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<|MaskedSetence|> Convolutional neural networks (CNNs) are a class of deep neural networks characterized by a shared-weight architecture of convolution kernels (or filters) that slide along input features and provide translation equivariant features known as feature maps. One of the main advantages of CNNs is that the network learns to optimize the filters through automated learning, requiring very little pre-processing compared to other machine learning techniques. Since their introduction in the 1990’s [4], CNNs have shown excellent performances in the most challenging visual classification tasks and are currently dominating this research field [5]. When applied to medical imaging, CNNs demonstrated excellent performance and have been successfully used for the identification of retinal diseases from fundus images [6, 7, 8], tuberculosis from chest radiography images [9, 10] and malignant melanoma from skin images [11]. <|MaskedSetence|> In this study, I use a dataset of more than 300,000 lymph node images derived from CAMELYON, known as the PCAM (Patch CAMELYON) dataset [13] and the IDC dataset, composed of more than 220,000 images derived from whole slide images of invasive ductal carcinoma tissue [14, 15], one of the most common forms of breast cancer. <|MaskedSetence|>
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**A**: I used these datasets to characterize and analyze the performance of different CNNs network architectures and GPU accelerators, using a standard, off–the–shelf, deep learning computational library.
Material and methods
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**B**: CNNs have also been used for the detection of lymph node metastases in women with breast cancer in an algorithm competition known as CAMELYON16 (Cancer Metastases in Lymph Nodes Challenge), with the best models showing equal or slightly better performances than a panel of pathologists [12].
**C**: Recently, deep learning algorithms have made major advances in solving problems that have resisted the machine learning and artificial intelligence community such as speech recognition, the activity of potential drug molecules, brain circuits reconstruction and the prediction of the effects of non-coding RNA mutation on gene expression and disease [3].
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While single jumps across a fitness valley can be regarded as metastable transitions, the limiting jump chain can be related to the concept of adaptive walks or flights. Those are stochastic processes that directly study the motion of the macroscopic population on the trait space, focussing on successful invasions and omitting the microscopic dynamics (see [27] for an overview). <|MaskedSetence|> Based on these, properties of interest are the distribution and accessibility of fitness maxima [35, 32, 3, 4], as well as the time or path length to reach those maxima [33]. <|MaskedSetence|> <|MaskedSetence|>
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**A**: In adaptive flights, transitions are not just possible between neighbouring traits but from one local fitness maximum to another [23, 24, 22, 30].
**B**: This relates back to the limiting processes derived in this paper, where the population jumps between equilibrium states that are surrounded by valleys of traits of lower fitness.
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**C**: There are two sources of randomness in adaptive walks: A random fitness landscape and a random motion towards neighbours of higher fitness, according to some transition law.
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The subsequent sections of the paper unfold as follows: Section 2: Model formulation- In this section, we meticulously detail the formulation of the model, providing a comprehensive overview of its deterministic aspects. <|MaskedSetence|> <|MaskedSetence|> Section 5: Numerical experiments- this section is dedicated to presenting the numerical solutions derived for the proposed model. Through numerical simulations, we offer insights into the practical implications and outcomes of the model. Section 6: Conclusion - we present the conclusive remarks and findings of the entire paper. <|MaskedSetence|>
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**A**: This section serves to summarize key results, implications, and potential avenues for future research.
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**B**: Section 3: Dynamics of the deterministic model- we discuss the reproduction number and stability of the system.
**C**: Section 4: Formulation and description of stochastic COVID-19 model- we explore and elucidate the dynamic properties and behaviors inherent in the stochastic aspects of the model.
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<|MaskedSetence|> Although numerous studies report high heritability for anatomical features such as gray matter density, there are few rs-fMRI studies reporting heritability of rs-fMRI (Glahn et al., 2010; Korgaonkar et al., 2014). <|MaskedSetence|> <|MaskedSetence|> (Korgaonkar et al., 2014) reported HI of 0.41 in the connection between the posterior cingulate cortex and right inferior parietal cortex in the default mode network involving 79 MZ- and 46 same-sex DZ-twins. Other connections are all reporting very low HI below 0.24. We believe our topological method is clustering topologically similar functional network patterns and significantly boost genetic signals.
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**A**: (Glahn et al., 2010) reported HI of 0.104 in the left cerebellum, 0.304 in the right cerebellum, 0.331 in the left temporal parietal region, 0.420 in the right temporal parietal region.
**B**: We reported 10 connections that give the highest HI values in all three states in Tables 3, 3 and 3.
**C**: Most of these studies report low HI compared to our high HI.
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System (50) with its initial and boundary conditions is also interesting from a mathematical viewpoint: it describes a novel sort of taxis cascade, in which tumor cells are chemotactically following ECs, which in turn bias their motion towards gradients of a chemical signal (VEGF) produced by tumor cells and depleted by themselves. The global well-posedness of a system featuring this complexity has not been investigated and raises manifold challenges, due to the intricate couplings and nonlinearities involved in the source and motility terms. The passage from KTEs to the macroscopic dynamics has been done here in a merely formal way, the rigorous convergence is still open and might probably use some of the ideas in [55], where a much simpler system has been considered.
In [31] we commented about the feasibility of using such multiscale models to predict tumor spread and establish CTV and PTV margins for treatment planning. Those observations still apply here - the main issue remains the relatively large number of parameters and therewith related uncertainties. <|MaskedSetence|> <|MaskedSetence|> In fact, chemo- and radiotherapy primarily act on the level of single cells and ultimately lead to the observed effects on the whole tumor and this mathematical approach allows us to account for dynamics on both levels in a reasonably detailed manner. Our numerical experiments also suggest that letting the clinical studies have a longer follow-up might provide useful information about the tumor behavior after ceasing the actual therapy. <|MaskedSetence|> Mathematical models could help in identifying the adequate duration of such studies. Moreover, they have the potential to investigate a great variety of therapeutic scenarios (of which we showed here just a few examples) in an unprecedented complexity and accuracy - provided the necessary quantitative information becomes available. Intra- and interdisciplinary studies including such models are called upon to shed light on the intricate biological processes associated with tumor growth, expansion, and treatment response..
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**A**: However, the increasingly fast development of biomedical imaging, computing power, and technology for necessary cell biology experiments will provide a means to assess at least some of the missing quantitative information.
**B**: On the other hand, such multiscale models seem to offer an adequate frame for studying the effects of various therapy ansatzes.
**C**: That would presumably lead to higher costs, but these might be justified by the achieved understanding.
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Our analyses leverage brain images sourced from academic publications and the open-access website www.brainmuseum.org. The calculated gyral sizes across species are visually represented in Fig. 12 and enumerated in Tables 1, 2, and 3. Note that our data are sample-based. <|MaskedSetence|> The limitations imposed by the number of available samples prevent us from providing an accurate analysis for each individual species. <|MaskedSetence|> <|MaskedSetence|> We predominantly employed computational methods (as shown in Fig. 2), reverting to width characterization (as illustrated in Fig. 1) when limitations necessitated it.
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**A**: Additionally, factors such as image quality and scale bar size could affect the accuracy of measurements.
**B**: Instead, we focus on discerning patterns between gyral size and other factors across multiple species.
**C**: Specifically, when more than one sample is available for the same species, each sample is measured and presented independently.
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<|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> We initially selected random hyperparameter values for the training of each model on a random fold (out of 5555 folds). Subsequently, we repeated the training of each model on all 5555 folds based on the best-performing hyperparameters of the initial random fold. Finally, the trained models (on all 5555 folds) were tested on the corresponding test split.
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**A**: Additionally, 10%percent1010\%10 % of the training partition of each fold was reserved for validation and hyperparameter tuning.
**B**:
In the model training process, we adopted a Stratified 5-Folds cross-validation strategy.
**C**: This method ensures that the test split maintains a balanced representation of samples for each class, preserving the proportionality of class distributions in each train-test split.
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<|MaskedSetence|> Hodge theory provides a unified framework combining simplicial homology and spectral geometry, offering insights into network topology [9, 10, 11]. <|MaskedSetence|> Hodge decomposition breaks data defined on edges (edge flow) into three orthogonal components: gradient, curl, and harmonic flows, each providing unique topological insights. <|MaskedSetence|> The curl flow, arising from triangle-induced flows, captures rotational patterns, while the harmonic flow exposes loop structures and topological signatures [10]. Using a Wasserstein distance-based statistical approach on each component, this study assesses the topological similarities and differences between loop and non-loop flows. Further, leveraging on the properties of the decomposed networks, the study seeks to elucidate the most discriminating topological disparities in female and male functional brain networks.
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**A**: The gradient flow, driven by node gradients, represents the network’s gradient-like behavior.
**B**: While the Hodge Laplacian, a generalization of the graph Laplacian, offers insights into the topological features of higher order simplices, the Hodge decomposition allows to establish relationships between simplices of different dimensions [10].
**C**:
PH quantifies multiscale topological features of data through a filtration process [8].
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Fig. 4: Interpretability and visualization of FACL. Randomized selections of WSIs from external datasets, DiagSet-A and QHD, are arranged in the first and second rows, respectively. The sequence progresses from left to right, showcasing the complete WSI, followed by its heatmap, a close-up of a local patch, and finally the heatmap of the patch. <|MaskedSetence|> <|MaskedSetence|> The average Kappa across the six centers (Hebei-1, Hebe-2, PANDA-1-1, PANDA-1-2, PANDA-2-1, and PANDA-2-2) was 0.7379, whereas FACL achieved a Kappa of 0.8463. This highlights the effectiveness of federated learning for prostate cancer diagnosis across multiple categories. <|MaskedSetence|> The Kappa scores for the FACL surpassed those for the FedAvg, and the FACL-N𝑁Nitalic_N outperformed the FedAvg-N𝑁Nitalic_N. This underscores the efficacy of the proposed attention-consistent learning method.
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**A**: The zoomed-in view of the local patch image indicates our model’s precise identification and representation of cancerous regions.
The validation results for the Gleason scoring task are listed in Table 7.
**B**: Compared to models trained on single-center data, the FACL model exhibited significant improvements in the Kappa score and AUC.
**C**: Notably, the proposed FACL model consistently outperformed the FedAvg model in terms of the Kappa score, regardless of the addition of noise (N𝑁Nitalic_N).
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Beyond, the recent use of SBs has been motivated by an important task in molecular biology: Cells change their molecular profile throughout developmental processes (Schiebinger et al., 2019; Bunne et al., 2022b) or in response to perturbations such as cancer drugs (Lotfollahi et al., 2019; Bunne et al., 2021). <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> Weinreb et al. (2020) capture cell differentiation processes by clonally connecting cells and their progenitors through barcodes (see illustrative Figure in Supplement).
Motivated by these observations, the goal of this paper is to propose a novel algorithmic framework for solving DSBs with (partially) aligned data. Our approach is in stark contrast to existing works which, due to the lack of data alignment, all rely on some variants of iterative proportional fitting (IPF) (Fortet, 1940; Kullback, 1968) and are thus prone to numerical instability. On the other hand, via a combination of the original theory of Schrödinger bridges (Schrödinger, 1931; Léonard, 2013) and the key notion of Doob’s hℎhitalic_h-transform (Doob, 1984; Rogers and Williams, 2000), we design a novel loss function that completely bypasses the iterative proportional fitting (IPF) procedure and can be trained with much lower variance..
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**A**: (2022b) propose a transcriptome profiling approach that preserves cell viability.
**B**: For example, Chen et al.
**C**: As most measurement technologies are destructive assays, i.e., the same cell cannot be observed twice nor fully profiled over time, these methods aim at reconstructing cell dynamics from unpaired snapshots.
Recent developments in molecular biology, however, aim at overcoming this technological limitation.
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<|MaskedSetence|> We do so for a one-dimensional i-state (i.e., the variable capturing the relevant differences among individuals ‘lives’ on the real line), so for an i-state space that comes equipped with an order relation. In fact we shall assume that the presence of ‘larger’ individuals has a negative impact on the growth rate of ‘smaller’ individuals (as a motivating example one might think of trees and shading, with the i-state interpreted as ‘height’; but please note that we ignore spatial structure and that, consequently, the model is but a caricature).
For the incorporation of space into physiologically structured population models see [27]. For an alternative approach to hierarchically structured models see [25].
The organisation of the paper is as follows. <|MaskedSetence|> <|MaskedSetence|> In Section 3 a dynamical systems framework for the renewal equation is outlined. In Section 4 we give conditions guaranteeing the existence of a non-zero stationary birth rate. In Section 5 we apply the principle of linearised stability for delay equations [11] to prove that, for a certain two-parameter family of fertility functions, such a stationary birth rate (whenever it exists) is locally asymptotically stable. We also show that, under natural hypotheses on the ingredients, the zero stationary birth rate is a global attractor when it is the only stationary birth rate..
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**A**: In Section 2 we first present the classic PDE formulation of the model.
**B**: Here our aim is to investigate in the context of a toy model the consequences of density dependence that only affects development directly (fertility is affected indirectly, since it depends on the developmental stage of the individual).
**C**: Then we present biological assumptions underlying the model and deduce a scalar nonlinear renewal equation for the population birth rate (the so called delay formulation).
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8.2 Brain Networks from fMRI Data
Functional MRI is a non invasive technique for collecting data on brain activity that measures the increase in the oxygenation level at some specific brain region, as long as an increase in blood flow occurs, due to some brain activity. The construction of a network from fMRI data requires first the identification of a set of functional vertices, such as spatial regions of interest (ROIs), and then the analysis of connectivity patterns across ROIs. The data set we use for this application comes from a pilot study of the Enhanced Nathan Kline Institute-Rockland Sample project that are time series recorded on 70707070 ROIs at 404404404404 equally spaced time points. <|MaskedSetence|> <|MaskedSetence|> (2021) we apply our method to the residuals estimated from the vector autoregression models, carried out to remove the temporal dependence. <|MaskedSetence|> The main difference is that subject 14141414 is 19191919 years old whereas the subject 15151515 is 57575757 years old..
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**A**: Following Ranciati et al.
**B**: We consider two subjects indexed by 14141414 and 15151515, who have the same psychological traits with no neuropsychiatric diseases and right-handedness.
**C**: A detailed description of the project, scopes, and technical aspects can be found at http://fcon_1000.projects.nitrc.org/indi/enhanced/.
