liangzid/robench2024b_all_setphysicsSCP-s · Datasets at Hugging Face

shuffled_text stringlengths 268 3.92k	A stringclasses 6 values	B stringclasses 6 values	C stringclasses 6 values	D stringclasses 6 values	label stringclasses 4 values
A: We first show the principle by considering a two-qubit toy model for solving the Exact Cover problem, and then consider more extensive simulations up to 8 qubits for solving MaxCut, in the presence of photon losses. We then compare the performance of QAOA with cat qubits to the one with standard qubits given the same average gate fidelity of the two systems. We provide our conclusive remarks in Section IVB: In Appendix A we recall the definition of quantum gates acting on cat qubits. In Appendix B we provide some details regarding the numerical optimization. Finally, in Appendix C we introduce a bosonic version of QAOA by Trotterizing the relevant quantum annealing Hamiltonian, and we compare its performance to QAOA for the case of a single Ising spin.C: The paper is structured as follows. In Section II we recall the definition of cat qubits as well as the gates needed to operate them. In Section III we outline how QAOA can be run on cat qubits	CAB	CBA	BCA	BAC	Selection 3
A: For this reason, from now on we are going to focus on models that are inflations of classical models. In the next section we are going to characterise them. B: We aim to interpret models of inaccessible informations as refinements of classical modelsC: Specifically, we’re intrigued by the implications of considering that each classical model might be a part within a larger model of inaccessible information	ABC	CBA	CBA	CAB	Selection 4
A: In order to generate random samples from a complex and high-dimensional probability distributions functions (PDF), we considered the Monte Carlo Markov Chain (MCMC) technique, based in Metropolis-Hastings AlgorithmB: It starts with an initial sample and iteratively proposes new samples based on a proposal distributionC: It then accepts or rejects the proposed sample based on an acceptance criterion that ensures the chain converges to the desired distribution. The posterior PDF getted around their most likely values allows us to obtain the best-fit model parameters with robust uncertainties.	ACB	CBA	BAC	ABC	Selection 4
A: Light-driving of materials leads to the photon-dressing of their Bloch bands and the formation of Floquet-Bloch states [4, 5, 39, 6]. Light’s frequency and intensity can tune these states that display properties not present in their parent equilibrium systemB: The main effects of light on the magnetic exchange mediated by these spin-degenerate systems are displayed through a light-controlled Fermi wavevector that leads to photo-controlled RKKY oscillations, and the “draining out” of the Fermi sea, either by an increasing photoinduced gap (for graphene) or by the migration of the zeroth Floquet band (for 2DEGs) above the Fermi level, which lead to a non-oscillatory behaviour of the exchange coupling in what resembles the Bloembergen-Rowland interaction [41]. On the other hand, 3D and 2D spin-orbit coupled materials offer a rich platform to explore the interplay between magnetic and spin-orbit effects to provide the basis for wide-ranging spintronics phenomena [42]. These systems also allow for the exploration of optical induction and control of non-collinear magnetic couplings which play an essential role in the formation of magnetic skyrmions [43], spin helices [44], and chiral domain walls [45].C: Hence, photon-dressing of electrons in light-driven materials is key to dynamically controlling the magnetic exchange coupling. However, it has been shown in Refs. [23, 22, 40] that the effects of periodic monochromatic light-driving on the magnetic exchange interaction mediated by two dimensional (2D) spin-degenerate systems, such as 2D electron gases (2DEGs) and graphene, are limited to light-controlled collinear exchange couplings	CBA	ACB	CBA	CBA	Selection 2
A: italic_Y, and Z.X=i⁢Y=−X.Zformulae-sequence𝑍𝑋i𝑌𝑋𝑍Z.X=\text{i}Y=-X.Zitalic_Z . italic_X = i italic_Y = - italic_X . italic_Z. The N𝑁Nitalic_N-qubit observables and the multiplicativeB: that X2=Y2=Z2=Isuperscript𝑋2superscript𝑌2superscript𝑍2𝐼X^{2}=Y^{2}=Z^{2}=Iitalic_X start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = italic_Y start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = italic_Z start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = italic_I, X.Y=i⁢Z=−Y.Xformulae-sequence𝑋𝑌i𝑍𝑌𝑋X.Y=\text{i}Z=-Y.Xitalic_X . italic_Y = i italic_Z = - italic_Y C: italic_X, Y.Z=i⁢X=−Z.Yformulae-sequence𝑌𝑍i𝑋𝑍𝑌Y.Z=\text{i}X=-Z.Yitalic_Y . italic_Z = i italic_X = - italic_Z	BAC	CAB	BAC	BCA	Selection 2
A: The (inverse) magnetic catalysis can be observed from the holographic QCD modelB: The dynamical breaking of conformal symmetry is realized by the nontrivial profile of the dilaton field in bottom-up holographic QCD models. In bottom-up holographic QCD, one can fit the model parameters to match the properties of real QCD such as the deconfinement phase transition, equations of state, and Regge trajectory of meson mass spectrum. C: The dilaton field in the Einstein-Hilbert action is dual to the running of the coupling constant and the expression of the dilaton field is correctly solved by the gravity equations	BAC	ACB	BCA	BCA	Selection 2
A: (2.7)B: the same covariance as ξ𝜉\xiitalic_ξ, cfC: But ξ~~𝜉\tilde{\xi}over~ start_ARG italic_ξ end_ARG and ξ𝜉\xiitalic_ξ are independent. In fact consider two test function φ,ψ𝜑𝜓\varphi,\psiitalic_φ , italic_ψ such that ⟨⟨φ⟩⟩=0delimited-⟨⟩delimited-⟨⟩𝜑0\langle\langle\varphi\rangle\rangle=0⟨ ⟨ italic_φ ⟩ ⟩ = 0 and	ABC	BAC	ABC	CAB	Selection 2
A: “absorption significance,” of different spectral componentsB: In this case, the design problem should be formulated by taking into account the relative contribution to the absorption, i.eC: The need to tailor properly the absorption for different spectral components, implies that the absorber has to have a suitably designed non-local behaviour. This can naturally be achieved in a planar layered media [26].	CBA	CAB	ABC	BAC	Selection 4
A: The objective of this study is to formulate a simple model, termed iterative percolation, in which critical percolation clusters are iteratively reorganized, and to investigate its percolation propertiesB: For convenience, we call the occupied (unoccupied) sites and clusters black (white), and percolation clusters are constructed by adjacent sites with the same color, thus, any pair of adjacent clusters must have different colors. Then, by randomly reassigning the color of each cluster, the original adjacent clusters could share the same color, and, as a consequence, larger clusters are formed. This cluster-merging rule can be applied iteratively to the newly formed clusters, allowing for the sequential construction of new generations of percolation configurations.C: We focus on the iterative site percolation on the triangular lattice, which begins with a critical site percolation configuration	CBA	ACB	CAB	BAC	Selection 2
A: This change in perception, just like the result the friend initially observed, is not directly accessible to Wigner and does not correspond to any observable on the joint system of S+F. However, identifying the friend with states of perception and inner thoughts begs the question in how far she can be aware of what happens to her memoryB: We considered the compatibility of certain models of the observer’s (the friend’s) internal thoughts in Wigner’s friend scenarios with the no-signaling condition. In general, Wigner’s measurement affects the record of the measurement result stored in the friend’s memory registerC: We considered the idea that the friend might have some perception of the change Wigner’s measurement induces to her memory. More concretely, we described the case where the friend can have multiple registers available for storing results which are then each measured by Wigner in some fixed basis. The friend could have a notion of the overall change to these memory registers (for example, the probability of entries being flipped during Wigner’s measurement) without having a persistent perception of individual results across Wigner’s measurement.	BAC	ABC	BCA	CBA	Selection 1
A: Deviations in this case remains significant for essentially any value of γ𝛾\gammaitalic_γB: For γ=2𝛾2\gamma=2italic_γ = 2, our treatment predicts a circularization timescale that is about 2 times shorter than the standard formula. C: The contribution from the fast moving particles has also an effect on e𝑒eitalic_e	CBA	BCA	ACB	BAC	Selection 2
A: First, in section IV.1 we give the result for a simplified version of the computational model wherein we only allow Pauli measurements, no Clifford gates, and in particular, we allow only sequences of independent and commuting Pauli measurementsB: In this section we present our main result—the amount of classical data that the simulation procedure Algorithm 1 must track is smallC: This simplified model is still universal for quantum computation [15, 16]. Then, in Section IV.2 we give a more general statement of the main result where we allow computations consisting of any sequence of Clifford gates and Pauli measurements.	BCA	ABC	BAC	ABC	Selection 3
A: This paper is organized as follows: In Section II, we briefly review the WSD formalism we utilize in this paperB: In Section V and show how this formalism can be mapped to the SMEFT framework, and in particular derive the UV scale that corresponds to the upper limit on the FV Wilson coefficient. Finally, we present our conclusions in Section VI. We relegated much of the calculational details to the appendices A - D.C: In Section III, we present our complete analysis on the FV through the di-Higgs couplings in the leptonic sector, whereas in Section IV, we do the same analysis in the quark sector	BAC	CAB	BAC	ACB	Selection 4
