. The optimum value is the maximum among the sum user rate on each scheme. Let (d) Jain\u2019s fairness  max-SINR, we also consider the BS-centric algorithm (BS-centric), proposed in Ref. [max-SINR shows an uneven UE share. However, we can see that a considerable amount of UEs are being offloaded to Pico and Femto BSs in the case of Prob. scheme 1, Prob. scheme 2, and BS-centric. UEs associated with macro BS are being offloaded to both Pico and Femto BSs, which verifies the effectiveness of our proposed probability schemes. The d-choices schemes, on the other hand, focus on tier-wise balanced UE allocation. d-choices 1 and d-choices 2 schemes. A similar trend can be seen in non-uniform deployment. More UEs are offloaded to pico and femto BSs.Along with the traditional  in Ref. , as our Prob. scheme 1, Prob. scheme 2, d-choices 1, d-choices 2, and BS-centric schemes perform quite well at spectrum efficiency as compared to the traditional max-SINR scheme. When considering the BS-centric one, our proposed schemes give better service to the majority of UEs\u2014approximately 65%\u2014in terms of spectrum efficiency. In all the schemes (except the max-SINR) a majority of the UEs have a higher spectrum efficiency. Approximately 80% of UEs in all the schemes have higher spectrum efficiency, as compared to max-SINR. This is because the macro BS is highly loaded, and the total resource is divided among the UEs. This, in turn, lowers the spectrum efficiency of the associated UEs. For non-uniform UE deployment, although many UEs are placed around the lower-powered BSs, the outcome is similar to that of uniform deployment. All of our proposed schemes performed better in the mid-segment of the CDF graph, where the spectrum efficiency of the UEs are higher than that of max-SINR. Our proposed scheme, Prob. scheme 1, continuously performs better as compared to BS-centric for non-uniform deployment, as shown in One way to give a better experience to the UEs experiencing low spectrum efficiency is to take the resource from strong UEs and assign it to weak UEs. This task of taking the resource from strong UEs is done through load-balancing. max-SINR is about 0.30, while Prob. scheme 1 and Prob. scheme 2 show improved performance. Prob. scheme 1 shows a 70% improvement, while a similar trend can be seen for Prob. schemes 2. d-choices 1 and d-choices 2 show good results, and the minimum UE rate is higher, as compared to max-SINR. This gain in minimum user rate ensures that our scheme performs well for the cell edge UE, which mainly suffers with low data rate. All our proposed schemes perform better than BS-centric and max-SINR, while Prob. scheme 1 achieves the highest minimum user rate. A similar trend can be seen in non-uniform deployment, as shown in Prob. scheme 1 continues to perform well in non-uniform deployment. The max-SINR scheme, on the other hand, continues to perform poorly. The metric \u201cnormalized sum rate\u201d, denoted as max-SINR schemes, the UEs near to the BSs receive higher signal strength. As can be seen in max-SINR. On the other hand, for the non-uniform deployment, as shown in max-SINR performs slightly better. However, the max-SINR can achieve a higher sum user rate while ignoring the user fairness.Another performance metric for evaluation of the network performance is considering the normalized data rate of the UEs. The normalized minimum user rate, max-SINR in uniform deployment is 0.1, which is very low. Unlike max-SINR, our proposed schemes perform better. The fairness index nearly equals to 0.6 for all the proposed schemes. The same outcome can be observed in the non-uniform UE deployment scenario.Jain\u2019s fairness index of UEs\u2019 received data rate in a network shows the overall fairness. The fairness index becomes 1 when all UEs receive the same rate. d-choices load1 and d-choices load2 schemes. Each time the UE encounters a different load environment, it tries to balance the load of the network. For non-uniform UE deployment, the UEs are restricted to moving around the BS. d-choices schemes continue to show good results, and there is slight poor performance by the Prob. schemes, but it is better than max-SINR.User mobility is an unavoidable condition in a network. A network needs to perform well in a mobility environment. We considered Jain\u2019s fairness index for the UE share in different schemes to show our performance on the mobility. A network is said to be balanced in a mobility environment if the fairness index is high in different time instances. We monitored the network for ten time instances and noted the fairness. We adopted a random walk for the UEs. In The spatial distribution of network elements, such as BSs and UEs, plays an important role for the calculation of different network parameters. From an analytical and tractability point of view, many researchers have considered the Poisson point process (PPP), a clustered point process for BS and UE deployment. The authors in Ref.  assumed Prob. and d-choices schemes. In the K-tier HetNet, the user association, conventionally connected to the BS with maximum SINR, results in less association with pico and femtocells. This ultimately leads to load imbalance in the whole network. Unlike the max-SINR, in the Prob. scheme, UE selects the BS in a probabilistic manner upon arrival into the network by considering both SINR and the load of a BS. This technique eventually offloads the UEs toward small cells. Inspired by the \u201cballs and bins\u201d load-balancing problem and the power of two choices, we proposed the d-choices association scheme. The UE can choose d number of BSs and selects the BS which has the lightest load among the chosen BSs. Prob. scheme 2 showed better results in minimum user rate, while d-choices 2 showed good results for tier-wise load-balancing in both uniform and non-uniform kinds of UE deployment. Load-balancing naturally provides the possible inclusion of more numbers of UEs in the network, typically giving better fairness and improving UE experience. These distributed schemes show an impressive result in dynamic environments by reducing the signal overhead between UE and BS, increasing the throughput per UE and network load balance. Future work includes the optimization of small cells in k-tier HetNet, while considering both energy and spectral efficiency with high user mobility. In this paper, we considered a three-tier HetNet environment, proposing user association schemes and dynamic load-balancing through"}
+{"text": "Nature Communications 10.1038/s41467-019-11373-9, published online 31 July 2019.Correction to: The original version of this Article contained an error in Figure\u00a03. In panel b, the legend embedded in the panel was incorrect and indicated a solid grey line for w/w and a dotted black line for f/f. The correct legend is now provided and shows a dotted black line for w/w and a solid grey line for f/f. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "The lack of holes due to the high activation energy of acceptors greatly limits the performance and practical applicability of wide-bandgap semiconductor devices. Here, we study a novel effect which allows homojunction semiconductor devices, such as p-i-n diodes, to operate well above the limit imposed by doping of the p-type material. Using a rigorous numerical approach, we show that the density of injected holes can exceed the density of holes in the p-type injection layer by up to four orders of magnitude depending on the semiconductor material, dopant, and temperature, which gives the possibility to significantly overcome the doping problem. We present a clear physical explanation of this unexpected feature of wide-bandgap semiconductor p-i-n diodes and closely examine it in 4H-SiC, 3C-SiC, AlN, and ZnS structures. The predicted effect can be exploited to develop bright-light-emitting devices, especially electrically driven nonclassical light sources based on color centers in SiC, AlN, ZnO, and other wide-bandgap semiconductors.Electrically driven light sources are essential in a wide range of applications, from indication and display technologies to high-speed data communication and quantum information processing. Wide-bandgap semiconductors promise to advance solid-state lighting by delivering novel light sources. However, electrical pumping of these devices is still a challenging problem. Many wide-bandgap semiconductor materials, such as SiC, GaN, AlN, ZnS, and Ga The possibility to create a high density of nonequilibrium charge carriers in the active region of semiconductor optoelectronic devices is essential for a wide range of optoelectronic applications, from light emitting diodes (LEDs)  and injeThe traditional solution to this problem is to use the superinjection effect in double heterostructures ,18,19. AFor decades, it was believed that the superinjection effect was a unique feature of semiconductor heterostructures, while the maximum density of injected electrons and holes in homojunction structures could not exceed the free carrier densities in the n-type and p-type injection layers, respectively . HoweverkBT300K, which limits the density of holes in the p-type doped material to less than 1010 cm\u22123. However, in this work, we show that at high forward bias voltages, it is possible to significantly overcome this doping limit using the superinjection effect in homojunction p-i-n diodes and inject far more holes into the i-region of the p-i-n diode than the doping of the p-type layer provides.In this work, using a rigorous numerical approach, we investigate for the first time the possibility to observe and exploit the superinjection effect in homojunction diodes based on wide-bandgap semiconductor materials beyond diamond. We discuss in detail how to improve the efficiency of hole injection in SiC p-i-n diodes, which recently demonstrated great promise for quantum applications as single-photon sources ,24,25. INd = 1018 cm\u22123. The activation energy of donors is 0.06 eV [\u03b7n = 5%, which provides an electron density of neqn = 5.5 \u00d7 1017 cm\u22123. The p-type injection layer is doped with boron. The acceptor compensation ratio is also equal to \u03b7p = 5% [Na = 1018 cm\u22123 and their activation energy equals 0.32 eV [peqp = 4.3 \u00d7 1014 cm\u22123 in equilibrium. The electron and hole mobilities in the p-, i-, and n-type regions are calculated using the theory from [ 0.06 eV . The nit \u03b7p = 5% . The con 0.32 eV , which pory from . The sizory from . Both meJ = 6 A/cm2 (V > 2.8 V), the maximum densities of both electrons and holes in the i-region of the p-i-n diode are found near the i\u2013n junction, which is counterintuitive, since one expects to find the maximum density of electrons in the proximity of the i\u2013n junction and the maximum density of holes in the proximity of the p\u2013i junction, especially in the presence of recombination. Even more surprising is the fact that at a current density of 380 A/cm2, the hole density near the i\u2013n junction exceeds the hole density in the p-type injection layer by a factor of 44 , the band bending is very strong in the p-type region, i.e., the electric field E is high. At the same time, the bands are almost flat, i.e., E \u2248 0, in the n-type region. The reason for this is that the activation energy of acceptors is much higher than the activation energy of donors, and accordingly, the density of free carriers in the n-type region is three orders of magnitude higher than in the p-type region. Therefore, at high bias voltages, the drift hole transport dominates in the p-region, while the diffusion hole transport dominates in the n-region, which can be seen in Jp can be expressed as p is the hole density, E is the electric field, \u03bcp is the hole mobility, and q is the electron charge. On the contrary, in the n-type region near the i\u2013n junction,Dp is the hole diffusion coefficient, Lp is the hole diffusion length in the n-type layer, and d is the size of the i-region. The hole current at the p\u2013i junction and the hole current at the i\u2013n junction are connected to each other via the current continuity equation:R(z) is the net recombination rate. We can rewrite this equation as K represents the hole current reduction factor due to recombination in the i-region. If the recombination rate is low, K \u2248 1 and Jp|zd+0= \u2248 Jp|z= \u22120. Using Equations (1)\u2013(4), we obtain a relation connecting the hole densities at the p\u2013i and i\u2013n junctions:kB is the Boltzmann constant and T is the device temperature.To understand the observed superinjection of holes in the 4H-SiC p-i-n diode, let us look at K is not very high), the hole density p|zd+0=  in the n-region in the vicinity of the i\u2013n junction can exceed the hole density in the p-type layer. Moreover, the hole diffusion current at the i\u2013n junction is positive, i.e., the gradient of the hole density at z = d is negative. This means that the hole density in the i-region in the vicinity of the i\u2013n junction is even higher than p|zd+0= .Equation (5) shows that if the electric field in the p-type layer is strong and the recombination rate in the i-region is low or moderate  accurately predicts that at high forward bias voltages, the hole density at the i\u2013n interface increases above the hole density in the p-type injection layer. If the recombination in the i-region is strong, we should take into account the bias-dependent hole current reduction factor K. Nevertheless, we find that at a bias voltage of 4 V, p|z=d+0 = 7.0 \u00d7 1014 cm\u22123, which is 1.6 times higher than the hole density in the p-type injection layer. This value agrees with that obtained in the self-consistent simulations . The hjunction d,e, whicThe above explanation shows that the superinjection effect in the 4H-SiC p-i-n diode arises at high bias voltages due to the high contrast in the hole transport mechanisms of the p-type and n-type injection layers, which is naturally provided by the very high activation energy of acceptors. The potential well for holes near the i\u2013n junction, which is formed at high bias voltages and where holes are accumulated, is a consequence rather than a cause of the superinjection effect. The real reason for the superinjection effect is the requirement for the current continuity, which can be ensured only by an area with a high hole density between two regions (the p-type and n-type regions of the diode) with different (drift and diffusion) hole transport mechanisms. Therefore, the superinjection of holes can be observed in many wide-bandgap semiconductor p-i-n diodes that feature a similar asymmetry in the hole conduction mechanisms of the n-type and p-type layers. The key requirement for such an asymmetry is a low density of free carriers in the p-type layer and a high density of free carriers in the n-type layer.pmax increases with the injection current. At a current density of 15 kA/cm2, pmax reaches 2.1 \u00d7 1017 cm\u22123, which is 500 times higher than the hole density in the p-type injection layer. Although such an injection current seems to be too high for practical applications, a significant improvement of hole injection can be achieved at current densities as low as ~100 A/cm2 peqp=Na is the acceptor concentration, gA is the degeneracy factor of the acceptor level, and Nv is the effective density of states in the valence band. \u03b7p = 5%. At EA = 0, the density of holes in the p-type region peqp is as high 8.2 \u00d7 1017 cm\u22123. However, at EA = 0.23 eV, peqp decreases by a factor of 70, to 1.14 \u00d7 1016 cm\u22123. This activation energy corresponds to aluminum, which is the most shallow acceptor in 4H-SiC [EA = 0.5 eV, peqp is as low as 4.1 \u00d7 1011 cm\u22123, i.e., six orders of magnitude lower than the concentration of acceptors. However, the lower the density of holes in the p-type layer, the higher the asymmetry in the conduction properties of the p-type and n-type regions, and therefore the stronger the superinjection effect in the p-i-n diode.Here, n 4H-SiC . At EA =EA = 0.23 eV), the maximum density of injected holes can exceed the hole density in the p-type layer by more than tenfold  and (7) show that the densities of free carriers in the p-type and n-type injection layers greatly depend on the device temperature. Since the activation energy of acceptors is very high, even a small decrease in temperature significantly decreases the hole density. If the p-type layer of the diode is doped with aluminum, the density of holes decreases by a factor of 160 as the temperature drops from 300 K to 200 K a. In theActivation energies of acceptors and other material parameters in 6H-SiC are roughly the same as in 4H-SiC . AccordiThe activation energies of acceptors in 3C-SiC are very similar to those in 4H-SiC: 0.26 eV for Al  and 0.3414\u20131015 cm\u22123, the p-type doping problem is even more pronounced in such materials as gallium nitride, aluminum nitride, and zinc sulfide. If in the case of GaN , one cacceptors , the ext[10 cm\u22123 . Therefo[10 cm\u22123 ). The la10 cm\u22123. Therefore, it was proposed not to use p\u2013n and p-i-n structures and try to implement the hole injection mechanism in metal/insulator/semiconductor structures [9 cm\u22123 until the current density exceeds 0.02 A/cm2. Above 0.02 A/cm2, the maximum density of injected holes rapidly increases with the injection current and can reach 7.8 \u00d7 1012 cm\u22123, which is three orders of magnitude higher than the hole density in the p-type layer. Another example of a wide-bandgap semiconductor, which can hardly be used as an active layer of the double heterostructure, is zinc sulfide . At the ructures . Figure We have numerically demonstrated the superinjection of holes in homojunction p-i-n diodes based on different wide-bandgap semiconductors. This effect gives the possibility to create a high density of nonequilibrium holes in the i-region of the p-i-n diode at high forward bias voltages. The created density of holes exceeds the hole density in the p-type injection layer by more than two orders of magnitude, which can be exploited to improve the performance of light-emitting devices. The highest hole density is found near the i\u2013n junction, which contradicts the common belief about p-i-n diodes, since in the i-region, one could expect to find the highest hole density near the p\u2013i junction. However, we have provided a clear physical explanation for the observed effect, which is based on the asymmetry in the free carrier densities in the n-type and p-type layers. In SiC, GaN, AlN, ZnS, and many other wide-bandgap semiconductors, this asymmetry is naturally provided by the high activation energy of acceptors, which greatly limits the density of holes in the p-type layer of the diode. Hence, for optoelectronic devices, it is crucially important to overcome this doping limit, especially if it is not possible to use heterostructures. We have demonstrated that the superinjection of holes can be observed at high forward bias voltages. At the same time, the superinjection effect does not show itself at low and moderate injection currents (bias voltages). The higher the density of holes in the p-type layer, the higher the threshold current see b. This iEA, as it determines the hole density in the p-type region. We found that the superinjection of holes can hardly be detected at doping levels above 1017 cm\u22123 if EA is lower than ~0.15 eV. On the other hand, at high activation energies (EA \u2273 0.4 eV), it is strong even at relatively low injection currents. Assuming the density of electrons to be high in the n-type region of the p-i-n diode (neqn \u2273 1017 cm\u22123), the results of the numerical simulations and Equation (5) show that the higher the activation energy of acceptors, the stronger the effect. However, we should emphasize that the absolute value of the density of injected holes in a diode with a high activation energy of acceptors in the p-type layer  cannot exceed the absolute value of the density of injected holes in a diode with a low activation energy of acceptors in the p-type layer   see . TherefoTo directly measure the theoretically predicted strength of the superinjection effect, one should study two single color centers ,25,46,472 for the ZnS diode and more than ~1 kW/cm2 for other considered diodes. This should also be taken into account in practical applications.A disadvantage of the superinjection effect is that when a very high density of injected holes is achieved, the electron current is at least an order of magnitude higher than the hole current. Therefore, the energy efficiency of LEDs based on the superinjection effect in homojunction p-i-n diodes will be lower than that of those based on double heterostructures. A strong effect also requires high bias voltages (>6 V for 4H-SiC diodes and >30 V for AlN) that can create a high electric field in the p-type region of the diode (see Equation (5)). Accordingly, the heat generation rate is considerably high: more than 100 W/cmpeqp, but also provides it in the vicinity of the i\u2013n junction, where the density of injected electrons is maximal (see We should emphasize that the superinjection effect not only gives a unique possibility to create a density of nonequilibrium holes which is orders of magnitude higher than the doping limit imal see c,d. Thus"}
+{"text": "Most existing algorithms for modeling and analyzing molecular networks assume a static or time-invariant network topology. Such view, however, does not render the temporal evolution of the underlying biological process as molecular networks are typically \u201cre-wired\u201d over time in response to cellular development and environmental changes. In our previous work, we formulated the inference of time-varying or dynamic networks as a tracking problem, where the target state is the ensemble of edges in the network. We used the Kalman filter to track the network topology over time. Unfortunately, the output of the Kalman filter does not reflect known properties of molecular networks, such as sparsity.Drosophila Melanogaster.To address the problem of inferring sparse time-varying networks from a set of under-sampled measurements, we propose the Approximate Kernel RecONstruction (AKRON) Kalman filter. AKRON supersedes the Lasso regularization by starting from the Lasso-Kalman inferred network and judiciously searching the space for a sparser solution. We derive theoretical bounds for the optimality of AKRON. We evaluate our approach against the Lasso-Kalman filter on synthetic data. The results show that not only does AKRON-Kalman provide better reconstruction errors, but it is also better at identifying if edges exist within a network. Furthermore, we perform a real-world benchmark on the lifecycle  of the Drosophila melanogaster than the Lasso-Kalman filter. Finally, all of the code reported in this contribution will be publicly available.We show that the networks inferred by the AKRON-Kalman filter are sparse and can detect more known gene-to-gene interactions for the  Understanding the dynamical behavior of living cells from their complex genomic regulatory networks is a challenge posed in systems biology; yet it is one of critical importance . Gene expression data can be used to infer, or reverse-engineer, the underlying genomic network to analyze the interactions between the molecules. Unfortunately, most of the existing work on reverse-engineering genomic regulatory networks estimates one single static network from all available data, which is often collected during different cellular functions or developmental epochs. The idea that molecular networks are remodeled as a function of time and stage is well understood; this conclusion is supported by the developmental networks of sea urchin embryos . Throughn large p problem . In particular, the system is under-determined. However, exploiting the fact that molecular networks are sparse, one can use compressive sensing to find a solution. Compressive sensing is concerned with the optimal reconstruction of a sparse signal from an under-determined linear system  controls the tradeoff between the Kalman estimate and sparsity. An \u03b1 close to zero will result in a solution that is close to the Kalman estimate, but that may not be sparse. The opposite happens when \u03b1 is close 1, which will produce a sparser solution, but may be far from the Kalman estimate. This is achieved by minimizing the reconstruction error .l0-optimization problem, which finds the optimal sparsest solution in a linear under-determined system. Consider the following 0 is the l0-norm, which is defined as the support of the vector, p\u226bn and denote in the sequel s=p\u2212n. Without loss of generality, \u03a6 is assumed to be full-rank. Compressive sensing theory [\u03a6, the l1-norm solution is equivalent to the l0-norm solution. Unfortunately, it is impossible to check if the RIP condition is satisfied for a given matrix. Despite this strict condition, l1 has been routinely used to find a sparse solution in systems of the form  is an approximation to computationally complex Kernel RecONstruction (KRON) problems . KRON isl1 regularization in  starts off from the l1-regularized Kalman estimate in  find the indices with the (s+\u03b4) smallest magnitudes of the l1 solution, (ii) set exactly s of these indices to zero, (iii) re-solve the system \u03a6x=y. All the possible l1 approximation to make it closer to the l0-norm. The size of the neighborhood \u03b4 is tunable depending on the computational power available, and vary from 0 (l1-approximation) to n .Following this reasoning, AKRON finds a sparser solution by exploring ution of  are evalExample: To understand the AKRON algorithm and illustrate the importance of the \u03b4-neighborhoods, we present a simple numerical example. Consider the following randomly generated noiseless system as in  indices in \u0398 are such that x1\u2212x\u2217\u22252\u2264\u03b5. \u25a1Let l0-solution are bounded from below. We first need the following Lemma.The following proposition derives an upper bound for l0-solution x\u2217 and approximate l1-solution x1. Denote by \u0398 and x\u2217, respectively. Assume that \u2225x1\u2212x\u2217\u22252\u2264\u03b5. Let R be the number of indices 1)j|\u2264\u03b5. If \u03b4=R, then AKRON yields the optimal solution.Consider the system in  with thel0-solution, it is sufficient to choose s zeros in \u201ccorrect places\u201d, i.e., with indices in \u0398. Recall that AKRON sets s out of the smallest-magnitude (s+\u03b4) entries in x1 to zero. Therefore, AKRON will yield the optimal solution if out of these (s+\u03b4) smallest-magnitude entries, there are at least s entries from \u0398. But all entries from \u0398 have |(x1)j|\u2264\u03b5, for otherwise the assumption \u2225x1\u2212x\u2217\u22252\u2264\u03b5 would be violated. This means that only those entries from x1)j|\u2264\u03b5, could be chosen by AKRON, and there are only R of them. Hence \u03b4=R will yield the optimal l0-solution.To obtain the sparsest \u03b4 for optimality of AKRON, namely, if \u03b4=R, then we are guaranteed the optimal l0-solution. Since this condition is not necessary, we could reach optimality with \u03b4\u2264R. \u25a1Lemma 1 provides a sufficient condition on l0-solution x\u2217 and approximate l1-solution x1. Let x\u2217. Assume that the non-zero entries of x\u2217 are bounded from below, i.e., x1\u2212x\u2217\u22252\u2264\u03b5. If \u03b5<\u03b7, then l0-solution. In particular, if \u03b4=0 suffices.Consider the system in  with thex\u2217)j|\u2265\u03b7 for \u03b4\u2264R from Lemma 1. Thus, Since |: This algorithm is the output of the Kalman filter with the l1 projection applied to the state vector. The (S) indicates whether the smoother was implemented.l1-KF(S) to seed AKRON. It is also implemented with and without the smoother.AKRON-KF(S): This is the proposed approach using the output of Our experiments make use of the following algorithms for a sparse reconstruction of a time-varying network: TP), true negative (TN), false positive (FP) and false negative (FN) rates. These rates are summarized through accuracy (acc), sensitivity (sen), specificity (spe), and Matthew\u2019s correlation coefficient (mcc), which are defined below. Both of the above algorithms can reconstruct a network that represents the interactions between genes. We compute the true positive .Matthew\u2019s correlation coefficient provides a more balanced statistic for examining the overall trade-offs between the different rates  on data that we have complete control over. All results in this section are presented as the average over 25 monte carlo simulations. Averaging is performed because there could be a large degree of variation in the time-varying networks that are randomly generated.\u03b1 in . Given these results, we choose \u03b1=0.2 for the remainder of the experiments since this value provides a reasonable trade-off between the different statistics that were assessed. Figure\u00a0First, we evaluate the impact of \u03b1 in  on the en  benefit significantly from a larger value of \u03b4. For example, consider a network that is 9\u00d750\u00d74. \u03b4=1 provides a little reduction in error; however, increasing \u03b4 to 3, significantly reduces the error and increases the other statistics. Finally, we observe that smoothing improves the error of the system; however, we should note that this improvement comes at a computational cost.Second, we expand the synthetic experiments to evaluate the impact of \u03b1=0.2 based on the experiments in the previous section for l1-KF and AKRON-KF.The application of interest is the inference of the time-varying wing-muscle genomic network of the Drosophila Melanogaster (fruit fly). The Drosophila\u2019s microarray dataset originally consists of 4028 genes taken over 66 different time points . The datIn this application, we considered a list of 11 genes that are responsible for the wing muscle development, which has been considered by many researchers before \u20139, 20. Tl1-KF and AKRON-KF are shown in Figs.\u00a0l1-KF. AKRON-KF was able to find all the connections reported in Flybase:  appears in the embryonic, larval, and pupal stages,  appears in all four stages,  appears in the embryonic, larval, and pupal stages,  appears in the embryonic, larval, and pupal stages and  appears in the embryonic and larval stages. The other two connections appear through one medium gene  appears in the embryonic, pupal and adulthood phases through one additional gene and  appears through one or more additional genes only in the embryonic and larval phases.The networks reconstruction using the l1-KF and AKRON-KF with smoothers are shown in Figs.\u00a0l1-KF.The networks reconstruction using the l1-KF [l1-KF are the only algorithms able to recover all known interactions and specify the developmental stage where these interactions occur. Although the l1-KF also finds all reported interactions, the networks are denser (less sparse) than the AKRON-KF. With regard to the MDL results in Table\u00a0Table\u00a0l1-KF , SMURC [l1-KF  and Dynal1-KF  considerl1-KF , random l1-KF , and nonl1-KF ) assumedIn this work, we addressed the problem of inferring time-varying molecular networks as a tracking problem that can be solved using the Kalman filter. The major difficulty, however, is that there is not a sufficient number of observations at each time point, which makes the state-space model unobservable and the tracking senseless. Fortunately, molecular networks are known to be sparse because the dynamics of every gene are governed by only a small number of genes. By incorporating the sparsity condition, we show that the tracking problem becomes feasible.l1-KF). Our proposed approach leverages the AKRON algorithm to find a sparser solution that is more representative of the ground truth. The proposed tracker/smoother first computes the output of l1-KF; then explores growing neighborhoods of the l1-projection to look for sparser solutions, eventually reaching the optimal sparsest estimate. The size of these neighborhoods is a tunable parameter that depends on the computational power available. AKRON-KF was benchmarked on synthetic and real-world data against l1-KF. The results demonstrate that the proposed approach is better at recovering sparse time-varying networks than l1-KF. Not only was the reconstruction error of the proposed approach lower than l1-KF, but it was also better at detecting whether an edge exists in a network. AKRON-KF tracker was applied to infer the wing muscle gene regulatory network of the Drosophila Melanogaster during four developmental phases of its life cycle, and successfully identified all seven known interactions reported in Flybase. We should also note that our proposed approach will work for time-series networks that have more than four times steps and sparsity levelsWe presented the AKRON Kalman filter, which builds on our previous work on the Lasso-Kalman filter (Our future work includes applying the AKRON-KF to other types of data, particularly data related to different types of cancers to create a predictive network biomarker for clinical outcome. These ideas have applicability in translational clinical cancer research, basic cancer research, and in network-based drug discovery."}
+{"text": "Scientific Reports 10.1038/s41598-019-49900-9, published online 23 September 2019Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cgraphene\u201d was incorrectly given as \u201cgrapheme\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Subcellular localization prediction of protein is an important component of bioinformatics, which has great importance for drug design and other applications. A multitude of computational tools for proteins subcellular location have been developed in the recent decades, however, existing methods differ in the protein sequence representation techniques and classification algorithms adopted.In this paper, we firstly introduce two kinds of protein sequences encoding schemes: dipeptide information with space and Gapped k-mer information. Then, the Gapped k-mer calculation method which is based on quad-tree is also introduced.>From the prediction results, this method not only reduces the dimension, but also improves the prediction precision of protein subcellular localization. Proteins must be in a particular area in the cell for the participation in normal life activities . However, a multitude of protein sequences are increasingly identified into public biology databanks in post genome era, which results from the development of high-throughput technology. Therefore, it is indispensable to develop an automated method for fast and accurately annotating the subcellular attributes proteins. Predicting the subcellular locations of proteins can provide useful hints about the function of proteins, increase our understanding of the mechanisms of certain diseases, and ultimately help develop new drugs . Such, mApoptosis refers to the orderly death of genetically controlled cells in order to maintain internal environmental stability. Apoptosis is not only a special cell death type, but also has important biological significance and complex molecular biology mechanism , 7. Therk-peptide information. Compared to AAC, k-peptide information could be get a better predict results. But when k is larger, there exist dimension disaster, bad effects and some other problems. When doing the homologous sequence alignment, we will consider space penalty. By this, the best match between two sequences will be found. When extracting k-peptide information of sequences, we also take k-peptide information extraction with the space into consideration. The detailed description of the novel representation will be shown in the following section.The amino acid composition of protein sequence is the simplest sequence statistics. However, AAC only take the information of the whole protein sequences into consideration, and ignore the partial order information. Therefore, some scholars consider the dipeptide composition information, and someone also proposed a prediction method which is based on We first use two benchmark datasets constructed by the previous investigators. The ZD98 dataset, constructed by Zhou and Doctor , which hDipeptide information with the blank space Before we start to discuss peptide information with spaces, we first study the simple dipeptide information with spaces. The basic form is \u201cXDY\u201d, where X and Y are one of amino acids, D is a certain number of spaces. D is reduced to d, 0\u2009\u2264\u2009d\u2009\u2264\u2009l\u2009\u2212\u20092. The l is the length of protein sequence. It indicates the common dipeptide information when d\u2009=\u20090. Obviously, the d value will affect the results of prediction directly.k-mer and with spaces method was abbreviated as Gapped k-mer. In brief, with a space instead of some amino acids in dipeptide information method, then statistics all the different types of the peptides frequency.Peptide information extraction method without spaces was abbreviated as k-peptide information of 20 kinds of amino acids directly, then it will get 20k and 21k dimension vector for k-mer and Gapped k-mer, respectively. The dimension of feature vector is very high when k\u2009>\u20093. This case will result in time-consuming classification forecast operation and cause too much redundant information. So in order to reduce the dimension, we adopted the following two kinds of measures:k-peptide information, we only consider that kind of k-peptide, which was used in the training dataset, instead of all the different types of k-peptide. If we take all kinds of k-peptide, it will produce many zero vectors which have no effect on classification and cause the large dimension. Take the ZD98 dataset as test, if we consider all of the different 4-peptide when k\u2009=\u20094, k-mer will get 204 =160,000 dimension feature vector. If only statistical all 4-peptide of ZD98 datasets, it will produce 22,265-dimensional feature vector. Compared to the former, dimension was reduced by 86.09%. Though dimension is still very big, it reduces the dimension feature vector in a certain extent. What\u2019s more, the larger the k, the greater the proportion of reduced.In statistical The amino acid reduced. 20 kinds of amino acids in a certain way were reduced into a few classes, which can greatly reduce the feature vector dimensions. Here we use a reduced solution which was used by a lot of researchers. According to the physical and chemical properties of amino acids, 20 kinds of amino acid were reduced to classify. Table\u00a0If statistics k-mer and Gapped k-mer, the dimensions of the feature vector will be greatly reduced. Such as extracting k-mer characteristic information with k-mer in ZD98 dataset, the dimension has been reduced to 1071. The dimension was reduced by 99.33%.Through these two measures, when extracting characteristic information with k-mer was used to statistic k-frequency of protein sequence. For example, a protein sequence S can be represented as follows:n is the varity of k-peptide, vi is the frequency of i-th k-peptide in protein sequence S.The k-mer is statistics frequency with space k-peptide in the protein sequence S:m is the varity of k-peptide with g spaces, vi is the frequency of i-th k-peptide with g spaces in protein sequence S.The meaning of Gapped k-mer method. The number of spaces will be considered by Gapped 3-mer. If the number of spaces is 1, then the types of Gapped 3-mer are \u201c_BB, _BW, _WW, _WG, L_B, B_W, W_G, B_B, LB_, BB_, BW_, WW_\u201d. There are 12 kinds of types. Thus, a 12-dimension vector can be obtained by Gapped k-mer.Such as, a piece of protein sequence \u201cRIAVYYPG\u201d. According to the reduced solution of Table\u00a0k-mer can be thought of a special case for Gapped k-mer .Here we should note that the \u201cBBB\u201d and \u201cBBW\u201d of 3-mer statistics in the above example will be regarded as belonging to the same type \u201cBB_\u201d. t classes. So the dimension of feature vector is tk for k-mer method. However, the dimension of feature vector is k-mer method (the number of space is g). In general, when k is small, feature vector dimensions of Gapped k-mer is lower than k-mer.For a long enough protein sequence, according to some kind of reduced solution, the sequence can be reduced into k and spaces (g).In the classified prediction model of training and testing, we need to consider selection problem of parameters k-mer calculation method, which is based on multi-tree. For a scheme reducing amino acids into n classes, k-mer statistics of k peptide can be regarded as the kinds of statistics, i.e. a full depth k of n types leaf nodes in the tree. The first amino acid of n peptide is the head node, the second is the second straton node and so on. Finally the k layer is the leaf node. By comparing all k peptide in protein sequence to traverse the full n fork tree, and accumulating number of occurrences corresponding to a leaf node at the same time. Finally, the frequency of the leaf node corresponds to frequency of k-peptide. For Gapped k-mer, we need to consider the location of the space appears. If spaces appear in the m location of k peptide, the m layer of the original k peptide would be removed. Then merging the lower subtree, summing the frequency of the corresponding leaf node, and the frequency of gapped k-mer is obtained. It\u2019s similar for the multiple spaces. The following is a simple example.Here we first introduce a simple Gapped A short sequence which has been reduced, Seq\u2009=\u2009BBBWWBBWB. Through the statistics of binary tree 3 peptide, frequency is shown in Fig.\u00a0k-mer. If the second position is space, such as the 3-peptides frequency of \u201cX_Y\u201d type. At this time you only need to delete the second floor. Merging its lower subtree, as shown in the Fig.\u00a0Statistics the frequency of type 3-peptides with 1 space in Gapped The frequency of all three peptides, such as \u201cX_Y\u201d is obtained by this method. The frequency of \u201cB_B\u201d types of the peptides is 2.When using the same method to statistic form, such as \u201c_XY\u201d, the frequency of all 3 peptides, we just eliminating the head node, and merging the lower two subtrees.k-mer multi-tree. Then we can get all Gapped k-mer characteristic information vector, which is a simple statistical method.Through the tree structure, we only need to construct the k-classification problem, k*(k-1)/2 classifiers need to be constructed. Meanwhile, the radial basis function (RBF) was selected as the kernel function due to that it outperforms the other kinds of kernel functions. Then a simple grid search strategy over C and \u03b3 values based on 10-fold cross-validation for each dataset was selected, where C and \u03b3 were allowed to take the values only between 2\u22125 to 25.Among these classifier, SVM exhibits quite promising results . SupportTP, TN, FP and FN were the number of true positives, true negatives, false positives and false negatives, respectively; N is the total number of locative proteins and k is the class number.As is well known, independent dataset test, K-fold (such as five-fold or ten-fold) cross-validation (subsampling test), and jackknife test ) are often used to examine a predictor\u2019s effectiveness in practical application. Because considerable arbitrariness exists in the independent dataset test and K-fold cross-validation, and only the jackknife test is the least arbitrary that can always yield a unique result for a given benchmark dataset. Accordingly, the jackknife test is adopted here to examine the quality of the present predictor. For comprehensive evaluation, sensitivity (Sn), specificity (Sp) and Matthew\u2019s correlation coefficient (MCC), as well as the overall accuracy (OA) over the entire dataset are reported. These parameters were detailed in the following equations:d are shown in Fig.\u00a0We first use dipeptide information with the blank space in ZD98 and CL317 datasets. By the form of \u201cXDY\u201d, a 400-dimension vector was gotten, and then was put into SVM to predict. The predicted results with the change of the parameter d don\u2019t have very big effect on the prediction classification. In CL317 dataset, with the increasing of d, the prediction result tends to decline. It shows that dipeptide information with the blank space is not very good.From Fig.\u00a0k-mer, the dimension of eigenvectors and overall accuracy in different k value and g value are shown in Tables\u00a0By the extraction algorithm based on Gapped k-mer polypeptide Gapped has been reduced a lot, Note that a blank line in the table 0 is the results of k-mer feature method, the result show that Gapped k-mer are better than k-mer. Moreover, the number of space is better not too lager, best one or two spaces, which can be considered as in the protein evolution, mutations occur only in a few location of protein sequences, while the majority of other position without mutations, by matching with a few space, we can match the similarity of two protein sequences better, as above, \u201cBBB\u201d and \u201cBBW\u201d, they are regarded as the same type \u201cBB_\u201d in statistics with a space of 3-peptide information. Namely the space can matching any character, so in the process of practice, use the \u201cBB_\u201d to regular matching the original sequence, statistic the frequency. Conversely, \u201cBBW\u201d can belong to \u201cBB_\u201d, but to \u201c_BW\u201d and \u201cB_W\u201d, namely a variety of types of Gapped k-mer can matching to a k-peptide in the sequence, compared to the precise k-mer matching, the fuzzy matching can extract more similar information.From Tables\u00a0k-mer and Gapped k-mer on two data sets, respectively. The results show that with the k value increase, the accuracy of the two methods is generally improved, when extracting the same k-peptide information, the accuracy of Gapped k-mer is higher than k-mer in whole. The accuracy of Gapped k-mer reached a maximum value both in ZD98 and CL317. But accurate did not improve when k\u2009=\u20096, that meaning unable to extract more information at this time. So the effect is best when k\u2009=\u20095 in using the Gapped k-mer method to extract feature information.Figure\u00a0k-mer method, we compare it with other approaches that have been reported. In recent years, mostly through a variety of characteristics of method of information fusion in the protein subcellular location prediction research. In order to facilitate comparison, we also incorporate other information. At present, many scholars use GO information or GO information and it features information fusion used for protein subcellular localization prediction. Here, we fusing GO information with Gapped k-mer , SVM as classifier, compare with other method, the result in Table\u00a0To illustrate the effectiveness of Gapped -mer k\u2009=\u2009, g\u2009=\u20091, k-mer. Extracting reduced k-peptide component information with the space k-peptide representation. Then multi-tree calculating Gapped k-mer was also introduced. The new feature representation are used to construct a model and combined with dimension reduction to make the subcellular localization prediction of proteins. Meanwhile, we also discussed the effects of different parameters on the experimental results. The influence of parameters k and g on the experiment are discussed. Prediction accuracy got the highest when k\u2009=\u20095, g\u2009=\u20091. Compared to k-mer, our method not only reduces the dimension, but also improves the prediction precision, as shown in Table\u00a0In this paper, we proposed a new method to predict protein subcellular localization based on Gapped k-mer and GO information, no matter overall accuracy or absolute true overall accuracy, the achieved results by the proposed method are much higher than Li and Yu.Li and Yu  applied"}
+{"text": "Background: Healthcare-associated infections (HAIs) are a serious public health problem. They can be associated with morbidity and mortality and are responsible for the increase in patient hospitalization. Antimicrobial resistance among pathogens causing HAI has increased at alarming levels. In this paper, a robust method for analyzing genome-scale metabolic networks of bacteria is proposed in order to identify potential therapeutic targets, along with its corresponding web implementation, dubbed FindTargetsWEB. The proposed method assumes that every metabolic network presents fragile genes whose blockade will impair one or more metabolic functions, such as biomass accumulation. FindTargetsWEB automates the process of identification of such fragile genes using flux balance analysis (FBA), flux variability analysis (FVA), extended Systems Biology Markup Language (SBML) file parsing, and queries to three public repositories, i.e., KEGG, UniProt, and DrugBank. The web application was developed in Python using COBRApy and Django.Results: The proposed method was demonstrated to be robust enough to process even non-curated, incomplete, or imprecise metabolic networks, in addition to integrated host-pathogen models. A list of potential therapeutic targets and their putative inhibitors was generated as a result of the analysis of Pseudomonas aeruginosa metabolic networks available in the literature and a curated version of the metabolic network of a multidrug-resistant P. aeruginosa strain belonging to a clone endemic in Brazil (P. aeruginosa ST277). Genome-scale metabolic networks of other gram-positive and gram-negative bacteria, such as Staphylococcus aureus, Klebsiella pneumoniae, and Haemophilus influenzae, were also analyzed using FindTargetsWEB. Multiple potential targets have been found using the proposed method in all metabolic networks, including some overlapping between two or more pathogens. Among the potential targets, several have been previously reported in the literature as targets for antimicrobial development, and many targets have approved drugs. Despite similarities in the metabolic network structure for closely related bacteria, we show that the method is able to selectively identify targets in pathogenic versus non-pathogenic organisms.Conclusions: This new computational system can give insights into the identification of new candidate therapeutic targets for pathogenic bacteria and discovery of new antimicrobial drugs through genome-scale metabolic network analysis and heterogeneous data integration, even for non-curated or incomplete networks. Acinetobacter baumannii, Pseudomonas aeruginosa, and Enterobacteriaceae family), and R&D on new antibiotics against these is considered to be of critical priority , previously called hospital infections, are a serious public health problem and can develop either as a direct result of medical or surgical treatment or from being in contact with a healthcare setting. These infections include central line-associated bloodstream infections, catheter-associated urinary tract infections, ventilator-associated pneumonia (VAP), and surgical site infections. Among the pathogens related to HAI, the group of bacteria is the one that stands out. More than 2 million HAIs occur each year in the USA , with 50priority . In humafibrosis  and is aGiven the potential severity of multidrug-resistant bacteria and the lack of treatment options, the identification and implementation of effective strategies to prevent such infections are urgent priorities.The integration of mathematical, statistical, and computational methods for biological data analysis to enable the discovery of new therapeutic targets for any bacteria is extremely relevant. The combination of bioinformatics, system modeling, and heterogeneous data integration can be a powerful tool for this purpose.Several strategies have been proposed to search for drug targets from genome-scale models of bacterial metabolism. More often, essential genes are identified from single virtual knockouts where flux balance analysis (FBA)  is used The construction of genome-scale metabolic network is a laborious endeavor. It combines automated steps with manual curation. The most used protocol, proposed by Tier 1 corresponds to PGDBs that have received at least 1 year of manual curation and are updated continuously. Tier 2 includes PGDBs that have received moderate (less than a year) amounts of review and are usually not updated on an ongoing basis. Finally, Tier 3 refers to PGDBs that were created computationally and received no subsequent manual review or updating.The BioCyc database  classifidraft metabolic reconstructions are considered Tier 3 models. Published curated metabolic models are classified as Tier 2, unless the model is identified in the literature as Tier 1.In this work, the same classification for genome-scale metabolic network models is adopted. The focus here is on metabolic network models that can be classified as Tier 2 and Tier 3, according to the BioCyc database classification. In this manuscript, FindTargetsWEB. The proposed method is computationally efficient, user-friendly, and robust to errors in reconstructed genome-scale metabolic networks, which are more frequent in Tier 3 (draft) metabolic networks. The web interface of the application is straightforward, and results are sent directly to an email address informed by the user. To demonstrate the flexibility of FindTargetsWEB, 10 genomic-scale metabolic networks of bacterial strains are analyzed in this paper. Nine of the 10 networks are available in the literature, all classified as Tier 2 models in this work: P. aeruginosa PAO1\u2014version 2008   . Both reThe web application proposed in this work combines FBA, flux variability analysis (FVA) , extendeCOnstraint-Based Reconstruction and Analysis Toolbox (COBRA)   methods  (COBRA)  is a Pyt (COBRA) Figure 1Target identification is carried out through a computational workflow that runs the metabolic network analysis and pinpoints genes whose virtual knockout interrupts the generation of biomass. Therefore, the minimum level of curation required for a metabolic network model to be processed by FindTargetsWEB is to have a biomass reaction flux greater than zero. The list of potential targets is filtered using FVA (if the user decides to do so), and the workflow retrieves possible inhibitors for the identified genes, verify if such inhibitors are available as approved drugs, and evaluate their toxicity to humans by querying several repositories.https://www.gnu.org/software/glpk/), which is the COBRApy default solver that is easily deployable on Linux platforms. The system is deployed in an Ubuntu v18.04 server with 64GB RAM. Prior to processing, when needed, SBML files were converted to the SBML level 3 format using the command cobra.io.sbml3.write_sbml_model from COBRA. The SBML files processed in this manuscript were retrieved from the BioModels repository  relations. In the same way as the previous step, if the value of the generation of biomass has zeroed, the corresponding gene information is stored in a second list. It is worth noting that one gene can be associated with more than one reaction, and one reaction may require the expression of several genes.5. Consolidation/unification of knockouts results\u2014In this step, both lists generated in the previous steps are unified, i.e., the list of reactions generated in step 3 and the gene list generated in step 4. In order to a gene to be included in the final list, it should be included in the list of step 4 and be associated with at least one reaction stored in step 3 (see Algorithm 1). These are the candidate genes that the workflow is going to consider in the following steps. It should be highlighted that the final list is filtered according to the FVA processing performed in step 2, if the option FBA+FVA is selected by the user.Algorithm 1: Consolidation of knockout results (SBML with mapped genes)Input: List of genes from knocked-out reactions/list of knocked-out genesOutput: Unified list of target genes in a text fileprocedure UnificationTargetsList\t2:\t\t\tread targetGeneListFromReact\t3:\t\t\tread targetGeneList\t4:\t\t\topen file \u201ctargetgenes.txt\u201d\t5:\t\t\tfor all targetgene in targetGeneListFromReact do\t6:\t\t\t\tif targetgene in targetGeneList then\t7:\t\t\t\twrite targetgene in file \u201ctargetgenes.txt\u201d\t8:\t\t\t\tend if\t9:\t\t\tend for\t10:\t\t\tclose file \u201ctargetgenes.txt\u201d\t11:\tend procedure\t1:\t6a. Search for EC numbers of consolidated genes. In this step, the system queries the KEGG repository to obtain the EC number of each gene included in the final gene list obtained in the previous step (file \u201ctargetgenes.txt\u201d). KEGG (Kyoto Encyclopedia of Genes and Genomes) is a knowledge base for systematic analysis of gene functions, linking genomic information with higher order functional information  metabolic network models, EC numbers are retrieved from KEGG based on reaction information. This step is particularly important for incomplete metabolic reconstructions that do not include GPR relations and is directly related to the application\u2019s requirement of robustness to incompleteness on metabolic network data. The KEGG search is performed using all the compounds involved in the corresponding reaction. See Algorithm 2 for a detailed description of the processing related to this step. It is worth emphasizing that this step is executed only for incomplete descriptions of genome-scale metabolic networks. The complexity of Algorithm 2 is O(C), where C is the number of compounds included in the SBML file.Algorithm 2: Search for EC numbers using reaction information (SBML without mapped genes)Input: List of chemical compounds of reactionOutput: List of EC numbers foundread listCompoundFromSBML\t4:\t5:\t# Instance of biomodels python module\t6:\tk <- KEGG instance\t7:\t8:\t# setting timeout in seconds\t9:\tk.timeout <- 200000\t10:\t11:\t# All compounds in SBML file. Ex.: 2 A \u2013> B\t12:\tfor all compound in listCompoundFromSBML do\t13:\t14:\t\t\t# find all stoichiometric values with regex method in compound. Ex.: A \u2013> B\t15:\t\t\tcompound_no_stoich <- remove all stoichiometric values in compound\t16:\t\t\tparam_splt <- empty\t17:\t18:\t\t\t# Verify if reaction is reversible or irreversible\t19:\t\t\tif \u201c< = >\u201c in compound_no_stoich then\t20:\t\t\t\tparam_splt <- \u201c< = >\u201c\t21:\t\t\telse\t22:\t\t\t\tparam_splt <- \u201c\u2013>\u201c\t23:\t\t\tend if\t24:\t25:\t\t\t# Separate compounds in reactant and product. Ex.: compound_splt = \t26:\t\t\tcompound_splt <- compound_no_stoich.split(param_splt)\t27:\t28:\t\t\t# If compound belongs to a transport reaction (influx or eflux), jump to next iteration\t29:\t\t\tif compound_splt.length < 2 then\t30:\t\t\t\tcontinue\t31:\t\t\tend if\t32:\t33:\t\t\tlist_ec_number_0 <- initialize empty list\t34:\t\t\tlist_ec_number_1 <- initialize empty list\t35:\t\t36:\t\t\t# Start iterating compound_splt list with reactant and product\t37:\t\t\tfor  do\t38:\t39:\t\t\t\t# Get reactant or product in this variable\t40:\t\t\t\titem_compound <- compound_splt[x] without spaces\t41:\t\t\tlist_id_cpd_KEGG <- initialize empty list\t42:\t\t\t43:\t\t\t# If reactant or product contains \u201c+\u201d, find ID in KEGG for components.\t44:\t\t\t# Else, find ID in KEGG for only one component.\t45:\t\t\tif \u201c + \u201c in item_compound then\t46:\t\t\t\titem_compound_splt <- item_compound.split(\u201c + \u201c)\t47:\t\t\t\tfor all cpd_item in item_compound_splt do\t48:\t\t\t\t\t# find id compound in KEGG for cpd_item\t49:\t\t\t\t\t# and insert in ids list\t50:\t\t\t\t\tresult_id_cpd <- k.find\t51:\t\t\t\t\tinsert result_id_cpd in list_id_cpd_\u200bKEGG\t52:\t\t\t\tend for\t53:\t\t\telse\t54:\t\t\t\tresult_id_cpd <- k.find\t55:\t\t\t\tinsert item_compound in list_id_cpd_KEGG\t56:\t\t\tend if\t57:\t\t\t58:\t\t\t# Here, all list_id_cpd_KEGG are concatenated\t59:\t\t\t# found to search the reaction in KEGG.\t60:\t\t\t# In Python, if list_id_cpd_KEGG length is less than 2,\t61:\t\t\t# don\u2019t put the \u201c+\u201d in end of string.\t62:\t\t\tstr_item_compound_in_cpd <- list_id_cpd_KEGG concat with \u201c+\u201d\t63:\t\t\t64:\t\t\t# find all reactions in KEGG with IDs of compounds\t65:\t\t\tresult_link_reactions_cpd <- k.link\t66:\t\t\t67:\t\t\t# All results of result_link_reactions_cpd are inserted here\t68:\t\t\tset_id_reaction_KEGG <- insert all reactions found in KEGG.\t69:\t\t\t70:\t\t\t# find all EC numbers in KEGG with reactions IDs\t71:\t\t\t# in set_id_reaction_KEGG and insert in result_list_ec\t72:\t\t\tresult_list_ec = k.link\t73:\t\t\tif x = 0 then\t74:\t\t\t\tinsert result_list_ec in list_ec_number_0\t75:\t\t\telse\t76:\t\t\t\tinsert result_list_ec in list_ec_number_1\t77:\t\t\tend if\t78:\t79:\t\tend for\t80:\t81:\t\tlist_ec_number_intersect <- initialize empty list\t82:\t\ttxt_file <- initialize txt file\t83:\t\t84:\t\t# Starts to iterate the list of ECs to identify intersections\t85:\t\t# If found, related EC numbers are written in a text file\t86:\t\tfor all ec_number_0 in list_ec_number_0 do\t87:\t\t\tif ec_number_0 in list_ec_number_1 then\t88:\t\t\t\trecord ec_number_0 in a txt_file\t89:\t\t\tend if\t90:\t\tend for\t91:\t\t92:\tend for\t93:\t94: end procedure\t1:\tprocedure alternativeStepToGetECNumberWithoutGenes(listCompoundFromSBML)\t2:\t# file with all compounds in SBML.\t3:\t7. Search for EC numbers on DrugBank\u2014With the EC numbers obtained in the previous steps, the system queries the DrugBank repository to verify if this database has any record of the listed EC numbers. The DrugBank database is a repository that combines detailed drug data with comprehensive drug target information  is necessary to confirm whether the protein retrieved has a homologue in the target bacterium. Clearly, exact matches are also possible. In any case, the retrieved data is validated in the next step.8. Search for homologues on UniProt\u2014Finally, the system searches for sequence similarity between the proteins described by UniProt IDs retrieved in the last step and the proteins encoded by the genome of the target bacterium using the BLAST  (ch tool)  applicatIn this step, the homology between the target protein and human proteins is also considered. If the sequence similarity with a human protein is greater than the similarity with the target bacterium, the protein under analysis is discarded, since the inhibition of that protein could be harmful to the host. Otherwise, several data are stored, such as metabolic pathway, function, and catalytic activity, among others. This step of the workflow is the most time-consuming, since BLAST is executed for all proteins identified in the previous step.9. Search for existing inhibitors\u2014The last step is to query the DrugBank repository, using the stored UniProt IDs, in order to retrieve known inhibitors, if available. After this last step, the system generates spreadsheets containing all results that are sent to the user in a compressed file.This method presents as results candidate genes that, when knocked-out, will cease the biomass production of the microorganism. Candidate genes must be associated with potential drug targets in DrugBank, and their sequence similarity to human proteins is also checked. The application then identifies available ligands, most often inhibitors, to the selected genes.Results of FindTargetsWEB\u2019s analysis are sent to the user as a compressed file, to the e-mail address informed at the start of execution. Five spreadsheets are included in the compressed file:08-filter_ECNumbers_DrugBank\u2014This spreadsheet contains the EC number of putative targets, along with product, organism name, UniProt ID, and DrugBank ID- 11- hits_Uniprot\u2014This spreadsheet contains additional information related to UniProt queries, such as percentage of sequence similarity, BLAST e-value, gene name, pathway, function, and catalytic activity.- 13-list_inhibitors_per_target\u2014This spreadsheet lists all inhibitors found for all targets. Included information are drug name, drug group , and drug action.- 14-list_inhibitors_approved\u2014This spreadsheet lists all inhibitors with approved drugs found for all targets. Included information are drug name, drug group (approved), and drug action.- model_data\u2014This spreadsheet lists data related to the input SBML file, such as gene IDs and associated reactions. The complete information of which reactions are associated with each gene in the metabolic network model is included in this file.- summary_results\u2014This spreadsheet contains a summary\u200b of data included in the previous files. Included fields are EC numbers, product, organism name, gene name, pathway, function, catalytic activity, drug name, drug group, and drug action.- P. aeruginosa, K. pneumoniae, H. influenzae, S. aureus, P. putida, and a host-pathogen genome-scale reconstruction based on the M. tuberculosis metabolic network are presented. It should be highlighted that FindTargetsWEB can carry out analysis for other bacterial species, as indicated by the list box on the initial web page of the application. Indeed, even this list can be easily expanded to include additional species of interest, through a user request to FindTargetsWEB support team.In this section, analysis results for several strains of P. aeruginosa is discussed. A survey of the literature is also presented to confirm the feasibility of the candidate genes as antibacterial drug targets. Gene function and related pathways are also considered in the evaluation of results.To evaluate the accuracy of results for several metabolic networks, initially, the analysis of four metabolic networks of P. aeruginosa strains analyzed by FindTargetWEB were: PAO1 version 2008\u2014iMO1056 (BioModels ID 1507180020)  , PAO1 ve7180020) , PA14\u2014iP7180020) , and a cCCBH4851 . The SBMP. aeruginosa spp., which may vary between 0.3 and 0.8 h-1, depending on cultivation conditions  and murB (EC 1.3.1.98) genes encode enzymes involved in bacterial cell wall synthesis and have been identified as essential in both Pseudomonas spp. and Escherichia coli (folP gene product (EC 2.5.1.15) is important for folic acid biosynthesis, which is fundamental for bacterial growth and reproduction (folA gene product (EC 1.5.1.3) is related to the biosynthesis of cofactors, being an important intermediary of folate metabolism. It is considered the key enzyme of this process and essential for microbial growth (aroE gene (EC 1.1.1.25), which has been described as a potential therapeutic target of both P. putida and E. coli  and lysine. Lysine is utilized for protein synthesis in bacteria and forms part of the peptidoglycan cross-link structure in the cell wall of most gram-positive species, whilst meso-DAP is the peptidoglycan cross-linking moiety in the cell wall of gram-negative bacteria   are favorable candidate drug targets and several inhibitors have been already reported  . Becausereported . SpecififabA participates in fatty acid synthesis (FAS) processes, which includes also fabB, fabD, fabI, and fabH. The proteins encoded by these genes have an essential role during the synthesis of bacterial phospholipid membranes, lipopolysaccharide (LPS), and lipoproteins, thus representing attractive targets due to the structural differences between the human and bacterial proteins and the essentiality of FAS  of the overall method. The growth rate of the Tier 3 version of the P. aeruginosa CCBH4851 network is 1.757 h-1, which is less consistent to the biology of P. aeruginosa spp. than the growth rate obtained by the Tier 2 version of the network. The processing of this Tier 3 network generated 32 targets in the FBA+FVA analysis, and 48 targets using the FBA-only method. It is remarkable that this less curated version of P. aeruginosa CCBH4851 network generated more potential targets in the FBA+FVA analysis than the corresponding Tier 2 network.To evaluate the robustness of FindTargetsWEB regarding Tier 3 networks, which generally are networks generated automatically without manual curation, FindTargetsWEB processed a preliminary version of the metabolic network model of dapA is present as a potential target in the Tier 3 network.Among targets identified using the FVA+FBA method, 10 targets are common between the Tier 2 and Tier 3 networks. For the FBA-only analysis, 21 targets are common between the two versions. It is worth mentioning that many targets found in Tier 2 networks are present in the analysis of the CCBH4851 Tier 3 network, which corroborates the relevance of the targets found even in draft versions of metabolic networks. This comparison also highlights the importance of careful curation of automatically generated metabolic networks. For instance, from the targets discussed in the previous subsection, only P. aeruginosa were also processed using FindTargetsWEB. In the previous subsections, results for P. aeruginosa metabolic network models were presented, but it is also possible to analyze networks of other species of bacteria. In this subsection, FindTargetsWEB results for a metabolic network reconstruction of K. pneumoniae MGH78578\u2014iYL1228 (BioModels ID 1507180054) (H. influenzae\u2014iCS400 (BioModels ID 1507180053) (Metabolic networks of bacteria other than 7180054)  and H. i7180053)  are pres7180053) Table 4.K. pneumoniae, a total of 45 unique potential targets were found using the FBA+FVA method and also 45 for the FBA-only method. Some of the more representative targets are listed in For lpxA gene is involved in the initial steps of lipid A production through the Raetz pathway. As stated in the previous subsection, fabA, fabB, and fabF participate in FAS processes and represent attractive targets due to the structural differences between the human and bacterial proteins and the essentiality of FAS. The cytoplasmic protein N-acetylglutamate (NAG) kinase (encoded by argB), which promotes phosphorylation of NAG in a rate-limiting step of bacterial L-arginine production, occurs through acetylated intermediates, unlike mammals which use non-acetylated intermediates, and for this reason, it was previously considered a candidate drug target  and P. aeruginosa (folA). Both methods, FBA+FVA and FBA-only, generate exactly the same results. Therefore, the FVA ranges for all targets in It is worth mentioning that the genes M. tuberculosis H37Rv model, iNJ661 , which integrates a cell-specific alveolar macrophage model, iAB-AM\u00d8-1410, from the global human metabolic reconstruction, with an , iNJ661 . The intM. tuberculosis survival   , reconstmurB, aroC), while others such as mvaA , tkt , and dfrA  are defined as essential for S. aureus in both minimal and rich medias  networks, pointing out that such metabolic network models are very common and are the only models available for some organisms. The system is deployed as a web application and is asynchronous: the user is notified when results are available. The performance of the system is optimized, since the COBRApy framework can make use of multiple cores available in the host machine, and it is able to process the metabolic network of various bacteria, as described in the previous section. The only requirement is the availability of an SBML level 3 file describing the corresponding genome-scale metabolic network. The user interface is straightforward see 2, and tE. coli and Bacillus subtilis, without pinpointing any potential drug. K. pneumoniae. However, their method is not automated, and it was not applied to other species of bacteria. None of these works go as far as FindTargetsWEB, which can process metabolic network models of several species of bacteria, identify potential targets, confirm homology with the analyzed gene, and identify all available drugs for the potential target in a fully automated manner.Other proposals for the analysis of metabolic networks at genomic scale are available in the literature. FBA+FVA and FBA-only, one can conclude that the FBA+FVA method represents a way to prioritize the targets identified by the FBA-only method, since the set of targets identified by FBA+FVA is a proper subset of the set of targets identified by FBA-only. However, as stated in the detailed description of the targets of the Results section, potential targets that are associated with the FBA-only method and do not appear as results of the FBA+FVA method should not be disconsidered. Many important targets described in the literature have a FVA range greater than zero, and a careful analysis of both sets of potential targets is advised.Regarding the options to identify potential targets, i.e., P. aeruginosa and other bacteria and can be effective against non multidrug-resistant strains. As expected, for the multidrug-resistant strain, most of the approved drugs are not effective. For instance, it is known that P. aeruginosa can be resistant to both to trimethoprim and sulfamethoxazole  is both essential to metabolic growth and biofilm formation, according to the FUNCTION field returned by FindTargetsWEB and literature sources License: Not ApplicableAny restriction to use by non-academics: Not ApplicableThe user must provide a SBML level 3 file describing the metabolic network reconstruction and an e-mail address to which the results will be forwarded.All datasets generated for this study are included in the manuscript and the supplementary files.TCM, FPSJ, and FABS designed the system. TCM was the main programmer. MWC and ADC-A tested the system and evaluated its correctness. All authors have equally participated in the writing of this paper.The authors would like to thank CAPES, FAPERJ, CNPq and FIOCRUZ (INOVA-FIOCRUZ VPPCB-007-FIO-18-2-29) for financial support.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Scientific Reports 10.1038/s41598-018-24002-0, published online 11 April 2018Correction to: The original version of this Article contained typographical errors in title of the paper, where \u2018QRS\u2019 was incorrectly given as \u201cQrs\u201d and a colon was omitted. This has now been corrected in the PDF and HTML versions of the Article and in the accompanying Supplementary Information file."}
+{"text": "Moreover, an example is given to support one of our results, and an application is proposed.In this paper, we introduce the concept of  In this paper, b-metric-like spaces which is considered to be an interesting generalization of metric spaces, b-metric spaces [b-metric-like spaces.The Banach contraction mapping principle in metric spaces is an important tool in nonlinear analysis, many authors have been devoting in generalizing metric spaces and the Banach contraction mapping principle. And then, many generalized metric spaces were introduced. In 2013, Alghamdi et al. [c spaces \u20138. Firstb-metric-like on a nonempty set X is a function if  The pair b-metric-like space with coefficient s.A b-metric-like spaces were introduced as follows.Some concepts in b-metric-like b on X generalizes a topology X whose base is the family of open b-balls Each b-metric-like space A sequence b-metric-like space A sequence b-metric-like space is called to be complete if every Cauchy sequence X converges with respect to A \u03b2:Let On the other hand, in , GeraghtLetbe a complete metric space andbe a mapping. IfTsatisfiesfor anywherethenThas a unique fixed point.Recently, many papers about generalization of Geraghty contraction appeared \u201313. In 2paces in , and theLetbe a complete metric-like space andbe a mapping. If there existssuch thatfor allwherethenThas a unique fixed point.In this paper, we define the new concept of In this section, we begin with the following definitions.X be a nonempty set, f and g be self-mappings on X and f and g are called to be weakly compatible if x is called to be a coincidence of f and g, and w is called to be a point of coincidence of f and g.Let b-metric-like space with coefficient Let Letbe a b-metric-like space, Tandgbe self-mappings onXsuch thatis acontraction of Geraghty type. Ifis a point of coincidence ofTandg, thenT and g, then there exists Suppose that Letbe ab-metric-like space with coefficientbe two mappings withandgXis complete. If the pairis acontraction of Geraghty type, thenTandghave a unique point of coincidence. In addition, ifTandgare weakly compatible, thenTandghave a unique common fixed point.T and g have a point of coincidence. If there exists some T and g, so T and g. We assume that For an arbitrary mentclass2pt{minimmentclass2pt{minimCase I: Case of Applying , 10), a, a\\documApplying , we obtamentclasspt{minimaCase II: Case of (k)). By , taking }s=1, by  and 11)\\documentyn(k))|. , 15) an an\\documgX. Since gX is complete, then there exist From the above discussions, we get that  holds. TBy , we haveNext, we prove Case I. }n\u2192+\u221e in , applyin}n\u2192+\u221e in , we obtaT and g have a coincidence point u, and v is a point of coincidence of T and g. By Lemma T and g, then we can find T and g have a unique point of coincidence. Moreover, T and g are weakly compatible, then we have T and g have a unique common fixed point.\u2003\u25a1Case II. }n\u2192+\u221e in , and takmentclass2pt{minimmentclass2pt{minimLetting Letbe a complete b-metric-like space with coefficientandbe a mapping. If there existssuch thatfor anywherethenThas a unique fixed point.Taking Letbe a complete metric-like space andbe a mapping. If there existssuch thatfor anywherethenThas a unique fixed point.Corollary Taking Letbe a metric-like space andbe two mappings withandgXis complete. Suppose that there existssuch thatwhereThenTandghave a unique point of coincidence. In addition, ifTandgare weakly compatible, thenTandghave a unique common fixed point.Now, we use an example to illustrate the validity of our main result.Let Case 1: Case 2: We get Case 3: We get Case 4: We get T has a unique fixed point, 0 is the unique fixed point of T.From the above discussions, we know that X with the b-metric-like:Consider the following integral equation:f.Let ution to  is equivNow, we prove the following result.Suppose that the following hypotheses hold: (i)is continuous;(ii)For allthere exists continuoussuch that(iii)There existssuch thatThen the integral equation (has a unique solutionequation  has a unFrom  and 29)29), for f has a unique fixed point x is the unique solution for the integral equation (From the above, we can see that all the conditions of Corollary equation .\u2003\u25a1In this paper, we introduce a new concept of m 2.1 in . At the"}