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Cardiac MRI scans contain high-dimensional spatial and temporal features generated throughout the cardiac cycle. The small number of samples compared to the high-dimensional features poses a challenge for machine learning classifiers. To address this issue, Multilinear Principal Component Analysis (MPCA) [11] utilizes a tensor-based approach to reduce feature dimensions while preserving the information for each mode, i.e. spatial and temporal information in cardiac MRI. Hence, the MPCA method is well-suited for analyzing cardiac MRI scans. <|MaskedSetence|> Existing MPCA-based pipelines for cardiac MRI [17, 18, 2] rely on manually labeled landmarks that are used for aligning heart regions in cardiac MRI. The manual labeling of landmarks is a cumbersome task for physicians and impractical for analyzing large cohorts. Moreover, even small deviations in the landmark placement may significantly impact the classification performance of automatic pipelines [16]. <|MaskedSetence|> We also extract complementary information from multimodal data from short-axis, four-chamber, and Cardiac Measurements (CM). <|MaskedSetence|>
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**A**: We use CM features (i.e., left atrial volume and left ventricular mass) identified in the baseline work by Garg et al. [5] for PAWP prediction.
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**B**: To tackle this challenge, we leverage automated landmarks with uncertainty quantification [15] in our pipeline.
**C**: The application of the MPCA method to predict PAWP might further increase the diagnostic yield of cardiac MRI in heart failure patients and help to establish cardiac MRI as a non-invasive alternative to RHC.
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<|MaskedSetence|> <|MaskedSetence|> This yields significantly worse performance −6.9%percent6.9-6.9\%- 6.9 %. We hypothesize that the “true full attention” has low-entropy, making it more challenging to be approximated by low-rank methods [8], and that sparse attention patterns offer better approximations.
Figure 3: Multi-level interpretability visualization in a breast cancer patient. Top: Low-risk patient. Bottom: High-risk patient. Genes and pathways in red increase risk, and those in blue decrease risk. Heatmap colors indicate importance, with red indicating high importance and blue indicating low importance. The pathways and morphologies identified as important in these cases generally correspond well with patterns that have been previously described in invasive breast cancer (e.g. <|MaskedSetence|>
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**A**: Both branches bring complementary information (observed decrease of −5.6%percent5.6-5.6\%- 5.6 % and −7.5%percent7.5-7.5\%- 7.5 % in c-index), justifying the need to model both pathway-to-patch and patch-to-pathways interactions.
**B**: We further adapt SurvPath with Nyström attention that enables training on very long sequences by simplifying self-attention with a low-rank approximation.
**C**: Estrogen Response Late).
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3.6 Non-local feedback to alter system robustness
Another way in which systems can potentially increase their robustness to input noise is through non-local feedback or feedforward loops. <|MaskedSetence|> <|MaskedSetence|> A similar late to early-stage feedback is seen in positive-strand RNA viruses in which newly replicated RNA strands are either encapsidated or reutilised in translation and replication [40]. <|MaskedSetence|> Less concretely, replication of the measles virus comprises several feedback and feedforward mechanisms, particularly during the transition and polymerase stages [43].
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**A**: More generally, positive- and negative-strand RNA viruses have very similar replication structures and an identical feedback mechanism, however are in part distinguished by their feedforward structures [41, 42].
**B**: Hepatitus B, an enveloped DNS virus, recycles new viral DNA that is awaiting repackaging back into the nucleus [38, 39]: analogous, in our simple linear model, to a feedback from the final to an early compartment.
**C**: Such a phenomenon, where progression through the virus life cycle is not unidirectional, is common with evidence in the virus literature: for example, the complex network-like replication cycle seem in the human ademovirus [37].
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II-E Recurrent Neural Networks (RNN)
Elman networks, more commonly known as vanilla recurrent neural networks (RNN), attempt to introduce the concept of a time-dependent dynamic memory [16]. <|MaskedSetence|> Context-based predictions can be done for four input-output schemes: one-to-one, one-to-many, many-to-one, and many-to-many. <|MaskedSetence|> Fig. <|MaskedSetence|>
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**A**: One-to-one models are a variation of a classic neural network, one-to-many models are best for image caption generation, many-to-one models are best for sentiment analysis, and many-to-many models are best for translation or video frame captioning.
**B**: The idea is to make predictions about inputs based on contextual information.
**C**: 1 is an example of the basic structure of a vanilla RNN..
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<|MaskedSetence|> <|MaskedSetence|> Indeed, as we will show in Section I.3, the quenched regime assumes that, before each topology update, the epidemic has almost reached its equilibrium.
In the annealed regime, the epidemic evolves very slowly compared to the network. The epidemic spreads as on an “average” network. <|MaskedSetence|> Additional results in the annealed regime have been derived under the degree-based mean-field theory by Pastor-Satorras and Vespignani [10, 11, 12, 13, 14]..
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**A**: General results for the annealed regime show that the annealed process shares attributes with the static process on the edge-average graph [7, 8, 9].
**B**: Quenched processes are well approximated with processes on static networks and therefore well studied over the last two decades.
**C**:
In the quenched regime, the network changes very slowly compared to the evolution of the epidemic.
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<|MaskedSetence|> <|MaskedSetence|> We explore features of covers arising from networks, and characterise many of the familiar classes in terms of properties of their associated covers. <|MaskedSetence|> Different classes of networks are defined in different ways, and it can be difficult to present a clear hierarchy (there have been several visual attempts, for instance [16, Fig.12] and [11, Fig.6]). Being able to characterise different network classes by the properties of their covers gives a unified framework for defining networks, in the sense that one may add or remove axioms depending on the class of networks one wants to describe. In that sense, moving from one class to another may be just a matter of changing the axioms, providing a potentially useful lens for visualizing the relationships among classes.
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**A**: The class of labellable networks contains many commonly studied classes.
**B**: They have been shown to correspond to a set of covers of finite sets that satisfy a property called “expanding”.
**C**: It is to be hoped that encoding network properties in the properties of sets of sets will enable some new directions to be pursued in studying phylogenetic networks.
This paper aims to demonstrate how this encoding of labellable networks into covers may be of broad use in the classification of network classes.
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The ancestral selection graph is an augmented coalescent model for the joint distribution of the gene genealogy and the allelic states of the sample (Krone and Neuhauser, 1997; Neuhauser and Krone, 1997). It includes the usual coalescent rate 1111 per pair of lineages and mutation rate θ/2𝜃2\theta/2italic_θ / 2 per lineage. Additionally, under the stationary model of Section 1, it includes a branching rate of |α|/2𝛼2\lvert\alpha\rvert/2| italic_α | / 2 per lineage. When a branching event occurs, the lineage splits into an incoming lineage and a continuing lineage. <|MaskedSetence|> The other is virtual, meaning it is there only to model the gene genealogy correctly with selection. Which is which could be resolved if their allelic states were known: the incoming lineage is real if its allelic type is the one favored by selection, otherwise the continuing lineage is real. <|MaskedSetence|> <|MaskedSetence|> This allows a simplification in which there is a reduced rate of branching and only virtual lineages of the disfavored type are produced (Slade, 2000a). A second simplification is possible if mutation is parent-independent: then any lineage which mutates may be discarded (Fearnhead, 2002).
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**A**: In this case it is known which lineages are real and which are virtual.
**B**: One of these is real, meaning it is included in the gene genealogy.
**C**: But the allelic states are not known in the construction of the ancestral selection graph.
The conditional ancestral selection graph models gene genealogies given a sample with allelic states specified (Slade, 2000a, b; Fearnhead, 2001, 2002; Stephens and Donnelly, 2003; Baake and Bialowons, 2008).
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Firstly, the introduction of annealed disorder in the GLV equations, for any finite correlation time, has exerted a substantial positive influence on the biodiversity of the system. Specifically, when the dynamics of the system converge to the stationary distribution, we observe the quasi-cycles of species populations dynamics, where species abundances alternate between high and low values, favoring the coexistence of all species (if we do not artificially introduce any minimal threshold under which we consider the species extinct). <|MaskedSetence|> <|MaskedSetence|> In other words, due to the non-linear nature of the corresponding Fokker-Planck equation and known pathologies in the GLV model (also observed in the quenched case), the dynamics may not converge to the stationary solution, leading to divergent trajectories.
Eventually, we have presented a refinement of the model, through the inclusion of a simple functional response. <|MaskedSetence|> Thus, it enhances the model’s realism and applicability without sacrificing its fundamental characteristics and predictive capabilities..
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**A**: We have shown that it not only maintains the core phenomenology described above, but also rectifies any non-physical divergences.
**B**: Again, similar truncated fat-tailed distribution has been recently shown in the chaotic phase [36] and in the strongly interacting limit [5, 41] of the QGLV with immigration.
We have successfully obtained the phase diagram for the case of annealed white noise (AWN), and numerical simulations for the case J(x)=x𝐽𝑥𝑥J(x)=xitalic_J ( italic_x ) = italic_x have revealed the potential for unbounded growth when the initial conditions possess large values, despite the existence of an analytically stationary solution.
**C**: This is, in fact, a similar outcome to what QGLV models found in the chaotic phase [19, 36] when introducing an immigration rate λ𝜆\lambdaitalic_λ.
Second, in the white noise limit, the DMFT leads to the stochastic logistic model, a phenomenological model that proved to be consistent with several macro-ecological laws in microbial ecosystems [4, 40].
In particular, the analytical species abundance distribution derived from the DMFT follows the Gamma distribution, a widely utilized probability distribution in macroecology [32, 1].
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1.5 Structure of the paper
The rest of the paper is structured as follows. In Section 2 we construct a system of MTBDPs that can model the properties and interactions between particles we have discussed so far. <|MaskedSetence|> <|MaskedSetence|> In Section 4 we analyze a special case of an MTBDP system numerically. <|MaskedSetence|>
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**A**: Moreover, this section contains our main theoretical results.
**B**: Finally, in Section 5, we discuss our findings, and compare them to other relevant results from the literature..
**C**: Section 3 is dedicated to their proofs.
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Table 2: Test set results for different size variations of Prot2Text. <|MaskedSetence|> <|MaskedSetence|> This configuration demonstrates improved performance compared to the smaller model while still maintaining reasonable computational costs. The inference time is in seconds for text generation of each model on the whole test set. <|MaskedSetence|>
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**A**: Larger models outperform their smaller counterparts across most evaluation metrics, indicating the benefits of employing larger language models in the Prot2Text framework.
**B**: The Prot2TextMEDIUM model, strikes an optimal balance between performance and computational efficiency.
**C**: The inference time here is computed during text generation using two NVIDIA RTX 6000 with 48GB memory in parallel and batch size of four per device..
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From the model-centric perspective, the framework adopted a typical encoder-decoder architecture to extract hierarchical features and integrate them through skip connections. Concretely, SegFormer [48] served as the encoder, while MA-Net [13] was employed as the decoder, utilizing the Mish [34] activation function. The network jointly predicted cell probability maps and regressed cell-wise vertical and horizontal gradient flows, followed by a gradient tracking post-processing to separate touched cells, which was originally proposed in Cellpose [41].
From the data-centric perspective, they tailored two cell-aware augmentations to extensively enrich the diversity of the dataset and combined them with commonly used intensity and spatial augmentation methods to improve model generalization. <|MaskedSetence|> Moreover, a two-phase pre-training and fine-tuning pipeline was used to retrain the knowledge from external datasets, including TissueNet [16], Omnipose [8], Cellpose [41], and LiveCell [2]. Furthermore, to address minor modalities, they were selected through unsupervised clustering with the latent embedding and subsequently over-sampled during training, thereby aiming to enhance the performance of these less-represented modalities.
The model inputs were three-channel images. <|MaskedSetence|> <|MaskedSetence|> During the merging of predictions from these small window patches, an importance map was generated and applied to the predictions, thereby preventing the recognition of the same cells at the patch boundary as multiple cells..
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**A**: The inference process relied on the sliding window strategy, a highly efficient approach for processing whole-slide images.
**B**: The overall loss function was the combination of binary cross-entropy loss and mean-square error loss.
**C**: Specifically, image intensities were randomized in a cell-wise manner and cell boundary pixels were excluded to separate the crowded cells.
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<|MaskedSetence|> For example, a higher-order reduced model is derived using the Haken-Kelso-Bunz (HKB) equation in [36]. <|MaskedSetence|> <|MaskedSetence|> Similarly, there is no restriction to applying our method to questions of coordinated movement, e.g., [25], or studies of coupled population dynamics [39].
Our method may aid in addressing questions of synchrony and phase-locking in general finite populations of coupled oscillators with heterogeneity where order parameters are typically used. For example, the heterogeneous systems and coupling functions considered in [1] can not exhibit synchrony and a “bounded synchronization” measurement [22] is necessary. Our method could provide a far more detailed understanding of the bounded synchronization state alongside other possible phase-locked states. Moreover, similar questions could be asked in much more realistic and complex neurobiological models..
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**A**: The higher-order terms are the lowest-order Fourier terms of our ℋℋ\mathcal{H}caligraphic_H functions, thus the same questions of existence can be answered with our method and further explored with additional Fourier terms and multi-body interactions.
**B**:
Our method is both a generalization of existing methods that consider higher-order phase-isostable interactions and a general framework from which to study higher-order effects.
**C**: Larger networks of the HKB equation that consider interactions well beyond dyadic [74] fit comfortably within the limitations of our method (see Section 6.1 below for details).
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Recently, the cases of non-Gaussian stable noises acting on QIFs started to attract the attention in mathematical neuroscience. <|MaskedSetence|> In this paper, we explore the possibility of the implementation/generalization of the pseudocumulant approach for/to the populations of QIFs subject to δ𝛿\deltaitalic_δ-correlated non-Gaussian noise.
The paper is organized as follows. <|MaskedSetence|> Further, we formulate the fractional Fokker–Planck description for the macroscopic dynamics of the recurrent synaptic network of quadratic integrate-and-fire neurons subject to non-Gaussian noise in Sec. II.3. <|MaskedSetence|> In Sec. IV, the theoretical results for macroscopic states of homogeneous populations of QIFs are reported..
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**A**: In Sec. II.4, we derive the governing equation for the dynamics of the characteristic function of the membrane voltage distribution and present the pseudocumulant formalism.
In Sec. III, for the case of noninteger α𝛼\alphaitalic_α, we construct a first-order perturbation theory for the effect of noise on the characteristic function and derive macroscopic observables: population-mean voltage and firing rate.
**B**: However, currently, this interest is limited to the only exactly solvable case of a Cauchy noise. Pietras-etal-2023 ; Pyragas2-2023 The circular cumulant formalism was found useful for dealing with non-Gaussian noises, Dolmatova-Tyulkina-Goldobin-2023 but specifically for the case of QIFs the more recent formalism of pseudocumulants can be even more promising.