A: Similarly, the existence domains of moving PW and SW bright solitons are also obtained, which are stationary solitons in the moving frame. Besides, we analyze the stability of these bright solitons by linear stability analysisB: Furthermore, we investigate the existence and stability domains of PW and SW bright solitons when the Zeeman field exists, based on the single-particle energy spectrum and a large number of numerical solutions. We find that the linear Zeeman effect is advantageous (disadvantageous) to the stability of SW (PW) bright solitons. Stable SW and PW bright solitons in both ferromagnetic and antiferromagnetic BECs are found. Finally, we discuss some interesting collision dynamics of stable bright solitons. C: In this work, we systematically investigate stationary and moving bright solitons in spin-1 BECs with SOC in a Zeeman field, focusing mainly on the bright solitons corresponding to the PW phase and the SW phase. Without the Zeeman field, we establish a connection between the single-particle energy spectrum and exact soliton solutions, whereby we obtain the existence domains of stationary PW and SW bright solitons	ACB	BAC	BCA	ABC	Selection 3
A: To this end, in this paper we extend the notion of uniquely decodable (or completely lossless) quantum codes to be used for quantum block data compressionB: We hope that our work would be supportive in the quest towards answering the above questions, which have been left open in the current work. C: As the main result (Theorem 2.18), for a fixed m⁢l𝑚𝑙mlitalic_m italic_l many pure states emitted by a given quantum stochastic source, we derive the optimal lower bound of the average codeword length over a subset of uniquely decodable quantum codes called “special block codes”, which are applied to encode the pure states in m𝑚mitalic_m many blocks each of block size l𝑙litalic_l	CAB	CAB	ACB	CAB	Selection 3
A: For high-dimensional real-valued PDEs, there exist a variety of classic and deep learning-based approaches that rely on sampling from diffusion processes, e.g., Cliffe et al. [39], Warin [40], Han et al. [14], Weinan et alB: This requirement limits the applicability of this approach to our setting. BSDE methods studied by Nüsken and Richter [43, 44] are closely related to our approach, but they are developed for the elliptic version of the Hamilton–Jacobi–Bellman (HJB) equation. We consider the hyperbolic HJB setting, for which the existing method cannot be applied. C: [16]. Those works rely on the Feynman-Kac formula [41] to obtain an estimator for the solution to the PDE. However, for the Schrödinger equation, we need an analytical continuation of the Feynman-Kac formula on an imaginary time axis [42] as it is a complex-valued equation	CAB	BAC	BAC	ACB	Selection 4
A: Understanding the projector approach to open quantum systems is a powerful asset not only to derive effective dynamics in any open quantum system, but also to understand the deep connection between all the known methods and to help clarify confusing nomenclature conflicts across different fields 111Most prominently, the term “adiabatic elimination” refers to slightly different procedures in the atomic physics and the optomechanics communities [6, 10], a past source of confusion for the author and the spark that ignited this tutorial..B: Although needed to efficiently study paradigmatic systems, this “case-by-case” approach can make it difficult to derive effective equations for systems where conventional approaches are not applicable. A solution to this problem is offered by a more general formulation of open quantum systems in terms of projection superoperators in density matrix space, which allows to derive a single general equation describing the quantum dynamics of subsystems, the Nakajima-Zwanzig equation [13, 14, 16, 17, 18]C: Any effective description, including adiabatic elimination and Born-Markov master equations, can then be derived as a particular case of the Nakajima-Zwanzig equation	CAB	ACB	CBA	CBA	Selection 1
A: On the other hand, dipolar systems present rich physics due to the unique combination of traits of the dipole-dipole interaction (DDI): its anisotropy and long range character in three dimensionsB: This mix gives rise to a wide variety of phenomena, such as the emergence of ultra-dilute self-bound droplets [36, 37, 38, 39, 40, 41], supersolids [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58] which may be even self-bound in the case of a dipolar mixture [59], striped liquids [60] and the anomalous emergence of supersolidity upon increasing temperature [61, 62, 63], among othersC: In the context of the polaron problem, an immediate question emerges: how do the unique properties of the DDI affect the quasiparticle properties and dynamics of an impurity immersed in a dipolar medium? Several theoretical works have addressed this question in a variety of different conditions: from non-dipolar [24, 27] and dipolar [29] impurities immersed in a dipolar fermionic medium, to an impurity-medium bilayer configuration [34, 25] or dipolar [26, 31, 32] as well as non-dipolar [33, 28] impurities immersed in a dipolar BEC. It has also been shown that dipolar impurities can potentially function as tools to probe the properties of dipolar bosonic quantum droplets due to their neglectable back-action on the droplets [31]. In almost all cases, though, theoretical studies are restricted to an ultra-dilute bath, meaning that the characterization of the polaron properties for large gas parameters of the background is still a rather unexplored subject.	ACB	BCA	ABC	BCA	Selection 3
A: The game of Rock-Paper-Scissors, where rock smashes scissors, scissors cut paper, and paper wraps rock has been employed by evolutionary biologists to investigate the interactions between competing populations of species, where one species has an advantage over only one of its opponentsB: We explore the evolution of this dynamical system in accordance with a sociological model [34, 35], where each population, following a unique strategy, seeks to minimize the difference between the average payoff of the population and the individual payoff.C: The game dynamics that describe the evolution of the populations following a particular strategy can be examined with the use of evolutionary game theory [27]	ACB	BAC	BAC	BAC	Selection 1
A: Figures 6a, c, e, and f, show the entire spectrum from 200 nm to 1000 nm at different detunings of the driving field labeled in a and d. Within the sensitivity limit of our spectrometer, we observe no pronounced fluorescence except from the two driving lasers at 780 nm (probe field) and 480 nm (coupling field), and the same background values for the on-resonant [c and f] and the far-detuned [b and e] excitation. This is consistent with fluorescence imaging of the vapor cell using a qCMOS camera (HAMAMATSU, C15550-20UP) for bandpass-filtered wavelengths between 500 nm and 700 nm after background subtraction, where no obvious fluorescence signal is detected. B: First, we confirmed that our spectrometer reliably detects the fluorescence from the vapor cell, by monitoring the 780 nm photons when scanning the detuning. As shown in Figs. 6a and 6d, the counts of 780 nm photons decrease significantly around the transmission peaks, which is a direct consequence of the reduced occupation of the intermediate state \|5⁢P3/2⟩ket5subscript𝑃32\|5P_{3/2}\rangle\| 5 italic_P start_POSTSUBSCRIPT 3 / 2 end_POSTSUBSCRIPT ⟩ due to the electromagnetic induced transparency (EIT)C: To further search for the presence of plasma, we have performed additional measurements of the fluorescence spectrum. As discussed in Ref. weller2019interplay , the presence of a plasma should lead to radiative emission at a broad range of wavelength due to recombination and population of different Rydberg levels	CBA	ABC	BCA	BCA	Selection 1
A: We then treat the full analytical covariance matrix as a block diagonal matrix with the individual covariance matrix sitting in its corresponding blockB: We assume there is no correlation between different surveys mainly because of the large cosmological distances and weak overlap between the different samples. However within the BOSS survey, there is overlap between the z⁢1𝑧1z1italic_z 1 and z⁢2𝑧2z2italic_z 2 bins, which cannot be modelled without extending the analytical covariance matrix work of WadekarC: We test the procedure’s suitability described above by constructing individual analytical covariance matrices for each of the nine clustering samples we consider	ACB	CAB	BCA	ABC	Selection 3
A: It is also supported by the Open Fund for Key Laboratories of the Ministry of Education under grant number QLPL2024P01.B: This work is supported by the National Science Foundation of China (NSFC) under grant numbers 12405154, 12175100, and 11975132C: The authors thank Zi-qiang Zhang for his useful discussions	BCA	ABC	CBA	BCA	Selection 3
A: We will see that the choice of architecture significantly influences the presence of IGBB: For instance, sigmoid activations can achieve dynamical isometry, maximizing signal propagation depth (schoenholz2016deep), unlike ReLUs (pennington2017resurrecting). These activations are also compared in terms of generalization performance, revealing distinct behaviors for ReLUs and sigmoids (oostwal2021hidden). Notably, these studies often consider averaging over weight initializations. C: Architecture design, particularly the selection of activation functions, has been extensively studied (dubey2022activation), with a focus on ReLU versus differentiable activations such as sigmoid	CBA	BAC	ACB	CAB	Selection 3
A: Weisbrich and J.C. Cuevas for useful discussionsB: W.B. acknowledges support from the DFG via SFB 1432 (ID 425217212) and BE 3803/14-1 (ID 467596333). W.W. acknowledges support from the Swiss National Science Foundation (grant number 200020_207538). F.N. acknowledges support from the European Research Council (grant number 804273) and the Swiss National Science Foundation (grant number 200021_201082). C: We thank the Cleanroom Operations Team of the Binnig and Rohrer Nanotechnology Center (BRNC) for their help and support. We are grateful to H	BCA	CBA	ACB	ABC	Selection 1