+{"text": "A solid k-mer is a k-mer frequently occurring in NGS reads. The other k-mers are called weak k-mers. A solid k-mer does not likely contain errors, while a weak k-mer most likely contains errors. An intensively investigated problem is to find a good frequency cutoff f0 to balance the numbers of solid and weak k-mers. Once the cutoff is determined, a more challenging but less-studied problem is to: (i) remove a small subset of solid k-mers that are likely to contain errors, and (ii) add a small subset of weak k-mers, that are likely to contain no errors, into the remaining set of solid k-mers. Identification of these two subsets of k-mers can improve the correction performance.NGS data contains many machine-induced errors. The most advanced methods for the error correction heavily depend on the selection of solid k-mers and a mixture of Gaussian distributions to model correct k-mers, and combine them to determine f0. To identify the two special subsets of k-mers, we use the z-score of k-mers which measures the number of standard deviations a k-mer\u2019s frequency is from the mean. Then these statistically-solid k-mers are used to construct a Bloom filter for error correction. Our method is markedly superior to the state-of-art methods, tested on both real and synthetic NGS data sets.We propose to use a Gamma distribution to model the frequencies of erroneous z-score is adequate to distinguish solid k-mers from weak k-mers, particularly useful for pinpointing out solid k-mers having very low frequency. Applying z-score on k-mer can markedly improve the error correction accuracy.The  The massively parallel next-generation sequencing (NGS) technology is revolutionizing a wide range of medical and biological research areas as well as their application domains, such as medical diagnosis, biotechnologies, virology, etc . It has https://www.ncbi.nlm.nih.gov/sra/ERR091571/) is 6.92 billion; however, this number can be reduced to only 1.98 billion after error correction. This reduction significantly alleviates the burden of graph manipulation.The information contained in NGS data is deep and broad, but the raw data is still error prone. Various kinds of errors exist in the raw sequencing data, including substitution, insertion and deletion. The substitution error rate can be as high as 1 to 2.5% for the data produced by the Illumina platform ; and thek-spectrum-based approach, including Quake [k-spectrum-based. It provides a very good scalability and competitive performance. Scalability is crucial for NGS data analysis since the input volume is usually huge.Owing to the importance of error correction, dozens of approaches have been proposed to cope with various types of errors. Depending on the key ideas that have been used, existing approaches can be categorized into three major approaches: (i) the ng Quake , Reptileng Quake , DecGPU ng Quake , SGA [11ng Quake , Musket ng Quake , Lighterng Quake , Blue [1ng Quake , BFC [16ng Quake , MECAT [ng Quake  (ii) theng Quake , HSHREC ng Quake , HiTEC [ng Quake , Fiona [ng Quake  and;  add a small subset of weak k-mers that are likely to contain no errors, into the set of solid k-mers. This is achieved by using f0 as well as z-score of k-mer, z(\u03ba). With the purified set of solid k-mers, the correction performance can be much improved.In this research, we focus on a more challenging but less-studied problem: (i) remove a small subset of solid k-mer frequencies by using KMC2 [z-scores of k-mers. Later, the statistically-solid k-mers are mined by considering both frequency and z-score. After that, the Bloom filter is constructed by the statistically-solid k-mers, and the weak k-mers are corrected. The newly proposed approach is named as ZEC, short for z-score-based error corrector.Our approach starts with counting ing KMC2 , then cak-mer is conventionally defined as a k-mer which occurs in a data set of NGS reads with high frequency. A solid k-mer is usually considered error-free, and taken as the template for error correction. If a k-mer is not solid, then it is defined as a weak k-mer considered as error-containing. Existing k-mer-based approaches use a frequency cutoff, f0, to identify solid and weak k-mers from NGS reads, e.g., BLESS2 [f0 is determined.A solid , BLESS2 , Musket , BLESS2 , and BFC, BLESS2 . The maik-mer is not definitely error-free. Sometimes, it may contain errors with a small chance. It is also true for the weak k-mers \u2014 a weak k-mer can be absolutely error-free. The reason that a solid k-mer is not always correct is that the coverage is not under uniform distribution. Thus the cutoff f0 itself is unable to perfectly distinct correct k-mers from erroneous k-mers; cf. the part labeled as \u03b1 and \u03b2 in Fig.\u00a0k-mers as many as possible.In fact, a solid k-mer set as well as the weak k-mer set, so that more correct k-mers can be identified.In this study, we present a time and memory efficient algorithm to purify the solid R be the input set of NGS reads, and K be the set of k-mers contained in R. To determine whether a k-mer, say \u03ba, of K is correct or not, the following metrics are examined: f(\u03ba), the frequency of \u03ba;z(\u03ba), the z-score of \u03ba.Let f(\u03ba) is as follows: (i) scan each read r of R from the beginning to the end; (ii) sum over the occurrence that \u03ba appears. Then the summation is f(\u03ba). This approach works for one k-mer, but it cannot be applied to all the k-mers simultaneously as the number of k-mers can be very large, demanding a huge size of memory.The straightforward approach to determine k,x)-mer; and (iii) it applies the minimizer idea to deal with k-mer.In this study, we make use of the k-mer counting algorithm, KMC2 , to solvk-mer \u03ba, we define the neighbor of \u03ba, N(\u03ba), as D is the edit distance between \u03ba and \u03ba\u2032, and the d0 is the predefined maximum distance. The default value of d0 is 1 as used in this study, but user can adjust this value to any reasonable integer.Given a k-mer cluster centered at \u03ba is defined as k-mers is defined as The z-score of \u03ba, z(\u03ba), is computed by \u03bc is the averaged frequency of F(\u03ba) and \u03c3 is the standard deviation of F(\u03ba).The z-score of each k-mer given the frequency of the k-mer as well as that of its neighbor that have been determined by the aforementioned approach.It is straightforward to calculate the k-mers based on their frequency only, we examine their z-scores as well.Unlike existing approaches that determining solid f0 is used to distinct weak and solid k-mers, which is determined as the count minimizing misclassification rates , and those correct ones by a mixture of Gaussian distributions PN(X). A Gamma distribution is defined as: k accounts for the shape of the distribution, \u03b8 is for the scale of the distribution, i.e., how the data spread out, \u0393(k) is the Gamma function evaluated at k; cf. the dash sky-blue line in Fig.\u00a0\u03c0i is the mixture parameter, \u03bci and \u03c3i represent the mean and standard deviation of the component i, and K is the number of Gaussian components. In this study, K is set as 2, with one accounting for k-mers that are from GC rich or poor regions, and the other for the rest correct k-mers.Traditionally, an optimal mentclass2pt{minimk-mers. An example of the two distributions are shown in Fig.\u00a0f0, such that it can minimize the area marked as \u03b1 and \u03b2. Note that, the threshold f0 determined in this way may not be the intersection point of the two density functions.The two distributions are estimated by using EM algorithm based on the frequencies of f0 cannot perfectly distinct the solid k-mers from the weak k-mers. Taking Fig.\u00a0k-mers marked by \u03b1 will be wrongly corrected although they do not have errors but just because their frequencies are lower than f0; likely, the ones marked by \u03b2 will keep unchanged although they have errors because they have high frequency. To further refine the purity as well as the completeness of solid k-mers, we borrow the statistical idea of using z-score to solve the problem. The purity is defined as It is clear that the optimal pcorrect is the proportion of correct k-mers in the solid k-mers, and perroneous is the proportion of erroneous k-mers in the solid k-mers. The completeness is calculated as where k-mers in the solid k-mers, and Ncorrect is the total number of correct k-mers.where z-score as well as the frequency are collectively incorporated into solid k-mer identification through the following two situations: f(\u03ba)<f0 and z(\u03ba)\u2265z0, then \u03ba is removed from the weak k-mers and added to the solid k-mers, i.e., increases the completeness.If f(\u03ba)\u2265f0 and \u03ba is removed from the solid k-mers and added to the weak k-mers, i.e., improves the purity.If The f0 is the minimum frequency that has been determined, while the z0 and z-score and minimum z-score for weak k-mers and solid k-mers, respectively.The z0 and z-score distribution automatically. To obtain the optimal z0, the z-scores of the k-mers having frequency less than f0 are collected. Later, the distribution of these z-scores is estimated and z0 is set as the value having the lowest density between two peaks . Analogously, z-scores of k-mers having frequency greater than f0.The k-mers and; (ii) correct errors in weak k-mers by the Bloom filter.Our error correction model contains two main steps: (i) build Bloom filter from solid h, the false positive rate p, the size of the bit vector n, and the actual number of elements m is Bloom filter  is a prom is the number of solid k-mers that have been determined from all the k-mers by means of the aforementioned algorithm. Per existing approaches, p is set to 1%. One can also tune p, h and n to fit the real hardware limitations.In our study, k-mers that are used to construct Bloom filter, which directly improves the error correction performance in theory. Note that, the solid k-mers play the key role in error correction, as all the rest k-mers (viz. the weak k-mers) are to be corrected based on the solid ones.It has been reported that the Bloom filter has been successfully used to correct NGS errors, such as BLESS2  and BFC Figure\u00a0k-mer of the read from the beginning to the end sequentially. (ii) partition the k-mers into groups that each group contains only solid k-mers or weak k-mers, deemed as solid group Gs or weak group Gw, respectively. The order of the groups is kept according to their appearance in the read. (iii) correct the errors causing the weak group Gw according to the following situations: Gw is the first group and there exists a successive group Gs that is solid, we iteratively change the first base of each k-mer of Gw to its alternatives and check the existence of the k-mers against the Bloom filter. Once there exist a solution that makes all the weak k-mers solid, the amendment of the bases is accepted, thus the correction of the error. This process is applied to the k-mers of Gw from the last one to the first one. In case the number of k-mers contained in Gw is less than a predefined value, say \u03c4, the processive solid k-mers that are extended from the corrected k-mers will be generated until the total number of k-mers in Gw is \u03c4. If this criterion cannot be satisfied, the solution is abandoned. On the other hand, if Gs does not exist, we will alter the bases to their alternatives of all the k-mers iteratively until a solution that make all the k-mers solid can be found.If Gw has a solid processive group Gs and a solid successive group k-mer in Gw by its alternatives from the first k-mer to the last k-mer, namely the forward search. Solutions that make all the k-mers solid till the current substitution are recorded. Similarly, the backward search is conducted on the first base of the k-mers from the last one to the first one. A solution is accepted if the forward search and the backward search meet and the k-mers contained in both of them are solid. In case the number of k-mers in Gw is less than k, we will only alter the last base of the first k-mer.If Gw is the last group and there exists a solid processive group Gs, we will apply the backward search to obtain the solution. Analogously to the first situation, if the number of k-mers of Gw is less than \u03c4, we will extend the k-mers toward their downstream until the number is satisfied. In case Gs does not exist, it is the same as the second part of the first situation, thus the same approach is applied.If By using Bloom filter, the errors contained in each read can be correct as follows: (i) check the existence of each We collected six data sets to test the performance of our proposed method in comparison with the state-of-art methods. Four of the six data sets are the NGS reads produced by the Illumina platform, including Staphylococcus aureus (S. aureus), Rhodobacter sphaeroides (R. sphaeroides), Human Chromosome 14 (H. chromosome 14) and Bombus impatiens (B. impatiens). These data sets are the gold standards used by GAGE  for NGS gain, recall, precision and per base error rate (pber). Gain is defined as (TP\u2212FP)/(TP+FN), recall is TP/(TP+FN), precision is TP/(TP+FP) and pber is Ne/N, where TP stands for the number of corrected bases that are truly erroneous bases, FP represents the number of corrected bases that are not sequencing errors intrinsically, FN is the number of erroneous bases that remain untouched, Ne is the number of erroneous bases and N is the total number of bases. Among these metrics, gain is the most informative.The error correction performance is evaluated through the widely accepted procedure implemented by . MetricsAll experiments are carried out on a cluster having eight Intel Xeon E7 CPUs and 1Tb RAM. Each CPU has eight cores.Overall Performance of ZEC. The experimental results of ZEC are presented in Table\u00a0Relation with GC-content. A previous study by Ross et al. [k-mers obtained from the reads sequenced from these regions are more likely to be treated as weak. Figure\u00a0k-mer frequency derived from H. chromosome 14. It can be seen that the k-mers having a low frequency can spread out wider than those having a high frequency, and the wide range is coincident with the GC content. This result is in accordance with the performance shown in Table\u00a0k-mers is necessary, particularly for the subset of k-mers that have a low frequency. More importantly, it empirically supports our idea of using mixture model to treat solid k-mers and weak k-mers separately.s et al.  shows thComparison with State-of-the-art. The performance of ZEC is much superior to the state-of-the-art methods, including Lighter [gain. For instance, on the dataset R4, the gain of ZEC is 0.746, while the best performance produced by the other methods is 0.705. For the synthetic datasets, ZEC also has higher gain than other methods. For example, on the dataset S2, the gain of ZEC is 0.853, while the best and worst gain generated by the other methods are 0.849 and 0.058, respectively. The lowest average per-base error rate of ZEC also consolidates its effectiveness. Lighter , Racer [ Lighter , BLESS2  Lighter , Musket  Lighter , SGA [11 Lighter . See Tabz-score for identifying the two special subsets of k-mers from the sets of solid k-mers and weak k-mers. An example of z-score distribution pertaining to k-mer frequency is shown in Fig.\u00a0k-mers shown in the figure have relatively low frequencies\u2014less than 9, while the z-scores are pretty high\u2014greater than 1. Interestingly, almost all the solid k-mers (the top right region) have the similar level of z-scores comparing to these highlighted ones. These observations indicate that the highlighted k-mers are very likely to be correct k-mers instead of erroneous k-mers although their frequencies are very low. The z-score distribution pertaining to the other three real data sets has similar patterns compared to the one shown here.The key to the performance improvement is the idea of using k-mers that can be refined comparing to the solely frequency determined k-mers are 12.3%, 14.2%, 11.4%, 7.1% for the real data R1, R2, R3 and R4, respectively; see Fig.\u00a0By exploring the four real data sets, we found that the proportion of k-mers is not trivial for very large data sets, as the k-mers and their frequencies are usually too large to be hold by a main memory of a moderate computer. We designed a novel algorithm and solved this problem. The efficiency of the algorithm in terms of the memory usage and running speed are studied.Calculating z-score of k-mers as well as their frequencies) that can be held by only one bit vector. The memory saving ratio is calibrated as the ratio between the real memory allocation and the input data volume. For instance, the ratio of 0.01 pertaining to the data R4 means that the allocated memory is one percent of the input size of R4. That is, 70Mb memory is allocated for holding the 6.97Gb data. It is promising that, with one percent memory allocation, around 22 percent input data can be hold by only one bit vector. When the memory allocation increased to 2.5 percent, 30 percent input data and even more can be held by one bit vector. Obviously, keep increasing the size of allocated memory does not guarantee the linear scale of holding the input data. Based on the experiments, we set the memory allocation ratio to 2.5 percent through the whole study. Typically, three bit vectors are constructed for holding all the input. Note that, the size of bit vector decreases along with the reduced size of input. The ratios between the input and the total allocated memory are 20.0, 13.4, 7.0 and 7.9 for the four real datasets, respectively.Figure\u00a0k-mer in a bit vector is O(1) pertaining to time complexity by using hash, this algorithm is pretty fast. For instance, based on our computing power, it only takes 387 s to construct the bit vectors and calculate the z-scores of all the k-mers of R4\u2014the largest data set.Regarding the running speed, this algorithm is linearly scaled. Since locating each z-score of a k-mer different from its genuine value. However, the false positive rate is pretty small, usually less than 1%, thus this impact can be neglected.Since a Bloom Filter has false positives, this may cause the k-mers having low frequency, achieving an improvement of 11.25% on weak k-mers. However, some issues still remain further exploration, including neighbor inclusion and neighbor retrieval.Our model effectively pinpoints out correct k-mers are determined given a k-mer of interest, say \u03ba. Our current approach takes k-mers having edit distance of 1 as neighbors of \u03ba, but there still has a small chance that a true neighbor having edit distance larger than 1. Suppose the error rate is e, the probability of a k-mer having exactly one error is k\u00b7e(1\u2212e)k\u22121/k\u00b7e=(1\u2212e)k\u22121. When e=1% and k=1, the probability is (1\u22120.01)31\u22121=73.97%. That been said, about 26% real neighbors are excluded. However, even extending the minimum edit distance from 1 to 2 significantly elongates running time. This is because the number of candidate k-mers increases from 3\u2217k to 3\u2217k\u22173\u2217(k\u22121).Neighbor inclusion means how neighbor k-mers is too large to fit into a main memory. Hence, a more sophisticated approach is required to solve this problem. We use Bloom Filter to overcome the limitation. For k-mers having small count, say 5, we use classical Bloom Filters to save them, each Bloom Filter saves k-mers having the same count. For k-mers having large count, we use coupled-Bloom Filter to save them. One Bloom Filter for k-mer encoding, while the other is for count representation. This approach significantly reduces memory usage while achieving constant time complexity of k-mer retrieval. However, it may cause false positives although the probability is small. Hence, more effort is required to handle this problem.Neighbor retrieval is another issue to be considered. Usually, the size of counted k-mers to construct the Bloom filter. These k-mers are mined from all the k-mers of a NGS data set by considering both their frequency and z-score, particular the latter one that can effectively fishing out the solid k-mers having low frequency. Pinpointing out such k-mers has been a very challenging problem. The experimental results show that our approach markedly outperforms the existing state-of-the-art methods in terms of error correction performance.We have proposed a novel method for correcting the NGS errors. The novel idea is the use of statistically-solid"}
+{"text": "The development of high-throughput sequencing technologies for 16S rRNA gene profiling provides higher quality compositional data for microbe communities. Inferring the direct interaction network under a specific condition and understanding how the network structure changes between two different environmental or genetic conditions are two important topics in biological studies. However, the compositional nature and high dimensionality of the data are challenging in the context of network and differential network recovery. To address this problem in the present paper, we proposed two new loss functions to incorporate the data transformations developed for compositional data analysis into D-trace loss for network and differential network estimation, respectively. The sparse matrix estimators are defined as the minimizer of the corresponding lasso penalized loss. Our method is characterized by its straightforward application based on the ADMM algorithm for numerical solution. Simulations show that the proposed method outperforms other state-of-the-art methods in network and differential network inference under different scenarios. Finally, as an illustration, our method is applied to a mouse skin microbiome data. However, a more reasonable assumption is that the difference between the precision matrices are sparse, not that both matrices are sparse, since direct interactions may not be sparse while the changes under different conditions are often sparse . To be specific, \u03b8ij is replaced with \u03b8ijsij, where l, u) = ,  and (0.0.2) separately to study the performance of CDTr loss when the exchangeable condition is satisfied by different degrees. These scenarios are named as Band-exact (Band-e), Band-approx1 (Band-a1), Band-approx2 (Band-a2) and Cluster-exact (Cluster-e), Cluster-approx1 (Cluster-a1), Cluster-approx2 (Cluster-a2), respectively. To obtain a positive definite precision matrix \u0398, we first compute the smallest eigenvalue of \u0398 (denoted by e); then the diagonal elements of \u0398 are set as |e| + 0.3. The deviation to the exchangeable condition is measured with dev = \u2016G\u03a3 \u2212 \u03a3G\u2016F. The deviations under the aforementioned six scenarios are listed in n = 50, 100, 150, 200, a total of 100 datasets are generated and used to recover the network structure. Four state-of-the-art methods for network recovery are investigated, including gCoda  \u222a , if |i \u2212 j| = m, m = 1, 2, 3, 4.Neighbor graph: Select p points from Scale-free graph: A scale-free graph is produced, following the B-A algorithm  \u222a .lgorithm . The iniHub graph: Partition the nodes into 3 disjoint groups evenly and select a node as hub for each group. The hubs are connected with the non-hubs in the same group with strength uniformly distributed in  \u222a .Block graph: Divide p nodes into 5 blocks evenly. Connect pairs in the same block with probability 0.3 and pairs in different blocks with probability 0.1. The strength between connected nodes is uniformly distributed in  \u222a .We further conducted several experiments on the following six representative network structures, without considering the exchangeable condition.e| + 0.3, where e is the smallest eigenvalue of \u0398. The deviations from the exchangeable condition of these networks are listed in Similarly, the diagonal elements of \u0398 are set as |G\u03a3xln G and assumes that the inverse of G\u03a3xln G also approximates the inverse of \u03a3. However, as Fang et al.  \u222a .Band graph: Connect pair  with strength uniformly distributed in  \u222a , if |i \u2212 j| = m, m = 1, 2, 3, 4.Neighbor graph: Select p points from Scale-free graph: The scale-free graph is generated with the B-A algorithm  \u222a .Block graph: Divide p nodes into 5 blocks evenly. Connect pairs in the same block with probability 0.5 and pairs in different blocks with probability 0.3. The strength between connected nodes is uniformly distributed in  \u222a .We investigate the performance of DCDTr loss with some experiments in this section. The first precision matrix \u0398 is generated as follows:e| + 0.3, where e is the smallest eigenvalue of \u0398 or \u0398*, respectively. The deviations from the exchangeable condition of \u0398 and \u0398* are listed in \u21131-M, are used to estimate the true differential matrix \u0394. Similarly, we evaluate the true positive rate and true negative rate at different tuning parameters and then compute the area under the ROC curve (AUC). We take the sample size n = 100, 200, 300, 400 and repeat this procedure 100 times.Then 10% of the connected pairs in \u0398 will change to an unconnected state, while the same number of unconnected pairs in \u0398 will change to a connected state, such that we get another precision matrix \u0398*. For scale-free and hub graph, the ratio of change is 40% based on the sparsity of the two graphs. The diagonal elements of \u0398 and \u0398* are set as |p = 77 OTUs and n = 232 samples . We use Bayesian-multiplicative replacement + used in Algorithm 1 and Algorithm 2 for the numerical solutions of lasso penalized CDTr and DCDTr loss are presented in this Supplementary. We also demonstrate the relationship between D-trace loss and CDTr loss, as well as the relationship between DTL loss and DCDTr loss. The detailed formulas of \u21131-minimization method and joint graphical lasso  are listed in this Supplementary.The matrix operators (PDF)Click here for additional data file."}
+{"text": "Nature Communications 10.1038/ncomms9025, published online 13 August 2018.Correction to: 13).\u2019 This should say \u2018C-terminus\u2019 instead of \u2018N-terminus\u2019. The error has not been fixed in the PDF or HTML versions of the Article.This Article contains an error in the first sentence of the \u2018KIF1A purification and labelling\u2019 section of the Methods, which incorrectly reads \u2018A construct containing the first 382 residues of KIF1A with a His-tag and a Cys residue in the N-terminal, was kindly provided by N. Hirokawa (University of Tokyo, Japan; see ref."}
+{"text": "Nature Communications 10.1038/s41467-019-10278-x, published online 03 June 2019.Correction to: AppNL-G-F\u2019 mice at 24 months  was inadvertently duplicated from the image to its left, the representative image for the \u2018WT\u2019. This has been corrected in both the PDF and HTML versions of the Article.The original version of this Article contained an error in Fig.\u00a02b, in which the representative image for \u2018"}
+{"text": "Scientific Reports 10.1038/s41598-018-37122-4, published online 29 January 2019Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cmetalloproteinases\u201d was incorrectly given as \u201cmetallorproteinases\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "C. albicans,\u201d panel F. Please see the complete, correct There is an error in the caption for"}
+{"text": "Correction to:npj Digital Medicine 10.1038/s41746-019-0099-8, Published online 10 April 2019The original version of the published Article contained an error in the spelling of the first Author\u2019s name. \u201cPaisan Raumviboonsuk\u201d has been changed to \u201cPaisan Ruamviboonsuk\u201d. This has been corrected in the HTML and PDF version of the Article."}
+{"text": "Nature Communications; 10.1038/s41467-018-07599-8; published online 10 December 2018Correction to: The original PDF version of this Article contained an error in Fig.\u00a02, in which only the central part of the figure, between \u2018Mass loading\u2019 and \u2018Gravimetric performance\u2019, was visible. This has been corrected in the PDF version of the Article. The HTML version was correct from the time of publication."}
+{"text": "A generalisation of the Jaynes-Cummings-Hubbard model for coupled-cavity arrays is introduced, where the embedded two-level system in each cavity is replaced by a \u039e-type three-level system. We demonstrate that the resulting effective polariton-polariton interactions at each site are both two-body and three-body. By tuning the ratio of the two transition dipole matrix elements, we show that the strength and sign of the two-body interaction can be controlled whilst maintaining a three-body repulsion. We then proceed to demonstrate how different two-body and three-body interactions alter the mean field superfluid-Mott insulator phase diagram, with the possible emergence of a pair superfluid phase in the two-body attractive regime. Almost all of these studies have focused on the case where each lattice element of the system is comprised of a two-level system interacting with a single photonic mode, resulting in the emergence of quasiparticles, referred to as polaritons.Recently, there has been considerable effort applied to the study of solid-state phenomena in Jaynes-Cummings-Hubbard (JCH) systems. These studies have predicted a superfluid-Mott insulator phase transition15. For example, with a view to better understanding these Pfaffian states, methods of introducing effective three-body interactions in dilute gas Bose-Einstein condensates have been proposed19. In the context of the Bose-Hubbard model20, it has been predicted that three-body interactions can significantly change the superfluid-Mott insulator phase diagram enabling a pair superfluid phase to manifest itself25, for attractive (repulsive) two-body (three-body) interactions. Accordingly, here, we consider a three-level JCH system which supports both two-body and three-body effective contact interactions, on each site of the JCH lattice, and analyse the zero-temperature phases that this system exhibits.In this work we consider the properties of a generalised JCH system where each lattice element is comprised of a three-level system interacting with a single photon mode. Such a model provides an opportunity to construct a Hamiltonian in which three-body interactions are dominant. The effects of such interactions have been of great interest for some time, in part due to their connection to the Pfaffian state that plays a key role in the theory of the fractional quantum Hall effect26 an effective two-body repulsion, for the polariton quasiparticles, is provided by the interactions between the two-level atom and the photons. In this work we wish to consider the impact of three-body interactions and the interplay between two-body and three-body interactions on the properties of the mean-field superfluid-Mott insulator phase diagram. As such we introduce an additional, local, three-body interaction. To achieve this, we generalise the two-level system on each site to a three-level system. There exist a number of possible configurations for a cavity containing a three-level system. Parity considerations restrict the number of viable transition configurations to three - the cascade (\u039e), \u039b and V-type27. However, the restriction to a single cavity mode and the use of the rotating wave approximation28 necessitates the use of solely the cascade configuration, represented in Fig.\u00a0In the standard two-level coupled atom cavity Jaynes-Cummings system\u03b5, see Fig.\u00a0\u03c9. This results in a coupled-cavity array identical to one that has previously been proposed as a platform for the emulation of Pfaffian states via cavity QED14. As we assume that the three-level system is in the \u039e-configuration, we allow for photon-mediated atomic transitions only between the |0a\u232a\u2009\u2192\u2009|1a\u232a and |1a\u232a\u2009\u2192\u2009|2a\u232a atomic levels; we denote the corresponding transition dipole moments as \u03b201 and \u03b212 respectively, with \u03b202\u2009=\u20090. We also introduce the photonic creation and annihilation operators a\u232a\u2009\u2192\u2009|1a\u232a and |1a\u232a\u2009\u2192\u2009|2a\u232a respectively. Subsequently, with na\u2009+\u2009nph\u2009=\u2009n.For simplicity, we model an ideal system with three atomic energy levels equally spaced by n-particle subspace, we work in the ordered basis i\u2009=\u20090 for n\u2009=\u20090, i\u2009=\u20091 for n\u2009=\u20091 and i\u2009=\u20092 for n\u2009\u2265\u20092. For the vacuum, where n\u2009=\u20090, n\u2009=\u20091), 26. However, for n\u2009\u2265\u20092, these new atomic operators are representable via the Gell-Mann matrices, generators of su (3)29, given byFor each n, given byThis yields the matrix blocks to be diagonalised for each n\u2009=\u20090, 1 are necessarily identical to those in the Jaynes-Cummings model27 with the existence of two distinct eigenstates for n\u2009=\u20091. However, it is readily seen from Eq.  has the lowest energy for a given polariton number n. If the arccosine in Eq. .Therefore, the ground state for any polariton number 33. In the three-level system coupled to a single cavity mode, the existence of the third atomic level, and its interaction with the cavity mode, induces an additional three-body nonlinearity14. Furthermore, in this case, the sign of neither the two-body or three-body nonlinearities are immediately evident, but may nonetheless be discerned from inspecting the eigenenergies of the lowest energy polariton branches for each occupation n. For each n, we initially define the quantity Eg(n) to be the eigenenergy of the respective lowest polariton branch, i.e. E\u2212(1) for n\u2009=\u20091 and E(0) for n\u2009=\u20090. The quantity n polaritons in a cavity. Let us initially consider the case where there is a single polariton in the cavity. If the two-body nonlinearity is repulsive, there must be an energy cost associated with adding a second polariton to the cavity, i.e. An effective two-body repulsion for photons is provided in a Jaynes-Cummings cavity by the interactions between the two-level atom and the photons; this is the cause of the photon blockade effectn\u2009=\u20091, 2 yields the critical value 14. That the two-body repulsion-attraction crossover is independent of n\u2009=\u20091 and n\u2009=\u20092 regardless of In the Methods section, we show that taking the difference of the proportional energy 34z is the number of nearest-neighbour sites, a quantity that is dependent on the lattice geometry . This yields an energy approximation consisting of a sum over all sites of the HamiltonianWith the exact single-site solutions in hand we now consider a lattice of such systems with photon hopping permissible between nearest neighbours. For such a system, we wish to compute the resulting zero-temperature mean-field phase diagram. A reasonable first guess would be that the superfluid and Mott insulator phases also exist in this modified system, and thus we proceed to apply the mean-field approximation to the hopping terms to yield a purely local Hamiltonian. Explicitly, this involves the substitution of the expressionself-consistent field approach, which we shall briefly detail here. Initially, we truncate the single-site basis to Fock states |na, nph\u232a such that Nmax\u2009=\u200916. With an initial guess for \u03c8, we diagonalise \u03c8, and the process is repeatedly iterated until adequate convergence is achieved.To numerically diagonalise the Hamiltonian in Eq. , we empl\u03c8 in a given region of parameter space. However, analytical expressions for the phase boundaries may also be found via Landau theory, provided that the transitions are second-order continuous. Following Landau\u2019s prescription, the free energy (which reduces to the many-body ground state energy in the zero temperature limit) may be expressed as a power series in the order parameter \u03c8, i.e34.Subsequently, the phase diagram may be obtained from the solution space by plotting the self-consistently determined values of \u03c8 yields the criterion that the phase boundary is demarcated by solutions to the curve35a2\u2009=\u20090. Solutions to this are especially simple to find if the order parameter \u03c8 is manifest in a perturbative expansion of the ground state energy as a power series, which one finds to be the case in Hubbard-type systems34. To construct this expansion, we note that Eq. n\u232a is cleThe calculation of the second-order perturbative correction is somewhat tedious; we emphasise that in the summation over accessible virtual states in Eq. , the conWe first investigate the regime in which the two-body interaction is predicted to be repulsive, i.e. We now focus on the regime in which we predict the existence of an attractive two-body interaction, that is, when 34, or the JCH system5, or even the system in consideration for \u03c8 is continuous across the transition. A discontinuous, first-order phase transition features a jump in \u03c8 from zero in the disordered phase to a distinct non-zero value in the ordered phase, and the condition a2\u2009=\u20090 does not describe the value of the phase boundary for such transitions37.The discrepancy between the numeric and analytical predictions, for n\u2009=\u20091 Mott lobe for pair superfluid phase, in which superfluidity occurs due to the condensation of (quasi-)particle pairs25. The true pair superfluid phase occurs when \u03c8\u2009=\u20090 and \u03c6\u2009\u2260\u20090, and is associated with the partial breaking of the system\u2019s 24.To understand the nature of the transition it is instructive to recall from Fig.\u00a0see Fig.\u00a0, between38. The relevant Hamiltonian, scaled appropriately such that the interaction strengths are dimensionless, is provided byThis anomalous behaviour in the phase transitions of the three-level JCH system when 19 or a hardcore three-body constraint17. We note that in the Hamiltonian described by Eq. , a sophisticated procedure of spin-model mapping followed by the derivation of an effective field theory has provided a rich understanding of both the phase diagram and the dynamics of the system in each phase22. These studies demonstrate that in the presence of an additional three-body repulsion, the two-body-attractive Bose-Hubbard system exhibits both superfluid  and pair superfluid  phases, with the phase transition between the pair superfluid and the Mott phase being first-order25. Noting the similarities between this system and the three-level JCH system studied here, we predict that when This model has been studied in the context of experimental proposals which suggest that accounting for the three-body loss rate in a Bose-Hubbard model with attractive onsite two-body interactions may potentially result in either an effective finite three-body repulsion mechanismd by Eq. , a hardcvis-a-vis spatially off-diagonal correlations, inherent in the mean-field approximation. It would therefore seem that utilising one or more of the methods employed for the three-body-repulsive, two-body-attractive Bose-Hubbard model\u2013which include an effective potential mechanism with both single and paired source fields23, and quantum Monte Carlo methods24 \u2013 would serve to elucidate the possible pair superfluid phase in the three-level JCH system.However, it is also noted that in these previous studies of similar systems, the phase boundary between the zeroth and second Mott phases is resolved in such a manner that the pair superfluid phase is not merely confined to a straight line at The addition of a third energy level to each \u2018atom\u2019 in a Jaynes-Cummings cavity array is seen here to result in an additional effective three-body repulsion between the resonant cavity photons, analogous to existing modified Bose-Hubbard models with an additional onsite three-body repulsion. By uniformly adjusting the ratio of the two transition dipole moments of each atom, we predict that a crossover manifests itself, between the regimes of two-body repulsion and attraction. Strikingly, this is seen to result in a possible first-order phase transition between the superfluid and Mott vacuum phases, and the coexistence of first- and second-order superfluid-Mott insulator phase transitions across the second Mott lobe. Furthermore, the first Mott lobe vanishes in the regime of two-body attraction.However, the presence of a pair superfluid phase, which our results seem to suggest, is not provable via the methods employed here. Its existence in the three-body constrained Bose-Hubbard model, demonstrated via exact diagonalisation, effective potential and quantum Monte Carlo simulations, motivated our hypothesis that it is also present in this modified Jaynes-Cummings-Hubbard system. Thus it would seem prudent to employ one or more of these to verify the existence of a pair superfluid of polaritons in such a coupled-cavity array.Below we show that the crossover from two-body repulsion to two-body attraction in the modified cavity system occurs when From Eqs , 8, thisThe left-hand side of Eq.  is equalfrom Eq.  that \\doFrom Eqs , 5, 24 wa0 is not required for the determination of the phase boundaries at second-order phase transitions, we include them for the sake of completeness. However, we do require the second-order Landau coefficients, Ek(n) represents the unperturbed energy eigenvalues. We note here that a solution to a2(n)\u2009=\u20090, for a given value of While"}
+{"text": "In this paper, we investigate the existence of common fixed points of a certain mapping in the frame of an extended b-metric space. The given results cover a number of well-known fixed point theorems in the literature. We state some examples to illustrate our results. Throughout the manuscript, we denote b-metric, a number of authors have reported several interesting results in this direction X be a nonempty set and  The function d is called a b-metric and the space b-metric space, in short, bMS.Let b-metric is the following.The immediate example of Let b-metric space. Notice also that if It is evident that b-metric becomes a usual metric.It is clear that for Recently, Kamran  introducX be a nonempty set and b-metric if, for all  The pair b-metric space, in short extended-bMS.Let bMS.If Let (i)Let (ii)For b-metric space.In conclusion, for any Obviously, bMS, are defined as follows [Some fundamental concepts, like convergence, Cauchy sequence, and completeness in a extended- follows .bMS. (i)X is said to converge to A sequence (ii)X is said to be Cauchy if, for every A sequence Let b-metric space X is convergent.An extended-Letbe a complete extended-bMS. Ifis continuous, then every convergent sequence has a unique limit.Letbe an extended-bMS such thatis a continuous functional. Letsatisfyfor allwhereis such that, for eachhereThenThas precisely one fixed pointu. Moreover, for eachFor our purposes, we need to recall the following definition which is proposed by Popescu .T is an \u03b1-orbital admissible if, for all Let X is regular with respect to mapping X such that n and n.A set bMS Suppose that We start with the following lemma which is essential in our main results.Letbe an extendedb-metric space.If there existssuch that the sequencefor an arbitrarysatisfiesand alsofor anythen the sequenceis Cauchy inX.Let equality  recursivOn the other hand, by b-metric space On the other hand, by employing the ratio test, we conclude that the series Letbe two self-mappings on a complete extended-bMSsuch that the pairforms anorbital-cyclic admissible pair. Suppose that(i)for eachwherefor each(ii)there existssuch that(iii)eitherSandTare continuous, or(iii*)ifis a sequence inXsuch thatthenandMoreover, if for allandthen the pair of the mappingspossesses a common fixed pointu, that is, By assumption (ii), there exists a point Recursively, we obtainS and T, which finalizes the proof. More precisely, to see that u is the common fixed point of S and T, we shall examine the following two cases. First, we assume that T. Now we shall prove that T and S. Analogously, one can derive the same conclusion for the case Without loss of generality, we assume that x2k+1 in  and 12)\\documentThus, throughout the proof, we suppose thatCase (a): Let equality , 12), w, w\\documCase (b): Let equality , 12), w, w\\documT and S, we getT and S have a common fixed point u.\u2003\u25a1Combining  and 17)17), we cmentclasspt{minimaegarding  and 22)18\\documeLet bMS : For Case (b): Let Case (c): Let Case (d): Let T has a unique fixed point, Therefore, all the conditions of Theorem X be a nonempty set, T is an Let for all LetTbe a self-mapping on a complete extended-bMSsuch that the mappingTforms anorbital-cyclic admissible mapping. Suppose that(i)for eachwhere(ii)there existssuch thatand(iii)eitherTis continuous, or(iii*)ifis a sequence inXsuch thatthenandMoreover, if for allandthen the pair of the mappingsTpossesses a fixed pointu, that is, It is sufficient to take Let Define also T is X such that We show that For (a): For laced in  we get\\(b): For his case  is obvio(c): For ent}y=2,  becomesT has a fixed point, (d): For all other cases, equality  holds. TLetTbe a self-mapping on a complete extended-bMSsuch thatTis an\u03b1-orbital admissible mapping. Suppose that(i)for eachwhere(ii)there existssuch that(iii)eitherTis continuous, or(iii*)ifis a sequence inXsuch thatthenMoreover, if for allandthen the pair of the mappingsTpossesses a fixed pointu, that is, It is sufficient to take b-metric Let T for T. We show that T is an \u03b1-orbital admissible mapping. If T is \u03b1-orbital admissible. In reason of the above arguments, Define also T has a unique fixed point, Note that, for each Let (H)For all  Here, T and S.Notice that in this section we investigate the existence of (common) fixed points of certain operators. For the uniqueness of a fixed point of the observed results, we will consider the following hypothesis. Adding condition (H) to the hypotheses of Theorem\u00a0we obtain thatuis the unique fixed point ofT.v is another fixed point of T. From (H), there exists T satisfies , one can suggest different conditions, see, e.g.,\u00a0.b-metric space.It is clear that one can list several consequences from our results. By letting On the other hand, regarding the techniques used in , one can"}
+{"text": "Materials and Methods section, subsection 3D Microfluidic Co-Culture and Blocking Experiments, where it was written that 100\u2009\u00b5g/mL of anti-PD-L1-blocking or anti-PD-1-blocking antibody or their respective isotype control was used. The correct concentration is 10\u2009\u00b5g/mL. The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way.In our original research article, there was an error in the The original article has been updated.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Correction to: BMC Genomicshttps://doi.org/10.1186/s12864-019-5947-zFollowing the publication of the original article , the autIn the section \u201cPhasiRNA analysis\u201d there was an error in the first equation in the PDF version of the article. A fraction bar was erroneously introduced between (20\u2009m and n-x), (m and x), and (21\u2009m and n).The incorrect version was:The correct version is:Furthermore, due to the formatting of Table\u00a0The publisher would like to apologize to the authors and readers for any inconvenience caused. The original article has been corrected."}
+{"text": "The main results are the identification of several shape-preserving properties of these operators, including their monotonicity- and convexity-preserving properties with respect to n and q of In this paper, we introduce a new family of generalized Bernstein operators based on  In 1997, Phillips [q-Bernstein polynomials, and for decades thereafter the application of q integers in positive linear operators became a hot topic in approximation theory, such as generalized q-Bernstein polynomials [q-Bernstein operators [q-Bernstein operators [q integers play important roles not only in approximation theory, but also in CAGD. Based on the Phillips q-Bernstein polynomials [q-B\u00e9zier curves using the basis functions of Phillips q-Bernstein polynomials. Di\u015fib\u00fcy\u00fck and Oru\u00e7 [q generalization of rational Bernstein\u2013B\u00e9zier curves and tensor product q-Bernstein\u2013B\u00e9zier surfaces. Moreover, Simeonov et al. [q blossom, which is specifically adapted to developing identities and algorithms for q-Bernstein bases and q-B\u00e9zier curves. In 2014, Han et al. [q-analog B\u00e9zier curves with one shape parameter, and established degree evaluation and de Casteljau algorithms and some other properties. In 2016, Han et al. [q integers, and investigated the generalized rational B\u00e9zier curve from a geometric point of view, obtaining degree evaluation and de Casteljau algorithms, etc.A\u00a0generalization of Bernstein polynomials based on Phillips  proposedynomials \u20136, Durrmperators \u201313, etc.ynomials , which aynomials \u201316. In [ynomials , Oru\u00e7 anand Oru\u00e7 , 16 defiv et al.  introducn et al.  proposedet al. [\u03b1-Bernstein operators, and investigated some approximation properties, such as the rate of convergence, Voronovskaja-type asymptotic formulas, etc. They also obtained the monotonic and convex properties. For \u03b1, the \u03b1-Bernstein operators they introduced are defined as\u03b1-Bernstein polynomial n is defined by Recently, Chen et al.  introducq analogue of \u03b1-Bernstein operators, called Motivated by above research, in this paper we propose the q integers, the details of which can be found in [k, we denote q-integers by q-factorial and q-binomial coefficients are defined as follows:q-analog of q derivative and q derivative of the product are defined as Here, we mention some definitions based on found in , 22. Forn and q of The rest of this paper is organized as follows. In the next section, we give some basic properties of the operators For proving the main results, we require the following lemmas.We have the following equalities:By , we havea and\u00a0b.From Lemma\u00a0We immediately obtain Lemma\u00a0For all functionsfandgdefined inreal numbers\u03bb, \u03bcdefined inandthe following statements hold true. (i)Endpoint interpolation: and(ii)Linearity: (iii)Non-negative: Forandiffis non-negative onso isBernstein operators(iv)Monotone: For fixedandifthen(i)TheBernstein operators may be expressed in the formwherewith(ii)The higher-order forward difference ofmay be expressed in the formwherewhich is defined in , we notn.Finally, if Ifis convex onfor fixedandwe havef and g are convex on Combining  and 18)18), and ;x) (see ). The deLetting the convex function n and q of In this paper, we proposed a new family of generalized Bernstein operators, named"}
+{"text": "The employment of mobile vehicles to charge sensors via wireless energy transfer is a promising technology to maintain the perpetual operation of wireless sensor networks (WSNs). Most existing studies assumed that sensors are powered with off-the-shelf batteries, e.g., Lithium batteries, which are cheap, but it takes some non-trivial time to fully charge such a battery . The long charging time may incur long sensor dead durations, especially when there are many lifetime-critical sensors to be charged. On the other hand, other studies assumed that every sensor is powered with an ultra-fast charging battery, where it only takes some trivial time to replenish such a battery, e.g., 1 min, but the adoption of many ultra-fast sensors will bring about high purchasing cost. In this paper, we propose a novel heterogeneous sensor network model, in which there are only a few ultra-fast sensors and many low-cost off-the-shelf sensors. The deployment cost of the network in the model is low, as the number of ultra-fast sensors is limited. We also have an important observation that we can significantly shorten sensor dead durations by enabling the ultra-fast sensors to relay more data for lifetime-critical off-the-shelf sensors. We then propose a joint charging scheduling and routing allocation algorithm, such that the longest sensor dead duration is minimized. We finally evaluate the performance of the proposed algorithm through extensive simulation experiments. Experimental results show that the proposed algorithm is very promising and the longest sensor dead duration by it is only about 10% of those by existing algorithms. Wireless sensor networks are widely used in many Internet of Things (IoTs) applications, including video monitoring, traffic control, structural health monitoring, radiation detection, forest fire and volcanor monitoing, etc. ,2,3,4,5.Many researchers proposed to prolong sensor lifetimes by enabling them to harvest energy from their surrounding environments, such as solar energy, wind energy, etc. ,10. HoweA lot of attention has been paid to the vehicle charging scheduling for wireless sensor networks. Most of these studies assumed that sensors are powered with off-the-shelf batteries ,23,24,25Although excellent studies have been conducted for shorten sensor dead durations,\u00a0some sensors still expire their energy for some durations,\u00a0as the charging time of a sensor is non-trivial . For example, in ing time . It can On the other hand, other researchers ,28,29,30It is obvious that the adoption of ultra-fast sensors can significantly shorten sensor dead durations or even avoid their energy expirations. For example, in It can be seen that, although the adoption of off-the-shelf sensors is cheap, but the dead durations of sensors may be long due to the long charging time of the sensors. Contrarily, the adoption of many ultra-fast sensors can significantly shorten sensor dead durations, but the adoption will incur a high purchasing cost. For example, the price of an ultra-fast charging battery is usually about 30\u201340 dollars, which is about ten times the cost of an off-the-shelf battery, e.g., a Lithium battery with the same capacity costs only 2\u20133 dollars ,31. TherIn this paper, we propose a novel heterogeneous sensor network model, in which there are only a few ultra-fast sensors and many low-cost off-the-shelf sensors in a sensor network. The ultra-fast sensors are deployed at some strategic locations near to the base station, as the sensors close to the base station need to relay a large amount of data from other remote sensors.We here illustrate a heterogeneous sensor network. In We, however, observe that we can further reduce sensor dead durations by jointly considering charging scheduling and routing allocation in the heterogeneous sensor network. We can enable ultra-fast sensors to relay more data than off-the-shelf sensors, since the former can be quickly charged. For example, sensor n v3 see c.Then, the residual lifetime In this paper, we propose a novel heterogeneous network model, where a sensor network consists of only a few ultra-fast sensors and many low-cost off-the-shelf sensors. Then, the cost of deploying such a sensor network is low, due to the limited number of deployed ultra-fast sensors. On the other hand, we can significantly shorten sensor dead durations by not only scheduling the charging vehicle but also allocating routing among sensors smartly.Unlike existing studies that either assumed that all sensors are powered with low-cost off-the-shelf batteries, or assumed that every sensor is equipped with a high-cost ultra-fast charging battery, in this paper, we propose a novel heterogeneous sensor network model, where a sensor network consists of a few ultra-fast sensors and many low-cost off-the-shelf sensors. The deployment cost of such a network then is very low.Under this novel network model, we study a fundamental problem of joint charging scheduling and routing allocation, such that the longest sensor dead duration is minimized. We also propose an efficient algorithm for this problem.We finally evaluate the performance of the proposed algorithm through extensive simulation experiments. The experimental results show that the proposed algorithm is very promising, and the longest sensor dead duration by it is only 10% of those by existing algorithms.The main contributions in this paper are highlighted as follows:The rest of this paper is organized as follows: In this section, we first introduce a novel heterogeneous network model and then present the charging model. We finally define the problem.b is a base station for collecting data from all sensors.We consider a wireless sensor network We assume that there are two types of sensors in the network. The first type of sensors are powered by off-the-shelf batteries, e.g., Lithium battery, and it usually takes a while to fully charge such a sensor, e.g., 30\u201380 min . The othWe now consider the placement of sensors. We assume that the off-the-shelf sensors are randomly deployed. On the other hand, since the communication range of a sensor is limited, sensors close to the base station have to relay sensing data from other remote sensors. Therefore, the former sensors consume more their energy on relaying data than the latter ones. We thus assume that the ultra-fast sensors are deployed at some strategic locations near to the base station, as they can be quickly charged.\u00a0For example, the ultra-fast sensor can be co-located with the most energy-consuming off-the-shelf sensors.We assume that there is an edge t. On the other hand, following [t is t, respectively, t is Assume that each sensor  routing ,33. Eachollowing , the enes m/s.As the energy stored in every sensor battery is limited, it will run out of its energy due to data sensing, data transmission and data reception. To provide controllable and perpetual energy to sensors, we employ a charging vehicle equipped with a recharging device to replenish sensor energy. Denote by The energy consumptions of different sensors vary significantly, i.e., some sensors may have little energy left while the others consume only a small fraction of their energy. Then, it is unnecessary for the vehicle to charge all sensors in each round, and sensors should be charged in an on-demand manner. To this end, each sensor V be the set of to-be-charged sensors in the current charging round. There are two types of sensors in set V, the lifetime-critical off-the-shelf sensors in V, as they are deployed at strategic locations where data traffics are extremely heavy. Moreover, it only takes a very short time to fully charge an ultra-fast sensor, and the number of ultra-fast sensors Let C of the charging vehicle for the sensors in V and allocate routing for the network V along tour C one by one  shows the flow reservation of each sensor In this section, we devise a joint charging scheduling and routing allocation algorithm for the dead duration minimization problem. We first present the framework of the algorithm, which invokes two algorithms for two subproblems of the original problem. We then detail the two algorithms.C for the charging vehicle to replenish sensors in V, such that the longest dead duration of sensors is minimized. It can be seen that the allocation of routing C are tightly coupled. On one hand, the residual lifetime of each sensor is highly related to the routing C is delivered, the start charging time that each sensor will be charged by the vehicle can be derived, by following Constraint\u00a0(7). The routing C, such that the longest dead duration of sensors in V is minimized, and this subproblem is referred to as the charging scheduling subproblem. In the second subproblem, we assume the charging tour C is given, and the subproblem is to allocate the routing the routing allocation subproblem. We will propose two algorithms for the two subproblems in two later subsections, respectively. Having the two algorithms, we devise a joint charging scheduling and routing allocation algorithm as follows.Recall that the dead duration minimization problem is to allocate the routing Kth iteration, respectively. Similarly, denote by Kth iteration, respectively, where K, the algorithm consists of two steps. In the first step, with the given routing The algorithm iteratively finds the routing and charging tour. Denote by Algorithm 1 Joint charging scheduling and routing allocation algorithm (CSRA).Input: a set V of to-be-charged sensors, the residual energy Output: routing C. \u00a0\u00a01:Obtain a routing \u00a0\u00a02:fordo\u00a0\u00a03:\u2003Find a charging tour \u00a0\u00a04:\u2003Obtain a routing \u00a0\u00a05:\u2003Let \u00a0\u00a06:ifthen\u2003\u00a0\u00a07:\u2003\u2003\u00a0\u00a08:\u2003\u2003break;\u00a0\u00a09:else\u200310:\u2003\u200311:end if\u200312:ifthen\u200313:\u2003\u2003/* the difference of the longest sensor dead durations 14:\u2003\u2003break;15:end if\u200316:end for17:return charging tour C, and routing The algorithm for the dead duration minimization problem is presented in Algorithm\u00a01.V is minimized, i.e.,Given a set Assume that the charging time of each lifetime-critical off-the-shelf sensor in nstant\u00a0\u03b4 , e.g., \u03b4 vs. 1 h . Let \u0394=\u03b4Since it takes only a very short time to fully charge ultra-fast sensors in Algorithm 2 Algorithm for the charging scheduling subproblem.Input: a set V of to-be-charged sensors, routing Output: charging tour 1:V; Calculate the residual lifetime 2:Find a charging sub-tour 3:Sort sensors in 4:Find a charging sub-tour 5:Let 6:return charging tour The algorithm for the charging scheduling subproblem is presented in Algorithm\u00a02.\u00a0We later will showthat Algorithm\u00a02 delivers an optimal solution to the charging scheduling subproblem see .AlgoritV of to-be-charged sensors, and the charging tour V, the routing allocation subproblem is to find the routing V is minimized, i.e.,V, Given a sensor network To obtain the optimal flow rates, we rewrite constraint\u00a0 as:(10)tWe note that the objective function in problem nstraint  is not aV. The basic idea behind is to guess the optimal value To solve problem When P P4 see . OtherwiAlgorithm 3 Algorithm for the routing allocation subproblem.Input: a set V of to-be-charged sensors, the residual energy Output: routing \u00a0\u00a01:V by Constraint\u00a0(7);Calculate the start charging time \u00a0\u00a02:Let \u00a0\u00a03:whiledo\u2003\u00a0\u00a04:\u2003Let \u00a0\u00a05:if there are no feasible solutions then\u2003\u00a0\u00a06:\u2003\u2003/* the guess \u00a0\u00a07:\u2003\u2003Let \u00a0\u00a08:else\u2003\u00a0\u00a09:\u2003\u2003/* the guess 10:\u2003\u2003Let 11:end if\u200312:end while13:Let 14:Find a feasible solution 15:return routing The algorithm for the routing allocation subproblem is given in Algorithm\u00a03.In this section, we analyze the proposed algorithms for the charging scheduling subproblem and routing allocation subproblem in V, such that the longest dead duration of sensors in V is minimized, given routing Recall that the objective of the charging scheduling subproblem is to find a charging tour Theorem\u00a01.Given a set V of to-be-charged sensors, Algorithm 2 delivers an optimal solution to the charging scheduling subproblem.Proof\u00a0of\u00a0Theorem\u00a01.For the sake of convenience, assume that n in In the following, we show that sub-tour i) Consider  and (17), we have thatTherefore, we have We finally analyze the time complexity of Algorithm 2. We first obtain a sub-tour In this subsection, we show that Algorithm 3 delivers an optimal solution to the routing allocation subproblem by Theorem 2.Theorem\u00a02.Algorithm 3 delivers an optimal solution to the routing allocation subproblem.Proof\u00a0of\u00a0Theorem\u00a02.i) there are no feasible solutions to the Linear Programming (LP) In i) there are no feasible solutions to LP We first show , by increasing the number of iterations In the following, we study the impact of the network size, the maximum data sensing rate, the off-the-shelf sensor charging rate, the vehicle traveling speed, and the number of ultra-fast sensors.We first evaluate the performance of the proposed algorithm CSRA against existing algorithms TSP, NETWRAP, AA, TSCA, by varying the number We then investigate the performance of the algorithms, by increasing the maximum data sensing rate We also evaluate the algorithm performance, by varying the charging rate s on the algorithm performance, by varying the speed s from 1 m/s to 10 m/s. We further study the impact of the vehicle traveling speed We finally investigate the performance of different algorithms, by increasing the number of ultra-fast sensors In summary, it can be seen from the experimental results that the longest and average sensor dead durations by the proposed algorithm CSRA are much shorter than those by existing algorithms TSP, EDF, NETWRAP, AA and TSCA.The employment of mobile charging vehicles is a promising technique to replenish sensor energy, and the vehicle scheduling for prolonging network lifetimes has been studied in literature. Most of these studies assumed that every sensor is powered with a low-cost off-the-shelf battery ,38,39,40Some studies employed only one charging vehicle to charge sensors in a sensor network ,19,20,23On the other hand, some other studies ,38,39,40It can be seen that, although excellent studies have been conducted for replenishing sensor energy and shortening their dead durations, some sensors may still expire their energy, as the charging time of a sensor is non-trivial, e.g., 30\u201380 min .We note that other researchers ,28,29,30Different from these mentioned existing studies, in this paper, we propose a novel heterogeneous network model by deploying a few ultra-fast sensors at some strategic locations near the base station. The network cost is low, since we deploy only a few expensive ultra-fast sensors. On the other hand, we show that the network performance can be significantly improved with even such a small number of ultra-fast sensors, by enabling ultra-fast sensors to relay more data for other lifetime-critical sensors.Unlike exiting studies that deployed only off-the-shelf sensors or ultra-fast sensors, in this paper, we proposed a novel heterogeneous sensor network model, in which a sensor network consists of a few ultra-fast sensors and many low-cost off-the-shelf sensors. Then, the deployment cost of the network is low as the number of ultra-fast sensors is limited. Under the novel network model, we studied a problem of finding a charging tour and allocating routing, such that the longest sensor dead duration is minimized. We further devised an efficient algorithm for the problem, by enabling ultra-fast sensors to relay more data from lifetime-critical off-the-shelf sensors. We finally evaluated the proposed algorithm through extensive simulations. In addition, experimental results showed that the longest sensor dead duration by the proposed algorithm is much shorter than those by existing algorithms, e.g., 90% shorter."}
+{"text": "Recently, Abadie et al.  have expanded synthetic control methods by the so-called cross-validation technique. We find that their results are not being reproduced when alternative software packages are used or when the variables\u2019 ordering within the dataset is changed. We show that this failure stems from the cross-validation technique relying on non-uniquely defined predictor weights. While the amount of the resulting ambiguity is negligible for the main application of Abadie et al. , we find it to be substantial for several of their robustness analyses. Applying well-defined, standard synthetic control methods reveals that the authors\u2019 results are particularly driven by a specific control country, the USA. As a tool for policy evaluation, cross-validation: the predictor weights, whose data in the training period (first part of the pre-treatment period) are used to find optimal donor weights for synthesizing the treated unit, are selected such that the out-of-sample error in the validation period (second part of the pre-treatment period) is minimized.Over the last few years, many studies have applied SCM across several fields, e.g., When measuring the effect of the 1990 reunification on Germany\u2019s GDP per capita using the software package R, another set of predictor weights: 71.0% (GDP), 11.1% (investment), 7.9% (trade), 6.4% (schooling), 2.7% (inflation), and 0.9% (industry). The corresponding weights for the countries synthesizing Germany were much closer to, but still different from the values found by Abadie et al. (2015)When trying to replicate these results using the software package Stata, however, we found different predictor weights: 84.5% (GDP), 4.5% (investment), 5.1% (trade), 4.2% (schooling), 0.5% (inflation), and 1.2% (industry). The corresponding synthetic Germany was slightly different from the one obtained by Closer inspection shows that the failure to reproduce the results of We therefore investigate the corresponding ambiguity by conducting large-scaled Monte Carlo studies. The variation of the estimated post-treatment development of West German GDP is very small, with all estimates being significantly above Germany\u2019s actual GDP. Concerning several robustness studies of The remainder of the paper unfolds as follows: the \u201cIn the following, we describe how synthetic control methods work both with and without the cross-validation technique. Many additional explanations, in particular on how to select potential comparison units and predictor variables, are provided in Abadie et al. (2015)Y, and predictor variables, usually denoted by X. These are considered both for a unit that has at some point in time been \u201ctreated,\u201d usually denoted by the subscript \u201c1,\u201d and for so-called donor units. The latter are units not too different from the first one, but unaffected from the treatment, and denoted by the subscript \u201c0.\u201d In the example discussed throughout this paper, the treated unit is Germany which has been reunified in 1990, the variable of interest is GDP per capita, and predictors are (pre-treatment) GDP per capita, a measure for trade openness, the inflation rate, the industry share of value added, the amount of schooling attained, and the investment rate. The donor units consist of sixteen OECD countriesW: these weights describe to what extent each donor country is used to produce a \u201csynthetic\u201d  Germany. Thereby, the weights should be such that synthetic Germany mimics actual Germany as well as possible with respect to the (pre-treatment) predictor variables. For the example at hand, this means that the differences between actual and synthetic Germany with respect to GDP per capita, trade openness, inflation rate, industry share, schooling, and investment rate should be as small as possible. As we have six predictors (k=6), operationalizing the last statement requires introducing some weighting scheme. These non-negative so-called predictor weights are usually denoted by vm or V, and the cross-validation technique introduced in For the synthetic control method, we have two types of data: the variable of interest, often denoted by the letter k\u00d7J)-matrix k-dimensional vector V=, the donor weights J-dimensional non-negative donor weights W summing to unity, i.e., as the solution of In the training period, one makes use of the -matrix L-dimensional vector V, i.e., V\u2217 is a minimizer of8In the validation period, one uses the -matrix k-dimensional vector where the  by Eq. . These \u201cmentclass2pt{minimIn contrast, the standard synthetic control method consists of only one step, not distinguishing between a training and validation period.k\u00d7J)-matrix k-dimensional vector V=, the standard SCM approach defines the donor weights W\u2217(V) as the minimizer of Instead, all pre-treatment data are used, in our application those from 1971 to 1990, to build the following quantities: the  are then used for synthesizing the treated unit. For a schematic overview of standard SCM, see Fig.\u00a0The donor weights unique minimizer of the out-of-sample error V\u2217 unambiguously. The reason is that the mapping V are different after scaling. Less formally, it is often the case that different predictor weights lead to the same \u201ctraining\u201d weights. The problem of the cross-validation approach is that such different predictor weights V, although scaled and entailing identical A crucial insight as to why the cross-validation technique of entclass1pt{minimap of Eq. .W weights training\u201d rows of columns \u201cADH,\u201d \u201cOrig.,\u201d and \u201cAlph.\u201d of Table\u00a0V are equivalent with respect to Eq.  are used, but only five donor units obtain positive weights in the training period  although V are different after scaling. However, in contrast to the cross-validation method, this is not a problem, as predictor weights are not used as input for a second step with different predictor data. Instead, the unique donor weights W\u2217(V\u2217) are the only quantity needed to synthesize the treated unit and estimate treatment effects, and therefore the standard synthetic control method leads to well-defined estimators, in contrast to the cross-validation approach. This can also be seen from Table\u00a0Eventually, the standard synthetic control method does \u2217 to Eq. , in comp\u2217 to Eq. . Again, d by Eq.  is oftenhttps://dataverse.harvard.edu/dataverse/ajps) both the data and all code of For the upcoming analysis, we retrieved from the AJPS Data Archive on Dataverse =0 for all j with For any given predictor weights \u2217 of Eq.  must fulj, consider fj at \u03b4=0, \u03b4)W\u2217+\u03b4ej would for small positive \u03b4 yield a smaller value in (W\u2217. For j with \u03b4)W\u2217+\u03b4ej will have non-negative components summing to unity even for negative \u03b4 that are small enough in absolute value. Therefore, \u03b4)W\u2217+\u03b4ej for small negative \u03b4 would yield a smaller value than W\u2217 in Eq. \u22650 for all j with dj=0 for all j with dj is a linear function of v1,\u2026,vk, the conditions for V to belong to k unknown quantities v1,\u2026,vk, we have \u03b1 linear equations and J\u2212\u03b1 linear inequalities, with J denoting the number of donor units, and Fixing k\u2212\u03b1 between the number of economic predictors (k) and the number of donor units with positive W weight in the \u201ctraining\u201d period (\u03b1) is positive. The larger the difference k\u2212\u03b1, the larger is typically the ambiguity induced by the cross-validation technique.The cross-validation method is typically not well-defined if the difference V weights. In particular, this entails that as soon as k\u2212\u03b1.Finally, notice that"}
+{"text": "A dataset of measurements of ETSI ITS-G5 Dedicated Short Range Communications (DSRC) is presented. Our dataset consists of network interactions happening between two On-Board Units (OBUs) and four Road Side Units (RSUs). Each OBU was fitted onto a vehicle driven across the FLOURISH Test Track in Bristol, UK. Each RSU and OBU was equipped with two transceivers operating at different frequencies. During our experiments, each transceiver broadcasts Cooperative Awareness Messages (CAMs) over the licensed DSRC band, and over the unlicensed Industrial, Scientific, and Medical radio (ISM) bands 2.4 GHz-2.5 GHz and 5.725 GHz-5.875 GHz.Each transmitted and received CAM is logged along with its Received Signal Strength Indicator (RSSI) value and accurate positioning information. The Media Access Control layer (MAC) layer Packet Delivery Rates (PDRs) and RSSI values are also empirically calculated across the whole length of the track for any transceiver. The dataset can be used to derive realistic approximations of the PDR as a function of RSSI values under urban environments and for both the DSRC and ISM bands \u2013 thus, the dataset is suitable to calibrate (simplified) physical layers of full-stack vehicular simulators where the MAC layer PDR is a direct function of the RSSI. The dataset is not intended to be used for signal propagation modelling.The dataset can be found at https://doi.org/10.5523/bris.eupowp7h3jl525yxhm3521f57, and it has been analyzed in the following paper: I. Mavromatis, A. Tassi, and R. J. Piechocki, \u201cOperating ITS-G5 DSRC over Unlicensed Bands: A City-Scale Performance Evaluation,\u201d IEEE PIMRC 2019. [Online]. Available: https://arxiv.org/abs/1904.00464. When two vehicles were present, one was driven in a clockwise direction while the other in an anticlockwise fashion. Each vehicle was equipped with an OBU operating the same set of transceivers that we employed in each RSU. Further details about both the hardware and software pertaining to the RSUs and OBUs can be found in All the RSUs and OBUs communicate using ETSI's ITS-G5 standard Each transmitted and received CAM has been recorded both in the CSV and PCAP traces. When a packet appears in the transmission or reception queue of a transceiver, a decision is made whether it is going to be recorded or not. The flowchart describing that, can be seen in In particular, for what concerns an RSU, raw data recorded during a specific day of trial and pertaining to a specific transceiver, is recorded under the following filename and directory naming convention:./rawData/ddmmyyyy/RSUs-ddmmyyyy/log_XX_YY.txt and./rawData/ddmmyyyy/RSUs-ddmmyyyy/log_XX_TCP_YY.pcap where \u201cddmmyyyy\u201d signifies the date when the experiment took place, \u201cXX\u201d can either be \u201cHP\u201d or \u201cLP\u201d depending on the transceiver under consideration, and \u201cYY\u201d refers to one of the four RSUs . Thus, for instance, files \u201c./rawData/11022019/RSUs-11022019/log_HP_MVB.txt\u201d and \u201c./rawData/11022019/RSUs- 11022019/log_HP_TCP_MVB.txt\u201d refer to the HP transceiver of the RSU located on the MVB site during the 11th February 2019. A similar conversion has been adopted for recording raw data associated with the OBUs, which is defined as follows:./rawData/ddmmyyyy/OBU-ZZ-ddmmyyyy-TT/log_XX.txt and./rawData/ddmmyyyy/OBU-ZZ-ddmmyyyy-TT/log_XX_tcpd.pcap where \u201cZZ\u201d can be either equal to \u201c00\u201d or \u201c01\u201d depending of the fact the data refers to the first or the second OBU, respectively. Then, if data refers to an experimental session that took place in the morning then \u201cTT\u201d is equal to \u201cMorning\u201d, otherwise, \u201cTT\u201d is set equal to \u201cAfternoon\u201d. For instance, files \u201c./rawData/11022019/OBU-00-11022019-Morning/log_HP.txt\u201d and \u201c./rawData/11022019/OBU-00-11022019-Morning/log_HP_tcpd.pcap\u201d refer to the experimental session recorded in the morning of 11th February 2019 and referring to the HP transceiver of the first OBU.The raw data part of our dataset has been filtered by means of our MATLAB framework \u2022Heatmaps for the PDR values associated with the HP/LP transceivers across the roads forming the FLOURISH Testing Track. A sample of the sixteen resulting figures is shown in \u2022Awareness horizons for both HP and LP transceivers showing the PDR as a function of the distance to a given RSU. A sample of the sixteen resulting figures is shown in \u2022RSSI value for both HP and LP transceivers as a function of the distance to a given RSU. A sample of the thirty-two resulting figures is shown in \u2022Our framework can be used to generate the entire set of figures for all the above-mentioned KPIs. It can also be further extended to accommodate different or more specific KPIs per-taining to the network interactions at specific road junctions at specific time of the day, or the network interactions among moving vehicles. As for the latter, for convenience, our MATLAB framework Our MATLAB framework 1.Modifying the two main loops of the script, namely, the loops associated with the day and the transmission power. The user can then choose to evaluate the results for a specific day or TX power. Based on that, our framework will load only the network interactions related to the chosen day and TX power.2.Modifying the internal loops of our script, namely, the ones related to the OBUs and the RSUs. One or more specific pairs of OBU/RSU can be chosen to be processed.3.Similarly to the \u201cv2vInteractions.m\u201d script, the unique sequence number for the transmitted packets per session, as well as the MAC address of the transmitter can be parsed at first.4.Using the above information, it can be identified whether a packet is successfully delivered or not, i.e., checking whether a packet with the given MAC address and sequence number exists in the list of received packets.5.Having this pairwise correlation between transmitted and received packets, a table can be later generated by incorporating all the given interactions between a set of devices (as in \u201cv2vInteractions.m\u201d).6.The above steps can be replicated for the requested number of OBU-RSU pairs generating a list of all the desired network interactions.Our MATLAB framework also gives the reader the option of filtering the entire dataset to retrieve all the network interactions between the pair of OBUs considered in our experiments. In particular, when the script \u201cv2vInteractions/v2vInteractions.m\u201d is executed, it produces a table-formatted MAT file (for each day and transceiver) defined by the columns summarized in"}
+{"text": "N\u2009=\u2009101) ASD traits (measured using the Autism-spectrum Quotient) were associated negatively and significantly with the strength of both explicit gender self-concept  and implicit gender self-concept (measured using an Implicit Association Task). Further analyses showed that a subgroup with high/clinically significant ASD traits showed significantly weaker explicit and implicit gender self-concepts than a subgroup with low ASD traits. Results were similar in both males and females, although there was some evidence of a selective influence of ASD traits on implicit gender self-concept among females only.A link between autism spectrum disorder (ASD) and gender identity difficulties has been suggested. In this study, we found that, among adults from the general population (The online version of this article (10.1007/s10803-019-04262-z) contains supplementary material, which is available to authorized users. Gender describes a constellation of traits, behaviours, and roles attributed to males and females within society .Despite their extensive use in research, these self-report measures rely on accurate self-awareness of one\u2019s own traits  and are considered susceptible to the effects of self-presentation . ASD is a neurodevelopmental disorder diagnosed on the basis of significant behavioural difficulties with social-communication and a restricted, repetitive pattern of interests and behaviour  took part in the current online experiment. Their average age was 36.93  years. Ninety-four percent of participants reported English as their first language and all were cisgender. Thirteen of the 101 participants had a formal diagnosis of autism, according to self-report. Participants were recruited through the Amazon\u2019s online crowdsourcing platform MTurk and received compensation for their time. Informed consent was obtained from all individual participants included in the study. Ethical approval for this study was obtained from Kent School Psychology Research Ethics Committee.To measure implicit gender self-concept, we employed the IAT described by Greenwald and Farnham . The tasWords appeared on the middle of a computer screen in a random order and category labels were always presented in the upper right and left corners of the screen.All stimuli were presented to participants before the beginning of the task, and they were instructed to study the items that belonged to each category for 25\u00a0s. In block 1, the \u201cself\u201d category label was presented in the upper left corner of the screen and the \u201cother\u201d category label in the upper right corner. Participants had to sort words that belonged either to the \u201cself\u201d or the \u201cother\u201d category, by pressing the \u201cz\u201d key of a keyboard for words related to \u201cself\u201d and the \u201cm\u201d key for words related to \u201cother\u201d. In block 2, categories referred to \u201cfeminine\u201d and \u201cmasculine\u201d attributes. The \u201cfeminine\u201d category label was presented in the upper left corner and the \u201cmasculine\u201d category in the upper right corner. Participants were instructed to press the \u201cz\u201d key for words belonged to \u201cfeminine\u201d category and the \u201cm\u201d key for items belonged to \u201cmasculine\u201d category.In block 3, the four categories were presented combined  and participants practiced the sorting task, by pressing the key that was assigned to each category in the preceding two blocks . In block 4, they completed the first experimental condition of the sorting task. In block 5, the \u201cself\u201d category label was presented in the upper right corner and the \u201cother\u201d category label in the upper left corner, subsequently the assignment of the key for each category was reversed compared to the first block. Participants had to press \u201cm\u201d for items belonged to the \u201cself\u201d category and \u201cz\u201d for items belonged to the \u201cother\u201d category.In block 6, they practiced the combined task using the switched key assignments. That is, participants were instructed to press the \u201cz\u201d key to categorise items that belonged either to the \u201cother\u201d or to the \u201cfeminine\u201d category and the \u201cm\u201d key for words that belonged either to the \u201cself\u201d or \u201cmasculine\u201d category. In the last block, they completed the second experimental condition of the combined sorting task. The order of the blocks was counterbalanced across participants. Figure\u00a0D) in response latencies between the two practical blocks  and the two experimental blocks . The resulting D scores formulate a bipolar scale that ranges from masculinity to femininity. The faster the responses in the \u201cself-masculine vs other-feminine\u201d combined sorting condition, than in the \u201cself-feminine vs other-masculine\u201d condition, the stronger the implicit masculine gender self-concept. Whereas, the faster the responses in the \u201cself-feminine vs other-masculine\u201d combined sorting condition than in, the \u201cself-masculine vs other-feminine\u201d condition, the stronger the implicit feminine gender self-concept. However, in the current study, the key dependent variable on the IAT related to the strength of the implicit gender self-concept, regardless of whether the participant was male or female. Therefore, all D scores were transformed to positive values with higher scores denoting stronger implicit gender self-concept.The dependent measure for the IAT was the strength of the automatic associations calculated with the scoring algorithm recommended by Greenwald et al. . That isThe PAQ . Therefore, only the dimensional scales of PAQ and the transformed D scores of the IAT were included in the analyses described below. The bipolar scales of these measures were used only in an initial analysis to explore the association with untransformed D score, for comparison with the equivalent result reported by Greenwald and Farnham  in the critical blocks was above chance, t(100)\u2009=\u200962.12, p\u2009<\u2009.001, d\u2009=\u20096.18, BF10\u2009=\u20096.99. Likewise, participants showed the expected effect on the IAT, producing a mean D-score  that was significantly above zero, t(100)\u2009=\u200912.13, p\u2009<\u2009.001, d\u2009=\u20091.21, BF10\u2009=\u20092.03.The average AQ score across participants was 19.65 (SD\u2009=\u20097.31). The average score on PAQ Masculinity and PAQ Femininity scale was 2.43 (SD\u2009=\u20090.73) and 2.85 (SD\u2009=\u20090.72), respectively. Participants were accurate when sorting items on the IAT. The mean proportion of correct item categorisation  and r\u2009=\u2009\u2212\u2009.35, p\u2009<\u2009.001, BF10\u2009>\u2009100 (one-tailed), respectively. These results indicate that the higher the number of ASD traits manifested, the lower the explicitly reported strength of gender self-concept (for both feminine and masculine traits). Next, we examined the relation between AQ score and implicit gender self-concept (indexed by D score). As predicted, AQ was negatively and significantly associated with D score, r\u2009=\u2009\u2212\u2009.25, p\u2009=\u2009.006, BF10\u2009=\u20095.45 (one-tailed), indicating a negative association between the number of self-reported ASD traits and the strength of the implicit gender self-concept (high AQ score\u2009=\u2009low D score).A series of correlation analyses was conducted to explore the relation between ASD traits, on the one hand, and the explicit and implicit gender self-concept, on the other hand. In line with our predictions, AQ was negatively and significantly associated with both PAQ Femininity and PAQ Masculinity scale scores, SD) scores on PAQ Femininity and PAQ Masculinity scale and on the IAT among participants who scored above and below the median of the sample on the AQ.Table\u00a0t-tests was conducted to examine differences between the low-AQ group and the high-AQ group in the explicit and implicit gender self-concept. Groups were equated for age and sex. The average age was 38.61 (SD\u2009=\u20099.02) in the low-AQ group and 35.22 (SD\u2009=\u200910.93) in the high-AQ group, a difference that was non-significant, t(94.85)\u2009=\u20091.70, p\u2009=\u2009.093, d\u2009=\u20090.38, BF10\u2009=\u20090.75. The low-AQ group included 23 birth-assigned-males and 28 birth-assigned-females, whereas the high-AQ group included 28 birth-assigned-males and 22 birth-assigned-females. The difference between the high and low AQ groups in ratio of birth-assigned-males to birth-assigned-females was non-significant, \u03c72(1)\u2009=\u20091.20, p\u2009=\u2009.273, Cramer\u2019s V\u2009=\u2009.11. As predicted, relative to participants in the low-AQ group, those in the high-AQ group had significantly lower scores on both PAQ scales, as well as significantly lower D scores on the IAT .In a set of exploratory analyses, we checked whether there were any of the effects reported above differed significantly between birth-assigned males and birth-assigned females. Fisher\u2019s D score on the gender IAT and total score on the AQ, Z\u2009=\u20092.49, p\u2009=\u2009.013. The association between AQ and D score was significant within birth-assigned-females, indicating that the higher the number of ASD traits, the lower the strength of the implicit gender self-concept, r\u2009=\u2009\u2212\u2009.41, p\u2009=\u2009.003, BF10\u2009=\u200911.30. However, this association was non-significant among birth-assigned-males, r\u2009=\u2009.08, p\u2009=\u2009.584, BF10\u2009=\u20090.20.First, there was a significant difference between males and females in the size of the association between F\u2009=\u200911.02, p\u2009=\u2009.001, D score among birth-assigned-females in the low AQ subgroup  was significantly higher than among birth-assigned-females in the high AQ subgroup , t(46.73)\u2009=\u20093.44, p\u2009=\u2009.001, d\u2009=\u20090.96, BF10\u2009=\u200917.73. This indicates that females with a high number of ASD traits had a weaker gender self-concept than females who had a low number of ASD traits. In contrast, the IAT D score among birth-assigned-males in the low AQ subgroup  was non-significantly different from the IAT D score among birth-assigned-males in the high AQ subgroup , t(49)\u2009=\u2009\u2212\u20090.90, p\u2009=\u2009.379, d\u2009=\u20090.25, BF10\u2009=\u20090.39.Second, in a 2 \u2009\u00d7\u20092 (AQ subgroup: High-AQ/low-AQ) ANOVA on the gender IAT data, there was a significant group\u2009\u00d7\u2009sex interaction, The first notable set of findings of the current study was about the link between ASD traits and the explicit gender self-concept. As predicted, AQ score was significantly negatively associated with both Femininity and Masculinity scale scores of PAQ, indicating that as the number of self-reported ASD traits increases the strength of the explicit gender self-concept decreases. The associations were moderate in magnitude and Bayesian analyses consistently suggested that the data supported the alternative hypothesis. This is the first study, to our knowledge, to show a link between explicit gender self-concept and number of ASD traits among members of the general population. We also addressed this issue by dividing our sample into a high AQ group and a low AQ group. In keeping with our predictions, the results complemented the findings from the correlation analyses. That is, relative to the group of participants with low ASD traits, the group with high ASD traits scored significantly lower on both scales of PAQ. These results indicate that people with high ASD traits explicitly/consciously identify themselves with less strong masculine and feminine attributes relative to individuals with low ASD traits; they have weaker gender self-concepts, on average. Effects were moderate and Bayesian analyses again suggested that the data supported the alternative hypotheses.feminine gender identity/self-concept. The studies by Bejerot and Eriksson (n\u2009=\u20099) and birth-assigned-females without ASD (n\u2009=\u20099) in Gender Feminine scale, it is possible that a Type 2 error was made. Also, the Bem Sex Role Inventory, used by Bejerot and Eriksson  was significantly negatively associated with number of self-reported ASD traits, indicating that as the number of reported ASD traits increased the strength of the implicit gender self-concept decreased. The size of the association was relatively modest , but it was highly statistically significant and Bayesian analysis suggested that the data supported the alternative hypothesis. Complementary to this, relative to the group of participants with low ASD traits, the group with high ASD traits scored significantly lower (D-score) on the IAT, indicating that among people with high ASD traits the automatic identification of self with either masculine or feminine attributes was weaker relative to individuals with low ASD traits. Again, group differences were moderate-to-large in statistical magnitude and associated with Bayes factors that strongly favoured the alternative hypothesis. These results suggest that high ASD traits in the general population might signify an implicit/unconscious gender self-concept that is neither strongly masculine nor strongly feminine, among individuals who otherwise report themselves to be cisgender.Arguably more notable, is the second set of findings from the current study, regarding the relation between number of ASD traits and implicit gender self-concept. To our knowledge, the current study is the first to investigate the potential link between ASD and gender self-concept at a level deeper than that tapped by self-report. In keeping with our predictions, we found that the strength of the implicit gender self-concept (indexed by r\u2009=\u2009\u2212\u2009.26 in our study and r\u2009=\u2009.20 in their study). Moreover, these associations are of an order of magnitude suggested by Hofmann et al.  and birth-assigned females (n\u2009=\u200950). That is, in the association analyses, the strength of explicit gender self-concept was negatively associated with number of ASD traits in both males and females. Likewise, in the case\u2013control analyses, those with high ASD traits had a weaker gender self-concept than those with low ASD traits, regardless of whether they were male or female. However, results appeared to be not so straightforward when considering the effects of ASD traits on implicit gender self-concept. Here, in the association analyses, number of ASD traits was negatively associated with strength of implicit gender self-concept in birth-assigned females only. Likewise, in the case\u2013control analyses, only females with high ASD traits had a weaker gender self-concept than females with low ASD traits . What should be made of these apparent sex differences in the relation between ASD and implicit gender self-concept? On the one hand, the existence of gender differences might be treated with some scepticism, given that the analyses were entirely post hoc and between-sex differences were not predicted. On the other hand, sex differences were reported by Nobili et al.  observed in the whole sample of 101 participants held in i et al.  in theiri et al.  found thOverall, the results from the explicit and implicit measures of gender self-concept imply that people with high ASD traits  have a weaker propensity to identify with, and incorporate into their self-concept gender differentiated traits. As levels of ASD increase, so too may be susceptible to gender identity difficulties. If this interpretation is correct, then this could explain gender non-conforming feelings and gender identity difficulties in ASD  that ASD is characterised by a diminished general tendency to identify with, or represent, the perspectives and attitudes of others  to incorporate these into their self-concept. Given that such a difficulty could provide an explanation for the high co-occurrence of gender identity difficulties in ASD, the current study makes an important contribution to our still limited understanding of this phenomenon.Supplementary material 1 (DOCX 18\u00a0kb)Below is the link to the electronic supplementary material."}