**C**: In Sec. II, we provide mathematical preliminaries: a brief introduction for the α𝛼\alphaitalic_α-stable distributions and δ𝛿\deltaitalic_δ-correlated non-Gaussian noises, the fractional Fokker–Planck equation for additive noise.
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<|MaskedSetence|> <|MaskedSetence|> Prediction forces a network to learn spatial proximity and not merely image similarity. <|MaskedSetence|> While similar scenes might be proximate in space, similar scenes can also be spatially divergent. For example, the virtual environment we constructed has two different ‘forest’ regions that are separated by a lake. Thus, in the two forest environments might generate similar images but are actually each closer to the lake region than to one another (Figure 1(a))..
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**A**: Predictive coding network learns spatial proximity not image similarity
In the previous section, we show that a neural network that performs predictive
coding learns an internal representation of its physical environment within its latent space.
**B**: Here, we demonstrate that the prediction task itself is essential for spatial mapping .
**C**: Many frameworks including principal
components analysis, IsoMap\autocitetenenbaumGlobalGeometricFramework2000, and autoencoder neural networks can collocate images by visual similarity.
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6 Conclusion
Through more careful counting and bounding compared to previous efforts in this area, we showed that rooted balanced species quartets have no anomaly zones. <|MaskedSetence|> The statements of various Propositions also provide a partial ranking of uniformly sampled gene tree topologies, in results somewhat analogous to Allman et al. (2011).Moreover, the rooted caterpillar topology on four leaves has branch length settings, provided the birth rate is sufficiently large. As with the MSC, anomalous gene trees occur when both the interior branch lengths approach 00. It is not clear what maximal branch lengths provide existence of anomaly zones. Because the anomaly zones in Section 5.2 required a much larger birth rate λ𝜆\lambdaitalic_λ than the death rate, we can hypothesize that GDL anomaly zones may exist, but they are fairly remote. The utilized birth and death parameters in the fungal data set of Rasmussen and Kellis (2012) and the simulation study of Yan et al. <|MaskedSetence|> the birth rate is taken to be close if not equal to the death rate. <|MaskedSetence|>
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**A**: So, it might be expected that anomaly zones for the caterpillar tree are not an important confounding factor, given their remoteness..
**B**: We also showed that if anomaly zones exist, we have shown the respective anomalous gene trees must be balanced quartets.
**C**: (2022) are comparable to each other, i.e.
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In brain science, predictive coding is one of the most influential hypothesis that can implement hierarchical information processing [3, 4]. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> Second, this principle shares exactly the same spirit adopted in variational free energy framework [6]. Recently, there appeared
intense interests in studying the biological implementation of this hypothesis [8, 9, 10], in developing algorithmic applications [11, 12, 13], and in studying the trade-off between energy minimization and information robustness in a linear model of lateral predictive coding [14].
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**A**: The framework of predictive coding has several benefits for theoretical research.
**B**: First, the framework can be derived from the first principle that the brain is a biological machine of optimizing neural dynamics and synaptic connections to maximize the evidence of its internal model of the outside world [7].
**C**: The predictive coding derives the neuroplasticity rule based on local error signal [5], whose goal is to minimize the surprise between the prediction and belief of a generative model of the outside world [6].
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<|MaskedSetence|> <|MaskedSetence|> The images were captured using Leica DMi8 microscope (Leica) equipped with 10×/0.32 objective lens. We obtained one whole slide image from each group.
SegmentAnything and post processing. In our research, we utilized the Python API for SegmentAnything and evaluated three pretrained models [4], namely ViT-B, ViT-H, and ViT-L, ultimately selecting the ViT-H model for inference due to its consistent performance across various microscopy analyses. <|MaskedSetence|> 2, which required post-processing to achieve accurate cell identification..
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**A**: Data acquisition.
**B**: Bright-field images used in this paper were obtained under the protocol described in [5].
**C**: However, we encountered challenges with the SegmentAnything-generated masks, as is shown in FIg.
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<|MaskedSetence|> <|MaskedSetence|> In this model the local updating rule of the connection parameters in BNNs turns out to be a zero-order optimization procedure. More precisely, it is shown in [10] that the expected value of the iterates coincides with a modified gradient descent. However, this holds only on average. The noise for such zero-order methods is so high that one can hardly imagine effective learning based on it, see [3, 8, 1]. <|MaskedSetence|>
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**A**: In this seminal study, the author proposes a very persuasive stochastic model for brain-supervised learning
which has a thorough biological foundation in terms of spike-timing-dependent plasticity.
We review and discuss this setup in Section 2.
**B**:
The starting point for the present paper is the recent article [10] just cited.
**C**: The author himself writes in [10, Section 4]: “It remains to reconcile the observed efficiency of learning in biological neural networks with the slow convergence of zero-order methods.”
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Our memristor is inspired and supported by a comprehensive theory directly derived from the underlying physical equations of diffusive and electric continuum ion transport. <|MaskedSetence|> The theory exclusively relies on physical parameters, such as channel dimensions and ion concentrations, and enabled streamlined experimentation by pinpointing the relevant signal timescales, signal voltages, and suitable reservoir computing protocol. Additionally, we identify an inhomogeneous charge density as the key ingredient for iontronic channels to exhibit current rectification (provided they are well-described by slab-averaged PNP equations). Consequently, our theory paves the way for targeted advancements in iontronic circuits and facilitates efficient exploration of their diverse applications.
For future prospects, a next step is the integration of multiple devices, where the flexible fabrication methods do offer a clear path towards circuits that couple multiple channels. Additionally, optimising the device to exhibit strong conductance modulation for lower voltages would be of interest to bring electric potentials found in nature into the scope of possible inputs and reduce the energy consumption for conductance modulation. From a theoretical perspective, the understanding of the (origin of the) inhomogeneous space charge and the surface conductance is still somewhat limited. These contain (physical) parameters that are now partially chosen from a reasonable physical regime to yield good agreement, but do not directly follow from underlying physical equations. <|MaskedSetence|> Lastly, our theoretical model treats the complex porous structure in terms of slab-averages, thereby possibly missing out on detailed features. These constraints of the theoretical model could account for some of the discrepancies between theory and experiment, which is notable in the steady-state current in Fig. 1(b) and the decrease in conductance in Fig. 1(f). <|MaskedSetence|>
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**A**: We also assume that the inhomogeneous ionic space charge distribution is constant, while it might well be voltage-dependent.
**B**: We experimentally quantitatively verified the predictions of our theory on multiple occasions, amongst which the specific and surprising prediction that the memory retention time of the channel depends on the channel diffusion time, despite the channel being constantly voltage-driven.
**C**: For the purposes of this work our current approach is sufficient, however, a more in-depth study could offer a more profound understanding into the interesting features of the channel.
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As mentioned previously, between 2015 and 2016, there was a concerning event in Brazil and Colombia associated with the co-infection of two major viral diseases: Zika and HIV/AIDS brasil2016 ; calvet2016 ; villamil2018 . <|MaskedSetence|> This co-infection not only required costly medical resources but also highlighted the need for further research, extensive surveillance, and implementation of prevention and prompt reaction strategies to mitigate the impact of these two infections rothan2018 .
Due to the absence of temporal records on HIV/ZIKV co-infection to date, it was not possible to estimate the parameters of Model (2.1) in this section. <|MaskedSetence|> When there was insufficient data available, these values were either estimated based on specific assumptions or adapted from research conducted on different regions or diseases. <|MaskedSetence|>
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**A**: The following outlines the main assumptions for extracting these parameter values.
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**B**: However, specific parameter values were derived from available demographic information, previous research on Zika and HIV/AIDS in Colombia and Brazil, and epidemiological assumptions.
**C**: This problem became a complicated public health issue that posed a challenge to the healthcare systems in these countries brasil2016 ; calvet2016 ; villamil2018 .
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II Spiking Neural Network of The Basal Ganglia
We are concerned in spiking neural networks for the BG. In 2001, based on the functional anatomy proposed by Gurney et al. GPR1 , they developed an artificial neural network for the BG GPR2 . Later, in 2006, based on the anatomical and physiological data, Humphries et al. Hump1 in the Gurney group developed a physiological neural model for the BG by employing the leaky integrate-and-fire neuron model with one dynamic variable LIF . But, the effects of dopamine on the BG cells and synaptic currents were not considered there. <|MaskedSetence|> <|MaskedSetence|> In 2017, Fountas and Shanahan CN6 ; CN7 extended the work of Humphries et al. Str2 ; SPN1 to the whole BG (including GP, STN, and SNr in addition to the striatal cells) by employing the Izhikevich neuron model, and studied oscillatory firing behaviors in the BG CN6 ; CN7 where dopamine effects were also considered. Also, in 2015 Mandali et al. Man used the Izhikevich neuron models arranged on a 2D lattice for the BG cells and studied synchrony, exploration, and action selection. Recently, in 2021 Navarro-López et al. CN1 also developed the BG-thalamo-cortical network (where the Izhikevich neuron models were also used), and investigated the BG-thalamo-cortical oscillatory activity. <|MaskedSetence|>
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**A**: In some other spiking neural networks for the BG, instead of the Izhikevich neuron model, the adaptive exponential integrate-and-fire model with two dynamic variables AdEx was used for the BG cells for study of signal enhancement by short-term plasticity CN11 and learning stimulus-action association CN20 .
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**B**: Str2 ; SPN1 by using the Izhikevich neuron models Izhi1 ; Izhi2 ; Izhi3 ; Izhi4 .
**C**: In 2009, such effects of dopamine modulations on the striatal cells (D1 and D2 SPNs and fast-spiking interneurons) and the synaptic currents into the striatal cells were studied intensively by Humphries et al.
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<|MaskedSetence|> MCR and VIC do not account for instability. For example, after computing MCR for 738 bootstrap iterations, we find that the MCR for the LINC00486 gene has overlap with 0 in 96.2%percent96.296.2\%96.2 % of bootstrapped datasets, meaning MCR would not allow us to distinguish whether LINC00486 is important or not 96.2%percent96.296.2\%96.2 % of the time. Without RID, we would not have strong evidence that LINC00486 is necessary for good models. By explicitly accounting for instability, we increase trust in our analyses.
Critically, RID also found very low importance for the majority of variables, allowing researchers to dramatically reduce the number of possible directions for future experiments designed to test a gene’s functional role. <|MaskedSetence|> <|MaskedSetence|>
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**A**: Such experiments are time consuming and cost tens of thousands of dollars per donor, so narrowing possible future directions to a small set of genes is of the utmost importance.
**B**:
Note that previous methods – even those that account for the Rashomon effect – could not produce this result.
**C**: Our analysis provides a manageable set of clear directions for future work studying the functional roles of these genes in HIV..
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<|MaskedSetence|> Excitatory and inhibitory connections are denoted by lines with triangles and circles, respectively, and dopamine-modulated cells and connections are represented in blue color. Striatum and STN (subthalamic nucleus), receiving the excitatory cortical input, are two input nuclei to the BG. In the striatum, there are two kinds of inhibitory spine projection neurons (SPNs); SPNs with the D1 receptors (D1 SPNs) and SPNs with D2 receptors (D2 SPNs). <|MaskedSetence|> In contrast, the D2 SPNs are connected to the SNr through the indirect pathway (IP; red color) crossing the GP (globus pallidus) and the STN. <|MaskedSetence|>
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**A**: The D1 SPNs make direct inhibitory projection to the output nuclei SNr (substantia nigra pars reticulate) through the direct pathway (DP; green color).
**B**: The inhibitory output from the SNr to the thalamus/brainstem is controlled through competition between the DP and IP.
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**C**: Finally, we give summary and discussion in Sec. III.
Figure 1: Box diagram of our spiking neural network for the basal ganglia (BG).
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Key results are explicit and computationally efficient time-dependent expressions for the expected mean and the expected variance of an additive quantitative trait under exponential selection. They are presented in Section 4, seem to be entirely new, and provide highly accurate approximations to corresponding Wright-Fisher simulations. <|MaskedSetence|> They are not only derived from first principles by assuming the infinite sites model but also recover and refine classical results. Proofs are given in Appendix D. <|MaskedSetence|> They are based on a combination of branching process methods with (in part new) approximations for the expected time to loss or to fixation of a new beneficial mutant. The latter are deduced and numerically tested in Appendix B. In Section 5.2, we use the approximation for the number of segregating sites to characterize the numerically determined initial response patterns. <|MaskedSetence|>
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**A**: This allows us to examine the genomic patterns associated with the early phase of phenotypic adaptation.
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**B**: In Section 5.1 (and Appendix E), we derive explicit, approximate expressions for the evolution of the expected number of segregating sites.
**C**: Interestingly, they even allow the derivation of expressions for the long-term, quasi-stationary response of the trait’s mean and variance.
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Acknowledgement
XL, ZKZ, and BH were supported by the NSFC General Program No. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> 2022ZD0160703), 111 plan (No. BP0719010), and National Natural Science Foundation of China (No. 62306178)..
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**A**: RC-FNRA-IG/22-23/SCI/04, and HKBU CSD Departmental Incentive Scheme.
JCY was supported by the National Key R&D Program of China (No.
**B**: 62376235, Guangdong Basic and Applied Basic Research Foundation Nos.
**C**: 2022A1515011652 and 2024A1515012399, Tencent AI Lab Rhino-Bird Gift Fund, HKBU Faculty Niche Research Areas No.
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<|MaskedSetence|> <|MaskedSetence|> In case of measuring the accuracy as a function of position on the list, these experiments were repeated 5 times with 5 different random seeds providing in total 150 repetitions. <|MaskedSetence|> This data is wholly characterized by specifying the mean accuracy at that position in the list. For such binary data, the accuracy is already by itself a sufficient statistic..
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**A**: In all cases all names and objects/occupations/places were distinct.
**B**: Consequently, for each position in the list we get 150 binary answers (true/false recall).
**C**:
Technical details
In order to ensure that none of the names or objects biases the results, the names and objects were independently permuted 30 times and the appropriate number of facts was selected.
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<|MaskedSetence|> In this setting, taxonomic information is compositional by nature[1, 2], and there exists only limited ways to compute absolute biomass of taxa[3, 4]. <|MaskedSetence|> <|MaskedSetence|> The result is the relative abundance of each bacterial strain identified among bacteria, and separately the relative abundance of each fungal strain identified among fungi. Notably, the relative abundance of each taxa among the complete set of taxa is unknown. While established techniques can be used to handle compositional data[5, 6, 7], these techniques are designed to work when the composition is known relative to the total data set. When dealing with transkingdom data, we must therefore take into careful consideration if we are properly handling the compositional data.