A: JK is funded through the NSERC CGS-D program. JW is supported by the European Union’s Horizon 2020 Framework: ERC grant 682608 and the “Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics”. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.B: Acknowledgements.We would like to thank Chris Beem, Pieter Bomans, Ramiro Cayuso, Kevin Costello, Richard Eager, Owen Gwilliam, Ji Hoon Lee, Surya Raghavendran, and Keyou Zeng for useful conversations. This research was supported in part by a grant from the Krembil FoundationC: DG is supported by the NSERC Discovery Grant program and by the Perimeter Institute for Theoretical Physics. KB and DG are supported by the Simons Foundation through grant 994308 for the Simons Collaboration on Confinement and QCD Strings	BAC	CBA	BAC	CAB	Selection 4
A: The first says that the asymptotic subrank of any concise tensor is at least the cube-root of its smallest dimensionB: We prove two general lower bounds on the asymptotic subrank of concise tensors that depend only on the dimensions of the tensorC: The second says that the asymptotic subrank of any “narrow enough” tensor (meaning that one dimension is much smaller than the others) is maximal.	ABC	BAC	BCA	BCA	Selection 2
A: (2012)B: For the moving frame and partial wave decomposition of the scattering amplitude in the finite volume, we follow the procedure described in Doring et alC: The two-meson loop function in the finite volume, G~~𝐺\widetilde{G}over~ start_ARG italic_G end_ARG in Eq. (13) projected in partial waves, is a matrix with non-diagonal elements due to the partial weave mixing. Its elements are,	CBA	CBA	ABC	BAC	Selection 4
A: We have derived analytical expressions for the auto-correlators and cross-correlators of the current-current fluctuations in a double quantum dot that are valid at both zero and finite voltages, temperatures and frequencies, whatever the values of inter-dot and dot-reservoirs couplings are. We have highlighted specific features such as the reduction of the zero-frequency noise, as well as the possibility of having a negative Δ⁢TΔ𝑇\Delta Troman_Δ italic_T-noise, meaning that the noise can be further reduced by applying a temperature gradient between the two reservoirsB: Moreover, it leads at finite frequency to a change of sign in the cross-correlator in the vicinity of honeycomb vertices. By including Coulomb interactions at the Hatree-Fock level, one shows that a change of sign in the cross-correlator can also be obtained due to the presence of interactions, even at zero-frequencyC: The approach presented in this work can be extended to take spin-orbit coupling into account, leading to effective g-factor[50] and Pauli spin blockade[51, 52], which are all the more important to describe realistic situations in double quantum dot systems and spin qubits, as experimentally studied. We believe that the tools developed in this article will be invaluable in the realization of such project, which remains to be done.	CBA	ABC	BCA	BCA	Selection 2
A: The observed ForcePho photometry for the disc (blue), core (red) and combined core+disc galaxy (lilac) is overplotted. We find the synthetic photometry matches the photometry of the combined core + disc galaxy, highlighting that the combined medium- and broad-band photometry traces both the stellar continuum and nebular emission line.B: The 1D NIRSpec spectrum (black) and synthetically derived photometry from the spectrum (orange points)C: Figure 16: The NIRSpec spectrum compared to the ForcePho photometry	CBA	CAB	BCA	ABC	Selection 1
A: The convergence with respect to the number of active bands in Hartree-Fock (HF) calculations requires careful consideration. Including more bands allows states to lower their energy by accessing higher bands, which is generally beneficial as it suggests the system is approaching the correct physical Hilbert spaceB: As shown in Fig. S6, states can indeed reduce their energy when more active bands are included. For states discussed in the main text, the energy reduction remains within 0.1%percent0.10.1\%0.1 %, leaving no changes in the phase diagramC: Second, adding more bands introduces new degrees of freedom, which can lead to new, potentially competing states. However, whether these new degrees of freedom are physically relevant depends on the system under study.	CAB	CAB	ABC	CBA	Selection 3
A: In Sect. 3 we study the asymptotic expansion of the Borodin–Forrester hard-to-soft edge transition law (6)B: Here we lay the foundational work for the concrete functional form of all the expansion terms in this paperC: Whereas the general structure of the expansions, which gives their uniformity and differentiability, is found by expanding operator determinants, the appealing functional form of the expansion terms, as displayed in (31), is established by combining the Tracy–Widom theory with factorizations of the β=2𝛽2\beta=2italic_β = 2 hard- and soft-edge distributions. By going beyond the first order terms, the proof of the functional form is subject to the linear form hypothesis, the evidence of which is detailed in Appendix D.	CBA	CAB	ABC	ACB	Selection 3
A: The data refers to a spin chain with the same parameters as in Fig. S2, but N=2,M=2formulae-sequence𝑁2𝑀2N=2,M=2italic_N = 2 , italic_M = 2B: The plots represent the exact time evolution (black solid line) and the dynamics predicted by the ML algorithm (red dashed line). In this case, the overall dynamics is well captured.C: Figure S3: Full plot of the ML algorithm’s performance. In figure the 15151515 non-trivial components of the coherence vector visubscript𝑣𝑖v_{i}italic_v start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT	ABC	CAB	BCA	CAB	Selection 3
A: Determining the exact optimal POVM for our system in order to fully utilize its precision potential for maximizing temperature information is an intriguing question with significant practical implications. If an experimental approach can be devised, possibly involving a combination of field quadrature measurements, it would be immensely valuable. However, due to the analytical complexities involved, we leave this avenue open for future research. B: Experimental access to temperature-sensitive field quadratures and their second moments is feasible through techniques such as homodyne, heterodyne, and tomographic state reconstruction methods Cenni et al. (2022); Khan et al. (2022)C: We can infer the temperature through straightforward quantum optical quadrature measurements Raymer and Beck (2004) on the cavity photons. The calculations show that the corresponding CFI (∼3similar-toabsent3\sim 3∼ 3) is about 20%percent\%% of the QFI ( ∼15similar-toabsent15\sim 15∼ 15), as determined by comparing Figs. 4 and 6. Therefore, while our exploration of suboptimal measurements holds practical relevance, our investigation into QFI highlights the fundamental potential of the system	ACB	ABC	CAB	ABC	Selection 3
A: (1996); Polychronakos (1999); Cattani and Bassalo (2009); Surya (2004), ewkons Hoyuelos and Sisterna (2016) modifications of statistics due to quantum gravity Swain (2008); Balachandran et al. (2001); Baez et al. (2006), non-commutative geometry Arzano and Benedetti (2009) and others Maslov (2009); Trifonov (2009); Bagarello (2011); Niven and Grendar (2009). B: Earliest work along these lines dates back to Gentile and his attempt to interpolate between two statistics Gentile j. (1940), and since then, we have seen dozens of generalized and exotic statistics, such as parastatistics Green (1953), quons and intermediate statistics Greenberg (1991, 1999); Lavagno and Narayana Swamy (2010); Fivel (1990), infinite statistics Greenberg (1990); Medvedev (1997), generalizations of fractal and topology-dependent statistics CHEN et alC: While these approaches agree at the level of ordinary statistics (bosons and fermions), all of them have been criticized for their ad hoc nature Messiah and Greenberg (1964); Mirman (1973); van Enk (2019). This leaves the door open for various generalizations, many of which resort to somewhat arbitrary assumptions added to the quantum formalism	CAB	CAB	ABC	CBA	Selection 4
A: The survey is supported by several software and data processing pipelines. The imaging from the public DESI Legacy Imaging Surveys (Zou et al., 2017; Dey et al., 2019; Schlegel et al., 2023) supports the target selection pipeline for spectroscopic follow-upB: Specific details are provided for the Bright Galaxy Survey (BGS; Ruiz-Macias et al., 2020), luminous red galaxies (LRGs; Zhou et al., 2020, 2023), emission line galaxies (ELGs; Raichoor et al., 2020, 2023a), and quasars (QSOs; Yèche et al., 2020; Chaussidon et al., 2023). A planning pipeline optimizes the tiling of observations throughout the survey (Schlafly et al., 2023). Fibres are assigned to targets for each pointing in another pipeline (Raichoor et al., 2023b). Resultant spectra are processed with a ‘spectroperfectionist’ (Bolton & Schlegel, 2010) data reduction pipeline (Guy et al., 2023) followed by a template fit yielding redshifts and a final classifications for each source (Bailey et al., 2023).C: Target selection employs quality cuts, as well as various colour selections and machine learning classification tools, tailored to provide a highly complete and low contamination sample for each tracer type. Identification and prioritization of all targets are described in Myers et al. (2023)	CBA	BCA	BCA	ACB	Selection 4
A: Returning to immobility, the Carroll symmetry effects only the CoM and implies, for a two-particle Carroll system with the BGL potential (I.2), the immobility of the latterB: fig.1a. C: The relative coordinates are not affected by the Carroll action (III.7) and they can indeed move, as illustrated in sec.III, cf	CBA	CAB	ACB	BAC	Selection 3
A: In this section, we provide a few numerical tests and compare our algorithm with previous worksB: First, we briefly introduce the three different algorithms for QPE : ML-QCELS[12], MM-QCELS [16] and QMEGS [17]C: The last two can be used for QEEP as well.	ABC	BAC	CBA	BCA	Selection 1