+{"text": "In this paper, we propose computationally efficient parametric and semiparametric tests based on a set of specialized matrix techniques dubbed as the PB-transformation. The PB-transformation has two advantages: 1. The PB-transformed data will have a scalar variance-covariance matrix. 2. The original H-T problem will be reduced to an equivalent one-sample H-T problem. The transformed problem can then be approached by either the one-sample Student\u2019s t-test or Wilcoxon signed rank test.For many practical hypothesis testing (H-T) applications, the data are correlated and/or with heterogeneous variance structure. The regression t-test produces notably better results than the weighted LMER test, especially in the high correlation case, using only a small fraction of computational cost (3 versus 933 s). We apply these two methods to a set of RNA-seq gene expression data collected in a breast cancer study. Pathway analyses show that the PB-transformed t-test reveals more biologically relevant findings in relation to breast cancer than the weighted LMER test.In simulation studies, the proposed methods outperform commonly used alternative methods under both normal and double exponential distributions. In particular, the PB-transformed https://github.com/yunzhang813/PBtest-R-Package.As fast and numerically stable replacements for the weighted LMER test, the PB-transformed tests are especially suitable for \u201cmessy\u201d high-throughput data that include both independent and matched/repeated samples. By using our method, the practitioners no longer have to choose between using partial data (applying paired tests to only the matched samples) or ignoring the correlation in the data (applying two sample tests to data with some correlated samples). Our method is implemented as an R package \u2018PBtest\u2019 and is available at The online version of this article (10.1186/s12859-019-2783-8) contains supplementary material, which is available to authorized users. As proof, R packages genefilter [t-tests, respectively, both of which are hundreds times faster than the stock R function t.test. However, it is common to observe heterogeneous variabilities between high-throughput samples, which violates the assumption of the Student\u2019s t-test. For example, samples processed by a skillful technician usually have less variability than those processed by an inexperienced person. For two-group comparisons, a special case of the heterogeneity of variance, i.e., samples in different groups have different variances, is well studied and commonly referred to as the Behrens-Fisher problem. The best known (approximate) parametric solution for this problem is the Welch\u2019s t-test, which adjusts the degrees of freedom  associated with the t-distribution to compensate for the heteroscedasticity in the data. Unfortunately, the Welch\u2019s t-test is not appropriate when the data have even more complicated variance structure. As an example, it is well known that the quality and variation of the RNA-seq sample is largely affected by the total number of reads in the sequencing specimen [sequencing depth or library size, which may vary widely from sample to sample. Fortunately, such information is available a priori to data analyses. Several weighted methods [Modern statistical applications are typically characterized by three major challenges: (a) high-dimensionality; (b) heterogeneous variability of the data; and (c) correlation among observations. For example, numerous data sets are routinely produced by high-throughput technologies, such as microarray and next-generation sequencing, and it has become a common practice to investigate tens of thousands of hypotheses simultaneously for those data. When the classical nefilter  and Rfasnefilter  implemenspecimen , 4. This methods \u20137 are prbias, the heterogeneity of variance remains to be an issue. Besides, the clustering nature of these data may induce correlation among observations within one center/batch. Correlation may arise due to other reasons such as paired samples. For example, we downloaded a set of data for a comprehensive breast cancer study [t-test and paired t-test are not ideal for comparing the gene expression patterns between normal and cancerous samples, because they either ignore the correlations of the paired subjects or waste information contained in the unpaired subjects. To ignore the correlation and use a two-sample test imprudently is harmful because it may increase the type I error rate extensively [As the technology advances and the unit cost drops, immense amount of data are produced with even more complex variance-covariance structures. In multi-site studies for big data consortium projects, investigators sometimes need to integrate omics-data from different platforms (e.g. microarray or RNA-seq for gene expression) and/or processed in different batches. Although many normalization \u201310 and ber study , which censively . On the p-values for the fitted models. The R package lmerTest [t- and F-tests for lme4 outputs with appropriate DFs. A fast implementation of LMER is available in the Rfast package, which is based on highly optimized code in C++ [One of the most versatile tools in statistics, the linear mixed-effects regression (LMER), provides an alternative inferential framework that accounts both unequal variances and certain practical correlation structures. The standard LMER can model the correlation by means of random effects. By adding weights to the model, the weighted LMER is able to capture very complex covariance structures in real applications. Although LMER has many nice theoretical properties, fitting it is computationally intensive. Currently, the best implementation is the R package lme4 , which ilmerTest  is the ce in C++ ; howevert-tests, have their corresponding rank-based counterparts, i.e. the Wilcoxon rank-sum test and the Wilcoxon signed rank test. A rank-based solution to the Behrens-Fisher problem can be derived based on the adaptive rank approach [t-distribution is more appropriate than the normal approximation for the Wilcoxon test when the design has low DFs. Their method is implemented in the svyranktest function in R package survey. But most of the rank-based tests are designed for group comparisons; rank-based approaches for testing associations between two continuous variables with complex covariance structure are underdeveloped.Many classical parametric tests, such as two-sample and paired approach , but it approach  derived approach  derived approach  proved tone-group testing problem. After the PB-transformation, classical parametric and rank-based tests with adjusted DFs are directly applicable. We also provide a moment estimator for the correlation coefficient for repeated measurements, which can be used to obtain an estimated covariance structure if it is not provided a priori. In \u201ct-test to an RNA-seq data for breast cancer. Utilizing the information of the paired samples and sequencing depths, our method selects more cancer-specific genes and fewer falsely significant genes (i.e. genes specific to other diseases) than the major competing method based on weighted LMER.Based on a linear regression model, we propose two H-T procedures (one parametric and one semiparametric) that utilize a priori information of the variance (weights) and correlation structure of the data. In \u201chttps://github.com/yunzhang813/PBtest-R-Package.Lastly, computational efficiency is an important assessment of modern statistical methods. Depending on the number of hypotheses to be tested, our method can perform about 200 to 300 times faster than the weighted LMER approach in simulation studies and real data analyses. This efficiency makes our methods especially suitable for fast feature selection in high-throughput data analysis. We implement our methods in an R package called \u2019PBtest\u2019, which is available at For clarity, we first present our main methodology development for a univariate regression problem. We will extend it to multiple regression problems in \u201cConsider the following regression-type H-T problem: y is the response variable, x is the covariate, and \u03b5 is the error term that follows an n-dimensional multivariate normal distribution \u03a3. By considering a random variable Y in the n-dimensional space, the above problem can also be stated as Here, \u03bc is the intercept or grand mean that is a nuisance parameter, and \u03b2 is the parameter of interest that quantifies the effect size. We express the variance-covariance matrix of \u03b5 in the form In this model, \u03c32 is a nonzero scalar that quantifies the magnitude of the covariance structure, and S is a symmetric, positive-definite matrix that captures the shape of the covariance structure. Additional constraints are needed to determine \u03c32 and S; here, we choose a special form that can subsequently simplify our mathematical derivations. For any given \u03a3, define where From the above definition, we have the following nice property S the standardized structure matrix satisfying Eq. Hereinafter, we refer to S is proportional to I, the identity matrix, it is well-known that regression t-test is a valid solution to this H-T problem. If S\u2260I, e.g. the observed data are correlated and/or have heterogeneous variance structure, the assumptions of the standard t-test are violated. In this paper, we propose a linear transformation, namely As a special case of Model , if S isweighted mean of the original data), and subtract n\u22121)-dimensional subspace of Y(1) (i.e. the centered data). It\u2019s clear that H0 is true.Estimate Y(1) to reshape its \u201celliptical\u201d distribution to a \u201cspherical\u201d distribution. The intermediate data from this step is Y(2).Use the eigen-decomposition of the covariance matrix of unique rotation that transforms the original H-T problem to an equivalent problem of testing for a constant deviation along the unit vector. The equivalent data generated from this step is Use the QR-decomposition technique to find a To shed more lights on the proposed method, we first provide a graphical illustration in Fig.\u00a0In the proposed PB-transformation, B-map performs both transformations in Step 1 and 2; P-map from Step 3 is designed to improve the power of the proposed semiparametric test to be described in \u201cJ=1\u00b71\u2032 . With some mathematical derivations  is a semi-orthogonal matrix containing the first n\u22121 eigenvectors and \u039bn\u22121\u2208Mn\u22121)\u00d7(n\u22121)\u00d72\u00d72\u00d7(n\u22121)(\u2212Q(I2\u00d72\u2212Rot)Q\u2032 is the unique orthogonal transformation that satisfies the following properties: Matrix See Additional file\u00a0P defined by Theorem 1 the \u201cP-map\u201d. Equation z is mapped to 1n\u22121 scaled by a factor \u03b6. Equation 1n\u22121 and z, i.e. Lz=span. This property defines a uniqueminimum map that only transforms the components of data in Lz and leaves the components in We call the linear transformation  used in .B and P, we define the final transformed data as With both i.i.d. normal distribution, for i=1,\u22ef,n\u22121. The location parameter of the common marginal distribution is to be tested with unknown \u03c32. Therefore, we can approach this equivalent H-T problem with the classical one-sample t-test and Wilcoxon signed rank test , the above estimator coincides with the maximum likelihood estimator of \u03c1, which has the form Moreover, if See Additional file\u00a0Standard correlation estimates are known to have downward bias , which ct-test and the paired t-test. Suppose there are n observations in each group, the former test has DF=2n\u22122 for i.i.d. observations, and the latter only has DF=n\u22121 because the observations are perfectly paired. These trivial examples indicate that we need to adjust the DF according to the correlation structure in our testing procedures.The degree of freedom (DF) can have nontrivial impact on hypothesis testing when sample size is relatively small. Intuitively, a correlated observation carries \u201cless information\u201d than that of an independent observation. In such case, the effective DF is smaller than the apparent sample size. Simple examples include the two-sample We adopt the degrees of freedom approximation proposed by  , g(\u2212y)=g(y). Assume that Y\u2217 be a random number that is independent of \u03c32. For every symmetric semi-definite u,v, such that Let n-dimensional random vector with Y, the result is a sequence of (n\u22121) equal variance and uncorrelated random variables with zero mean if and only if \u03b2=0.is an See Additional file\u00a0i.i.d. sequence of random variables with a symmetric common p.d.f., we can use linear transformations to generate a family of distributions that is expressive enough to include a non-normal distribution with an arbitrary covariance matrix and a mean vector specified by the effect to be tested. This distribution family is semiparametric because: a) the \u201cshape\u201d of the density function, g(y), has infinite degrees of freedom; b) the \u201ctransformation\u201d  has only finite parameters.The essence of this Proposition is that, starting with an t-distribution with an adjusted DF. Note that Wilcoxon signed rank test is only valid when the underlying distribution is symmetric; therefore, the symmetry assumption in Proposition 2 is necessary. In summary, this PB-transformed Wilcoxon test provides an approximate test (up to the second order moment) for data that follow a flexible semiparametric distributional model.As mentioned before, applying both the B- and P-maps enables us to use the Wilcoxon signed rank test for the hypotheses with this semiparametric distribution family. This approach has better power than the test with only the B-map as shown in \u201cIn this section, we present an extension of the proposed methods for the following multiple regression \u03b5 is assumed to have zero mean but does not need to have scalar covariance matrix. For example, \u03b5 can be the summation of random effects and measurement errors in a typical LMER model with a form specified in Eq. Here the error term \u03b2k,k=1,\u2026,p, we need to specify two regression models, the null and alternative models. Here the alternative model is just the full Model  from XTo test the significance of ll Model , and thenuisance covariates in the multiple regression case are Xk\u2212\u03b2k\u2212 instead of 1\u03bc in Eq. Xk\u2212E)=\u03c32(S\u2212Xk\u2212X\u2212k\u2032). The P-transformation is derived the same as before, but with the new B matrix.Compared with the original univariate problem, we see that the \u03c1=0.2, \u03c1=0.4,\u03c1=0.6, and \u03c1=0.8). We compare the parametric and rank-based PB-transformed test with oracle and estimated correlation to an incomplete survey of alternative methods. Each scenario was repeated 20 times and the results of \u03c1=0.2 and 0.8 for normal and double exponential distributions are summarized in Figs.\u00a0\u03c1=0.4 and 0.6, and results for logistic distribution.We design two simulation scenarios for this study: SIM1 for completely paired group comparison, and SIM2 for regression-type test with a continuous covariate. For both scenarios we consider three underlying distributions  and four correlation levels . Of note, lmer may fail to converge occasionally, e.g. 0 \u2013 25 failures  in each repetition of our simulations. We resort to a try/catch structure in the R script to prevent these convergence issues from terminating the main loop.We record the system time for testing 2000 simulated hypotheses using our method and lmer, since they are the most appropriate methods for the simulated data with the best statistical performance. Our method takes less than 0.3 s with given n=40 with nA=nB=20. It is straightforward to calculate the DFs used in the two-sample t-test and the paired t-test, which are 38 and 19, respectively. Using lmerTest (weighted LMER) with default parameters, it returns the mean DF = 35.51 with a large range  from the simulated data with \u03c1=0.2. Using the oracle \u03a3SIM, our method returns the adjusted DF = 14.35; if the covariance matrix is estimated, our method returns the mean DF = 14.38 with high consistency . When \u03c1=0.8, the adjusted DFs become smaller. The weighted LMER returns the mean DF = 20.63 . Our method returns DF = 12.48 for the oracle covariance, and mean DF = 12.56  for the estimated covariance. Also, the rank-based test svyranktest returns a DF for its t-distribution approximation, which is 18 for both small and large correlations.We also check the degrees of freedom in all applicable tests. In this section, we report the DFs used/adjusted in SIM1, i.e. the completely paired group comparison. Recall that We download a set of RNA-seq gene expression data from The Cancer Genome Atlas (TCGA)   level combined with a fold-change (FC) criterion (FC<0.5 or FC>2), the PB-transformed t-test selected 3,340 DEGs and the weighted LMER selected 3,485 DEGs  for the weighted LMER. Expression level of these genes are plotted in Fig.\u00a0To make the comparison between these two methods more fair and meaningful, we focus on studying the biological annotations of the top 2,000 genes from each DEG list. Specifically, we apply the gene set analysis tool DAVID  to the 1t-test are known to be involved in cell survival, proliferation and migration. The CXCR4-CXCL12 chemokine signaling pathway is one of the deregulated signaling pathway uniquely identified by PB-transformed t-test in HER2+ breast cancer cells. This pathway is known to play a crucial role in promoting breast cancer metastasis and has been reported to be associated with poor prognosis [t-test identifies more genes whose protein products can be targeted by pharmaceutical inhibitors. CXCR4 inhibitors have already demonstrated promising anti-tumor activities against breast [Those 11 genes uniquely identified by the PB-transformed rognosis , 34. Comt breast , 36, prot breast  and lungt breast  cancers.t-type test and rank-based test. In the simulation studies, our proposed tests outperform the classical tests (e.g. two-sample/regreesion t-test and Wilcoxon rank-sum test) by a large margin. In a sense, this superiority is expected, because the classical methods do not consider the correlation nor heteroscedasticity of the data.In this paper, we present a data transformation technique that can be used in conjunction with both the Student\u2019s t-test and the weighted LMER. The fact that the PB-transformed t-test outperforms the weighted LMER, and this advantage is more pronounced for data with higher correlation , hypothesis testing, among other things; whereas our methods are only designed for the hypothesis testing. We envision that in a typical high-throughput data application, an investigator may quickly run PB-transformed t-test for individual covariates, not the ANOVA F-test for the significance of several covariates simultaneously. In fact, the B-map can be defined in this case so we can define a transformed parametric test easily; but there is no clear counterpart for the P-map, which is needed to overcome the identifiability issue for the semiparametric generalization. 2. The performance of PB-transformations depends on a good estimation of S, the shape of the covariance matrix of the observations. Currently, our moment-based estimator only works for problems with just one random intercept, which is only appropriate for relatively simple longitudinal experiments. It is a challenging problem to estimate the complex covariance structure for general LMER models , and we think it can be a nice and ambitious research project for us in the near future.In \u201ct-test provides the same test statistic and degrees of freedom as those from the paired t-test for perfectly paired data and the regression t-test for i.i.d. data. In this sense, the PB-transformed t-test is a legitimate generalization of these two classical tests. The rank-based test is slightly different from the classical ones, since we used a t-distribution approximation instead of a normal approximation for the rank-based statistic. The t-distribution approximation is preferred for correlated data because the effective sample size may be small even in a large dataset [Numerically, the PB-transformed  dataset .Recall that the PB-transformation is designed in a way that the transformed data have the desired first and second order moments. For non-normal distributions, the transformed samples may not have the same higher order moments. Note that, the P-map is currently defined in part by Eq. , the minIn this study, we presented an example in RNA-seq data analysis. In recent bioinformatics research, advanced methods such as normalization and batch-effect correction were developed to deal with data heterogeneities in bio-assays. While most of these approaches are focused on the first moment , our approach provides a different perspective based on the second order moments (i.e. the covariance structure). The dramatic computational efficiency boost of our method also opens the door for investigators to use the PB-transformed tests for ultra-high-dimensional data analysis, such as longitudinal studies of diffusion tensor imaging data at the voxel-level \u201341, in wAdditional file 1This file contains: a) proofs of the main theorems; b) details of the moment-based correlation estimator; c) details of simulation design; and d) additional information about the real data analysis. (PDF 3523 kb)"}
+{"text": "Nature Communications 10.1038/s41467-019-12017-8, published online 18 September 2019.Correction to: +GrzB+ cells in PbAluc-infected mice was incorrectly given as \u20180\u2019 and should have been \u201869.6\u2019. This error is now corrected in both the PDF and HTML versions of the Article.The original version of this Article contained an error in one of the dot plots in Fig.\u00a02d. The percentage of Pb1"}
+{"text": "G. We investigate the question \u201cWhen is G and internally via structural properties of the group G.Let  G has been the topic of several previous investigations  is a nonzero cyclic subgroup of p of x,\u00a0G]. Therefore, for Let Define We actually have a little more.G is a nonabelian p-group, If From the proof of Theorem G be a p-group, G is 2-generated (generated by 2 elements) then Let If We remark that Example G is abelian by cyclic, or G is said to be an extension of an abelian group by a cyclic group if there exists an abelian normal subgroup A of G such that G\u00a0/\u00a0A is cyclic. For finite G one may always take A to be a maximal abelian normal subgroup.Recall that a group G be a nonabelian p-group, Let A be a maximal abelian normal subgroup such that G is nonabelian there exists G is of class 2 so We let Using this decomposition we define G be a nonabelian p-group, Let Let As we did following Theorem G be a p-group, nilpotent of class 2, which is abelian by cyclic. Then Let A be a maximal abelian normal subgroup with G. Let As above we let c is a sum of commutators. Since A is a maximal abelian normal subgroup we have G is nilpotent of class 2, p, a contradiction. Thus Further Now let G has a partition In Theorems p-groups, G be a group of order G is abelian so We apply the above results to G be a nonabelian p-group, G is nilpotent of class 2. Then Let (i)g is nonabelian we have (ii)G. We know G is generated by k elements [G is generated by 2 elements. Using Theorem G has a unique maximal normal subgroup which cuts G. The result now follows from Theorem elements . If \\doc(iii)G is of class 2. For G is of class 2, G and G is abelian by cyclic so the result follows from Theorem Z(G) cuts G is a finite abelian p-group then G is 1-affine complete. For nonabelian p-groups, p-group for which G is 1-affine complete. We thus close with the following.In conclusion we have found that when p-groups G is 1-affine complete.For finite nonabelian"}
+{"text": "Correction to: npj Digital Medicine 10.1038/s41746-017-0007-z, Published online: 12 February 2018The original version of the published Article contained an error in the spelling of the fifth Author\u2019s name. \u201cCarly Winakor\u201d has been changed to \u201cCarly Winokur\u201d. This has been corrected in the HTML and PDF version of the Article."}
+{"text": "Correction to:npj Digital Medicines 10.1038/s41746-019-0189-7, published online 18 November 2019The original version of the published Article omitted of the last Author\u2019s middle initial. \u201cMatthew Lungren\u201d has been changed to \u201cMatthew P. Lungren\u201d. This has been corrected in the HTML and PDF version of the Article."}
+{"text": "Scientific Reports 10.1038/s41598-018-20106-9, published online 26 January 2018Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cdiverse\u201d was incorrectly given as \u201cdivers\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Information file."}
+{"text": "Nature Communications 10.1038/s41467-019-10303-z, published online 14 June 2019.Correction to: 2\u2019 was inadvertently added. This has been corrected in both the PDF and HTML versions of the Article.The original version of this Article contained an error in Fig.\u00a04a, in which an extra label \u2018HThe correct version is:It replaces the incorrect version:"}
+{"text": "In the Materials and Methods, there is an error in the equation for the calculation of an asynchronous gait. Please view the complete, correct equation here: Dg-a = Dm-p+3/4SL"}
+{"text": "Scientific Reports 10.1038/s41598-018-37997-3, published online 12 February 2019Correction to: The original version of this Article contained an error in the title of the paper, where the phrase \u201ccells overexpressing\u201d was incorrectly given as \u201ccellsoverexpressing\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Nature Communications, 10.1038/s41467-018-06915-6; published online 31 October 2018Correction to: In the original version of this Article, the author name \u2018Shengzhong Liu\u2019 was incorrectly given as \u2018Liu Shengzhong\u2019. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Scientific Reports 10.1038/s41598-018-32296-3, published online 20 September 2018Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cReservoir\u201d was incorrectly given as \u201cReservior\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supporting Information file."}
+{"text": "With this approach, a limit of 10\u22127 mol L\u22121 was clearly detected. To improve the detection to lower p-MBA concentration, as 10\u22128 mol L\u22121, the SDME technique was applied. The p-MBA Raman signature was detected in two performed extractions and its new concentration was determined to be ~4.6 \u00d7 10\u22125 mol L\u22121. This work showed that coupling SDME with SERS allowed a rapid (5 min) and efficient pre-concentration (from 10\u22128 mol L\u22121 to 10\u22125 mol L\u22121), detection, and quantification of the analyte of interest, proving to be an interesting analytical tool for SERS applications.Single-drop microextraction (SDME) was coupled with surface-enhanced Raman scattering (SERS) to provide sample extraction and pre-concentration for detection of analyte at low concentrations. A gold nanohole array substrate (AuNHAS), fabricated by interference lithography, was used as SERS substrate and para-mercaptobenzoic acid (p-MBA) was tested as a probe molecule, in the concentration range 10 Theolecules .\u22126 mol L\u22121, many nanostructured materials may not be sensitive enough for an efficient detection. To overcome this, a pre-concentration technique, such as the single-drop microextraction (SDME), can be introduced as an analytical strategy to improve low concentration detection.Moreover, several nanofabrication strategies have been explored for the fabrication of SERS substrates with enhanced electric fields (hot spots), and three main classes of SERS substrates have been developed: Metallic rough surfaces, colloidal nanoparticles, and periodic nanostructures . A reproSDME is a liquid-phase microextraction technique, where a micro drop of an organic solvent is used to transfer a dissolved substance from one liquid phase to another liquid phase  in contact with it . SDME haIn this context, we proposed the application of a single-drop microextraction technique as a pretreatment step before SERS analysis of low concentration analytes. For this purpose, p-MBA was used as a Raman probe molecule and gold nanohole array was used as SERS substrate. The off-line coupling of SDME with SERS was applied only when direct p-MBA detection was no longer possible.2 each, the photoresist was developed for 50 s with the Microposit AZ 351 developer diluted 1:3 in water. The photoresist template was coated with an 80-nm gold film by e-beam evaporation, and then the photoresist was removed using acetone. The AuNHAS were characterized by FEG  with 20 kV of acceleration voltage, and energy-dispersive X-ray spectroscopy (EDS) for elemental analysis; the sample presented a homogeneous gold surface and periodic holes over an area of 2 cm2, as can be seen in 2). The gold nanohole array substrates (AuNHAS), with period \u028c = 500 nm, were fabricated using a combination of two-beam interference lithography (IL) and a lift-off step. Details of the experimental process can be found in Menezes et al. . Briefly2-cooled charge-coupled device (CCD) detector. The excitation source was a He-Ne laser at 633 nm. The laser power at the sample surface was about 2.5 mW. The laser was focused with a 100x focal-lens objective, to obtain a diameter of 1 \u00b5m at the surface, for an exposure time of 10 s. All the measurements were done in triplicate. After that, aliquots of 25 \u03bcL from each solution of p-MBA were dropped onto the surface and dried. The surface Raman mapping data was carried out using the p-MBA solution of 10\u22126 mol L\u22121, collecting a total of 169 SERS spectra.SERS spectra were acquired using a confocal Jobin-Yvon T64000 Raman spectrometer system, equipped with a liquid-N\u22128 mol L\u22121. A toluene drop of 2 \u03bcL was generated inside the p-MBA solution, which was kept at 22 \u00b0C and stirred at 100 rpm for 5 min. After this time, the drop was collected back and dropped onto the AuNHAS. The procedure was repeated one more time, dropping the extracted solution (p-MBA in toluene) on a different area of the same AuNHAS. After solvent evaporation, the SERS spectra were collected.The experimental setup shown in \u22121 can be related to the \u03b4(CSH) bending mode, and the band at 1176 cm\u22121 was associated with the \u03b4(CH) deformation vibration. Moreover, the intensity of the band at 1074 cm\u22121, assigned to the p-MBA aromatic ring breathing [\u22121 was selected as an indicator for the SERS data. Moreover, in \u22127 mol L\u22121 was considered the lowest concentration with a distinctly detected SERS signal on the fabricated AuNHAS.Thiophenol-based molecules, such as p-MBA, are a class of compounds commonly used as Raman probe for SERS studies due to the large Raman signal of the benzene ring, offering great sensitivity and specificity . Figure \u22121 for each p-MBA concentration were analyzed , leading to a coefficient of determination (R-squared) of 0.956. This result suggests that the SERS intensities are proportional to the molecular amount of p-MBA on AuNHAS. A similar result was reported by Saleh et al. [\u22121 band from the 169 SERS spectra of the Raman mapping is plotted as a histogram: The black line in h et al. ; therefop-MBA at 10\u22128 mol L\u22121 resulted in a very weak signal  spectra.In terms of sensitivity, the SERS detection of k signal , which c studies . As can \u22124 mol L\u22121 and 10\u22125 mol L\u22121. Moreover, the value of RSD 20%, obtained with the combination of SDME and SERS, perfectly matches the performance of the substrate; thus, the new p-MBA concentration of ~4.6 \u00d7 10\u22125 mol L\u22121 can be extrapolated from the calibration curve  during the SDME procedure. This value is comparable with the average SERS intensity of the p-MBA solution between the concentrations 10on curve a. This rmolecule ,22. Alth\u22124 mol L\u22121 up to the concentration of 10\u22127 mol L\u22121. To improve the analytical applicability of SERS, and lower the detection limit of this analyte, the SDME technique was successfully applied for the pre-concentration of the 10\u22128 mol L\u22121 p-MBA solution. In only five minutes, the SDME method allowed us to obtain a solution of analyte almost a thousand times more concentrated, from 10\u22128 to ~4.6 \u00d7 10\u22125 mol L\u22121. Moreover, the tailored choice of extraction solvent, time, and temperature can largely improve the detection of specific analytes in dense or rich matrices, greatly expanding the versatility and applicability of SDME-SERS analysis. Ultimately, for the first time, this work demonstrated that the coupling of the SDME technique with SERS analysis is a very promising method for a rapid and easy-to-apply quantitative detection of molecules at very low concentrations.AuNHAS with a periodicity of 500 nm was fabricated by interference lithography and its SERS performance was investigated using p-MBA as Raman probe molecule. Different concentrations of p-MBA were easily detected by SERS with a good reproducibility (RSD 21%), from 10"}
+{"text": "To the editor, recently, a very interesting study on errors in search strategies used in systematic reviews was published in the Journal of the Medical Library Association  OR \u201cchronicintervillositis\u201d[tw] OR \u201cchronic histiocyticintervillositis\u201d[tw] OR \u201chistiocytic intervillositis\u201d[tw] OR\u201cintervillositis\u201d[tw]But it could well be that upon judging the retrieved references, a decision would be made to do the opposite . As it is not easy or even possible to predict whether this will happen, it is, in my view, best to keep these redundancies in, just to be sure.So, as most search strategies will be revisited in the future, be it after a few months or sometimes years, these redundant terms and variations play a role in further developing a search and deciding whether to add or delete terms. As Salvador-Oliv\u00e1n et al. write, these \u201csearch errors\u201d do not affect recall or negatively affect information retrieval with respect to either recall or precision. They do play a positive role in the composition of the search strategy.Jan W. Schoones,j.w.schoones@lumc.nl, http://orcid.org/0000-0003-1120-4781, Collection Development Expert/Information Specialist, Walaeus Library, Leiden University Medical Center, P.O. Box 9600 C1-Q, 2300 RC Leiden, The Netherlands"}
+{"text": "Nature Communications 10.1038/s41467-019-08625-z, published online 08 February 2019Correction to: y-axis were given in the wrong order: \u2018800\u2019 at the bottom through to \u20180\u2019 at the top. This has been corrected in both the PDF and HTML versions of the Article.The original version of this Article contained an error in Fig.\u00a02c, in which the numbers on the Also, the Source Data file initially published online was corrupted and was replaced."}
+{"text": "G-representation contains a rigid type. This is a generalization of the unitarity criterion of Barbasch and Moy for representations with Iwahori fixed vectors.We prove that for every Bushnell\u2013Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories. Moreover, we show that every irreducible smooth  F denote a non-Archimedean local field with finite residue field. Let G be the F-points of a connected reductive algebraic group F. Fix a Haar measure G. Let G, i.e., G-representation and this induces an equivalence between the category G-representations and the category of nondegenerate Let K in G. Then e as its identity element. Let G-representations and let e is self-adjoint, i.e., G  with the Plancherel measure G-representations. Denote by S of Let l et al.  give an G-representations with unitary G-representations.) In complete generality, this is clearly false, as seen, for example, by taking V is any irreducible representation with a It is natural to ask if in fact  induces e, define e is special if G-subquotients. This is equivalent K-signaturoved in , 19. We ras from .K-signature character of a Hermitian G-representation and adapt Vogan\u2019s signature theorem to our setting. The main result of the section is Theorem We give a brief outline of the paper. In Sect. K-character and signature K-character for an admissible G-representation K is a compact open subgroup, and explain an analogue of a formula of Vogan for the signature character [In this section, we recall the definition of the multiplicity entclass1pt{minimaharacter .p-adic group G. A star operation V such thatV is Hermitian if it has a nondegenerate We begin by recalling the idea of the Grothendieck group of modules with nondegenerate Hermitian forms from . As in tK is a compact open subgroup of G. Every smooth irreducible K-representation K-invariant form K-representations. If V is admissible, denote by V, and byV has an invariant Hermitian form, let V is admissible, let V is irreducible, V has a nondegenerate Suppose entclass1pt{minimaU is an U in V with respect to If R is any admissible module, define the hyperbolic form on If V is a smooth admissible U is an V and R is the radical of the form U, we haveK, we have a well defined signature homomorphismFun denotes the set of functions.[L ranges over the irreducible Hermitian The following result expresses the Hermitian form of an admissible module in terms of the Hermitian forms of its composition factors.As in , a betteentclass1pt{minimaV can be written uniquely in K, the K-signature character of V is[V is positive definite fi the coefficient of s in the signature is zero.In this notation, a nondegenerate Hermitian form F. Let F. We will denote by F-points of F-points of P,\u00a0A) is defined by a standard parabolic F-split torus in the center of P,\u00a0A), we regard G. Let i.Fix a minimal parabolic subgroup c. As in , \u00a7XI.1, G, denote by N-coinvariants). Let M, an open normal subgroup of M. Let R(G) the Grothendieck group of admissible G-representations. We may regard For a standard parabolic subgroup M-representation, and G-action given by right translations.If P,\u00a0A) is a standard pair, p-adic case, and summarizes [A Langlands datum is a triple P.g on compacta, and it is an intertwining operator with respect to the G-actions.The integral operator Let G-representation. Then there exists a Langlands datum Let Suppose Let G-representations is well known. The p-adic case, see for example [From now on, we restrict to the case of Hermitian representations with respect to the natural star operation  example , \u00a75, is A in G, such thatw in the normalizer Let M be a Levi subgroup of G with the subgroup M.We recall the definitions of the Bernstein center and the inertial equivalence class. Let M is a Levi subgroup and M. Define the relation of equivalence such pairs: G.Consider the set of pairs Define the weaker relation of inertial equivalence on the same pairs: As it is well known, if M of a standard parabolic subgroup P, let The Bernstein center G). From , one dec by \\ies, see , \u00a72.4.loc. cit. that for every e such that We call the inertial class mentclasspt{minimasults of , 3.6) saK be a compact open subgroup. The goal is to express the K-signature of an irreducible smooth G-representation in terms of that of tempered modules. A first step is the simpler result for K-multiplicity functions.Let G-representation in G-representations K,Let G-representations, all in Set Suppose Now let p-adic analogue.We summarize the necessary results about the Jantzen filtration and the signature character, see , \u00a73, 2,,2, \u00a714, X. Explicitly, let K, the restriction of K is independent of t.Let X such thatX;n at for all Define a Hermitian form The Hermitian forms [G-representations.K-signature.The radical of the form For small For small Equivalently,K-signature of With the notation as above, the Jantzen filtration Before we get to the signature theorem, we need a lemma which will insure that the inductive algorithm terminates  Let n\u2208W (see ) such thloc. cit., except that we need to explain in our setting the independence of K, the Bernstein component The proof is the same as in V in terms of the Langlands classification as V is:Write ,m.As in , 3.38, tY which have a nondegenerate Hermitian form, then it holds for Y itself. This is because of Proposition One remarks, as in [V as well, by  denotes the G-representations.Recall that G . The Hecke algebra K-biinvariant functions, where K ranges over a system of good compact open subgroups . For exy\u2013Prasad  filtratiDefine P ranges over the set of parabolic subgroups, (cf. ) Let \\doG is semisimple, this is the same notion as that of the rigid quotient from [In the case when ent from .G-representations.The space R(G) is spanned by the Langlands standard modules G. By the Langlands classification, The elliptic representation space is example .G-representations. LetLet  example , \u00a72.2.p-adic groups proved in [The following result is essentially the abstract Selberg principle for roved in .(see [The map K ranges over the compact open subgroups of G and The space We will not need these finer results.More is known about d in the  thatThe (i)M-representation For every standard Levi subgroup (ii)K such that There exists a compact open subgroup Denote by R(G). The following is the classical trace Paley\u2013Wiener theorem.As in , \u00a71.2, a The mapU(G) denote the inverse limit algebraU(G) has the equivalent description as the convolution algebra of essentially compact distributions:U(G) by settingU(G). The Bernstein center U(G). This also gives an action of R(G) via infinitesimal characters (on each irreducible representation), see Sect. We need to look at the action of the Bernstein center. Let is known , see alsis known , the alg[For every idempotent element Here, we think of For every Bernstein component The map The first part is immediate from Theorem R(G) spanned by the irreducible objects in Now suppose that V not in If The restriction of the trace map The category mentclasspt{minimaLet rigid if the composition of the natural mapsWe say that a pair (not necessarily a type) In Sect. We are now in position to prove Theorem Firstly, we can sharpen Theorem G-representation with inertial support V admits a K, the K-signature of V is(The signature theorem II) Let Notice that, in this version, we cannot say that the scalars K-character of every irreducible tempered representation K) of In light of Theorem p-adic groups, we may decompose ).As in , \u00a74.4, d[W is a unitary In particular, we have a natural bijection between the unitary modules for the two algebras. Finally, the correspondenceWe retain the notation from Sect. I be an Iwahori subgroup and Let If I. Since G-conjugacy classes of maximal compact open subgroups of G, the natural mapLet K-type of positive level is rigid.A Moy\u2013Prasad unrefined minimal This is immediate from Proposition K-type of positive level is a Bushnell\u2013Kutzko type. This proves Theorem G-representations which contain a Moy\u2013Prasad type of positive level. By [G-representation contains a level zero type.By [loc. cit. for the necessary structural results from Bruhat\u2013Tits theory, in particular, about parahoric subgroups. Fix an Iwahori subgroup I, and recall the Bruhat decompositionW is the Iwahori\u2013Weyl group and G of w. Let I and W of elements of length zero. Let W generated by the reflections W(J) is a subgroup of W.We now look at the case of level zero types \u201334. We rA level zero type is a pair w of minimal length in w has finite order in W. Therefore the compact cocenter of w has finite order, the subgroup W is finite. By the Bruhat\u2013Tits fixed point theorem [G and The main result of  is a desEvery level zero type Notice that now the proof of Theorem As shown in , \u00a77.3, tputed in , \u00a77.11. Here The algebra p-adic group G is equivalent with the classification of the unitary dual of the Hecke algebras in Theorem G is adjoint and In other words,  Lusztig  gives a When the cocycle lable by , 25.G. In this case, there exists a unique conjugacy class of maximal compact open subgroups. Let Suppose now that D is a F-algebra, GL) and [If  work of  (for GL(\u00a0F)) and  (in gene"}
+{"text": "Previous research has indicated that adults have a future-oriented cognitive bias, one illustration of which is their tendency to report more thoughts about the future than the past during mind-wandering. We examined whether children showed a similar bias, and whether there were any developmental changes in the magnitude of such a bias. Children aged 6\u20137 and 9\u201310 years, adolescents, and adults completed two tasks in which they could report either past or future thoughts: a mind-wandering task assessing spontaneous past and future thinking and a cued episodic thinking task in which they were free to describe either past or future events. Only adults showed a future-oriented bias in the mind-wandering task. Participants in all groups were much more likely to describe past events in the cue word task, and the proportion of future events described did not change developmentally. However, more than a third of the youngest age group produced no descriptions at all of future events, which was a significantly larger proportion than in any other age groups, and illustrates the difficulty that some children of this age have with future thinking. Our findings indicate that future-oriented bias and developmental changes in such bias may be task-specific. Research on thinking in adults has suggested that there is what has been termed a \u201cfuture-oriented\u201d or \u201cprospective\u201d bias . Studies with adults suggest that the rated clarity of remembered events might be greater than imagined future events , alongside an adolescent group (aged 14\u201315) and an adult group. Use of these age groups allowed us to examine the development profile of spontaneous and cued past and future thinking in detail. In addition to the mind-wandering and word-cue tasks, participants completed a task assessing working memory capacity. The latter task was included because of previous suggestions that future-oriented thinking in mind-wandering may make more demands on working memory resources than past-oriented thinking , thirty one 9- to 10-year-olds , twenty three 14- to 15-year-olds  and thirty-seven adults . All participants were tested in the developmental laboratory in the home department of the first author. Two participants from the youngest age group did not contribute data to the word cue task due to equipment error and experimenter error, respectively. One further participant from the youngest age group refused to give any responses during the digit span task. One participant each from the 14- to 15-year-olds, and adult age groups did not contribute data to the mind-wandering data task due to equipment failure. Adult participants were primarily recruited through notices across the university, and were paid \u00a315 (UK) for their participation. Child and adolescent participants were primarily recruited by advertising in social media and through information distributed in schools.There were four groups of participants in the study: forty two 6- to 7-year-olds , and asked to try to match them to specific faces. This was to encourage them to use faces that were not at the ends of the scale. After completing the pre-training, participants began the word cue task.Participants were introduced to the word cue task by the experimenter explaining that they would see some words on a screen and that each time they saw a word they had to think about something that had already happened or something that was going to happen that was related to that word. The experimenter then gave two examples and also demonstrated the ratings that had to be made. The word \u201cball\u201d came on the screen, and the experimenter described an event s/he had participated in that involved playing in a netball competition and losing a game when the other team scored late in the game. This event was described as \u201ca bit annoying\u201d by the experimenter, because valence was one of the event properties to be reported. The experimenter then said \u201cThis is something that has already happened, so I need to touch the Past button.\u201d Getting participants to explicitly report whether the event was in the past or future functioned to prepare them for making similar judgments in the mind-wandering task. The experimenter then showed participants the speed of retrieval scale and explained it to them as a way of reporting how quickly something came to mind. The experimenter selected the tortoise button to match the speed at which the netball event was retrieved. The clarity scale appeared on the next display, and the experimenter explained that this could be used to report how clearly the event looked in your head, selecting the fourth picture on the scale for the netball event. Finally, the emotion scale appeared, and the experimenter chose the third face from the left (\u201ca bit sad\u201d). After this initial demonstration, a second word appeared on the screen, the word \u201ccake\u201d. The experimenter then described an event that was going to happen next week, which was a party for his/her mother for which s/he was going to bake her favorite chocolate cake, and then moved through the screens reporting on this event, pressing the \u201cfuture\u201d button on the first display. Before moving on to the task itself, descriptions of each of the scales were reiterated.https://corpus.byu.edu/bnc/). The cues were presented in a randomized order and included the following words: book, game, pet, song, friend, bicycle, family, rain, winter, and park.Following this introduction and demonstration, participants completed the task themselves. In each of ten trials, a cue word appeared on the screen  and participants described either an event that had happened or that was going to happen \u201cjust one time\u201d. If participants described a repeated or ongoing event, they were reminded that the experimenter wanted them to talk about an event that had happened or was going to happen just one time. Participants then made the speed, clarity, and emotion judgments for each event before moving on to the next cue. Cue words were all nouns; the words that were selected all had neutral or mildly positive emotional significance, an age of acquisition rating between one and four years, and were of high frequency in the British National Corpus , 3 of the 9- to 10-year-olds (10%), and 1 of the adolescents (4%). The majority (8/12) of these participants responded to 9 out of 10 cues, and the lowest number of cues responded to was 6. Only data for the cues for which these participants produced a response were included in the analyses.F\u2009=\u20092.26, p\u2009=\u2009.09, \u03b7p2\u2009=\u20090.05. Because of the relatively low numbers of future events described in all groups, we also examined the proportions of participants in each group who produced no future event descriptions at all; 14 (35%) of 6- to-7-year-olds, four (13%) 9- to-10-year-olds, two (9%) 14- to-15-year-old, and 3 (8%) adults never produced descriptions of future events; chi-squared analyses showed that the proportion of participants who produced no future events varied by age group, \u03c72 \u2009=\u200912.40, p\u2009<\u2009.01. A greater proportion of 6- to 7-year-olds produced no future events than of either 9- to 10-year-olds, \u03c72 \u2009=\u20094.51, p\u2009=\u2009.03, 14- to 15-year-olds, \u03c72 \u2009=\u20095.33, p\u2009=\u2009.02, or adults, \u03c72 \u2009=\u20098.08, p\u2009<\u2009.01. There was no significant difference between the three older age groups in the proportion of participants who produced no future events .The first analyses examined the proportion of the described events that were from the past versus the future. Figure\u00a0F\u2009=\u20091.51, p\u2009=\u2009.22, \u03b7p2\u2009=\u20090.01, however, there was an interaction between temporal focus and age group, F\u2009=\u20093.95, p\u2009=\u2009.01, \u03b7p2\u2009=\u20090.10. The interaction was explored with four paired samples t tests. Future episodes were judged as coming to mind quicker than past episodes in the adult group, t(33)\u2009=\u20092.79, p\u2009<\u2009.01. There was a marginal effect in the same direction for the adolescent group, t(20)\u2009=\u20092.03, p\u2009=\u2009.06. There was no difference between past and future speed estimates for either of the child groups . Figure\u00a0F\u2009=\u200912.26, p\u2009<\u2009.01, \u03b7p2\u2009=\u20090.11, with past events reported as being clearer in the mind (M\u2009=\u20094.60) than future events (M\u2009=\u20094.15). Finally, Fig.\u00a0F\u2009=\u200925.49, p\u2009<\u2009.01, \u03b7p2\u2009=\u20090.20.In subsequent analyses, we looked at the other measures in this task as a function of temporal focus and age group; these analyses excluded participants who did not describe any future events. Figure\u00a0F\u2009=\u20091.04, p\u2009=\u2009.38, indicating that there was no developmental change in the likelihood that participants were task-focused. To examine mind-wandering, an ANOVA was then conducted on absolute numbers of thoughts with a between-subjects factor of group and a within-subjects factor of temporal focus . There was a main effect of temporal focus, F\u2009=\u200910.92, p\u2009<\u2009.01, \u03b7p2\u2009=\u20090.08, with a greater number of future (M\u2009=\u20092.38) than past (M\u2009=\u20091.84) thoughts reported, and an interaction between age group and temporal focus, F\u2009=\u20095.19, p\u2009<\u2009.01, \u03b72\u2009=\u20090.11. Subsequent paired t tests showed that only the adult group produced more future than past thoughts, t(34)\u2009=\u20095.56, p\u2009<\u2009.001. One-way ANOVAs showed that the effect of age on the number of future thoughts reported did not reach significance, F\u2009=\u20092.54, p\u2009=\u2009.06, but there was a significant effect of age on the number of past thoughts reported, F\u2009=\u20095.30, p\u2009<\u2009.01, with post hoc tests showing that the adults produced significantly fewer past thoughts than either the 6- to 7-year-olds or the 9- to 10-year-olds, both ps\u2009<\u20090.05.Figure\u00a0F\u2009=\u20096.43, p\u2009<\u2009.01, with post hoc Tukey tests showing that the adult group reported a higher percentage of mind-wandering episodes to the future than all of the other groups , who did not differ from each other.A final analysis examined whether there was a developmental change in the percentage of mind-wandering episodes that were to the future . A one-way ANOVA found a significant effect of age, F\u2009=\u200924.18, p\u2009<\u2009.01, \u03b7p2\u2009=\u20090.36, and direction, F\u2009=\u2009189.65, p\u2009<\u2009.01, \u03b7p2\u2009=\u20090.60, but no significant interaction between age and direction. Post hoc Tukey tests revealed that average digit span (the average of forward plus backward) of 9- to 10-year-olds was significantly greater than of 6- to 7-year-olds. Average digit span of 14- to 15-year-olds was significantly greater than of 6- to 7-year-olds and 9- to 10-year-olds. There was no significant difference between adults\u2019 total digit span and that of 14- to 15-year-olds.An ANOVA on scores on the digit span task with a between-subjects factor age group and a within-subjects factor of direction (forward versus backward) revealed a main effect of age, p values\u2009>\u20090.1).The final analyses examined the correlations between measures. We examined, for the sample as a whole, whether there were correlations between the percentage of mind-wandering episodes that were future-oriented, the overall number of mind-wandering reports (summed across past and future), the proportion of future events described in the word cue task, and digit span performance. None of the correlations were significant  of participants\u2019 event descriptions were of past events.Our mind-wandering task was somewhat unusual, in that, for the reasons described in the introduction, mind-wandering was assessed during a task that primarily involved motor skills rather than higher-level cognitive abilities. Under these sorts of circumstances, it would be expected that a future-oriented bias would be particularly large in adults, and indeed they reported around twice as many episodes of future-oriented mind-wandering than past-oriented mind-wandering. Strikingly, though, we did not see this pattern in any of our other groups. Although the overall number of times that participants reported future thoughts did not change developmentally, there was a developmental change in the percentage of mind-wandering episodes that were future-oriented relative to those that were past-oriented. Notably, the age pattern that we observed could not be explained by the differential availability of working memory resources in the groups; we found no relation between the percentage of mind-wandering reports that were future-oriented and working memory capacity, unlike Baird et al. , but repOur findings are the first to suggest that there are developmental changes in future-oriented bias in mind-wandering. However, the fact that none of the age groups other than adults showed a future-oriented bias stands in contrast to the findings of Ye et al.  and ZhanSuch an explanation, though, is at odds with the idea that levels of future-oriented mind-wandering decrease as a function of the extent to which the primary task recruits working memory , we did not ask participants to describe the contents of their mental states, making it impossible to be completely sure that their self-reports accurately reflected the temporal focus of their thoughts. However, we believe it is unlikely that the data could be explained by failure to understand the task. First, children had already been trained to report on the temporal focus of their thoughts (past versus future) in the word cue task, and were able to do this accurately . This is consistent with other studies that indicate that by 6\u20137-year-old children can reliably report on the deictic status of events  was not found in the child/adolescent groups. Thus, our findings suggest that in the context of spontaneously produced thoughts about other times, the future is less dominant than the past in the minds of children and adolescents than adults. Taken together, these findings indicate that there are some developmental changes in future thinking, and that even adolescents may not resemble adults in the degree to which they focus on the future relative to the past."}
+{"text": "AbstractVelellavelella) for Ecuador. Twelve individuals were found along different beaches of San Crist\u00f3bal and Santa Cruz Islands in Gal\u00e1pagos Archipelago, Ecuador. These sightings may be influenced by El Ni\u00f1o Southern Oscillation events.We present the first official record of the by-the-wind-sailor ( Velellavelella  is a holoplanktonic athecate hydroid (Hydrozoa: Anthoathecata) from the Porpitidae family that is well known as \u201cby-the-wind-sailor\u201d , its common distribution is in the northern hemisphere in the Pacific and Atlantic Oceans, as well as in the Mediterranean Sea . On 28 August 2017, approximately eight individuals of V.velella were spotted on La Lober\u00eda beach  at San Crist\u00f3bal Island. We photographed one individual that corresponded to a \u201cright-by-the-wind-sailor\u201d due to the direction of its sail , a beach at Santa Cruz Island. Although no exact counts are available, at least four different individuals were photographed  and Physaliaphysalis  washed up along with V.velella (Fig. Southwest orientated, Tortuga Bay is a dissipative beach with a gentle slope exposed to southern swells. These features make Tortuga Bay a trap for drifting organisms when winds hit from the south. In this respect, we also observed several specimens of lla Fig. . These mlla Fig. .V.vellella in Ecuador. We suggest that they are likely uncommon in the Gal\u00e1pagos Archipelago. V.velella arrived at the Gal\u00e1pagos (To the best of our knowledge, this is the first official record of al\u00e1pagos ."}
+{"text": "In the last June 2017, Dr. Martin Buchheit alerted the Sport's community with an editorial entitled \u201cHouston, we still have a problem,\u201d , although professional teams spend a lot of money using products without evidences  and psychological variables  which are influenced by both training and non-training stressors  and exogenic factors . Among all endogenic factors, biological sub-factors are the significant predictors of happiness  and a significant predictor of successful performance (Uphill et al., Time will tell, but we must remember that once again, we think this applies to all jobs within social services as we are working with people and impacting on their lives. Therefore, we could say: \u201cHouston we still have a problem\u201d but we could add., \u201cRemember that \u201cWe are physicians, but first and foremost, human beings\u201d\u201d Kimura, .JC-G and NT: First Idea; RM-A: Review; CL-P: Coauthor; IJ: Review; JM-A: Writer; DM-J: References; AD: Language; SO: Main director.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Nature Communications 10.1038/s41467-019-10380-0, published online 06 June 2019Correction to: The original version of this Article contained an error in the spelling of the word \u201cadaptation\u201d both in the Title and Abstract, which was incorrectly written as \u201cadaption\u201d. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Nature Communications 10.1038/s41467-019-09301-y, published online 27 March 2019.Correction to: In the original version of this Article, the legend in the upper panel of Fig.\u00a02 incorrectly read \u2018paternal imprinting\u2019 and should have read \u2018maternal imprinting\u2019. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "The data were used to obtain the limiting apparent molar volumes, limiting apparent molar compressibilities and the corresponding transfer parameters. Limiting apparent molar expansibilities and their second order derivatives and volume interaction coefficients were also estimated. These parameters are discussed in terms of d-sorbitol and co-solute (amino acid or sodium chloride) interactions in aqueous solutions.Apparent molar volumes and apparent molar compressibilities for  In recent years, sugar alcohols, owing to their desirable properties, have found applications in many branches of industry. Properties of polyols, such as good taste, low calorie content and little effect on blood sugar levels have paved the way for the use of these compounds in the production of prepared foods, cosmetics and pharmaceuticals \u20133. It had-sorbitol, a six-carbon sugar alcohol, is widely used as sweetening agent, plasticizer, as well as capsule and tablet diluent [d-sorbitol, despite having a structure similar to that of its isomer d-mannitol, shows a real difference in solubility in water and in osmotic pressure coefficients [d-sorbitol is a relatively stronger disruptor of the water structure than d-mannitol [Among various polyols,  diluent , 7. It ificients . It has mannitol .d-mannitol and xylitol [d-sorbitol and amino acids. Density and sound velocity data at 298.15\u00a0K for some ternary mixtures (amino acid\u2009+\u2009d-sorbitol\u2009+\u2009water) have been reported by Jha and Kishore [d-sorbitol solutions for amino acids and they postulated the existence of hydrophilic/polar group interactions in the systems. The same conclusion was reached by Banipal et al. who studied volumetric properties of d-sorbitol in aqueous solutions of l-glycine [To the best of our knowledge, reports on the effects of amino acids on the structure of water modified by sugar alcohol are still scare. Most of the thermodynamic data have been collected for systems with  xylitol \u201315. So f Kishore . Moreove Kishore . The aut-glycine .d-sorbitol in aqueous amino acid solutions using volumetric and acoustic measurements. The densities at T\u2009=\u2009 K and sound velocities at T\u2009=\u2009298.15\u00a0K for d-sorbitol in  mol\u00b7kg\u22121 aqueous solutions of l-alanine, l-cysteine and l-histidine are reported. Additionally, corresponding data for d-sorbitol in aqueous solutions of NaCl was also collected. The paper presents calculations of the apparent molar volumes and the apparent molar compressibilities, as well as their limiting values. The corresponding transfer parameters and limiting apparent molar expansibilities are also estimated. The evaluated parameters were correlated and interpreted in terms of the different types of interactions that can occur in ternary systems. The structure making/breaking tendency of d-sorbitol in aqueous amino acid or NaCl solutions is also analyzed.The present study was aimed at providing some additional data on the properties of d-sorbitol (\u2265\u20090.98), l-alanine (\u2265\u20090.99), l-cysteine (\u2265\u20090.99) and l-histidine (\u2265\u20090.99) were obtained from Carl Roth GMbH\u2009+\u2009Co. KG, sodium chloride (\u2265\u20090.999) was purchased from POCh and were used without further purification. Table\u00a0d-sorbitol and all amino acids and NaCl were dried under reduced pressure at 323\u00a0K. Deionized, doubly distilled, degassed water with a specific conductance of 1.15\u2009\u00d7\u200910\u22126\u00a0S\u00b7cm\u22121 was used for the preparation of  mol\u00b7kg\u22121 solutions of l-alanine and l-cysteine, whereas in the case of l-histidine only three solutions  mol\u00b7kg\u22121 were made due to its lower solubility. All the solutions were prepared by weight dilution of the stock solution of d-sorbitol using a Mettler Toledo balance with a precision of\u2009\u00b1\u20090.0001\u00a0g.\u22123\u00a0kg\u00b7m\u22123.The densities of the ternary mixtures were measured at different temperatures using a digital vibrating-tube analyzer , equipped with a built-in solid-state thermostat that controls the temperature by means of a combination of thermoelectric Peltier elements and an intergrated Pt-100 resistance thermometer with an accuracy of 0.01\u00a0K. The measurement cell in the apparatus is made of borosilicate glass. Prior to each series of measurements, the apparatus was calibrated using doubly distilled and degassed water and with dry air at atmospheric pressure (0.1\u00a0MPa). The standard uncertainty in the density measurements was within\u2009\u00b1\u200935\u2009\u00d7\u200910\u22121 using the sound analyzer OPTIME 1.0 from OPTEL (Poland), based on the time of flight method. Measurements are based on the determination of the time that the acoustic signal with a frequency of 8\u00a0MHz takes to pass through a sample of known length. The length of the quartz measurement cell was determined with doubly distilled water, with the value 1496.69\u00a0m\u00b7s\u22121 used as the sound velocity in pure water at 298.15\u00a0K. Temperature during measurements was stabilized by a constant temperature bath (model: PolyScience 8202) at 298.15\u2009\u00b1\u20090.01\u00a0K.The sound velocities were determined with a standard uncertainty of 0.15\u00a0m\u00b7sd-sorbitol in aqueous l-alanine, l-cysteine, l-histidine and NaCl are reported in Tables\u00a0d-sorbitol and also with the molality of amino acids or sodium chloride. Irrespective of temperature, the increase in density resulting from increased concentration of d-sorbitol is greatest in the case of solutions in water. The greater the amount of amino acid or NaCl in the solution, the smaller is the increase. Moreover, with increasing temperature the observed effect, i.e. the increase in density with increasing concentration of d-sorbitol, becomes less pronounced. For all the systems studied, the density decreases with an increase in temperature.The experimental values of molality, density and apparent molar volume at various temperatures of the solutions of \u03d5V of d-sorbitol in the ternary systems were calculated from the densities of the solutions using the following equation:m denotes the molality of solution, d and d0 are densities of solution and solvent, respectively, and M2 is the molar mass of the solute.The corresponding values of the apparent molar volumes d-sorbitol in 0.3\u00a0mol\u00b7kg\u22121l-alanine at temperatures between 288.15 and 318.15\u00a0K. As seen from the plots, the relationship is linear across the whole d-sorbitol molality range and the whole temperature range studied. Therefore, the limiting apparent molar volumes d-sorbitol in water [d-sorbitol in aqueous 2 and 4\u00a0mol\u00b7kg\u22121 NaCl at 298.15\u00a0K reported by Jasra and Ahluwalia and the data for  ternary solutions obtained by Jha and Kishore and by Ren et al. [l-alanine in fixed concentrations of aqueous d-sorbitol, not d-sorbitol in fixed concentrations of aqueous l-alanine as in the present study. Moreover, different temperature ranges and distinctly higher concentrations of d-sorbitol were studied. Thus, direct comparison of the results is impossible.Figure\u00a0in water . As is sn et al. , 17, 21.d-sorbitol is very small and therefore the standard deviations of the experimental slope SV are relatively high. However, a decrease of SV with temperature and co\u2013solute concentration can be observed. The results indicate that increasing temperature and increasing molality of amino acid or NaCl make the solute\u2013solute interactions weaker. Additionally, the values of the experimental slope for the same molality of co-solute and the same temperature follow the following order:d-sorbitol\u2009+\u2009NaCl\u2009+\u2009water) ternary system.As can be seen from Tables\u00a0d- sorbitol are positive and increase with increasing molality of amino acid or sodium chloride, as well as with increasing temperature. The limiting apparent molar expansibilities A0, A1 and A2 are constants. As is seen, the values of the limiting apparent molar expansibilities for all the systems studied are positive. This suggests that the temperature increase causes the liberation of solvent molecules from the solvation layer of d-sorbitol, thereby increasing the total volume of the system. Moreover, the fact that the limiting apparent molar expansibility values decrease with rising temperature indicates that at higher temperatures this effect is weaker.An examination of the data also reveals that the limiting apparent molar volumes of d-sorbitol is a structure breaker in water, as well as in aqueous amino acid and sodium chloride [The calculated values of the second derivate chloride .d-sorbitol, l-alanine, l-cysteine, l-histidine and NaCl. The values of Figure\u00a0Vint is the intrinsic molar volume, \u03c3 is the shrinkage in the volume due to hydrogen bonding between water and the hydrophilic solute and n denotes the number of hydrogen bonding sites [Vint consists of the van der Waals volume and the associated void or empty volume. For dilute solutions, it is reasonable to assume that the intrinsic molar volume is nearly constant with respect to concentration. Thus, the observed positive volume change accompanying the transfer of d-sorbitol from water to aqueous amino acid or NaCl solution may result from a decrease in the shrinkage in volume because of solute co-solute interactions. Additionally, the increasing values of the limiting apparent molar volumes of transfer with molality of NaCl or amino acid reveal that the interactions resulting in the dehydration of the sugar alcohol increase with the concentration of co-solute.It has been established by Shahidi, Farrell and Edward that the limiting apparent molar volume of a hydrophilic solute in water can be divided into two terms as:ng sites . Moreoved-sorbitol\u2009+\u2009NaCl\u2009+\u2009water) ternary system.As can be seen from Fig.\u00a0d-sorbitol and l-alanine, l-cysteine, l-histidine and NaCl in aqueous solutions can also be explained on the basis of the co-sphere overlap model [hydrophilic\u2013ionic interactions between hydrophilic groups of solute and ions of co-solute;hydrophobic\u2013ionic interactions between the hydrophobic alkyl chain of solute and ions of co-solute;hydrophilic\u2013hydrophilic interactions between the hydrophilic groups of solute and the hydrophilic groups of co-solute;hydrophobic\u2013hydrophobic interactions between the hydrophobic alkyl chain of solute and the hydrophobic alkyl chain of co-solute;hydrophobic\u2013hydrophilic interactions between the hydrophobic alkyl chain of solute and the hydrophilic groups of co-solute.The interactions between ap model . Accordid-sorbitol in aqueous amino acids all five types of interactions are possible, while in solutions of d-sorbitol in aqueous sodium chloride only two types of interactions, i.e. (1) and (2), can occur. Hydrophilic\u2013ionic interactions and hydrophilic\u2013hydrophilic interactions result in positive values of the limiting apparent molar volumes of transfer, whereas hydrophobic\u2013ionic, hydrophobic\u2013hydrophobic and hydrophobic\u2013hydrophilic interactions result in negative d-sorbitol in aqueous NaCl interactions of type (1) and for d-sorbitol in aqueous amino acids interactions of types (1) and (3) are predominant.It is obvious that in solutions of d-sorbitol versus molalities of l-alanine and NaCl at 298.15\u00a0K together with the literature data for d-sorbitol in aqueous l-glycine and sodium chloride [d-sorbitol in aqueous l-cysteine and L- histidine solutions are not shown. As is seen from Figs.\u00a0d-sorbitol displays highest positive values of the limiting apparent molar volumes of transfer in aqueous l-glycine, the smallest amino acid studied, while lowest values of l-alanine, the most hydrophobic amino acid studied. Comparison of the limiting apparent molar volumes of transfer of d-sorbitol between amino acids of the same alkyl chain length, i.e. l-alanine, l-cysteine and l-histidine, indicates that l-histidine is more hydrophilic than l-cysteine. This results in stronger hydrophilic\u2013ionic and hydrophilic\u2013hydrophilic interactions between d-sorbitol and l-histidine than those between d-sorbitol and l-cysteine, leading to more positive values of the limiting apparent molar volumes of transfer [Figure\u00a0chloride , 21. Fortransfer .Fig.\u00a04Thd-sorbitol in aqueous sodium chloride are consistent with that in literature. Moreover, the observed values of the limiting apparent molar volumes of transfer for that system are lower than those for (d-sorbitol\u2009+\u2009l-glycine\u2009+\u2009water). This is clearly the result of the strong hydrophilic\u2013hydrophilic interactions between d-sorbitol and l-glycine which do not take place between sugar alcohols and NaCl.As mentioned above, the experimental data on Vab and Vabb are the pairwise and triplet interaction coefficients, respectively, and mb is the molality of the co-solute [d-sorbitol in aqueous L-aniline, l-cysteine, L- histidine and NaCl solutions obtained in the present study. As is seen, in all cases the pairwise interaction coefficients are positive while the triplet interaction coefficients are negative. In general, the magnitude of volume interaction coefficients decreases with rising temperature. The fact that the pairwise interaction coefficients are positive and larger in magnitude than the triplet interaction coefficients suggests that the volumetric properties of the studied solutions are determined by the strong interactions between d-sorbitol and the amino acids or sodium chloride and that these interactions dominate over triplet interactions. Moreover, the decrease of volume interaction coefficients with rising temperature indicates that pair-wise interactions, as well as triplet interactions, become weaker at higher temperatures.In line with the proposition of Friedman and Krishnan, according to which the thermodynamic transfer properties of solutes in dilute aqueous solution are determined by solute and co-solute interactions without the consideration of solute\u2013solute interactions, and in conformity with the McMillan\u2013Mayer theory, the limiting apparent molar volume of transfer can be expressed as:o-solute , 27. Tabd-sorbitol in aqueous l-alanine, l-cysteine, L- histidine and NaCl are reported in Tables\u00a0d-sorbitol and water and intramolecular hydrogen bonds within d-sorbitol molecules themselves become stronger, resulting in a more ordered solution. Moreover, for solutions with the same molality of d-sorbitol, an increase in sound velocity with growing concentration of co-solute is also observed. This suggests that association among the molecules of the solution becomes stronger as the amount of amino acid or NaCl in solution increases.The experimental values of molality, sound velocity and apparent molar compressibility at 298.15\u00a0K of the solutions of \u03d5KS, of d-sorbitol in the ternary systems were calculated from the densities and the sound velocities of the solutions according to the equation:KS and The apparent molar compressibilities, KS was obtained from density and sound velocity values using the Laplace equation:The isentropic compressibility mentclasspt{minimad-sorbitol. Thus, the apparent molar isentropic compressibilities at infinite dilution were obtained by using the method of linear regression of the following relation:d-sorbitol in water obtained by Banipal et al. [d-sorbitol in aqueous amino acid or NaCl solutions is available for comparison purposes.The apparent molar compressibilities were found to increase linearly with the molality of l et al. . As is sd-sorbitol increase (become less negative) with the increase in molality of co-solute. Obviously, this is the result of the fact that when sugar alcohol is dissolved in aqueous amino acid or salt solution, interactions between co-solute and water and between water molecules themselves are disrupted and interactions between solute and co-solute and between solute and water are formed. Thus, with increasing concentration of co-solute, more water molecules are released into the bulk solution and the solution becomes more compressible.The values of the limiting apparent molar compressibilities of d-sorbitol from aqueous to aqueous amino acid or sodium chloride solutions according to the equation:The obtained values of d-sorbitol versus molalities of l-alanine, l-cysteine, L- histidine and NaCl. It can be seen that the l-alanine\u2009<\u2009l-cysteine\u2009<\u2009l-histidine\u2009<\u2009sodium chloride. The results obtained from acoustic studies are in accordance with the results from volumetric studies discussed earlier. They support the conclusion that the hydrophilic\u2013ionic and hydrophilic\u2013hydrophilic interactions in solutions of d-sorbitol in aqueous amino acids are predominant, while the properties of solutions of d-sorbitol in aqueous sodium chloride are determined by hydrophilic\u2013ionic interactions. Moreover, the absence of hydrophobic\u2013hydrophobic and hydrophilic\u2013hydrophobic interactions in the ternary system (d-sorbitol\u2009+\u2009NaCl\u2009+\u2009water) results in more positive values of the limiting apparent molar properties of transfer.Figure\u00a0d-sorbitol from water to aqueous solutions of l-alanine, l-cysteine, l-histidine and NaCl. Positive d-sorbitol in aqueous sodium chloride and the co-domination of hydrophilic\u2013ionic and hydrophilic\u2013hydrophilic interactions in solutions of d-sorbitol in aqueous amino acids. As the obtained values of the limiting apparent molar expansibilities are positive and decrease as the temperature rises, these dominating effects also increase with rising temperature.The limiting apparent molar volumes and the limiting apparent molar compressibilities of transfer have been determined for the transfer of d-sorbitol\u2009+\u2009NaCl\u2009+\u2009water) ternary system indicates that interactions between solute and co-solute in this system are stronger than in (d-sorbitol\u2009+\u2009amino acid\u2009+\u2009water) mixtures. Moreover, the order of d-sorbitol in aqueous solutions of l-alanine, l-cysteine and l-histidine, i.e. three amino acids with the same alkyl chain length, strongly suggests that the strength of alcohol sugar and amino acid interactions is determined by the hydrophobicity of amino acid.The fact that the highest values of the limiting apparent molar volumes and the limiting apparent molar compressibilities were obtained for the (d-sorbitol and amino acids or sodium chloride.The fact that the pairwise interaction coefficients are positive and of greater magnitude than the triplet interaction coefficients supports the conclusion that the properties of the studied solutions are determined by the strong interactions between"}