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**A**: The most common example of this is the use of 16S rRNA amplicon sequencing to identify the bacteria in a sample paired with ITS rRNA amplicon sequencing to identify the fungi.
**B**: Furthermore, data on two or more kingdoms of taxa (called “transkingdom” data) are often collected with separate methods for each kingdom.
**C**:
This relatively simple example demonstrates a profound problem for scientists studying the microbiome, where instead of animals and trees we are concerned with, for example, bacteria and fungi.
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The graph depicts the epidemic control time as a function of vaccine allocation time in both country 1 and country 2. In scenarios 1 and 2, illustrated in Fig.4(a) and Fig.4(b), and scenarios 3 and 4, shown in Fig.4(c) and Fig.4(d), respectively, the trend is examined. From the purple line in both Fig.4(a) and Fig.4(b), we see that if the country 1 has immediately allocated vaccines since its acquisition of the vaccines on the 300th day, the epidemic control times of both countries are the same, i.e. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|>
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**A**:
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**B**: on the 1168th day for the first scenario without mutual migrations.
**C**: However, if country 1 starts to distribute vaccine resources after the 300th day, the epidemic control time of country 1 would be shortened as expected, whereas the control time in country 2 would be significantly prolonged.
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<|MaskedSetence|> <|MaskedSetence|> Edge thickness indicates strength of support for the edge (thick solid: >80% of samples, thin solid: >60%, dashed: >40% support). A: Genes set for the pre-treatment cohort; nodes in pink belong to the Regulation of cell differentiation strength, while the one in yellow to the Reg. <|MaskedSetence|> B: Gene set for the post-treatment cohort; node belonging to MAPK cascade are in purple,
Reg. of cell in green,
Toll like receptor cascades, and NFKappa B sig. in yellow and
BCR pathway in red..
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**A**:
Figure 6: STRING network of the harmonic persistent homology identified genes.
**B**: apoptotic process.
**C**: The edges indicate both functional and physical association.
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<|MaskedSetence|> More recently, these models have been applied to other types of data. <|MaskedSetence|> Textualized tabular data offers the advantage of being able to handle inputs with different feature sets and is more robust in dealing with missing values. Prior work also investigated the use of LLMs on a variety of geoscience applications (mai2023opportunities, ).
Figure 1. The overall flow of FREE. <|MaskedSetence|> These descriptions are then processed by a separate language model (LM) to generate embeddings, which are fed to an LSTM layer for making predictions. Simulated data generated by a physics-based model are used to pre-train the LM and LSTM layers,
followed by fine-tuning with true observations of the target variable..
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**A**: Recent advancements in large language models (LLMs) have demonstrated remarkable performance in solving language tasks based on human instructions (brown2020language, ; chowdhery2022palm, ; touvron2023llama, ; zhang2022opt, ; vicuna2023, ; alpaca, ).
**B**: For example, LLMs have been used to textualize tabular information and handle question-answering tasks (borisov2022language, ; zhao2023large, ).
**C**: Input features are first transformed into natural language descriptions.
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Biological relevance
Enhancers are short, noncoding segments that contribute to regulating gene expression. <|MaskedSetence|> <|MaskedSetence|>
Data
Experimentally validated enhancer-gene pairs were taken from CRISPR interference experiments (Fulco et al. <|MaskedSetence|> (2019) and paired with the main TSS of each gene from Avsec et al. (2021)..
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**A**: (2019); Gasperini et al.
**B**: They can be located anywhere from a few thousand to a million bp away from their target gene and work by being brought into physical proximity to the gene’s promoter.
**C**: Their annotation is a highly challenging task that requires detection of long-range interactions.
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2.1 Gene expression data and pre-processing step
The gene expression measure y𝑦yitalic_y are generally of count data type from sequencing reads. Various SVG detection models have been developed to specifically model count data following some mandatory filtering and quality control steps. <|MaskedSetence|> The gene expression count data often exhibit over-dispersion and contain numerous zero values, mainly due to the technology employed for data generation or simply because many genes are poorly expressed for biological reasons. These particular issues in count data are generally taken care of by using negative binomial models which handle over-dispersion well. For the issue of zero-inflation, Zhao et al, 2022 [21] showed that modeling zero inflation is not necessary in spatial transcriptomics, thus is not a concern in many method development. On the other hand, some methods, for example SpatialDE[6], nnSVG[9], and BOOST-MI[22], use normalized gene expression data in the model for easy implementation, where in most of cases, the data is modeled using multivariate normal distribution after transformation. Authors in SPARK[8] proposed two different data models, SPARK and SPARK-G which uses count data and normalized data, respectively. <|MaskedSetence|> The normalization step generally removes the bias due to differences in sequencing depth using size factors and normalizes the data using log transformation(log10 or log2 transformations after adding a pseudo-count value c𝑐citalic_c, preferably 1). <|MaskedSetence|> Other normalization methods, such as scran, scuttle, and scater R/Bioconductor packages[23, 24], can also be applied. Table 1 provides information on some selective methods together with their required input data type and the implemented model:.
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**A**: The method sepal[13] uses a slightly different normalization procedure which involves mapping the log-transformed values to the interval [0,1] and using a pseudocount 2.
**B**: Some examples of these models include SPARK-X[18], BOOST-GP[10], SINFONIA[19], and GPcounts[20].
**C**: The data normalization method is not unique for these methods.
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<|MaskedSetence|> <|MaskedSetence|> Models without pre-training (represented by ’w/o pretrain’) perform worst in all tasks. Pre-training strategies without data augmentation (represented by ’w/o img aug’) perform second best, yet they show a significant performance increase compared to models without any pre-training. <|MaskedSetence|> The ’w/o img aug’ strategy, although not using data augmentation, still shows a noticeable improvement, indicating the effectiveness of our pre-training strategy. MolIG improves across all six datasets, suggesting that the data augmentation strategy further enhances robustness and generalization capabilities of the model..
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**A**: As shown in Figure 2, MolIG, which utilizes both pre-training and data augmentation strategies (represented by the grey bar), performs best among all model architectures.
**B**: Excluding either of these two components can easily lead to a decrease in performance.
Compared to models completely without pre-training, MolIG improves the ROC-AUC metric by 13.0% on the ClinTox dataset, by 7.8% on the SIDER dataset, and an average of 5.9% across all six datasets.
**C**:
This ablation study aims to evaluate whether pre-training strategies and data augmentation strategies can help the model achieve better performance in downstream tasks.
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<|MaskedSetence|> <|MaskedSetence|> On the other hand, the models which have been pretrained via SSL yield far superior results. In all cases, the models trained with the proposed framework surpass the baseline by 11.68% on average and even outperform it by 21.04% in the case of the PhysioNet22 OOD task. Even more so, the SSL models were surprisingly able to surpass both the effectiveness of the baseline and their ‘In-Distribution’ counterpart, in the case of the Pascal OOD evaluation. <|MaskedSetence|> Furthermore, even though there is a decrease in effectiveness when the OOD datasets are left out during model pretraining, the SSL models continue to outshine the baseline across the board, with the exception of the case where the downstream task is the PhysioNet2022 data and models are evaluated on OOD data from Pascal. Finally, we would like to note that the above findings are aligned with
the results of our preliminary SSL method ballas_listen2yourheart_2022
submitted in the PhysioNet2022 challenge, where the proposed model was able to
avoid overfitting on the available training distribution and demonstrated
adequate generalization effectiveness on completely hidden data..
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**A**: Additionally, in all cases the baseline models appear to have overfit their training data distribution and fail to maintain their classification ability across distinct datasets.
**B**: Specifically, the downstream models trained on data from PhysioNet2016 and PhysioNet2022 were able to yield better results than the fully-supervised model trained solely on Pascal data.
**C**: and OOD data is apparent.
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Figure 6: Real patient data. Recurrence of the enhancing core overview. a,b Recurrence coverage of selected volume radiotherapy plans. <|MaskedSetence|> Output tumor cell distribution thresholds found through a grid search to match the Standard Plan volumes. <|MaskedSetence|>
It’s important to note that the high standard deviations in the Recurrence Coverage column reflect the inherent complexity of predicting tumor recurrences, which can vary significantly in difficulty from case to case. <|MaskedSetence|>
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**A**: c,d Average Recurrence Coverage and direct patient-by-patient comparisons to the Standard Plan.
**B**: All radiotherapy plans have the same total volume.
**C**: Despite this natural variance, the averages in the Recurrence Coverage column are a reliable predictor of the effectiveness of each planning method, as the hierarchy of the recurrence scores translated to the direct comparisons with the Standard Plan..
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<|MaskedSetence|> On the other hand, the range of [IP3] values corresponds to having
∼similar-to\sim∼100 molecules/μm3𝜇superscript𝑚3\mu m^{3}italic_μ italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT. Cell sizes vary over various orders of magnitude. The volume of the cells used in the experiments in which the exponential scaling between
external stimulus strength and interpulse times was observed (hepatocytes and HEK293 cells [9]) are between 103superscript10310^{3}10 start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT and 3 104μm3superscript3104𝜇superscript𝑚33\,10^{4}\mu m^{3}3 10 start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT italic_μ italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT. <|MaskedSetence|> <|MaskedSetence|> Thus, according.
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**A**: which the dynamics of the simple model (Eqs. (3)–(4)) is excitable with slope dβ/d𝑑𝛽𝑑d\beta/ditalic_d italic_β / italic_d[IP]3∼1.4{}_{3}]\sim 1.4start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT ] ∼ 1.4.
**B**: Using Poisson statistics
to estimate the ratio between the fluctuations and the mean of this number we conclude that δβ/⟨β⟩𝛿𝛽delimited-⟨⟩𝛽\delta\beta/\langle\beta\rangleitalic_δ italic_β / ⟨ italic_β ⟩, which is equal to this
ratio, ranges between 4 10−4superscript10410^{-4}10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT and 3 10−3superscript10310^{-3}10 start_POSTSUPERSCRIPT - 3 end_POSTSUPERSCRIPT.
**C**: Thus, according to our estimates, in the excitable regime, the number of IP3 molecules in these cells is between 105superscript10510^{5}10 start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT and 3 106superscript31063\,10^{6}3 10 start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT.
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<|MaskedSetence|> <|MaskedSetence|> Each case with a Dice score of 00 for the corresponding segment was counted as a false positive or a false negative respectively, depending on the ground truth labels. <|MaskedSetence|> The top three values for each metric from each track are marked as gold, silver and bronze cells in decreasing order. A ‘nan’ indicates that the corresponding value could not be computed due to division by zero.
The winning team names are in bold.
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**A**: Group 2 CoW components) for CTA (Top) and MRA (Bottom) tracks.
**B**: Table 6: Detection performance in terms of precision and recall for the R-Pcom, L-Pcom, Acom and 3rd-A2 (i.e.
**C**: Hereby a positive refers to a segment that is present, a negative to a segment that is absent.
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<|MaskedSetence|> GFMDiff and recent SOTA methods show no major difference in stability of atoms, but the performance lead of GFMDiff over the second-best method using the same generative methods in terms of stability of molecules is 2.1%. This indicates that our model is capable of genrating stable molecules. We believe that the molecule stabilty could be further improved using latent diffusion in GeoLDM. <|MaskedSetence|> The superior performance in validity means that GFMDiff generates molecules not only with accurate conformations, but also with correct valid and unique structres. It is intriguing to find out that GFMDiff exhibits lower performance in terms of the negative log-likelihood of data (NLL) compared to GCDM, but still surpasses other baselines. <|MaskedSetence|> Among GFMDiff and its abalation models, GFMDiff w/o tri achieves the lowest results. This means the incorporation of complete local geometry information contributes more to the performance lift than GFLoss. In summary, GFMDiff exhibits the ability to generate stable molecules while addressing validities of samplessimultaneously..
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**A**:
As it is shown in Table 1, GFMDiff outperforms all baselines and achieves the best performance in stability, validity, and uniqueness times validity.
**B**: The performance lead of GFMDiff over the SOTA method in validity and validity times uniqueness is 1.1% and 1.3%, respectively.
**C**: A possible explanation could be the different ways of applying geomteric information between GFMDiff and GCDM.
Moreover, the ablations of GFLoss and triplet-wise geomtery illustrate the effectiveness of them.
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As the program has been rigorously examined, we anticipate to extend its applications to other functions in Amber software, such as post-processing of the trajectories in MM-PBSA or MM-GBSA. The calculation in dSASA is geometry based, obtaining accurate results with the provided atomic coordinates and radii. Therefore it can be used for diverse types of systems without restrictions, such as the simulations of larger proteins, protein-ligand complexes, and protein-nucleic acids complexes. 1 nanosecond GB/SA simulation for 200-residue proteins with dSASA takes around two hours. Even though it is slower than pwSASA, the accuracy of the method will allow us to explore the impact of the nonpolar term on the simulations in the future.
Given the accuracy of dSASA, the calculation of atomic and molecular SASA values can be benchmark data set for the training of the parameters in pwSASA approach for RNAs in the future, which will combine the advantage of its speed on GPUs and the accurate calculation from dSASA. The SASA is certainly an approximation to nonpolar solvation, but many studies have shown that including it improves agreement with experiment for things like protein stability or binding affinities12. <|MaskedSetence|> Inclusion of the volume term will provide a more complete description for the nonpolar solvation term.
With the volume derivatives, we can further examine the impact of the term on the stability of molecules in the MD simulations. <|MaskedSetence|> <|MaskedSetence|>
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**A**: Moreover, the current algorithm being used for weighted Delaunay Tetrahedrization, gReg3D, is designed to work on a set of random points and the size of the workspace depends on the distribution of points in the workspace.
**B**: As it consumes nearly 70% of wallclock time of our surface area calculation, improvement on this algorithm will further speed up the simulations.
The program of dSASA written in CUDA will be freely available from the authors..
**C**: In addition, dSASA, a more accurate SASA with derivatives implemented on GPUs, will also enable fast polar solvation methods for MD.
Furthermore, the calculation of SASA is based on the diagram of Laguerre intersection cells, so it can be easily extended to the computation of molecular volumes along with the corresponding atomic derivatives.
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<|MaskedSetence|> (2018), we use ROC-AUC as the evaluation metric for classification tasks. <|MaskedSetence|> To ensure fairness, we use Optuna (Akiba et al. 2019) to search 10 learning rates (LRs) for each model. We repeat each task 3 times and report the mean and standard deviation. <|MaskedSetence|>
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**A**:
Following the recommendation of Wu et al.
**B**: Due to space limitations, the standard deviations are included in the appendix.
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**C**: For the regression task qm8, we use MAE, and for other regression tasks, we use RMSE.