A: It is worth noting that solving PDEs using ANNs has sound theoretical foundations, e.g., Hornik et alB: [28, 29] have shown that ANNs with multiple layers can approximate any continuous functions, and recently Zhou et alC: [30] have extended the earlier work to CNNs. In addition to the direct solution of PDEs using ANNs, neural solvers with convergence guarantees have been proposed for fast iterative solutions [31].	CAB	ABC	BAC	BAC	Selection 2
A: The anemometer on the left side of the fin, anemometer one, increased in value and when the percent difference threshold was exceeded, the foil began to converge towards that sensor, decreasing the percent difference measurement until it was within an acceptable range [Fig. 2]. The position of the hydrofoil depicts a clear story of what was occurring within the system, moving to positions of approximately 90°, 140°, 105°, 60°, 150°, 105°, 150°, and 130°throughout timeB: The foil was able to quickly and consistently move to the new location and maintain its position until a new flow direction was encountered [Fig. 3]. We can see that the rise and fall time of the foil heading is approximately forty degrees per second with the servo motor used. The sign of the percent differences indicate what side the flow was originating, i.e. left or right, and we can further assess the hydrofoil’s ability to accurately orientate itself in the direction of flow. C: After calibrating the anemometers, we see they exhibit a percent difference, with no flow speed, of approximately 1.72% with anemometer one having a resting voltage of 0.58 volts and anemometer two with 0.59 volts. The first 10 seconds of the data set were devoted to allowing the temperature dependent resistor to stabilize. Afterwards the fan was turned on at the 140°location	BCA	BAC	ACB	CBA	Selection 1
A: My goal in introducing spacetime representation theory (and the ISE Method) is to gain some mathematical control over the range of all possible spacetime representations of our theoriesB: This should then help us answer some of the interesting philosophical questions which are raised by the possibility of alternative spacetime framings for our theories. C: This paper has introduced spacetime representation theory as a general framework for understanding our capacity to topologically redescribe our spacetime theories	CAB	BCA	CAB	ABC	Selection 2
A: We choose occupancies n~l=1subscript~𝑛𝑙1\tilde{n}_{l}{=}1over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = 1 and n~u=0subscript~𝑛𝑢0\tilde{n}_{u}{=}0over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT = 0B: n~lsubscript~𝑛𝑙\tilde{n}_{l}over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT and n~usubscript~𝑛𝑢\tilde{n}_{u}over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT of the orbitals \|Θl⟩ketsubscriptΘ𝑙\|\Theta_{l}\rangle\| roman_Θ start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ⟩ and \|Θu⟩ketsubscriptΘ𝑢\|\Theta_{u}\rangle\| roman_Θ start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT ⟩, respectivelyC: Orbiton frequencies	BAC	CAB	ABC	ACB	Selection 1
A: Performing a measurement on spin N𝑁Nitalic_N, we studied whether its influence will be achieved spin 1111 or notB: (3)C: In this paper, we considered a spin chain, from spin 1111 to spin N𝑁Nitalic_N, which interact through the free Hamiltonian H𝐻Hitalic_H in Eq	BCA	ACB	CBA	BAC	Selection 3
A: Experimental proposals over several decades have considered superfluid helium as a target material [7, 8, 9, 10], with increasing theoretical attention over the past few years [11, 12, 13, 14, 15, 16, 17, 18]B: There are a number of proposals at various stages of development based on this idea, including HeRALD [19], DeLIGHT [20], ALETHEIA [21], and others [22, 23]. These experiments are projected to be sensitive to dark matter masses above 𝒪⁢(1)𝒪1\mathcal{O}(1)caligraphic_O ( 1 ) MeV.C: Recent experimental proposals have focused on nuclear scattering leading to the quantum evaporation of helium atoms, which can then be detected	ABC	CAB	ABC	ACB	Selection 4
A: There is also evidence that the intermediate velocity cloud (IVC) gas is organized into filaments that are aligned with their local magnetic fields (Panopoulou et al., 2019; Pelgrims et al., 2021). The difference could be caused by the Hessian algorithm being more sensitive than the RHT to artifacts in low-signal velocity channels. We explore this in Section 4.3. B: Using the RHT algorithm for determining the polarization angle, the H i intensity maps as the weighting (see Section 4), and the Spearman rank correlation coefficient and mean angle alignment as the correlation metrics, Clark & Hensley (2019) did not see the decrease in the correlation after a certain velocity that we see in Figure 1C: The correlation asymptotes instead	BAC	CBA	CAB	CBA	Selection 3
A: It is therefore concluded that a BSM resolution of the fine-structure anomaly in heavy muonic atoms with a single new boson is disfavouredB: Finally, new experimental data including additional elements with improved precision could also shed light on the muonic puzzle, or even bring back some of the previously excluded resolutions. C: This motivates further a careful re-investigation of the wide range of effects entering the binding energy calculations as was accomplished with NP in Ref. [8] or SE in Ref. [9]	CBA	CBA	ACB	ABC	Selection 3
A: Nowadays, the most advanced ones are superconducting qubits (used, for example, by IBM, Google, and Rigetti), trapped ions (used by AQT, Quantinuum and IonQ), neutral atoms (used by PasQal, QuEra, and Atom Computing), and photons (used by Quandela and Xanadu)B: In principle, a DQC system could integrate heterogeneous QPUs, based on different quantum technologiesC: Other promising quantum technologies are emerging, such as molecular nanomagnets [24] (which are particularly suitable to act as multilevel logical units, i.e., qudits).	ACB	ACB	CBA	BAC	Selection 4
A: In the previous section, we discussed the example of rare-earth trihalides, where the giant magnetic response of chiral phonons originates from the coupling of CEF-split electronic levels with chiral optical phononsB: We begin with a general analysis of orbital configurations and then perform calculations for the concrete example of CoTiO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT. C: In this section, we show that chiral optical phonons in 3⁢d3𝑑3d3 italic_d-electron magnets with octahedral ligand configuration can yield a similarly strong response	ACB	BAC	CBA	ABC	Selection 1
A: A detailed analysis of the complexity of Algorithm 1 is provided in Sec. 2.5B: In Sec. 2.3, the correctness of Algorithm 1 is established. Example quantum circuits are provided in Sec. 2.4 to illustrate how Algorithm 1 worksC: Quantum state preparation of a class of nonuniform superposition states using a variation of Algorithm 1 is described in Sec. 3 and some illustrative examples along with relevant quantum circuits are given in Sec. 3.1. Finally, the conclusion of the article is summarized in Sec. 4.	BAC	ABC	CAB	ABC	Selection 1
A: In Szegedy’s quantization this requirement is satisfied due to Proposition 2.1. Because dependence of the result on the state of the coin it is important to include this additional degree of freedom into the definition of the correspondence.B: It is natural to demand the same one-step transition probabilitiesC: In order to compare quantum walks with discrete random walks one needs to establish a correspondence between them	CBA	BCA	ABC	ABC	Selection 1
A: This work formulates the problem of quantum soft-covering in its most natural setting, and presents a one-shot characterization of the problem in terms of smoothed one-shot quantum entropic quantitiesB: We also contribute to the study of second-order asymptotics and provide achievability bounds for the same. As a part of future work, we aim to study optimal second order performance limits for the formulated quantum soft-covering problem.C: By leveraging the one-shot result, we provide a single-letter characterization of the optimal rate of the quantum soft-covering problem in terms of the minimal coherent information	ACB	ABC	BCA	BCA	Selection 1
A: Besides the Zeeman effect lifting the degeneracy of the Landau levels, the splitting also spatially separates spin-polarized edge states with opposite spin [58]B: This separation occurs in the direction perpendicular to the boundary (y-direction in this case)C: Thus, in a QH/SC heterostructure in the LLL, one edge state moves closer to the interface and the other moves further away. To account for this spatial shift, we consider the modified tunneling Hamiltonian,	CAB	BCA	ACB	ABC	Selection 4
A: Left: A 3D joint configuration of edges and vertex colors under the Edwards–Sokal coupling, including the full interface, ℐℐ\mathcal{I}caligraphic_IB: Figure 5C: Right: The same model, with just the full interface displayed. Note that the full interface should not be thought of as a surface — there are many sheets of faces sticking out and creating overhangs.	CAB	BCA	BAC	ACB	Selection 3
A: As shown in Fig. 2(a)-(c), there are many extrema for these quantitiesB: The typical local minima marked with the gray dashed lines in Fig. 2(a) manifest that the extended degree suddenly drops at specifical chemical potentials. Interestingly, the local extrema of the DOS and ΔΔ\Deltaroman_Δ shown in Fig. 2(b) and (c) almost coincide with those of the extended degree shown in Fig. 2(a). These results show that the more localized the single particle state around the Fermi energy is, the smaller the DOS is and the weaker the pairing gap amplitude is. C: The μ𝜇\muitalic_μ- dependences of the DOS at Fermi level and the pairing gap amplitude ΔΔ\Deltaroman_Δ at zero temperature are shown in Fig. 2(b) and (c), in comparison with the extended degree shown in Fig. 2(a)	BAC	BAC	BCA	ABC	Selection 3