+{"text": "The Fokker\u2013Planck equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity equation. The x-ray Fokker\u2013Planck equation can simultaneously account for both propagation-based phase contrast, and the diffusive effects of sample-induced small-angle x-ray scattering, when forming an x-ray image of a thin sample. Two derivations are given for the Fokker\u2013Planck equation associated with x-ray imaging, together with a Kramers\u2013Moyal generalisation thereof. Both equations are underpinned by the concept of unresolved speckle due to unresolved sample micro-structure. These equations may be applied to the forward problem of modelling image formation in the presence of both coherent and diffusive energy transport. They may also be used to formulate associated inverse problems of retrieving the phase shifts due to a sample placed in an x-ray beam, together with the diffusive properties of the sample. The domain of applicability for the Fokker\u2013Planck and Kramers\u2013Moyal equations for paraxial imaging is at least as broad as that of the transport-of-intensity equation which they generalise, hence the technique is also expected to be useful for paraxial imaging using visible light, electrons and neutrons. A, and the \u201clocal converging lens\u201d at C, the nominal focal length f for each lens being much larger than \u0394. This is the key situation, of combined coherent and diffusive energy transport in a near-field paraxial imaging setting, that we wish to consider in the present paper. While we focus on the case of hard x rays, the methods considered here will also be applicable to paraxial imaging using visible light, electrons, neutrons etc.Suppose that coherent visible-light plane waves normally illuminate a thin lens made of glass that is slightly cloudy. For such a lens, a large percentage of the light will be coherently focused or defocused upon propagation beyond the lens. Conversely, a small percentage of the light will be diffusely scattered by the random cloudy inclusions within the glass. In the hard-x-ray analogue of this experiment, replace the glass lens with a thin semi-transparent sample whose large-scale projected structure locally resembles an aberrated converging or diverging lens see Fig.\u00a0, and rep3. One of the most often-employed, and most elementary, means is to first use the projection approximation to quantify the passage of an incident coherent scalar x-ray beam through the sample, and then use the Fresnel diffraction formalism to propagate the resulting exit-surface wave field to the surface of a detector4. The projection approximation assumes that: (i) the radiation is of sufficiently high energy that individual rays within the sample  are unchanged within the volume of the said sample in comparison to the streamlines that would have existed in the absence of the sample, and (ii) both phase and amplitude shifts are accumulated continuously and locally, as one traverses any such ray from the entrance surface of the sample to the exit surface\u2013see e.g. Sec. 2.2 of Paganin4. The Fresnel approximation, which is a consequence of the paraxial approximation, assumes that spherical Huygens-type wavelets can be approximated as having parabolic wave fronts. If the sample-to-detector propagation distance is sufficiently small, and if diffuse scattering is negligible, Fresnel diffraction implies that the transport-of-intensity equation5 (TIE) may be used to model the evolution of image intensity with respect to propagation distance downstream of the sample, for a paraxial quasi-monochromatic beam. The TIE, which is the continuity equation for paraxial wave fields, expresses local energy conservation6. It forms a basis for several imaging techniques in coherent x-ray optics7. Like the formalism of Fresnel diffraction upon which it is based, the TIE models what may be called \u201ccoherent energy transport\u201d downstream of a thin sample. That is, at each point in the space downstream of the sample, there is one time-independent energy-flow vector . However, if there is unresolved spatially random micro-structure within the sample11, then,\u00a0as hinted in our opening paragraph,\u00a0small-angle x-ray scatter12 (SAXS) will also be present. This augments the previously mentioned coherent energy-flow vector at each point in space, with an ensemble (\u201cSAXS fan\u201d) of energy-flow vectors associated with diffusive energy transport. How can this additional effect be taken into account, in modelling paraxial hard x-ray imaging of thin objects?We make the simplifying assumptions that: (i) magnetic effects such as x-ray circular dichroism in the sample can be ignored; (ii) the sample is non-crystalline, allowing x-ray Bragg-diffraction effects to be ignored; (iii) the sample is sufficiently thin that dynamical x-ray diffraction effects, within the volume of the sample, can also be ignored; (iv) all polarisation-sensitive effects can be ignored. Many well-known means exist, for the quantitative modelling of an x-ray beam interacting with such a sample and subsequently forming a paraxial image as it propagates through space13. The latter equation, which can model flows in radiation and matter wave fields that have both a coherent and a diffusive component, may be obtained in a very general setting as a limit case of the still more general Boltzmann equation of classical statistical mechanics14. The Fokker\u2013Planck equation is used in many fields: examples include Brownian motion14, hydrodynamics15, electron and photon transport in biological tissues17 and homogeneous media18, high-temperature atomic-level disorder in pre-melting surfaces19, gaseous micro-flows20, droplet nucleation21, dilute polymer dynamics22, hot plasmas23, biaxial fluids24, cold turbulent gas jets25 and quark gluon plasmas26. Notable also is the use of the Fokker\u2013Planck equation in the non-imaging context of x-ray kinematical and dynamical diffraction from imperfect crystals with stochastically distributed defects28. An extremely recent application, which is particularly close to that developed in the present paper, uses Fokker\u2013Planck concepts to model the position probability density of a nano-particle in a near-field optical trap29.One answer is provided by a more general equation than the TIE, namely the the Fokker\u2013Planck equation30);Local absorption by the object ;Local lensing by the object which concentrates or rarefies energy density due to local focusing or defocusing (propagation-based Laplacian-type phase contrast31);Local prism-like effects of the object which transversely shift optical energy .The first three effects are associated with the \u201cTIE part\u201d of the Fokker\u2013Planck equation, with the fourth effect associated with the \u201cdiffusion equation\u201d part. Of particular interest is the use of an x-ray form of the Fokker\u2013Planck equation for modelling forward problems in paraxial x-ray imaging in a simple manner, e.g. by expressions valid in the near field  the transport-of-intensity equation for coherent energy transport in paraxial monochromatic x-ray beams, with (ii) the diffusion equation for diffusive paraxial energy transport associated with small-angle x-ray scattering within a sample. The second\u00a0derivation is a microscopic treatment based on first principles, which relies on the crucial assumption that the phase at the exit surface of the object can be written as a sum of (i) a component that varies slowly with respect to the detector pixel size, and (ii) a component that fluctuates many times over one detector pixel and is therefore unresolved. We then give a generalised form of the Fokker\u2013Planck equation, known as the Kramers\u2013Moyal equation, as a means for treating the in-sample SAXS in a more precise manner. Next we\u00a0sketch some indicative means by which the Fokker\u2013Planck and Kramers\u2013Moyal equations may be used in the forward problem of modelling near-field intensity contrast in coherent x-ray imaging, together with the associated inverse problem of phase retrieval and SAXS determination. We also consider some broader implications of the Fokker\u2013Planck formalism.Here we give two complementary derivations of the x-ray Fokker\u2013Planck equation. The first is phenomenological, based on local conservation of energy in the presence of both coherent and diffusive paraxial x-ray energy transport. The second is a microscopic first-principles analysis. The former derivation is more general, while the latter is more physically illuminating.5 for coherent paraxial x-ray energy transport and then separately consider the diffusion equation for diffusive paraxial x-ray energy transport. We then show that these two equations may be merged, in a manner that conserves energy both locally and globally, to give the Fokker\u2013Planck equation for paraxial x-ray imaging.X-ray beams \u201cflow\u201d in the sense that they stream optical energy as they propagate. As a descriptor of such energy flows, the Fokker\u2013Planck equation may be viewed as a diffusive generalisation of coherent paraxial photon energy transport. Adopting this perspective, below we consider the transport-of-intensity equation5 describes the intensity evolution of a paraxial complex coherent scalar wave field as it propagates. This continuity equation, arising from the parabolic equation of paraxial scalar wave optics, expresses local energy conservation. It states that the negative divergence\u00a0\u2013\u00a0which may loosely be spoken of as the \u201cconvergence\u201d\u00a0\u2013\u00a0of the transverse Poynting vector (energy flow vector) is proportional to the longitudinal rate of change of intensity5:I is the intensity of the monochromatic scalar\u00a0wave field, \u03d5 is its phase, k is the wave-number and \u2207\u22a5 is the gradient in  planes perpendicular to the optical axis z. Equation (The transport-of-intensity equationcoherent x-ray energy transport. The conserved (Noether39) current is the transverse Poynting vector, which up to a multiplicative constant is10As previously mentioned, the TIE is a continuity equation expressing local energy conservation under The corresponding constant Noether charge in vacuo through a distance \u0394\u2009\u2265\u20090 that is sufficiently small\u00a0for the Fresnel number to be much greater than unity, a longitudinal finite-difference approximation to the TIE can be used to model the resulting propagation-based phase contrast4:For propagation speculum). Rays passing through A have a positive divergence, hence the intensity at B is reduced compared to that which would have been registered if the rays passing through A had all been parallel to the optical axis z. Similarly, rays passing through C have a negative divergence (positive \u201cconvergence\u201d), hence the intensity at D is increased compared to that which would have been obtained had the rays exiting C been parallel to the optical axis. This phase contrast effect is increased with increased propagation distance \u0394, reduced x-ray energy (decreased wave-number k) or faster spatial variations in wave-field phase (larger D being slightly shifted from the point x\u2009=\u2009x0. Concentration or rarefaction of energy density (and hence\u00a0intensity) may be thought of as due to the lensing term proportional to 31.The underpinning physics is sketched in an imaging context in Fig.\u00a0) in Eq. , while tD to describe the effects at distance z\u2009=\u2009\u0394 downstream of an illuminated thin object in the plane z\u2009=\u20090. The fact that this coefficient depends on x and y reflects the fact that the SAXS fan will in general vary with position over the nominal exit surface z\u2009=\u20090 of the thin sample. Bearing all of this in mind, the intensity evolution of the beam may then be described by the diffusion equation:If there were only diffusive energy transport on account of unresolved micro-structure in the sample (i.e. SAXS), but no specular refraction, we could instead introduce a diffusion coefficient D, since SAXS-induced diffusive blur has a characteristic transverse width that scales with \u0394 rather than \u03941/2.Note that a formal dependence on \u0394 has been added to the diffusion coefficient x illuminates a slab containing SAXS-inducing unresolved micro-structure. This width \u0394x is assumed to be large compared to the characteristic length scale of the projected micro-structure, but small compared to the characteristic transverse width associated with the macroscopic projected phase and attenuation coefficients of the object. The illuminated region E of the slab, located at transverse coordinate x\u2009=\u2009x0, results in a smooth SAXS fan of opening angle \u03b8(x0), which smears the propagated intensity over the plane z\u2009=\u2009\u0394. The characteristic width of this blur, which may be considered as a broadening of the local rocking curve due to the sample41, isThe effect shown in one transverse dimension in Fig.\u00a0\u03b8(x0) of the SAXS fan is taken to completely characterise its diffusive effects at each location x0; a more sophisticated treatment which replaces the single number \u03b8(x0) (or its associated diffusion coefficient) with a hierarchy of tensors, will be given later.Thus, local diffuse scattering by a thin object leads to a transverse smearing of intensity upon propagation. This blur increases with increased propagation distance \u0394. At the level at which diffusion is here being considered, the opening angle diffusive x-ray energy transport. Here, the conserved current is given by Fick\u2019s first law as42Like the TIE, the diffusion equation may be viewed as a continuity equation expressing local energy conservation, albeit under F is the fraction of the optical energy converted to SAXS43 when illuminating a thin sample in the plane z\u2009=\u20090 at the point . If 11 and hard44 x-rays) one can replace 1\u2009\u2212\u2009F in the above expression by 1. The resulting convection\u2013diffusion equation (forward Kolmogorov equation13) is the Fokker\u2013Planck equation in two transverse dimensions. It models both effects in Fig.\u00a0If both specular refraction and local-SAXS effects are present simultaneously, we can add the TIE and diffusion equations together, in an energy-preserving manner. This gives the continuity equation:mentclass2pt{minimF is slowly varying with x and y, we obtain the 2\u2009+\u20091-dimensional Fokker\u2013Planck equation:If the expressions for the coherent current In one transverse dimension, this becomes the one-dimensional Fokker\u2013Planck equation:The corresponding finite-difference forms, which are to be preferred for reasons that have already been outlined, are respectively given by the following pair of equations:D may be considered to be sufficiently slowly varying with respect to transverse coordinates that D commutes with the transverse Laplacian, we may instead work with the simpler finite-difference expressions:We close this section by noting that, if FD plays the role of an effective diffusion coefficientIn the above two finite-difference Fokker\u2013Planck equations, Here we derive the x-ray Fokker\u2013Planck equation from first principles. We consider two length scales of sample-induced wave-field variation. The larger scale corresponds to the length scales in the sample that are sufficiently large for their absorptive and refractive effects to lead to detector-resolvable intensity variations. The smaller length scale corresponds to diffuse scattering from unresolved micro-structure resulting in SAXS. This derivation clarifies the physical mechanisms underpinning both coherent and diffusive x-ray energy transport, in a paraxial x-ray imaging context.\u03c8 be the spatial part of the complex scalar amplitude at the exit surface of a sample. Subsequent Fresnel diffraction gives4P\u0394(x) is the Fresnel propagator corresponding to free-space diffraction through a distance \u0394\u2009\u2265\u20090, and paraxial radiation is assumed throughout. The squared modulus of the above convolution integral gives the propagated intensity as the following linear combination of contributions from every pair of points x\u2032, x\u2033 in the unpropagated wave field45:We work in one transverse dimension for simplicity, ignore polarisation and assume monochromatic x rays. Let z\u2009=\u20090. Many models exist for incorporating unresolved micro-structure into this sample47. Follow Voronovich47, Nesterets45 and Yashiro et al.49 in decomposing the phase \u03d5 of \u03c8 as\u03d5s(x) is a phase component that varies slowly with respect to the detector pixel size, and (ii) \u03d5f(x) is a fast-varying spatially\u00a0random phase due to the sample micro-structure, which fluctuates many times over one detector pixel and is thus unresolved . Further assume a slowly-varying intensity Is(x), together with x-rays that are of sufficiently high energy for the projection approximation to hold for a given sample. Hence45:The sample is assumed to be thin, normal to the incident plane-wave illumination, and with nominal exit surface d so Eq.  becomes4\u03d5f(x)52. Denoting this average by an over-line,Average over an ensemble of realisations of the unresolved fast phase-maps \u03d5f to be spatially statistically stationary over transverse displacements that are small compared to the characteristic length scale over which \u03d5sfluctuates appreciably, the over-lined expression in Eq. (x\u2032\u2009\u2212\u2009x\u2033. Assuming \u03d5f(x\u2009\u2212\u2009x\u2032) and \u03d5f(x\u2009\u2212\u2009x\u2033) to be Gaussian variables,\u00a0with zero mean, this correlation function is53x-dependent variance of the ensemble of fast phase maps {\u03d5f(x)}, and54 as a function of coordinate separation \u0394x and transverse coordinate x.Assuming the fast phase maps n in Eq.  depends et al.55).The quantity e of Eq.  does not51 in separating out the asymptote term from C is a re-normalised correlation function\u03c4 is the transverse correlation length , if we 59 and the frozen-phonon model of electron diffraction theory. Note also that a non-zero specular-diffraction component  indicates the SAXS-induced speckle to be\u00a0\u201cpartially developed\u201d60; this may be contrasted with the case of \u201cfully developed\u201d SAXS speckle, which is not relevant to our context, in which the specular component would be fully extinguished.Note that a similar bifurcation of energy flows occurs, for similar reasons, in statistical dynamical x-ray diffraction theoryIs(x) to be sufficiently slowly varying that the square-root term in Eq. (Is(x). For the complex exponent in Eq. (\u03d5s(x) with respect to x; the above equation makes implicit use of the fact that \u03d5f varies much more quickly than \u03d5s. Then write P\u0394(x\u2032) in Eq. :Assume m in Eq.  may be rt in Eq. , make th) in Eq.  as a FouC in Eq.  as Fourix, integrates over a fan of rays making angles \u03d5f(x)}. The whole fan of SAXS rays is rotated by the angle x\u2009=\u2009x0, are integrated over a single pixel. See Fig.\u00a063, while the fan rotation angle 64. The function 43, is proportional to the power spectrum of the ensemble of fast-phase fields 65); this power spectrum  g(cf. Eq. ).d is a diffusive blur kernel given byIf the object-to-detector distance \u0394 is large enough that the SAXS-induced fan of rays in Fig.\u00a0d is simply a transverse re-scaling of kx  to a function of the transverse coordinates x over the detector plane. Stated differently, d is the intensity distribution of SAXS, as a function of position x on the detector, due to x rays incident at position x0. If the object-to-detector distance \u0394 is sufficiently small, two additional approximations can be made.(i)d to be sufficiently narrow for its Fourier transform x to be sufficiently broad that it can be represented by a second-order Taylor expansion in kx. The term in the Taylor series for kx will vanish since C is approximately even in \u0394x (cf. Eq. (x0-dependent blurring width (this blurring being due to SAXS), and Q is a positive constant. Invoke conservation of energy, which implies that the total scattered intensity,\u00a0due to an incident x-ray pencil beam of intensity Is(x) and with small thickness \u0394x,\u00a0will have the same integrated intensity after scattering from the object; see Fig.\u00a0Q\u2009=\u20091, so that et al.67). Hence we may approximate Eq. . Given \u2297 in Eq.  is well mate Eq.  as:36\\dod depends on x0. We use the convolution notation for clarity, however, to denote such smearing with a position dependent point spread function that results from the position-dependent SAXS. See also the next section, for an analysis that considers the same linear integral transform using a more conventional and explicit notation.Before proceeding, let us back-track a little, and point out that in Eq.  we consi(ii)5 may be applied to the first term on the right of Eq. 37) are sAssume only a small fraction of the incident x rays to be converted to SAXS, so that Upon comparing the final term of Eq.  with theDeff obeys Eq.  and (b);The link between D and L follows from Eq.  and (d);The link between D and \u03b8 follows upon eliminating L from relations (a) and (d);The link between D and Deff follows from Eqs (The link between from Eqs  and 41)D and Deffrom Eqs .We close this section with Fig.\u00a0L is directly proportional to the angular spread \u03b8 of the SAXS fan; the blur width L is directly proportional to the sample-to-detector distance \u0394; (b) the angular width \u03b8 of the SAXS fan is inversely proportional to the transverse length scale l of the projected unresolved micro-structure, etc.All physical dependencies, for the quantities in Fig.\u00a0\u03b8 at each point over the exit surface z\u2009=\u20090 of a thin sample. Here, we show that a less-crude treatment leads to the Kramers\u2013Moyal generalisation of the Fokker\u2013Planck equation, in a form suitable for x-ray near-field imaging of thin objects.The preceding analysis gives only a crude treatment of the angular distribution of the local SAXS fan, which is described merely via its angular spread F of the x-ray beam which is channelled into SAXS. The two-transverse-dimensional forms of Eqs  an anF\u2009\u2192\u20090, Eqs z\u2009=\u20090, whd\u03a9 is an infinitesimal element of solid angle and \u03b8x, \u03b8y describe angular deflections (scattering angles) in the x, y transverse directions, respectively69. Hence conclude that 66 associated with unresolved micro-structure in the sample, namely a differential scattering cross section x\u2032, y\u2032), as well as upon the scattering angles \u03b8x, \u03b8y. Thus we have the proportionalityz\u2009=\u20090, superposes a micro-structure-independent near-field Fresnel diffraction pattern that is damped with a decoherence factor45 1\u2009\u2212\u2009F, with a diffusely-scattered signal et al.36; this amounts to a measurement of Recall the usual definition of a differential scattering cross section d in Eq.  is propoquations  and 43)\\documentz\u2009=\u20090. In these same equations, \u0394 may be sufficiently large that the SAXS fan x\u2032, y\u2032, 0) over the exit surface z\u2009=\u20090 of the thin object, and considered as a function of coordinates  over the detector in the plane z\u2009=\u2009\u0394\u2014can have a width that is several pixels or more 43), the cf. Fig.\u00a0. If thesthen Eqs  and (43)\u03b8 of all differential scattering cross sections contained in x, y), so that Eq. 43). Thisx\u2032, y\u2032) over the exit surface of the sample to produce an intensity distribution that is a function of detector coordinates  in the plane z\u2009=\u2009\u0394\u2014obeys:We have assumed that each SAXS fan F is a scattering fraction which accounts for the fact that only a certain percentage of the incident beam is converted to SAXS upon passage through the sample.This normalisation condition is appropriate since the multiplicative factor of We have assumed thatr in Eq. . This eld in Eq. . There iet al.67), which arise from terms of progressively higher order in the Taylor expansion of Is about :We have defined the following hierarchy of diffusion tensors \u2009=\u20090 case of Eq.  and all higher-order diffusion tensors to zero, and assuming rotationally-invariant SAXS fans viaSetting D(3) and all higher-order diffusion tensors to zero, thereby reducing Eq.  may be obtained using Eqs ;;72 from Eschewing the Kramers\u2013Moyal and Fokker\u2013Planck approximations and instead working with Eqs  and 43)43) direcThe e of Eq.  is the c(see Eq. ). The fin in Eq.  if we caThe primary goal of this paper is to give several means by which the Fokker\u2013Planck equation  may be used to model forward and inverse problems of near-field x-ray imaging, in the presence of both phase\u2013amplitude shifts and non-negligible small-angle x-ray scattering from unresolved micro-structure in a thin sample.76, is studied in detail in a companion paper77 that gives a number of analytical expressions based on the finite-difference expression in Eq. ,\u00a0this being the fraction of the incident radiation that is converted to SAXS,\u00a0may be brought into the second square brackets on the right hand side of Eqs 76, is ste of Eqs , and thee of Eqs , 29) an an76, ise of Eqs , in addi (i) Eqs  and 36)76, is st (i) Eqs  and 43)76, is st (i) Eqs  and 45)76, is stThe above indications, of the forward problem of near-field and intermediate-field x-ray imaging for a thin sample in the presence of both coherent and diffusive scattering, set up Fokker\u2013Planck and Kramers\u2013Moyal equations that can be used to consider the associated inverse problem of reconstructing intensity, phase and diffusion from measured intensity data. It is again beyond the scope of our paper to explore this point further, beyond the indicative suggestions given in the three examples below.72, and the scattering fractions F obtained using the same data. Since both k are known, the only remaining unknown in Eq. .As a first example of inverse problems that may be tackled based on the formalism of this paper, observe that the diffusion-tensor moments may be\u00a0measured e.g. using the previously-mentioned technique of raster scanning a focused quasi-monochromatic x-ray probe over a lattice of points at the entrance surface of a\u00a0thin objectn in Eq.  would be82. The technique of x-ray speckle tracking illuminates an object with a known resolved reference speckle field, and then measures one or more distorted forms of that speckle field which arise when a sample is placed in the illuminating speckle beam. The diffuse-scatter signal, considered in the present paper, arises naturally in x-ray speckle tracking\u00a0\u2013\u00a0via unresolved sample-induced speckles that should be carefully distinguished from the titular illuminating speckles\u00a0\u2013\u00a0and gives useful information that may be extracted using a variety of techniques. These techniques are typically based on the reduction in illuminating-speckle visibility due to SAXS-induced diffusion: see e.g. the review by Zdora83, and references therein. The geometric-flow approach to speckle tracking, which has recently been developed for x-rays87 but has also been very recently applied to visible-light imaging88, takes as a starting-point the following equation:A second application of the formalism of the present paper, is to the field of x-ray speckle trackingIR of a reference speckle image obtained in the absence of a sample, to the distorted/coded/encrypted form of that speckle image, denoted IS, obtained in the presence of a pure-phase-object sample; D\u22a5 is a transverse\u00a0displacement-vector field, which distorts the reference speckle image IR into the speckle image IS obtained in the presence of the sample. The above equation, modelled on the continuity equation that has played such a dominant role in the present paper, conserves photon energy both globally and locally. It may be used to reconstruct the speckle displacement D\u22a5 induced by the phase object, and hence a map of the phase shift \u03d5 due to the object, in a simple and efficient manner that implicitly rather than explicitly tracks speckles87. Note that the displacement field is related to the phase shift of the object, viak is the wave-number of the x-rays. A Fokker\u2013Planck form of Eq.  and effective diffusion coefficient Deff, is:This relates the intensity m of Eq. , suitabl\u03d5 and Deff rather than just \u03d5. Of possible\u00a0relevance in such a context\u00a0\u2013\u00a0namely, of separating out the signal due to coherent versus diffusive energy flow\u00a0\u2013\u00a0is the fact that Deff will transform as a scalar upon rotation of the sample through 180 degrees , whereas D\u22a5 will transform as a vector under the same rotation.This incorporates both coherent flow and diffuse flow, into the geometric-flow method for x-ray speckle tracking. It would be interesting to investigate an augmented form of the geometric-flow x-ray speckle-tracking method, which takes Eq.  rather t489. The associated unresolved micro-structure is left arbitrary, and the exit surface of the sample is assumed to correspond to the plane z\u2009=\u20090. Further assume normally-incident unit-intensity illumination by z-directed quasi-monochromatic x-ray plane waves. This single-material approximation, together with the projection approximation4, implies that the x rays at the exit surface of the sample have an intensity As a third and somewhat more detailed example of inverse problems that may be tackled using the formalism outlined in the present paper, consider a static non-magnetic non-crystalline sample that is made of a single material. This sample may and in general will have varying spatial density, with complex refractive index\u03bc\u2009=\u20092k\u03b2 is the linear attenuation coefficient of the material from which the sample is composed, and T is the projected thickness of the sample along the z direction. The fact that7Here n in Eq.  to be trDeff. Equation ] of the single-material sample with projected thickness T, and is an algebraic equation for the unknown effective diffusion coefficient  Deff. Note that the Deff\u2009\u2192\u20090 limit of Eq.  to vanish, we may solve Eq.  and T, as follows. Suppose propagation-based phase contrast images are obtained at two different propagation distances, \u03941 and \u03942. From Eq. (f) in Fig.\u00a0Here, we have used Eq.  to incorEquation  is a lint of Eq.  is the bolve Eq.  for bothz\u2009=\u20090 of the object and the entrance surface z\u2009=\u2009\u0394 of the detector, is not a diffusive medium. Thus the width of the SAXS fans scales linearly with \u0394, rather than being proportional to \u03941/2 (as would be the case for true diffusion). Setting D\u2009\u221d\u2009\u0394 ensures that the final term on the right side of Eq. 2\u2009=\u2009\u0394, as required. As is the case throughout the paper, the artifice of a \u0394-dependent diffusion coefficient is a price to be paid for the simplicity of being able to work simultaneously with both diffusion concepts and free-space coherent propagation concepts, in the context of the Fokker\u2013Planck and Kramers\u2013Moyal equations for x-ray imaging. To proceed we write the z\u2009=\u2009\u03941 and the z\u2009=\u2009\u03942 cases of Eq. . Hence:This scaling results from the already-mentioned fact that the slab of vacuum, in between the exit surface e of Eq.  is propos of Eq. , and thes of Eq.  to elimiet al.7, and may therefore be solved using the same Fourier-transform method. This gives:Equation  is mathex and y, in any convention that transforms \u2202/\u2202x into ikx and \u2202/\u2202y into iky;  are Fourier coordinates corresponding to , and 1 and \u03942, may be combined to yield the projected thickness T of a thin single-material sample, in a manner that is independent of SAXS scattering by the sample . Once T has been so obtained, Eq. . Such a phase/dark-field retrieval approach that incorporates dark-field effects might benefit samples from a range of fields including materials development  and biomedical imaging (e.g. diagnostic imaging of the lungs91).Here, Equation  shows honed, Eq.  can thenThe first contributor to the hierarchy of diffusion tensors is the sample-induced scatter due to unresolved micro-structure, that has been a main theme of the present paper.44 that is now known to be due to unresolved sharp edges92, and which may be viewed as a Young\u2013Maggi\u2013Rubinowicz type boundary wave97 or a Keller-type98 diffracted ray. This is examined in further detail in the previously mentioned companion paper77.The second contributor to the diffusion tensors is an edge-scattering signalDeff to a constant Deff(\u0394) that is independent of x, y so as to model penumbral blur due to finite source size in a linear shift-invariant imaging system, and then note that the resulting equation has a solution identical to that recently published by Beltran et al.99.The third contribution to the diffusion tensors is associated with incoherent aberrations  of the imaging system that is used to measure images of the sample. As an example: take Eq. , set DefIn the third example above, and indeed throughout the paper, the effective diffusion coefficient ) wi) wi50)) All three effects will in general be present simultaneously, so that e.g. the SAXS fans associated with sample-induced blurring will need to be convolved with the intensity point-spread function of a given optical imaging system, and similarly with the signal associated with unresolved sharp edges. These interesting complications,\u00a0which may be summarised in the statement that \u201cpartial coherence can come from the source, or the object itself\u201d,\u00a0are beyond the scope of the present paper.101. From an unsharp-mask image processing perspective, the linear differential\u00a0operator102I\u00a0to which it is applied, with a characteristic position-dependent partial-deconvolution transverse length scale equal to w; cf. Eq. , is 102:64\\dThis blurring is rotationally symmetric. If this rotational symmetry is not present, we can use a Kramers\u2013Moyal type linear differential\u00a0operator to effect local blurring with a position-dependent point-spread function, namelyx\u2009\u2261\u2009\u2202x, \u2202/\u2202y\u2009\u2261\u2202y. This gives another perspective on the use of derivative operators to effect blurring associated with a position-dependent point spread function. Similar ideas are used in image sharpening via coherent defocus67 and image blurring operations of the convolution type103.The notation above is analogous to the diffusive terms in\u00a0Eq. , and we 104 would be an interesting avenue for future research, since Wigner functions naturally capture the idea that there can be a distribution of energy flow vectors at each point in space105. See e.g. Eq. (19) of Nugent and Paganin106, which was obtained via a Wigner-function formulation of paraxial optics, and which may be readily manipulated into a Fokker\u2013Planck form given by Eq.  the partial coherence of the illuminating beam and its associated spatio-temporal speckles, and (ii) unresolved speckle associated with sample micro-structure. In the present paper, the spatial width w of the point-spread function (PSF) of the position-sensitive detector\u2014a lower limit on which is given by the pixel size\u2014defines a natural transverse length scale. Speckles much smaller in size than w will be spatially averaged when registering an image. If ergodicity of the associated stochastic process can be assumed, over the area of each pixel, then by definition the spatially-averaged intensity at each pixel location can be replaced with a corresponding ensemble average over many realisations of the ensemble of fields illuminating each pixel. Physically, and as has been used in the present paper, this corresponds to a statistical ensemble of objects, each of which has the same coarse-grained projected complex refractive index distribution, but differing spatially-random micro-structure. This construct permits us to approximate the resulting measured intensity map, with a probability distribution obeying the 2\u2009+\u20091-dimensional Kramers\u2013Moyal equation, including the special case of the 2\u2009+\u20091-dimensional Fokker\u2013Planck equation. Refraction and prism terms are associated with the resolved coarse-grained structure of the ensemble of objects and the ensemble of illuminations, with the diffusion term being associated with the unresolved speckles. What is deemed SAXS is a detector-resolution-dependent construct associated with unresolved sample-induced speckles. Thus, the component of the scattered radiation attributed to SAXS is dependent on w, and thereby detector dependent. This last statement ties in with the broader idea that there is a close link between partial coherence and the spatio-temporal resolution of one\u2019s detector\u2014see e.g. Sec. 3.6.3 of Paganin4. It is also closely related to what component of the x-ray energy flow is classed as \u201ccoherent energy transport\u201d, and what is classed as \u201cdiffusive energy transport\u201d, in the Fokker\u2013Planck and Kramers\u2013Moyal constructions: the finer the spatio-temporal resolution of the intensity detection, the smaller the fraction of the x-ray energy flow that will be classed as diffusive. Both the TIE-type and SAXS-type scattering (resolved and unresolved structures) arise from the same fundamental physics, as is clear in the first-principles derivation\u00a0of the x-ray Fokker\u2013Planck equation. Again, what length scales ultimately fall into either category is determined by the resolution of the detector.Unresolved speckle lies at the heart of many phenomena observed in imaging using partially coherent optical fields109, electrons110, neutrons111 and x-rays7, there is every expectation that the formalism of the present paper may be utilised for paraxial-imaging scenarios using all of the just-listed radiation and matter wave fields. Extensions of the present paper, to imaging applications beyond those listed previously, include a Fokker\u2013Planck approach to neutron phase contrast imaging112, x-ray magnetic circular dichroism imaging113, x-ray edge-illumination imaging114, x-ray Zernike phase contrast\u00a0imaging115, neutron grating imaging116, electron out-of-focus contrast imaging (Fresnel contrast imaging)117 and visible-light out-of-focus contrast imaging109. As with the present study, a core motivation for such an approach is its potential simultaneously to model, under the aegis of a single powerful formalism, both deterministic and stochastic aspects of paraxial thin-object imaging using partially coherent radiation and matter wave fields.We close this discussion by emphasising the broader applicability, beyond the margins delineated in the present paper, of the Fokker\u2013Planck and Kramers\u2013Moyal equations to (i) partially coherent paraxial x-ray imaging in particular, and (ii) partially-coherent paraxial imaging more generally. Context may be given to this claim, by the huge domain of applicability of Fokker\u2013Planck and Kramers\u2013Moyal concepts. Of equal relevance is the likelihood that the domain of validity of the paraxial-imaging Fokker\u2013Planck and Kramers\u2013Moyal equations is at least as broad at that of\u00a0the transport-of-intensity equation which they generalise; and, since the transport-of-intensity equation has been applied to visible lightFokker\u2013Planck and Kramers\u2013Moyal equations were obtained, to model near-field and intermediate-field paraxial quasi-monochromatic x-ray imaging of thin samples exhibiting both phase\u2013amplitude and small-angle-scattering contrast. Two complementary derivations were given. Possible applications, to both forward and inverse imaging problems, were discussed."}
+{"text": "The aim of present work is to study some kinds of well-posedness for a class of generalized variational-hemivariational inequality problems involving set-valued operators. Some systematic approaches are presented to establish some equivalence theorems between several classes of well-posedness for the inequality problems and some corresponding metric characterizations, which generalize many known results. Finally, the well-posedness for a class of generalized mixed equilibrium problems is also considered. Nowadays, well-posedness has been drawing great attention in the field of optimization problems and related problems such as variational inequalities, hemivariational inequalities, fixed point problems, equilibrium problems, and inclusion problems see , 23, 33), 3323, 3As an important and useful generalization of variational inequality, hemivariational inequality, which was first studied by Panagiotopoulos , has a g\u03d5-quasimonotonicity and obtained some existence theorems when the constrained set is nonempty, bounded (or unbounded), closed, and convex in a reflexive Banach space. Hereafter, Wangkeeree and Preechasilp tonicity , a resultonicity , and somtonicity .K be a nonempty, closed, and convex subset of a real Banach space X with its dual u in the direction v. In this paper, we discuss the following generalized variational-hemivariational inequality (GVHVI):Let Find If Find g and He .If Find nd Huang .If Find  The existence of solutions to this inequality was studied by Wangkeeree and Preechasilp [Now, let us consider some particular cases of GVHVI. echasilp .\u03b1-well-posed GVHVI in the generalized sense. In particular, we present equivalence results on weak \u03b1-well-posedness for GVHVI, which were considered by few authors.Inspired by previous works, we study the well-posedness for GVHVI, which generalizes many known works. Under relatively weak conditions, we establish some equivalence results and some metric characterizations for the strong and weak This paper is organized as follows. In Sect.\u00a0R, N be the sets of real numbers, nonnegative real numbers, and natural numbers, respectively. Let X be a real Banach space with norm X. Let X with weak topology.Let K be a nonempty subset of X. A\u00a0function (i)K if for all finite subsets convex on (ii)u if for any sequence (weakly) upper semicontinuous (u.s.c. for short) at (iii)u, if for any sequence f is said to be (weakly) u.s.c. (l.s.c.) on K if f is (weakly) u.s.c. (l.s.c.) at all (weakly) lower semicontinuous (l.s.c. for short) at Let K be a nonempty subset of X. An operator Let (i)lower semicontinuous (l.s.c.) at (ii)F to every line segment of K is lower semicontinuous with respect to the weak topology in lower hemicontinuous (l.h.c.) if the restriction of A set-valued operator A set-valued operator S be a nonempty subset of X. The measure \u03bc of noncompactness for the set S is defined byLet \u03c6 at the point \u03c6 at Now, let us recall the definitions of the Clarke generalized directional derivative and generalized gradient for a locally Lipschitz function X\u2192R (see ). The Clis u.s.c. as a function ofand, as a function ofvalone, is Lipschitz of ranknearuonXand satisfies(ii)the gradientis a nonempty, convex, and weakly\u2217compact subset ofbounded by a Lipschitz constantnearx;(iii)for everywe have\u03b1-approximating sequences and \u03b1-well-posedness for GVHVI. Let We end this section with the notions of several classes of K is an \u03b1-approximating sequence for GVHVI if there exist A sequence \u03b1-well-posed if it has a unique solution u and every \u03b1-approximating sequence u. In particular, if GVHVI is said to be strongly  \u03b1-well-posed in the generalized sense if the solution set \u0393 of GVHVI is nonempty and every \u03b1-approximating sequence GVHVI is said to be strongly  \u03b1-well-posedness  implies weak \u03b1-well-posedness , but the converse is not true in general.Strong \u03b1-well-posed.In this section, we establish metric characterizations and derive some conditions under which GVHVI is strongly (weakly) For any Assume that: (i)Kis a nonempty closed subset of a real Banach spaceX;(ii)is continuous;(iii)is u.s.c. with respect to the first variable;(iv)is such thatwheneverThen, for everythe setis closed inX.X. Then Let Assume that: (i)Kis a nonempty convex subset of a real Banach spaceX;(ii)is l.h.c. and monotone;(iii)is convex with respect to the second variable;(iv)is convex withfor allandThenfor allF, we obtainWe first show that K is convex, for any F is l.h.c.). Taking the limit as Now we show that The following result is a consequence of Lemmas Assume that: (i)Kis a nonempty closed convex subset of a real Banach spaceX;(ii)is l.h.c. and monotone;(iii)is continuous;(iv)is u.s.c. with respect to the first variable and convex with respect to the second variable;(v)is continuous and convex withfor allandThenis closed inXfor allMoreover, that is, GVHVI is equivalent to the following problem:Findsuch thatGVHVI is strongly\u03b1-well-posed if and only if \u0393 is nonempty andg.\u2003\u25a1The proof is similar to that of Theorem 4.3 in  by the aAssume that all the assumptions of Theoremare satisfied. Then GVHVI is strongly\u03b1-well-posed if and only if\u03b1-well-posed. Then GVHVI has a unique solution \u03b1-approximating sequences of GVHVI, and thusSuppose that GVHVI is strongly ove that  holds. C part of , arguingK be an \u03b1-approximating sequence for GVHVI. Then, there exist F we obtain that, for every Conversely, assume that condition  holds. Londition  we deducIt follows from Theorem u is unique. If there exists another solution Finally, we prove that the solution Assume that: (i)Kis a nonempty closed convex subset of a real reflexive Banach spaceX;(ii)is l.h.c. and monotone;(iii)is compact;(iv)is weakly u.s.c. with respect to the first variable and convex with respect to the second variable;(v)for allwheneveras(vi)is a continuous and convex functional withfor allandThen GVHVI is weakly\u03b1-well-posed if and only if GVHVI has a unique solution and there existssuch thatis nonempty and bounded.\u03b1-approximating sequence for GVHVI. Then, there exist X. Indeed, since X.The necessity is obvious. We now prove the sufficiency. Let X is reflexive, we can choose a subsequence of F we obtain that\u03b1-well-posed by the uniqueness of the solution to problem GVHVI. This completes the proof.\u2003\u25a1Since the Banach space K is bounded or that there exists In the theorem, condition (v) can be found in , and the1n0. See , 36, 39 \u03b1-posedness in the generalized sense.Next, we give some equivalence results for the strong Assume that all the assumptions of Theoremare satisfied. Then GVHVI is strongly\u03b1-well-posed in the generalized sense if and only if \u0393 is nonempty compact andwherewithg.\u2003\u25a1The proof is similar to that of Theorem 5.1 in  by the aAssume that all the assumptions of Theoremare satisfied. Then GVHVI is strongly\u03b1-well-posed in the generalized sense if and only ifg.\u2003\u25a1The proof is similar to that of Theorem 3.2 in [Assume that all the assumptions of Theoremare satisfied. Then GVHVI is weakly\u03b1-well-posed in the generalized sense if and only if there existssuch thatis nonempty and bounded.g.\u2003\u25a1The proof is similar to that of Theorem In this section, we consider the following generalized mixed equilibrium problem (GMEP):Find found in .\u03b7-monotonicity ..\u03b7-monotoF is said to be \u03b7-monotone if there exists a function Let F is monotone.If \u2208X, then  becomesFor any We can obtain similar results.Assume that all the assumptions of Theoremare satisfied and, in addition, is continuous onwithfor anyand affine with respect to the first variable. Letbe such that: (i)for all(ii)for allis u.s.c.,(iii)for allis convex.Thenis closed inXfor allMoreover, that is, GMEP is equivalent to the following problem:Findsuch thatAssume that all the assumptions of Theoremare satisfied and, in addition, is continuous onwithfor anyand affine with respect to the first variable. Letbe such that: (i)for all(ii)for allis u.s.c.,(iii)for allis convex.Then GMVHVI is strongly\u03b1-well-posed if and only ifAssume that all the assumptions of Theoremare satisfied and, in addition, is continuous onwithfor anyand affine with respect to the first variable. Letbe such that: (i)for all(ii)for allis weakly u.s.c.,(iii)for allis convex.Then GMEP is weakly\u03b1-well-posed if and only if GMEP has a unique solution and there existssuch thatis nonempty and bounded.Assume that all the assumptions of Theoremare satisfied and, in addition, is continuous onwithfor anyand affine with respect to the first variable. Letis such that: (i)for all(ii)for allis u.s.c.,(iii)for allis convex.Then GMEP is strongly\u03b1-well-posed in the generalized sense if and only ifAssume that all the assumptions of Theoremare satisfied and, in addition, is continuous onwithfor anyand affine with respect to the first variable. Letbe such that: (i)for all(ii)for allis weakly u.s.c.,(iii)for allis convex.Then GMEP is weakly\u03b1-well-posed in the generalized sense if and only if there existssuch thatis nonempty and bounded.F, T, g, J (see Theorems \u03b1-well-posed GVHVI in the generalized sense. Our results generalize and improve many known results and can be applied to many other problems.In this paper, inspired by the previous works, we study the well-posedness for GVHVI. Under relatively weak conditions for the data"}
+{"text": "We estimate the rate of convergence of such operators for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate \u03bb-Bernstein\u2013Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence.In this paper, we introduce a family of  In 1912, Bernstein [\u03bb-Bernstein operators with parameter f. These operators, which they called \u03bb-Bernstein operators, are defined as follows:Recently, Cai et al.  proposedentclass1pt{minima\u03bb-Bernstein\u2013Kantorovich operators asIn , Cai intentclass1pt{minimaB-continuous functions was established by Badea et al. in [q-integers, studied the uniform convergence theorem and the degree of approximation of these operators. Very recently, Kajla and Micl\u0103u\u015f [As we know, the generalized Boolean sum operators  to , we obtamentclasspt{minima\u03bb-Bernstein\u2013Kantorovich operators with GBS operators. Consider the function \u03bb-Bernstein\u2013Kantorovich type for B-continuous and B-differentiable functions by using the mixed modulus of smoothness, as well as obtain the Voronovskaja type asymptotic formula for bivariate \u03bb-Bernstein\u2013Kantorovich operators.In this paper, we deduce the rate of convergence of GBS operators of bivariate tensor product of"}
+{"text": "The \u201cZ-shaped\u201d flexure hinges and the parallel-six-connecting-rods structure are utilized to obtain the lowest working stress while compared with other types of flexure hinges. In order to achieve the optimized structure, matrix-based compliance modeling (MCM) method and finite element method (FEM) are used to evaluate both the static and dynamic performances of the proposed 2-DOF piezoelectric-driven platform. Experimental results indicate that the maximum motion displacements for x-stage and y-stage are lx = 17.65 \u03bcm and ly = 15.45 \u03bcm, respectively. The step response time for x-stage and y-stage are tx = 1.7 ms and ty = 1.6 ms, respectively. A compact 2-DOF (two degrees of freedom) piezoelectric-driven platform for 3D cellular bio-assembly systems has been proposed based on \u201cZ-shaped\u201d flexure hinges. Multiple linear motions with high resolution both in  The 3D cellular bio-assembly system has become a hot research topic during recent years. In order to manipulate cells and biological tissues in 3D space, micro/nano-positioning systems with high resolution and multi-DOF (multiple degrees of freedom) should be utilized in 3D cellular bio-assembly systems . PI, Attocube and SMartAct, have already developed the commercial parallel-type piezoelectric-driven multi-DOF platforms [Piezoelectric-driven multi-DOF platforms are widely utilized in 3D cellular bio-assembly systems for their own advantages: high speed, simple control, high resolution, and multiple degrees of freedom ,3. Up tolatforms ,9,10, thlatforms ,12,13, ilatforms ,15,16,17latforms ,19,20. Alatforms ,21,22,23latforms ,25,26. NIn 3D cellular bio-assembly systems, the size of tissue cells is almost around 10 \u03bcm, which means that the positioning platform with submicron accuracy and multiple degrees of freedom is enough for the cell manipulation. The working frequency needs not to be too high. Additionally, high reliability is also required, since the 3D cellular bio-assembly process always takes a long time for thousands of cells or more. Hence, the nested form serial-type piezoelectric-driven platform is quite suitable for 3D cellular bio-assembly systems to achieve the submicron accuracy, simple structure and control system, and low cost. In order to achieve high reliability and long service lifetime, the used flexure hinges for piezoelectric platforms should have low working stress. However, the most utilized right-angle and right-circle flexure hinges always have high working stress, which greatly influences the working lifetime and the reliability. Therefore, it is of great significance to develop the piezoelectric-driven platforms with lower stress on the flexure hinges.In this study, in order to reduce the working stress of flexure hinges and obtain multiple degrees of freedom motions for 3D cellular bio-assembly systems with high reliability, a compact serial-type piezoelectric-driven platform based on \u201cZ-shaped\u2019\u2019 flexure hinges is proposed and manufactured. The \u201cZ-shaped\u2019\u2019 flexure hinge is compared with right-angle and right-circle flexure hinges by matrix-based compliance modeling (MCM) method and finite element method (FEM) to confirm it has the lowest working stress under the same condition. The parallel-six-connecting-rods structure is optimized by FEM method to enhance platform stiffness and make the platform stable. The experimental system is established to test the performance of the proposed two degrees of freedom (2-DOF) piezoelectric-driven platform. Additionally, the open-loop control method with respect to the coupling error is developed to achieve high positioning resolution.Flexure hinges are widely exploited in piezoelectric-driven platforms, due to their unique superiorities: high resolution, compact size, no friction and simple structure. Several kinds of flexure hinges have been developed for different applications. Among them, the right-angle flexure hinge and right-circle flexure hinge are the most used ones. However, during the application of right-angle and right-circle flexure hinges, the working stress is always high, which greatly influences the working lifetime of the whole piezoelectric-driven platform. Compared with other kinds of flexure hinges, the \u201cZ-shaped\u201d flexure hinge achieves larger output displacement with smallest working stress, which is ideally qualified for the piezoelectric-driven platform with long working lifetime.OaOa1; the structure is L = 16 mm, w = 6 mm and t = 1 mm. OrOr1 (basic right-angle), part Or1Or2 (basic right-circle) and part Or2Or3 (basic right-angle); the structure is l1 = l2 = 5 mm, R = 3 mm. The \u201cZ-shaped\u201d flexure hinge is shown in OzOz1, part Oz1Oz2 and part Oz2Oz3; the size is l3 = l5 = 8 mm, l4 = 6 mm. According to the references [Cra for the right-angle flexure hinge is gotten by the following:E is the elastic module of the applied material; G is the shear module; L, w, t are the structural parameters of the basic right-angle flexure hinge.In order to compare the working stress of right-angle, right-circle and \u201cZ-shaped\u201d flexure hinges under the same condition, matrix-based compliance modeling (MCM) method is applied for the theoretical calculation. ferences ,28, the Crc is shown in the following [For the basic right-circle flexure hinge, the compliance matrix ollowing :(2)Crc=[g = R/t:ux, uy and uz are the linear deformation along the x, y and z directions; \u03b8x, \u03b8y and \u03b8z are the rotational angles around the x, y and z directions; Fx, Fy, Fz, Mx, My and Mz are the applied forces and torques in the x, y and z directions.Define Since the right-angle flexure hinge shown in Ori with respect to point Or, which are achieved by:Rori(\u03b1ori) and Sori are the rotation matrix and position matrix of point Ori with respect to point Or, respectively; \u03b1ori is the rotation angle of point Ori relative to point Or; rxri, ryri and rzri are the relative positions between point Ori and point Or. The right-circle flexure hinge is divided into three parts b, and itOzi with respect to point Oz; Rozi(\u03b1ozi) and Sozi are the rotation matrix and position matrix of point Ozi to point Oz, respectively. The developed \u201cZ-shaped\u201d consists of three basic right-angle flexure hinges c, and thTherefore, the total compliance matrixes of the right-angle, right-circle and \u201cZ-shaped\u201d flexure hinge are achieved by the Equations (11), (12) and (16), respectively.E = 206 GPa, and the Poisson ratio is \u03bc = 0.288 during the FEM simulation. The structural parameters are the same with those shown in F = 20 N along y direction is applied at the right end surface of each flexure hinge. The FEM mesh size is 0.1 mm for these three flexure hinges.In order to confirm the theoretical calculation by MCM method, FEM has been applied to simulate the deformation of these three flexure hinges. Three kinds of flexure hinge  have been calculated by FEM, and the material of them is steel. The elastic module is set as y direction is Dz = 323.5 \u03bcm by the MCM method, while that from the FEM method is Dz\u2019 = 340.1 \u03bcm; the error between the MCM and FEM methods is ez = 4.9% based on Equation (20), which confirms the application feasibility of the MCM method. The maximum deformation for the right-angle flexure hinge is Dra = 265.8 \u03bcm with an error of era = 1.7%. The error of the right-circle flexure hinge is erc = 2.2%, considering the influence of the torque induced by input force F in Equation (10). The comparison of FEM and MCM methods under other forces can be obtained in Dy along y direction is applied on the right end surface of each flexure hinge. The left end of each flexure hinge is fixed to the ground without freedom. The FEM mesh size is 0.1 mm for these three flexure hinges. Since the working stroke of the utilized piezo stack is around 10 \u03bcm while the driving voltage is 100 V, the applied displacement is chosen as Dy = 10 \u03bcm. It is shown that the maximum working stress of these three flexure hinges are \u03c3ra = 10.9 MPa, \u03c3rc = 46.5 MPa and \u03c3z = 8.8 MPa. The working stress of the \u201cZ-shaped\u201d flexure hinge is the smallest among them, which is of great significance to extend the working lifetime of piezoelectric-driven platforms. Hence, the \u201cZ-shaped\u201d flexure hinge is utilized for the design of the proposed 2-DOF nano-positioning platform.The deformation results both from the MCM and FEM methods are shown in x-stage and y-stage instead of the generally used parallel-four-connecting-rods, and it is helpful to enhance the output stiffness of the whole platform. Additionally, it makes the platform more stable and the coupling error smaller, since the stiffness of x- and y-stages is enhanced to reduce coupling deformation of reaction forces. FEM method is also used to calculate the performance of the proposed 2-DOF piezoelectric-driven platform. During the FEM calculation, the four holes on the base corners are fixed to the ground without motion degrees of freedom; an input force F = 50 N was applied on x-stage in the surface to nest the piezoelectric stack; meanwhile, the reaction force Fr = 50 N was also applied on the surface to nest the piezoelectric stack on y-stage. y-stage are \u201cZ-shaped\u201d flexure hinges, the deformation of area A in y-stage is about 3 \u03bcm, as shown in x direction is nested inside y-stage, the reaction force makes the y-stage generate this unwanted deformation, which should be avoided. Meanwhile, in the case that two right-angle flexure hinges are utilized to replace \u201cZ-shaped\u201d flexure hinges for y-stage, the unwanted deformation of area A is rather small since the stiffness of right-angle flexure hinge along x direction is higher than the \u201cZ-shaped\u201d flexure hinge. Additionally, the output force of the used piezoelectric stacks is around Fstack = 800 N, which is large enough to reduce the influence of the increased stress for y-stage motion stroke. Therefore, both \u201cZ-shaped\u201d flexure hinges and right-angle flexure hinges are utilized in the 2-DOF piezoelectric-driven platform. Based on \u201cZ-shaped\u201d flexure hinges, a 2-DOF piezoelectric-driven platform has been proposed and manufactured. The parallel-six-connecting-rods structure is applied both in x-piezo stack and y-piezo stack), x-stage, y-stage, screws, \u201cZ-shaped\u201d flexure hinges, right-angle flexure hinges and the base. The x-piezo stack is used to drive x-stage; y-piezo stack is applied for y-stage. These two piezo stacks  are from NEC COMPANY; the maximum output force of them is around Fstack = 800 N, and the motion stroke is about Lstack = 17 \u00b1 2 \u03bcm in the case of input voltage V = 150 V; they are working on the d33 model and the value is d33 = 720 \u00d7 10\u221212 m/V. The x-stage is nested inside of y-stage, which means that the proposed nano-positioning platform is in serial type. This serial structure can make the proposed platform in a compact size and with small coupling errors. Two kinds of flexure hinges (\u201cZ-shaped\u201d and right-angle) are exploited to form a parallel-six-connecting-rods structure for y-stage; the flexure hinges in x-stage are all \u201cZ-shaped\u201d flexure hinges. The material of the proposed 2-DOF piezoelectric-driven platform is structural steel. Wire electrical discharge machining (WEDM) was utilized to manufacture the platform, so as to make the whole platform in an integrated structure. The size of the proposed 2-DOF piezoelectric-driven platform is l1 \u00d7 l2 \u00d7 l3 = 130 mm \u00d7 150 mm \u00d7 8mm.Ek and potential energy Et keeps the same during the motion. In the case that force Fa is applied on y-stage, the platform moves a distance s. Kinetic energy Ek of the proposed platform is divided into two parts: kinetic energy Ek1 induced by the linear motion, kinetic energy Ek2 induced by the rotation motion of flexure hinges. Kinetic energy Ek is achieved by the following equation [m1 is the mass of the \u201cZ-shaped\u201d flexure hinge; m2 is the mass of the right-angle flexure hinge; m3 is the mass of y-stage; m4 is the mass of x-stage; s is the motion displacement of y-stage; \u03b8 = arctan (s/L) \u2248 s/L is the rotation angular displacement of flexure hinge; Jz is the inertia moment of the \u201cZ-shaped\u201d flexure hinge; Jr is the inertia moment of the right-angle flexure hinge. equation :(21)EK1=Et is mainly induced by the six flexure hinges for y-stage, and it is obtained by the following equation:k\u03b8z is the rotational stiffness of the \u201cZ-shaped\u201d flexure hinge; k\u03b8r is the rotational stiffness of the right-angle flexure hinge. Potential energy E0 keeps the same and it can be achieved by the following equation:Therefore, the total energy f1 = 678 Hz, f2 = 965 Hz, f3 = 1297 Hz, f4 = 1553 Hz, f5 = 1832 Hz and f6 = 2002 Hz. It can be seen that the undesired transverse motion (z and \u03b8x) is introduced in high frequency since the use of \u201cZ-shaped\u201d flexure hinges, which is not good for the 2-DOF nano-positioning platform. Generally, the proposed 2-DOF nano-positioning platform works under several dozens of Hertz; hence, the resonance phenomenon could be avoided. We are still working on this platform, and hope to overcome this disadvantage in future work.However, it is difficult to get the accurate solution of Equation (25). Hence, FEM method is applied to analyze the dynamic performance of the proposed 2-DOF piezoelectric-driven platform. FEM dynamic analysis results are obtained in x, y) and one industrial personal computer (IPC). The signal producer  generates the needed voltage signal for the piezo-stacks, and the voltage signal is amplified by the voltage amplifier  to a high value to drive the piezo-stacks in x- and y-stages. The maximum output voltage of this HPV is UHPV = \u00b1150 V with a voltage resolution of eHPV = 1%; the maximum output current is IHPV = 0.5 A. The laser reflectors are attached to the x- and y- stages to reflect the laser signal. Laser sensor LK-G10 (KEYENCE COMPANY) is utilized to generate the laser signal to record the motion of the laser reflector. The laser head is placed in line with the motion direction of x-/y- stage which has the attached laser reflector. The measurement range of LK-G10 is LLK = \u00b11 mm with a resolution of eLK = 10 nm which is high enough for the proposed piezoelectric-driven platform. All data is processed and changed by the AD/DA card which is integrated inside the laser sensor LK-G10, and then saved by the IPC. The commercial software from KEYENCE COMPANY is utilized to control the laser sensor and save the data with a sampling time of tsa = 0.1 ms. The software from BOSHI COMPANY is exploited to control the signal producer. All this equipment is placed on the air-floating vibration isolation platform to isolate the vibration out of the experimental system.x, y and z directions (80 mm \u00d7 80 mm \u00d7 120 mm). However, the 3-DOF motor-driven platform is a traditional one, not the originality of our paper, and the resolution is not high enough for cell manipulation; hence, it is not mentioned in our paper. Here, the shown experiments are for the proposed 2-DOF piezoelectric-driven platform.In the real application, the proposed piezoelectric-driven platform is fixed to a motor-driven 3-DOF platform to obtain enough motion strokes. This motor-driven platform is composed of three motors, three ball screws and linear guiders to obtain large working stroke in x direction(a) Motion performance in x-stage under different input voltage Vx is illustrated in Vx goes up from Vx = 0 V to Vx = 150 V, and then falls down to Vx = 0 V. The motion displacement lx of x-stage increases to lx = 17.65 \u03bcm in the case of input voltage Vx = 150 V. This experiment is repeated three times, and the repeatability is found excellent. The maximum displacement error between the loading (up) and unloading (down) curves is ex = 0.36 \u03bcm, which is thought to be induced by the hysteresis and system errors. Compared with the maximum motion displacement, the maximum relative displacement error is exr = 2.03%. Many researchers have paid attention to reduce the hysteresis of piezoelectric actuators by closed-loop control systems and compensation algorithms. However, these methods make the whole system complicated and very costly. The requirement of the resolution in 3D cellular bio-assembly systems is not so high, since the size of cells is almost around 10 \u03bcm. Therefore, the influence of hysteresis is not discussed deeply here.The motion performance of y direction(b) Motion performance in y-stage under different input voltage Vy. The input voltage Vy also increases from Vy = 0 V to Vy = 150 V, and then decreases to Vy = 0 V. The maximum motion displacement of y-stage is ly = 15.45 \u03bcm in the case that the input voltage Vy = 150 V. This experiment is also repeated three times, and the maximum displacement error between the loading (up) and unloading (down) curves is ey = 0.56 \u03bcm, which is also thought to be induced by the hysteresis and system errors. Hence, the maximum relative displacement error is about eyr = 3.62%, which is a little larger than that in x-stage. The difference between the repeated three groups is thought to be caused by the assembly errors of the piezoelectric stacks and the system errors. (c) Displacement coupling errorecy and ecx are achieved from Vx is applied to the x piezo stack, the laser sensor is utilized to measure the displacement of y-stage in y direction. Hence, the displacement coupling error ecy is shown in ecy increases with input voltage Vx. The maximum displacement coupling error for y-stage is ecy = 0.76 \u03bcm, in the case that the input voltage Vx = 138 V. The relationship between the input voltage Vx and the displacement coupling error ecy is simplified by the following equation with a correlation coefficient of R2 = 0.95: The displacement coupling errors ecx for x-stage is obtained in the case that input voltage Vy is applied for y-piezo stack  Output forcex-stage during the measurement. The motion displacement ly of y-stage keeps almost the same, in the case that stand weight increases from m = 0 g to m = 1000 g, which indicates that the proposed 2-DOF piezoelectric-driven platform works stably with high output force.The performance of the proposed 2-DOF piezoelectric-driven platform under different output force has been measured, as shown in (e) Step responsex-piezo stack and y-piezo stack. The sampling time of the laser sensor is about 0.1 ms. The step response time for x-stage is tx = 1.7 ms; the stable displacement is about lx = 12.84 \u03bcm; therefore, the response velocity is vx = 7.84 \u00d7 10\u22123 m/s. The step response time for y-stage is around ty = 1.6 ms; the stable displacement is about ly = 10 \u03bcm; therefore, the response velocity is vy = 6.25 \u00d7 10\u22123 m/s. x and y-stages. Generally, if the closed-loop control method is utilized, it is easy to avoid these coupling errors ecx and ecy. However, displacement sensors are needed for the closed-loop control system, which makes the whole system complicated and expensive. In order to get high positioning accuracy with open-loop control system, we have to analyze the motion displacement and the coupling error. For example, the real motion displacement Ly of y-stage contains two parts: one is the displacement ly caused by input voltage Vy, the other part is the coupling error ecy induced by input voltage Vx. Therefore, the real motion displacement Ly is achieved by the following:ly and Vy is obtained from Since the designed platform is a 2-DOF platform, this means that there are coupling errors in both Ly: firstly, the input voltage Vx should be known to calculate the error ecy; next, wanted ly is got by using wanted Ly subtracts the error ecy; finally, the need Vy is obtained by Equation (28). Vy under different input voltage Vx. It is illustrated that, in order to get high accuracy, different Vy should be given under different Vx. The largest voltage error of the applied Vy is evy = 5.39 V, in the case that Vx = 0 V and 100 V. By applying the needed Vy from the Equation (19), the wanted real motion displacement Ly is obtained by this open-loop method.In this open-loop control method, three steps are needed to achieve the real motion displacement x-stage is lx = 17.65 \u03bcm in the case of input voltage Vx = 150 V; the maximum motion displacement of y-stage is ly = 15.45 \u03bcm in the case of input voltage Vy = 150 V. The step response time for x-stage is about tx = 1.7 ms, while that for y-stage is ty = 1.6 ms. All the experimental data indicate that \u201cZ-shaped\u201d flexure hinges are quite suitable for the design of piezoelectric-driven platforms to obtain submicron accuracy and microsecond response time. This study is meaningful for the application of piezoelectric-driven platform in 3D cellular bio-assembly system. A compact 2-DOF piezoelectric-driven platform based on \u201cZ-shaped\u201d flexure hinges has been proposed; the experimental system was established to test its performance. Different types of flexure hinges are calculated and compared; and \u201cZ-shaped\u201d flexure hinge was confirmed to have the smallest working stress under the same deformation. MCM and FEM methods were utilized for the optimization of the proposed 2-DOF piezoelectric-driven platform. The maximum motion displacement for"}
+{"text": "Nature Communications 10.1038/s41467-018-05874-2, published online 17 August 2018.Correction to: The original version of this Article contained an error in Fig.\u00a01g in which a top x-axis was shown with incorrect labels for the wavelength. The correct version of Fig.\u00a01g, which removes this labelling, is:which replaces the previous incorrect version:This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Increasing evidence shows that real networks interact with each other, forming a network of networks (NONs). Synchronization, a ubiquitous process in natural and engineering systems, has fascinatingly gained rising attentions in the context of NONs. Despite efforts to study the synchronization of NONs, it is still a challenge to understand how do the network sizes affect the synchronization and its phase diagram of NONs coupled with nonlinear dynamics. Here, we model such NONs as star-like motifs to analytically derive the critical values of both the internal and the external coupling strengths, at which a phase transition from synchronization to incoherence occurs. Our results show that the critical values strongly depend on the network sizes. Reducing the difference between network sizes will enhance the synchronization of the whole system, which indicates the irrationality of previous studies that assume the network sizes to be the same. The optimal connection strategy also changes as the network sizes change, a discovery contradicting to the previous conclusion that connecting the high-degree nodes of each network is always the most effective strategy to achieve synchronization unchangeably. This finding emphasizes the crucial role of network sizes which has been neglected in the previous studies and could contribute to the design of a global synchronized system. For these real-world systems, one component is often an individual network within a much larger complex multilayer network10, forming a part of a network of networks (NON). Comparing to a single network, the connection between networks brings more complex and complicated properties of NONs, such as robustness13, epidemic eruption14, and the self-organization in evolutionary game15. Among these properties, synchronization16 is an important behavior in biological17, engineering18, climatological19, and ecological systems20. The synchronization of a single network has been intensively investigated in the past few decades. However, the synchronization of NONs, which is more universal in real world, has not gained enough understanding21 yet. There has been a limited number of studies on the synchronization of NONs. Martin et al.22 showed the existence of a critical number of diagonal interlinks, beyond which synchronization could not be enhanced, while Francesco23 introduced a unique Master Stability Function that determines the stability of synchronization. The study on the synchronization of NONs has certain practical significance. For instance, the smart-grid, which can be regarded as NONs24, is a combination of microgrids and the traditional power networks. More and more microgrids are integrated into the power system, consequently decreasing the couplings of the power system and thus driving this NON into the boundary of its synchronization18.The present high attention to network science roots in its capability of explaining the behavior of complex real systems, including Interneti.e. the linkage between different networks; the dynamics, i.e. the universally nonlinear behavior in the real world; and the structure, i.e. the connections between a certain amount of nodes. While research on these three factors have led to some important findings, some scientific gaps remain. Some studies found that the optimal connection strategy for the case of a single connection is always to link the high-degree nodes from different networks26. No model, to our best knowledge, are available to systematically study and theoretically explain the optimal connection strategies for more than one connection. Previously, the most commonly applied predictive tools to study the dynamics of NONs, such as Master Stability Function27 and the eigenvalues of the adjacency matrix28, are based on the linearization . We present a mechanical analog of this model in Fig.\u00a0\u03bb. The nodes are synchronized if they rotate around a circle\u00a0with angular velocity\u00a0\u03c9 and avoid collisions. In the single network Kuramoto model, the system undergoes a first order38 or a hysteresis transition39 when the coupling strength crosses a critical value. Comparing to a single network, NONs behaves much more complex since it has two kinds of coupling strengths: the internal coupling strength \u03bb and the external coupling strength \u03b2 , the hub connects to the leaf (H-L) and the leaf connects to the leaf (L-L). Here, we not only consider the connection strategy with one link but also with two links (see Method Connection Strategy).One of the most widely studied models of synchronization is the Kuramoto model37 is r(t) is the order parameter at time step t, N is the network size, \u03b8(t) is the phase at time t, and i denotes an imaginary number. The order parameters for network I and network II are set as rI(t) and rII(t). The upper indices (I) and (II) stand for \u2018Network I\u2019 and \u2018Network II\u2019 respectively. Furthermore, we define the order parameter for interconnected networks R(t) as:H-H strategy. Then numerically mimic the order parameter r(t) by solving the ordinary differential equations of the coupled Kuramoto model (See Method Coupled Kuramoto model) for the given internal and external coupling strengths, where \u03b2, i.e. \u03b2s in the legend) both order parameters rI(t) and R(t) show a periodic function as time t and we denote the period as \u0394T (Case I), indicating that the interconnected networks are not globally synchronized. When i.e. \u03b2l in the legend), however, both rI(t) and R(t) converge to their steady states (Case II), demonstrating that the interconnected networks are in the globally synchronized state, showing in Fig.\u00a0\u03bb, determines the synchronization of interconnected networks, we decrease \u03bb from 3 to 0 gradually with a constant interval \u03bb at the final state asr is similar to equation . Meanwhile, for the large value \u03b2l, there exists the critical value of \u03bb that separates the synchronized phase and the unsynchronized phase, indicating the existence of a minimum value of \u03b2, below which the system can never synchronize , only when Next, we derive the analytical solutions for the case of two-links connection. The analytical critical internal coupling strength can be mathematically described as\u03b2c but also has the upper limit \u03b2max.It means that in this case the system not only has the lower limit H-L equals to L-H. Figure\u00a0NI, NII) presents the critical coupling strength with certain networks sizes NI and NII. Figure\u00a0H-H, H-H L-L, and H-L L-H. This \u03bbc increases with 43 and is analogous to the discovery in etiological systems44. Figure\u00a0\u03bbc for H-L, L-L, L-L L-L and H-L L-L respectively. We observe that Fig.\u00a0H-L) is the combination of Fig.\u00a0H-H) and Fig.\u00a0L-L), along the diagonal line H-L L-L, i.e., L-L L-L. Such property depends on whether the hub with larger network size acts as the connector  and and\\docunge (Eqs ). If \\doT), while the y-label denotes the simulation results (using superscript S). When the derived results are as the same as the simulation results, the corresponding dots are on the diagonal line H-L L-L etc. In Fig.\u00a0\u03bbc, \u03b2c and \u03b2max respectively. The comparisons show that our theory aligns with the simulation.The derived critical coupling strengths are validated in Fig.\u00a0The above analysis points out the significant role of network sizes for the synchronization of NONs. In real systems, the network sizes are not constant and may change over time. Thus, it\u2019s important to develop an approach to keep the system synchronized in a fast and efficient way, facing the time-variable network sizes.45. The \u201cmaximum allowable network sizes\u201d refers to the maximum network sizes that the system can tolerate. If the network sizes are larger than this value, the system fails to remain synchronized. For H-H, the maximum allowable network sizes can be obtained from equation  is much easier to be synchronized than that with H-L L-L (yellow zone), although the system with H-L L-L has a high-degree node as the connector. Besides, all the connection strategies except H-L L-L share similar operating space when i.e. near the diagonal line in Fig.\u00a0H-H L-L connects the high-degree nodes while H-L L-H connects the high-degree node to the low-degree node. However, the former  and the external coupling strength (\u03b2) on operating space; the former one sizes the operating space while the latter, shapes. This finding helps to decide which coupling strength should be utilized and how much it should be enhanced, guiding the time-demanding control to maintain synchronization.Facing the fast-changed network sizes, our results contribute to the time-demanding control. With certain coupling strengths  and SF networks (SASF), the ratios of different connection strategies are almost along a universal line , \u03bb. The other is the coupling strength between networks , \u03b2.The coupled Kuramoto model for Network I and Network II is\u03bb drops gradually and everytime \u03bb changes, the initial phases are the end states of the last \u03bb. In all these plots, the natural frequency of all oscillators were 1 and \u03b2 remained unchanged. \u03bb was a fixed value in the simulation shown in Figs\u00a0\u03bb was kept unchanged for 10000 iterations and passed to another value for another 100000 iterations with The coupled Kuramoto model was applied to the simulations shown in Figs\u00a046. The initial network had one node. A new node was added to a existed node i with the probability k is the degree of one node and the mean degree is 1. \u03b7 is the fitness randomly chosen between Scale-Free network was generated using BB modelH-H , H-L (short for hub-leaf), L-L, H-H L-L, H-L L-H, L-L L-L, and H-L L-L. Note that our results can be extended to multiple couplings between two networks. Connection Strategy indicates the adjacency matrix between networks M. When the nodes i and j act as the connector linking two networks, then Connection strategy refers to which node acts as the connector that linking different networks. All the connections between two networks discussed in this study are \u03bb were randomly chosen from \u03bb for all nodes started from 1.20 that the system could be synchronized, then \u03bb for all nodes deceased gradually until 0.98 to check whether the system could be synchronized or not.The derived results were validated on the heterogeneous networks, as shown in Fig.\u00a0Supplementary Information"}