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IV-A Impact of Biological Sex on Blood Pressure
To analyze the impact of sex on BP values, we categorized the final pre-processed dataset into females and male groups. Subsequently, we calculated the mean and standard deviation (STD) of SBP and DBP for each group. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> The mean SBP and DBP for male and female groups are marked with dots.
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**A**: Our findings revealed significant differences in mean BP levels between females and males, as summarized in Table I.
**B**: The difference between the mean SBP and DBP values between the two sex groups are 2.98 and 2.03 mmHg, respectively.
**C**: Fig. 1 illustrates the 95% percentile range contours for males vs females BP distribution.
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<|MaskedSetence|> Adaptive KFs attempt to estimate their internal parameters from data [brown1985adaptive]. Many extensions of KFs have also been developed to estimate model parameters as observable state variables [sarkka2023bayesian]. The PKF builds on these ideas by adaptively updating both its process uncertainty (via update equation 8) and the internal model parameters via the internal Bayesian model computation described in section 4. <|MaskedSetence|> <|MaskedSetence|>
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**A**: Unlike other approaches, the PKF uses analytically tractable internal models to directly compute Bayesian parameter posteriors which results in higher accuracy and more scalability.
**B**:
Comparison to Parameter Estimation Algorithms:
Parameter estimation is an immense topic, so here we focus on parameter estimation as it relates to KFs.
**C**: To our knowledge, no other methods iteratively update these parameters the way the PKF does.
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<|MaskedSetence|> <|MaskedSetence|> Diffusion-like processes can be applied to discrete data
(Avdeyev et al., 2023), but LDMs are preferred for their computational efficiency - this is due to the compaction and smoothness of the latent space (Rombach et al., 2022). Current state-of-the-art models are usually domain-specific and rely on pre-trained language models to form latent embeddings (Lovelace et al., 2022; Zhang et al., 2023). Additionally, discrete generation using diffusion models often encounters rounding errors when mapping from the latent space to text tokens (Zhang et al., 2023; Li et al., 2022; Lin et al., 2022). <|MaskedSetence|> Specifically, the accumulation of rounding errors can result in the production of invalid DNA sequences, this effect is more prominent in the generation of longer sequences..
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**A**: This technique is widely employed in language modelling, where text is transformed into a continuous format using tools like word2vec or neural network-based embeddings (Dieleman et al., 2022; Li et al., 2022; Han et al., 2022).
**B**:
Latent Diffusion Models (LDMs).
LDMs convert discrete inputs into a continuous latent space.
**C**: Similar issues arise in the generation of DNA sequences.
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Since we wanted to assess the molecule’s reactivity, we also compute the Gasteiger charges [41] (Figure LABEL:fig:QM9_design(f) for a visual overview). The molecule features an aromatic ring containing a ketone (C=O), which is more electrophilic compared to carbon-carbon or carbon-hydrogen bonds, making it susceptible to nucleophilic attacks. The combination of the aromatic ring containing nitrogen and the ketone group forms a pyridone ring structure. This ring is more reactive than a simple aromatic ring because the presence of the heteroatom (nitrogen) and the ketone group introduces sites for potential chemical reactions, such as nucleophilic addition to the carbonyl carbon or electrophilic substitution at the ring. The nitrogen within the ring, being part of the heteroaromatic system, contributes to the aromaticity and reactivity of the compound by altering the electron density and distribution across the ring. This can affect how the molecule interacts with other chemical entities, making the nitrogen-containing ring a site for potential chemical reactions, particularly those involving electrophilic attack on the ring due to the electron-donating nature of the nitrogen atom.
The carbon atom in the ring, which is adjacent to both an oxygen and a nitrogen atom, having a partial positive charge (+0.25) suggests it is somewhat electron-deficient. This happens because oxygen, being more electronegative, pulls electron density towards itself, making the carbon less electron-rich. The effect is somewhat balanced by the adjacent nitrogen, which is less electronegative than oxygen but more electronegative than carbon. However, the presence of the partial positive charge indicates that the carbon is a likely site for nucleophilic attacks, where a nucleophile (an electron-rich species) would be attracted to this electron-deficient carbon.
The nitrogen atom having a partial negative charge (-0.33) indicates it is relatively electron-rich compared to its usual state. <|MaskedSetence|> <|MaskedSetence|> The partial negative charge suggests that nitrogen is more nucleophilic, meaning it has a higher propensity to donate electrons, either forming bonds with electrophiles or engaging in protonation reactions. Further quantum mechanical calculations should be done to investigate this.
The carbon with a partial positive charge is a reactive site for nucleophilic attacks. Other molecules might react with this site through mechanisms that involve nucleophiles targeting electron-deficient carbons.
The hydrogen atom bonded to the nitrogen atom, with a positive partial charge of 0.17, is a good candidate for forming hydrogen bonds with other molecules or atoms. <|MaskedSetence|> This makes the molecule potentially capable of acting as a hydrogen bond donor, which is an important factor in determining the molecule’s solubility in water and other polar solvents, as well as its interactions in biological systems..
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**A**: Hydrogen bonds are a type of dipole-dipole interaction that occurs when a hydrogen atom, which is bonded to a highly electronegative atom (e.g.: nitrogen, oxygen, or fluorine), interacts with another electronegative atom bearing a lone pair of electrons.
**B**: This can be due to its lone pair of electrons and the effect of the aromatic ring’s electron system.
**C**: In aromatic heterocycles, nitrogen’s lone pair can participate in the delocalized π𝜋\piitalic_π-electron system, but the exact contribution depends on the ring’s structure and the electronegativity of adjacent atoms.
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Motivated by the best results produced in Section 4.1.2, we further proved the effectiveness of the models by using the transductive learning methodology outlined in Yang et al. (2016), where during the training phase the models were given access to the feature vectors of all nodes. While the concept of transductive learning has been explored in various domains, its application to flow cytometry data is relatively novel, and there is little literature explicitly discussing its implications in this field. Hu et al. (2020) and Zhang et al. <|MaskedSetence|> They discuss the advantages of leveraging unlabeled data to improve model generalization and robustness, which is crucial in the context of heterogeneous and high-dimensional cytometry data to reduce the need for extensive manual gating and annotation.
In FlowCyt, our primary goal was to classify the status of cells, distinguishing between the five different classes, while also evaluating the reliability of the classification performances in a semi-supervised setup utilizing up to one million cells per patient. <|MaskedSetence|> We randomly assigned 10% of the nodes for validation and 10% for testing while keeping the classes’ ratio balanced, the same as in the full dataset. Since our model is strongly imbalanced, we used a weighted negative log-likelihood loss function. <|MaskedSetence|> We can therefore think of our problem as having a large graph where half of the graph is unlabeled, and our goal is to predict the labels based on the ones that we have.
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**A**: (2019) proposed a robust and interpretable end-to-end deep learning model for cytometry data and scRNA-Seq analysis, incorporating elements of self-supervised and semi-supervised learning.
**B**: To achieve this, we conducted five different seed iterations using our models.
**C**: Then we randomly masked the labels of 50% of the training, validation, and test set.
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A critical examination of the AT methodology reveals significant shortcomings. Firstly, proponents of AT failed to conduct basic control experiments, a foundational aspect of introducing a new scientific metric. Benchmarking against established indices, particularly in coding and compression algorithms, is crucial to validating any new metric in the domain. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|>
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**A**: Previous work on AT
has never included meaningful experimental comparisons of the assembly index with other existing measures on false grounds that their measure is completely different [8] (Figs.
**B**: 1 and 2).
**C**: Yet, we have shown that other algorithms, such as RLE, Huffman coding (the first dictionary-based universal compression algorithm), and other compression algorithms based on dictionary-based methods and Shannon Entropy produced equivalent or superior results compared to the results published by the authors of AT [4].
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While the phasor-based HDC algebra developed by McDonald et al. is effective for complex-valued data such as classical analog signals processing, for example,[McDonald_phasor_hdc_ai] it is insufficient for our purposes. <|MaskedSetence|> The Bloch sphere262626A graphical representation of a qubit, where each axis corresponds to one of the three Pauli matrices whose weighted sum (normalized to unit length) describes a qubit. <|MaskedSetence|> While describing the statistics of distances between purely random cogits could be quite problematic in some approaches to formulating the problem, the distances are uniformly distributed if assessed in terms of angular distances rather than surface distances. <|MaskedSetence|> Measurement error can be assessed similarly to how one would analyze distances between classical HV, but with some additional caveats we will discuss later.
4.1 Cogit Hypervectors.
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**A**: This drastically simplifies the problem of analyzing error-tolerance in Projective Cognition prior to measurement.
**B**: provides a convenient representation for this, and is shown in Figure 2.
**C**: With qubits we must additionally account for whatever property (often spin) is to be mapped to measurement outcomes – and likewise for cogits.
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Language-Conformation Pairs: Using Molecule3D Xu et al. <|MaskedSetence|> <|MaskedSetence|> This process resulted in 161K language-conformation pairs.
Conformation-Protein Pairs: By leveraging data from PDBBind Wang et al. <|MaskedSetence|> (2020), we extracted and refined conformation-protein pairs. After filtering based on RMSD thresholds and clustering for sequence identity, we consolidated our findings into 72K unique pairs, ensuring no overlap with previously identified pocket proteins.
Graph-Conformation Pairs: Converting 3D molecular structures from the language-conformation dataset into 2D graphs allowed us to generate 161K graph-conformation pairs.
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**A**: (2005) and CrossDocked Francoeur et al.
**B**: (2022) with 37M higher-quality conformations, we matched molecular IDs (CIDs) and InChIs in them with textual descriptions from PubChem.
**C**: (2023), which contains 3.9M ground-state molecular conformations, and the GEOM dataset Axelrod et al.
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We use AiZynthFinder [11] with default parameters to compute the routes of both datasets. A route is considered to be solved if all leaves are purchasable molecules. If more than one route is found for a molecule, the route scored the highest by AiZynthFinder is retained. For solved routes, we compute the depth of the tree. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> This reduces the depth of the tree when the intermediate is found along the longest branch of the tree.
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**A**: At a synthesis tree level, this effectively results in the removal of any nodes beyond the intermediate molecule.
**B**: We do the latter by treating the sampled intermediate as an available building block, meaning that we can ignore the synthesis steps needed to create it.
**C**: Since the maximum tree depth allowed by AiZynthFinder’s default parameters is 7, we assign a depth of 10 for molecules where a route is not found.
To create target molecule-intermediate pairs, we randomly sample a maximum of three intermediate molecules for each route and recompute the depth accordingly.
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Different aspects of cyclically dominant dynamical systems have been studied intensively in the last years Menezes and Barbalho (2023); Park (2022); Szolnoki and Chen (2020); Serrao and Täuber (2021); Avelino et al. <|MaskedSetence|> <|MaskedSetence|> By choosing a similar system, the key question in our present work is to clarify how a blocking mechanism affects the vitality of the involved formation. Importantly, such blocking, when the interaction between two actors is influenced by the vicinity of a third partner, is a common phenomenon in microbiological systems or even in human societies Alvarez-Rodriguez et al. (2021).
While this kind of blocking may stabilize a coexistence in a three-member system Bergstrom and Kerr (2015), there are two reasons why such blocking could be harmful for a cyclic loop in a more complex situation. The first one is plausible because members may impede each other to invade successfully an external party, which can be detrimental for the whole alliance. The other one is the consequence of retarded inner rotation. <|MaskedSetence|> And the increase of local homogeneity is always disadvantageous for a defending alliance which is based on cyclic dominance.
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**A**: In this case the average size of domains formed by the members of the loop grows.
**B**: (2018); Roman et al.
**C**: (2016).
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Micro-ultrasound is a newly developed technology that allows visualization of tissue microstructures at much higher resolutions than conventional ultrasound. <|MaskedSetence|> <|MaskedSetence|> This approach has seen some measure of success, but still struggles with a number of issues. For instance, ROI-scale PCa detection suffers from weak labelling: ground-truth histopathology labels describe tissue properties of the entire biopsy core, and ROI labels are only an approximation of the true distribution of cancer in the core. <|MaskedSetence|>
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**A**: Typically, deep learning is used during targeted biopsy to classify small regions of interest (ROI) across a needle trace region[2].
**B**: Moreover, ROI-scale models do not consider the broader contextual information encoded in multiple overlapping patches as clinicians typically do.
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**C**: As such, this imaging modality is a prime candidate for training deep learning models to detect prostate cancer in ultrasound images.
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4.2 Plant Winterkill in Northern Latitudes
Plant winterkill impacts the winter annual and perennial ground cover that society uses for recreation and ecosystem services. <|MaskedSetence|> Winter injury to golf course turfgrass has negative ecological impacts when perennial ground cover is absent, and economic losses when recreational activities are postponed for vegetation to re-establish in the springtime. <|MaskedSetence|> Often the specific physiological reasons for winterkill in turf systems are difficult to understand and may include the frequency and magnitude of ice encasement, gas exchange, low temperatures, desiccation, or disease. <|MaskedSetence|>
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**A**: Winterkill is unpredictable and this has been due largely to the inability to capture microclimate data that characterizes these complex physiological stressors..
**B**: Golf course superintendents in northern latitudes are faced with the problem of winter damage risk every year, and undertake cultural practices to prevent injury.
**C**: To date, few viable solutions have been developed by the turfgrass research community.
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Overall, the frALBERT-based models have the lowest carbon footprint. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> Labrak et al. (2023) reported the overall carbon emissions of their 7 DrBERT-based models, which is 376.45 kg CO2 eq.
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**A**: (2023) reported that the carbon emissions for pre-training their CamemBERT-bio model is estimated to 0.84 kg CO2 eq.
**B**: Touchent et al.
**C**: These models offer a decrease of carbon emission between 20% and 63% compared to other models, depending on models and corpora.
Note that Carbon tracker does not consider the execution environment or energy production.
As a result, the obtained measures in our experiments remain approximative.
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4.3 Data Visualization
We use the t-distributed Stochastic Neighbour Embedding (t-SNE) algorithm to create 2-dimensional representations of the different embeddings [14]. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> On the other hand Morgan Fingerprint daylight are giving different scattered patterns. We can see the merged pattern with heavy inheritance from daylight when merged with Morgan. The proposed MERGE displays a mix of all in Figure 3(h), which is inherited clearly from Figure 3(f) and Figure 3(g).
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**A**: Figure 3 shows the scatter plots produced by t-SNE for various embedding techniques.
**B**: To have a visual inspection and determine whether different embedding strategies are keeping the structure of the data the t-SNE plots are generated.
**C**: The MACCS fingerprint displays some clustering overall, which is similar for k𝑘kitalic_k-mers and weighted k𝑘kitalic_k-mer.