A: Furthermore, it was suggested that quantum coherence in energy transfer may be responsible for its high efficiency [14, 15, 16]B: However, while fully quantum models for exciton transfer are available, classical models can equally well describe it or are compatible with the experimental findings on the process – hence it has been difficult to assess whether it is genuinely quantum [17, 18]. C: We focus on energy transfer via excitons because it is key for several biological processes, e.g., photosynthesis, in different biological systems of different scales, e.g., Fenna-Matthews-Olson (FMO) complex or polydiacetylene	CAB	BCA	CBA	CAB	Selection 2
A: AUROC metric, higher is better: mAUC denotes the AUROC averaged over all the mediator masses for a given signalB: Entries associated to an () were averaged over three random seeds: 42424242, 51515151, and 73737373. Top three best results in boldface.C*: Table 1: Comparison of anomaly detection baselines and models on test-set, best scores only	BCA	ABC	ACB	CBA	Selection 1
A: We thank RoaRQ consortium for useful discussions on dataset coverage, Shrihan Agarwal for useful discussions on TSP, Timothy Proctor for manuscript feedback, and Neil Mehta for testing portions of the dataset. We acknowledge support from Sandia National Laboratories’ Laboratory Directed Research and Development Program under the Truman Fellowship. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.SB: Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.C: Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis	BCA	ACB	CBA	ABC	Selection 2
A: The KS theorem rules out non-contextual hidden-variable theories via the existence of a finite set of three-dimensional vectors, referred to as a KS vector system [3]B: The first KS vector system, discovered in 1967, contains 117 vectors [3]. Another theorem that relies on the existence of KS systems in an essential way is the “Free Will” theorem of John Conway and Simon Kochen [5].C: A KS vector system (or simply a KS system) is a combinatorial object that witnesses a contradiction between non-contextuality (i.e., the assumption that observables can be assigned values prior to measurement and independent of measurement context) and the SPIN axiom of QM	ABC	BAC	BCA	ACB	Selection 4
A: We can utilize biholomorphic mappings to extend the solution from the unit disk to more general, simply connected domainsB: The Riemann mapping theorem establishes that any simply connected domain is biholomorphically equivalent to the unit disk with boundary regularity for smooth Jordan domainsC: Therefore, by leveraging this theorem, the solutions can be readily extended (Theorem 3.4). However, we need the following result before generalizing the equivalence of problems to any such domain.	CBA	BCA	ABC	CBA	Selection 3
A: In FigB: 4, we visualize the energy conditions, for positive and negative values of the model parameter ϵ1subscriptitalic-ϵ1\epsilon_{1}italic_ϵ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, in terms of the total stress-energy tensorC: The plots verify that all energy conditions are fulfilled by the present model of the pulsar J0740+6620.	BCA	ABC	ACB	BCA	Selection 2
A: The top original network is divided into boxes of a fixed diameter, some of which are marked with different colours. In the new network after renormalization (shown below), these boxes are replaced by nodes with the corresponding colours. Again, the macroscopic and microscopic characteristics of the network after renormalization (represented by red triangles in Fig. 2) are similar to those of the original network.B: It is divided again into new smaller boxes, some of which are marked with different colours. Both macroscopic and microscopic characteristics of this new network (represented by green squares in Fig. 2) are similar to those of the original network (indicated by navy circles in Fig. 2). Part b) of this figure illustrates renormalization procedure applied to the same network as in part aC: Figure 1: Schematic illustration of the idea of geometric self-similarity in complex networks on the example of the fractal model of nested BA networks (for the definition of the model, see “Methods” section). Part a) of the figure shows that the network can be subdivided into parts—boxes of a given diameter—each of which is (at least approximately) a reduced-size copy of the entire network. In the top picture shown, one such box, marked in red, is extracted from the original network and treated as a new network (shown below)	CAB	BCA	ACB	CBA	Selection 4
A: The relation among I-Love-Q, Quasi Normal modes (QNMs) frequencies and the combination of mass and radius, moment of inertia and QNMs frequencies, and moment of inertia and compactness of NSs are insensitive to EoS [67]. Pappas and Apostolatos found three hair theorems for NSs in GR, which is an approximate generalization of the BH no-hair theorem [68] . Among all the universal relations, I-Love-Q relations are more insensitive to EoS than others. Therefore, studying these I-Love-Q relations in the different modified theories of gravity is of utmost interestB: Pani and Berti [69] calculated the I-Love-Q relations in scalar-tensor theory, Sham et al. [70] in EiBI gravity and Yagi et al. [71] in dCS gravity. Kleihaus et al. [72] studied the I-Q relation for rapidly rotating NSs in EdGB gravity.C: In modified theories of gravity, the blackhole solution is the Kerr metric, the blackhole solution in GR, or is deviated from the Kerr solution by a small margin such that these modified theories cannot be distinguished from GR using present and future astrophysics observations. Unlike the blackholes, the coupling of matter with gravity in the NS provides alternative ways to test modified theories of gravity in the strong field regime [66]. The cost of the coupling of matter with gravity is paid off by the fact that the mass-radius relation is sensitive to both the EoS and the underlying theory of gravity. However, various universal relations, independent of EoS, can be found for NSs which opens the windows of possibilities of the comparative studies of NSs in different modified theories of gravity without prior details knowledge of EoS	ABC	BCA	CAB	CBA	Selection 2
A: We have so far remained entirely agnostic as to the Yukawa couplings with charged leptons that generate neutrino massesB: Scalar masses above 30⁢μ⁢eV30𝜇eV30~{}{\rm\mu eV}30 italic_μ roman_eV are both consistent with constraints from BBN, and predict RHNs in the mass range of a few GeV. It is well known that leptogenesis by oscillations (or ARS leptogenesis for Akhmedov, Rubakov, and Smirnov Akhmedov:1998qx ) is operational in this mass range. It is therefore tempting to ask if the mechanism may operate within the model at hand, thereby supplying an explanation of dark matter, neutrino masses, and the observed baryon asymmetry. C: Before moving on to phenomenological signatures, let us comment on the possibility of explaining the baryon asymmetry within the model	BAC	CAB	CAB	BCA	Selection 4
A: Whereas the V-magnitudes displays a large spread or a dip that spans for months caused by the active pulsation and foreign variable dust (Kiss et al., 2006; Massey et al., 2009). This is likely due to lower bolometric corrections and minor extinction values in the said photometric region (Cardelli et al., 1989). B: As previously mentioned in the 1st section, the analysis includes the use of NIR K-band magnitudes with a wavelength of ∼similar-to\sim∼2.20 ±plus-or-minus\pm± 0.10 μ𝜇\muitalic_μm to determine the luminosity Lbol more precisely than the use of conventional V-band magnitudesC: It may appear that the K-magnitudes are constant showing almost no variation in time	CBA	CAB	BCA	CBA	Selection 2
A: Further, one can observe some bouncing profiles because we are exploring early and late-time expansion of the universe through a single cosmological model. When the model shifts from an inflationary-dominated phase to late-time acceleration through the matter-dominated phase, at that moment we can observe the bouncing behaviour. We can see this type of evolution in pressure (p𝑝pitalic_p) and equation of state parameters (ω𝜔\omegaitalic_ω) as these profiles play an important role in the evolution process, whereas density profiles evolve smoothly as time goes on for both models. B: Our observations reveal that both models exhibit accelerated expansion during early and late-time cosmic evolution. Specifically, Model-I demonstrates a ΛΛ\Lambdaroman_ΛCDM-like expansion during early and late epochs, whereas Model-II exhibits quintessence-like behaviour in the early universe and evolves toward a phantom-like expansion in late timesC: This late-time accelerated expansion can be attributed to a substantial amount of negative pressure within the universe. The comprehensive evolution of the equation of state parameter delineates a trajectory commencing with early-time inflation, transitioning into a decelerated phase, and subsequently entering a second phase of accelerated cosmic expansion	BAC	BCA	CBA	CAB	Selection 4
A: However, the encoding maps generated by such tensor networks are generally non-isometric. Hence they are distinct from the conventional quantum codes and cannot always be unitarily encoded.B: To scale up beyond small atomic examples, one can also create more complicated tensor network encoding maps that inherit some non-trivial area operators by gluing these atomic “legos” with Bell fusion — each connected edge in the tensor network is prepared by projecting two physical qubits of the respective seed codes into a Bell stateC: Some of the code properties can be deduced from a more refined version of operator pushing	BCA	CAB	ACB	ABC	Selection 2
A: In this section, we discuss under which conditions they could be also exploited to explore the dynamical phase transition studied in the present paper.B: Recently, this platform has been extensively used to investigate a variety of non-equilibrium phenomena with light [59, 44, 40, 43, 57, 41, 58, 42, 20, 45]C: A representative example of nonlinear dispersive medium for light are vapors of hot atoms optically illuminated in the vicinity of an atomic resonance	ACB	CBA	BAC	ACB	Selection 2