+{"text": "Firstly, two wave-breaking criteria are derived by employing the transport equation theory and the localization analysis method. Secondly, a sufficient condition of the blow-up solutions is established by using the classic method. The results obtained in this paper are new and different from those in previous works.The two-component  Moreover,(III)X into X, is bounded on bounded sets in Y, and satisfiesWe make the following assumptions, where Assume that conditions (I), (II), and (III) hold. Giventhere is a maximaldepending only onand a unique solutionvto system . Then  and 40)\\document). Using , we getequality , we deduSolving , we obta\u03bc-version Camassa\u2013Holm equation under \u03bc-version Camassa\u2013Holm equation, the reader is referred to [If we let mentclass2pt{minim\u03bc-version Camassa\u2013Holm equation essentially. So the blow-up phenomena in [\u03bc-version Camassa\u2013Holm equation.It is worthwhile to mention that comparing with the results in , our blomentclass2pt{minim"}
+{"text": "Correction to: npj Digital Medicine 10.1038/s41746-018-0066-9, Article Published online 16 Oct 2018The original version of the published Article contained an error in the spelling of the third Author\u2019s name. \u201cJohn Halamaka\u201d has been changed to \u201cJohn Halamka\u201d. This has been corrected in the HTML and PDF version of the Article."}
+{"text": "O-glycosylation has been made. Thus, predicting the likelihood of O-glycosylation with sequence and structural information using classical regression analysis is quite difficult. In particular, if a binary response is used to distinguish between O-glycosylated and non-O-glycosylated sequences, an appropriate set of non-O-glycosylatable sequences is hard to find.To-date, no claim regarding finding a consensus sequon for S/T-site are analyzed: N-glycosylation, O-mucin type  glycosylation, and phosphorylation. Results found include: 1) The consensus composite sequon for O-glycosylation is: ~(W\u2013S/T\u2013W), where \u201c~\u201d denotes the \u201cnot\u201d operator. 2) The consensus sequon for phosphorylation is ~(W\u2013S/T/Y/H\u2013W); although W\u2013S/T/Y/H\u2013W is not an absolute inhibitor of phosphorylation. 3) For linear probability model (LPM) estimation, N-glycosylated sequences are good approximations to non-O-glycosylatable sequences; although N \u2013 ~P \u2013 S/T is not an absolute inhibitor of O-glycosylation. 4) The selective positioning of an amino acid along the sequence, differentiates the PTMs of proteins. 5) Some N-glycosylated sequences are also phosphorylated at the S/T-site in the N \u2013 ~P \u2013 S/T sequon. 6) ASA values for N-glycosylated sequences are stochastically larger than those for O-GlcNAc glycosylated sequences. 7) Structural attributes  are significant LPM predictors of O-GlcNAc glycosylation. The LPM with sequence and structural data as explanatory variables yields a Kolmogorov-Smirnov (KS) statistic of 99%. 8) With only sequence data, the KS statistic erodes to 80%, and 21% of out-of-sample O-GlcNAc glycosylated sequences are mispredicted as not being glycosylated. The 95% confidence interval around this mispredictions rate is 16% to 26%.Three sequences from similar post-translational modifications (PTMs) of proteins occurring at, or very near, the O-glycosylation; and underscores the germaneness of structural information for predicting the likelihood of O-glycosylation.The data indicates the existence of a consensus sequon for The online version of this article (10.1186/s12860-019-0200-9) contains supplementary material, which is available to authorized users. N-linked and O-linked )\u201381)76\u201381ldberger  suggesteficients . And theficients . Yes, \u201cp0\u2264 Xb \u22641  = Xb and ||v||p denotes the \u201cp-norm\u201d of a vector v. In contrast, RR uses the constraint (||b||2)2\u2264 t. That is, the sum of squared coefficients, instead of absolute coefficients, is constrained. In Lagrangian form [The LPLM is estimated by minimizing the negative log-likelihood function, ian form , 96, the\u2013L(\u00b7) + \u03bb \u00d7 sum(|b|). This minimization is done using Nesterov\u2019s method [\u03c1i, where 0 < \u03c1 < 1 and i is the ith step in Lasso selection, is used for \u03bb in the ith step. Variable subset selection, via the Lasso, is done, using up to 200 steps, so as to minimize the Schwarz Bayesian Criterion (SBC) [\u03c1 and the resultant number of variables (excluding the intercept) selected, the KS statistic values, the Brier Scores, and twice the negative log-likelihood values are shown in Table\u00a0\u03c1 = 0.815; and this is also nearly \u201coptimal\u201d in terms of Brier Score and KS statistic value. To assess LPLM performance out-of-sample as \u03c1 varies, 5-fold cross validation (CV) is done. LPLMs are fit on a set of 4 \u201ctraining\u201d folds and the Brier Score is calculated on the holdout  fold. Thus, for a particular choice of \u03c1, five out-of-sample Brier Scores are available. The signal-to-noise ratio (SNR), which is \u03bc/\u03c3, of these 5 Brier Scores is calculated. Per the Rose criterion [\u03c1 of 0.82, the SNR is a maximum and satisfies the Rose criterion. Thus, overall, it is reasonable to take \u03c1 = 0.82 as \u201coptimal\u201d.s method . Here, aon (SBC) . In-sampriterion , SNRs abO-glycosylation in Nature, would they, post-Lasso, continue to be statistically significant if they were put into a classical logit model to reestimate Y ?The resultant LPLM is shown in Table\u00a0Y with the independent variables in Table\u00a0Y separates a subset of the predictors to a large enough degree. To resolve this problem, we used Firth\u2019s penalized maximum likelihood method [Y is reestimated using the LPM with the predictors in Table\u00a0t-values, at the 10% level of significance are noted in Table\u00a0Using the classical logit model, we reestimated d method , 101. SeY. However, a philosophical question arises. Suppose, Nature operates along a logit surface to reveal the probability of O-glycosylation, given sequence and structural information in the neighborhood of the S/T site; and the Lasso has identified the relevant predictors. It appears to us that the selected predictors should, for the most part, be statistically significant, in the classical sense, when they are put into a classical logit model. The fact that 23 of the 51 LPLM predictors are not significant is troubling.Of course, given a set of predictors, the estimated coefficients produced by the classical logit model, the LPM, and the LPLM are not comparable, because different optimization procedures are used to estimate Y as 1 when it is empirically 0  in the estimation dataset, and 0 when it is empirically 1 , is shown in Table\u00a0The rates at which the estimated models mispredict As can be seen in Table\u00a0psi angle. It is not a predictor in Table\u00a0phi and psi angles go together, an important question is whether the LPM in Table\u00a0t-values [p-values less than 10% \u2013 i.e., variable subset selection is done, manually, using White t-values instead of classical t-values. The selected model is in Table\u00a0Consider the case of the t-values , are useR2 of about 76%. However, its standardized (studentized) residuals are not normally distributed as indicated by the Q-Q plot in Fig.\u00a0psi is a \u201ccircular\u201d measure and has heavy tails as can be seen by its tendency to cluster (with phi) in certain (and remain sparse in other) regions of the X-Y plane, which can be seen in the Ramachandran plot in Fig.\u00a0psi. However, as fitting a model to psi is not the focus of this paper, we did not pursue that goal at this time (our focus is on answering the question raised in the last paragraph). Nonetheless, the t-values can be viewed as approximations  for model selection by viewing linear regression, in this case, as purely an optimization method. In particular, we held the 99 variables in Table\u00a0t-values), the new CVPRESS tends to exceed the minimum CV PRESS of about 4,253,609 \u2013 the reduction of 106 variables to 99 variables is fairly small and likely explains this movement. This variability, with its associated summary statistics, is shown in Fig.\u00a0The model in Table\u00a0\u03c1 varies in Table\u00a0\u03c1 takes 13 values in Table\u00a0\u03c1, an optimal LPLM is selected. In all, there are 13 optimal LPLMs. All possible variables are shown in a rectangular format in Table\u00a0S/T in Table\u00a0G; and this cell would represent the dummy variable p3G \u2013 that is, the dummy variable representing amino acid G in position +3. The variables (predictors) in the LPM of Table\u00a0m3G as a predictor. Similarly, the 13 in cell  means that p8N was selected as a predictor by all of the 13 LPLMs; and, additionally, because this cell is shaded green, p8N is also a predictor in the selected LPM of Table\u00a0BH (Beta Hairpin) was only selected in 3 of the 13 LPLMs, but is in the LPM of Table\u00a0\u03c1 varies, is captured in Table\u00a0The number of times predictors are selected by the LPLM as The KS statistic is an alternative measure to the well-known Gini coefficient \u2013107. TheThe LPM in Table\u00a0ASA measures the extent to which a sequence is exposed. As mentioned previously, there are two sequences in our data that have ASA values of 0, but are deemed to be O-glycosylated. In our model, ASA_zero is a statistically significant variable. Because of its special status as an \u201cobservation specific\u201d dummy variable, it is not estimable within the classical logit modeling framework [O-glycosylated. Although, we do not know the answer to that, we think that until empirical evidence to the contrary comes up, it does not hurt keeping ASA_zero in the LPM. Furthermore, the good news is that dropping it from the model does not change any of our major conclusions. That is, in our case, dropping ASA_zero as an explanatory variable, simply allowed its effect to be distributed among the other coefficients without disrupting anything. However, we did not drop it, because it is of interest to consider (until evidence to the contrary) its marginal contribution toward encouraging O-glycosylation.ramework . Its staASA_zero in the LPM, but not ASA, raises another important question: is ASA_zero a spurious dummy variable in the LPM, because the fundamental variable underlying it, ASA, is not in the LPM? The answer is \u201cno\u201d. And we discuss the reason for this next.The presence of O-glycosylation. This means a significant amount of the information carried by ASA should be embedded in the amino acids and the positions they occupy in the sequences. To test this assumption, we searched for a linear regression model with the natural logarithm (log) of ASA as the dependent variable and sequence information as independent variables. Our search followed the same principles that were used to model psi. We used the log transformation to get ASA \u201ccloser\u201d to normality, and, as a consequence, the two observations with ASA values of 0 also get eliminated from the estimation dataset (because log(0) is undefined). ASA, like psi, has \u201cheavy\u201d tails. The selected model is shown in Table\u00a0R2 of about 80%. Its in-sample average squared error (ASE) is about 0.0425. The studentized residual distribution in Fig.\u00a0ASA values of 0  can discriminate between O- and non-O- glycosylated sequences . The KS statistic would be a measure of this. In the estimation sample, if Y is ranked by estimated log(ASA), the resultant KS statistic is about 32.0%, which is a strong enough value to not reject the assumption that the distribution of amino acids along the sequence does meaningfully drive ASA. Like in the case of psi, we do 5-fold CV (holding the 103 predictors \u201cconstant\u201d), 20 times, to study the variability in the resultant 100 realizations of the out of sample ASEs and KS statistics. These variabilities, which are not unreasonable relative to the baseline ASE and KS statistic, are shown in Fig.\u00a0The information content in N-glycosylation occurs in the rough ER and the process ends in the Golgi apparatus; phosphorylation occurs in the cytoplasm/nucleus; and O-GlcNAc proteins are also cytosolic/nuclear. So, the question is whether our \u201ccontrol\u201d dataset  is the correct \u201cnegative control\u201d? The answer is \u201cyes\u201d. By virtue of their differences in their mechanisms and cellular compartmentalization, it makes logical sense to use N-glycosylated sequences as the negative control for O-glycosylation. For example, in the absence of a consensus sequon for O-glycosylated sequences, using sequences with the S/T motif within the O-glycosylated set of sequences makes little sense, because there is no guarantee that such sequences will not get O-glycosylated.The PTMs occur in different parts of the cell by a very complex process involving many different enzymes. For example, the initial processing of the The LPM models a binary outcome. For example, when tossing a \u201cfair\u201d coin, if one wants to model  whether the coin will come down as \u201chead\u201d, then one needs to start with two distinct data subsets: a set of heads and a set of tails . One canO-glycosylated. Now the way we do this, is by starting with \u201cpartial\u201d or \u201cincomplete\u201d information. That is, we start with explanatory variables in the \u00b110 positions around the S/T site. The distribution of amino acids in this neighborhood is considered. And the structural information at S/T is considered. For example, we have not considered the distribution of amino acids further away from S/T, which must also carry key information. So, for example, the LPM is \u201cunaware\u201d of the existence of the signal peptide in N-glycosylated proteins that sends it to a specific part of the cell.Similarly, our use of the complex concept called \u201cprobability\u201d , in thisS/T site is sufficient for predicting the likelihood of O-glycosylation. To validate this assumption, we started with Table\u00a0O-glycosylated proteins having the N \u2013 ~ P \u2013 S/T sequon is tiny . Given this empirical observation, we assumed that the \u201csignature\u201d N \u2013 ~ P \u2013 S/T discourages O-glycosylation \u2013 i.e., it appears to be an approximate inhibitor of O-glycosylation. Now, a reason that only a tiny number of sequences with the N \u2013 ~ P \u2013 S/T sequon are O-glycosylated may be because the remaining signature around the O-glycosylated S/T site is quite similar to the corresponding one around the N-glycosylated S/T site. And, there may be some \u201csignal\u201d outside of our chosen \u00b110 neighborhood that may occasionally allow a protein with the N \u2013 ~ P \u2013 S/T sequon to get O-glycosylated. However, the LPM is not trained on data outside of the \u00b110 neighborhood and, thus, such a signal, if it were to exist, is unobservable from the LPM\u2019s frame of reference. So, our selecting the N-glycosylated sequences as the negative control set is independent of cell \u201ccompartments\u201d. We are simply training the LPM on the signatures around the \u00b110 neighborhood of the N- and O- glycosylated sequences. Furthermore, if our assumption regarding the signature is unreasonable, we would have seen material deterioration in prediction accuracy under CV, but did not.So, we assumed that sequence and structural information in the neighborhood of the composite sequon for O-glycosylation is ~ (W\u2013S/T\u2013W), where \u201c~\u201d denotes the \u201cnot\u201d operator. This means ~W \u2013 S/T \u2013 W, W \u2013 S/T \u2013 ~W, or ~W \u2013 S/T \u2013 ~W are necessary for O-glycosylation. The RR estimated LPM approach was instrumental in making this finding. The consensus sequon for phosphorylation is ~ (W\u2013S/T/Y/H\u2013W); although W\u2013S/T/Y/H\u2013W is not an absolute inhibitor of phosphorylation. Structural attributes  are significant predictors of O-GlcNAc glycosylation.The consensus N-glycosylated sequences are good approximations to non-O-glycosylatable sequences; although N \u2013 ~P \u2013 S/T is not an absolute inhibitor of O-glycosylation. The selective positioning of an amino acid along the sequence, differentiates the PTMs of proteins. Some N-glycosylated sequences are also phosphorylated at the S/T-site in the N \u2013 ~P \u2013 S/T sequon. ASA values for N-glycosylated sequences are stochastically larger than those for O-GlcNAc glycosylated sequences.For LPM estimation it is found that and structural data as explanatory variables yields a KS statistic value of 99%. With only sequence data, the KS statistic erodes to 80%. With 50% as the cutoff probability for predicting O-GlcNAc glycosylation, this LPM mispredicts 21% of out-of-sample O-GlcNAc glycosylated sequences as not being glycosylated. The 95% confidence interval around this mispredictions rate is 16% to 26%. This study underscores the germaneness of structural information for predicting the likelihood of O-glycosylation.The LPM with sequence O-glycosylation. These studies have employed \u201cmachine learning\u201d techniques, like random forests and factor analysis, to predict O-glycosylation [explanatory process driving O-glycosylation. Thus, classical hypothesis testing is germane to the present work, and algorithmic modeling with its pervasive focus on prediction is not, in this paper, an end in itself. In this sense, Cox\u2019s crucial comment to Breiman is echoed, which is that the \u201cstarting point\u201d in this paper is not the data, but the underlying process generating it [O-glycosylation prediction process.Several other studies are available for the predicting the likelihood of sylation \u2013114. Howating it . Furtherglycos_public.xlsx. This data, and key operations performed on it, are described in Table\u00a0Data collected on the glycosylated sequences used for analysis herein is stored in an Excel spreadsheet: glycos_public.xlsx in the column labeled PDBID. In dbOGAP, the total number of UniProt sequences is 376; and, of these, 39 have structural information. Several unique structures exist for each of the 39 sequences. This results in the 39 sequences having a total of 998 structures with unique PDB-IDs. Each structure is unique in terms of different ligands/drugs bound to them. Although there is redundancy in this data from a sequence standpoint, these 39 sequences have different structural attributes as defined by phi-psi angles and ASA, which are important structural variables. In order to make sure that these are real structural differences, similar structures were superposed to calculate a RMSD (root-mean-squared-deviation). It is confirmed that the resolution of the structures is high enough to believe in the subtle conformational changes captured in the data. The 10 residues to the left of the S/T-site, and the 10 residues to the right of the S/T-site, are superposed to see if the S/T-site displays slightly different conformations. An example is presented in Fig.\u00a0S-site, in this example, is flexible enough to accommodate its role in a multitude of cellular processes. Residues that have maximum deviation (0.5-1.0\u00c5) are close to the S-site. Residues farther out superimpose with less than 0.1\u00c5 RMSD.Structural data is obtained from the Protein Data Bank (PDB) , and thewww.uniprot.org) and shown in columns labeled Uniprot_Accession_No and Protein_Organism in glycos_public.xlsx [Ligand_Sequence in glycos_public.xlsx) is obtained from the PDBsum database [The sequence and taxonomy information for the data used in the analysis are extracted from the UniProtKB database (lic.xlsx . The ligdatabase ASA in glycos_public.xlsx) are obtained using the ASAView tool and database [R, K, H), negatively charged residues , polar uncharged residues , Cysteine (C), and hydrophobic residues .Accessible Surface Area (ASA) values"}
+{"text": "Nature Communications 10.1038/s41467-019-08536-z, published online: 05 February 2019Correction to: The original version of this Article contained an error in the title, which was previously incorrectly given as \u201cNegative differential resistance as a critical indicator for the discharge capacity of lithium-oxygene batteries\u201d. The correct version states \u201clithium-oxygen\u201d in place of \u201clithium-oxygene\u201d. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Scientific Reports 10.1038/s41598-019-52159-9, published online 30 October 2019Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cStriatum\u201d was incorrectly given as \u201cStratum\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "While previous word-frequency approaches calculated rough measures of sequence similarity or dissimilarity, some new alignment-free methods are able to accurately estimate phylogenetic distances between genomic sequences. One of these approaches is Filtered Spaced Word Matches. Here, we extend this approach to estimate evolutionary distances between complete or incomplete proteomes; our implementation of this approach is called Prot-SpaM. We compare the performance of Prot-SpaM to other alignment-free methods on simulated sequences and on various groups of eukaryotic and prokaryotic taxa. Prot-SpaM can be used to calculate high-quality phylogenetic trees for dozens of whole-proteome sequences in a matter of seconds or minutes and often outperforms other alignment-free approaches. The source code of our software is available through Github:  Here, groups of orthologous sequences have to be identified first, for which then multiple alignments are to be calculated. There are generally two different strategies of resolving phylogenies based on multiple alignments. In the so-called supermatrix approach, multiple sequence alignments of single genes or proteins are concatenated. A phylogenetic tree is inferred from the resulting matrix, kelihood  or Bayeskelihood . Alternakelihood  or superkelihood  approachAll of these steps are time consuming, and manual intervention is often required. Therefore, word-based or alignment-free alternatives have been proposed recently, which are much faster and require much less data preparation. Most alignment-free methods compare the word composition of sequences , 9, 10, Accurate alignment-free tools are urgently needed because of the huge volume of data generated by new sequencing techniques. Another advantage of alignment-free methods, compared to alignment-based approaches, is the fact that they can be applied to incomplete data, e.g., to unassembled sequencing reads or to partially sequenced genomes . Note thad hoc measures of sequence similarity or dissimilarity. They are not based on stochastic models of molecular evolution, and they do not try to estimate distances between sequences in a statistically rigorous way. More recently, some alignment-free approaches have been proposed that are based on explicit models of DNA evolution. These methods are able to estimate the number of substitutions per site that have happened since two nucleic-acid sequences have evolved from their last common ancestor [The above-mentioned approaches to alignment-free sequence comparison calculate ancestor , 34, 35.A main application of alignment-free approaches is comparison of whole genomes. Consequently, most alignment-free methods have been designed to work on DNA sequences. If distantly related species are studied though, phylogenetic trees are usually inferred from protein sequences rather than from DNA sequences. The reason for this is that protein sequences are more conserved than DNA sequences, as synonymous substitutions are not visible in proteins. Thus, for distal species, it may be hard to detect similarities between genes at the DNA sequence level, while homologies may still be detectable among protein sequences. It is therefore highly desirable to have accurate alignment-free software tools that work on protein sequences, in addition to the available tools for DNA sequence comparison. Generic word-frequency methods can be applied to both DNA and protein sequences; the program Feature Frequency Profile (FFP), e.g., has been used for whole-proteome comparison . As mentHere, we propose an alignment-free method that estimates the phylogenetic distance between two taxa based on the average number of amino-acid substitutions in the whole proteoms since they evolved from their last common ancestor. Our approach is based on filtered spaced word matches (FSWM), a concept we introduced recently for whole-genome sequence comparison ; see 3131, 35 foTo evaluate our approach, we used simulated protein sequences and real-world whole proteomes. Test runs on the simulated sequences show that our distance estimates are very close to the true distances for distance values of up to around 2.0 substitutions per sequence position. On the real-world sequences, we evaluated our approach indirectly by phylogenetic analysis, as is common practice in the field. We used Prot-SpaM to estimate pairwise distances for various sets of taxa, and we applied the neighbor-joining algorithm  to calcuP of length \u2113 \u2013 , i.e., for a length-\u2113 word P over {0, 1} \u2013, a spaced-word with respect to\u00a0P is a length-\u2113 word\u00a0W over the alphabet W(i) = * if and only if P(i) = 0. An index i \u2208 {1, \u2026, \u2113} is called a match position of P or W, respectively, if P(i) = 1, and a don\u2019t care position otherwise. The number of match positions in a pattern or spaced-word is called its weight\u00a0w. We say that a spaced word W with respect to P occurs in a sequence S at some position i if one has W(k) = S(i + k \u2212 1) for all k \u2208 {1, \u2026, \u2113} with P(k) = 1 \u2013 ,i.e., for all match positions of P.We consider sequences over an alphabet P between two sequences S1 and S2 at  if the same spaced word w.r.t P occurs at position i1 in S1 and at position i2 at S2. In other words, there is a spaced-word match between S1 and S2 at  if and only if one has S1(i1 + k \u2212 1) = S2(i2 + k \u2212 1) for all match positions k of P. Below is an example for a spaced-word match between two sequences S1 and S2 at  with respect to the pattern P = 1100101; the spaced word TN**D*P occurs at position 2 in S1 and at position\u00a03 in S2:Moreover, we say that there is a spaced-word match w.r.t. Similar to our original FSWM approach, we estimate distances between protein sequences based on selected spaced-word matches between them, with respect to one or several pre-defined patterns. Distance values are obtained by comparing the amino-acid residues that are aligned to each other at the don\u2019t-care positions of the selected spaced-word matches. This is similar to estimating distances in standard alignment-based approaches; the only difference from those standard approaches is that we are using don\u2019t-care positions of spaced-word matches instead of full sequence alignments.T, then a spaced-word match is considered a random match and is not further considered. As a default, we use a threshold value of T = 0. To see that this threshold accurately separates homologous from background spaced-word matches, one can plot the number of spaced-word matches with a score\u00a0s against\u00a0s, see Fig.\u00a0-match histogram, or spamogram for short. In these plots, two peaks are typically visible, a peak on the right-hand side representing homologous spaced-word matches and a peak on the left-hand side representing background matches. By default, we are using patterns with a weight of w = 6 and with 40 don\u2019t-care positions, i.e., with a length of \u2113 = 46.To estimate distances in this way, one has to make sure that only those spaced-word matches are selected that represent homologies, i.e., that the involved spaced-word occurrences go back to the same origin in the last common ancestor of the two proteins that are compared. To distinguish such \"homologous\" spaced-word matches from random background matches, we calculate a score for each spaced-word match using the BLOSUM62 substitution matrix . SimilarS1 and S2 are compared and a spaced word\u00a0W occurs n time in S1 and n\u2032 times in S2, then this gives rise to a total of n \u00d7 n\u2032 spaced-word matches. Taking all of these spaced-word matches into account for phylogeny reconstruction would overemphasize repeated regions where the same spaced words occur multiple times. Instead of using all possible spaced-word matches, we therefore use a one-to-one mapping of spaced-word occurrences in the compared sequences. That is, we ensure that each spaced word occurrence is involved in at least one of the selected spaced-word matches. Formally, if there are two spaced word matches at  and at , respectively, then we can include both of them simultaneously in our list of selected spaced-word matches only if W, we calculate the scores of all spaced-word matches involving\u00a0W. We then select them one-by-one in descending order of their scores, always ensuring that each occurrence of\u00a0W is used in at least one of the selected spaced-word matches.Moreover, we use a one-to-one mapping of spaced-word occurrences. Note that if sequences eviously . For a gFinally, in order to estimate pairwise distances between two input sequences, we consider the pairs of amino acids aligned to each other at the don\u2019t-care positions of the selected spaced-word matches. Here, we are using the Kimura model\u00a0 that appP. More precisely, we are using a set m binary patterns such that all patterns in w but have their match and don\u2019t-care positions arranged differently. We then use spaced-word matches with respect to all patterns m = 5 patterns. To find suitable pattern sets, we integrated the tool rasbhari\u00a0[The accuracy and statistical stability of the described approach depends on the number of selected spaced-word matches; the more matches we obtain, the more accurate and stable the results of our method will be. To increase the number of spaced-word matches, the default version of our program uses multiple patterns instead of one single pattern\u00a0rasbhari\u00a0 into ourrasbhari\u00a0 of patteT = 0 to discard background spaced-word matches, and sets of m = 5 patterns. We compared our program to the following four other alignment-free methods that can be run on protein sequences: Average Common Substring Approach (ACS) [k = 0. The competing tools were used with their default parameters. In addition to evaluating these tools on protein sequences, we ran filtered spaced word matches on the complete genome sequences of the same taxa. All test runs were done on a 10 x Intel(R) Xeon(R) central processing using E7-4850 with 2.00\u2009GHz with four cores each, equaling 40 cores and 1,000\u2009GB of random access memory.To assess the quality of our new approach and to compare it to other alignment-free methods, we used artificially generated as well as real-world protein sequences. For the test runs, we used the default parameters of our program, namely, 6 match positions and 40 don\u2019t care positions, i.e., a total pattern length of 46 \u2013, a threshold of ch (ACS) , FFP [36ch (ACS) , kmacs [ch (ACS) , and CVTch (ACS) . Here, wm = 5 patterns , we did a second series of test runs with m = 1, i.e., with single patterns. Figure\u00a0To evaluate the distances estimated by our program, we simulated sequences with the tool pyvolve . Pyvolveentclass1pt{minimaNext, we applied the above alignment-free methods to calculate phylogenetic trees from real-world protein sequences. For four different groups of species, we downloaded all available protein sequences from GenBank , in addin taxa is 2 \u00b7 n \u2212 6\u00a0[As mentioned above, Prot-SpaM uses a probabilistic algorithm to generate pattern sets, so the results of different program runs on a sequence set can differ slightly, even if the same parameter values are used. We therefore performed 100 program runs on each dataset. Table\u00a0 \u00b7 n \u2212 6\u00a0. Program \u00b7 n \u2212 6\u00a0. Neighbo \u00b7 n \u2212 6\u00a0.Escherichia coli and Shigella. For each strain, we were able to download about 4,000-5,000 protein sequences; the total size of this dataset is around 41 MB. Figure\u00a0Our first dataset consists of 29 strains of Wolbachia strains, a group of Alphaproteobacteria that are intracellular endosymbionts of arthropods and nematodes [Wolbachia, 16 distinct genetic lineages (\u201csupergroups\u201d) are currently distinguished (named by letters A-F and H-Q) that may differ in host specificity and type of symbiosis [Wolbachia I). A tree generated with Prot-SpaM from this dataset is shown Fig.\u00a0As a second test case for benchmarking, we analyzed the phylogeny of ematodes . Within ymbiosis . We re-aymbiosis , therebyWolbachia benchmarking dataset, we analyzed relationships between supergroups based on available (draft) genomes see below (Wolbachia II). For within supergroup relationships (Wolbachia I), a program run of Prot-SpaM on the whole proteome recovered a tree that is largely congruent in topology and branch lengths in comparison to a phylogenomic supermatrix analysis of 252 single-copy orthologs that excluded genes that showed signs of recombination. A comparison based on RF distances showed that our new method outcompetes other available alignment-free programs  proteomes for all available Wolbachia draft and fully assembled genomes  of the binary patterns and spaced words, their length\u00a0\u2113, the number\u00a0m of different binary patterns used by the program, and the cutoff value\u00a0T to separate homologous from background spaced-word matches. To see how these parameters influence the results of our software and to find suitable default values, we ran Prot-SpaM with varying values of these four parameters. Here, we modified one parameter at a time, using the respective default values of the remaining three parameters. The results are summarized in Tables\u00a0w, \u2113, and T that work best for all datasets, but our default values seem to be a reasonable compromise. Using sets of m = 5 binary patterns does not improve the quality of the produced trees in terms of their RF distances to the reference trees compared to program runs with single patterns. Table\u00a0E.\u00a0coli/Shigella dataset where most taxa are closely related to each other and another one in the Metazoan dataset that contains taxa with very large evolutionary distances. In the pairwise comparison of E.\u00a0coliO157:H7 strain EDL933 with E.\u00a0coliO157:H7 Sakai (EHEC), Prot-SpaM selected more than 6,000,000 spaced-word matches. These two proteomes have less than 1,600,000 amino acids each, so in this case >3.75 spaced-word matches per sequence position were selected. By contrast, less than 13,000 spaced-word matches were selected in the comparison of Brugia malayi and Homo sapiens. The latter proteome has a length of more than 75,000,000 amino acids, so here less than 0.00017 spaced-word matches per sequence position were selected.The number of spaced-word matches in a pairwise sequence comparison depends on how similar the two sequences are to each other; see  for detak-mer frequencies or on the length of common substrings. These approaches have been applied not only to DNA but also to protein sequences. A drawback of these methods is that they can only calculate rough measures of sequence similarity or dissimilarity; they do not estimate phylogenetic distances in a rigorous way. More recently, word-based methods have been developed that can accurately estimate phylogenetic distances between genomic sequences based on stochastic models of DNA evolution. One of these approaches is FSWM.A number of so-called alignment-free approaches have been proposed in recent years to rapidly calculate phylogenetic distances between genomic sequences. Earlier approaches are based on In this study, we introduced Prot-SpaM, a new implementation of FSWM to compare complete or incomplete proteome sequences to each other. To our knowledge, Prot-SpaM is the first tool that can accurately estimate phylogenetic distances between protein sequences without the need to calculate full sequence alignments. Our benchmark results show that distance estimates obtained with our approach are accurate for a large range of phylogenetic distances. Distances calculated with CVTree,ACS,FFP, and kmacs, by comparison, are monotonously increasing with the number of substitutions between the compared sequences. The obtained distance values are far from proportional to the real distances, and they flatten out somewhere between 0.5 and 1.5 substitutions per position see Fig.\u00a0. By contk-mer length of k = 4, so we used this value in our study. It has been reported, however, that FFP may perform better on protein sequences if larger values of k are used\u00a0[In our program evaluation, we used all competing software tools with their respective default parameters, if such default values were recommended by their developers. It should be mentioned, however, that some of the evaluated programs might produce better results with different parameter settings. The program FFP, e.g., uses a default are used\u00a0. A comprE.coli/Shigella and plant datasets, as shown in Table\u00a0Wolbachia datasets, it still performed reasonably well and was again superior to competing approaches on the whole-proteome sequences, but it was outperformed by word-frequency methods on the 252 selected orthologous proteins. A possible explanation of this result is discussed below. On the large prokaryote dataset and for the metazoan set, by contrast, none of the compared programs could reproduce the reference trees that we used in our evaluation. These are difficult datasets since they span very large evolutionary distances. Also, it should be mentioned that there are no absolutely reliable reference trees available for these datasets. For the metazoan dataset, e.g., the position of the ctenophores is still a matter of debate [Prot-SpaM produced high-quality trees and was superior to other alignment-free methods for the f debate , 74, 75.An interesting result is the performance of Prot-SpaM compared to our previous approach FSWM that takes genomic sequences as input. For most groups of taxa in our study, the results of Prot-SpaM and FSWM were of similar quality in the sense that the RF distances to the reference trees were comparable for both approaches. However, for the set of 813 prokaryote taxa, our new spaced-words approach performed better on whole proteomes than our previous approach on whole genomes, as shown in Fig.\u00a0Wolbachia I, we actually obtained better RF distances with Prot-SpaM and FSWM when we applied these programs to the whole-protein or whole-genome sequences, respectively, than when we applied them to the 252 selected orthologous proteins or to the genes coding for those proteins : linuxProgramming language: C++Other requirements: noneLicense: GNU GPLAny restrictions to use by non-academics: nonehttp://projects.gobics.de/data/protspam/paperData.tgz. Additional supporting data and snapshots of the code are available in the GigaScience repository, GigaDB\u00a0[The sequence datasets and trees used for the program evaluation can be downloaded from , GigaDB\u00a0ACS: Average Common Substring Approach; BLOSUM: Blocks Substitution Matrix; CVTree: Composition Vector Tree; FFP: Feature Frequency Profile; FSWM: filtered spaced word matches; indel: insertions and deletions ; kmacs: k-Mismatch Average Common Substring Approach; PHYLIP: PHYLogeny Inference Package; Prot-SpaM: proteome-based spaced-word matches; rasbhari: Rapid Approach for Seed optimization Based on a Hill-climbing Algorithm that is Repeated Iteratively; RF: Robinson-Foulds; spamogram: Spaced-Word-Match Histogram.The authors declare that they have no competing interestsThe project was partially funded by the Volkswagen Foundation, project VWZN3157. We acknowledge support by the Open Access Publication Funds of the G\u00f6ttingen University.Wolbachia and wrote parts of the manuscript. B.M. co-supervised the project and wrote most of the manuscript.C.A.L. designed the study, co-supervised the project, and drafted parts of the manuscript. J.S. implemented the software and did most of the program evaluation. S.D. contributed to the program evaluation. M.G. and C.B. analyzed and discussed the results on GIGA-D-18-00169.pdfClick here for additional data file.GIGA-D-18-00169_R1.pdfClick here for additional data file.GIGA-D-18-00169_R2.pdfClick here for additional data file.Response_to_Reviewer_Comments_Original_Submission.pdfClick here for additional data file.Response_to_Reviewer_Comments_Revision_1.pdfClick here for additional data file.Response_to_Reviewer_Comments_Revision_2.pdfClick here for additional data file.Reviewer_1_Report_ -- Sharma Thankachan5/31/2018 ReviewedClick here for additional data file.Reviewer_3_Report_ -- Se-Ran Jun6/18/2018 ReviewedClick here for additional data file.Reviewer_3_Report_revision_1 -- Se-Ran Jun9/17/2018 ReviewedClick here for additional data file.Reviewer_3_Report_Revision_2 -- Se-Ran Jun9/29/2018 ReviewedClick here for additional data file.Reviewer_4_Report_ -- Sriram Chockalingam6/20/2018 ReviewedClick here for additional data file.Reviewer_4_Report_Revision_1 -- Sriram Chockalingam9/18/2018 ReviewedClick here for additional data file.Reviewer_5_Report_ -- Alexey Kozlov6/21/2018 ReviewedClick here for additional data file.Reviewer_5_Report_Revision_1 -- Alexey Kozlov9/18/2018 ReviewedClick here for additional data file.Supplemental FileClick here for additional data file."}
+{"text": "Scientific Reports 10.1038/s41598-018-34386-8, published online 29 October 2018Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201ceGFR\u201d was incorrectly given as \u201cEgfr\u201dThis has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Communications Biology 10.1038/s42003-019-0360-3, Published online 26 March 2019Correction to: In the original version of the paper, Fig.\u00a04 contained an error in the labels for \u201cIntermediate\u201d and \u201cInsignificant\u201d in the figure key, making the symbols partially illegible. This error has been corrected in the HTML and PDF versions of the paper."}
+{"text": "Multi-trait single step genetic evaluation is increasingly facing the situation of having more individuals with genotypes than markers within each genotype. This creates a situation where the genomic relationship matrix\u00a0( Within the last decade, genotyping thousands of individuals with single nucleotide polymorphism\u00a0(SNP) chips has become common practice in breeding programs of many species of economic relevance. However, due to cost effectiveness these individuals are being genotyped with low- to medium-density SNP chips, with usually not more than 50,000 markers.To date, genetic evaluation systems accommodate SNP genotypes via the so-called single step model, in which\u00a0most often markers are used to pre-calculate a relationship matrix, which subsequently augments the usual pedigree derived relationship matrix into a so-called mentclass2pt{minimHowever, the situation described above of having more genotyped individuals than markers has led to a situation where  such as  offer hu such as  or deman such as . However such as , 6. SS-TSNP-BLUP\u00a0, 5, 7.In this paper, we will examine the computational advantage of SS-T-BLUP for a large-scale multi-trait BREEDPLAN single step genetic evaluation of Australian Angus beef cattle. We will compare the results to those obtained by\u00a0using an ordinary SS-H-BLUP approach.In the following, three equivalent representations of the inverse of the mentclass2pt{minimlsewhere , 6, 8\u201311The  markers .Replacing mentclass2pt{minimAssuming that The differences between the three approaches regarding computational time spent on preparing necessary data and solving the MME iteratively can be reduced to a set of very specific operations unique to the respective representation of the inverse of Assuming that mentclasspt{minimaion once\u00a0.z, with a dense matrix, which is ]. It requires the multiplication of a vector with the MME coefficient matrix once per iteration. Therefore, this method is affected by the way the inverse of Differences in peak memory requirement directly result from the size of the arrays, which must be kept in RAM simultaneously during preparation and iteration. Furthermore, for SS-H-BLUP and SS-The SS-H-BLUP, SS-aluation\u00a0. The dataluation\u00a0. To incrDummy genotypes for 91,295\u00a0 individuals, sampled from the pool of non-genotyped individuals, were generated by The BREEDPLAN multi-trait model included pre-corrected phenotypes\u00a0, a singlecessary\u00a0. The totFor all three models matrix, The system of equations was solved with AGBU\u2019s current large-scale linear mixed model library solver, which uses the PCG algorithm for iteratively solving linear mixed models and integrates Intel(R) MKL(R), version 2017 update 8. For research and commercial purposes, the solver is available on request. Block-diagonal and diagonal pre-conditioners were used for random and fixed factors, respectively.Xb\u2009=\u2009y, where X is the coefficient matrix, b is the solution vector and y is the right hand side vector, convergence was achieved when the L2 norm of vector (y\u2009\u2212\u2009Xb) scaled by the L2 norm of vector y was Denoting the MME as Results for the different parts of the setup and solving steps are in Table mentclass2pt{minimThe preparation time for model specific parts for SS-T-BLUPy, with matrices y\u2009=\u2009 requirements in gibabyte due to matrices and operations that are unique to the approaches are in the last row in Table The last column in Table SS-T-BLUP has been proposed as a single step model which can be helpful for datasets for which\u00a0the number of genotyped individuals exceeds the number of markers and the i may then be i in the different traits. This expansion is not possible for the models applied here. However, SS-SNP-BLUP usually comes at the cost of much higher model dimensionality and slow convergence rates when solved iteratively\u00a0[In terms of modelling capacity SS-T-BLUP, SS-H-BLUP, and SS-ratively\u00a0. The latratively\u00a0. To our Since all models were equivalent, it was expected that the number of iterations needed for convergence was the same. However, surprisingly there was no difference in the number of iterations for convergence when using only the 58,705 real genotypes\u00a0(results not shown), 150k genotypes or 400k genotypes. A possible explanation is the way the dummy genotypes were generated. Thus, it is very likely that a dataset with 400k real genotypes may require more iterations but that the time needed for preparation and per iteration will be similar to that observed in this study.As shown by the results, SS-T-BLUP clearly outperforms SS-H-BLUP in terms of total processing time mainly due to the huge computational cost of setting-up These results support the conclusion that SS-T-BLUP provides a feasible algorithm to calculate exact solutions for estimated breeding values when the number of genotyped individuals exceeds the number of markers. A limitation to the number of genotyped individuals is only set by the available RAM. Therefore, SS-T-BLUP allows solving single step equation systems iteratively without generating"}
+{"text": "However, SBM still has great potential in complex applications due to the following two points; Bregman Iteration (BI), employed in SBM, may not make good use of the phase information for complex variables. In addition, the converting technique may consume more time. To address that, this paper presents the complex-valued Split Bregman method (CV-SBM), which theoretically generalizes the original SBM into the complex domain. The complex-valued Bregman distance (CV-BD) is first defined by replacing the corresponding regularization in the inverse problem. Then, we propose the complex-valued Bregman Iteration (CV-BI) to solve this new problem. How well-defined and the convergence of CV-BI are analyzed in detail according to the complex-valued calculation rules and optimization theory. These properties prove that CV-BI is able to solve inverse problems if the regularization is convex. Nevertheless, CV-BI needs the help of other algorithms for various kinds of regularization. To avoid the dependence on extra algorithms and simplify the iteration process simultaneously, we adopt the variable separation technique and propose CV-SBM for resolving convex inverse problems. Simulation results on complex-valued l1-norm problems illustrate the effectiveness of the proposed CV-SBM. CV-SBM exhibits remarkable superiority compared with SBM in the complex-to-real transforming technique. Specifically, in the case of large signal scale n = 512, CV-SBM yields 18.2%, 17.6%, and 26.7% lower mean square error (MSE) as well as takes 28.8%, 25.6%, and 23.6% less time cost than the original SBM in 10 dB, 15 dB, and 20 dB SNR situations, respectively.The Split Bregman method (SBM), a popular and universal CS reconstruction algorithm for inverse problems with both  Thus, a more general algorithm for CS recovery in complex variables is needed.In recent years, there have been many papers focusing on this problem, such as Complex Approximate Message Passing (CAMP)  and M-lal1-norm and TV-norm regularization problems. By the idea of decomposing the original problem into several subproblems worked out by Bregman Iteration (BI) [A to 2m \u00d7 2n, which consumes more memory and time within the iteration process.The Split Bregman method (SBM) proposed in  is a uniion (BI) ,30, SBM ion (BI) ,32, e.g.ion (BI) , SAR imaion (BI) , forwardion (BI) , SAR imaion (BI) , and masion (BI) . Howeverl1-norm problems reveal the effectiveness of CV-SBM compared with existing methods. Particularly, the proposed CV-SBM exhibits 18.2%, 17.6%, and 26.7% lower mean square error (MSE) and takes 28.8%, 25.6%, and 23.6% less time than SBM through the complex-to-real transforming technique in 10 dB, 15 dB and 20 dB SNR cases with large signal scale n = 512.To tackle the aforementioned problems, this paper theoretically generalizes the original SBM into the complex domain, named the complex-valued Split Bregman method (CV-SBM). We first define the complex-valued Bregman distance (CV-BD) and replace the associated regularization term with the CV-BD in the inverse problem. Then, complex-valued Bregman Iteration (CV-BI) is proposed to solve this new problem. In addition, according to the calculation rules, Wirtinger\u2019s Calculus, and optimization theory for complex variables, how well-defined the CV-BI is and its convergence are analyzed in detail. The proof of the above two properties reveals that CV-BI can settle inverse problems if the regularization term is convex. Since CV-BI requires the help of additional algorithms to find the solution to the specific regularization, as BI does, its solution is still complicated and computationally expensive. Inspired by SBM, we adopt the variable separation technique to avoid the requirement of other optimization algorithms and then present CV-SBM to settle the convex inverse problems with the simplified solution. Simulation results on the complex-valued The rest of this paper is organized as follows. In l1-norm and TV-norm regularization [SBM, whose main idea is to decompose the original unconstrained problem into several equivalent subproblems solved by BI ,30, has rization . For theJ(x) is a real convex function but not necessarily differentiable, and H is a real convex and differentiable function. By replacing J(x) with corresponding Bregman distance (BD) J(x) at the point v, and J(x) at v, BI focuses on the optimization problemDJp ,38, BI tDefinition\u00a01.T at z0 if T at z0 is called the subdifferential of T at z0 and is denoted by Let found in .J(x) so that (5) is still a convex problem. Furthermore, it can be used as the measurement of the closeness of two points in J(x) [A key property of the BD is that it has the same convex characteristic as  in J(x) ,30.l1-norm and TV-norm problems, Equation (6) is easily calculated, whereas dealing with (5) is more complicated and needs the help of another algorithm [As for the lgorithm , such aslgorithm  or FPC [lgorithm . To avoid and considers an equivalent constrained problem to Equation (7)SBM aims to find a solution to the unconstrained problemE = ||d||1 + H(x) and \u03bc is a positive constant to balance the two terms in Equation (9) within the iterations. Since there are two unknown variables completely fulfilling the demand of BI for optimization problems, BI can be performed for each of them:The corresponding unconstrained version of (8) can be formulated as follows:Let kx by fixing kd\u22121 and then clearing up kd by fixing kxFor (13), one can decompose it into resolving two subproblems alternately, i.e., working out Evidently, the combination of BI and SBM can be adopted to settle plenty of convex optimization problems in a real system ,41. HoweT(c) = RT(c) + IjT(c) in complex variables c = Rc + Ijc, the complex differentiability equals to the satisfied Cauchy\u2013Riemann conditions:As is well-known, convex optimization theory requires the differentiability of the objective function. For l1-norm regularization problem:F(x) does not obey (17) so that calculating the complex gradient directly is unavailable. For a complex-valued T at Rc and Ic, which can be obtained by the traditional ways. According to Equations (19) and (20), one can calculate the W-gradient of c* and the CW-gradient of c:To overcome such a problem, an alternative tool for computing the complex gradient was brought into light recently called Wirtinger\u2019s calculus . It rela*c and the CW-gradient for c are equal to zero, in Wirtinger\u2019s calculus we can treat c and c* as two irrelevant or independent variables, which is the main approach allowing us to utilize the elegance of Wirtinger\u2019s calculus. Here is an example: if T(c) = c(c*)2, then we have Considering that both the W-gradient for found in .l1-norm in F(x) at zero. In this case, the conjugate Wirtinger\u2019s subgradients (CW-subgradients) [T at c if T at Rc and Ic. The set of all CW-subgradients of T at c is called Wirtinger\u2019s differential of T at c and is represented by T, the Wirtinger\u2019s differential only contains one element, i.e., its CW-gradient. Wirtinger\u2019s differential of modulus |ix| and i is the index for the element of vector x and s is some complex number verifying In general, for the convex function in complex variables, the optimization condition is the CW-gradient equal to zeros vector. Nevertheless, in practice, some functions may not be differentiable everywhere, e.g., adients)  can be a follows .(25)\u2202x*\u2208\u2202x*F(x) . By the To prevent the BD becoming complex-valued, we first generalize the BD into the complex domain and introduce the CV Bregman distance (CV-BD) theoretically.Definition\u00a02.For Lemma 1 and Lemma 2 prove that the CV-BD is as the same convex as J(x) and can measure the closeness at two points in J.To ensure that the CV-BD can be utilized as the objective function as the BD, in the following Lemma\u00a01.Letbe a CV-BD associated with real convex or strictly convex function J, whereThenis as the same convex property as J for variable u in each v.Proof.\u00a0J is a real convex function and let Assume J is a real convex function, J satisfiesu as J. Considering that J is a real strictly convex function, we assume J satisfiesu as J. Then, it can be concluded that J for variable u in each v.\u2003\u25a1For Lemma\u00a02.\u00a0Letbe a CV-BD associated with real strictly convex function J and assume a pointis on the line segment connecting u and v, where,. Thenand equality holds if and only if u = v.Proof.\u00a0Lemma 1Lemma 2. Then, the CV-BD at two points in convex function J would decrease when they get closer, and may become zero if and only if the two points coincide. This property makes the CV-BD the measurement of closeness at two points.Assume J(x) as the objective function:Thus, inspired by the original BI, we use the CV-BD between the variables to be solved and the current solution to replace real convex function H(x) and the CV-BD. However, the CV-BD kx-1, which inevitably interferes with the solution of kx. As we shall prove below, this issue is not vital, since CV-BI introduced in the following subsection automatically chooses a suitable CW-subgradient when dealing with Equation (36).Obviously, CV-BI for Equation (36) is proposed directly and the definition and the convergence are proved in the following.x0 = 0, p0 = 0, for k = 1,2,Algorithm 1. Let kx as a minimizer of the convex function kQ(x)1. compute 2. compute x0 and p0 whatever satisfy x0\u22600, its CW-subgradient requires optional calculation, which is not desired in practical.Generally, we can initialize kx exists in kQ(x) and the iteration can find an appropriate CW-subgradient kp automatically.In this subsection, we reveal that the iterative procedure in Algorithm 1 is well defined. Specifically, a minimizer Proposition\u00a01.\u00a0Assume that0=0,J(x) is convex and bounded, and let x. Then, for eachk in Qk(x), and there exists an appropriate CW-subgradient, there exists a minimizer xandsuch thatk is unique.Moreover, if A has no null space, a minimizer xProof.\u00a0k = 1, Q1(x) becomes the original function F(x), of which the existence of minimizers and the optimality condition p1 + q1 = p0 = 0 is well known [p1 = HrA1.We prove the result by induction. In the case of ll known . In addik\u22121 to k and assume kQ(x). Recalling the l2-norm greater than or equal to zero, kQ(x) can be estimated asThen, we proceed from J(x) is not constant, the boundedness of kQ(x) implies the boundedness of J(x). This shows that the level sets of kQ are weak-* compact [kQ exists due to the optimization theory. Besides, if A has no null space and H(x) as well as J(x) is strictly convex, kQ(x) is also strictly convex, and therefore the minimizer is unique. This completes the proof of the existence of minimizers for all k > 1.Since only  compact . Hence, kp and kq exist for all k > 1. According to the optimality conditions for kQ(x)kp\u22121 exists, one can get that The following proves p0 = 0, we obtain thatRecalling Equation (38) and The definition of CV-BI has been proved as mentioned above. The whole CV-BI can be summarized as follows:Algorithm 1: CV-BIx0 = 0 p0 = 0 k = 1 \u03bb, Initialization: \u2003\u2003While \u201cstopping criterion is not met\u201d do \u2003\u2003\u2003\u2003K = k + 1;End whileJ(x) in Equation (18) if J(x) is a real convex function in complex variables. Furthermore, since each step of Algorithm 1 obeys the optimization rules in the complex domain instead of converting the objective function kQ(x) and variable x into the real domain, one can summarize that CV-BI preserve phase information for complex variables.Review the entire process of proof and one can find that CV-BI possesses the ability to solve any kind of regularization term In this subsection, the convergence property of CV-BI is analyzed. To be specific, two monotonicity properties are proved with the help of the CV-BD.Proposition\u00a02.k) obtained from the CV-BI is monotonically nonincreasing, we getUnder the above assumption, the sequence of H < \u221e, then we even haveProof.\u00a0kx is the minimizer of the convex function kQ(x), we obtainRecall the nonnegative property of the CV-BD and that We can derive a formula motivated by the identity of the original BD :(48)DJpkProposition\u00a03.\u00a0Under the same assumption as Proposition 2, letbe a minimizer of H(x) with, then we haveProof.\u00a0H(x), we get an inequalityRecall the nonnegative property of the CV-BD and that According to Equations (49), (51) can be derived asfound in .\u2003\u25a1For various kinds of regularization terms corresponding to Equation (43), CV-BI still has to employ other algorithms as BI does, which makes the solution process complicated and computationally expensive. Inspired by SBM, we separate the original variable and present CV-SBM to settle the convex inverse problems with the simplified solutions.A constrained optimization problem in complex variablesF is convex in x and d. Thus, by applying CV-BI to Equation (54) in each variable, we can derive thatEvidently, C1 is a constant. Substituting Equation (58) in Equations (55)\u2013(57) yieldsx and dTo simplify the above iteration step Equation (55), we assume J(x) in any convex optimization task.The above two subproblems can be worked out easily. Considering the property of CV-BI, it can be inferred that CV-SBM is also universal for convex The overall CV-SBM is shown as Algorithm 2Algorithm 2: CV-SBMx0 = 0, d0 = 0, p0 = 0, \u03bb, \u03bc, k = 1Initialization: \u2003\u2003While \u201cstopping criterion is not met\u201d do\u2003\u2003\u2003\u2003k =k+1;End whileAssuming \u03a6 = I, then we can work out Equation (18) through CV-SBM by three steps :x subprobleml2-norm is differentiable, Equation (63) can be tackled by taking the CW-gradient of x equal to zero, and yieldStep1: Clear up the d subproblemStep2: Find a solution to the bStep3: Update l1-norm problem can be presented as Algorithm 3CV-SBM for Algorithm 3: CV-SBM for l1-norm problemx0=0, d0=0, p0=0, \u03bb, \u03bc, k=1Initialization: \u2003\u2003While \u201cstopping criterion is not met\u201d do\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003k = k+1;\u2003\u2003\u2003\u2003\u2003\u2003\u2003\u2003End whilel1-norm problems in the complex domain. We apply the proposed method to recover a complex-valued random sparse signal x from the noisy measurements y generated by y = Ax + \u03b5, where x consists of L nonzero elements and the amplitudes of both x\u2019s and A\u2019s real part and imaginary part obey Gaussian Distribution N . The noise vector \u03b5 is assumed to be i.i.d zero-mean complex Gaussian noise. The contrastive means for the proposed scheme in the following subsections are as follows: classical OMP [This section presents the performance of the proposed CV-SBM by conducting a wide range of experiments solving ical OMP , CAMP, Mical OMP . Noted ttol = 2e\u22124 denotes the tolerance and kmax = 2000 is the maximum iteration times. All the experiments are carried out in MATLAB 2016b on the PC with Intel I7 7700K @4.2 GHz with 32 GB memory.The stopping criterion for all algorithms is given as follown = 256 and m = 128, respectively. Moreover, the sparsity level of x is fixed L = 32 and the Signal to Noise Ratio (SNR) is set to 15 dB.In this subsection, an illustrative example is devised to demonstrate the effectiveness of the proposed method in comparison with OMP, CAMP, M-lasso, and RV-SBM. We consider that the signal and measurement dimension is x remain hidden to emphasize the nonzero ones in In this subsection, CV-SBM is applied in ISAR imaging with real data of the Yak-42 plane to demonstrate its superiority, comparing with RV-SBM, the range-Doppler (RD) algorithm, and the CS recovery method . DetaileIn this subsection, we test the robustness of the proposed technique against the measurement noise. The experimental parameters are set as follows: SNR varies from 5 dB to 20 dB and other parameters are fixed the same as in the previous subsection. For each SNR, we average the MSE of 100 independent trials as the experimental result, as shown in As the SNR increases, the MSE of the proposed scheme declines, which implies CV-SBM is robust to the noise. Before the SNR reaches 7 dB, the MSEs of CAMP and CV-SBM are almost the same, but when SNR goes beyond 7 dB, the MSE of CV-SBM surpasses CAMP\u2019s and becomes the lowest among all the algorithms. Both OMP\u2019s and RV-SBM\u2019s MSE numerically exceed CV-SBM\u2019s. In addition, CV-SBM behaves better than M-lasso, except at the point when the SNR is equal to 7 dB, at which they are approximately the same. This demonstrates that the proposed algorithm has better robustness against the measurement noise among the methods.n = 256, SNR = 15 dB, L = 32, and m varies from 29 to 128. As in the previous subsection, we measure the average MSE over 100 independent trials, as shown in In this subsection, how the dimension of measurements influences the recovery result is presented. We set In n from 128 to 1024 and fix SNR = 20 dB, m = 0.5n, L = 0.125n. For each n, we conduct 20 independent trials and average the CPU time cost as the result, as shown in In this subsection, the computational cost of the proposed method is measured with increasing dimension of the signal. To this end, we vary A to 2m \u00d7 2n, which leads to an inverse matrix with 2n \u00d7 2n elements and takes more memory and time within the resolving process, while CV-SBM only needs to calculate a complex inverse matrix with n \u00d7 n elements. Nevertheless, CV-SBM takes a little more time than CAMP in large signal scale situations thanks to CAMP\u2019s specific design for l1-norm problems, whereas CV-SBM contains an inverse operator. However, CV-SBM still has great potential to exceed CAMP considering that the gap between CAMP and CV-SBM is not large.The result shows that CV-SBM takes less CPU time than OMP and M-lasso in all test dimensions. Before the dimension reaches 512, RV-SBM requires the least time. However, when the dimension is more than 512, CV-SBM requires less CPU time than RV-SBM. This is because the complex-to-real transformation utilized in RV-SBM expands the dimension of the sensing matrix \u03bb = 0.005 and \u03bc = 120 and the stopping criterion (the tolerance tol and kmax) varies. Furthermore, other experimental parameters are as follow: L = 0.125n, m = 0.5n and SNR varies from 10 dB, 15 dB, and 20 dB. For each stopping criterion and SNR, 20 independent trials were carried out and the average MSE, CPU time cost, and iteration time are selected as the result. The average MSE and CPU time cost of the proposed method are also presented if CV-SBM presents better performance.The tests mentioned above have shown that the proposed CV-SBM presents remarkable performance compared with RV-SBM in the same experimental environment. Thus, in this subsection, we focus on the convergence, time cost, and performance of CV-SBM and RV-SBM by implementing experiments with various parameters. In the following experiments, two main parameters for CV-SBM and RV-SBM are set to n = 256 and fix tol = 2e\u22124, kmax = 2000, as shown in In the first test, we examine CV-SBM and RV-SBM in small scale tol = 2e\u22125 and keep the other parameters consistent with the previous experiment (To inspect the performance regardless of the convergence condition, we reduce the tolerance to periment . For anyn = 512 is taken into consideration (tol and the maximum iteration times kmax are set the same as in At last, large scale deration . The toll1-norm problem to recover a complex-valued sparse signal. Experimental results demonstrate the superiority of CV-SBM over other existing CS reconstruction methods, especially RV-SBM, in both recovery accuracy and time cost for large-scale cases.In this paper, a new CS recovery algorithm named CV-SBM is presented, which generalizes the widely employed SBM into the complex domain. CV-SBM induces a theoretical support to directly reconstruct the sparse signal in complex-valued variables, instead of converting them into real ones. We apply the proposed CV-SBM to a A significant goal for future work lies in applying CV-SBM to more complicated regularization problems, since CV-BI and CV-SBM are theoretically able to deal with any convex optimization problem."}
+{"text": "While the h-index is determined by the maximum square that fits under the citation curve of an author when plotting the number of citations in decreasing order, the \u03c7-index is determined by the maximum area rectangle that fits under the curve. The height of the maximum rectangle is the number of citations ck to the kth most-cited publication, where k is the width of the rectangle. The \u03c7-index is then defined as h-index and other similar indices. We present a comprehensive empirical comparison between the \u03c7-index and other bibliometric indices, focusing on a comparison with the h-index, by analysing two datasets\u2014a large set of Google Scholar profiles and a small set of Nobel prize winners. Our results show that, although the \u03c7 and h indices are strongly correlated, they do exhibit significant differences. In particular, we show that, for these data sets, there are a substantial number of profiles for which \u03c7 is significantly larger than h. Furthermore, restricting these profiles to the cases when ck > k or ck < k corresponds to, respectively, classifying researchers as either tending to influential, i.e. having many more than h citations, or tending to prolific, i.e. having many more than h publications.We propose the  P) as a measure of quantity and the total number of citations to these publications (C) as a perceived measure of quality; several variants of these, such as the average number of citations per publication, the number of citations to the top or the 10th most cited publication, and the number of publications with at least 10 citations, have also been suggested [h-index [g-index [The debate in bibliometrics on quality versus quantity in evaluating academic research performance is still an ongoing concern . One peruggested . Althoug[h-index , the g-i[g-index  and gene[g-index , combineh-index and some of its variants was provided by Egghe in [h-index was given by Bornmann et al. in [h-index and its variants, and proposed a family of bibliometric indicators that do not suffer from these inconsistency problems. Of particular interest are extensions of the h-index, which take into account the full publication list of a researcher such as the taperedh-index [h-index continue to appear, for example [An extensive review of the Egghe in , and, a t al. in . In addit al. in  discusseh-index . Proposa example \u201313, as d example , 15.h-index and its variants do not normally take into account the full citation list of a researcher. This could be perceived as a drawback; however, the total citation count has the disadvantage of biasing the index in favour of researchers with very highly-cited top publications or very many publication with a relatively small number of citations. We now review the h-index and some of its variants, and then introduce the \u03c7-index, a new index that addresses some of the drawbacks mentioned.Nevertheless, the h-index of a researcher is the maximum number h of the researcher\u2019s publications such that each has at least h citations [citation vector, \u2329c1, c2, \u2026, cn\u232a of a researcher, where the ci, the number of citations to publication i, are sorted in descending order, i.e. ci \u2265 cj if i < j. Here we assume that for all i, ci > 0, and that h will be zero in the absence of any citations; this is consistent with defining the value of a bibliometric index of a researcher to be zero if none of the researcher\u2019s publications have been cited [h-index is thus the largest rank h for which ch \u2265 h. The h-index is completely insensitive to the fact that a researcher\u2019s top few publications may be very highly cited, and conversely also to a researcher having a fair number of publications whose number of citations is less than but close to h [h-index, which gives extra weight to highly cited publications, is the g-index. The g-index of a researcher is the largest rank g for which g \u2265 h. A problem with the g-index is that it may still be biased since, if a researcher has a few publications that are very highly cited and the rest have very few citations, the g-index will still be high. This is because the g-index is equal to the largest rank g such that the average number of citations up until that rank is at least g. Suppose the h-index of a researcher is h, then the h-core is the set of the h most highly-cited publications for this researcher. The A-index, which is the average number of citations to the publications in the h-core, i.e. h-index does not take into account the total number of citations to publications in the h-core [A-index suffers from the fact that taking an average will, all other things being equal, often favour authors with fewer publications when they are highly cited. To remedy this issue, the R-index has been proposed, where h \u2264 R \u2264 A. Nevertheless, the A and R indices, and to a lesser extent the g-index, ignore the effect of publications outside the h-core, which are also part of a researcher\u2019s output. A recent proposal is the Euclidean-index [E-index), designed to take account of the full list of an author\u2019s cited publications; it is defined as the Euclidean norm of the citation vector, i.e. The itations . Equivalen cited . The h-iose to h . A sugge=1gci\u2265g2 ; it is ee h-core . However=1hci=Ah . It is ean-index   1 publication with 100 citations, (ii) 10 publications with 10 citations each, and (iii) 100 publications with 1 citation each, are considered as equally desirable. So the \u03c7-index is essentially the largest product ici where 1 \u2264 i \u2264 n; however, for comparison purposes with the h-index, we will actually define the \u03c7-index to be the square root of this, i.e. \u03c7-index of the researcher is 10; see k denote the value of i that maximises ici, we see that in all three cases, the researcher has exactly k publications with ck or more citations. It is clear that the h-index cannot be larger than the \u03c7-index, since In order to motivate the \u03c7-index with other indices, along the lines of the two-variable metrics examined in [A possible future line of research would be to investigate pairwise combinations of the mined in .\u03c7-index is formally introduced in Section 2, generalising the h-index by allowing the interplay between k  and ck . We also list some properties of the \u03c7-index, which could form the basis of its axiomatisation  when k is significantly greater than h and (iii) when k is significantly less than h. We further partition that data according to whether \u03c7 is approximately equal to h or significantly larger than h to get a sense of when these two indices differ. Membership of the classes is determined by a basic bootstrap percentile method [The ion cf. , 20), an, an\u03c7-inde method , Sectioncitation curve is the curve resulting from plotting the number of citations against the ranking of the publications, as specified by the citation vector. The \u03c7-index is the square root of the maximum area rectangle that can fit under the citation curve .The onotonic , 19, in \u03c7-index is scale-invariant [h-index is not scale-invariant).The nvariant , in the \u03c7-index is not independent [\u03c7 indices of both \u23292, 2\u232a and \u23291, 1, 1, 1\u232a are 2, however the \u03c7-index of \u23292, 2, 1\u232a is still 2 but the \u03c7-index of \u23291, 1, 1, 1, 1\u232a is h-index is also not independent).The ependent , since a\u03c7-index, comparing it to the citation indices mentioned in the introduction, however, focusing our attention on the comparison of the \u03c7-index and the h-index. We make use of a large data set compiled by Radicchi and Castellano from Google Scholar [In the following sections we carry out an empirical analysis of the  Scholar , and alsP, the number of cited publications. We carry out a more in-depth comparison of the \u03c7 and h indices in Section 4, by separating authors whose \u03c7 and h indices are approximately the same from those for which they are significantly different.Our initial comparison between the indices is carried out using the Spearman rank-correlation coefficient , which dbootstrap method [basic bootstrap percentile method [h-index for each resample, and then compute a 99% one-sided confidence interval for the h-index values, starting from the lowest one from the 1000 resamples. This allows us to determine for a given author whether k is approximately equal to h and, additionally, whether \u03c7 is approximately equal to h by checking whether k or \u03c7 are in the confidence interval or not.We make use of the p method , which ie method , Sectione method , which ak \u2248 h, (ii) k > h, or (iii) k < h, where \u2248 means approximately equals. The second and third classes capture a tendency of an author towards being prolific when k > h, or influential when k < h. . We further partition each class according to whether \u03c7 \u2248 h or \u03c7 > h to see when the indices differ, and to get a sense of the proportion of researchers for which \u03c7 \u2248 h. Finally, we also consider the subclasses of \u03c7 > h, depending on whether ck > k or ck < k.We thus first partition the authors into three classes, according to whether (i) We now introduce the two data sets, provide some basic statistics of these data sets, and compute the correlations between various indices for the researchers concerned. In Subsection 3.1 we consider the Google Scholar data set and in Subsection 3.2 we consider a data set of Nobel prize winners.For our main analysis, we made use of a large data set of Google Scholar profiles compiled and made available by Radicchi and Castellano . The fulh, g, A, R, \u03c7, P, stand for the h-index, the g-index, the A-index, the R-index, the square root of the Euclidian-index, the \u03c7-index, the square root of the total number of citations and the number of publications, respectively. . We obsh and \u03c7 indices, h being the most commonly employed index, and leave detailed comparison to other indices for future work.From now on, we will concentrate on comparing the h and \u03c7 indices both follow log-normal distributions [Jensen-Shannon divergence (JSD) [p = (pi) and q = (qi), where i = 1, 2, \u2026, n.We start by showing, as was done in , that thibutions , 29. To ce (JSD) , which iJSD, which is a symmetric version of the Kullback-Leibler divergence and is based on Shannon\u2019s entropy [pi = 0 or qi = 0, or both, 0 ln 0 and 0 ln (0/0) are both defined to be 0. . We observe that the JSD is equal to 0 when p = q.The formal definition of the  entropy , is give\u03bc, and standard deviation \u03c3 of the log-normal distributions fitted by the maximum likelihood method, and the JSD between the empirical distributions of the h and \u03c7 indices and the fitted log-normal distributions. The low JSD values indicate good fits for both indices. We also note that the means and standard deviations are quite close.In A is more of an outlier than P. On the other hand, the correlations are comparable to the Google Scholar data set, although, on average lower.For our second data set, we collected the citation vectors of 99 Nobel prize winners across a variety of disciplines from the Web of Science platform . We inclh and \u03c7 indices and the fitted log-normal distributions. As for the Google Scholar data set, the low JSD values indicate good fits for both indices. We again note that the means and standard deviations are quite close.In k \u2248 h or not, or whether \u03c7 \u2248 h or not. In Subsection 4.1 we analyse the Google Scholar data set, and in Subsection 4.2 we analyse the Nobel prize winners data set.We now analyse the data sets introduced in Section 3, with the aim of revealing how authors are separated into classes depending on whether k \u2248 h, (ii) k > h, or (iii) k < h, exhibiting the geometry of the h and \u03c7 indices. When k > h there are many publications, each with fewer than h citations (tending towards prolific), and when k < h therefore fewer publications, each with more than h citations .In k < h is the largest class, the other two comprising just over 53.50% of the data set. It is also apparent that, within the class k < h, there are by some margin, more authors for which \u03c7 > h. What this means is that, when \u03c7 is significantly larger than h, we expect that k will be significantly smaller than h, i.e. we expect the author to have several publications with more than h citations, contributing to \u03c7 being larger h; this can be justified from the data in \u03c7-index addresses a problem of the h-index that it does not sufficiently take into account highly cited publications. The statistics in \u03c7-index, showing higher average values for the \u03c7-index when k < h.In \u03c7 is significantly larger than h, clearly demonstrating the potential of the \u03c7-index to separate authors that may have similar h indices. In addition, the statistics shown in \u03c7 > h. The breakdown of the \u03c7 > h class, when ck > k and ck < k, can be seen in ck > k, are much higher than those for the smaller subclass, ck < k.Moreover, it can be seen in h values and therefore also very high \u03c7 values. In \u03c7-index for this data set. These examples can be contrasted to the ones shown in \u03c7-index when k > h or k < h.The Nobel prize winners data set looks at the extreme case of researchers having, on average, very high k < h and, of those, for over 75% of the authors \u03c7 > h. As expected, this implies that, overall, Nobel prize winners are influential. Looking at the statistics in k < h, on average, the \u03c7 values of researchers are much larger than the h values. This is due to publications with a large number citations, significantly more than h. An interesting observation is that unlike \u03c7-index are the highest when k < h, in \u03c7 is highest for the smaller class when k > h. This is most likely due to a long tail of highly cited publications for these few laureates.In \u03c7 > h for over 60% of laureates. However, as the statistics in h-index for those Nobel prize winners with \u03c7 \u2248 h, is actually, on average, higher than both the h and \u03c7 indices of the laureates with \u03c7 > h. This may indicate that for very influential researchers, such as Nobel laureates, when \u03c7 > h the h-index undervalues their contribution. The breakdown of the \u03c7 > h class, when ck > k and ck < k, can be seen in ck > k are, in fact, much lower than those for the subclass ck < k. This latter class is quite small as there are only three such Nobel prize winners; see In contrast to \u03c7-index, which addresses some shortcomings of the h-index in terms of the balance between number of citations and number of publications. The \u03c7-index has a simple geometric characterisation in terms of the largest area rectangle that fits under the citation curve; this generalises the h-index for which the rectangle is constrained to be a square.We have presented a new citation index, the \u03c7-index. First, as with many of the citation indices that combine number of citations  with number of publications (quantity), the \u03c7-index correlates strongly with the square root of the total number of citations, yet it is selective in its choice of publications to include in the index. Second, as we have seen from our analysis, there are many researchers whose \u03c7-index is significantly larger than their h-index due to their tendency to be influential, in the case k < h, or prolific in the case k > h. We believe that this property of the \u03c7-index is beneficial and could lead to a more satisfactory ranking of researchers than that obtained using the h-index.We have analysed two data sets, a large one from Google Scholar and a small one of Nobel prize winners. Studying these data sets clearly shows the utility of the"}