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In other words, the signal may not be able to transfer the desired on/off patterns to the reaction systems at a receiver cell if the waveform of the signal at the receiver is distorted as shown in Fig. 1. <|MaskedSetence|> Specifically, we first introduce indices evaluating signal distortion by the gain and the phase delay characteristics and derive these characteristics of MC channels based on the diffusion equation and the rate equation. <|MaskedSetence|> Using the proposed method, we demonstrate the design procedure of specific MC channels that satisfy given specifications. <|MaskedSetence|>
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**A**: We then show design conditions for MC channels in which the magnitude of distortion becomes below a specified level based on the indices.
**B**: Finally, the roles of MC channels in nature are discussed from the perspective of signal distortion.
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**C**: Therefore, to guarantee the quality of the transmitted signals, it is crucial to assess the degree of distortion that is added in MC channels.
In this paper, we propose a method to analyze signal distortion caused by one-dimensional diffusion-based MC channels.
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Three different types of intrinsic rewards have been proposed: prediction-based, count-based, and memory-based intrinsic reward functions. <|MaskedSetence|> The greater the difference from stored memories, the higher the reward[26]. However, memory-based methods have to compare the current state with all previous states. Therefore, they are considered resource-intensive approaches that require an extensive memory record.
Count-based intrinsic reward methods are computed by counting how often the agent visits each state. <|MaskedSetence|> <|MaskedSetence|> However, they may be infeasible for problems of vast sizes, such as those involving chemical space[32]..
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**A**: Memory-based intrinsic reward methods involve maintaining a record of previously encountered states in memory, promoting exploration for finding novel states by assessing the novelty of the current state in comparison to stored memories.
**B**: These methods have the advantage of being simple and easy to implement.
**C**: They are used in both tabular settings[27] and more complex models, including context-tree switching density models[28], pseudo-counting[29], and locality-sensitive hashing (LSH) techniques[30].
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<|MaskedSetence|> In the inter-layer connections, the BPT-SAN models the local nonlinearity of dendritic trees by breaking down the standard layer into two stages. In the initial stage, dendritic branches perform a mutually exclusive partition of the input and subsequently execute a weighted summation of the sparsely connected inputs. In the subsequent stage, the outputs of all branches converge to produce the neuron output via a maxout strategy. <|MaskedSetence|> <|MaskedSetence|>
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**A**:
Figure 1:
The schematic diagram of our proposed BPT-SAN, which integrates spiking neurons with rich spatial-temporal dynamics and network topologies featuring biologically-plausible connectivity patterns.
**B**: These two network topologies work synergistically to significantly enhance the information processing capacity of the network, enabling efficient decision-making in DRL.
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**C**: Furthermore, within the intra-layer connections, the BPT-SAN introduces lateral interactions to incorporate spiking states from neighboring neurons effectively.
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As generative models, Template-free methods opt to generate reactants directly from the given products. In comparison to generating graph structures, SMILES provides a way to represent molecules as strings. <|MaskedSetence|> In particular, Graph2SMILES [29] replaces the Transformer encoder with a graph neural network, resulting in a permutation-invariant pipeline. <|MaskedSetence|> Existing template-free methods generally follows an auto-regressive generation strategy and use beam search for the generation process. Consequently, preserving a level of diversity in the resultant outputs has emerged as a critical consideration for template-free methods [33]. Due to the use of SMILES as input and output, most of template-free methods often overlook the rich topological and chemical bond information present in molecular graphs. Moreover, as reactants molecules need to be generated from scratch, template-free methods frequently suffer from validity issues and fail to leverage an important property of retrosynthesis prediction, i.e., the presence of many common substructures between products and reactants.
In this paper, we focus on the template-free generative approach for retrosynthesis prediction. Existing sequence-to-sequence methods have limitations in extracting robust molecular representations. They overlook the abundance of topological information and chemical bonds, and lack the ability to utilize atom descriptors as rich as those in graph-based methods. Furthermore, template-free methods overlook the fact that the molecular graph topology remains largely unaltered from reactants to products during chemical reactions, as they generate reactants from scratch. While there are methods that attempt to solve this problem using supervised SMILES alignment, they require complex data annotation and impact model training. <|MaskedSetence|>
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**A**: There are also methods [21, 40] formulates the generation of reactants as a series of graph generation or editing operation and solve it auto-regressively.
**B**: Taking advantage of this, most template-free methods [28, 15, 34, 42, 25] use Transformer models to translate between product SMILES and reactants SMILES.
**C**: Given these limitations, the following question naturally arises:.
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Molecular graphs (Shi et al., 2020) and simplified molecular input line entry systems (SMILES) strings (Weininger, 1988) constitute the two primary representations of molecules in deep generative models. <|MaskedSetence|> <|MaskedSetence|> Due to the inability of GANs to calculate rewards for partially generated molecules, Monte Carlo tree search (MCTS) is frequently utilized for sampling and completing molecules (Li et al., 2022). Unfortunately, the integration of RL algorithms with GANs further exacerbates the instability of the training process. <|MaskedSetence|>
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**A**: Most prior studies related to generative adversarial networks (GANs) (Yu et al., 2017; Guimaraes et al., 2017; De Cao & Kipf, 2018) typically update the generator by integrating the output probability of the discriminator with the chemical properties of generated molecules as a reward for reinforcement learning (RL), following the REINFORCE algorithm (Williams, 1992).
**B**: However, generating molecules with desired chemical properties using such discrete representations is a non-trivial task.
**C**: Stabilizing MCTS demands a substantial number of samples, significantly lengthening the process (Li & Yamanishi, 2023).
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Number of Iterations. Table 5 also studies the impact of the number of iterations. For enzyme reaction classification, increasing T𝑇Titalic_T from 1 to 4 leads to better performance (i.e., 84.7%→→\rightarrow→89.6%). <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|>
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**A**: This may be because over-clustering finds insufficient and insignificant amino acids, which are harmful to representation learning.
**B**: However, the accuracy drops significantly from 89.6% to 86.3% when T𝑇Titalic_T is set as 5555.
**C**: Similar trends can be observed in the results of other tasks.
Percentages of Missing Coordinates..
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To address the first point, two possible definitions of the probability of infection will be considered to address the first point: The probability that a given host becomes infected after ingesting a dose with specific infectivities and the average probability of infection for a set of hosts. Previous works have predominantly focused on the latter definition, as it is well-suited for interpreting experimental data. In such cases, variability has been addressed by treating infectivity and/or dose as random variables. This has led to dose-response formulas that map the expected value of the dose to the expected value of the probability of infection, as derived from infectivity and dose probability distributions. <|MaskedSetence|> <|MaskedSetence|> However, the link between these parameters and the variance of infectivity has not been exploited to understand the effect of such variance on the expected probability of infection. The approximate beta-Poisson formula has also been used to mathematically justify an ubiquitous flattening of the dose-response curve that cannot be explained assuming homogeneous infectivity [8]. <|MaskedSetence|> Indeed, the demonstration was based on the so-called median effective dose and parameter α𝛼\alphaitalic_α in such a way that both the mean and variance of the infectivity vary simultaneously. A complete proof of whether the decrease of the slope is directly related to the infectivity variance is still lacking..
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**A**: However, an explicit link between the slope and the variance of infectivity was again not established.
**B**: Despite the widespread use of this modeling approach, a comprehensive analysis of how the probability of infection varies with infectivity dispersion remains lacking.
For instance, the exact beta-Poisson model or its widely-used approximation, the “approximate” beta-Poisson formula, assume Poisson and beta distributions for the dose and infectivity, respectively [16, 18].
**C**: The shape parameters of the infectivity distribution, usually denoted as α𝛼\alphaitalic_α and β𝛽\betaitalic_β, encode the dependence of the probability of infection on the variance of infectivity.
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Scaffold-Domain Adaptive Molecule Generation.
In the task of scaffold-domain adaptive molecule generation, the baselines are trained on both the entire dataset (††\dagger†) and solely on the source domain (‡‡\ddagger‡), respectively. In contrast, our GADM is trained exclusively over the source domain dataset. After training, each model generates 15,000 molecules for the source domain and target domains I and II, respectively. <|MaskedSetence|> We observe that with EDM or GeoLDM, the scaffold proportion of the generated molecules indeed mirrors that of the training samples (see proportion and coverage visualization in Figure 3). However, they all struggle to generate molecules with scaffolds falling into targeted domain I or II; they can only achieve 3.3% success rates at most (see EDM‡‡\ddagger‡ and GeoLDM‡‡\ddagger‡ in Table 4). <|MaskedSetence|> <|MaskedSetence|>
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**A**: In contrast, our proposed GADM, trained solely on the source domain, can generate molecules containing the target scaffolds under the corresponding supervision, achieving at least 95.5% proportion in both new domains.
**B**: Note that the target scaffolds were not seen during training.
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**C**: The quantitative results using various metrics are presented in Table 4, Table 5 and Figure 3.
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<|MaskedSetence|> The performance across duration shows that using 400ms of data achieves a slightly higher performance than 200ms, despite the fact that other images have started showing by this time. See Appendix A for examples of reconstructions from subject 1. <|MaskedSetence|> <|MaskedSetence|> Using 3 second duration averaged over 3 NSD presentations and 7T fMRI recording.
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**A**: To put the performance in context, the reported THINGS-MEG data performance is slightly higher than ours (Benchetrit et al., 2024).
**B**: Although they did not use the provided test set but rather took out parts of the training set as the test set, and thus did not have multiple trials to average during test time.
**C**:
3.1 Basic Performance Metrics
The performance across the 10 subjects are relatively consistent with a reasonable amount of variation.
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<|MaskedSetence|> 7) with geographic location, category, and time range specified as ‘Worldwide’, ‘Web Searches’, and ‘Between 9/21/23 and 9/27/23’ (i.e., 3 days before and after the 9/24/23 spike in Fig. 6); we also filtered for ‘health’-related searches.
Similar to Fig. <|MaskedSetence|> <|MaskedSetence|> 7 represents a spike (Table 3; Pre-MAF <<< Post-MAF) in searches for ‘Dulaglutide’, ‘Ozempic’, ‘Liraglutide’, ‘Trulicity’, and ‘Rybelsus’ on September 25, 2023..
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**A**: 6, Fig.
**B**: 7 shows a spike on September 25, 2023, for the search terms ‘Dulaglutide’, ‘Ozempic’, ‘Liraglutide’, ‘Trulicity’, and ‘Rybelsus’.
The black dashed line in Fig.
**C**:
To better understand the spike, we queried Google Trends [80]
for the entries on our Medication List (Fig.
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Among the NDC that did have a linked RxCUI but did not have an ATC associated with the RxCUI 13,289 (77.4%) had an RxCUI status of "not current", 1,974 (11.5%) had an RxCUI status of "obsolete", 1,195 (7%) had an RxCUI status of "remapped", and 75 (0.4%) had an RxCUI status of "quantified". 635 "active" RxCUI were unsuccessfully mapped to an ATC. Of the "obsolete" RxCUI, 1,078 (54.6%) were matched to an RxCUI with an associated ATC; 947 (79.2%) of the "remapped" RxCUI and 74 (99%) of the "quantified" RxCUI were matched to a new RxCUI with a corresponding ATC. As an audit for accuracy, we took a 0.01% sample of the non-"active" NDC that were linked to an ATC code and did an ad-hoc search for their appropriate ATC category. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> Of these, six were glucose testing strips, two were condoms, one was needle and one was a chamber used for an inhaler.
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**A**: The results of this check are shown in Table 2.
**B**: combinations with expectorants) while the correct classification was "R05F" (cough suppressants and expectorants, combinations).
Table 3 shows the concept names for the five most common "active", "alien", or "obsolete" NDC and the five most common "unknown" NDC that were not linked to an ATC code.
**C**: There were two NDC incorrectly classified NDC; both NDC were classified as "R05D" (cough suppressants, excl.
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Structured approaches sidestep the binning problem by modelling the spectrum as a distribution over chemical formulae, whose masses can be calculated trivially with extremely high precision. Some methods predict the formula distribution directly, using either autoregressive formula generation (Goldman et al., 2023a) or a large fixed formula vocabulary (Murphy et al., 2023). <|MaskedSetence|> <|MaskedSetence|> Methods that infer fragment distributions are most informative, since they explicitly describe how the molecule breaks apart. However, these models tend to involve stronger priors and more complex prediction schemes (Wang et al., 2021; Zhu & Jonas, 2023; Goldman et al., 2024) to facilitate efficient exploration of the combinatorial fragment space. <|MaskedSetence|>
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**A**: Others rely on recursive fragmentation (Wang et al., 2021; Zhu & Jonas, 2023) or autoregressive generation (Goldman et al., 2024) to model a distribution over fragments, which induces a distribution over formulae.
**B**: While structured MS2C models can generate very high resolution spectra, they tend to be slower than binned approaches due to the increased complexity of the output space.
There is a natural trade-off between a model’s scalability and the amount of information it can provide about the fragmentation process.
**C**: FraGNNet takes a pragmatic approach, achieving a level of interpretability that approaches that of the most sophisticated fragmentation models, while maintaining high performance and scalability (see Appendix C)..
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<|MaskedSetence|> GNNs are capable of learning embeddings for individual nodes and edges as well as complete graphs. <|MaskedSetence|> SMILES) or vectorial representations (e.g. molecular fingerprints), is their capability to learn fine-grained representations that are still explainable in graphical form. In drug synergy prediction, GNNs are used to model molecular graphs as well as biological networks of drugs, targets and cell lines [38, 44, 56]. Graph Convolutional Network (GCN) is one of the most widely used type of GNN [52, 57, 17, 42, 14, 58]. Graph Attention Networks (GAT) combine graph convolution with attention units for added flexibility [38].
Siamese Network share parameters between subnetworks processing different data items arising from paired objects, such as pairs of drugs [18]. <|MaskedSetence|>
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**A**: The main benefit of GNNs over text (e.g.
**B**: They are particularly valuable for assessing the similarity or complementarity of drug properties, an essential factor in predicting drug synergy.
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**C**: Graph Neural Networks (GNN) specialize in analyzing relational data represented as graphs or networks.
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<|MaskedSetence|> A rule consists of two graph patterns, one to match the input, and the other to specify the output. An application of a rule to a graph which contains a match of the input pattern replaces the matched part by the output pattern. <|MaskedSetence|> Such a model encodes behavior in the usual form of a transition system, where states are graphs and transitions are all possible rule applications. <|MaskedSetence|>
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**A**: This explicit representation of the encoded behavior may be arbitrarily larger than the rule set itself, possibly even infinite.