**A**: We first show the principle by considering a two-qubit toy model for solving the Exact Cover problem, and then consider more extensive simulations up to 8 qubits for solving MaxCut, in the presence of photon losses. We then compare the performance of QAOA with cat qubits to the one with standard qubits given the same average gate fidelity of the two systems. We provide our conclusive remarks in Section IV**B**: In Appendix A we recall the definition of quantum gates acting on cat qubits. In Appendix B we provide some details regarding the numerical optimization. Finally, in Appendix C we introduce a bosonic version of QAOA by Trotterizing the relevant quantum annealing Hamiltonian, and we compare its performance to QAOA for the case of a single Ising spin.**C**: The paper is structured as follows. In Section II we recall the definition of cat qubits as well as the gates needed to operate them. In Section III we outline how QAOA can be run on cat qubits

CAB

CBA

BCA

BAC

Selection 3

**A**: For this reason, from now on we are going to focus on models that are inflations of classical models. In the next section we are going to characterise them. **B**: We aim to interpret models of inaccessible informations as refinements of classical models**C**: Specifically, we’re intrigued by the implications of considering that each classical model might be a part within a larger model of inaccessible information

ABC

CBA

CAB

Selection 4

**A**: In order to generate random samples from a complex and high-dimensional probability distributions functions (PDF), we considered the Monte Carlo Markov Chain (MCMC) technique, based in Metropolis-Hastings Algorithm**B**: It starts with an initial sample and iteratively proposes new samples based on a proposal distribution**C**: It then accepts or rejects the proposed sample based on an acceptance criterion that ensures the chain converges to the desired distribution. The posterior PDF getted around their most likely values allows us to obtain the best-fit model parameters with robust uncertainties.