+{"text": "Scientific Reports 10.1038/s41598-018-25048-w, published online 30 April 2018Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cReservoir\u201d was incorrectly given as \u201cReservior\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supporting Information file."}
+{"text": "Nature Communications; 10.1038/s41467-017-01713-y, published online 23 Nov 2017.Correction to: The original version of this Article contained an error in Fig.\u00a01. In panel d, the model on the right of the panel was incorrectly labeled \u2018+Heme\u2019, and should have read \u2018\u2212 Heme\u2019. This has now been corrected in both the PDF and HTML versions of the Article."}
+{"text": "Neuroscience of Consciousness, Volume 2019, Issue 1, 2019, https://doi.org/10.1093/nc/niz009In the original version of this article, the section \u2018The reason for metacognitive inflation\u2019 contained a small error. The corrected sentence reads as follows:Therefore, metacognitive noise likely contributed to the increase in metacognitive efficiency scores (meta-d\u2032/d\u2032 and meta-d\u2032\u2013d\u2032) in the current analyses but not to the increase in metacognitive sensitivity scores  .The authors would like to apologize for any confusion this may have caused."}
+{"text": "Automated machine-learning systems are able to de-identify electronic medical records, including free-text clinical notes. Use of such systems would greatly boost the amount of data available to researchers, yet their deployment has been limited due to uncertainty about their performance when applied to new datasets.We present practical options for clinical note de-identification, assessing performance of machine learning systems ranging from off-the-shelf to fully customized.We implement a state-of-the-art machine learning de-identification system, training and testing on pairs of datasets that match the deployment scenarios. We use clinical notes from two i2b2 competition corpora, the Physionet Gold Standard corpus, and parts of the MIMIC-III dataset.Fully customized systems remove 97\u201399% of personally identifying information. Performance of off-the-shelf systems varies by dataset, with performance mostly above 90%. Providing a small labeled dataset or large unlabeled dataset allows for fine-tuning that improves performance over off-the-shelf systems.Health organizations should be aware of the levels of customization available when selecting a de-identification deployment solution, in order to choose the one that best matches their resources and target performance level. Over the past several years, health service researchers have significantly expanded their use of free text in medical research . For exaDe-identified clinical datasets are created by labeling all words and phrases that could identify an individual, and replacing them with surrogate data or context-specific labels. For example, \u201cJohn London complains of chest pain that started on January 1st 2012\u201d becomes \u201c[PersonNameTag] complains of chest pain that started on [DateTag]\u201d. The de-identification process needs to have high recall (sensitivity) since publicly releasing text containing protected health information (PHI) represents a legal and ethical liability. On the other hand, it also needs to have reasonable precision, because unnecessarily removing non-identifying text limits the data\u2019s usefulness to researchers . Notice Automatic de-identification systems have not been widely adopted on a commercial level, despite the fact that their performance already surpasses that of human annotators: fully customized de-identification systems achieve precision and recall of 97% or higher , 6, whilguarantee performance on all medical text it will ever encounter. Structured data such as forms are easy to de-identify, e.g., by removing \u201cName\u201d and \u201cDate\u201d fields; however, free-text clinical notes vary widely with note purpose and institutional conventions, and include PHI in ways that are challenging to identify and redact.A blocking factor is that, like many other tools based on machine learning, a de-identification system cannot This challenge may necessitate customizing the de-identification system in order to teach it about the formatting and jargon used in a particular organization. Consider a note with the line \u201cJohn referred to Alzheimer\u2019s clinic ...\u201d. An off-the-shelf system knows \u201cAlzheimer\u2019s\u201d as a medical condition and de-identifies to \u201c[PersonNameTag] referred to Alzheimer\u2019s clinic...\u201d; a system customized on a target organization\u2019s labeled data where Dr. Alzheimer and his clinic appear frequently, would correctly give \u201c[PersonNameTag] referred to [PersonNameTag]\u2019s clinic...\u201d.As reviews of de-identification strategies in healthcare concluded, \u201cTrue anonymization is challenging, and further work is needed in the areas of de-identification of datasets\u201d  and \u201cde-Therefore, in such a privacy-sensitive field, healthcare organizations need to employ de-identification systems in a controlled manner, with performance assurances specific to each deployment. In order to help organizations make an informed decision, we use publicly available clinical note datasets to assess the performance of automated de-identification systems in several deployment scenarios.Our first scenario is a fully customized system: a healthcare organization employs human annotators to label a sufficiently large number of PHI examples for training a new machine learning model to perform automated de-identification. We assess performance in this scenario using 3 medical datasets, training the model on part of a dataset and evaluating on the remainder of the dataset.Our second scenario is off-the-shelf use: the organization provides no labeled data, instead using a pre-trained model as-is. We replicate this scenario by training custom models on 3 datasets and testing each model on all other datasets.some labeled data. Since labeled data is an expensive resource, requiring the work of human annotators, we study how many labeled examples are needed to improve performance over the off-the-shelf scenario, and how many are required to obtain results equivalent to the fully customized scenario.Our third scenario is partial system customization with labeled data: the organization has the resources to provide unlabeled data. With this data we create a custom token embedding (data representation) for the machine learning system.Our last scenario is partial system customization with unlabeled data: the organization can avoid the legal and privacy concerns involved with annotating data, and instead improve performance using a large set of its The first automated approaches for medical free-text de-identification were proposed in the late 1990s and were mainly rule-based , 11. SubOur partial customization scenario with labeled examples is an example of semi-supervised transfer learning/domain adaptation; we build on the work of Lee JY et al. in neural networks . Lee H-JThe US HIPAA de-identification standard specifies the use of either \u201cExpert Determination\u201d or the \u201cSafe Harbor\u201d method to de-identify data . In the From the i2b2 National Center for Biomedical Computing for the NLP Shared Tasks Challenges, we use the i2b2-2006  and i2b2We also use the PhysioNet gold standard corpus of de-identified medical text , containFinally, we use the Medical Information Mart for Intensive Care III (MIMIC-III) dataset . This daThe i2b2-2006, i2b2-2014, and Mimic-III de-identification guidelines vary regarding which entities are considered PHI. When dataset pairs in an experiment were annotated with the same guideline, we report results on all PHI types in the guideline; in cross analyses, we use the Name PHI, which is labeled consistently across all guidelines. The train/test splits were made by patient. The i2b2 datasets were released with a supplied partition, and the remaining datasets were split randomly. Descriptive statistics are given in Table\u00a0Our machine learning model implements the state-of-the-art in de-identification of medical notes , 6 and nPatient, prescribed, 50, mg, ...).A Tokenizer, breaking down the input text into tokens, e.g. \u201cPatient prescribed 50mg...\u201d is split into , and the number of spaces and line breaks before the token.A Named Entity Sequence Tagger, responsible for converting a token sequence to a tag sequence while taking into account context information. For example, in the sentence \u201cMr. Jack London was examined\u201d, \u201cLondon\u201d should be tagged as a person\u2019s name. The Tagger consists of the following:A Token BiRNN, adding context information to the extracted token information.A Tag prediction layer, projecting the 200 dimensional BiRNN into a probability distribution over the PHI tags , including the \u201cnot PHI\u201d tag.A Conditional Random Field, imposing an additional structured prediction layer to make sure that PHI labels make sense as a sequence.Figure\u00a0Model training was carried out using cross entropy loss over the given set of labeled examples as the loss function, and applying Adagrad  as the sEvaluation results are given for recall , precision (percent of detected PHI which was indeed PHI), and F1 score . We can tune the balance between recall and precision by setting the activation bias for \u201cnot PHI\u201d prior to the Conditional Random Field block. In an off-the-shelf system, this tuning would be accomplished using heuristics or manual monitoring.p\u2009=\u200985%), while not adjusting if precision is less than this cutoff. As shown in Table Because recall is of highest importance for patient privacy, we compare system recall using R@P as described in, e.g., Eban et al. , 35 The We perform four experiments using the text de-identification system described in the previous section.We follow the standard machine learning setup of training and testing on the same dataset \u201cA\u201d.We follow the standard machine learning setup of training on a dataset \u201cA\u201d and testing on a different dataset \u201cB\u201d.Train from scratch: A new model is trained using these \u201cn\u201d datapoints. We call this model \u201conly B\u201d.Further tune an existing model: A model pre-trained on \u201cA\u201d receives further training on \u201cB\u201d. We call this model \u201cA then B\u201d.Jointly train a new model: A model is trained from scratch using an even mixture of \u201cA\u201d and \u201cB\u201d. We call this model \u201cA mix B\u201d.We train the system on \u201cA\u201d augmented with \u201cn\u201d labeled PHI instances from \u201cB\u201d, and test on \u201cB\u201d. We consider three ways to make use of the additional \u201cn\u201d samples from \u201cB\u201d:We train the system on \u201cA\u201d only, using a custom token embedding that is generated using unlabeled dataset \u201cB\u201d. A token embedding maps a discrete word to a floating-point vector; vectors corresponding to similar words cluster together, thus providing information about the language to the machine learning system. Token embeddings are built using large unlabeled text corpora; in some settings, using domain-specific corpora improves system performance , 37. We We go through our four scenarios, presenting results and discussing their implications.We train custom models on the three datasets that contain sufficient PHI for a fully trained model. The fully customized results are given in Table\u00a0To illustrate the challenges remaining in even the best-performing de-identification scenario, we consider the errors on the i2b2-2014 model. From the 15,201 PHI elements in the evaluation set, the model classified 15\u2009K true positives, 116 false negatives, and ~\u20092.5\u2009K false positives.We focus on the errors in Name, as the most identifying field. Name had 14 false negatives, i.e. undiscovered PHI: 3 doctor initials, 1 patient single-letter suffix (\u201cI\u201d as in \u201cJohn Smith I\u201d), 1 dataset-mislabeled apostrophe-s, and 9 names. All 9 names were dictionary words , showing remaining challenges in automated de-identification.False positives remove information useful to researchers; they are worth reviewing both to see what is being unnecessarily lost, and to get an intuition for the workings of the algorithm. The Name false positives included medical terms similar to names , which could be corrected using heuristics based on medical terminology; errors due to overreliance on sentence structure, e.g. the second word after a title being labeled a name (\u201cawoke\u201d was labeled in \u201cMs Mitchel awoke feeling...\u201d); and misspellings creating non-dictionary words (\u201cInteresetd (sic) in quitting smoking\u201d).Our next deployment scenario is an organization using an off-the-shelf system with no customization. We use our custom models from the previous section. We test each model on the datasets with compatible labeling schemes, reporting recall/precision/F1 for all PHI types combined. We then present a full cross-dataset analysis using Name only.The i2b2-2014 model tested on physionet yields 76.6/60.5/67.6. Error analysis shows that 272 of the 441 false negatives (i.e. missed PHI) are of type Location, and consist mainly of \u201cMICU\u201d, \u201cPMICU\u201d, \u201ccath lab\u201d, and similar. Investigation revealed that these initials appear only in physionet, not i2b2-2014, thus providing a good example of an off-the-shelf system missing local jargon. Dropping Location from the analysis yields an improved 89.1/59.8/71.6; this improvement shows that a real deployment could consider using an off-the-shelf model together with heuristics  gleaned from a manual error analysis.The mimic-discharge model tested on mimic-radiology yields 65.7/90.9/76.2. Error analysis shows that 595 of the 597 false negatives are of type Id; of these errors, 577 are the 7-digit record number at the top of every note. This error is again dataset-specific and easily fixed with a simple heuristic. Including the heuristic yields 99.4/95.2/97.3, on par with a custom model.The mimic-discharge model test on mimic-echo yields 99.7/98.7/99.2, on par with a custom model and thus showing that de-identification of some datasets can be accomplished without a customized system.Table\u00a0For the large labeled dataset \u201cA\u201d we use i2b2-2014; for the partially labeled dataset \u201cB\u201d we run experiments using physionet, mimic-radiology, and mimic-discharge.Figure\u00a0The larger mimic-discharge shows that over ~\u2009500 labels, one can train solely on \u201cB\u201d. Around 1000 labels, performance reaches that of fully customized (97.1%); around this number, one sees diminishing returns from further labeling effort. At ~\u200980 labels, the \u201cA then B\u201d model is already better than the off-the-shelf system, again demonstrating the usefulness of even small labeled datasets.We train using i2b2-2014 as dataset \u201cA\u201d with different token embeddings, and select test dataset \u201cB\u201d from physionet, mimic-radiology, mimic-discharge, and mimic-echo. For each choice of \u201cB\u201d, we evaluate three different token embeddings: the generic GloVe embedding, embed-mimic, and the embed-mimic-* that matches \u201cB\u201d. . For the mimic datasets, we give recall/precision/F1 on Name PHI; for physionet, whose labeling matches i2b2-2014\u2019s, we also report on all types.Table\u00a0In our work we follow the same datasets through various levels of system customization, thereby creating a robust picture of the performance a health organization can expect from a de-identification system under different scenarios. This is while obtaining results on par with the available literature at comparable data points , 20, 37.Automated de-identification systems can be used to add an extra layer of security while working with trusted research collaborators, or to minimize exposure of PHI to human annotators who will complete the de-identification task. Automated de-identification can also play a role in a HIPAA-compliant data release, with the additional step of \u201cExpert Determination,\u201d wherein a human expert in the field determines if the de-identification process has ensured that \u201cthe risk is very small that the information could be used ... to identify an individual.\u201d  SelectinBased on our results, we present broad guidelines to inform an organization\u2019s approach to de-identification using machine learning.Organizations able to label on the order of 10\u2009K PHI examples can expect their fully customized system to have a recall of 97\u201399%. Organizations also have the control to fine-tune the balance between recall and precision.Organizations should try using an off-the-shelf system before committing to customization. Although performance varied widely, our experiments showed that recall can be dramatically improved (to 89\u201399%) with simple heuristics gleaned from manual error analysis.Organizations with the resources to provide a small amount of labeled data will benefit from partial customization. Labeling even a small amount of PHI, ~\u200920 to ~\u200980 examples, will raise system performance over an off-the-shelf solution. Labeling ~\u20091000 PHI will give results on par with full customization.Organizations can avoid the cost and privacy concerns of labeling data, yet still gain in performance over off-the-shelf-systems, by creating a custom embedding using a large set of their unlabeled data.These guidelines generalize from results on available datasets, and thus cannot provide performance guarantees. In practice one can ensure better baseline performance with additional de-identification techniques, such as adding organization-specific or generic heuristics, or enhancing a pure machine learning system with a human in the loop.Our results highlight the need for additional medical corpora with identical labeling schemes. Contributions of notes from a variety of healthcare systems, large and small, encompassing different jargon and distributions of identifiers, would go a long way towards the goal of building a truly generic, off-the-shelf system requiring no customization. Such a collection could also form a universally recognized benchmark for evaluating commercial offerings."}
+{"text": "The next generation sequencing technology allows us to obtain a large amount of short DNA sequence (DNA-seq) reads at a genome-wide level. DNA-seq data have been increasingly collected during the recent years. Count-type data analysis is a widely used approach for DNA-seq data. However, the related data pre-processing is based on the moving window method, in which a window size need to be defined in order to obtain count-type data. Furthermore, useful information can be reduced after data pre-processing for count-type data.z-values for a follow-up analysis. For an illustration, an application to the DNA-seq data from a pair of normal and tumor cell lines is presented with a change-point analysis of z-values to detect DNA copy number alterations.In this study, we propose to analyze DNA-seq data based on the related distance-type measure. Distances are measured in base pairs (bps) between two adjacent alignments of short reads mapped to a reference genome. Our experimental data based simulation study confirms the advantages of distance-type measure approach in both detection power and detection accuracy. Furthermore, we propose artificial censoring for the distance data so that distances larger than a given value are considered potential outliers. Our purpose is to simplify the pre-processing of DNA-seq data. Statistically, we consider a mixture of right censored geometric distributions to model the distance data. Additionally, to reduce the GC-content bias, we extend the mixture model to a mixture of generalized linear models (GLMs). The estimation of model can be achieved by the Newton-Raphson algorithm as well as the Expectation-Maximization (E-M) algorithm. We have conducted simulations to evaluate the performance of our approach. Based on the rank based inverse normal transformation of distance data, we can obtain the related Our distance-type measure approach is novel. It does not require either a fixed or a sliding window procedure for generating count-type data. Its advantages have been demonstrated by our simulation studies and its practical usefulness has been illustrated by an experimental data application.The online version of this article (10.1186/s12864-019-5491-x) contains supplementary material, which is available to authorized users. The next generation sequencing technology has advanced significantly during the recent decade. It allows us to obtain a large amount of short DNA sequence (DNA-seq) reads at a genome-wide level . DNA-seqDNA-seq has been widely used for the detection of copy number variation/alteration , 4. BothDue to the limitations of current sequencing techniques, the sequencing data cannot be obtained for certain genomic regions. Then, the related count-type measure is simply zero. For a DNA sequence containing such a genomic region, a large gap without any short reads is observed. Then, the related distance-type measure can be very large  and an artificial censoring can be considered.In this study, we consider distance-type measure. Distances are measured in base pairs (bps) between two adjacent alignments of short reads mapped to a reference genome. Our distance-type measure approach is novel. It does not require either a fixed or a sliding window procedure for generating count-type data. Furthermore, we propose artificial censoring for the distance data so that distances larger than a given value are considered potential outliers. Our purpose is to simplify the pre-processing of DNA-seq data.Statistically, we consider a mixture of right censored geometric distributions to model the distance data. Additionally, to reduce the GC-content bias, we extend the mixture model to a mixture of generalized linear models (GLMs). Our approach can be considered as an alternative to the method proposed by Shen and Zhang . The estIn the following, we first demonstrate how to conduct experimental data based simulation study to confirm the advantages of distance-type measure approach in both detection power and detection accuracy. Then, we introduce our statistical models and the related estimation procedure. The model performance can be demonstrated by simulation studies. The practical usefulness of our approach can be illustrated by an application to the DNA-seq data from a pair of normal and tumor cell lines  as well We consider a novel distance-type measure approach to the analysis of DNA-seq data. Distances are measured in base pairs (bps) between two adjacent alignments of short reads mapped to a reference genome. An illustration is shown in Fig.\u00a0We first introduce how to compare the distance-type vs. count-type data so that more advantages of distance-type data can be confirmed. Then, we introduce a finite mixture , 14 of gThe widely used coverage depth (or count-type) based approach can be briefly described as follows. For a genomic region, it is divided into non-overlapping smaller regions (windows or bins) and the number of sequencing reads is counted for each bin. For example, if a genomic region is divided into 100 bins, then 100 count-type data can be obtained from these bins. The original sequencing read data are then simplified to count-type data by this approach. In this study, the DNA sequencing data were collected for the detection of copy number variations. A certain type of data (distance or count) is generated from the original sequencing read data . Between these two types of data, our choice is decided based on the statistical power for detecting changes. To demonstrate the advantage of our approach, we perform a simulation study to evaluate whether the distance based approach can be more statistically powerful than the coverage depth based approach. We consider a relatively simple scenario: if two genomic regions are known to be different in copy numbers, then which approach is more likely to detect the change? Furthermore, can accurate detection of change location be achieved when the distance-type data are used in the copy number variation/alteration analysis?Application to Sequencing Data, but we used the original sequencing read data). In this region, we randomly selected two bins with length L for each bin. For each of the original sequencing reads from the second bin, we removed it randomly with 50% probability. (The purpose was to simulate a deletion of 50% copy number.) We kept all the original sequencing reads from the first bin. In this way, we simulated sequencing data for two genomic regions with different copy numbers. The distance-type data can be obtained as described at the beginning of Methods section. To obtain count-type data, we divided each region into bins with length W for each bin (and then counted the number of sequencing reads in each bin). To achieve an unbiased comparison between the distance-type data and the count-type data, we used the non-parametric Komogorov-Smirnov two-sample test to compare the empirical distributions of simulated data for two genomic regions. Notice that either the distance based approach or the coverage depth based approach is to generate a certain type of data . It is necessary to compare which type of data can be more statistically powerful in the detection of changes. Our evaluation strategy does not depend on data type, as it does not require any parametric or statistical distribution assumptions.To address which type of data is more likely to detect the change (detection power), we consider the following simulation. Our simulation data were generated based on some real experimental sequencing data . We generated data based on the region with position 10-30Mbps from the normal sample  For each setting, we repeated our simulation and analysis for 5000 times.p-value as the identified change location. In this way, from each simulation repetition, we obtained the identified change location and its related p-value. Although the lowest p-value was considered, some cutoff values would still be usually considered in practice. As all the possible change locations were screened, a cutoff value lower than the conventional cutoff value 0.05 would be usually considered. Therefore, we considered the following cutoff values for the lowest p-values: 0.01, 0.001, 0.0001, 0.00001, 0.000001 and 0.0000001. Based on the results for detection power comparison , we obtained more analysis results from the above simulation setting. In each simulation repetition, we considered the data for two genomic regions were connected. We evaluated how accurate the boundary (change) between two regions could be detected. As the data for two regions were ordered, the change location could be between any two consecutive data (for both distance-type and count-type). Therefore, we screened all the possible locations and considered the location with the lowest p-value was lower than the cutoff value, then we calculated the difference between the identified and true change location; otherwise, we considered the difference as no-detection (ND). Then, we would evaluate whether the overall difference based on the distance-type data was lower than the overall difference based on the count-type data. (Notice that a lower difference means a more accurate detection.) Statistically, the traditional Wilcoxon-Mann-Whitney rank sum test would be an appropriate choice (for testing \u201cdistance-type based difference\u201d < \u201ccount-type based difference\u201d). In the test, for these ND differences, we changed them to be a value larger than any observed differences as no-detection (ND) would be the worst scenario.For each simulation repetition, if the returned Y is a random variable (e.g. distance-type measure) with a right censored geometric distribution with p as the probability of success. Notice that a geometric distribution can be considered as a model for the number of failures until first success. Let T be a given constant for the censoring value . The indicator function \u03b4\u2009=\u20091 if y\u2009\u2265\u2009T and \u03b4\u2009=\u20090 if y\u2009<\u2009T. The probability distribution function of right censored geometric distribution is given by:Suppose Mixture of Right Censored Geometric Distribution.Y1,\u2009\u2026\u2009, Yn denote a random sample of size\u00a0n. Each mixture component is a right censored geometric distribution given by Eq.  censored at the same value T.g-component GLMs. Let y1,\u2009\u2026\u2009, yn be n independent observations of the response variable. For each\u00a0yi, there is a covariate\u00a0xi. \u03c01,\u2009\u2026\u2009, \u03c0g are the component proportions as defined above. The mixture is given by:fj\u2009=\u2009(pj(x)(1\u2009\u2212\u2009pj(x))y)\u03b4((1\u2009\u2212\u2009pj(x))T\u2009+\u20091)\u03b4)(1\u2009\u2212\u2009. Notice that each pj is a function of\u00a0x. We first define\u00a0\u03bcj\u2009=\u2009(1\u2009\u2212\u2009pj)/pj and then we use a link function \u03b7j\u2009=\u2009log(\u03bcj)\u2009=\u2009\u03b2j0\u2009+\u2009\u03b21x for\u00a0j\u2009=\u20091,\u2009\u2026\u2009, g. Here, \u03b21 is common for all different components since it represents the GC-content effect. Furthermore, the component proportions \u03c01,\u2009\u2026\u2009, \u03c0g do not depend on the covariate since they are considered as global parameters . Therefore, the vector \u03a8 of parameters is given by\u00a0\u03a8\u2009=\u2009. The intercepts  are different for different distribution components.Based on the above mixture of right censored geometric distribution, a mixture of right censored geometric distribution based GLMs can be described. Eq.  can be eThe log-likelihood based on Eq.  is given\u03a8. For each\u00a0yi, missing component information can be considered. Accordingly, the vector {zij} is introduced: zij\u2009=\u20091 if yi belongs to the j-th component of the mixture model; zij\u2009=\u20090 otherwise\u00a0. Then, the log-likelihood of \u201ccomplete data\u201d is given by:The EM algorithm  can be uFor the E-step, we calculate:For the M-step, we first calculate:\u03b210,\u2009\u2009\u2026\u2009,\u2009\u03b2g0,\u2009\u03b21) requires a numerical optimization procedure, which is used to solve the following equation system.The calculation for :Based on the Newton-Ralphson method, we have the following iterative equation for\u00a0The details for this iterative equation as well as the EM algorithm are given in the Additional file g0\u2009<\u2009g1. We test the null hypothesis H0\u2009:\u2009g\u2009=\u2009g0 against\u00a0H1\u2009:\u2009g\u2009=\u2009g1. We first use the observed data to fit a mixture model with g0 components and a mixture model with g1 components. A LRT score can be calculated for the observed data. Then, we can simulate data based on the fitted model with g0 components (parametric bootstrap). For each set of simulated data, we can calculate the related bootstrapped LRT score. After B rounds of parametric bootstrap repetitions, the p-value of observed LRT score can be approximately calculated based on B bootstrapped LRT scores. The number of components in the mixture model is determined by a likelihood ratio test (LRT) based approach. Consider two integers\u00a0p-values less than the cutoff value). When the regions are as long as 200\u2009kbps, the advantage of distance based approach (distance-type data) can be clearly observed. It is more difficult to detect changes as the regions become shorter. However, the advantage of distance based approach (distance-type data) becomes even clearer when the regions are as short as 50\u2009kbps. When the regions are as long as 1Mbps, two approaches perform overall similarly. From Table For the detection power based comparison, our evaluation results are summarized in Table p-value less than a given cutoff value is presented for each type of data. The proportion based on the distance-type data is always higher. Then, the one-sided p-value for each pair of comparison test is presented in Table p-values for Wilcoxon-Mann-Whitney rank sum test is actually simple.) When L is relatively short as 150,000\u2009bps, the detection accuracy based on the distance-type data is always better than the detection of accuracy based on the count-type data. When L is increased to 300,000\u2009bps, the detection accuracy based on the distance-type data is still clearly better when the cutoff value is 0.001 or lower. When L is relatively long as 450,000\u2009bps, the detection accuracy based on the count-type data is better, but the detection accuracy based on the distance-type data is still better when the cutoff value is 0.0001 or lower. For the detection accuracy based comparison, our evaluation results are summarized in Table\u00a01\u2009=\u20090.3, \u03c02\u2009=\u20090.5, \u03c03\u2009=\u20090.2\u00a0and\u00a0p1\u2009=\u20090.002, p2\u2009=\u20090.02, p3\u2009=\u20090.2  to generate the empirical distribution of p-values. The empirical distribution plots for these p-values show uniform distribution like patterns (results not shown). Therefore, the hypothesis testing p-values can be appropriately calculated by the parametric bootstrap procedure.1\u2009=\u20090.3, \u03c02\u2009=\u20090.5, \u2002\u03c03\u2009=\u20090.2 and \u03b210\u2009=\u20096.0, \u2002\u03b220\u2009=\u20093.6, \u03b230\u2009=\u20091, 1, \u03b21\u2009=\u20092.0. The choice of the component proportions are the same as above and the choice of\u00a0\u03b210, \u03b220, \u03b230 was based on setting\u00a0\u03b21\u2009=\u20092.0\u00a0and using p1\u2009=\u20090.002, p2\u2009=\u20090.02, p3\u2009=\u20090.2 as above (consistent with a previous simulation). For estimation performance evaluation, we simulated 1000 times with 10,000 samples each with no censoring (NC), censoring at 570, 937, and 1309 respectively . For estimation performance evaluation, we simulated 1000 times with 10,000 samples each with no censoring (NC), censoring at 1241, 895 and 549  decreases with the increasing censoring value. The RMSE also decreases as the artificial censoring value for observations increases. The median gets closer to the true value with the increasing censoring value of the observations. The inter-quartile range gets narrower with increasing sample size and the censoring value of the observations as well. Overall, both simulation studies support the use of right censoring in mixture GLM.p-values.  Additional file Furthermore, we have evaluated the effect of censoring on the testing performance. A data set can be simulated as above and we can test the hypothesis of 3 components vs. 4 based on 100 parametric bootstrap p-values. These steps can be repeated 200 times for the first simulation scenario or 100 times for the second simulation scenario  to generate the empirical distribution of the We considered an application to the DNA-seq data from Chiang et al. . The dathttp://bioinfo-out.curie.fr/projects/freec .) Notice that, as the GC-content data were based on a reference genome, the model coefficient for GC-content was first estimated based on the normal sample data and then fixed in the model for tumor sample data . This approach (pseudo-maximum likelihood estimation) was based on the work by Gong and Samaniego [A 4-component mixture of right censored geometric distribution based generalized linear models was estimated for the normal sample and then for the tumor sample Table\u00a0. GC-contamaniego .  was calculated by:Fj was the CDF based on fj given in Eq.  have been widely considered in practice. The purpose is to make the (transformed) data more similar to normal distributions. Both rank-based INTs and non-rank based INTs can be considered \u201326. We cn in Eq. . Then, aThe comparison between the distance data (log2 of distance+\u20091) and the related INT values  is shown in Fig.\u00a0p-value calculation [Then, for the INT values related to these artificially right censored distance data, we simply assign a value 10 /2), where m is the number of bins .For a change-point analysis of the above selected region (as an illustration), we considered a recursive combination approach . For eachttp://www.genome.ucsc.edu/cgi-bin/hgTracks) shows that the cytobands p13.2, p13.3, p21.1, p21.2, p21.3 and p22.1 are related to this detected region. To understand biological significance of this detected deletion, a literature search shows that this region has been investigated by many studies on the relationship between these cytobands and breast cancer [The change-point analysis results are shown in Fig.\u00a0t cancer , 31.Fig.Count-type data analysis is a widely used approach for DNA-seq data. It requires either a fixed or a sliding window procedure for generating count-type data, and useful information can be reduced after this data pre-processing. In this study, we proposed to analyze DNA-seq data based on the related distance-type measure. Our experimental data based simulation study confirmed the advantages of distance-type measure approach in both detection power and detection accuracy. Furthermore, we proposed a mixture of generalized linear models for analyzing the recent DNA-seq data. Our model was based on the right censored geometric distribution. According to the mathematical details provided in the Additional file Similar as the exponential distribution (for continuous measurements), which is widely used to model waiting time processes, the geometric distribution (for discrete measurements) is also a memoryless probability distribution. The artificial right-censoring has been proposed to overcome the difficult in modeling extreme distance values.  Due to different biological properties in different genomic regions, which results in different distance distributions, different geometric components are necessary to model the data. As one geometric distribution does not well fit the distance data, a mixture of right-censored geometric distributions has been proposed. To understand the connection between a probability distribution component and its related underling biological properties, we need further statistical and biological investigations, which will be an interesting topic for our future research.In our application, interesting change-points were observed from the tumor cell line data. The impact from GC-content was considered in our analysis. In this study, we chose a set of relatively simple DNA-seq data for the purpose of illustration of our approach. Our approach can also be applied to paired-end DNA-seq data. In practice, either paired-end reads or single-end reads can be considered in sequencing experiments. If only the starting position of each paired-end read is considered, then the analysis scenario is equivalent to the analysis of single-end reads. However, this strategy may not well utilize the advantage of paired-end reads.  To consider the distance based approach and to utilize the advantage of paired-end reads, we will need to investigate which modifications or extensions are necessary to our method proposed in this study. This will be an interesting topic for our future research.With the next generation sequencing technology, a large amount of short DNA sequence reads can be obtained at a genome-wide level. DNA-seq data have been increasingly used in different areas of biomedical studies. Although the count-type based approaches have been widely used for DNA-seq data analysis, a moving window based data pre-processing (or similar) is required with a pre-specified window size. Useful information can be reduced after the data pre-processing. In this study, we have developed a distance-type measure based method. Distances are measured in base pairs (bps) between two adjacent alignments of short reads mapped to a reference genome. This is a novel approach. Its advantages have been demonstrated by our simulation studies and its practical usefulness has been illustrated by an experimental data application.Additional file 1:Mathematical details. (PDF 271 kb)Additional file 2:Supplemental figures. (PDF 1697 kb)"}
+{"text": "The convergence results are illustrated with specific examples of expansions in q-Fourier\u2013Bessel series.We study Fourier\u2013Bessel series on a  In the following we will use the standard notation for the q-calculus . The third Jackson q-Bessel function or, for some authors, the Hahn\u2013Exton q-Bessel function, is defined asq-analogues of the Bessel function defined by Jackson. We will often drop the superscript for notational convenience and simply write q-integral.However, for a certain l follow  for basil follow  for q-caulus and  for q-Be,3, from  is used own fact , 42 thatq-linear grid was developed, using a q-analogue of the exponential function and the corresponding q-trigonometric functions introduced by Exton  to denote the greatest integer which does not exceed x will be adopted.Now we will consider the sumFor a given sequence m it can be proved thatUsing induction on q-linear grid associated with f is defined as the sumThe Fourier\u2013Bessel series on a q-Fourier\u2013Bessel series but also other Fourier systems based on discrete orthogonality relations, as in [With a view to studying pointwise convergence of the series  when \\domentclasspt{minimas, as in \u201324. TherLet Let Let given in , satisfiq-integral  in \\docfined in  convergection of .q-Sturm\u2013Liouville systems was developed. In particular, it was shown that the set of all normalized eigenfunctions forms an orthonormal basis for q-Sturm\u2013Liouville systems are pointwise convergent.In  a rigoroBy  and 4.24.2 one mgiven by ,6.1\\docun in the variable x andFor n. Consider the basic difference relation (2.12) of , p. 693\\n and j are nonnegative integers, relation .For C, independent of k and n, such thatk and n. Using Theorem A we may write, for k large enough,One must show that there exists (i) When ary 3 of ,\\documen (12) in , p. 1205ary 2 of , the fun(ii) Now, let us consider q-shifted factorial q-Bessel function and its derivative.The asymptotic behavior of stigated , Lemma 1q)\u221e from  with theq)\u221e from . We provk,For large values of p, one can resort to (We will present only the main steps of the proof. Computing the derivative of the function esort to \u20132.8) to to\\documo Jacobi , p. 500 Notice that the above lemma implies that q-integral  upper bound for the q-Fourier\u2013Bessel series.We are now in conditions to prove our main result. The beef of the proof consists of finding an q-H\u00f6lder type inequality [q-integrals appearing on the right side of ,,6.22),  and 6.2 into ine term in  can be b2),using . To deal\u037eq).From  it follok\u2192\u221e and \u20134.3) gi gi\\documudied in , \u00a718.22 q-binomial Theorem [g is a q-analogue of g in uniform convergent q-Fourier\u2013Bessel series. Setting g is q-linear H\u00f6lder of order q-Fourier series Consider mentclass2pt{minimerefore, \u20134.3) en en\\docum"}
+{"text": "Triacylglycerol (TAG) from photosynthetic microalgae is a sustainable feedstock for biodiesel production. Physiological stress triggers microalgal TAG accumulation. However excessive physiological stress will impair the photosynthesis system seriously thus decreasing TAG productivity because of the low biomass production. Hence, it is critical to quantitatively and timely monitor the degree of the stress while the microalgal cells growing so that the optimal TAG productivity can be obtained.F/Fm\u2032, which is the chlorophyll fluorescence parameter that reflects the effective capability of PS II, was identified to be a critical factor to indicate the degree of stress of the cells. In addition, the concept of a nitrogen stress index has been defined to quantify the degree of stress. Based on this index and by monitoring \u0394F/Fm\u2032 and guiding the supply of nitrogen in culture medium to maintain a stable degree of stress, a stable and efficient semi-continuous process for TAG production has been established.The lack of an on-line monitored indicator has limited our ability to gain knowledge of cellular \u201chealth status\u201d information regarding high TAG productivity. Therefore, to monitor the degree of nitrogen stress of the cells, we investigated the correlation between the photosynthetic system II (PS II) quantum yield and the degree of stress based on the high relevancy between photosynthetic reduction and nitrogen stress-induced TAG accumulation in microalgal cells. \u0394F/Fm\u2032 indicator will have a significant impact on microalgal TAG production, especially for the outdoor controllable cultivation of microalgae on a large scale.The results indicate that the semi-continuous cultivation process with a controlled degree of stress by monitoring the \u0394 Microiodiesel . Physioliodiesel .2 fixation by degradation of ribulose-1,5-bisphosphate (RuBP) carboxylase/oxygenase (Rubisco) for the recycling of nitrogen. Limitation of CO2 fixation then decreases the consumption of ATP and NADPH and leads to an excess of NADPH and electrons [N-stress is the most effective means to trigger TAG accumulation , 6, 7. Wlectrons . The suflectrons , whereaslectrons \u201313. In alectrons , 15. ThePhotosynthesis is a coordinated physiological process that exclusively provides both energy and the material foundation for photoautotrophic microalgae . TherefoTetraselmis subcordiformis and Isochrysis zhangjiangensis, critical values of chlorophyll fluorescence existed where the maximum productivities of energy storage substances, such as carbohydrates, were obtained [Nannochloropsis oceanica IMET1, we established a reproducible TAG production process by monitoring photosynthetic activity to maintain a constant degree of N-stress under semi-continuous cultivation.Chlorophyll fluorescence analysis is a powerful tool for the study of photosynthesis in both plants and algae \u201319. It aobtained , 23. TheNannochloropsis oceanica IMET1 from the University of Maryland Biotechnology Institute was cultivated in seawater with modified F/2 medium at the ambient temperature of 25\u2009\u00b1\u20091\u00a0\u00b0C. In the present study, a 500-mL bubble column bioreactor (5\u00a0cm in diameter) was used with the air flow at 100\u00a0mL/min  filtered by a 0.22-\u03bcm membrane as described by Pan et al. [2\u00a0s cool white fluorescent lights were provided from one side of the bioreactor under a 14-h/10-h light/dark cycle. After pre-culture in the bioreactor with sufficient nutrient elements until the cells reached exponential growth phase, the cells were inoculated into new bioreactors at an initial biomass concentration of\u2009~\u20090.18\u00a0mg/mL .n et al. . AdditioF/Fm\u2032 was monitored. During the semi-continuous, \u0394F/Fm\u2032 was used as an indicator of the degree of N-stress. When \u0394F/Fm\u2032 reached the predetermined level, which was determined in batch cultivation as the monitoring point, harvest and dilution were conducted to start a new cycle of cultivation. During the dilution, the relative amount of fresh medium replenished to the system was defined as the \u201crenewal rate\u201d. For each cycle during the same semi-continuous cultivation process, the initial biomass concentration and supplementary N amount were the same.For the batch culture, the initial N amount was 15\u00a0mg/L in the medium, and no additional N was added into the medium until harvest. For the semi-continuous cultivation, the inoculum was the N-stressed cells from the batch. During cultivation, the fluorescence parameter \u03944HCO3 and were then dried at 60\u00a0\u00b0C to achieve a constant weight. The DW was the difference between the final weight and the weight of the empty tube as described by Zhu et al. [F/Fm\u2032 was measured using a chlorophyll fluorometer  by the method described by Yao et al. [Fm\u2032 and F\u2032 were obtained, and Fm\u2032 refers to the maximum fluorescence at the light-adapted state. The effective photosynthesis capability of PS II, \u0394F/Fm\u2032, was calculated according to Eq.\u00a0. The fatty acid composition was determined by gas chromatography after transesterification and according to Liu et al. [i and CiTAG\u2212 represent the DW and TAG content at the end of cycle i, and the symbols with the subscript of cycle 0 represent the corresponding data of the initial state of cycle i.The TAG content was calculated using the method developed by Wang and Shen and based on the concept of characteristic fatty acid, which provided a way to quantify TAGs in microalgae precisely by immediate transesterification from the wet biomass and required smaller samples than conventional methods , 28. Sheu et al. . TAG proF/Fm\u2032. As shown in Fig.\u00a0F/Fm\u2032, which reflects the effective photosynthesis capability of PS II, decreased consistently with changes in intracellular N from 0.56 to 0.42. As shown in Fig.\u00a0The N-stress indicator should be automatically and rapidly measured. It should be sensitive to N-stress, including the content of intracellular N and other parameters of physiology or biochemistry, such as the metabolite content, elemental content, photosynthesis activity, and respiration rate. Therefore, during cell growth and TAG accumulation under N-stress, the physiological characteristics and cellular biochemical properties were investigated including the DW, TAG content, intracellular N content and content of N in the medium and the chlorophyll fluorescence parameter \u0394F/Fm\u2032 is a promising indicator of N-stress in microalgae due to the high correlation between intracellular N and \u0394F/Fm\u2032. By investigating the growth of N. oceanica IMET1 under N-stress, it was found that during the period of day 3 to day 6 when the highest TAG productivity under N-stress was obtained, there was a high correlation between intracellular N and \u0394F/Fm\u2032. The correlation coefficient between intracellular N and \u0394F/Fm\u2032 reached 0.97 . In the other species of microalgae, a correlation also exists between intracellular N and \u0394F/Fm\u2032. For T. subcordiformis and I. zhangjiangensis, the correlations were y\u2009=\u20090.0741x\u2009+\u20090.151 (R2\u2009=\u20090.9779) and y\u2009=\u20090.168x\u2009+\u20090.1597 (R2\u2009=\u20090.9302), respectively (unpublished data). In short, it is not a special case where the \u0394F/Fm\u2032 and intracellular N synchronously change while cells are under the N-stress condition. The great advantages of \u0394F/Fm\u2032 are its characteristic of in situ and rapid measurement. In addition, the photosystem (whose activity \u0394F/Fm\u2032 reflects) plays the role of the hub in microalgal metabolism. Therefore, we propose monitoring the degree of N-stress using \u0394F/Fm\u2032 as an on-line indicator and then making the unsteady status of high TAG productivity reproducible to realize continuous TAG production.When comparing all of the parameters, intracellular N is a critical parameter to trigger the initiation of TAG accumulation. There were studies that made efforts on the determining the proper N-stress and emphasized the importance of accurate control of intracellular N when to optimize the lipid productivity , 31. HowF/Fm\u2032 stayed at a relatively high level, above 63\u00a0mg/mL\u00a0day and 0.45, which was 78% of the maximum value of 0.58, respectively, as shown in Fig.\u00a0Nmax is the maximum intracellular N content of the cells under N-replete conditions, Nmin refers to the minimum intracellular N for the cells to only keep alive subjected to severe N-stress for a long time, and Ni is the intracellular N of the cells at day i. Therefore, NSI ranges from 0 to 1 and a greater value of NSI indicates a higher degree of N-stress of the cells. Then, the NSIs of the day3-cell, day4-cell and day5-cell were 0.62, 0.72 and 0.81, respectively, and represent aggravated N-stress of the cells.F/Fm\u2032 was used as an N-stress indicator in situ. The cultivation of the day4-cell is used as an example to describe in detail the actual operation. The \u0394F/Fm\u2032 of the day4-cell was 0.503 at the inoculation, and this value was set as the critical point of monitoring. After supplying N into the medium and culturing for a few days, when the \u0394F/Fm\u2032 reached the same level as the preset critical point at inoculation, the cultivation was ended. Specifically, as shown in Fig.\u00a0F/Fm\u2032 reached 0.507, which was the same level as the initial \u0394F/Fm\u2032, that is, 0.503 for the day4-cell, the cultivation was ended. The operations of the day3-cell and day5-cell were the same as those of the day4-cell, and actual changes in \u0394F/Fm\u2032 can be seen in Fig.\u00a0F/Fm\u2032. In addition, from the results of the TAG productivity obtained by cultivation of the 3 types of N-stressed cells shown in Fig.\u00a0F/Fm\u2032 was higher and indicated a faster growth rate than the other two kinds of cells, the TAG accumulation was lower because the cells encountered a lower degree of N-stress, which ultimately resulted in less TAG productivity than the day4-cell. The result of the day3-cell indicated that the NSI of 0.62 was not large enough. Different from the day3-cell, a lower growth rate of day5-cells led to a lower TAG productivity. In contrast to the day3-cell, day5-cells encountered excessive N-stress with a large NSI of 0.81, which resulted in too much impairment of the cell growth. Therefore, according to the above results, the day4-cell experienced the proper degree of N-stress with an NSI of 0.72, and the corresponding \u0394F/Fm\u2032 of 0.503 could be considered the critical monitoring point.High TAG productivity is highly related to the degree of N-stress, and determination of the proper degree of N-stress of microalgal cells is required. The proper degree of N-stress could not only induce TAG accumulation but also maintain the cells at a relatively high photosynthesis capability for growth and thus ensure the balance of the contradiction between TAG accumulation and fast growth. From day 3 to day 5, as shown in Fig.\u00a0F/Fm\u2032 as an N-stress indicator, a semi-continuous cultivation of the proper N-stressed day4-cell was established by controlling the N supplying strategy. The initial N concentration in the medium and the renewal rate were optimized as the key operating parameters to improve the preliminary established semi-continuous process since the two operating parameters were reported to greatly affect the specific growth rate of the cells and productivity of the target products in a semi-continuous cultivation [F/Fm\u2032 was monitored daily to guide semi-continuous recycling, and the critical point of monitoring for \u0394F/Fm\u2032 was 0.503. When the \u0394F/Fm\u2032 reached the preset critical point of monitoring, a new cycle was restarted. The harvest and additional proportion of medium were the same and were operated according to the renewal rate in Table\u00a0The proper degree of N-stress has been disclosed for TAG stable production. Using \u0394tivation \u201334. The To keep the culture conditions consistent with that of the batch cultivation in \u201cF/Fm' recovered to the peak of 0.55 and 0.52 during each cycle in experiment b and c after N replenishment and recovered to 0.58 in experiment a. Obviously, resupplying the N amount has a large effect on the level of photosynthetic activity recovery. In experiments b and c, the cells did not recover to the health status as in experiment a, leading to the lower cell growth and lower TAG productivity.Experiments b and c were performed to investigate the effects of the initial N concentration in medium on TAG productivity. As shown in Fig.\u00a0Another critical operating factor was the renewal rate of the semi-continuous cultivation mode . In thisCompared to the healthy cells with sufficient nutrition, there was an obvious reduction in the photosynthesis activity of the proper N-stressed cells as shown in Fig.\u00a0F/Fm\u2032 is a rapid and in situ N-stress indicator and could precisely guide the control of the degree of N-stress during the cultivation of microalgae for efficient and stable TAG production.Taken together, the data indicate that \u0394F/Fm', was identified as a perfect online indicator for the degree of N-stress of the cells. Based on NSI, a novel semi-continuous cultivation strategy of precise N-stress control by the accurate monitoring of \u0394F/Fm' as an N-stress indicator was established for stable and efficient TAG production. The renewal rate and initial N concentration were optimized as 0.6 and 24\u00a0mg/mL, respectively. This new cultivation strategy provides significant guidance for outdoor microaglal cultivation in industrial applications and controlled indoor cultivation.It is vital to quantify the degree of N-stress when it is applied to obtain maximum TAG productivity during microalgal cultivation. The concept of the nitrogen stress index, NSI, was defined. The photosynthetic activity parameter of microalgae, \u0394"}
+{"text": "Scientific Reports 10.1038/s41598-018-37641-0, published online 06 February 2019Correction to: The original version of this Article contained an error in the title of the paper, where \u201ccatechinopyranocyanidins\u201d was incorrectly given as \u201ccatechiopyranocyanidins\u201d. This has now been corrected in the PDF and HTML versions of the Article, and in the accompanying Supplementary Information file."}
+{"text": "Nature Communications; 10.1038/s41467-018-05327-w; published online 06 August 2018Correction to: y-axis labels \u2018tDNA\u2019 and \u2018ctDNA\u2019 were inadvertently inverted. This has been corrected in the PDF and HTML versions of the Article.The original version of this Article contained an error in Fig.\u00a02, in which the left"}
+{"text": "Statistical Inference of Large-scale Gaussian Graphical Model) that includes four main approaches in statistical inference of high-dimensional GGM. Unlike the existing tools, SILGGM provides statistically efficient inference on both individual gene pair and whole-scale gene pairs. It has a novel and consistent false discovery rate (FDR) procedure in all four methodologies. Based on the user-friendly design, it provides outputs compatible with multiple platforms for interactive network visualization. Furthermore, comparisons in simulation illustrate that SILGGM can accelerate the existing MATLAB implementation to several orders of magnitudes and further improve the speed of the already very efficient R package FastGGM. Testing results from the simulated data confirm the validity of all the approaches in SILGGM even in a very large-scale setting with the number of variables or genes to a ten thousand level. We have also applied our package to a novel single-cell RNA-seq data set with pan T cells. The results show that the approaches in SILGGM significantly outperform the conventional ones in a biological sense. The package is freely available via CRAN at https://cran.r-project.org/package=SILGGM.Gene co-expression network analysis is extremely useful in interpreting a complex biological process. The recent droplet-based single-cell technology is able to generate much larger gene expression data routinely with thousands of samples and tens of thousands of genes. To analyze such a large-scale gene-gene network, remarkable progress has been made in rigorous statistical inference of high-dimensional Gaussian graphical model (GGM). These approaches provide a formal confidence interval or a p-value rather than only a single point estimator for conditional dependence of a gene pair and are more desirable for identifying reliable gene networks. To promote their widespread use, we herein introduce an extensive and efficient R package named SILGGM ( PLOS Computational Biology Software paper.This is a Gene co-expression network is an undirected graph, where each node represents a gene and each edge between two genes shows a significant co-expression relationship . It has Previous high-throughput sequencing technologies like microarray and bulk RNA-seq have generated many high-dimensional gene expression data sets with a huge number of genes, but these data sets usually have a small number of subjects or samples. Recently, the emergence of the droplet-based single-cell RNA-seq , 7 has mDue to the assumption of the intrinsically sparse structure of a gene network, two main streams of approaches have been developed in estimating conditional dependence of genes using high-dimensional GGM: (i.) the graphical Lasso, which is a penalized-likelihood approach for precision matrix of GGM \u201310 and  that includes B_NW_SL, D-S_NW_SL, D-S_GL and GFC_SL or GFC_L. SILGGM has significantly increased the efficiency of each approach using fast algorithms, the \u201cRcpp\u201d library [To enhance the influence of these cutting-edge statistical inference works in practical usage and address the computational challenge in high-dimensional settings even with large sample sizes, we develop a more comprehensive package called SILGGM \u2032 follows a multivariate normal distribution with mean \u03bc  and covariance matrix \u03a3. The conditional dependence between each pair of variables is reflected in a precision matrix \u03a9 = (\u03c9ij)p\u00d7p = \u03a3\u22121, the inverse of \u03a3. For instance, if Xi and Xj are conditionally dependent, then equivalently, the corresponding element in \u03a9 is \u03c9ij \u2260 0 [Xi as the ith gene. Therefore, the inference between gene i and j is equivalent to the inference of an individual \u03c9ij, and the global inference of whole-scale gene pairs is based on a multiple testing procedure with all \u03c9ij\u2019s.In GGM, a set of  \u03c9ij \u2260 0 . In the p (the number of genes) allowed to be far larger than n (the number of subjects). The SILGGM package has one main function SILGGM with various arguments and its workflow is described in We focus on the high-dimensional settings with n by p gene expression data matrix as an input. The gene names can be specified in each column by users. Without loss of generality, the data matrix is further centralized by subtracting its mean or standardized by subtracting the mean and adjusting the variance to one before the formal statistical inference, but the final results are returned in an original scale.The setup of the SILGGM function is very simple. It only takes an \u03c9ij, while the last one is proposed particularly for simultaneous inference of all \u03c9ij\u2019s. All of the four methods (see more details in O(p) or O(sp) runs of nodewise Lasso-type regressions are conducted among the other three methods. The second step is to obtain (p2 \u2212 p)/2 test statistics: (i.) the estimators The method argument in the function SILGGM supports four approaches in rigorous statistical inference: B_NW_SL, D-S_NW_SL, D-S_GL, GFC_SL or GFC_L. In the original four papers, the first three methods are developed for inference of each individual \u03c9ij\u2019s, so the implementations of the other three methods can also be extended to global inference under its FDR framework [\u03b1-level sequence with \u03b1 = 0.05,0.1 is pre-specified by the alpha argument in the function and it can be customized by users with different values.As it can be seen, GFC_SL or GFC_L essentially relies on asymptotically normal test statistics for testing on ramework  that hasi and j, SILGGM not only provides the estimator i and j is encoded in the th element of a p by p symmetric matrix with diagonal elements equal to 0. For global inference with a pre-specified \u03b1-level sequence, SILGGM further returns the estimated FDR sequence based on p by p adjacency matrices with each off-diagonal element value of 1 = conditionally dependent or 0 = conditionally independent). If the true structure of a gene network is available , SILGGM also includes the estimated power sequence with respect to the estimated FDR sequence. Users can input the true structure in a matrix format via the true_graph argument in the SILGGM function.Outputs are shown with the different type of inference. For individual inference of gene n = 258 asthmatic children [p = 1953 genes with the largest inter-sample variance  and obtain the corresponding network visualization shown in In addition to present the above outputs from both individual and global inference in a matrix format, the function SILGGM provides the cytoscape_format argument as an alternative to show them in a table format that can be saved as a .csv file by using the csv_save argument to a directory specified by the directory argument. The .csv file is compatible with multiple popular platforms for network visualization. In order to show the validity of this alternative, we have applied SILGGM to a public gene expression microarray data set on the lymphoblastoid cells of children , 30 and o asthma . The firComputational efficiency is a prominent advantage of SILGGM. The core algorithms in the package are developed with the \u201cRcpp\u201d library  which hiIn the first step, based on the same optimization in FastGGM , we pre-ested in ) are appested in  which isested in . To condested in  due to tested in . In addiested in  to boostO(p3) with na\u00efve calculation (see (7) and (10) in O(sp2), and s is usually much smaller than p in high-dimensional settings.In the second step, we facilitate inner product operations to derive each de-sparsified test statistic. To be more specific, we consider the sparsity of Lasso-type estimators from the first step and make inner product calculations only on the non-zero elements. For D-S_NW_SL or D-S_GL, to obtain In addition to the aforementioned optimizations, we optimize the inner product operations between the whole data matrix and regression coefficients by considering the sparsity of estimated coefficients when solving each scaled Lasso problem. The idea behind the optimization is same as the one used in the second step, and it reduces the redundant steps and enables B_NW_SL to perform even faster in SILGGM than in FastGGM.We illustrate the efficiency of SILGGM through simulation studies and a real data analysis. In simulation, we consider four popular graph structures for gene network studies: Band graph, Hub graph, Erd\u00f6s\u2013R\u00e9nyi (E-R) random graph and Scale-free random graph, as shown in http://math.sjtu.edu.cn/faculty/weidongl/Publication/code.rar in n = 100 and simulate three types of graph settings: Band, Hub and E-R  over 100 replications on a single CPU are recorded for GFC_L with FDR control at the 0.1 and the 0.2 levels using SILGGM and the MATLAB code, as shown in To the best of our knowledge, the online MATLAB code  times p, is around 4 or 5. The first column of Then, we evaluate the timing performance of B_NW_SL using SILGGM compared to the current package FastGGM. As shown in n = 800, p = 5000 and n = 800, p = 10000).In addition to the time evaluation, we validate the accuracy of estimation results from all the approaches for both individual and global inference in the very large-scale settings with relatively small sample sizes th gene pair (H0:\u03c9ij = 0 vs. H1:\u03c9ij \u2260 0) in terms of the estimation for an entire graph. The empirical Type I error  under a pre-specified level of 0.05 for p-values and the corresponding Type II error  are measured for Band graph  and the \u201czero partial correlation\u201d set  respectively. Since GFC_SL or GFC_L provides no confidence intervals, we involve the other three approaches here. According to the results from the three graph settings, the overall performance of the confidence intervals among B_NW_SL, D-S_NW_SL and D-S_GL are good in terms of the entire graph structure. But in terms of the confidence intervals for the non-zero partial correlations, B_NW_SL and D-S_NW_SL outperform D-S_GL. Moreover, the performance of B_NW_SL is more stable than that of D-S_NW_SL in the different settings , E-R grribed in ) and ScaH0:\u03c9ij = 0 vs. H1:\u03c9ij \u2260 0 with 1 \u2264 i < j \u2264 p simultaneously. Therefore, to make global inference of all gene pairs in a large graph, we always recommend controlling FDR to avoid the inflation of false positives. The testing results from the three graph settings indicate that the FDRs of all the methods are effectively controlled below the desired level for both p = 5000 and p = 10000. The corresponding power values  and the Matthews correlation coefficients (MCCs) also demonstrate comparably good performance of all the methods  used in individual inference. Unlike individual inference, global inference generally requires a multiple testing procedure for tests on all n = 3555 cells. After filtering out the unexpressed genes, we consider p = 2000 genes with the largest inter-sample variance  counts , we needp(m) \u221d m\u03bb\u2212 for some positive \u03bb. Here, m refers to the node degree and p(m) denotes the probability of the m-degree nodes. Many studies have indicated that biological networks are scale-free, and the node degrees possess a power-law distribution [n > p in this data set, the values of n and p share the same order such that MLE becomes unstable and increases bias of estimation. Thus, all the inferred network structures by SILGGM are biologically meaningful and much more reliable. Furthermore, we can see that the performance of the other three methods based on the nodewise Lasso-type regressions in SILGGM is even better than that of D-S_GL since the plot of D-S_GL shows some noise in the tail.Motivated by , we applribution \u201345. The https://cran.r-project.org/package=SILGGM. The details of package installation are described in The source code of the package and a complete reference manual including dependencies, usage of all package functions and associated examples are freely available via CRAN at The package SILGGM is computationally efficient compared to the MATLAB implementation of GFC_L and the R package FastGGM. Since R is a publicly free platform and has been more widely used in biological research compared to MATLAB which is a piece of commercially licensed software and has less accessibility to biologists, the R platform-based SILGGM will play a more important role in accelerating the biological gene network studies. SILGGM is also statistically efficient with both individual and global inference due to the theoretical justification of the four approaches and the validation of estimation accuracy in simulation studies. The analytical results from the single-cell data with Pan T cells further reflect the statistical efficiency of SILGGM since inferred gene networks are more reliable. Moreover, the comprehensiveness of SILGGM allows users to have more flexible choices of methods depending on the specific purpose of their study. Due to its computational feasibility, analytical reliability in results and methodological comprehensiveness, SILGGM can become a valuable and powerful tool to a wide range of biological researchers for high-dimensional or even whole genome-wide co-expression network analysis.n is small (e.g. n = 100) because the tuning selection in GFC_L is beneficial for FDR control. When n becomes larger (e.g. n = 800) but may be still relatively small to p, users can choose any of the four approaches due to their similar performance among the different settings Click here for additional data file.S2 Appendix(RAR)Click here for additional data file.S3 Appendix(PDF)Click here for additional data file.S1 File(PDF)Click here for additional data file.S2 File(PDF)Click here for additional data file.S3 File(PDF)Click here for additional data file.S1 Table(PDF)Click here for additional data file."}
+{"text": "A. In the classical case, this leads to a bibasic extension of Heine\u2019s formula, which was implicit in a paper of Andrews which he wrote in 1966. As special cases, we recover extensions of many of Ramanujan\u2019s q-Lauricella function, and show how to obtain very general transformation formulas of this type. The results obtained include transformations of an n-fold sum into an m-fold sum.We apply Heine\u2019s method\u2014the key idea Heine used in 1846 to derive his famous transformation formula for  Heine\u2019s method, so named by Andrews and Berndt , was whaented in , Ch. 1. q-rising factorials from Gasper and Rahman [q-rising factorial is defined as k is a positive integer,q is called the \u2018base.\u2019 The infinite q-rising factorial is defined, for q-rising factorials when k is an arbitrary complex number. The most fundamental of the q-summation theorems is the q-binomial theorem [q-Binomial theorem, and is as follows.h and t are complex numbers. This leads to a transformation formula that follows from a very general identity of Andrews [q-rising factorials to be defined, and w,\u00a0b) is replaced by .It is useful to recall Heine\u2019s method. We need the notation of d Rahman . The q-r.Heine\u2019s  proof ofentclass1pt{minimaq-binomial theorem, due to Milne [n is called the dimension of the sum. When classical. We use the notation A, namely,n and m are 1:n-dimensional sum into an m-dimensional sum. This is followed by some examples of multiple series extensions of Ramanujan\u2019s transformations in Sect.\u00a0The second variation of Heine\u2019s idea comes from using multiple series extensions of the to Milne , Milne ato Milne , Gustafsto Milne , Kajiharto Milne , and oneto Milne . The ser case of  below. Centclass1pt{minimaq-binomial theorem. Our intention is to illustrate the approach, not to provide a comprehensive list. There are six multiple q-binomial theorems of this kind that can be combined together to give 21 such results.In this section, we will give four multiple series extensions of , using dz are indeterminate, and are such that the terms in the sum are well defined. We require We begin by using a theorem of Milne and Lilly , Th. 4.7 and  and is vq-binomial theorems in the literature. The following are the product sides of q-binomial theorems due to Milne [q-binomial theorems. Unfortunately, the q-binomial theorem due to the author and Schlosser [We will not provide any further chlosser  is not ah and t are complex numbers, and we have the usual convergence conditions, namely, In this section, we find multiple series extensions of many of Ramanujan\u2019s  done in , Ch. 1. alent to , as we cIn the special cases we consider, many of the products appearing in the sum simplify. Our first set of examples is obtained as special cases of Theorem\u00a0 [q-binomial theorem. Using the q-analogue of Euler\u2019s transformation formula, we obtain the following transformation formula of double sums.In Heine\u2019s method, instead of the Aside from the usual convergence conditions  with base d,\u00a0e,\u00a0f,\u00a0w) with base The proof is a straightforward extension of the proof of . We use Note that when =e, then  reduces =e, then .There are many sions of . They folas. See , Th. 1.1 The symbols L,\u00a0P,\u00a0 and R are code for Left, Products, and Right, respectively. We will use two copies of this result. Let us represent the summands of the corresponding left- hand sides by The proof is similar to the proof to that of Theorem\u00a0k and j and The first copy of  is a \\doWe now see that the left-hand side can be written asq-Lauricella function. Andrews\u2019 formula was generalized to a multibasic formula by Agarwal, Jain, and Choi [We now present another variation, where Heine\u2019s method is iterated, to obtain a transformation formula that transforms a multiple sum to a single sum. This was first done by Andrews [and Choi , and indand Choi , which iq-Lauricella functions [We use the symbol for the dot productmentclass2pt{minimtions in  to whichp-fold sum and the right-hand side is a single sum. The identity has Note that the left-hand side of  is a p-fduces to .p times. The first step of the proof is as follows:q-binomial theorem asq-binomial theorems, such as . , , \\documeProperty H as follows. A q-binomial theorem of the form H ifp multi-sums corresponding to the left-hand side of  Let The proof is a straightforward iteration of Heine\u2019s method, and is left to the reader. Remark Recall the results of Sect.\u00a0H. So we can intermix q-binomial theorems with transformation formulas too.Theorem\u00a0q-binomial theorems appearing in the work of Milne and Lilly, Gustafson and Krattenthaler, and one implicit in the author\u2019s work with Schlosser.First we take We take  as our bP1) from , and \\doP2) from . Now Theq-binomial theorem (nq-binomial theorems to deal with a product of the formIn our second example of an extension of , we take theorem . We take case of  with basentclass1pt{minimaA. It is a continuation of our work [The objective of this paper is to study Heine\u2019s method as applied to series of type our work , which aour work , Ch.\u00a0 1.q-binomial theorems in [n-dimensional series to a multiple of an m-dimensional series. Early examples of such identities were given by Gessel and Krattenthaler [In Sect.\u00a0orems in , 23, 24.enthaler , Kajiharenthaler , and Kajenthaler .Previously, Gustafson and Krattenthaler , 13 gaveSection\u00a0d Berndt , Ch. 1. d Berndt  and Kratd Berndt  (who proentclass1pt{minimaq-Lauricella function given by Agarwal, Jain, and Choi [In Sect.\u00a0and Choi , and indand Choi . Previouand Choi , \u00a77 gaveq-binomial theorem of Macdonald [q-binomial theorems. The Property H follows from the homogeneity of the Macdonald polynomials. If we apply Heine\u2019s method to Macdonald\u2019s q-binomial theorem, we obtain bibasic Heine transformation formulas different in character from, but perhaps not as deep as, the Heine transformation formula given by Baker and Forrester [We have already noted that the master theorem applies to using transformation formulas as in Sect.\u00a0acdonald  (see Kanacdonald , Th. 3.5orrester , Th. 2.3"}