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**B**: A collection of such rules then defines a graph transformation model.
**C**:
In graph transformation, the rewriting of one graph into another is specified by the means of graph transformation rules, or rules for short.
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Given our assumptions about their chemostatting, the concentrations of input species and catalysts can be treated as parameters, rather than variables. <|MaskedSetence|> an intermediate or a product). All reaction rates therefore depend linearly on the concentration of the non-chemostatted species. <|MaskedSetence|> figure 1 (a)(i)), with nodes as species, edges as reactions and weights as reaction rates, absorbing the concentration of any chemostatted species involved into the reaction rates. We shall assume the graph produced is connected, as it must be if all species can be produced from the null state. <|MaskedSetence|>
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**A**: Under such assumptions, the CRNs are linear: the set of complexes contains only the null complex (containing no non-chemostatted species), and singletons (containing a single non-chemostatted species, i.e.
**B**: This graph defines a set of self-avoiding walks (SAWs) from the null state to each product; each SAW together with its inverse define a “pathway” between the null state and the products..
**C**: Transitions from the null complex correspond to the first association between inputs or inputs and catalysts to produce an intermediate.
We can draw a linear CRN as a graph (e.g.
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In addition, the rewire-to-same may lead to fragmentation Holme and Newman (2006); Kimura and Hayakawa (2008), which is unrealistic in the information and interconnected age.
Opinion dynamics on dynamical networks are typically based on simulations or numerical solutions Holme and Newman (2006); Horstmeyer and Kuehn (2020); Kozma and Barrat (2008); Zimmermann, Eguíluz, and San Miguel (2004); Oestereich et al. <|MaskedSetence|> <|MaskedSetence|> Existing theoretical analysis are not large in number compared with the simulation results. Theoretical approaches to tackle the coevolutionary dynamics often assume that social interactions evolve much faster than opinions, i.e., sufficiently large rewiring probability Wu et al. <|MaskedSetence|> (2016, 2019); Wu, Du, and Wang (2020); Wei, Lin, and Wu (2019); Shan and Wu (2022); Wang and Wu (2023); Liu et al. (2023); Baumann et al. (2020); Pacheco, Traulsen, and Nowak (2006); Du and Wu (2022, 2023, 2024). In this way, the network structure has converged to a steady state whenever the opinion is updated.
We extrapolate from this assumption and explicitly address how opinions reach consensus for arbitrary rewiring probability..
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**A**: (2012); Du and Wu (2023); Fu and Wang (2008).
**B**: (2010); Wu, Zhou, and Wang (2011); Wu et al.
**C**: (2023); Durrett et al.
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A common method to account for missing data is data-augmented Markov Chain Monte Carlo (MCMC). <|MaskedSetence|> Data-augmented MCMC methods have been applied to network epidemics for a variety of applications \citepbritton2002, groendyke2011, groendyke2012, embar2014, bu2022. However, when large amounts of data are missing, the latent variable space can become very high-dimensional. In such settings, data-augmented MCMC may not be computationally tractable unless the expressiveness of the model for either the epidemic or the network observations is appropriately limited.
Approximate Bayesian Computation (ABC) is another subset of methods for Bayesian inference, first developed in the study of genetics \citeptavare1997, beaumont2002. Under the ABC paradigm, results are forward-simulated from the model, given a proposal value of the parameters, and these results are compared to the observed data. Proposal parameter values are accepted if the simulation results they produce are deemed to be similar enough to the observed data. In order to maintain computational tractability while also avoiding poor results from the curse of dimensionality \citepblum2010, the similarity of results is usually evaluated as the difference between two sets of summary statistics. <|MaskedSetence|> <|MaskedSetence|> Thus, ABC is especially useful when considering models that are simple to describe in terms of mechanistic rules, but analytically complex..
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**A**: ABC only yields exact inferences when the summary statistics are Bayes-sufficient and the acceptance threshold is zero; this is rare in practice, as finite-dimensional sufficient summary statistics are available only in the exponential family.
**B**: However, approximate methods are nonetheless useful, as they allow for Bayesian inferences on sophisticated models that may not be analytically tractable.
**C**: In these settings, unknown variables, which can include the unknown transmission trees within the contact network, the contact network itself, or missing event times, are treated as latent parameters that are jointly inferred upon along with parameters of interest.
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<|MaskedSetence|> <|MaskedSetence|> We also incorporate neurogenesis in the hippocampus, assuming that this newborn neurons could play a role in memory erasure. <|MaskedSetence|> (a) Standard consolidation theory. Initially, the engram is initially present in neocortical areas (red), in a weak form (i.e., not stabilized), and in the hippocampus (dentate gyrus in green and CA1-CA3 subfields in blue), in a stable form..
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**A**: In addition to spike-frequency adaptation and synaptic plasticity, we assumed that the difference of connectivity structure of the neocortex and the hippocampus is playing a role in SCT, in particular the larger size and more sparse structure of the neocortex.
**B**: Using numerical simulations and mathematical analyses, we explore the short and long term dynamics of the model along the iterated phases of a typical consolidation process.
Figure 1: Interactions between the different brain areas involved in the standard consolidation theory.
**C**:
We present below a novel mathematical model of SCT that incorporates a set of potential neurobiological mechanisms.
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Yet, a number of these phenomena actually take place in non-flat and so-called curved spaces. Climbing plants for instance may growth on tree trunks or grounds that are not flat surfaces. Vein networks can develop in leaf blades that are markedly curved. Pollen tubes grow on the pin-like structures of papillae that are not flat [64]. Microtubules polymerize/depolymerize dynamically within the cell cortex that in general is not flat [2].
Examples are numerous and occur on a variety of scales. However, the modeling of plant form growth in curved spaces has been up to now only scarcely investigated. At the level of macro-molecules, simulations of microtubule dynamics have been carried out in 3D cell geometries to study the emerging properties of such a network of microfilaments subjected to local synthesis, decay and interaction rules, [43]. In this work, cell geometry is represented by a 3-D mesh, and microtubule trajectories are computed by assuming that microtubules are progressing in straight line in the 3-D Euclidean space. <|MaskedSetence|> Likewise, at organ scale a similar projection strategy is used in [26] to model climbing plants or in [65] to model branching venation patterns on the surface of petals. <|MaskedSetence|> The resulting form is then projected on the discrete curved surface represented as a 3-D triangular mesh. A more direct use of the concepts of differential geometry was described in a different application context to create artistic patterns on the surface of 3D objects by [36]. This approach exploits user-defined vector fields on surface meshes to locally drive drawings of curves at the surface. <|MaskedSetence|> However, similarly to what we do here, the authors construct a language that makes it possible to program patterns based on vector fields. A different approach, aimed at modeling the growth of plant lianas of their support and more generally the growth of parasite organisms on various types of hosts, analyzes how to grow surfaces by accretion formalized in [46] with the constraint of keeping on a reference surface representing the host [49]. In this approach, the trajectories of the parasite is defined analytically on the host surface and the focus is on the construction of the surface representing the parasite envelop. By contrast, our approach is primarily focused on the construction of the trajectories representing the patterns growing in curved spaces. In a preliminary work, we explored the possibility of using L-systems to model fractal structures on simple spheres [62]. Here, we largely extend this initial exploration with a complete formalization of the notion of Riemannian L-systems, that can be applied to both smooth curved surfaces and more abstract non-Euclidean smooth curved spaces.
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**A**: In both cases, to approximate the formation of a pattern in a curved space, the pattern growth is first evaluated in the 3-D Euclidean ambient space.
**B**: This is different from the approach that we use here which is based on the possibility to follow geodesics in curved spaces to construct forms.
**C**: The resulting displacement is then projected the local tangent plane to account for potential curvature of the cell geometry.
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In ecology, population escape from a long-lived metastable state plays an important role in the long-term stability of populations. Here, even a small population lingering on the brink of extinction can experience a rare fluctuation, securing its survival. On the other hand, a long-lived established population can undergo extinction. In both cases, escape occurs due to demographic noise, emanating from the stochastic nature of the reactions and discreteness of individuals Beissinger (2000); Lande et al. (2003); Kamenev et al. <|MaskedSetence|> (2008); Dykman et al. (2008); Levine and Meerson (2013); Vilk and Assaf (2018); Méndez et al. <|MaskedSetence|> Population escape is also highly relevant for studying gene regulation and genetic switching, which describes the process of cells transitioning between distinct phenotypic states Ackers et al. <|MaskedSetence|> (2002); Hornos et al. (2005); Raj and Van Oudenaarden (2008); Raser and O’shea (2005); Munsky et al. (2012); Biancalani and Assaf (2015); Weinreich and Chao (2005); Bressloff (2017). Notably, even in the absence of a driving signal, stochastic fluctuations of mRNA and proteins during the gene expression process can play an essential role in determining the stability of these states, and the corresponding transition rates Assaf et al. (2011).
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**A**: (2019).
**B**: (1982); Elowitz et al.
**C**: (2008); Leisner et al.
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In our analysis of veterinary-related risk factors we see that the veterinary practice conducting the test plays a significant role, despite low coverage of the test dataset with veterinary information. <|MaskedSetence|> The variability in testing outcomes by practice is partially correlated to the average size of herd tested and this may provide some clues as to reasons behind the result. This analysis does not provide evidence to indicate that variability by practice is a result of practice management, as there are many potential confounders; for example, there may be local disease-related risks which are not included in the model. <|MaskedSetence|> This could provide an alteration of the detection threshold used for the SICCT test which, in combination with the available epidemiological information, would be used to help decide on the withdrawal of OTF status. This would apply in much the same way as the current severe interpretation, but making use of many more varied risk factors. <|MaskedSetence|>
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**A**: We do not see any risk associated with tuberculin batch, though this may be because the test dataset coverage for tuberculin batch information is very low.
**B**: Nonetheless, by showing that the model can identify variability across practices, it does provide a foundation for further interrogation of management factors that could be used to improve outcomes for veterinarians.
Should the necessary data become available, further work could explore in detail a direct interpretation of the skin test measurement itself, rather than the binary outcome in the current model.
**C**: Any proposed change in testing regime or policy would, of course, need to be subject to further analysis.
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<|MaskedSetence|> <|MaskedSetence|> In older adults, measures of cardio-respiratory activity (e.g. heart rate variability) are known to decline with age [76]. <|MaskedSetence|> Additional video data from older subjects would likely help to improve this, which is discussed further in §C.
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**A**: We observe a decrease in performance with age, as observed in prior sleep staging work [56, 6].
**B**:
Population performance.
Figure 8 shows the distribution of Cohen’s κ𝜅\kappaitalic_κ values across participants from the OSV dataset plotted against age, sex and Fitzpatrick skin type222Plotted using representative skin tones from [70]. [14].
**C**: This likely reduces the distance between sleep stages in cardio-respiratory input space and thus makes them harder to distinguish.
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<|MaskedSetence|> SELFIES, on performance when predicting binding to the stress response target p53 (SR-p53), a task from the Tox21 data set. <|MaskedSetence|> However, the authors made an initial comparison by training a base model with either SMILES or SELFIES and evaluated both of them for drug-likeness prediction. The results showed very close performance when reporting the RMSE metric. <|MaskedSetence|> However, reporting the Pearson correlation coefficient metric reverses the conclusion with the SMILES model performing ∼0.004±0.01similar-toabsentplus-or-minus0.0040.01\sim 0.004\pm 0.01∼ 0.004 ± 0.01 better on average..
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**A**: The models trained with SELFIES performed ∼0.004±0.01similar-toabsentplus-or-minus0.0040.01\sim 0.004\pm 0.01∼ 0.004 ± 0.01 better on average.
**B**: They concluded that the difference was not significant (without showing further details).
For RT, given that the model was designed as a decoder that relies on generation, the authors opted for the SELFIES representation as it is designed to be used in DL generation tasks to produce valid molecules in terms of syntax and properties 107, 108.
**C**: The majority of the existing models have been trained exclusively using the SMILES representation (Table 4), except for ChemBERTa 39, RT 70, SELFormer 69, and MAT 63.
The authors of ChemBERTa studied the impact of the choice of chemical language, i.e., SMILES vs.
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Each patient’s images were prepared using SPM12 [7]. We coregistered the CT to the CTA, computed affine registration of the CT to MNI space, and applied this to both, reslicing images to 1x1x1 mm resolution. <|MaskedSetence|> In this study, we only run the first two steps of VTrails: (1) digital subtraction image pre-processing and (2) vascular contrast enhancement and seeds detection. In step 1, we created a digitally subtracted image (DSA) by composite registration (Affine + BSpline) with CTA as a reference image and CT as the moving image, followed by subtraction of CT from CTA. <|MaskedSetence|> In step 2, we extracted seed points from the vascular contrast-enhanced version of the DSA [8] and [9]. In this step, we first applied a gradient anisotropic filter to the DSA image as in Perona-Malik [10, 11]. The aim of this filter is to suppress noise while preserving edges (of the vascular structure in our case). We call this filtered DSA image or VSP. We then binarised the VSP image to segment the vessels. Any voxel in the VSP image with an intensity higher than 0.2 is considered a part of the vessel. Note that 0.2 is the default parameter in VTrails [8, 12]. <|MaskedSetence|> The skeleton depicts the centreline of the vascular structure. itkBinaryThinningImagheFilter3D was developed based on Lee et al. [14], which is a 3D decision tree-based algorithm aiming to thin the binary image. Any voxel along the skeleton image with its corresponding value in the VSP image at the same (x,y,z) location greater than its 75th percentile (VTrails’ default parameter) was considered a seed point.
The DSA and Seed images were later used to estimate time-of-arrival at each voxel. A fast marching algorithm was used to estimate the time-of-arrival at each voxel with the seed points as the source and the DSA as the speed potential matrix [15]..
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**A**: The binarised VSP was later converted into the skeleton image (SKEL) using itkBinaryThinningImagheFilter3D in ITK [13].
**B**: Later the DSA image was normalised by its maximum value.
**C**: The prepared images were inputs in VTrails [8, 9].
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In particular there might be other choices of the parameters that give a similar result.
Such a qualitative statement suggests we should be careful whenever we wish to determine parameters from the least squares fit, for any epidemic model. For example, in Figure 1, two SIR least squares fits to NYC Omicron outbreak data are shown. <|MaskedSetence|> <|MaskedSetence|> Here we explore the central question of how similar SIR solutions are to each other when their parameters are quite dissimilar. <|MaskedSetence|>
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**A**: These two SIR outbreaks are much more similar to each other than they were to NYC data.