ACB

CBA

BAC

ABC

Selection 4

**A**: Light-driving of materials leads to the photon-dressing of their Bloch bands and the formation of Floquet-Bloch states [4, 5, 39, 6]. Light’s frequency and intensity can tune these states that display properties not present in their parent equilibrium system**B**: The main effects of light on the magnetic exchange mediated by these spin-degenerate systems are displayed through a light-controlled Fermi wavevector that leads to photo-controlled RKKY oscillations, and the “draining out” of the Fermi sea, either by an increasing photoinduced gap (for graphene) or by the migration of the zeroth Floquet band (for 2DEGs) above the Fermi level, which lead to a non-oscillatory behaviour of the exchange coupling in what resembles the Bloembergen-Rowland interaction [41]. On the other hand, 3D and 2D spin-orbit coupled materials offer a rich platform to explore the interplay between magnetic and spin-orbit effects to provide the basis for wide-ranging spintronics phenomena [42]. These systems also allow for the exploration of optical induction and control of non-collinear magnetic couplings which play an essential role in the formation of magnetic skyrmions [43], spin helices [44], and chiral domain walls [45].**C**: Hence, photon-dressing of electrons in light-driven materials is key to dynamically controlling the magnetic exchange coupling. However, it has been shown in Refs. [23, 22, 40] that the effects of periodic monochromatic light-driving on the magnetic exchange interaction mediated by two dimensional (2D) spin-degenerate systems, such as 2D electron gases (2DEGs) and graphene, are limited to light-controlled collinear exchange couplings

CBA

ACB

CBA

Selection 2

**A**: italic_Y, and Z.X=i⁢Y=−X.Zformulae-sequence𝑍𝑋i𝑌𝑋𝑍Z.X=\text{i}Y=-X.Zitalic_Z . italic_X = i italic_Y = - italic_X . italic_Z. The N𝑁Nitalic_N-qubit observables and the multiplicative**B**: that X2=Y2=Z2=Isuperscript𝑋2superscript𝑌2superscript𝑍2𝐼X^{2}=Y^{2}=Z^{2}=Iitalic_X start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = italic_Y start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = italic_Z start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT = italic_I, X.Y=i⁢Z=−Y.Xformulae-sequence𝑋𝑌i𝑍𝑌𝑋X.Y=\text{i}Z=-Y.Xitalic_X . italic_Y = i italic_Z = - italic_Y **C**: italic_X, Y.Z=i⁢X=−Z.Yformulae-sequence𝑌𝑍i𝑋𝑍𝑌Y.Z=\text{i}X=-Z.Yitalic_Y . italic_Z = i italic_X = - italic_Z

BAC

CAB

BAC

BCA

Selection 2

**A**: The (inverse) magnetic catalysis can be observed from the holographic QCD model**B**: The dynamical breaking of conformal symmetry is realized by the nontrivial profile of the dilaton field in bottom-up holographic QCD models. In bottom-up holographic QCD, one can fit the model parameters to match the properties of real QCD such as the deconfinement phase transition, equations of state, and Regge trajectory of meson mass spectrum. **C**: The dilaton field in the Einstein-Hilbert action is dual to the running of the coupling constant and the expression of the dilaton field is correctly solved by the gravity equations

BAC

ACB

BCA

Selection 2

**A**: (2.7)**B**: the same covariance as ξ𝜉\xiitalic_ξ, cf**C**: But ξ~~𝜉\tilde{\xi}over~ start_ARG italic_ξ end_ARG and ξ𝜉\xiitalic_ξ are independent. In fact consider two test function φ,ψ𝜑𝜓\varphi,\psiitalic_φ , italic_ψ such that ⟨⟨φ⟩⟩=0delimited-⟨⟩delimited-⟨⟩𝜑0\langle\langle\varphi\rangle\rangle=0⟨ ⟨ italic_φ ⟩ ⟩ = 0 and

ABC

BAC

ABC

CAB

Selection 2

**A**: “absorption significance,” of different spectral components**B**: In this case, the design problem should be formulated by taking into account the relative contribution to the absorption, i.e**C**: The need to tailor properly the absorption for different spectral components, implies that the absorber has to have a suitably designed non-local behaviour. This can naturally be achieved in a planar layered media [26].

CBA

CAB

ABC

BAC

Selection 4

**A**: The objective of this study is to formulate a simple model, termed iterative percolation, in which critical percolation clusters are iteratively reorganized, and to investigate its percolation properties**B**: For convenience, we call the occupied (unoccupied) sites and clusters black (white), and percolation clusters are constructed by adjacent sites with the same color, thus, any pair of adjacent clusters must have different colors. Then, by randomly reassigning the color of each cluster, the original adjacent clusters could share the same color, and, as a consequence, larger clusters are formed. This cluster-merging rule can be applied iteratively to the newly formed clusters, allowing for the sequential construction of new generations of percolation configurations.**C**: We focus on the iterative site percolation on the triangular lattice, which begins with a critical site percolation configuration

CBA

ACB

CAB

BAC

Selection 2

**A**: This change in perception, just like the result the friend initially observed, is not directly accessible to Wigner and does not correspond to any observable on the joint system of S+F. However, identifying the friend with states of perception and inner thoughts begs the question in how far she can be aware of what happens to her memory**B**: We considered the compatibility of certain models of the observer’s (the friend’s) internal thoughts in Wigner’s friend scenarios with the no-signaling condition. In general, Wigner’s measurement affects the record of the measurement result stored in the friend’s memory register**C**: We considered the idea that the friend might have some perception of the change Wigner’s measurement induces to her memory. More concretely, we described the case where the friend can have multiple registers available for storing results which are then each measured by Wigner in some fixed basis. The friend could have a notion of the overall change to these memory registers (for example, the probability of entries being flipped during Wigner’s measurement) without having a persistent perception of individual results across Wigner’s measurement.

BAC

ABC

BCA

CBA

Selection 1

**A**: Deviations in this case remains significant for essentially any value of γ𝛾\gammaitalic_γ**B**: For γ=2𝛾2\gamma=2italic_γ = 2, our treatment predicts a circularization timescale that is about 2 times shorter than the standard formula. **C**: The contribution from the fast moving particles has also an effect on e𝑒eitalic_e

CBA

BCA

ACB

BAC

Selection 2

**A**: First, in section IV.1 we give the result for a simplified version of the computational model wherein we only allow Pauli measurements, no Clifford gates, and in particular, we allow only sequences of independent and commuting Pauli measurements**B**: In this section we present our main result—the amount of classical data that the simulation procedure Algorithm 1 must track is small**C**: This simplified model is still universal for quantum computation [15, 16]. Then, in Section IV.2 we give a more general statement of the main result where we allow computations consisting of any sequence of Clifford gates and Pauli measurements.