+{"text": "We approach the problem of combining top-ranking association statistics or P-values from a new perspective which leads to a remarkably simple and powerful method. Statistical methods, such as the rank truncated product (RTP), have been developed for combining top-ranking associations, and this general strategy proved to be useful in applications for detecting combined effects of multiple disease components. To increase power, these methods aggregate signals across top ranking single nucleotide polymorphisms (SNPs), while adjusting for their total number assessed in a study. Analytic expressions for combined top statistics or P-values tend to be unwieldy, which complicates interpretation and practical implementation and hinders further developments. Here, we propose the augmented rank truncation (ART) method that retains main characteristics of the RTP but is substantially simpler to implement. ART leads to an efficient form of the adaptive algorithm, an approach where the number of top ranking SNPs is varied to optimize power. We illustrate our methods by strengthening previously reported associations of \u03bc-opioid receptor variants with sensitivity to pain. L studies, potentially providing a higher level of assurance that the studied risk factor is associated with disease. Furthermore, if samples in those studies are taken from populations that are similar with respect to the effect size magnitude, the combined meta-analytic P-value will well approximate the one that would have been obtained by pooling together all raw data and performing a single test  mapping individual SNPs to genes, followed by combining their association P-values into gene-scores, and (2) grouping genes into pathways and combining gene-scores into pathway-scores.P-values can also be combined when the i,iP = 1, \u2026, L) are often based on the sum of iP\u2018s transformed by some function H. For example, H(iP)=\u201321n(iP), which are then added up to form a test statistics L degrees of freedom. When a portion of L distinct associations is expected to be spurious, it is advantageous to combine only some of the predictors using a truncated variation of combined P-value methods or emphasize the smallest P-values. For instance, I(iP\u2264 \u03b1), that is equal to zero if iP> \u03b1, and one if iP\u2264 \u03b1; 0 < \u03b1 \u2264 1 is a truncation threshold. The combined P-value, PTPM, is then given by the cumulative distribution function (CDF) of W is random. Similarly inspired methods include the \u201ctail strength measure\u201d Existing tools for combining P-values  . In RTP,P(i) is the ith smallest P-value, i = 1,\u2026,k. RTP leads to an appealing extension, where k can be chosen adaptively, to maximize statistical power  of possible values 1 \u2264 k \u2264 L. Adaptive extensions for TPM are not as straightforward because the threshold \u03b1 is a continuous variable, but one can resort to evaluating the distribution over a set of grid points  being a random variable: when P(k+1) happens to be relatively small, the k P-values have to squeeze into a relatively small interval from zero to that value. This induces positive dependency between random sets of k smallest P-values, similar to the clustering effect in random effects models. Although the linear correlation can be eliminated by scaling the largest P-value, P(k), the k values remain dependent, as illustrated in The RTP null distribution is considerably more complicated than that of TPM. Complexity of the RTP distribution is due to dependency between ordered P-values. When k is chosen beforehand and fixed) and for the adaptive variations of RTP and ART (aRTP and ART-A). Finally, we illustrate usefulness of the proposed methods by strengthening an overall, gene-based association via combining previously reported P-values between pain sensitivity and individual SNPs within the \u03bc-opioid receptor.Applications of combining independent P-values remain important in statistical research, and there is clear preference among practitioners for methods that are based on simple and transparent approaches, such as the Fisher or the inverse normal (Stouffer\u2019s) tests . Here, wk< L, as:Even when P-values are independent, previously proposed theoretical forms of the RTP distribution are cumbersome and result in expressions that involve repeated integration . For exak smallest P-values can be shuffled. This step does not change the value of the product, kW (or its logarithm), which is our statistic of interest, but implies that we can treat the joint k-variate distribution as governed by the same pair-wise dependence for every pair of variables. Moreover, variables of that shuffled distribution are identical marginally. The dependency is induced completely through randomness of P(k+1), and conditionally on its value, the {kW|p(k+1)} distribution is given by standard independence results. Then, PRTP is given by the marginal CDF of kW. Based on this conceptual model, we derived the following representation of RTP where a single integral is evaluated in a bounded interval , which allows one to evaluate the RTP distribution as a simple average of standard functions. Specifically, we derive a simple expression for the RTP distribution as the expectation of a function of a uniform (0 to 1) random variable:Theoretical forms of the RTP distribution  may retain order-specific terms. Here, we proceed to a simpler representation by noting that every random realization of k+1,L\u2212k) distribution, kG(\u00b7) is CDF of Gamma, and PRTP(k) is the combined RTP P-value. Notably, given the value of the product of k P-values, W = w, we can simultaneously evaluate PRTP(k+1):where Details and the derivation are given in k\u22121 smallest P-values, given a value of the beta-distributed k-th smallest P-value, leads to a simple statistic which (just as RTP) is a function of the product of the k-th smallest P-values. This statistic and its distribution are not an approximation to kW and the RTP distribution. However, similarly to RTP, the new statistic is designed to capture information contained in the first k smallest P-values. Motivation for our augmented RTP method (ART) follows from the intermediate results of the derivation of the RTP distribution. Note that the distribution of kW conditional on (k + 1) involves a product of k uniforms and a beta random variable. Moreover, the product and the beta variable are independent. On the one hand, we could have proceeded by dividing every P(1:k) value by the observed p(k+1) and employed the gamma CDF to P(k+1) magnitude. On the other hand, we can exploit the independence of the gamma-distributed sum and P(k+1) by transforming P(k+1) to a gamma random variable and adding the result to the sum. Specifically, to construct the new statistic, we propose the following transformation that involves the product k\u22121W and the variable (k)P. These transformations yield three independent variables, which are next added together and give a gamma-distributed random variable,The conditional independence of k,1),where k \u2013 1) \u00d7 E {\u2013 ln ((k)P)} = (k \u2013 1) (\u0393\u2032 (L + 1)/\u0393 (L + 1) \u2013 \u0393\u2032 (k)/\u0393 (k)),\u03bb = (kB(x) is the CDF of Beta distribution evaluated at x. The shape parameter \u03bb is chosen so that the two last terms in Eq. 4 (that are both transformations of (k)P) have the same expectation. The shape parameter here plays a role of a weight given to the last term. This is similar to the Lancaster method for combining P-values, where the gamma shape parameter  has been used to give differential weights to P-values  that ART has either the same or higher power than RTP. Furthermore, the combined P-value, ART, can be easily computed in R using its standard functions. A short example and an R code are given in Under the null hypothesis, as illustrated by Introduction, the number of k P-values to be combined by the RTP method (or ART) is fixed and needs to be pre-specified. The choice of k is somewhat arbitrary; so, a researcher may wish to evaluate ART at several values of k, consequently choosing k that corresponds to the smallest combined P-value. However, this additional step creates another layer of multiple comparisons, which needs to be accounted for. B\u00d7L matrix, with every row containing L P-values generated under the null distribution over B simulated experiments. As we discussed earlier in via decorrelation by orthogonal transformation approach, DOT. Let L correlated P-values,  originate from statistics that jointly follow a standard multivariate normal distribution, y \u223c MVN , under H0. For two-sided P-values, the elements of y are squared. Elements of the vector of squared variables, \u03a3, such that \u22121\u03a3 = Q\u039bQ, where Q is a square matrix, with ith column containing eigenvector qi of \u03a3, and \u039b is the diagonal matrix of eigenvalues \u03bb1, \u03bb2, \u2026, \u03bbL. Next, define an orthogonal matrix H = Q\u039b\u22121/2QT and ye = HTy. P-values are decorrelated as 1-\u03a6\u22121(ye). Then, the first k smallest decorrelated P-values can be used to calculate various combined statistics. The choice of this particular transformation is motivated by its \u201cinvariance to order\u201d property. Briefly, in the equicorrelation case, including the special case of \u03c1 = 0, i.e., independence, a permutation of y should yield the same (possibly permuted) values in the decorrelated vector, ye. Extensive evaluation of the decorrelation approach is presented by us elsewhere  and to the adaptive RTP [where k is varied and the distribution is evaluated by single-layer simulations as in et al. proposed a clever shortcut based on a rectangular matrix, in which each i-th row is a set of L P-values that corresponds to the i-th simulation. The shortcut avoids nested and slow simulations but has a downside of keeping quite large matrix in computer memory.We used simulation experiments to evaluate the type I error rate and power of the proposed methods relative to the previously studied RTP  \u2264 i\u03b1/L for at least one i. Equivalently, the overall (or the \u201ccombined\u201d) Simes P-value can be obtained as min {kp(i)/i}. The Simes test is a useful benchmark, because it is related to the combined P-value methods with truncation, as well as to multiple testing adjustment procedures. At the extreme, the RTP with k = 1 becomes equivalent to L. The Simes P-value is at least as small as Bonferroni-corrected P-value. In addition, there is a connection of the Simes test to the i, such that P(i) \u2264 i\u03b1/L, and rejects H0 for all P(j), j \u2264 i, to control the expectation of FDR.When various combined P-value methods are being compared, it is meaningful to gauge their performance against methods designed for multiple testing adjustments. This is especially relevant with methods that employ truncation due to their emphasis on small P-values. Therefore, we included the k or from 1 to L, if k = L. Both tables confirm that all methods maintain the correct Type I error rate at various \u03b1-levels.L statistics had the same underlying effect size (\u03bc = 0.5). From this table, it is evident that our ART has the highest power, closely followed by RTP. In general, the ART P-values tend to be similar to the P-values obtained by the RTP, and we show their similarity graphically in L tests and absence of true nulls. For the results in k (RTP and ART). Nonetheless, in practice, a good choice for k may not be immediately clear, so a small sacrifice in power may be preferable to an arbitrary and possibly poor choice of k. However, when L is large, it can be impractical or unreasonable to vary candidate truncation points all the way up to L. Therefore, the value of k in these tables is the upper bound for sets of candidate truncation points, and that explains the difference in powers. For example, for the combination k = 10, L = 200, the power of ART-A in k = 100, L = 200, the power is 0.37. Adaptive methods are considerably slower than methods where the value of k is fixed. A promising solution, which is currently under development, is removal of candidate truncation points for which the corresponding partial products are highly correlated.k = L, but for illustrative purposes, we also give power values for some choices where k < L. We emphasize that, in our tables, these chosen maximum k values do not have any specific meaning. In general, the maximum value of k for the adaptive methods can be varied up to L, unless L is either very large, or if there is a priori assumption that the real signals are rare. As discussed in k is usually lower than the actual number of real signals; however, the upper bound for k can be set to reflect a priori knowledge about potential maximum number of real signals.We note that power values in L hypotheses were true nulls (\u03bc = 0), while the remaining hypotheses were true signals (\u03bc = 0.5). The results follow the same pattern as in the previous tables, with ART having the highest power.Finally, k and L values. However, decorrelation-based methods become quite powerful, and their power is increasing with k and L. The steady power increase is due to the decorrelation effect on the combined noncentrality that involves the sum \u03bc. More details on the performance of the decorrelation approach are given by us elsewhere  with pain sensitivity. MOR gene, from which the 11\u00d711 LD correlation matrix can be computed. The ijP frequencies are given by the sum of frequencies of those 11-SNP haplotypes that contain both of the minor alleles for SNPs i and j. Similarly, ip allele frequency is the sum of haplotype frequencies that carry the minor allele of the SNP i. The LD correlations within the MOR region spanned by the 11 SNPs ranged from \u22120.82 to 0.99, with the average absolute value \u22480.55 and the median absolute value \u22480.66. Half of pairwise LD correlations were smaller than \u22120.23 or larger than 0.82. Our analysis . Similar to what we found via simulation experiments, where correlation is controlled by reshuffling the phenotype values while keeping the original LD structure intact, RTP and aRTP (without the decorrelation step) do not benefit from inclusion of additional SNPs. P-values in the ART column are very similar to those in the RTP column, which reassures our theoretical expectations. In contrast to previously proposed methods that control correlation by resampling , the results in columns marked by \u201cdecorr\u201d are substantially lower. In these columns, we used the proposed transformation to independence, which gives much stronger combined P-values. In all \u201cdecorr\u201d columns, k = 7 results in the smallest combined P-value, implying that the number of real effects (including proxy associations) is at least seven.In several popular variations of the gene-based approach , future k\u201d and its optimal value. Unfortunately, k cannot be interpreted as an estimate of the number of real signals, for the reason that the k value that yields the minimum P-value depends on both the numbers of real signals, as well as on their strength of association, both of which are unknown. This issue has been investigated in detail in \u03bc-opioid gene that have been shown to affect sensitivity to pain. We find strengthened evidence of overall association within the 11-SNP block. In this application, the LD correlation matrix was reconstructed from the haplotype frequencies, which might be slightly different from the correlation of  values between pairs of SNPs  has been designed with this objective in mind. The RTP and related approaches had been shown to be valuable tools in analysis of genetic associations with disease. In this article, we derive a mathematically simple form of the RTP distribution that leads a to new method, ART and its adaptive version, ART-A, which searches through a number of candidate values of truncation points and finds an optimal number in terms of combined P-value. Two important questions are the meaning of \u201c of SNPs . Furtherhttps://github.com/dmitri-zaykin/Total_Decor.The URL for software referenced in this article is available at: The datasets generated for this study are available on request to the corresponding author.DZ and OV conceived the study, interpreted the results, and wrote the manuscript. FH performed extensive simulations. All authors read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "A large number of topological materials with a CsCl-type structure in crystallographic databases are explored and their crystal and electronic structures are studied. i.e. simple in structure, ease of synthesis and good stability at room temperature, thus are an excellent choice for designing functional materials. Using high-throughput first-principles calculations, a large number of topological semimetals/metals (TMs) were designed from CsCl-type materials found in crystallographic databases and their crystal and electronic structures have been studied. The CsCl-type TMs in this work show rich topological character, ranging from triple nodal points, type-I nodal lines and critical-type nodal lines, to hybrid nodal lines. The TMs identified show clean topological band structures near the Fermi level, which are suitable for experimental investigations and future applications. This work provides a rich data set of TMs with a CsCl-type structure.CsCl-type materials have many outstanding characteristics,  Such enthusiasm was initially generated by the discovery of topological insulators  , CsCl-type materials have a simple crystal structure that possesses only two atomic positions, known as 1a  and 1b  Wyckoff sites. CsCl-type materials are quite easy to synthesize, and most of them can be directly prepared from melting without any further chemical treatment , which clearly shows a band-crossing point at the M\u2013R path near the Fermi level (at E \u2212 EF = 0.08\u2005eV). Excluding spin, this band-crossing point has a triple degeneracy formed by one non-degenerate band and one doubly degenerate band. It should be noted that, with the exception of the bands which form the triple nodal point, there exists no other extraneous band nearby. Such a clean band structure generally favors experimental detection of triple nodal points in YIr. One of the representative signatures of triple-nodal-point TMs is the existence of Fermi-arc surface states . We can clearly observe the Fermi-arc states originating from the triple nodal points. It is worth noting that, since the triple nodal points are nearly situated in the middle of the M\u2013R path, the Fermi arc in YIr spans a large scale of momenta. Evidence of Fermi-arc states in YIr can be readily detected by experiment.YIr is a typical triple-nodal-point TM; its electronic band structure is shown in Fig. 53.3.a), the band crossing forms a one-dimensional nodal line. On the nodal line, each point exhibits linear band crossing. According to the slope of band dispersion, band crossing can be termed as three types, namely type-I, critical-type and type-II, as shown in Fig. 6b). For type-I, the bands have conventional dispersion, where the electron-like and hole-like states are completely separated by the crossing point. For type-II, the conical spectrum is tipped over. As a result, the electron-like and hole-like states coexist at each energy level. For critical type, which is formed by a flat band and a dispersive band . At the \u0393\u2013M, M\u2013X and R\u2013M paths, there exists type-I band-crossing points, as indicated by the arrows in Fig. 7a). Because of the protection of the inversion symmetry (P) and the time reversal symmetry (T) in the CaTe system, these crossing points in fact reside on nodal lines centering on the M point. By performing more detailed computations, we find the nodal line is situated in the kz = \u03c0 plane, under additional protection of the mirror symmetry (Mz). Considering the cubic symmetry of the CaTe lattice, the system possesses in total three equivalent nodal lines crossing each other, as shown in Fig. 7b). CaTe is an excellent type-I nodal-line TM because of the following: (1) it has a clean nodal-line band structure; (2) the nodal lines are quite close to the Fermi level; and (3) the crossing bands have a very large linear energy range (\u223c2\u2005eV). With the SOC effect, the nodal line is gapped beside a pair of Dirac points leaving at the R\u2013M path (protected by the C4 rotation symmetry), as shown in Figs. 7c) and 7d). In fact, Du et al.  is shown in Fig. 7 al. 2017 reporteda), without the SOC effect, type-I band-crossing points occur at the \u0393\u2013X, X\u2013M and R\u2013X paths. Under the same protection mechanism with CaTe, these band-crossing points also belong to three crossing nodal lines. However, unlike CaTe, these nodal lines center on the X point instead of the M point, as shown in Fig. 8b). With the SOC effect, these nodal lines are fully gapped to a sizeable gap (SOC-induced gap) along all the high-symmetry paths involving the X point, as shown in Fig.\u00a08c).TiOs is another type-I nodal-line TM. As shown in Fig. 8a). It can be observed there are two band crossing points at the R\u2013X and X\u2013M paths. Different from CaTe and TiOs, the band-crossing points show a critical-type band-crossing feature, namely, one of the crossing bands is almost flat in CaPd. This band crossing produces a nodal line centering on the X point in the kz = \u03c0 plane. The three-dimensional energy dispersion of the two crossing bands is plotted in Fig. 9b). We can observe from the critical-type nodal-line signature that the flat band is nearly non-dispersive near the nodal line at every k-path in the kz = \u03c0 plane. Such a critical-type nodal line was first proposed by Liu, Jin et al. . For each k-path  from the M point in the plane, we can always obtain a type-II band crossing, as shown in Fig. 11b). However, we noticed that the slopes of the two crossing bands between M\u2013C and M\u2013D paths have opposite sign. Thus we select another four k-paths  between M\u2013C and M\u2013D to observe the evolution of the slope. The band structures along these paths are shown in Fig. 11d). It is evident that, the band crossing along these k-paths exhibits a type-II\u2013type-I\u2013type-II transition. Therefore, the nodal line in Fig. 11a) is a hybrid nodal line. In addition, we need to clarify that compared with common hybrid nodal lines, including Ca2As  and 12b), respectively. We can observe clear surface bands on each k-path from the point.We performed a careful investigation of the band structure around the type-II crossing point and found it belongs to a nodal line centering on the 2As . It manifests two band-crossing points near the Fermi level, which are denoted as point A and point B [see Fig. 13a)]. The two nodal points have different degeneracy without counting spin: point A is doubly degenerate and point B is triply degenerate. By performing more detailed computations, we find point A resides on a hybrid nodal line centering on the M point, which is similar with that in YCd. Point B is a triple nodal point at the R\u2013M path and is similar to that in YIr. As a result, a hybrid nodal line and a pair of triple nodal points coexist in YMg, as depicted in Fig. 13b). Benefiting from the clean band structure near the nodal line and the triple nodal point, topological surface states for the nodal line and the triple nodal point can be clearly identified, as shown in Figs. 13c) and 13d), respectively.Several CsCl-type materials possess multiple types of band crossing. YMg is one of these materials The band structure of YMg is shown in Fig. 134.E \u2212 EF| < 0.5\u2005eV). Most of the TMs identified show a clean topological band structure where there are no interfering bands around the band crossing. Moreover, these CsCl-type materials can be easily synthesized and are stable at room temperature, which greatly favors the experimental investigation of their topological properties.By using high-throughput computational screening based on first-principles, we have identified 61\u2005TMs in existing CsCl-type materials. The identified TMs show rich topological character, including triple nodal point, type-I nodal line, critical-type nodal line and hybrid nodal line. In their band structures, the band crossing occurs near the Fermi level (|"}
+{"text": "Callicebus nigrifrons). This species uses two alarm calls, the A-call and the B-call, and arranges them into diverse sequences. The composition of those sequences differs depending on the type and location of the predator  a. A raptor in a non-ground position (flying or perched in the canopy) elicits a sequence of A-calls, (hereafter A+)b. A raptor on the ground elicits a sequence of A-calls followed by B-calls (A+B+)c. A cat in the canopy elicits a sequence a single A-call followed by B-calls (AB+)d. A cat on the ground /the presence of a terrestrial animal/ a monkey descending near the ground elicits a sequence of B-calls only (B+).Schlenker et al.  proposed(2) a. A+ is given to a serious non-ground threatb. a raptor on the ground attacks by flying, hence it is treated as a non-ground threat (A+) that stops being serious at some point because it is not in a hunting position (hence B+)c. a cat in the canopy is a serious non-ground threat (hence A). However, the cat's hunting strategy relies on surprise, and spotting a felid may deter it from attacking  a. A+ is given to a serious threatb. A raptor on the ground is still a dangerous threat (A+) but stops being serious at some point for it is not in a hunting position (hence B+)c. a cat in the canopy is a serious threat (A) that stops being serious once spotted (B+)d. B are used in non-serious alerts.and the location of the threat (\u201cnon-ground\u201d) while we argue that A-calls only refer to the level of alarm. Our analysis is therefore more parsimonious, and in line with the animal communication literature that described several animal communication systems as urgency-based (e.g., Rauber and Manser, In Schlenker et al. , A-callsWhen hearing A-calls, titi monkeys mainly look upwards (C\u00e4sar et al., We reckon that decisive field experiments are now necessary to verify the meaning of A-calls. One could, for instance, present titi monkeys that are on the ground with a cat model. According to Schlenker et al. , this woBeyond reflecting on the titi monkeys alarm system, our own analysis proves that the approach introduced by Schlenker et al. ,b and enSC: conception and first draft; MB: further redaction and revision of the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest."}
+{"text": "Nature Communications 10.1038/s41467-019-10742-8, published online 28 June 2019.Correction to: The original version of this Article contained an error in Fig.\u00a06e, in which the labels \u2018IAA\u2019 and \u2018Phle\u2019 in the bottom right where inadvertently omitted. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "The structure of L-cysteine adsorption under acidic conditions can be further verified by the addition of an L-cysteine molecule through light-induced coupling reaction to form cystine. Finally, in-situ two-dimensional Raman scattering spectroscopy confirmed the feasibility and uniformity of the coupling reaction.Under a controlled adsorption environment, L-cysteine molecules can be chemically adsorbed to the dendritic silver (Ag-D) surface by electrochemical methods with different functional groups. It is verified by surface-enhanced Raman spectroscopy that under alkaline conditions (pH\u2009=\u200913.50), the two functional groups of thiol and acid are simultaneously adsorbed on the surface of Ag-D, while NH For example, abnormal concentrations of cysteine in the blood are important indicators of skin damage and Alzheimer\u2019s disease; the thiol groups of two L-cysteine molecules can form a disulfide-bonded Cys\u2013Cys via oxidation3. This dimer is called cystine. Its importance lies in (1) its role of stabilizing the spatial structure of the peptide chain, (2) the fact that more there are disulfide bonds, the more stably the protein adapts to the outside, (3) the stable tertiary structure4. It is commonly present in keratin and collagen in the hair and skin of the human body, providing structural support or retention of toughness, as well as insulin or oxytocin that regulates physiological functions. In addition, L-cysteine molecules can spontaneously self-assemble with metal surfaces through thiol groups, carboxyl groups, or amine groups, modifying metal properties or increasing the possibility of practical application10. The modified metal surface can be an important technical application in chemical sensing or catalysis14. For example, proteins can be more easily and stably adsorbed on the surface to facilitate the provision of a substrate for a nano-process involving biological substances16. This may help further understand the molecular characteristics of the L-cysteine monolayer and appropriately control the adsorption conditions of the protein; it may even be used to capture and detect heavy metals18.L-cysteine is a natural amino acid with a thiol side chain that plays a key role in the organism19. The selection of the substrate, the molecular environment, the adsorption time, and other conditions are also important factors affecting adsorption and thus the more single and stable adsorption of L-cysteine on the metal. There are many studies on the surface-enhancement Raman scattering (SERS) spectra and theoretical calculations of the adsorption behavior or structure of L-cysteine on the surface of silver nanostructures21. Because of the small Raman scattering cross section of Cysteine molecule and low molecular symmetry, however, the SERS signal of this type of biological small molecule is usually very weak22. Only weak enhancement effect occurs: this effect is due to the Herzberg\u2013Teller mechanism (Albrecht\u2019s term B), an enhancement that allows for enhanced non-complete symmetry modes25. Therefore, high concentrations of target molecules are usually required to generate detectable signals21, thus constituting a technical obstacle in the practical application of SERS to biomolecules.Many factors influence the adsorption morphology of L-cysteine on the metal surface, such as temperature, applied potential control, and environmental pH26. Generally, chemisorbed molecules show an effect more pronounced than that of physically adsorbed molecules27. In other words, chemisorbed molecules show the most significant enhancement effects, namely, the highest intensity electromagnetic mechanism (EM) and chemical mechanism (CM) effects28. The chemical amplification is affected by the degree of overlap and probability of the bond electron domain between the target molecule and the SERS substrate. However, in SERS measurements, the target molecule can contain a variety of functional groups that can dissociate and subsequently interact with the active substrate. Cysteine molecules contain three different functional groups of amine groups, carboxyl groups and thiol groups30. Their properties and electrokinetic behavior are largely dependent on the solution pH31. Thus, the formation of anionic, zwitterionic, or cationic species is suitable for studying the competitive interaction of functional groups with metal surfaces32. In addition, cysteine can form a chemical bond on the metal surface through lone pairs on the functional group. This promotes chemical enhancement through the charge-transfer mechanism, enhancing the Raman signal33. However, the cysteine molecule has a small scattering cross section and is not easy to measure, and there are three functional groups that can form a bond with the substrate atom. If the adsorption between the molecule and the substrate is not effectively controlled, the contribution of the chemical amplification effect to Raman scattering makes the signal complex and difficult to judge. In many studies, the adsorption mechanism for this molecular structure is still blurred in SERS analysis. Therefore, this study will examine in detail the adsorption behavior of this molecule on the surface of dendritic silver (Ag-D) on a SERS-active substrate. The cysteine ion state is adjusted by the pH of the solution, and its structure adsorbed on the surface is optimized by a step function. By control of cysteine molecular adsorption behavior, cystine was formed on the surface of SERS substrate by in situ SERS measurement and induced coupling reaction of cysteine molecules.On the surface of the SERS-active substrate, both the physically adsorbed and chemisorbed molecules exhibit an enhanced Raman signal due to the effect of the additive effect34. The dendritic Ag surface showed high Raman enhancement, enabling the detection of analytes from dilute solution by SERS. 4-Nitrothiophenol was used as the probe molecule to examine the analyte-concentrating ability and SERS activity of Ag-D. Quantitative SERS detection using the Ag-D has detection limits in the nanomolar (5\u2009nM) concentration range35. It is a very good substrate for SERS. However, surface silver atoms are reactive and easily oxidized, and preservation and SERS measurement conditions require precise control. In this study, we used L-cysteine as the target molecule, and the Ag-D electrode was a surface-enhanced Raman substrate; that is, the reactivity of the surface of the SERS substrate to the target molecule was investigated. In aqueous solution, the functional groups of L-cysteine ionize with different net charges as the pH changes  and material characterization are described in SI (Supporting Information). Ag-D is characterized by surface plasmon resonance (SPR), easy preparation, and surface modification. As shown in the Scanning electron microscope (SEM) image of Ag-D in Fig.\u00a0ges Fig.\u00a0, with pK\u22121 can be observed. They are for \u03bd(Ag\u2013S), \u03bd(C\u2013S), and \u03bd(COO\u2212) respectively, as shown in Table\u00a038. It can be seen that L-cysteine directly bonded to the silver surface by S\u2212, and that C\u2013S bond has a clear signal enhancement and a relatively low wavenumber compared with the L-cysteine solid powder. It is speculated that in this environment, the sulfur generates a strong interaction  between the negative charge of the deprotonation of thiol group and positive side of the silver surface, and the increase in the COO\u2212 signal intensity indicates that the COO\u2212 and the silver surface have a strong interaction. It can be seen that this part can also be verified by the \u03bd(Ag\u2013O) shoulder at 247\u2009cm\u22121. From this result, it is inferred that the adsorption behavior of L-cysteine is that COO\u2212 and S\u2212 adsorb on the surface of Ag-D, while NH2 is far from the surface, as shown in Fig.\u00a0\u22121, and its vibration corresponds to \u03bd(Ag\u2013O), indicating that COO\u2212 forms a bond with the silver surface. The characteristic peak is \u03bd(C\u2013S) at 674\u2009cm\u22121 shifts to 620\u2009cm\u22121. As the pH value is lower, S gradually changes to the form of SH. No bond formed at this time, but it was still close to the surface of the Ag-D, so that the increase in this signal was observable. Therefore, it is inferred that the adsorption behavior is such that COO\u2212 and SH are oriented toward the Ag-D surface, and that NH3+ is relatively far from the surface, as shown in Fig.\u00a0\u22121 and \u03bd(COO\u2212) at 1525\u2009cm\u22121 increased, indicating that COO\u2212 and the dendritic silver surface bonded. In addition, there is a tendency for the shoulder peak at 1586\u2009cm\u22121 to appear next to 1525\u2009cm\u22121. It is presumed that the signal is enhanced with the vibration \u03bd(NH3+) corresponding to 1127\u2009cm\u22121, indicating that NH3+ is also close to the surface of Ag-D. Finally, it was observed that there was no characteristic peak of \u03bd(C\u2013S) between 600 and 750\u2009cm\u22121, indicating that SH was far from the surface. Therefore, this adsorption behavior suggests that both NH3+ and COO\u2212 are oriented toward the Ag-D surface, and that SH is far from the surface, as shown in Fig.\u00a0\u22121 and for \u03bd(C\u2013N) at 950\u20131050\u2009cm\u22121. When the pH is 9.12, there are two structures, as shown in Fig.\u00a0\u22121 gradually shifts to 620\u2009cm\u22121. At this time, the torsion angle of L-cysteine \u03c71 (N\u2013C\u03b1\u2013C\u03b2\u2013S) is changed from trans to gauche. However, the \u03bd(C\u2013N) characteristic peak at 1024\u2009cm\u22121 is also gradually shifted to low frequency to 973\u2009cm\u22121. This phenomenon is presumed to be due to changes in adsorption behavior and structure, which in turn causes changes in the electron density of C\u2013S or C\u2013N and causes the change in Raman scattering signals.Figure\u00a0In different acid\u2013base environments, cysteine forms a chemical bond with the silver atoms on the surface of the dendritic silver SERS-active substrate. In addition to the electromagnetic field enhancement considering the SPR effect of dendritic silver, there is a clear chemical contribution. In addition, L-cysteine can be selectively adsorbed onto the surface of the Ag-D electrode by controlling the pH and potential. Thus, L-cysteine can be further used as a finishing layer for developing subsequent, broader applications by reaction with different exposed functional groups with additional added compounds.\u22121 is stronger than that of \u03bd(C\u2013N) 972\u2009cm\u22121; only at 680\u2009cm\u22121, is the \u03bd(C\u2013N) signal intensity consistent with the result for pH\u2009=\u200913.50 in Fig.\u00a0\u22121 was gradually stronger than that of \u03bd(C\u2013N) at 1042\u2009cm\u22121. This means that under the same illumination intensity, prolonged exposure causes L-cysteine to slowly undergo partial structure reorganization. When the laser power is increased to 80% (15.97\u2009mW), it is clear that after 10\u2009seconds of exposure, not only was the characteristic peak of 972\u2009cm\u22121 significantly enhanced, but also the \u03bd(C\u2013S) of 680\u2009cm\u22121 had a trend of signal enhancement. When the exposure time reached 30\u2009seconds, the intensity of the two characteristic peaks became stronger. Increasing the light intensity can make L-cysteine result in faster structure variation, further changing the electron distribution of C\u2013S and C\u2013N and resulting in this growth and decline. The SERS spectrum with pH has been judged to have an adsorption behavior at pH of 13.50, as shown as structure A. In the literature39, the NH2, COO\u2212 and S\u2212 groups in the three structures of L-cysteine are close to the silver surface, and the torsion angle of \u03c71(N\u2013C\u03b1\u2013C\u03b2\u2013S) is the most stable state when it is structure B. Therefore, the inference is due to the fact that L-cysteine itself has a rotating dihedral angle. When the laser source supplied additional energy to L-cysteine, driving the original structure A, it was easier to change to a state structure B, which is adsorbed on the Ag-D surface. On the other hand, L-cysteine modified with pH\u2009=\u20095.22 was further exposed to 60% (12.18\u2009mW) of the laser power, as shown in Fig.\u00a0The effects of laser intensity and exposure time on the adsorption structure of L-cysteine were further investigated Fig.\u00a0. The SERIt has been confirmed that the adsorption configuration of L-cysteine on the surface of the Ag-D electrode can be successfully controlled by the solution pH environment and the adsorption\u2013desorption potential. Next, the functional groups of the chemisorbed modified layer will be further utilized to form a dimer with a laser-light-induced dimerization reaction with an added L-cysteine molecule. Upon oxidation of the two L-cysteine monomers, a cystine with a disulfide bond is formed. From the experimental results Fig.\u00a0 it is kn\u22121 in the SERS spectrum, and no dimerization occurred at this time. The addition of a drop of 0.01 M L-cysteine aqueous solution onto the surface of the substrate will wet the surface and change the original chemical environment, so that the original signal disappears. When the reaction time was 6\u2009seconds, it was observed that \u03bd(S\u2013S) gradually appeared, indicating that the thiol groups of the two L-cysteine monomers began to dimerize to form cystine37. After 150\u2009seconds of continuous reaction, the intensity of the \u03bd(S\u2013S) signal peak had reached near saturation, and the relatively weak characteristic peaks of other signals were obvious; 602, 664, 1330, and 1401\u2009cm\u22121 correspond to vibrations of \u03bd(C\u2013S), \u03bd(C\u2013S), \u03b4(NC\u2013H), and \u03bd(COO\u2212), respectively.The excitation wavelength was 532\u2009nm, the objective lens was 50 times, and the integral time of each spectrum was 3\u2009seconds/time for real-time reaction measurement. Figure\u00a0\u22121 gradually appeared, and the other signal peaks increased with time. When the reaction reaches 90\u2009seconds, the signal peak intensity tends to be saturated, indicating that the cystine almost completely formed at this time. Comparing the reaction times for pH\u2009=\u20091.67 and 5.85, we found that the reaction time of the latter was longer than that of the former. It is speculated that at lower pH values, the presence of L-cysteine is relatively simple. As shown in Fig.\u00a0Figure\u00a0\u22121 still does not appear. This means that under these conditions, cystine cannot be formed by dimerization reaction. However, we observed a slight signal peak; we presume that unreacted L-cysteine monomer molecules randomly located on the surface of the L-cysteine-modified Ag-D substrate. From the experimental results of the pH control, it is known that in this pH environment, the sulfur end of L-cysteine bond with the silver surface, and that there is no exposed thiol group; thus, cystine does not form.Finally, Fig.\u00a0\u22121 corresponding to the \u03bd(COO\u2212) vibration of L-cysteine  was mapped by using an optical microscopy image. The SERS spectra of this range were scanned to match the results of L-cysteine modification on Ag-D at pH\u2009=\u20091.67 Fig.\u00a0. Accordiine Fig.\u00a0, the intsee Fig.\u00a0. After tAfter a series of SEM, XRD, and XPS characterization, it was proved that the high-density Ag-D electrode can be prepared by electrochemical deposition method. It is suitable for surface-enhanced Raman substrate, and it can successfully utilize the electrochemical method of adsorption of L-cysteine on it.\u2212 and S\u2212 with the silver surface, and NH2 movement away from the surface ; or with NH3+ and COO\u2212 reacts on the silver surface, while the SH moves away from the surface (acid). The last one is when NH3+, COO\u2212, and SH are all close to the silver surface. Therefore, it is possible to simultaneously adjust the environmental pH value and to control the adsorption and desorption potential, so that L-cysteine has different adsorption structures. However, in the SERS spectrum that changes the laser power and illumination time, L-cysteine is converted from the structure A (trans structure) to the more stable structure B (gauche) because of the applied energy (pH\u2009=\u200913.40).The structure of the adsorbed molecule L-cysteine can be optimized by adjusting the adsorption and desorption of the target molecule on the Ag-D surface multiple times by electrochemical potential. In the SERS spectrum of the effect of pH on the adsorption of L-cysteine, three different adsorption behaviors can be obtained by adjusting the pH. This is the action of COOFinally, the three adsorption states obtained under the control of pH were respectively subjected to oxidation reaction by light-induced L-cysteine. It was confirmed that the pH value at the most acidic and isoelectric point conditions, allows two L-cysteines to undergo oxidation reaction to form a disulfide because of the non-bonded thiol group. However, as the pH is higher, the reaction rate is slower and less likely to proceed. Two-dimensional Raman scattering spectroscopy confirmed the feasibility and uniformity of the coupling reaction. The modified cysteine on the dendritic silver electrode has the possibility of further react in the measurement range. It can be seen that in this study, we can effectively control the adsorption behavior of L-cysteine and that we can used it as a modification to improve the surface selectivity and to conduct more chemical reactions.35. The glassy carbon electrode (12\u2009mm \u00d7 5\u2009mm \u00d7 1\u2009mm) was polished with of 0.3 \u03bcm and 0.05 \u03bcm alumina powder, and then ultrasonically shaken with ethanol and deionized water for 15\u2009minutes. Finally, the glassy carbon electrode was rinsed with deionized water. The dendritic silver was directly deposited on the glassy carbon electrode and was easily peeled off. Therefore, before preparing the dendritic silver, nanogold was deposited on the surface of the glassy carbon electrode for 500\u2009seconds, and then dendritic silver was deposited thereon. About 30.0\u2009mL of 1.0\u2009mM tetrachloroauric acid, 0.10\u2009mM cysteine, and 0.50\u2009M aqueous sulfuric acid solution was prepared. A three-electrode electrochemical system (CHI6111) was used. The reference electrode was saturated calomel electrode (SCE), the auxiliary electrode was platinum wire, and the working electrode was glassy carbon. We used the step function for gold electrodeposition for 500\u2009seconds. The parameter settings were 0 to \u22120.8\u2009V potential range, 0.1\u2009s step time, and 5000 step segments. Next, dendritic silver deposition was performed. The solution was changed to 1.0\u2009mM silver sulfate, 0.10\u2009mM cysteine, and 0.50\u2009M aqueous sulfuric acid solution, and we used about 30.0\u2009mL. Three electrodes were reference electrodes: silver wire, auxiliary electrode (platinum wire), and working electrode (gold-modified glassy carbon electrode). We used the step function for silver electrodeposition for 1000\u2009seconds. Parameter settings were \u22120.2 to \u22121.2\u2009V potential range, 0.1\u2009s step time, and 10000 step segment. The deposited dendritic silver electrode was taken out, washed with deionized water, and dried with nitrogen. The dendritic silver electrode should be washed with 0.2\u2009M Na2S2O3 for 10\u2009seconds to remove the surface Ag2SO4 residue to obtain a Raman substrate with no background interference signal. The dendritic silver obtained was identified by SEM, XRD, and XPS.Ag-Ds were prepared through a modification of our previous report3 at approximately 30\u2009mL. We set up a three-electrode system: the reference electrode was silver wire, the auxiliary electrode was platinum wire, and the working electrode was dendritic silver electrode. We used a step function to adsorb L-cysteine for 1500\u2009seconds. Parameter settings were potential range of \u22120.2 to \u22121.2\u2009V, step time of 0.1\u2009s, and step segment of 15000. The L-cysteine-modified dendritic silver electrode was taken out, rinsed, dried with N2 gas, and then measured. Samples were irradiated with a laser illumination of 532 (25\u2009mW), focused on a sample of 1 \u03bcm diameter with a 50X objective lens , MRI532S, Protrustech Co., Ltd, Taiwan.First we prepared a 100 \u03bcM L-cysteine solution and adjusted the pH to be measured with KOH and HNO\u22121. The objective lens magnification was 50 times. The integration time was as indicated in the figure, and the instantaneous reaction measurement was performed. A drop of 0.01 M L-cysteine aqueous solution was placed onto the surface of the L-cysteine-modified dendritic silver obtained under the conditions of pH\u2009=\u20091.67, 5.85, 13.40. The coupling reaction was induced by a 532\u2009nm light source while the change in the SERS spectrum was monitored during the reaction. The source intensity was 9.42\u2009mW at the sample position.All Raman scattering spectra were obtained at 532\u2009nm excitation wavelength was corrected by the signal peak of polystyrene at 1001.4\u2009cmSupplementary Information"}
+{"text": "The charge-transfer electronic states appearing at the donor-acceptor interfaces in organic solar cells mediate exciton dissociation, charge generation, and charge recombination. To date, the characterization of their nature has been carried out on the basis of models that only involve the charge-transfer state and the ground state. Here, we demonstrate that it is essential to go beyond such a two-state model and to consider explicitly as well the electronic and vibrational couplings with the local absorbing state on the donor and/or acceptor. We have thus developed a three-state vibronic model that allows us: to provide a reliable description of the optical absorption features related to the charge-transfer states; to underline the erroneous interpretations stemming from the application of the semi-classical two-state model; and to rationalize how the hybridization between the local-excitation state and charge-transfer state can lead to lower non-radiative voltage losses and higher power conversion efficiencies. i.e., the local absorbing state on the donor and/or acceptor, needs to be considered.Previous descriptions of the charge-transfer absorptions in organic solar cells only involve the charge transfer state and the ground state. Here Chen et al. underline that a third state,  In OSCs, the excitons photogenerated in the donor (D) and/or acceptor (A) components dissociate at the D/A interfaces. This process results in either immediate long-range charge separation or formation of interfacial charge-transfer (CT) states; the nongeminate (bimolecular) recombination of initially separated charges also results in the formation of CT states. These interfacial CT states can either separate into free charges or recombine to the electronic ground state via radiative or non-radiative pathways. Thus, with respect to the energy of the local excitonic states on the absorbing species, there exist two significant sources of VOC (energy) losses, related to exciton dissociation and charge recombination that both are mediated by the CT states14. Thus, given the critical role played by these CT states, it is crucial to develop robust methodologies that provide reliable information on their electronic and optical characteristics.The most efficient organic solar cells (OSC) based on blends of conjugated polymers or oligomers (electron donors) and (non-)fullerene derivatives (electron acceptors) currently reach power conversion efficiencies (PCE) up to 14\u201315% in single-junction devices15. Then, extracting the electronic-structure information from the CT absorption bands has been commonly performed by analyzing the low-energy tail of the measured PDS or FTPS spectra in the framework of the semi-classical two-state Mulliken\u2013Hush model. Importantly, this model exclusively considers the ground (G) electronic state and the full electron-transfer (Coulomb-bound electron\u2013hole pair) state, which we refer to here as the D+A\u2212 state17; it completely neglects any potential role played by the strongly absorbing local-excitation (LE) state on the donor and/or acceptor, even though the LE and D+A\u2212 states have to be electronically coupled in order for exciton dissociation to take place.In most OSC materials, the CT absorptions are very weak, which means that highly sensitive photo-thermal deflection spectroscopy (PDS) or Fourier-transform photocurrent spectroscopy (FTPS) techniques are required to detect the CT statesVOC losses, a large number of experimental efforts have been devoted to develop D/A active layers in which there is as small as possible an energy offset between the LE and D+A\u2212 states25. In these instances, it can be anticipated that a strong coupling occurs between the LE and D+A\u2212 states; such a strong coupling has potentially a significant impact on the low-energy absorption of the D/A system and, consequently, on the charge-separation efficiency as well as on the radiative and non-radiative transitions. Therefore, especially in the case of such systems that form the basis of a next generation of efficient OSCs, it is critical to rely on a robust methodology that goes beyond the conventional two-state Mulliken\u2013Hush approach.Recently, in order to reduce +A\u2212, and LE states to investigate the electronic-structure properties in the framework of the perturbation theory27. Based on these early works, the impact of the LE-D+A\u2212 electronic coupling on the intensity of the CT absorption in polymer/fullerene systems has been discussed in terms of intensity borrowing, in the context of the weak electronic coupling limit28. Here, we go beyond the perturbation theory and develop a three-state dynamic vibronic model that incorporates the G, D+A\u2212, and LE states in order to describe reliably the nature of the CT absorptions in D/A active layers. Thus, the electronic couplings and electron-vibrational couplings are both treated non-perturbatively and the vibrational modes are treated quantum mechanically. Our objectives in the present work are: (i) to provide a comprehensive description of the nature of the CT absorptions in D/A complexes; (ii) to bring caution to the use of the semi-classical two-state Mulliken\u2013Hush models as they can lead to serious misinterpretations; and (iii) to describe a first application of our methodology to the PBTTT/PCBM and PIPCP/PCBM systems that have recently attracted a great deal of attention34.A number of earlier investigations on D/A small-molecule complexes or D-A isolated molecules have employed a three-state model that includes the G, D17:A(E) is the optical absorption intensity  per donor/acceptor pair; E, the photon energy; +A\u2212 state; +A\u2212-state excitation energy  state. The related potential energies are shown in Fig.\u00a0+A\u2212 state, in addition to being coupled to the ground state, is also coupled to the LE state by an electronic coupling The three-state model is obtained by considering in addition to the G and D\u03b8\u2009=\u20090\u00b0 or 180\u00b0 \u03b8\u2009=\u200990\u00b0 6037, the It is informative to consider two model cases that are related to the main geometric configurations (edge-on and face-on packing modes) appearing at the D/A interfaces: one where the axis corresponding to the electron transfer from D to A is parallel , since the orientations of the D/A complexes in actual OSC active layers are expected to be combinations of these limit configurations. Note that, in what follows, we denote by \u201cLE\u201d\u2019 the local-excitation absorbing state intrinsic to , say, the donor component, and by \u201cD+A\u2212\u201d the pure charge-transfer state corresponding to a full electron transfer from D to A; the coupled states are denoted by \u201cS1\u201d and \u201cCT\u201d.It is well-established that the details of the donor/acceptor interfacial molecular packings greatly impact the electronic structure of the CT states+A\u2212 states: (a) 1.1\u2009eV ; (b) 0.4\u2009eV ; and (c) 0.2\u2009eV . Without any loss of generality , we assume that the vertical excitation energy of the diabatic D+A\u2212 state is 1.0\u2009eV (8065\u2009cm\u22121); although the absolute value of the D+A\u2212-state energy chosen here is small, this choice does not affect the conclusions derived from the three-state approach since, it is the energy offset 42: a high-frequency (HF) vibration mode (\u210f\u03c9HF\u2009=\u20091200\u2009cm\u22121), typical of a carbon\u2013carbon bond stretch44, and a low-frequency (LF) vibration mode (\u210f\u03c9LF\u2009=\u2009100\u2009cm\u22121), which represents rotations between intramolecular fragments as well as intermolecular motions46 ). The values of electronic couplings and electron-vibration couplings are chosen in such a way as to match commonly used literature values48; they are summarized in Table\u00a0+A\u2212-G electronic coupling (30\u2009cm\u22121) while the D+A\u2212-LE electronic coupling is varied within the range from 0 to 300\u2009cm\u22121 in order to easily assess the role of the D+A\u2212-LE electronic coupling in the absorption spectra.We consider three values for the offset, mentclass2pt{minimmentclass2pt{minimmentclass2pt{minim\u22121) for the configuration where the electron-transfer axis is parallel (\u03b8\u2009=\u20090\u00b0) to the transition dipole of the LE state, i.e., 7 , a low-energy absorption shoulder, with an intensity some 102\u2013104 times weaker than that of the pure donor absorption, can be clearly distinguished. When the D+A\u2212 state is considered not to be coupled with the LE state  for the CT absorption derived from our vibronic solutions .We start with a discussion of the results in the case where mentclass2pt{minim+A\u2212 state and the LE state has a marked effect on both the shape and intensity of the resulting CT absorption band. There are two contributions to the CT absorption band (see Eq.\u00a0+A\u2212 state itself while the second is due to the hybridization between the intrinsic LE and D+A\u2212 states (corresponding to an intensity borrowing effect). Depending on the relative orientations between the dipole moment of the D+A\u2212state 27. In the case where \u03b8\u2009=\u20090\u00b0, these contributions are constructive. As a result, in comparison with the CT absorption band derived when \u22121, an increase in \u22121  results in an increase in absorption intensity by one order of magnitude.As seen from Fig.\u00a0see Fig.\u00a0. Importa+A\u2212, and G states would be described by the semi-classical two-state model, which we recall is the model that has been applied to date in order to characterize the CT absorption bands. There are two procedures commonly used to interpret the CT absorption bands:It is instructive at this point to address how the CT absorption bands derived on the basis of an explicit consideration of the couplings among the LE, D\u03bcCT) can be obtained, and the electronic couplings 54. Here, taking as example the absorption spectrum simulated via our three-state model in the case where +A\u2212 state and the ground state since the absorption intensity (or transition dipole moment) borrowed from the LE state is incorrectly attributed to the D+A\u2212 state itself; (b) overestimates the relaxation energy in the D+A\u2212 state; and (c) importantly underestimates the D+A\u2212-state energy, (a) The Mulliken\u2013Hush Eqs  and 3)  3) are e via Eq. . This pr11. For example, for the absorption spectrum simulated via our three-state model in the case where \u22121 (0.70\u2009eV)) is close to the input value in our three-state model (5713\u2009cm\u22121 (0.71\u2009eV)); on the other hand, the fitted \u22121 (0.27\u2009eV)) is smaller than our input value (2352\u2009cm\u22121 (0.29\u2009eV)), which comes from the fact that the quantum effect of high-frequency vibration is neglected in the semi-classical two-state model. When a series of Gaussian functions is used to reproduce the whole CT absorption band , as done in the recent work of Belova et al.40 However, according to the three-state approach, these higher-energy absorptions correspond in fact to hot hybrid (D+A\u2212-LE) vibronic states, which are induced by D+A\u2212-LE coupling. Thus, our results bring to light another explanation for the higher-energy absorptions observed experimentally40.(b) In the OPV community, the usual procedure is to use a Gaussian function to fit the low-energy absorption tails, in order to extract the electronic-structure parameters of the CT statessee Fig.\u00a0, the fitsee Fig.\u00a0, the gen\u03b8\u2009=\u2009180\u00b0, the contributions of the D+A\u2212 and LE states to the CT absorptions act in a destructive fashion. As a result, the D+A\u2212 and LE-state contributions cancel each other, especially in the low-energy tail  case are shown in Fig.\u00a0+A\u2212 state is not coupled with the LE state, the CT absorption for small \u22121) that a slight shoulder appears in the low-energy region of the absorption spectrum  to  to 32 an33. A low-energy shoulder is clearly observed in the experimental absorption spectra, with an intensity about 100 times weaker than that of the neat polymer absorption , and 3510\u2009cm\u22121 (0.44\u2009eV) for \u03bcCT, 32. Based on this Gaussian fit32, the relaxed D+A\u2212-state energy \u22121 (0.92\u2009eV) and 5555\u2009cm- 1 (0.69\u2009eV), respectively, and the D+A\u2212-G electronic coupling ca. 573\u2009cm\u22121 (0.07\u2009eV). In the framework of our three-state model, a very good comparison between the experiment and fit is obtained , 8400\u2009cm\u22121 (1.04\u2009eV), 5055\u2009cm\u22121 (0.63\u2009eV), and 450\u2009cm\u22121 (0.06\u2009eV) ; (b) an underestimation of the relaxed D+A\u2212-state energy by 1000\u2009cm\u22121 (0.12\u2009eV); and (c) an overestimation of the relaxation energy in the D+A\u2212 state by ca. 500\u2009cm\u22121 (0.06\u2009eV). Note also that the results of a two-state Gaussian fit specifically depend on the chosen procedure, which can sometimes lead to a significant error.We first apply our three-state approach to the PBTTT/PCBM system, which is representative of systems with large see Fig.\u00a0. In the see Fig.\u00a0 when \\domentclass2pt{minimVOC loss of about 0.52\u2009eV (4193\u2009cm\u22121)29. The experimental absorption spectrum in the blend is red-shifted by ca. 60\u2009meV (484\u2009cm\u22121) compared with that of the pure polymer, with no appearance of a low-energy CT absorption shoulder in either photo-thermal deflection spectroscopy (PDS) or external quantum efficiency (EQE) spectra29. The lack of a low-energy CT absorption shoulder in the experimental EQE spectra has also been reported in other, high-efficient systems with low-energy loss56. Now, we exploit the three-state vibronic model to fit the absorption spectrum of the PIPCP/PCBM blend.We now turn to the PIPCP/PCBM system  of the PIPCP backbone when going from the neat polymer film to the blend structure29. However, even when the absorption spectrum of the blend is displaced so that its vibrational structure matches that of the neat polymer absorption, the blend still shows an additional absorption feature at the low-energy edge ; a \u22121; and a \u22121 . Interestingly, the D+A\u2212-LE electronic coupling is seen to be much larger than the D+A\u2212-G coupling; this result is in fact consistent with the electronic couplings calculated via long-range corrected density functional theory (see Supplementary Table\u00a0ECT\u00a0\u2013\u00a0eVOC) energy loss of only ca. 0.4\u2009eV (3226\u2009cm\u22121). While there remain differences between the fitted and experimental spectra, the three-state approach is able to reproduce the main characteristics of the absorption spectrum: (1) the absence of any low-energy absorption shoulder; (2) the presence of vibronic peaks in the region above 1.6\u2009eV (12904\u2009cm\u22121); and (3) the red-shift of the low-energy absorption edge of the blend compared with that of the pure polymer. The three-state vibronic model locates the D+A\u2212 state about 0.2\u2009eV (1613\u2009cm\u22121) below the polymer LE state, which is about four times larger than the value of 50\u2009meV (403\u2009cm\u22121) estimated previously from the electroluminescence spectrum29.The experimental high-resolution transmission electron microscopy indicates that PIPCP in the blend has a somewhat higher crystallinity than in the polymer neat film.2\u2009eV 161\u2009cm\u22121; a 58, we assume the related reorganization energy to be ca. 0.3\u2009eV (2419\u2009cm\u22121). With \u22121) and ca. 1\u2009\u00d7\u20091014\u2009s\u22121. The experimental data of Menke et al. have shown that, in the PIPCP/PCBM blend, exciton dissociation after photoexcitation is very fast 31, which is consistent with a reasonable 0.2\u2009eV (1613\u2009 cm\u22121) driving force and a large D+A\u2212-LE electronic coupling.We note that the rate of exciton dissociation in PIPCP/PCBM can be crudely estimated via Marcus electron-transfer theory where, following earlier investigations59. As reported by K\u00f6hler et al. 51, static disorder can lead to a broadening of the CT absorption spectrum. Thus, when neglecting static disorder, the CT-state reorganization energies 59. Thus, our objective in future work will be to account for static disorder and electronic delocalization, although their inclusion is not expected to affect the main conclusions of the present work regarding the impact of the electronic coupling between the D+A\u2212 and LE states.Finally, we would like to point out that our present three-state approach is a starting point and does not consider other factors such as static disorder or electronic delocalization due to aggregation effects, which can also impact the CT absorption spectra+A\u2212) and LE states on the characteristics of the CT states at the D/A interfaces.We have developed a three-state vibronic model, with which we can explicitly take into account the electronic and vibronic couplings between the charge-transfer states appearing at the donor/acceptor interfaces and not only the ground state but also the strongly absorbing, local-excitation (LE) state on the donor and/or acceptor. We recall that coupling to only the ground state (two-state model) has been the hallmark of the analysis tools commonly applied to date to characterize the CT states appearing in the active layers of OSC. Here, the application of the three-state vibronic model has allowed us to clarify the impact of hybridization of the pure charge-transfer (D(i)+A\u2212 and LE states, a low-energy CT-absorption shoulder is clearly apparent. However, the electronic coupling between the D+A\u2212 and LE states makes the shape and intensity of the low-energy shoulder substantially different from those that the semi-classical two-state Mulliken\u2013Hush model would predict. In fact, application of the semi-classical Mulliken\u2013Hush model to analyze the whole CT absorption bands leads to an overestimation of the reorganization energy and electronic coupling with the ground state and an underestimation of the adiabatic energy of the D+A\u2212 state. In addition, if a Gaussian fit to the low-energy CT absorption tails is performed, this procedure could provide a good fit to the adiabatic energy of the D+A\u2212 state, but also misinterpret the higher-energy absorptions (which correspond to hot hybrid (D+A\u2212-LE) vibronic states induced by the D+A\u2212-LE coupling).In the case of a large energy offset  between the D(ii)+A\u2212-LE coupling gain a more substantial transition dipole moment; these hot CT vibronic states, which are directly optically accessible, have energies that can allow them overcome, entirely or at least in part, the electron-hole Coulomb barrier and to dissociate easily into free charge carriers. This feature could thus result in improved power conversion efficiencies.In comparison with the characteristics of the (two-state derived) conventional CT states, the hot CT vibronic states resulting from D(iii)+A\u2212 and LE states, which is representative of the next generation of highly efficient OSCs, the absorption spectra hardly show any low-energy absorption feature. Instead, the D+A\u2212-LE coupling leads to a red-shift of the whole low-energy absorption edge, which is consistent with the experimental data reported for the PIPCP/PCBM blend. In such instances, a three-state model is mandatory in order to extract reliable information on the CT states from the absorption spectra.In the case of a small energy offset  between the DA number of important conclusions can be drawn:Overall, our work provides a robust and comprehensive framework to understand the CT absorption spectra at donor/acceptor interfaces and also provides a pathway for a reliable extraction of the electronic-structure parameters describing the CT states from these spectra. However, more experimental data, such as temperature dependence and polarization dependence of the absorption, would be desirable to achieve these parameters. Our model can be further applied to multiple donor/acceptor complexes in order to account for the effects of electron delocalization and static disorder. Taking into account a three-state vibronic approach or its extensions is necessary to adequately characterize the voltage (or energy) loss mechanisms in efficient OSC devices and to guide the development of improved systems.The total Hamiltonian for a donor/acceptor molecular pair can be written as:r and q are standard notations for the electronic and nuclear coordinates, respectively.Here, +A\u2212 diabatic states, respectively, the \u03b1th eigenfunction In the basis of the three electronic states \u03b7(q) denotes the expansion coefficients. The electronic wavefunctions q\u2009=\u20090) of the G state is selected as the reference point, see Fig.\u00a0Here, mentclass2pt{minimqi, the eigenenergies The eigenenergies ith vibrational normal mode with energy \u210f\u03c9i, which is defined by \u03bb of the D+A\u2212 and LE states  in Eq. (\u03c7k(qi)\u232a60:The full dynamic solution of the vibronic Hamiltonian given by Eq.  can be o) in Eq.  in terms\u03a8\u03b1 is the superposition of the |\u03a6G\u232a, |\u03a6LE\u232a and ci terms are the expansion coefficients. By using a finite but large enough number of vibrational functions (large k), the eigenenergies and eigenfunctions of the vibronic Hamiltonian can be obtained with any desirable accuracy.Each adiabatic solution f(E\u03b1) stands for the thermal (Boltzmann) population of the vibronic state E\u03b1; 60. In the case of vibronic models including a few effective modes, the calculated vibronic peaks are separated by an energy related to that of the lower-energy vibrational mode. In these instances, it is a standard practice to use a Gaussian smearing of the vibronic peaks. In order to obtain a smooth profile of the simulated absorption spectra, we used a Gaussian broadening with a width (100\u2009cm\u22121) set according to the energy of the low-frequency vibration (100\u2009cm\u22121). We note that this procedure has a negligible impact on the overall width and asymmetry of the simulated absorption spectra. The transition dipole moment, \u03bcCT, of the CT absorption can be then obtained via the integration of A(E)/E54.Based on the calculated eigenenergies and eigenfunctions of the vibronic Hamiltonian, the optical absorption intensity  per donor/acceptor pair is obtained from:X axis, and the difference between the dipole moments of the G and D+A\u2212 states is given by 35, where Without any loss of generality, we assume that the LE state is localized on the donor and that the transition dipole moment Supplementary Information"}
+{"text": "Nature Commununications; 10.1038/s41467-018-07070-8, published online 7 Nov 2018Correction to: The original version of this Article contained an error in Fig.\u00a02. In panel a, the two legend items \u201crare\u201d and \u201ccommon\u201d were inadvertently swapped. This has been corrected in both the PDF and HTML versions of the Article."}
+{"text": "We propose a generalization of the Su-Schrieffer-Heeger (SSH) model of the bipartite lattice, consisting of a periodic array of domain walls. The low-energy description is governed by the superposition of localized states at each domain wall, forming an effective mono-atomic chain at a larger scale. When the domain walls are dimerized, topologically protected edge states can appear, just like in the original SSH model. These new edge states are formed exclusively by soliton-like states and therefore, the new topological states are qualitatively different from the regular SSH edge states. They posses a much longer localization length and are more resistant to on-site disorder, in marked contrast to the standard SSH case. Different experimental setups, such as plasmonic nanoparticles and phononic lattices, have been used as practical realizations of one-dimensional models8. This emergence of novel experimental escenarios, in turn, has motivated further theoretical research, often on basic aspects or phenomena beyond the scope of common electronic systems, such as non-linearities10 and Floquet insulators12. The interest on one-dimensional topologically protected modes is not only related to basic understanding, but to the practical implementation in the design of low-loss devices14.The last years have witnessed a growing interest on one-dimensional models of non-trivial topological systems. This has been largely favored by the rapid advance of photonics and nano-photonics as an ideal playground to experimentally corroborate theoretical predictions15 (SSH). It consists on a tight-binding model for the bipartite lattice, and displays soliton-like localized edge states at domain walls (i.e. stacking faults of the bipartite lattice). Recently, this model has been the subject of generalizations in order to observe new phenomena17. Other one-dimensional models, not restricted to the bipartite lattice, have been proposed and realized, showing novel edge states20.Perhaps, the most studied one-dimensional model with a non-trivial topology is the Su-Schrieffer-Heeger model of polyacetylene21. Similarly, it was shown that some edges states in 2D systems with a negligible spin-orbit coupling -for instance some terminations of black phosporus- are indeed topologically protected22. Also, the natural extension of the SSH model to two dimensions can host different topological phases, even with a zero Berry phase23.One of the main purposes behind the focus in simpler models as the SSH is to get insight on more complex systems or materials. For instance, depending on the termination, a non-trivial Zak phase in nanoribbons can arise, implying topologically-protected edge statesN interacting copies of the SSH model, originated from an array of domain walls. If the lattice of domain walls is dimerized -a bipartite lattice of domain walls-, we recover a SSH-like behavior formed by the superposition of localized modes. Naturally, this model has a non-trivial phase featuring edge states. In Sec. 3 the effect of disorder in the model is studied. Unlike the SSH model, the new edge modes are somewhat robust to on-site disorder.In this article we start by reproducing the results of the famous SSH model, Sec. 1, to set the notation and make its generalization easier. In Sec. 2, we introduce a new model, consisting on 15, or more precisely, the tight-binding formulation of the bipartite lattice, see Fig.\u00a024. In the optical context, the edge states from this model have been experimentally observed and theoretically explained in photonic superlattices25.We start with a brief summary of the SSH model of polyacetyleneIn a finite bipartite lattice, the two different orderings , Fig.\u00a0t and v are the hopping amplitudes and each cell has two equal \u2013but inequivalent\u2013 sites a, b (e.g. the sub-lattices). In spite of its simplicity, this system has a very rich physics. In the case of t\u2009<\u2009v, it has  zero-energy and sub-lattice polarized edge states solutions. In the limit N\u2009\u2192\u2009\u221e the zero-energy modes have a simple expression\u03c8L is localized at the left edge of the chain, with width \u03c8R is localized at the right edge. \u03b1, \u03b2 are normalization constants. For a finite chain size, N, the interaction between both edge states is small but finite The one-dimensional bipartite lattice, see Fig.\u00a0entclass1pt{minimai.e. excluding edge states) is The bulk-like states, have energies entclass1pt{minimaN sites, after imposing periodic boundary conditions, i.e. by setting Both bonding schemes of the bipartite lattice, see Fig.\u00a0\u03c8L, \u03c8R, Eqs , \u03c8a is localized at j\u2009=\u20090 and \u03c8b localized on \u03b5 just reverses the positions of the DW centers.We can use the previous solutions  \u03c8R, Eqs  and 3 asM mono-spaced DWs \u2013see Fig.\u00a0hN, h\u2032N are SSH-like Hamiltonians, but with different topological phase. The periodicity in HPDW is two DWs, or 2N cells, but the spacing between domain walls is just N. This Hamiltonian is quite cumbersome, but if we focus on its low-energy excitations, it can be greatly simplified, by just keeping the superposition of modes \u03c8a, \u03c8b, at each domain wall, see Eqs (A bipartite lattice with  see Eqs  and 6. UN sites is an effective \u2018cell\u2019 with two sub-lattices per cell (i.e. both DWs), just like in the standard bipartite lattice, but with just one single hopping t\u2032. Therefore, the effective low-energy excitations are just like those in a monoatomic chain with period N, see Figs\u00a0mN, (2m\u2009+\u20091)N aremN, we need to multiply Eq. (m\u2009+\u20091)N. The simple interpretation of this b sites, see the lower inset from Fig.\u00a0Each group of 2d in Eqs  and 6. Wd in Eqs  is alrea\u03b1\u2032, \u03b2\u2032 are almost independent of N, N the first term in the parenthesis dominates, but in some contexts -like in optics- the most common arrays consist of a limited number of waveguides.The interaction between two localized states is, approximately:locally sub-lattice polarized , but on a larger scale (NM sites) the sub-lattices are mixed. Also, their energy is genuinely finite, forming an s-band, Fig.\u00a026 and the results agree with ours.The low-energy states given by Eqs  or 10),,10), areIn this section we introduce a bipartite lattice of domain walls, starting by its Hamiltonian, and derive its low-energy version, which is a new version of the SSH model, but with smaller hopping strenghts. As the SSH model, this new model has a phase with topologically protected edge states, see Fig.\u00a0i.e. by setting the spacing from one DW to the next one as N cells to the right and N\u2032 cells to the left. This changes slightly the Hamiltonian of a periodic lattice of DWs, from HPDW, Eq. , and in the middle of it two zero-energy states appear. These states are built from DW states, localized at the edges of the system and are fully sublattice polarized  is the kernel of the Hamiltonian. We can decompose h(k) as a linear combination of the Pauli matrices \u03c3x, \u03c3y, \u03c3z),t\u2032\u2009+\u2009v\u2032cos(k), v\u2032sin(k), 0). Figure\u00a0N, N\u2032, and keeping the original hopping strengths constant. The geometric place of this vector is a circle and we can define a topological invariant related to it, the winding number or Chern number:nc is very simple, it counts how many times the curve k) encircle the origin. The two possible values of nc\u2009=\u2009{0, 1} defines the phase diagram of the system24, see Fig.\u00a0N\u2009>\u2009N\u2032 the system is in the \u2018topological phase\u2019, that is nc\u2009=\u20091, conversely N\u2009<\u2009N\u2032 is the trivial phase with nc\u2009=\u20090. In the remaining case, N\u2009=\u2009N\u2032, the curve nc\u2009=\u20091 has topologically protected edge states.The analogy with the regular SSH modelian, Eq. , gives19While ian, Eq.  in the n27. The band gap due to off-diagonal disorder is not shown since in the SSH model it is below our numerical precision. For the edges states of the BDW model, it lies below 10\u22124 for a disorder amplitude of \u03b4\u2009=\u2009. In smaller SSH chains the off-diagonal disorder is able to close the  gap, but the chains considered in Fig.\u00a0The resilience of topologically protected states in the SSH model to off-diagonal disorder is well-known, as well as its weakness against disorder on the on-site energiesThe non-uniformity of on-site disorder directly breaks the chiral symmetry, destroying the topological protection. Figure\u00a0\u03b5BDW \u2013which averages to zero for large \u03b5BDW. In the Figure, the asymptotic-like band gap is well below the band gap of the bands formed by the DWs states, which in turn is much smaller than the bandgap from the SSH model. Given t\u2009=\u20091, v\u2009=\u20091.5, the characteristic length of the SSH model is t, v\u2013 the characteristic length of the SSH model, see Eq. . At moderate disorder . The Bl\u00f6ch states of the SSH lattice become localized with disorder, regardless of whether it is on-site or off-diagonal disorder. The regular Bl\u00f6ch states of the BDW have a very similar behavior -they are Bl\u00f6ch states too-, but they are slighty more localized for any finite value of \u03b4. This is a consequence of the \u2018fragmentation\u2019 of the extended states  into smaller groups with smaller bandgaps \u2013see the green region in Fig.\u00a0IPR of these states is very similar to the regular Bl\u00f6ch states, and for clarity they are not included in Fig.\u00a0To get a deeper insight on the effect of disorder on both, the SSH and the BDW models, we calculated the inverse participation ratio (IPR)IPR doubling its value for tiny amounts of on-site disorder. When \u03b4 is of the order of the interaction between the edges states, they no longer form an bonding anti-bonding pair, i.e., the IPR should be ~0.18 for no disorder), but it shows that a very small on-site disorder can prevent the occurrence of charge fractionalization in the model29.The BDW\u2019s edges states  and local disorder (Anderson) is a necesary step towards the design of future robust low-loss devices. The effect of nonlinearity on the topological robustness of these systems is another subject of interest (under investigation) and will be reported elsewhere."}
+{"text": "Scientific Reports 10.1038/s41598-018-33609-2, published online 12 October 2018Correction to: The original version of this Article contained an error in the title of the paper, where the word \u201cgraphene\u201d was incorrectly given as \u201cgrapheme\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Scientific Reports 10.1038/s41598-018-25119-y, published online 27 April 2018Correction to: A supplementary file, \u201cExample of a dual-task trial for the Feedback group\u201d was omitted from the original version of this Article. This has been corrected in the HTML version of the Article; the PDF version was correct at time of publication."}
+{"text": "Longitudinal studies of tumor volume have used certain named mathematical growth models. The Bertalanffy-P\u00fctter differential equation unifies them: It uses five parameters, amongst them two exponents related to tumor metabolism and morphology. Each exponent-pair defines a unique three-parameter model of the Bertalanffy-P\u00fctter type, and the above-mentioned named models correspond to specific exponent-pairs. Amongst these models we seek the best fitting one.The best fitting model curve within the Bertalanffy-P\u00fctter class minimizes the sum of squared errors (SSE). We investigate also near-optimal model curves; their SSE is at most a certain percentage (e.g. 1%) larger than the minimal SSE. Models with near-optimal curves are visualized by the region of their near-optimal exponent pairs. While there is barely a visible difference concerning the goodness of fit between the best fitting and the near-optimal model curves, there are differences in the prognosis, whence the near-optimal models are used to assess the uncertainty of extrapolation.For data about the growth of an untreated tumor we found the best fitting growth model which reduced SSE by about 30% compared to the hitherto best fit. In order to analyze the uncertainty of prognosis, we repeated the search for the optimal and near-optimal exponent-pairs for the initial segments of the data (meaning the subset of the data for the first n days) and compared the prognosis based on these models with the actual data (i.e. the data for the remaining days). The optimal exponent-pairs and the regions of near-optimal exponent-pairs depended on how many data-points were used. Further, the regions of near-optimal exponent-pairs were larger for the first initial segments, where fewer data were used.While for each near optimal exponent-pair its best fitting model curve remained close to the fitted data points, the prognosis using these model curves differed widely for the remaining data, whence e.g. the best fitting model for the first 65\u2009days of growth was not capable to inform about tumor size for the remaining 49\u2009days. For the present data, prognosis appeared to be feasible for a time span of ten days, at most. Historically, the systematic application of mathematical models for tumor growth has begun in the 1960s . In the v(t) in mm3 over time t in days, using five model parameters that are to be determined from fitting the model to size-at-age data: Four parameters are displayed in the equations, namely the non-negative exponent-pair a\u2009<\u2009b and the constants p and q. A fifth parameter is the initial tumor volume at the start of monitoring, i.e. v (0)\u2009=\u2009v0\u2009>\u20090.This equation describes tumor volume a, b) defines a unique model with three free parameters . Thus, for these models the \u201cmodel muddle\u201d can be reduced by considering them within the context of the larger unifying class (1) of models. Figure a, b)\u2009=\u2009 defines exponential growth (i.e. v(t)\u2009=\u2009v0\u00b7eq\u00b7t-, assuming p\u2009=\u20090, q\u2009<\u20090), and bounded exponential growth (i.e. v(t)\u2009=\u2009(p/q)\u00b7(1-d\u00b7eq\u00b7t-), assuming p, q, v0\u2009>\u20090 and defining d from these parameters). The logistic growth model of Verhulst [a, b)\u2009=\u2009. The Gompertz [a\u2009=\u2009b\u2009=\u20091; it uses a different differential equation [In this paper, we perceive eq.  as a defng class  of modelVerhulst  is definng class  of modelGompertz  model isequation . These ma\u2009=\u20091, b\u2009>\u20091) and the generalized Bertalanffy model  are represented as classes of models. In the theory of economic growth, the latter model (class) is known as Solow-Swan model [Richards\u2019  model Fa\u2009=\u2009, b\u2009>\u20091 aan model \u201322.a\u2009=\u20092/3, as the inflow of energy would be proportional to the surface area , and the exponent b\u2009=\u20091, as the energy needs for sustenance would be proportional to volume (cell count). This model appears to be plausible for the avascular stage of a solid tumor (nutrients enter only through the periphery). However, other authors proposed different biophysical explanations of growth and different exponent-pairs [a) may be above the value 2/3 of [v\u00b4/v over time, as these would inform about metabolism [A drawback of this type of phenomenological models is the difficulty in relating the comparatively easy to observe macroscopic data (size-at-age) to actual biological processes. According to von Bertalanffy , 14, thent-pairs , 24. Thue 2/3 of . Furthere 2/3 of , a statie 2/3 of , 27 anale 2/3 of  in the ctabolism .A different modeling approach describes tumor growth at the more detailed tissue scale in terms of partial differential equations related to invasion-proliferation and diffusion-reaction; e.g. Fisher-Kolmogorov equation , 30. ForWe reconsider the findings of . They coAs these findings depended on a few models only, and as there is no generally valid tumor growth model, which ensures a clear understanding and prognosis of tumor growth, the present paper revisits this issue and considers models from a more comprehensive class. The differential eq. (1) defines such a class that encompasses the most popular models (see above). We therefore aim at comparing the models from the model class (1) in terms of their goodness of fit (see methods) to the data of  and we a\u2212\u200930) may result in very poorly fitting model curves.This approach has the following advantages: First, using a larger class of models with different growth patterns for comparison will provide a high flexibility in data-fitting and results in a better fit of the overall optimal model; for such a model we expect a better prognosis. Second, using a large class of models allows for a better comparability of the results with the literature. For even if a certain model may not be an element of the large class, some other element of the class may approximate it. And third, this approach allows estimating the uncertainty of prognosis. We claim that there may be limits to prognosis that are inherent to the research problem (c.f. prognosis of weather), and that near-optimal models might highlight these limits. For near-optimal models \u201334 the fa, b, p, q, and v0 of (1) may fail with standard optimization software. We will therefore also explain the optimization tools.This working plan has not yet been implemented in literature, because the optimization of the five parameters We aim at explaining the findings of  and we tWe demonstrate our method to find the best fitting and the near-optimal models for this dataset, only, as the paper aims at a \u201cproof of principle\u201d. While the conclusions about the limitations of prognosis may not apply to other data, the method to obtain such conclusions for concrete data generalizes. As a visual inspection of the data Fig.  would sua\u2009=\u2009m\u00b70.01, b\u2009=\u2009a\u2009+\u2009n\u00b70.01, with integers m\u2009\u2265\u20090, n\u2009\u2265\u20091). If the exponent-pair of the best fitting model was attained on the upper boundary line or on the right boundary line of this grid . Thus, if the exponent-pair with the best fitting model curve was a grid point next to the diagonal, then there remained the possibility that a Gompertz-type model could fit better. However, we expected that the improvement would be small. For, as noted by [a\u2009<\u2009b.The diagonal tial eq.  needs tonoted by , the GomSSE, which is defined as follows; v(t) is a solution of eq. (1), using certain exponents a\u2009<\u2009b and parameters p, q, v0, and vi are the data from above: assesseda, b) defines a unique model from class (1) with three free parameters . For each of these models (exponent-pairs) we wished to identify the best fitting model parameters p, q, v0. Thereby, we used the method of least squares; i.e. for each exponent-pair  on the grid we sought parameters  that minimized SSE. This defined the following function on the grid to identify, for each exponent-pair a\u2009<\u2009b, the minimal SSE that can be achieved:Thus, each exponent-pair  from the grid of Fig. SSEopt attained the minimum over the grid at this exponent-pair. The exponent-pair was defined as near-optimal, if SSEopt was at most a certain percentage  larger than this minimal SSE.In terms of this definition, an exponent-pair  are normally distributed, we tested this assumption using the Anderson-Darling and Cram\u00e9r-von Mises distribution fit tests [As using it tests . We inveAIC [Alternative criteria for model selection, e.g. the well-known Akaike information criterion AIC \u201342, focuAIC , for theSSEopt (i.e. optimization) was done using Mathematica\u00ae 12.0 software of Wolfram Research. The authors provide a Mathematica file as supporting material. The output was exported to a spreadsheet, Microsoft Excel\u00ae. It is provided as a supporting material in the format ) of the table.The computation of a, b) were visited by means of an outer loop running through a\u2009=\u2009m\u00b70.01 and an inner loop that for each a ran through the values b\u2009=\u2009a\u2009+\u2009n\u00b70.01. Given , the optimization of p, q, and v0 was done using a custom-made variant of the method of simulated annealing [p, q, v0\u2009>\u20090 for optimal parameters. The candidate parameters were altered by multiplying them with positive random numbers close to 1.  These new parameters were accepted as new candidates, if for them SSE became smaller, but in order to escape from suboptimal solutions, with a certain probability new parameter values were also accepted, if for them SSE became larger.  This step was then repeated with the accepted parameter. At the begin of each inner loop, i.e. at a grid point near the diagonal of the form , the optimization of p, q, v0 used 50,000 of these simulated annealing steps, starting with the estimate p\u2009=\u2009q\u2009=\u20091 and the initial condition v(t1)\u2009=\u2009v1 (first data point). For the subsequent grid points in the b-direction (inner loop), the previous optimization results were used as starting values and improved in 10,000 annealing steps. Thereby, after each 1000 steps the simulated annealing restarted with the hitherto best parameters. Further, the probability of accepting parameters with a higher SSE was lowered slightly. (This was made dependent on the hitherto obtained optimization results and is known as adaptive cooling: [SSEopt exceeded the minimum SSE by at most 1%) was visually inspected. Where the plot had a frayed appearance, the optimization exercise was repeated with more simulated annealing steps. CPU-time for the computations took about one week.For optimization, the grid-point exponent-pairs  To assv0, p, q (Mathematica command NonlinearModelFit) and further improve SSEopt.The optimal parameters from simulated annealing were finally used as starting values for a nonlinear regression for the model with the optimal exponent-pair, using standard methods to determine SSEopt \u2009=\u20091.274\u00b7105 with the parameters v0, p, and q from the caption of Fig. v0, p, and q as starting values for a standard nonlinear regression for the model defined from the exponent-pair a\u2009=\u20091.62, b\u2009=\u20092.44 resulted in a slight improvement below the displayed accuracy. Figure SSEopt\u2009=\u20091.61\u00b7105.  was sought for. Figure  1.62, 2.4\u2009=\u20091.27461\u00b7105. ( obtained3 (computed as the limit of the model curve v(t) for infinite t) remained close to the maximally observed volume  Further, as shown by Fig. 3. Distribution fit tests did not refute the implicit assumption for using the method of least squares, normally distributed fit residuals .The best fitting model curve supported the hypothesis of bounded growth, as its asymptotic volume of 4,034\u2009mmxcessive ) and as To explore the potential for prognosis,  fitted sSSE\u2009=\u200933,700 \u2009=\u200932,177 and identified a still smaller SSEopt \u2009=\u200932,087 (rounding to integers).Table Figure b, necessitated the use of extremely small parameters, q. The frayed character of the red region reflects the numerical problems of using such exponents and parameters; due to such problems conventional all-purpose optimization software was doomed to fail. For the former data, the optimal exponent-pair was still on the upper boundary of the search grid, whence the optimality of the exponent-pair was not secured.The optimization for the data for 98 and 107\u2009days was particularly time consuming, as 63,377 and 64,150 grid points were searched. For the latter data, Fig. Figure Our results confirm the finding of , that thFigure For a practitioner, who uses the past data to extrapolate into the future, the failure of forecasting may indicate problems for the patient, e.g. a different phase of growth, where the apparent trend of the growth curve changes due to a biological cause (e.g. angiogenesis). It may indicate problems with the data, such as the presence of outliers. Or it may merely indicate that the true nature of the growth curve could not be identified, because its S-shape could not (yet) be discerned from the data.v\u00b4/v over time for the best fitting models of the top-1% of the near-optimal exponents. Its reverted U-shape suggests that the tumor size may have approached the carrying capacity, whence further growth would be inhibited by lack of resources, unless other drivers of growth (e.g. angiogenesis) were activated. This information might not have been readily available, if v\u00b4/v were estimated from a numeric differentiation of the data (blue line).For the present data the latter reason may apply, as Fig.\u00a0The analysis of relative growth rates in Fig.\u00a0Further, the size of the region of near-optimal exponent-pairs is related to the information inherent to the growth data: The larger the region is, the fewer information can be retrieved, as for a larger region the data would be compatible with more (too many) possible shapes of the growth curve. As was shown in Fig.\u00a0For the data of  the progHowever, even for peculiar data, prognosis is not futile, as for practitioners any discrepancy between observed and forecasted growth may be an important warning signal that the tumor biology may change. The present paper provided methods for a more accurate prognosis.v\u00b4/v. However, for the present data also this analysis of the past did depend on how much information about the growth was available at the time when the assessment was done. For, the assessment switched from an initially decreasing relative growth rate, if only seven or eight data points were considered, to an initially increasing relative growth rate, when more data were utilized (Fig. In addition to prognosis, practitioners may use best fitting model curves to assess the character of past growth in terms of the relative growth rate zed Fig. ."}