**B**: Figures 5 and 6 are designed to address that question.
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**C**: It is difficult to use these fits to estimate the correct values of ρ𝜌\rhoitalic_ρ and τ𝜏\tauitalic_τ.
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Recently, a novel approach named the knockoff filter was introduced in [17], designed for FDR control in low-dimensional Gaussian linear models without relying on p-values. Subsequently, the model-X knockoffs framework [18] was proposed to generalize the knockoff filter to general high-dimensional nonlinear models with arbitrary dependency structure of the predictors. The model-X knockoffs framework essentially acts as a wrapper, seamlessly integrating with any feature selection methods that yield feature importance measures satisfying specific conditions. Recently, Lu et al. [19] proposed DeepPINK to combine the model-X knockoffs and deep neural networks for features characterized by joint Gaussian distributions, and Zhu et al. [20] introduced DeepLINK to generalize the distribution of input features via a latent factor model strategy for non-time series data. More recent developments on the extensions of model-X knockoffs inference include [21, 22, 23, 24, 25]. In particular, our current work was motivated by the idea of utilizing the latent factor structure in the recent work of IPAD knockoffs in [22].
These existing knockoffs based methods have primarily concentrated on scenarios involving independent observations, thus failing to address the widespread phenomenon of serial dependence that is commonly encountered in data from various domains, including ecology, medicine, and finance. <|MaskedSetence|> Motivated from this, we introduce a novel method for deep learning inference using knockoffs specifically tailored for time series data, named DeepLINK-T. There are three key components in DeepLINK-T: 1) a Long Short-Term Memory (LSTM) autoencoder for generating time series knockoff variables incorporating the serial dependence, 2) an LSTM prediction network for fitting a regression model using augmented features formed by both original and knockoff features, and 3) the application of the knockoffs framework for variable selection with FDR control. The use of LSTM networks enables DeepLINK-T to model and leverage the serial dependence in data, and hence produces more accurate variable selection outcomes. This is verified through intensive simulation studies in our paper. <|MaskedSetence|> <|MaskedSetence|> Specifically, DeepLINK-T pinpointed Parabacteroides as a key genus that alters the abundance level of Bacteroides in the gastrointestinal tract of early infants. Furthermore, our observations revealed that Pyramimonas and Heterosigma were notably associated with the concentration of chlorophyll-a in a marine metagenomic time series. Additionally, Ruminiclostridum and Rothia were identified to be significantly correlated with two distinct types of dietary glycans treatment. Overall, we anticipate that DeepLINK-T will contribute to the feature selection analysis of time series data, providing novel insights into unexplored aspects of the microbiome.
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**A**: Incorporating temporal information into the feature selection process has the potential to produce more accurate and interpretable variable selection results.
**B**: Additionally, we examine the robustness of DeepLINK-T to some misspecification of the time series latent factor model; our findings affirm that DeepLINK-T maintains control over FDR while retaining high variable selection power, provided that the number of training epochs is sufficiently large.
**C**: Finally, the practical usage of DeepLINK-T is tested on three metagenomic data sets.
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<|MaskedSetence|> <|MaskedSetence|> These two parameters were calibrated in a pilot study described above using healthy controls. <|MaskedSetence|> As we did not perform a separate calibration and validation study with ME/CFS and Long/COVID patients, we cannot be certain that these threshold parameters are adequately calibrated. However, despite the large absolute values, we do still believe that the step counts do provide a useful relative measure of subject activity level.
Figure 6: Linear regression analysis between UpTime and Hours of Upright Activity..
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**A**:
We acknowledge that the step counts reported seem unrealistically large.
**B**: The local variance algorithm depends on two related threshold parameters: the length of the sliding window from which local variance is calculated, and a peak threshold value.
**C**: The same threshold parameters were used in this study.
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<|MaskedSetence|> We therefore hope that our theoretical results will find use in the broader sphere of computation.
The remainder of the paper is organized as follows. In the next subsection, section 1.1, we point out that there are two natural ways to use chemical systems as computational machines and compare/contrast their strengths and weaknesses. In section 2, we (i) formally introduce the mathematical models that will serve as our algorithms for analog computation, which are deterministic chemical reaction networks with mass-action kinetics, (ii) discuss issues related to these models, and (iii) demonstrate, via example, the central purpose of this paper: the development of reaction network modules that can carry out arithmetic at speeds that are independent of inputs. In section 3, we provide the main mathematical analysis of this paper. <|MaskedSetence|> The work of section 3 is general enough that we hope and expect it to have applications in other areas of applied mathematics. In section 4, we provide the chemical reaction network modules that carry out the basic elementary operations discussed above (identification, addition, multiplication, inversion, etc.) and use the mathematical results of section 3 to prove that they have computational speeds that are independent of inputs. <|MaskedSetence|> In section 6, we demonstrate how to expand the constructions to handle calculations involving all real numbers (as opposed to non-negative numbers). Finally, in section 7 we provide a discussion, including many directions for future research..
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**A**: There are several bodies of research, outside the world of chemical reactions, on designing efficient hardware and software for analog as well as analog-digital hybrid computing [11, 12, 13, 14].
While we develop our results for a chemistry-based computer, the results apply equally well to any computational system that computes via nonlinear polynomial differential equations.
**B**: In section 5, we demonstrate how any calculation carried out via a combination of elementary operations using our constructions also has a computational speed that is independent of inputs.
**C**: In particular, we provide a rather detailed analysis of certain non-autonomous dynamical systems.
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ACB
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ACB
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ACB
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ACB
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Selection 3
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After obtaining the tractography data per subject, a groupwise whole-brain fiber clustering atlas was created using our robust, data-driven fiber clustering pipeline[36, 54, 55], as implemented in the whitematteranalysis (WMA) software (https://github.com/SlicerDMRI/whitematteranalysis). <|MaskedSetence|> The WMA fiber clustering pipeline has been successfully used for creating WM[36] and cranial nerve[69, 70] tractography atlases.
In our study, we pooled the tractography data of the 306 subjects from the CHCP and HCP datasets together for atlas creation. This allowed us to learn a tractography atlas for concurrent mapping of the WM connections across the two populations. <|MaskedSetence|> The WMA fiber clustering pipeline was used to parcellate all streamlines into K clusters. We chose K= 800𝐾800K\ =\ 800italic_K = 800, which was shown to be a good parcellation scale of the whole brain WM in previous studies[36, 71, 72]. We then performed anatomical curation of the fiber clusters by annotating each fiber cluster with an anatomical label belonging to a certain anatomical tract (e.g., the corticospinal tract) or an unclassified category. To do so, we leveraged the ORG atlas built only using the HCP data as a reference[36, 73]. <|MaskedSetence|> In total, the proposed atlas annotates 60 deep WM tracts and 222 superficial fiber clusters categorized into 16 groups based on their associated brain lobes, as detailed in Figure 2..
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**A**: Specifically, from each subject’s whole brain tractography, 10,000 streamlines were randomly selected, resulting in approximately 3 million streamlines for clustering.
**B**: We performed co-registration of the two atlases using a tractography-based registration[54] and calculated the mean closest point distances[55, 74] between the clusters in the new atlas and those in the ORG atlas and then assigned each new atlas cluster with the label of the closest ORG cluster.
**C**: The pipeline included two key processes: a group-wise tractography registration to align the tractography of all subjects to a common space, and a spectral clustering of tractography to subdivide the registered tractography data into multiple fiber clusters simultaneously.
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CAB
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Selection 2
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<|MaskedSetence|> We hypothesize that this may allow cells to better sense the electric field – i.e. <|MaskedSetence|> <|MaskedSetence|> If elongated galvanotaxing cells are more accurate when perpendicular to the field, how would this affect a group of cells’ ability to sense an electric field?
This question is particularly interesting because even in the absence of external cues like electric fields, confluent elongated cells tend to align with one another, resulting in the emergence of local nematic order [14, 15, 16, 17, 18]. If elongated cells are better sensors when they are perpendicular to the field, nematic cell-cell alignment may let groups of cells cooperate to ensure they are aligned in the best direction, improving collective galvanotaxis.
.
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**A**: that a cell’s accuracy at sensing the field direction is better if the cell is elongated perpendicular to the field.
**B**: Theoretical studies on chemical gradient sensing have demonstrated that elliptical cells possess higher accuracy in this orientation [12], and preliminary results extending our model of [13] to galvanotaxis also suggest galvanotaxing cells may – in some circumstances – be better sensors in this orientation.
**C**:
Galvanotaxing cells tend to align their long axes perpendicularly to the field [3, 7, 8, 9, 10, 11].
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CAB
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CAB
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CAB
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CBA
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Selection 2
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with R0=10−3,κ=1formulae-sequencesubscript𝑅0superscript103𝜅1R_{0}=10^{-3},\kappa=1italic_R start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 10 start_POSTSUPERSCRIPT - 3 end_POSTSUPERSCRIPT , italic_κ = 1/day. Values of λ,Y𝜆𝑌\lambda,Yitalic_λ , italic_Y
displayed along the curves are in units of /day. In panel (a) we set
Y=1𝑌1Y=1italic_Y = 1/day; as λ𝜆\lambdaitalic_λ is increased ⟨P(T)⟩delimited-⟨⟩𝑃𝑇\langle P(T)\rangle⟨ italic_P ( italic_T ) ⟩ also
increases. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|>
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**A**: In panel.
**B**: Small values of λ<2Y𝜆2𝑌\lambda<2Yitalic_λ < 2 italic_Y decease ⟨P(T)⟩delimited-⟨⟩𝑃𝑇\langle P(T)\rangle⟨ italic_P ( italic_T ) ⟩ below the baseline, whereas large fluctuations λ>2Y𝜆2𝑌\lambda>2Yitalic_λ > 2 italic_Y increase ⟨P(T)⟩delimited-⟨⟩𝑃𝑇\langle P(T)\rangle⟨ italic_P ( italic_T ) ⟩ beyond the baseline.
**C**: For λ=2Y𝜆2𝑌\lambda=2Yitalic_λ = 2 italic_Y results from the baseline are
recovered.
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CBA
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CBA
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BAC
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CBA
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Selection 4
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7 Discussion and Final Conclusion
Cell fate switching is a dynamic phenomenon often tied to regulatory network motifs that at the cellular level define the computational machinery of life. Most of these network motifs define molecular switches exhibiting diverse qualitative behaviors such as bistability, catastrophes, and hysteresis [1]. The most prominent examples of molecular switches involving minimal circuitry are the two-component positive feedback network motifs resulting from mutual repression or mutual activation of two genes. Traditional studies have shown that these motifs can exhibit at most bistable dynamics (two stable states or attractors) allowing the system to alternately switch between two states. <|MaskedSetence|> The biological programs underlying cell fate decision-making are however not just restricted to mono-and bistable regimes of dynamics. <|MaskedSetence|> This happens in differentiation programs such as differentiation of naive CD4+ T cells [37] as well as in diseases-inducing processes such as epithelial-mesenchymal transition (EMT) in which non-motile epithelial cells switch to mesenchymal and hybrid epithelial-mesenchymal cell fates which have migratory and invasive traits that often causes metastasis of carcinomas [26]. <|MaskedSetence|>
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**A**: In fact, higher-order dynamics such as tristability (three stable states/attractors/phenotypes) is now also prominently observed in biological mechanisms.
**B**: Further, the underlying cause of bistable dynamics is attributed to multimeric regulation (higher order Hill coefficient), in contrast to monomeric regulation that gives rise to only monostable dynamics.
**C**: Nevertheless, the minimal network motif that can exhibit tristability, or for that matter, mon, bi-and tri stability, remains largely unexplored.
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BAC
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BCA
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BAC
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BAC
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Selection 4
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<|MaskedSetence|> Moreover, as stressed during the paper, the gelatin is a very thin layer. A two-dimensional approach is then required. <|MaskedSetence|> <|MaskedSetence|> Indeed, the estimated parameters helps to quantify membrane permeability inside the Kedem-Katchalsky membrane conditions.
Finally, a more mathematical analysis on Model (2) can reveal interesting behaviour of solutions.
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**A**: However, this work could be a first step in studying not only basal membrane degradation, but also ECM one.
**B**:
More complex models considering the action of other cells involved in the invasion process, such as fibroblasts [24] could be very interesting to analyse.
**C**: ECM is in fact a thicker layer in which cells move thanks to degradation.
Furthermore, the understanding of the degradation process is crucial in modelling invasion.
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BAC
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BAC
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BAC
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CAB
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Selection 2
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<|MaskedSetence|> 3 shows list plots of the first 11111111 (top left) and the first 16161616 (top right) coordinates Pnsubscript𝑃𝑛P_{n}italic_P start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT of η0(x)subscript𝜂0𝑥\eta_{0}(x)italic_η start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_x ) with respect to the Hermite basis (12) and compares them with the coordinates of the “smallest” eigenvectors of M10subscript𝑀10M_{10}italic_M start_POSTSUBSCRIPT 10 end_POSTSUBSCRIPT and M15subscript𝑀15M_{15}italic_M start_POSTSUBSCRIPT 15 end_POSTSUBSCRIPT, respectively (i.e. the eigenvectors with the corresponding smallest eigenvalues). These eigenvalues (2.617…2.617…2.617...2.617 … and 2.531…2.531…2.531...2.531 …) are close to the Lerdahl ground state energy E0=2.528…subscript𝐸02.528…E_{0}=2.528\dotsitalic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT = 2.528 … (10), while one can still observe a clear deviation between the coefficients in the case of 11 dimensions (top left side of Fig. 3) the deviation already gets smaller in the case of 16 dimensions (top right side of Fig. 3). <|MaskedSetence|> 3 illustrates the fulfillment of the Schrödinger equation. The dashed curve shows the wave function E0η0(x)subscript𝐸0subscript𝜂0𝑥E_{0}\eta_{0}(x)italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT italic_η start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ( italic_x ), i.e. our predicted ground state stretched by the predicted energy eigenvalue E0subscript𝐸0E_{0}italic_E start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT, while the continuous curve shows the image of the smallest eigenstate under the action of HNsubscript𝐻𝑁H_{N}italic_H start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT, which is the approximation of the schematic Hamilton operator in terms of the truncated matrix MNsubscript𝑀𝑁M_{N}italic_M start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT. <|MaskedSetence|>
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**A**: The upper segment of Fig.
**B**: For growing N𝑁Nitalic_N the little oscillations of the Hermite components become smaller and smaller and their superposition approaches the predicted wave function.
5 Excited States of the Schematic Hamiltonian.
**C**: The plot in the lower segment of Fig.
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ACB
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CBA
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ACB
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ACB
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Selection 1
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