+{"text": "Game theory has been studied extensively to answer why cooperation is promoted in human and animal societies. All games are classified into five games: the Prisoner's Dilemma, chicken game (including hawk\u2013dove game), stag hunt game and two trivial games of either all cooperation or all defect, which are studied separately. Here, we propose a new game that covers all five game categories: the weight-lifting game. The player choose either to (1) carry a weight (cooperate: pay a cost) or (2) pretend to carry it (defect: pay no cost). The probability of success in carrying the weight depends on the number of cooperators, and the players either gain the success reward or pay the failure penalty. All five game categories appear in this game depending on the success probabilities for the number of cooperators. We prove that this game is exactly equivalent to the combination of all five games in terms of a pay-off matrix. This game thus provides a unified framework for studying all five types of games. It iEach of these five types of games is known to have a unique structure of dilemmas . BecauseIn this report, we propose a single game called a weight-lifting game that can evaluate all five categories together. In this game, a player has two choices: either carry (lift) a weight (cooperation: C) or pretend to carry it (defection: D); the possible combinations are , ,  and . Both players gain a reward if a weight is successfully carried, but they suffer the penalty of failure if they fail to carry it. The success/failure of carrying the weight depends on the number of cooperators: the probability of success increases with the number of honest lifters.ip . All five types of games are also quantitatively expressed by this game with a certain combination of success probabilities. Thus, the weight-lifting game is mathematically equivalent to all five categories of games. We also discuss the extension of this game to N-person games.This weight-lifting game becomes one of the five types depending on the specific values of the three probabilities 2.c \u2265 0) or defection (D) without any cost. If the baggage is carried successfully, both players obtain a gain (r > 0) irrespective of his/her strategy. For example, the net gain of a player is r \u2212 c if he/she cooperates in the successful case. By contrast, the gain is r if he/she is defective but the baggage is successfully carried. In the unsuccessful case, both players pay a fine (f > 0) in addition to the cost c of cooperation. Accordingly, the net gain is \u2212 f \u2212 c and \u2212 f for the cooperator and defector, respectively (a).In the weight-lifting game, baggage is carried by two players randomly selected from among an unlimited well-mixed population. Each player chooses a strategy from two choices: cooperation (C) in carrying the baggage by paying a cost  is the number of cooperators (0 \u2264 ip \u2264 1), we introduce two parameters: \u0394p1 = p1 \u2212 p0 (0 \u2264 \u0394p1 \u2264 1) and \u0394p2 = p2 \u2212 p1 (0 \u2264 \u0394p2 \u2264 1). These parameters express increments of the success probability by the presence of one cooperator. The difference between the success probabilities of two cooperators and no cooperator is \u0394p1 + \u0394p2 (b). The pay-off matrix of this game is represented in terms of the expected gains for two strategies (c):In terms of the probability of success p1 + \u0394p2 b. The parategies c:2.1FC=ri = 2 if the two players are both cooperative , i = 1 if one player is cooperative,  and , and i = 0 if neither player is cooperative . The pay-off matrix is simplified by introducing a parameter b = r + f (>0), which is the benefit of a successful game compared to a failed game (d).Note that led game d.a\u2013e black inequality symbols). The first two conditions, R \u2265 S and T \u2265 P, express that cooperation increases pay-offs. The last condition, T \u2265 S, represents that players with different strategies benefit the defector more than the cooperator. The three conditions indicate \u0394p1 \u2265 0, \u0394p2 \u2265 0 and c \u2265 0. In terms of the cost-to-benefit ratio c/b, the C-D games are classified according to whether the following inequalities are met .(i)p1 > c/bS > P, i.e. \u0394(ii)p2 > c/bR > T, i.e. \u0394(iii)p1 + \u0394p2 > c/b.R > P, i.e. \u0394We consider a general set of C-D games satisfying three conditions R \u2265 S, T \u2265 P and T \u2265 S for the four matrix elements R, S, T and P  is automatically satisfied if either (i) or (ii) is satisfied. Accordingly, among four possibilities for whether or not conditions (i) and (ii) are met, only one (both met) is divided into two cases by the last condition (iii). In total, then, we have the following five cases to consider.Because \u0394a): R > T \u2265 S > P, where all three conditions (i), (ii) and (iii) are met. Both players are cooperative in the Nash equilibrium.Trivial cooperation (TC): a: R > T b): T \u2265 R \u2265 S > P, where (i) and (iii) are met. A different set of strategies,  and , is the Nash equilibrium.Chicken game (CH): b: T \u2265 R c): R > T \u2265 P \u2265 S, where (ii) and (iii) are met. The two strategies  and  are the Nash equilibrium.Stag hunt (SH): c: R > T d): T \u2265 R > P \u2265 S, where only (iii) is satisfied. The Nash equilibrium of  is not Pareto optimal.Prisoner's Dilemma (PD): d: T \u2265 R e): T \u2265 P > R \u2265 S, where none of the three conditions (i), (ii) and (iii) is met. Both players choose defection in the Nash equilibrium.Trivial defection (TD): e: T \u2265 P f, which indicates that the game type is determined by the three parameters, \u0394p1, \u0394p2 and c/b. Every possible C-D game of all five types corresponds uniquely to a certain set of the three parameters .These results are summarized in figure\u00a023.p1, \u0394p2, b/c) . Instead of c/b, the benefit-to-cost ratio b/c is used as the third axis. While the former is convenient for use in mathematical expressions, the latter has a practical interpretation as an indicator of cooperation. The parameter regions for the five games are shown in colour: TC (yellow), CH (green), SH (red), PD (blue) and TD (violet). As the benefit-to-cost ratio b/c increases, the volume in the parameter space of the cooperative game (TC) increases, while TD and PD, in which cooperation is not promoted, decline. For b/c = 2, TD (violet) and PD (blue) are dominant, while the TC game (yellow) is excluded . For b/c = 5, TC (yellow) becomes dominant, while TD (violet) and PD (blue) shrink . The ratio b/c determines the three boundaries in a \u0394p1 \u2212 \u0394p2 cross-section . Cooperative behaviour  is promoted when \u0394p2 exceeds the cost-to-benefit ratio c/b. The relative magnitudes of \u0394p1 and \u0394p2 determine the boundary between CH and SH, and the game type becomes SH for \u0394p2 > \u0394p1. This means that when the effect of an additional cooperator is increased synergistically, the number of cooperators increases. The CH game is obtained in the opposite case, \u0394p2 < \u0394p1.The five types of C-D games are shown in a three-dimensional parameter space  a,b. Instexcluded a,c. For ) shrink b,d. The -section c,d. CoopHere we show the relationship between the game classes  of the current model and the two dilemma strengths introduced recently in the studies of game theory ,22,23. Tp1 = c/b and GID = 0 for \u0394p2 = c/b. As \u0394p1 increases, RAD decreases while GID increases. On the other hand, as \u0394p2 increases, GID decreases and RAD increases. As c/b increases (from figure\u00a04d\u2013f to figure\u00a04a\u2013c), the region in which GID and RAD are both positive enlarges, while the TC region shrinks. Accordingly. Cooperative behaviour becomes difficult to achieve.Here the game class becomes TC when neither of the two dilemmas exists, because there is no dilemma situation. When only GID is positive, the game becomes CH. Conversely, when only RAD is positive, the game becomes SH. If both dilemmas are positive, the game becomes PD game. Note that RAD = 0 for \u03944.p1, \u0394p2 and the cost-to-benefit ratio (c/b)\u2014the game-theoretical behaviours of three dilemma games  and two trivial games  are obtained in a unique manner. Therefore, players' optimal strategies may change as the parameters \u0394p1, \u0394p2 and b/c vary. Because the change in game type represents a change in the strength of the dilemmas [We proposed a weight-lifting game that covers all five types of games. Previously, the resolution of dilemmas has been studied for each individual game . We can now analyse the dilemmas in a unified manner using this single model. Depending on the three parameters\u2014\u0394dilemmas ,22,23, ip1 and \u0394p2, which are the increases in the success probability by a single cooperator when there is no or one other cooperator, respectively. The boundary between CH and SH games is determined by their relative magnitude.In the present model, the synergistic effect of cooperation  is repreIt should be noted that CH and SH games address different dilemmas. The gamble-intending dilemma (GID) in the CH game is the dilemma in which players exploit each other. The risk-averting dilemma (RAD) in the SH game is the dilemma of avoiding exploitation by the opponent ,17. It iN-player game appears to be a promising next step because it provides us with two advantages. The public goods game [N players allows us to investigate all possible dilemmas in a unified manner. Another merit is that it allows investigation into how the synergetic effect works depending on the manner in which the success probability changes. A unified treatment of N players and the synergetic effect has not been made before, although the effect of N players and the synergetic effect [Generalization to an ods game  has so fc effect  have beeN-player generalization of the present model, results different from that of the public goods game of a common type may be expected for the synergetic effect [pi increases as the number i of cooperators increases, how the increment in ip varies determines whether synergy is effective or not. If ip increases linearly in i, the public goods game of a common type is obtained, in which cooperation is promoted when the expected utility \u0394p \u00d7 (b/c) exceeds 1. By contrast, the success probability ip can be an arbitrary monotonic function in the present model. The synergetic effect depends on how \u0394ip varies. For example, in real-world society, it is expected that pi increases first slowly when there are a small number of cooperators, then moderately as the number increases, and finally slowly again when the cooperators become a dominant majority. In this case, there is a threshold value for the number of cooperators to promote cooperation. Moreover, defection is promoted as the population is saturated with cooperators. It is an interesting future problem to develop these ideas as N-player game simulations of realistic scenarios.In an c effect ,26. WhilThe current model can be applied to the history of social revolution ,28 to di"}
+{"text": "The Angioedema Quality of Life (AE-QoL) is the first patient reported outcome measure developed for the assessment of quality of life (QoL) impairment in patients with recurrent angioedema (RAE). This study aimed to evaluate the clinimetric properties of the AE-QoL in Thai patients and to establish categories of QoL impairment assessed by the AE-QoL.The validated Thai version of the Dermatology Life Quality Index (DLQI) and Patient Global Assessment of Quality of Life (PGA-QoL) were used to comparatively evaluate the Thai version of AE-QoL. Spearman correlations between the Thai AE-QoL and two other standard measurements (DLQI and PGA-QoL) were investigated to determine convergent validity. The Thai DLQI and PGA-QoL were used to categorize patients according to their QoL. Known-group validity of the Thai AE-QoL was later analyzed. The reliability of the Thai AE-QoL was investigated using Cronbach\u2019s alpha and intraclass correlation. Three different approaches including the distribution method, receiver operating characteristic curve analysis, and the anchor based-method were used for the interpretability.A total of 86 patients with RAE with a median age of 38.0\u2009\u00b1\u200915.1\u2009years (range 18\u201376) were enrolled. Of those, 76 patients (88%) had RAE with concomitant wheals, and 10 patients (11.6%) had RAE only. The AE-QoL assessed RAE-mediated QoL impairment with high convergent validity and known-groups validity, high internal consistency and test-retest reliability, and good sensitivity to change. Although the AE-QoL did not differentiate between patients with moderate and large effect as measured by PGA-QoL or DLQI in this study, AE-QoL total values of 0\u201323, 24 to 38, and\u2009\u2265\u200939 could define patients with \u201cno effect\u201d, \u201csmall effect\u201d, and \u201cmoderate to large effect\u201d of RAE on their QoL, respectively.This study supports the validity and reliability of the Thai version of the AE-QoL, which is a very different language from the original version. Categories allow to classify the effect of RAE on patients\u2019 QoL as \u201cnone\u201d, \u201csmall\u201d, and \u201cmoderate to large\u201d. Further studies are needed to confirm the applicability of AE-QoL in other Asian populations\u201d. Recurrent angioedema (RAE) is characterized by the unpredictable, sudden and recurrent onset of nonpitting swelling of the skin, subcutaneous tissues, and/or mucous membranes . AngioedRAE is classified into mast cell mediator-mediated and bradykinin-mediated, based on the underlying pathogenic mechanisms . In clinFor assessing HRQoL of angioedema patients, the Angioedema Quality of Life Questionnaire (AE-QoL)  and the As of now, there is the lack of and need for categorization/banding of HRQoL impairment in RAE patients. Also, we are lacking validated version of patient-reported outcome (PRO) outcome measures for assessing QoL impairment in Asian patients with RAE. Accordingly, this study generated the Thai version of the AE-QoL, evaluated its clinimetric properties in an Asian population of RAE patients, specifically in Thailand, and established categories of AE-QoL-assessed QoL impairment in this RAE population.Formal permission was given by MOXIE GmbH  to translate the original German version of the AE-QoL into Thai, and to validate the translated instrument . The AE-Misconceptions or misinterpretations during the translation process were resolved via a cooperative review and editing process that included the Thai research team and the instrument developers. After consensus was reached among all assessors, cognitive debriefing was performed with representatives of the target population and target language group to evaluate if the responders understand the questionnaire as intended , 18. TheThis study was approved by the Siriraj Institutional Review Board (SIRB), Faculty of Medicine Siriraj Hospital, Mahidol University, Bangkok, Thailand (COA no. Si271/2017). Adult Thai RAE patients aged 18\u2009years or older attending the Urticaria Center of Reference and Excellence  of the DThe DLQI is a general dermatologic HRQoL questionnaire that was established by Finlay et al. in 1994 . The DLQThe PGA-QoL is a patient evaluation instrument for assessing HRQoL during the preceding four-week period. A 5-point Likert-scale is used to rate level of effect, as follows: 0\u2009=\u2009no effect, 1\u2009=\u2009mild effect, 2\u2009=\u2009moderate effect, 3\u2009=\u2009severe effect, and 4\u2009=\u2009very severe effect , 23.At baseline, patients were informed how to complete the following questionnaires: Thai AE-QoL, Thai DLQI, and PGA-QoL. After patients acknowledged understanding of how to complete all three questionnaires, they were asked to complete the Thai AE-QoL, Thai DLQI, and PGA-QoL by themselves at the clinic. After 4\u2009weeks of treatment (2nd visit), all of the questionnaires were once again completed by the patients in the clinic.P- values of less than or equal to 0.05 were considered to be statistically significant.Consensus-based Standards for the Selection of Health Measurement Instruments (COSMIN), a standard protocol for evaluating the methodologic quality of studies in health measurement instruments, was applied in this study . The StaConvergent validity indicates the correlation between the Thai AE-QoL and other standard measurements for HRQoL (DLQI and PGA-QoL). Spearman correlation coefficients of <\u20090.3, 0.3\u20130.6, and\u2009>\u20090.6 were considered weak, moderate, and strong correlations, respectively .Known-group validity demonstrates the ability of the AE-QoL to discriminate groups that are assumed to be different. For HRQoL, patients were classified into three groups using the DLQI and PGA-QoL scores in this study, as follows: (i) \u2018no effect\u2019 ; (ii) \u2018small effect\u2019 ; and, (iii) \u2018moderate to large effect\u2019 .Cronbach\u2019s \u03b1 reliability coefficient was used to analyze internal consistency. Excellent, good, and acceptable reliability were defined as \u03b1 values of \u22650.9, 0.7\u2009\u2264\u2009\u03b1\u2009<\u20090.9, 0.6\u2009\u2264\u2009\u03b1\u2009<\u20090.7, respectively . InternaTest-retest reliability assesses the consistency of scores across multiple administrations. Stable patients should have comparable scores at two different administrations. Data from patients with no change in PGA-QoL score (stable in HRQoL) during 4\u2009weeks of treatment was used to determine test-retest reliability. Intraclass correlation coefficient (ICC) values of <\u20090.40, 0.4\u20130.75, and\u2009>\u20090.75 indicate poor, average, and strong reliability, respectively .Sensitivity to change is defined as the ability of an instrument to detect change over time, regardless of whether the change is meaningful . Correlai.Distribution method (MCID-1) indicates the numerical distribution of values. The standard error of measurement (SEM) is widely accepted to represent the MCID of an instrument \u201334. The ii.Receiver operating characteristic (ROC) curve analysis (MCID-2) shows the sensitivity and specificity over the range of absolute reductions in scores that can be used to identify \u201cimprovement\u201d , 35. Areiii.Anchor-based approach (MCID-3) compares changes in scores to an anchor value. MCID-3 is the difference between the mean \u201cimprovement\u201d score and the mean \u201cworsening/stable\u201d score. Patients with a decrease in PGA-QoL score of \u22651 and patients with an increased or unchanged PGA-QoL score were defined as \u2018improvement\u2019 and \u2018worsening or stable\u2019 HRQoL, respectively.Interpretability is the ability of an instrument to transform qualitative meaning to quantitative scores, i.e. the degree to which the values obtained by the use of the instrument produce information relevant to the patient and the physician in relation to the measured construct. Interpretability is composed of the minimal clinically important difference (MCID) and categorization. The MCID is defined as the smallest difference in a score that a patient can recognize as meaningful improvement , 31. DifCategorization is the process of determining cutoff scores for a measurement instrument that are then used to categorize patients into different groups. The DLQI and PGA-QoL were used to categorize patients into \u201cno effect\u201d , \u201csmall effect\u201d , \u201cmoderate effect\u201d , and \u201clarge and very large effect\u201d .A total of 86 patients with RAE with a median age of 38.0\u2009\u00b1\u200915.1\u2009years (range 18\u201376) were enrolled in this study. Of those, 76 patients (88%) had RAE with concomitant wheals, and 10 patients (11.6%) had RAE only. Of 10 patients who had RAE without wheals, 9 and 1 patients had idiopathic angioedema, and angiotensin-converting enzyme inhibitor-induced angioedema, respectively. Demographic data, scores at baseline, and treatments are shown in Table\u00a0p\u2009<\u20090.0001) and between AE-QoL total score values and PGA-QoL values .The AE-QoL showed high convergent validity, with strong positive correlations between AE-QoL and DLQI total score values  and with a small effect and a moderate to large effect  were significant. Overall, there were also significant differences in the mean AE-QoL score among patients with no effect, small effect, and moderate to large effect on HRQoL (p\u2009<\u20090.0001). However, the AE-QoL did not differentiate between patients with moderate and large effect as measured by PGA-QoL or DLQI. A statistical significance was not achieved when using the DLQI or the PGA-QoL to classify patients as those with \u201cno effect\u201d, a \u201csmall effect\u201d, a \u201cmoderate effect\u201d, and a \u201clarge effect\u201d.The AE-QoL also showed high known-groups validity as it was able to discriminate among patients who showed differences in HRQoL impairment as assessed by the use of the PGA-QoL and the DLQI. Figure\u00a0All Cronbach\u2019s \u03b1 values were higher than 0.72, which indicates good to excellent internal consistency of the Thai AE-QoL. Forty-four patients who had no change in HRQoL (no change in PGA-QoL score) during 4\u2009weeks were analyzed for intraclass correlation coefficients (ICCs). The ICC was 0.76 for the AE-QoL total score, which indicates strong intra-rater reliability. The ICCs (range: 0.64\u20130.75) for the AE-QoL domains were average (Table\u00a0p\u2009<\u20090.0001). This allowed us to further analyze MCID.The correlation between AE-QoL score changes and changes in PGA-QoL and DLQI were 0.39 and 0.42, respectively  and specificity (76.7%) for defining patients with meaningful improvement in HRQoL  of the AE-QoL, a change in the total score of >\u20096 was identified as the MCID . It is gAccording to the results of previous study, the linear correlation between AE-QoL total score and self-rated HRQoL impairments was well-demonstrated . HoweverThe maximum values to classify patients into \u201cno effect\u201d group were 23 and 25 using PGA-QoL and DLQI, respectively. The maximum value of 23 should be used as the cutoff score for the \u201cno effect\u201d category, as it had a higher AUC value than that of 25. Similarly, the minimum values to classify patients as those with a moderate to large effect were 38 and 36 using PGA-QoL and DLQI, respectively. The value of 38 should be chosen the cutoff value, as it had a higher AUC than that of 36. Thus, we propose that AE-QoL total score values from 0 to 23, from 24 to 38, and\u2009\u2265\u200939 define patients with \u201cno effect\u201d, a \u201csmall effect\u201d, and a \u201cmoderate to large effect\u201d of their RAE on their HRQoL, respectively. To provide a clinical perspective on this AE-QoL categorization: In the recent X-ACT study, in CSU patients with angioedema refractory to H1-antihistamine, patients had a \u201cvery large\u201d negative impact on their HRQoL as reflected by the mean DLQI total score of 14.6 at baseline. The mean AE-QoL total score at baseline of these patients was 56.2. Using our AE-QoL categorization, the patients in this study fall into the category \u201cmoderate to large effect\u201d of RAE on HRQoL. After 12\u2009weeks of omalizumab treatment in this study, the mean AE-QoL total score declined significantly from 56.2 to 27.7, which changed the AE-QoL category of patients from \u201cmoderate to large effect\u201d to \u201csmall effect\u201d of RAE on HRQoL .The strengths of this study include the use of three different approaches to establish the MCID of the Thai AE-QoL. However, several limitations should be noted including its small study population and the very high predominance of RAE patients with CSU. Secondly, no patients with HAE were enrolled in this study. Angioedema activity in HAE is generally more severe than in other causes of angioedema. Kulthanan, et al. reported that HAE was observed in 1 out of 105. Lastly, the AE-QoL did not differentiate between patients with moderate and large effect as measured by PGA-QoL or DLQI in this study. Further studies in larger study populations that include patients with high disease activity and causes of RAE other than CSU are needed to confirm the categorization of the AE-QoL.\u201dThe Thai version of AE-QoL was found to be a valid and reliable instrument for assessing disease\u2013specific impact on QoL in Thai RAE patients. A change in AE-QoL of >\u20096 points defines a meaningful change in HRQoL. RAE patients should be categorized for the impact of their disease on their QoL as those with \u201cno effect\u201d, \u201csmall effect\u201d, and \u201cmoderate to large effect\u201d based on AE-QoL total score values of up to 23, 24\u201338, and 39 and higher, respectively."}
+{"text": "Nature Communications 10.1038/s41467-018-07150-9; published online 07 November 2018Correction to: In the original version of this Article, the label \u201cRTK\u201d in Fig.\u00a06a was inadvertently changed to \u201cRTE\u201d. This has now been corrected in the PDF and HTML versions of the Article."}
+{"text": "Deep-learning based methods have succeed in modeling in-vivo protein-DNA binding, but they often (1) follow the fully supervised learning framework and overlook the weakly supervised information of genomic sequences that a bound DNA sequence may has multiple TFBS(s), and, (2) use one-hot encoding to encode DNA sequences and ignore the dependencies among nucleotides. In this paper, we propose a weakly supervised framework, which combines multiple-instance learning with a hybrid deep neural network and uses k-mer encoding to transform DNA sequences, for modeling in-vivo protein-DNA binding. Firstly, this framework segments sequences into multiple overlapping instances using a sliding window, and then encodes all instances into image-like inputs of high-order dependencies using k-mer encoding. Secondly, it separately computes a score for all instances in the same bag using a hybrid deep neural network that integrates convolutional and recurrent neural networks. Finally, it integrates the predicted values of all instances as the final prediction of this bag using the Noisy-and method. The experimental results on in-vivo datasets demonstrate the superior performance of the proposed framework. In addition, we also explore the performance of the proposed framework when using k-mer encoding, and demonstrate the performance of the Noisy-and method by comparing it with other fusion methods, and find that adding recurrent layers can improve the performance of the proposed framework.Modeling  Modeling 3, dramatically increases the amount and spatial resolution of available data, which is helpful for the in-depth study of in-vivo protein-DNA binding. However, DNA sequences directly extracted from ChIP-seq cannot precisely represent TFBS since the outputs of such experiments contain a lot of noisy4. Thus lots of methods have been developed for precisely predicting protein-DNA binding sites, including conventional algorithms9 and deep-learning based methods12. Not surprisingly, deep-learning based methods are better than conventional algorithms at modeling protein-DNA binding. DeepBind10 and DeepSea11 were two famous deep-learning based methods, which used convolutional neural network (CNN) to model the binding preference of DNA-proteins with a superior performance over conventional methods. DanQ12 designed a hybrid deep neural network to quantify the function of DNA sequences, which first used a convolutional layer to detect regulatory motif features from DNA sequences, and subsequently employed a bi-directional recurrent layer to capture long-term dependencies between motif features. Soon after, a number of deep-learning based methods are proposed for modeling in-vivo protein-DNA binding17.In the past decades, the introduction of high-throughput sequencing technologies, especially ChIP-seq.in-vivo protein-DNA binding, they usually overlook the weakly supervised information of genomic sequences that a bound DNA sequence may have multiple TFBS(s). In consideration of this information, Gao et al.18 developed a multiple-instance learning (MIL) based algorithm, which combines MIL with TeamD19, for modeling protein-DNA binding, and recently Zhang et al.20 also developed a weakly supervised convolutional neural network (WSCNN), which combines MIL with CNN, for modeling protein-DNA binding. Moreover, they are inclined to use one-hot encoding to encode DNA sequences, which means that it only considers the independent relationship among nucleotides. However, recent studies have shown that taking into consideration the high-order dependencies among nucleotides can improve the performance of modeling protein-DNA binding23. In consideration of this information, Zhou et al.24 evaluated DNA-binding specificities based on mononucleotide (1-mer), dinucleotide (2-mer), and trinucleotide (3-mer) identity, and stated that 2-mer and 3-mer may contain implicit DNA shape information and partially capture the effect of the DNA shape variation on binding. Zhang et al.25 proposed a high-order convolutional neural network, which first used k-mer encoding to transform DNA sequences into image-like inputs of high-order dependencies, and then applied CNN to extract motif features from these inputs.Although deep-learning based methods have achieved remarkable performance on modeling Noisy-and26 to replace them. (3) WSCNN, like other deep-learning based methods, used one-hot encoding to transform DNA sequences into image-like inputs. However, the relationship between nucleotides is not independent in practice. Therefore we use k-mer encoding to transform DNA sequences into image-like inputs of high-order dependencies, and explore the performance of the proposed framework when using dinucleotide (2-mer) and trinucleotide (3-mer) as inputs in the weakly supervised framework. In summary, the proposed framework firstly use the concepts of MIL to segment DNA sequences into multiple instances, and adopt k-mer encoding to transform sequences into image-like inputs of high-order dependencies, and then design a hybrid neural network to compute a score for all instances, and finally employ the Noisy-and method to fuse the predicted values of all instances as the final prediction of a bag. We conducted a lot of comparative experiments on in-vivo datasets to show that our proposed framework outperforms other competing methods. Besides, we also show the performance gain of the proposed framework when using k-mer encoding, and compare the performance of the Noisy-and method with other fusion methods, and demonstrate the effectivness of adding recurrent layers.Inspired by the above observation, we extend our previous work WSCNN from three aspects in this paper. (1) WSCNN mainly employed CNN to learn motif features from DNA sequences, and did not take into consideration the long-term dependencies between motif features. In the weakly supervised framework, therefore we add a bi-directional recurrent layer after the convolutional layer to capture the forward and backward long-term dependencies between motif features. (2) WSCNN attempted to use four fusion methods to fuse the predicted values of all instances in a bag, and then selected the best one of them as the final prediction. However, it is inconvenient for user to decide which one is better, so they have to try the four fusion methods one by one. Therefore we offer a better and more robust fusion method Noisy-and in Section II. We give a detailed analysis of the experimental results, and discuss the hyper-parameter settings in Section III.The rest of the paper is organized as follows. We give a detailed description of the proposed framework, and introduce the fusion method in-vivo protein-DNA binding. Actually, the task can be thought of as a binary classification problem that separates positive sequences (bound) from negative sequences (non-bound). The output of the network is a probability  distribution over two labels (1/0), since a binary classification problem can be addressed also through a binary output (1/0). This framework includes three stages in general: data processing, model designing, and results merging.In this section, we give a detailed description of the proposed framework for modeling 20, which ensures that (1) the weakly supervised information can be retained, and that (2) a large amount of instances containing TFBS are generated. This method is defined as a sliding window of length c, which divides DNA sequences of length l into multiple overlapping instances by a stride s. A bag is composed of all possible instances in the same sequence, and the number of instances in this bag is s and c are two hyper-parameters that need to be tuned by cross-validation. If (l\u2009\u2212\u2009c) is not a multiple of s, we pad \u20180\u2019 at the end of DNA sequences.Considering the weakly supervised information of DNA sequences, thus it is reasonable to use the concepts of MIL to deal with DNA sequences. Therefore we divided them into multiple overlapping instances following the worksk-mer encoding method25 to transform all instances into image-like matrices of high-order dependencies. This method can be implemented according to ; 2-mer encoding: taking into consideration the dependencies between two adjacent nucleotides, and each dinucleotide is mapped into a vector of size 16 ; 3-mer encoding: taking into account the dependencies among three adjacent nucleotides, and each trinucleotide is mapped into a vector of size 64 .After segmenting DNA sequences, all instances should be transformed into image-like inputs that can be handled by CNN. One-hot encoding is a commonly-used method in deep-learning based methods, but it ignores high-order dependencies among nucleotides. In order to capture the dependencies, therefore we use the rding to :1\\documek\u2009=\u20091 is shown in Fig.\u00a0l\u2009=\u200910, c\u2009=\u20098, s\u2009=\u20091, and the red dashed box denotes a sliding window of length c\u2009=\u20098. Through this stage, DNA sequences can be encoded into image-like inputs that can be easily handled by CNN.A graphical illustration of data processing when k\u2009\u00d7\u20091\u2009\u00d7\u2009(c\u2009\u2212\u2009k\u2009+\u20091) (batchsize \u00d7 channel \u00d7 height \u00d7 width), and then all instances of a bag can be concatenated along the height axis. Therefore a bag can be represented by a tensor of shape 1\u2009\u00d7\u20094k\u2009\u00d7\u2009n\u2009\u00d7\u2009(c\u2009\u2212\u2009k\u2009+\u20091), where n is the number of instances per bag  is another variant of ANN where connections between neurons form a directed graph. Unlike CNN, RNN can use its internal state (memory) to exhibit dynamic temporal or spatial behavior. In the designed model, the convolution layer is used to capture motif features, while the recurrent layer is used to capture long-term dependencies between the motif features. The model is arranged in this order: a convolutional layer\u2009\u2192\u2009a max-pooling layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a bi-directional recurrent layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a softmax layer.Considering the spatial and sequential characteristics of DNA sequences, we design a hybrid deep neural network, which integrates convolutional and recurrent neural networks in this stage. Convolutional neural network (CNN) is a special version of article neural network (ANN)30 (ReLU) layer. The early work13 has explored the performance of using different number of convolutional kernels, and found that adding more kernels can significantly improve performance. Thus the number of kernels was set to a fixed value 16 in the proposed framework.This layer is used to capture motif features, which can be thought of as a motif scanner to compute a score for all potential motifs, and often followed by a rectified linear unitBoth DeepBind and DeepSea used a global max-pooling layer to pick out the maximum response of the whole sequence, while our deep model uses a max-pooling layer of a certain size  to keep the local best values of the whole sequence.31 is a widely-used regularization technique for reducing overfitting in deep neural networks by preventing complex co-adaptations on data, which randomly sets the outputs of the previous layer to zero with a dropout ratio. The dropout ratio is a hyper-parameter that was investigated by cross-validation in the experiments.Dropout strategy32 is used. A LSTM unit usually consists of a cell, an input gate, a forget gate and an output gate, where the cell remembers values over arbitrary time intervals and the three gates regulate information flows into and out of the cell. In this paper, we did not use a fully-connected layer to follow this layer, as this will result into worse performance. The number of neurons in this layer was set to 32, so the output size of this layer is 64.In order to capture the forward and backward long-term dependencies between the motif features, a bi-directional recurrent layer composed of long short-term memory (LSTM) unitsIn order to get a probability distribution over two labels which separately represent bound or non-bound sequences, a softmax layer is used in this model. It is composed of two neurons, each of which is densely connected with the previous layer and computes a probability.Max function is frequently used as the fusion function in MIL. But Max only focuses on the most informative instance and overlooks other instances that may contain useful information. Therefore WSCNN used three additional fusion methods  to utilize all instances that may contain useful information. However, both Average and Linear Regression take advantage of all information, inevitably containing useless information, and Top-Bottom Instances needs to manually determine the number of the highest and lowest scoring instances. Moreover, how to effectively take advantage of abundant positive instances is also a key point. To solve the above problems, we find a better and more elegant fusion method, named Noisy-and26, which is based on a different assumption that a bag is labeled as positive if the number of positive instances in the bag exceeds a threshold. This method is defined as follows:Pi,j denotes the score of the j-th instance at the i-th bag, and ni denotes the number of instances in the i-th bag, and n instances in the i-th bag. Noisy-and is designed to activate a bag level probability Pi once the mean of the instance level probabilities a is a fixed hyper-parameter that controls the slope of Noisy-and. bi represents an adaptable soft threshold for each class i and needs to be learned during training. \u03c3(a(1\u2009\u2212\u2009bi)) and \u03c3(\u2212abi) are included to normalized Pi to  for bi in  and a\u2009>\u20090.MIL is commonly based on an assumption that a bag is labeled as positive if there is at least one instance that contains TFBS, and is labeled as negative if there are no any instances that contain TFBS. Therefore the Through this stage, the predicted values of all instances in a bag are fused to yield a final prediction (probability) over \u2018bound\u2019 and \u2018non-bound\u2019 labels.k-mer encoding)\u2009\u2192\u2009a convolutional layer\u2009\u2192\u2009a max-pooling layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a bi-directional recurrent layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a softmax layer\u2009\u2192\u2009a fusion layer. A graphical illustration of the proposed framework is shown in Fig.\u00a0In summary, the proposed framework is arranged in this order: data processing . For each public dataset, an average number of ~15000 top ranking sequences were chosen as the positive data where each sequence is composed of 200\u2009bps, and the corresponding negative data was generated by matching the repeat fraction, length and GC content of the positive ones following the work10, DanQ12, and WSCNN20, respectively.To better evaluate the performance of WSCNNLSTM, we constructed three deep-learning based models, which are similar to DeepBindModel 1: This model is a single-instance learning (SIL) based method, and has the similar architecture to DeepBind. It is arranged in this order: data processing (one-hot encoding)\u2009\u2192\u2009a convolutional layer\u2009\u2192\u2009a global max-pooling layer\u2009\u2192\u2009a fully connected layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a softmax layer.Model 2: This model is a single-instance learning (SIL) based method, and has the similar architecture to DanQ. It is arranged in this order: data processing (one-hot encoding)\u2009\u2192\u2009a convolutional layer\u2009\u2192\u2009a max-pooling layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a bi-directional recurrent layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a softmax layer.Model 3: This model is a multiple-instance learning (MIL) based method, and has the similar architecture to WSCNN. It is arranged in this order: data processing (segmentation\u2009+\u2009one-hot encoding)\u2009\u2192\u2009a convolutional layer\u2009\u2192\u2009a global max-pooling layer\u2009\u2192\u2009a fully connected layer\u2009\u2192\u2009a dropout layer\u2009\u2192\u2009a softmax layer\u2009\u2192\u2009a fusion layer.46.To comprehensively assess the performance of WSCNNLSTM, we adopted three standard evaluation metrics in this paper, including area under receiver operating characteristic curve (ROC AUC), area under precision-recall curve (PR AUC), and F1-score, which are widely used in machine learning and motif discovery47 and PR AUC two commonly-used metrics in which PR AUC is often used under the situation of imbalanced data. Since PR AUC needs not to consider the number of true negative samples, thus it is less prone to influenced by the class imbalance than the ROC AUC metric is48.ROC AUC49.F1-score is a solid metric to measure the classification performance of the classifier, which simultaneously takes into consideration the precision and the recall when computing the score of a testhttps://github.com/turningpoint1988/WSCNNLSTM. The parameters in the deep-learning based methods were initialized by Glorot uniform initializer50, and optimized by AdaDelta algorithm51 with a mini-batchsize of 300. For some sensitive hyper-parameters , we selected the best configuration using a grid-search strategy. Epochs of training were set to 60, where after each epoch of training, the accuracy of the validation set was assessed and monitored, and the model with the best accuracy in the validation set was saved. The instance length c and segmentation stride s were set to 120 and 10, since WSCNN has stated that the two hyper-parameters has little effect on the main conclusion. The hyper-parameter a in Noisy-and was set to 7.5 following the work26. The hyper-parameter settings of all the deep-learning based methods in this paper are detailed in Table\u00a0We implemented WSCNNLSTM and the competing methods by Keras with the tensorflow backend, which are freely available at: in-vivo ChIP-seq datasets is shown in Fig.\u00a0A comparison of WSCNNLSTM and the competing methods on 50 Figure\u00a0k-mer encoding method can take into consideration the high-order dependencies among nucleotides, which may improve the performance of modeling in-vivo protein-DNA binding. As stated by Zhou et al.24, 2-mer (dinucleotide) and 3-mer (trinucleotide) may contain implicit DNA shape information and partially capture the effect of the DNA shape variation on binding. Moreover, Zhang et al.25 has stated that the number of learnable parameters will grow exponentially with the increase of k. Therefore, in order to make a trade-off between performance and computational complexity, we transformed DNA sequences into matrices that consist of 2-mer or 3-mer by setting k to 2 or 3 in k-mer encoding.Unlike one-hot encoding, the k-mer encoding in the weakly supervised framework, we carried out some comparative experiments on 23 ChIP-seq datasets from the Gm12878 cell line, and the detailed results are shown in Supplementary Tables\u00a0To test the performance of k-mer encoding in WSCNN under the ROC AUC, PR AUC, and F1-score metrics. We can find that the performance of 2-mer and 3-mer encoding is much better than that of one-hot encoding, demonstrating the effectiveness of k-mer encoding for modeling in-vivo protein-DNA binding. Figure\u00a0k-mer encoding in WSCNNLSTM under the ROC AUC, PR AUC, and F1-score metrics. We can also find the same trend that the performance of 2-mer and 3-mer encoding is much better. Figure\u00a0k-mer encoding is superior to one-hot encoding. Moreover, we find that the performance of WSCNN and WSCNNLSTM is improved with the increase of k. We think that the reason of the good performance may lie in: it explicitly considers the high-order dependencies among nucleotides (which contains implicit DNA shape information).Figure\u00a0Max, Linear Regression, Average and Top-Bottom Instances) to fuse the predicted values of all instances in a bag, and then selected the best one as the final prediction. However, Max only focuses on the most informative instance and overlooks other instances that may contain useful information, and both Average and Linear Regression take advantage of all information, inevitably containing useless information, and Top-Bottom Instances needs to manually determine the number of the highest and lowest scoring instances. Moreover, how to effectively take advantage of abundant positive instances is also a key point. Thus we adopt a better and more elegant fusion method, named Noisy-and, in this paper.WSCNN employed four fusion methods (Noisy-and in the weakly supervised framework, we carried out some comparative experiments on 23 ChIP-seq datasets from the Gm12878 cell line, and the detailed results are shown in Supplementary Tables\u00a0To test the performance of Noisy-and and Max, Average in WSCNN under the ROC AUC, PR AUC, and F1-score metrics. We can find that the performance of Noisy-and is much better than that of Max and Average. Figure\u00a0Noisy-and and Max, Average in WSCNNLSTM under the ROC AUC, PR AUC, and F1-score metrics. We find that the performance of Noisy-and is also much better than that of Max and Average. Figure\u00a0Noisy-and that a bag is labeled as positive if the number of positive instances in the bag exceeds a threshold.Figure\u00a0in-vivo protein-DNA binding, but they ignores the long-term dependencies between motifs. Therefore we add a bi-directional recurrent layer after the convolutional layer in the weakly supervised framework, just like DanQ does, to capture the forward and backward long-term dependencies between motifs.Convolutional layers are often used as motif scanners to capture motifs in the task of modeling Figure\u00a0in-vivo protein-DNA binding. The proposed framework contains three stages: data processing, model designing, and results merging, where the first stage contains the segmentation process and k-mer encoding, and the second stage contains a hybrid deep neural network, and the last stage contains the Noisy-and fusion method. The experimental results on in-vivo ChIP-seq datasets show that our proposed framework performs better than the competing methods. In addition, we also explore the performance of the proposed framework when using k-mer encoding and show that the k-mer encoding can significantly improve the performance of modeling in-vivo protein-DNA binding, and demonstrate that the Noisy-and function is a better fusion method in the weakly supervised framework.In this paper, we propose a weakly supervised framework, which combines multiple-instance-learning with a hybrid deep neural network, for modeling k. However, the big k will bring out exponentially growing learnable parameters, and the performance of models may be degenerated when k reaches a certain value. Therefore, we will explore the performance of k-mer encoding with a big k value, and propose a corresponding solution to it in the future works.From the above results, we find that the performance of WSCNN and WSCNNLSTM is improved with the increase of Supplementary Materials"}
+{"text": "Pan paniscus) and chimpanzees (Pan troglodytes). As in most mammals, female bonobos and chimpanzees have longer life expectancy than males.Throughout life, physiological homeostasis is challenged and the capacity to cope with such challenges declines with increasing age. In many species, sex differences exist in life expectancy. Sex-specific differences have been related to extrinsic factors like mate competition and/or intrinsic proximate mechanisms such as hormonal changes. In humans, an intrinsic factor related to aging is soluble alpha klotho (\u03b1-Kl). Both sexes show an age-related decline in \u03b1-Kl, but throughout life women have higher levels than men of the same age. Sex differences in \u03b1-Kl have been linked to a shorter lifespan, as well as to specific morbidity factors such as atherosclerosis and arteries calcifications. In non-human animals, information on \u03b1-Kl levels is rare and restricted to experimental work. Our cross-sectional study is the first on \u03b1-Kl levels in two long-lived species: bonobos  contains supplementary material, which is available to authorized users. Some have suggested that ageing is too complicated for serious scientific study, or that it is like a slow-motion car crash \u2014 everything just gets wrecked\u201d [\u201cwrecked\u201d .Aging is defined as the age-related deterioration in physiological functions necessary for survival and fecundity \u20134. IndivPan paniscus) and chimpanzees (Pan troglodytes) are sister species and share life history traits such as slow maturation, late onset of reproduction [Bonobos  [When trying to explain sex-specific aging patterns, intrinsic markers are of strong interest. Investigating physiological markers that change with age is promising to help explain the sex-specific aging patterns observed in the two IGFBP-3) . This prIGFBP-3) \u201335. In bIGFBP-3) . FurtherMacaca mulatta) [One marker for detecting age-related changes in physiology in humans is soluble alpha klotho (\u03b1-Kl). The Klotho gene was originally described in a mutant mouse strain that could not express klotho . The klomulatta) .The human Klotho gene encodes either a transmembrane protein or a secreted form . The secIn animals, observed sex differences in life expectancy have also been linked to extrinsic factors. For instance, the intensity of male-male competition has a strong impact on sex differences in life expectancy, with males in polygynous societies experiencing a reduced lifespan compared to monogamous species , 60. MalThe aims of this study were to assess (a) if bonobos and chimpanzees experience an age-related decline in \u03b1-Kl levels, and (b) if \u03b1-Kl levels are associated with sex differences in life expectancy. We hypothesized that \u03b1-Kl levels would be lower in older individuals in comparison with younger ones, and lower in males compared with females. In case \u03b1-Kl levels reflect trajectories of aging that are due to extrinsic factors such as intensity of intra-sexual competition , we hypoP <\u20090.001). However, a likelihood ratio test revealed that the three-way interaction of sex, species, and age was not significant . We ran a reduced model, excluding the three-way interaction, while including all two-way interactions  and the random effects. In this reduced model none of the two-way interactions were significant . Further reducing the model revealed that the interactions of sex and age at sampling as well as species with age at sampling dropped out non-significant, while age at sampling remained as a main effect. This final reduced all-age-model revealed that with increasing age, \u03b1-Kl levels decreased significantly (Table We ran a linear mixed model (LMM ) to examN\u2009=\u2009140, rho\u2009=\u2009\u2212\u20090.632, p\u2009<\u2009\u00a00.001).We correlated age at sampling time with \u03b1-Kl levels in chimpanzees and bonobos. A Spearman correlation of rank showed a significant negative correlation of \u03b1-Kl levels with age (P\u2009<\u2009\u00a00.001), indicating that the test predictors age, sex, and species significantly influenced \u03b1-Kl levels in bonobos and chimpanzees older than 15\u00a0years. In this adults-only-model, the likelihood ratio test revealed that the three-way interaction of age, sex, and species was not significant . We ran a reduced adults-only-model with all two-way interactions  and random effects. As in the all-age-model, no two-way interaction including age at sampling was significant . However, the interaction of species and sex showed a significant effect on \u03b1-Kl levels , indicating that \u03b1-Kl levels differ between the two species and in a sex-specific way. Therefore, interactions with age at sampling day were removed, but the interaction of sex*species as well as age at sampling day as a main effect were kept in the second reduced adults-only-model. The results of the final reduced adults-only-model (including age at sampling and the sex*species interaction) revealed that also in adult individuals, \u03b1-Kl levels decline significantly with increasing age, and that males and females show significant differences in \u03b1-Kl patterns within a species (Table In a second LMM we investigated sex and species differences in \u03b1-Kl levels during adulthood (adults-only-model). In the adults-only-model, the full model was significantly different from the null model   . One possible explanation is that our sample pool included individuals from all ages whereas measures obtained for human studies are restricted to specific age categories, namely either children [As in humans, \u03b1-Kl levels of bonobos and chimpanzees decreased significantly with age , 75\u201377, \u2009\u2212\u20090.255 ) in humachildren , adults children , or oldechildren . AnotherBased on data from human studies , 76, 78,Pan species are explained by sex-specific exposure to stressors in relation to their social system? Prather et al. [One compelling question that our results raise is whether the differences in \u03b1-Kl levels between the sexes of the two r et al.  exploredr et al. ; cortisor et al. , 80, it r et al.  had alsor et al. . If the r et al. \u201383. Furtr et al. , 85. In r et al. , 87. Ther et al. , and aggr et al. . In addir et al. . Howeverr et al. , howeverr et al. \u201396. To wIn bonobos and chimpanzees, \u03b1-Kl levels decline with age suggesting that potential may arise from this marker for studying the process of aging on an individual, population, species, and on a comparative level. Bonobo females have higher \u03b1-Kl levels in comparison to males, which correspond to sex differences in life expectancy and mirrors sex differences found in humans. In chimpanzees, males have higher \u03b1-Kl levels than females posing a mismatch with sex differences in life expectancy. The observed sex differences \u03b1-Kl levels correspond with inter-sexual dominance relations of the two species and we cannot exclude that social stress and related cortisol levels affect \u03b1-Kl levels. Thus, considering interactions between \u03b1-Kl and other hormones, like glucocorticoids and AVP, potentially helps to explain species differences in \u03b1-Kl levels and how this relates to life expectancy and physiological aging.ad libitum access to fresh water, and food was offered at least three times a day and consisted mainly of a mixture of fruits and vegetables. All subjects had access to indoor and outdoor enclosures.We measured soluble \u03b1-Kl levels in 140 serum samples of 63 bonobos  and 77 chimpanzees  from 16 zoos  and 3 to 49\u00a0years for chimpanzees (average age 22.9\u00a0years). For 54 (86%) of the 63 bonobos, the exact birthdates were known; exact birthdates were available for 63 (82%) of the chimpanzees. For one male and two female chimpanzees for whom only the year and month of birth were known, we set the day of birth to the 15th of the respective month. For nine bonobos  and eleven chimpanzees , exact age was not known and the day of birth was set optionally to June 15th of the estimated year of birth. Individuals for whom the age was estimated were mainly older and therefore the relative error of estimated age was relatively small.For the analyses of \u03b1-Kl levels during adulthood, we created a subset with samples of individuals older than 15\u00a0years of age , 98. ThiN\u2009=\u20093), and the intra-assay coefficient of variation was 3.2%. Based on these results, the ELISA was considered to be appropriate for measuring \u03b1-Kl in serum samples of bonobos and chimpanzees. Two and more freezing cycles changed measured \u03b1-Kl levels by around 10% . The assay was originally developed for the measurement of soluble \u03b1-Kl in human serum and EDTA (Ethylenediaminetetraacetic acid)-plasma samples. Before we used the ELISA for routine measurements, we tested for parallelism of diluted pool serum samples for each species separately. Pooled samples consisted of one female and one male sample of each species. Serially diluted pooled samples were found to parallel the standard curve , one toIn the all-age-model investigating \u03b1-Kl levels during lifetime, the response variable, \u03b1-Kl, was log-transformed to approximate a normal distribution. The model included a three-way interaction of age (z-transformed), sex, and species (both dummy coded), as well as relevant random effects (see below). The three-way interaction was included in the all-age full model as mortality and life expectancy was expected to differ between sexes and species, and \u03b1-Kl is associated with human aging syndromes. We predicted that \u03b1-Kl levels decline with age in both species but at different times, or, depending on sex, with different steepness, leading to species-specific patterns that vary between the sexes. We included random intercepts for zoo-ID, to account for a possible influence of relevant animal husbandry conditions, and for subject, as eight individuals were included twice in the data set. There was considerable variation in terms of demography of ape groups across different zoo facilities; therefore, we included random slopes for age in zoo-ID.Model assumptions  were assessed by visual inspections of a histogram, a q\u2013q plot of the residuals, and by plotting residuals against fitted values. All model assumptions were met. We examined Variance Inflation Factors (VIF ) using tP\u2009=\u20090.05.To investigate the significance of the predictors age, species, and sex and their interactions, we compared the full model with a null model including only the random effects using a likelihood ratio test"}
+{"text": "Minimum Vertex Cover andMaximum Clique. Finally, we use the conceptof well-structured modulators to develop an algorithmic meta-theorem for decidingproblems expressible in monadic second order logic, and prove that this result istight in the sense that it cannot be generalized to LinEMSO problems.A modulator in a graph is a vertex set whose deletion places theconsidered graph into some specified graph class. The cardinality of a modulator tovarious graph classes has long been used as a structural parameter which can beexploited to obtain fixed-parameter algorithms for a range of hard problems. Here weinvestigate what happens when a graph contains a modulator which is large but\u201cwell-structured\u201d (in the sense of having bounded rank-width). Can such modulatorsstill be exploited to obtain efficient algorithms? And is it even possible to findsuch modulators efficiently? We first show that the parameters derived from suchwell-structured modulators are more powerful for fixed-parameter algorithms than thecardinality of modulators and rank-width itself. Then, we develop a fixed-parameteralgorithm for finding such well-structured modulators to every graph class which canbe characterized by a finite set of forbidden induced subgraphs. We proceed byshowing how well-structured modulators can be used to obtain efficient parameterizedalgorithms for  Theparameterized complexity ,34 paraA:Width measures Treewidth has become anextremely successful structural parameter with a wide range of applicationsin many fields of computer science. However, treewidth is not suitable foruse in dense graphs. This led to the development of algorithms that use theparameter clique-width  to denote the setA, then for a.The set of natural numbers  will bedenoted by internal nodes. If S is a set of leaves of a tree T,then T(S)denotes the smallest connected subtree spanning S.We will use standard graph theoretic terminology and notation (cf.). All grN(A) the set of neighbors of A in A contains a singlevertex v, we use N(v) instead of V and E as shorthand for V(G) and E(G), respectively, when thegraph is clear from context. Two vertex sets A,\u00a0B are overlapping if Gobtained by deleting\u00a0A.Given a graph modulator tohereditary if it is closed under vertex deletion. A graph H is an inducedsubgraph of G if H can be obtained by deleting vertices  from G. ForG[A] to denote the subgraph of G obtained by deleting free graphs is the class ofall graphs which do not contain any graph in obstructions, and we saythat the class of characterizedbyGiven a graph parameterizedproblemx the main part andk the parameter.We refer the reader to the standard textbooks , 16, 34 fixed-parameter tractable(FPT in short) if a given instance  can be solved in timef is an arbitrarycomputable function of k. Algorithms withrunning time in this form are called fixed-parameteralgorithms, and we also slightly abuse notaton and refer to thisruntime simply as FPT time.A parameterized problem paraNP-hard if theunparameterized problem corresponding to the restriction of Minimum Vertex Coverproblem parameterized by the degree of a graph is paraNP-hard, since Minimum Vertex Cover remains NP-hard even on graphsof degree at most 3.A parameterized problem The notions and terminology introduced in this subsection play animportant role in particular when formally defining our parametersSect.\u00a0 and for split of a connected graphV such that every vertexof frontiers of thesplit.A non-trivial if both sides have at least two vertices. A connectedgraph which does not contain a non-trivial split is called prime. A bipartition is trivialif one of its parts is the empty set or a singleton. Cliques and stars are calleddegenerate graphs; notice that everynon-trivial bipartition of their vertices is a split.A split is said to be split-modules instead of splits wheresuitable. A set split-module ofG if there exists a connected componentG such thatA is asplit-module then A can be partitioned intoV andadjacent if there existx and y are adjacent.Let Our algorithms for computing well-structured modulators will relyon two deep results related to splits, specifically Theorems\u00a0graph-labeled tree (which canbe viewed as a more modern approach to the previously used split-decompositions) is a pair T is a tree andu of T is labeled by a graph T incident to u andvertices of G(u). When clear from the context, we may use u as a shorthand for V(u) to denote V(G(u)) and we say that an edge of T incident to u is incident to the vertex of G(u) mapped to it. Graph-labeledtrees were introduced by Gioan and Paul ) bipartiteadjacency matrixRank-width was introduced by Oum and Seymour  and is cG andG. Thecut-rank function G is defined asfollows: For a bipartition  of the vertex set\u00a0X can be seen as a subgraph such thatFor a graph rank-decomposition of a graphG is a pair T is a tree of maximumdegree 3 and e of\u00a0T, the connected componentsof X,\u00a0Y) of the set of leavesof\u00a0T. The width of an edge e of arank-decomposition width of T. The rank-width of G,\u00a0rw(G) in short, is the minimum width over allrank-decompositions of G. A graph classunbounded rank-width iffor each A An example of a rank-decomposition is provided in Fig.\u00a0n-vertex graphG, we can output a rank-decomposition ofwidth at most k or confirm that therank-width of G is larger than k in time f is a computablefunction. Let\\doHere we introduce monadic second order logic, which will play acrucial role in our positive Sect.\u00a0 aswell x,\u00a0y,\u00a0z, and aninfinite supply of set variables, denoted by uppercase letters X,\u00a0Y,\u00a0Z. Formulas ofmonadic second-order logic (MSO) areconstructed from atomic formulas E,\u00a0X(x), andE expresses adjacency, X(x) expresses that the vertexx is in the set X. From this, we define the semantics of monadic second-order logicin the standard way  Let q,\u00a0l be non-negative integers.For a graph G and an l-tuple G,we define MSO-q-type of inG.types. Itfollows from Fact\u00a0Since we will only be dealing with MSO logic, throughout the paperwe will refer to MSO-types simply as q and l benon-negative integer constants. Let G be agraph, and let l-tuple of sets ofvertices of G. One can compute a formulal-tuple Let q aR be a system ofrepresentatives of q and l are constant, we can consider both the cardinality of R and the time required to compute it as constants.Let R is a constant, this can be done in time f) as checking whether Gsatisfied q).Let mentclass2pt{miniml-tuple of subsets ofR is a system ofrepresentatives of Let The remainder of the section introduces the classical notion of MSOgames  Let partial isomorphismbetweenandFor every For every In the definition of MSO games given below, we denote theconcatenation of tuple G and k-tuple of subsets ofV(G) andlet k-tuple of subsets ofq be a non-negativeinteger. The q-round MSO game onGandstarting fromPoint move: The Spoiler picks a vertex ineither G or Set move: The Spoiler picks a subset ofV(G) or a subset of Let q-round game, and let q-round game, so that  underT, soG.We define the mapping k. Given a rankdecomposition e ofX,\u00a0Y) of the leaves ofe of T. There is a natural bijection T to theedges of A issplit-module\u00a0either a in A and Bswitching their roles and b taking therole of a.A and Cswitching their roles and c taking therole of a.Since k. We concludethat the width of k and thusWe prove that the width of C, we obtainthe following corollary.By repeating the proof technique of Lemma\u00a0A,\u00a0B pairwise disjoint split-modules such thatLet Let k. LetA,\u00a0B and a,\u00a0b, respectively. Let mentclass2pt{minimThe following lemma in essence shows that the relation of being in asplit-module of small rank-width is transitive (assuming sufficiently highrank-width). The significance of this will become clear later on.G suchthat G andLet G. Let k.Since rank-width is preserved by taking induced subgraphs, the graphsk. We finish the proof by applying Lemma\u00a0A,\u00a0B, and C and a,\u00a0b, and c, respectively. If entclass1pt{minimaG be a graph andV(G) by letting M of G such that G is clear fromcontext.Let Using Lemma\u00a0U of G suchthat For every G be a graph andG, soG such thatG containing u,\u00a0v,\u00a0w. By Lemma\u00a0G) suchthat Let v, and let G) such thatG) andNow let G of rank-width atleast k.Every graph Next, we state a simple but useful observation.G. Then Let Now that we know mentclass2pt{minimn-vertex graphG of rank-width at least v,\u00a0w, we can decide whether f.Let G is connected. By Theorem\u00a0G is the bipartition of leavesof T induced either by removing an internaltree-edge of T or an edge created by anode-split of a degenerate vertex of T.From Observation\u00a0mentclass2pt{minimG are leaves ofT and we can find a path P between v andw in T intime linear in size of T. Since the number ofnodes in a split-decomposition is linear in the number of vertices of the originalgraph  is a completegraph. Our first examples deal with two classical NP-hard graph problems,specifically Establishing the following theorem is the main objective of thissubsection.FPT parameterized byLet G, the \u201conly if\u201ddirection is immediate; in other words, being polynomial-time tractable onSince MinVC ispolynomial-time tractable on a graph class FPT.If k-well-structured modulator Let FPT time . OtherwiG must be a superset of eitheri in signatures. Each vertex cover Yof G can be associated with at least onesignature f, constructed in the followingway: for each Since for each G and a signature f, we construct a partial vertex cover C of C intersects someZ it must hold that Ceither has rank-width at most k (in the casei), or C is in C does not intersectC has bounded rank-width) orthe polynomial algorithm  in the complementgraph.d is exactly theclass of d leaves. The degree bounds the size of a maximum clique, againresulting in a simple folklore branching algorithm. The class of graphsof degree at most k-well-structured modulators to examples of graph classes which arenot characterized by a finite obstruction set . In the following lemmas, ndenotes the size of the vertex set of the input graph.Next, we turn our attention to computing k-well-structured modulator to the class of forests in timef.It is possible to compute a G is at least k-well-structured modulator can be computed using Courcelle\u2019sTheorem in time at most f. V(G) into equivalenceclasses of f, and sets First, it uses Proposition\u00a0X,\u00a0Y,\u00a0Z) of equivalence classes of S, and restarts the second step withSecond, for each tuple  . If nosIt is easy to verify that the running time of f. As for correctness, let us assume for a contradiction thatH obtainedfrom G after deleting all vertices inelements of C.Clearly, neither C nor any other cycle inH intersects less than 4 equivalenceclasses of We begin by describing our algorithm X of C spans at least 4equivalence classes, H must contain at leasttwo neighbors of X in X ; let us denote these vertices X,the vertices Hwhich spans at most 3 equivalence classes, contradicting our previous conclusionthat no such cycles are present in H. Hencewe may conclude that X.Moreover, assume C intersects each equivalence class at most once. Butthen it must be the case that C also forms acycle in H mustindeed be acyclic.The only case we are left with now is that G contains a minimal k-well-structured modulator G after deleting j.For the other direction, assume that chordless if it is also an induced cycle of length atleast 4, and a graph is chordal if it containsno chordless cycles.For the next result, recall that a cycle is k-well-structured modulator to the class of chordal graphs in timeIt is possible to compute a G is at least k-well-structured modulator can be computed using Courcelle\u2019sTheorem in time at most f. V(G) into equivalenceclasses of First, it uses Proposition\u00a0X,\u00a0Y,\u00a0Z) of equivalence classes of S, and restarts the second step withSecond, for each tuple  Let q and k be non-negative integers,Gand k-well-structured modulators q-similar if all of the following conditions are met:There exists an isomorphism v isadjacent to For every If For each q and k be non-negative integers, Gand k-well-structured modulators q-similar, then it holds that Let q-round MSO gameplayed on W and assume without loss of generality that Suppose Spoiler makes a set move s and again assume without loss of generality thatSuppose Spoiler makes a point move Assume Duplicator plays according to this strategy and consider aplay of the q-round MSO game on G and V(G) and V(G) and Let Let Let G. Fromthe correctness of G.In the first case we have Let Let Let For Next, we show that small representatives can be computedefficiently.f,\u00a0g such that one can compute,for an input graph G of rank-width at mostk and Let T of intime T. By Fact\u00a0q-types isfinite for each q, so we can think of the totalnumber of checks and the size of each checked graph T and the size of the graphBy Lemma\u00a0mentclass2pt{minimFinally, in Lemma\u00a0q be a non-negative integerconstant and G and a k-well-structuredmodulator G into fsuch that one can in time k-well-structuredmodulator q-similar and for eachLet q-type asf. Now letWe construct a disjoint union of G, weadd edges between every If v and every for every It is easy to verify that q-similar.For G be a graph,q be the nesting depth ofquantifiers in k-well-structured modulatorto G andq-similar, it followsfrom Lemma\u00a0Let For completeness, we remark that the same proof can be used toobtain analogues of Theorem\u00a0mentclasspt{minimac-Coloring asks whether thevertices of an input graph G can be colored byc colors so that each pair of neighbors havedistinct colors. From the connection between c-Coloring, its generalizationList c-Coloring and modulators [List c-Coloring [We conclude the section by showcasing an example application ofTheorem\u00a0Coloring , Page 5,Coloring parameterized byFPT.For each Instance: A graph G and an integer\u00a0Question: Is there a set We say that dominating set if everyvertex in G either is in S or has a neighbor in S. We willneed the following lemma before we proceed to the main result of this secton.In the wake of Theorem\u00a0p-cardinality dominating set in a graph G having a k-cardinalitymodulator The problem of finding a D. We branch over the at most q in q to D. If G, we discard the current branch; hence this procedureproduces a total of at most Let X. For P of all such chosen representatives. We thenbranch over all subsets Q of Q into D. Since D is a dominating set, and output the minimum dominating setobtained in this manner.Now consider a branch where p, then thealgorithm will find such a set. So, assume there exists a p-cardinality dominating set G. Consider the brancharising from the first branching rule obtained as follows. Let L chosen by the algorithm, and consider the branch where anarbitrary D. Hence,after the first branching, there is a branch where i-th step ofthe first branching. If P. SinceLand X as G. Furthermore, It is easily observed from the description that the running timeis FPT. For correctness, from the final check it follows that any set outputed bythe algorithm will be a dominating set. It remains to show that if there exists adominating set of cardinality\u00a0FPT parameterized byparaNP-hard parameterizedby There exists an MSO formula dom(S)express that S is a dominating set in\u00a0G, and let cyc(S) express that S intersects every To prove Theorem\u00a0k be the cardinality of amodulator in G to k in G to G. Letr andk, and if G must intersect X and hence setting To argue that the above claim holds, let A of cardinality at most r whichintersects every B in G of cardinality at most r; this can also be done in FPT time by Lemma\u00a0So, assume A or B exists, then we output YES and otherwise we output NO.Hence the claim is indeed true.Finally, if Dominating Set problem, which takesas input a graph G and an integer j and asks to find a dominating set of size at mostj, is NP-hard on G,\u00a0j) be aDominatingSet of degree at most 3. Then we construct G by addingq adjacent toevery vertex of every such q and an arbitraryvertex of G. It is easy to check thatWe proceed by arguing that this claim is also correct. It is knownthat the t most 3   is a YES-instance of Dominating Set if and only if D in G ofcardinality j. Then the set We claim that  is a YES-instance of Dominating Set, so assume this is not the case. But thenG is also a dominating setof j in V(G). Consequently,  is a YES-instance of Dominating Set and the claim holds.On the other hand, assume there exists a set The theorem now follows from the two claims provedabove.Minimum VertexCover and Maximum Clique(Theorem\u00a0We have introduced a family of structural parameters which push thefrontiers of fixed-parameter tractability beyond rank-width and modulator size for awide range of problems. In particular, the well-structure number can be computedefficiently Theorem\u00a0 and usedTheorem\u00a0 as well Theorem\u00a0. We remaX can be seen as asubgraph such that For future work, it would be interesting to see whether the notionof split-modules introduced in this work can be naturally generalized. Inparticular, a split-module kernelization [Finally, we remark that well-structured modulators have also foundapplications in the area of data reduction and lization . Inpartconstant ."}
+{"text": "In this paper, we mainly consider the stochastic second-order cone complementarity problem (SSOCCP). Due to the existence of stochastic variable, the SSOCCP may have no solutions. In order to deal with this problem, we first regard the merit function of the stochastic second-order cone complementarity problem as the loss function and then present a low-risk deterministic model that is a conditional value-at-risk (CVaR) model. However, there may be two difficulties for solving the CVaR model directly: One is that the objective function is a non-smoothing function. The other is that the objective function contains expectation.  In view of these two problems, we present the approximation problems of the model by using a smoothing method and a sample average approximation technique. Furthermore, we give the convergence results of global optimal solutions and the convergence results of stationary points of the approximation problems, respectively. The second-order cone in Second-order cone complementarity problem (SOCCP) is as follows: Find a vector The KKT condition of second-order cone programming (SOCP) problem can be equivalent to a second-order cone complementarity problem. So, many researchers pay attention to considering SOCCP.x. \u201ca.s.\u201d is the abbreviation of \u201calmost surely\u201d. Because of the existence of stochastic factor \u03c9, generally there is no vector x satisfying  second-order cone complementarity function, that is, . And by ,2.1\\docIn this paper, we consider a Fischer\u2013Burimister(FB) second-order cone complementarity function, taking advantage of the knowledge about Jordan algebra, If the mapping In fact, we have Let \u03c4-Based on the definition of ction in , we pres\u03c4-A function \u03c4-A function \u03c4-equi-coerciveness.Similar to the definition of equi-coerciveness in  , we giv\u03c4-equi-coercive on A function x and a parameter u, its probability is defined as\u03c9. For a given confidence level \u03b1, the definition of x is given as follows:Before giving a CVaR model, we give the definition of Value-at-Risk (VaR). For a variable ferences , 18, Roc\u03b1, CVaR is defined as the conditional expectation of the loss associated with x relative to that loss being E denotes mathematics expectation. From references . From , 5.11),,\\documenx, we get that Next, we will prove that }\u03bc\u22600, by , we know. Taking  into accx, we obtain that Noting that \u03a9 is a compact set and In this paper, we consider a stochastic second-order cone complementarity problem. The boundedness of level sets of  problem  are boun, SSOCCP  may have"}