BCA

ABC

BAC

ABC

Selection 3

**A**: This paper is organized as follows: In Section II, we briefly review the WSD formalism we utilize in this paper**B**: In Section V and show how this formalism can be mapped to the SMEFT framework, and in particular derive the UV scale that corresponds to the upper limit on the FV Wilson coefficient. Finally, we present our conclusions in Section VI. We relegated much of the calculational details to the appendices A - D.**C**: In Section III, we present our complete analysis on the FV through the di-Higgs couplings in the leptonic sector, whereas in Section IV, we do the same analysis in the quark sector

BAC

CAB

BAC

ACB

Selection 4

**A**: Similarly, the existence domains of moving PW and SW bright solitons are also obtained, which are stationary solitons in the moving frame. Besides, we analyze the stability of these bright solitons by linear stability analysis**B**: Furthermore, we investigate the existence and stability domains of PW and SW bright solitons when the Zeeman field exists, based on the single-particle energy spectrum and a large number of numerical solutions. We find that the linear Zeeman effect is advantageous (disadvantageous) to the stability of SW (PW) bright solitons. Stable SW and PW bright solitons in both ferromagnetic and antiferromagnetic BECs are found. Finally, we discuss some interesting collision dynamics of stable bright solitons. **C**: In this work, we systematically investigate stationary and moving bright solitons in spin-1 BECs with SOC in a Zeeman field, focusing mainly on the bright solitons corresponding to the PW phase and the SW phase. Without the Zeeman field, we establish a connection between the single-particle energy spectrum and exact soliton solutions, whereby we obtain the existence domains of stationary PW and SW bright solitons

ACB

BAC

BCA

ABC

Selection 3

**A**: To this end, in this paper we extend the notion of uniquely decodable (or completely lossless) quantum codes to be used for quantum block data compression**B**: We hope that our work would be supportive in the quest towards answering the above questions, which have been left open in the current work. **C**: As the main result (Theorem 2.18), for a fixed m⁢l𝑚𝑙mlitalic_m italic_l many pure states emitted by a given quantum stochastic source, we derive the optimal lower bound of the average codeword length over a subset of uniquely decodable quantum codes called “special block codes”, which are applied to encode the pure states in m𝑚mitalic_m many blocks each of block size l𝑙litalic_l

CAB

ACB

CAB

Selection 3

**A**: For high-dimensional real-valued PDEs, there exist a variety of classic and deep learning-based approaches that rely on sampling from diffusion processes, e.g., Cliffe et al. [39], Warin [40], Han et al. [14], Weinan et al**B**: This requirement limits the applicability of this approach to our setting. BSDE methods studied by Nüsken and Richter [43, 44] are closely related to our approach, but they are developed for the elliptic version of the Hamilton–Jacobi–Bellman (HJB) equation. We consider the hyperbolic HJB setting, for which the existing method cannot be applied. **C**: [16]. Those works rely on the Feynman-Kac formula [41] to obtain an estimator for the solution to the PDE. However, for the Schrödinger equation, we need an analytical continuation of the Feynman-Kac formula on an imaginary time axis [42] as it is a complex-valued equation

CAB

BAC

ACB

Selection 4

**A**: Understanding the projector approach to open quantum systems is a powerful asset not only to derive effective dynamics in any open quantum system, but also to understand the deep connection between all the known methods and to help clarify confusing nomenclature conflicts across different fields 111Most prominently, the term “adiabatic elimination” refers to slightly different procedures in the atomic physics and the optomechanics communities [6, 10], a past source of confusion for the author and the spark that ignited this tutorial..**B**: Although needed to efficiently study paradigmatic systems, this “case-by-case” approach can make it difficult to derive effective equations for systems where conventional approaches are not applicable. A solution to this problem is offered by a more general formulation of open quantum systems in terms of projection superoperators in density matrix space, which allows to derive a single general equation describing the quantum dynamics of subsystems, the Nakajima-Zwanzig equation [13, 14, 16, 17, 18]**C**: Any effective description, including adiabatic elimination and Born-Markov master equations, can then be derived as a particular case of the Nakajima-Zwanzig equation

CAB

ACB

CBA

Selection 1

**A**: On the other hand, dipolar systems present rich physics due to the unique combination of traits of the dipole-dipole interaction (DDI): its anisotropy and long range character in three dimensions**B**: This mix gives rise to a wide variety of phenomena, such as the emergence of ultra-dilute self-bound droplets [36, 37, 38, 39, 40, 41], supersolids [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58] which may be even self-bound in the case of a dipolar mixture [59], striped liquids [60] and the anomalous emergence of supersolidity upon increasing temperature [61, 62, 63], among others**C**: In the context of the polaron problem, an immediate question emerges: how do the unique properties of the DDI affect the quasiparticle properties and dynamics of an impurity immersed in a dipolar medium? Several theoretical works have addressed this question in a variety of different conditions: from non-dipolar [24, 27] and dipolar [29] impurities immersed in a dipolar fermionic medium, to an impurity-medium bilayer configuration [34, 25] or dipolar [26, 31, 32] as well as non-dipolar [33, 28] impurities immersed in a dipolar BEC. It has also been shown that dipolar impurities can potentially function as tools to probe the properties of dipolar bosonic quantum droplets due to their neglectable back-action on the droplets [31]. In almost all cases, though, theoretical studies are restricted to an ultra-dilute bath, meaning that the characterization of the polaron properties for large gas parameters of the background is still a rather unexplored subject.

ACB

BCA

ABC

BCA

Selection 3

**A**: The game of Rock-Paper-Scissors, where rock smashes scissors, scissors cut paper, and paper wraps rock has been employed by evolutionary biologists to investigate the interactions between competing populations of species, where one species has an advantage over only one of its opponents**B**: We explore the evolution of this dynamical system in accordance with a sociological model [34, 35], where each population, following a unique strategy, seeks to minimize the difference between the average payoff of the population and the individual payoff.**C**: The game dynamics that describe the evolution of the populations following a particular strategy can be examined with the use of evolutionary game theory [27]

ACB

BAC

Selection 1

**A**: Figures 6a, c, e, and f, show the entire spectrum from 200 nm to 1000 nm at different detunings of the driving field labeled in a and d. Within the sensitivity limit of our spectrometer, we observe no pronounced fluorescence except from the two driving lasers at 780 nm (probe field) and 480 nm (coupling field), and the same background values for the on-resonant [c and f] and the far-detuned [b and e] excitation. This is consistent with fluorescence imaging of the vapor cell using a qCMOS camera (HAMAMATSU, C15550-20UP) for bandpass-filtered wavelengths between 500 nm and 700 nm after background subtraction, where no obvious fluorescence signal is detected. **B**: First, we confirmed that our spectrometer reliably detects the fluorescence from the vapor cell, by monitoring the 780 nm photons when scanning the detuning. As shown in Figs. 6a and 6d, the counts of 780 nm photons decrease significantly around the transmission peaks, which is a direct consequence of the reduced occupation of the intermediate state |5⁢P3/2⟩ket5subscript𝑃32|5P_{3/2}\rangle| 5 italic_P start_POSTSUBSCRIPT 3 / 2 end_POSTSUBSCRIPT ⟩ due to the electromagnetic induced transparency (EIT)**C**: To further search for the presence of plasma, we have performed additional measurements of the fluorescence spectrum. As discussed in Ref. weller2019interplay , the presence of a plasma should lead to radiative emission at a broad range of wavelength due to recombination and population of different Rydberg levels

CBA

ABC

BCA

Selection 1

**A**: We then treat the full analytical covariance matrix as a block diagonal matrix with the individual covariance matrix sitting in its corresponding block**B**: We assume there is no correlation between different surveys mainly because of the large cosmological distances and weak overlap between the different samples. However within the BOSS survey, there is overlap between the z⁢1𝑧1z1italic_z 1 and z⁢2𝑧2z2italic_z 2 bins, which cannot be modelled without extending the analytical covariance matrix work of Wadekar**C**: We test the procedure’s suitability described above by constructing individual analytical covariance matrices for each of the nine clustering samples we consider

ACB

CAB

BCA

ABC

Selection 3

**A**: It is also supported by the Open Fund for Key Laboratories of the Ministry of Education under grant number QLPL2024P01.**B**: This work is supported by the National Science Foundation of China (NSFC) under grant numbers 12405154, 12175100, and 11975132**C**: The authors thank Zi-qiang Zhang for his useful discussions

BCA

ABC

CBA

BCA

Selection 3

**A**: We will see that the choice of architecture significantly influences the presence of IGB**B**: For instance, sigmoid activations can achieve dynamical isometry, maximizing signal propagation depth (schoenholz2016deep), unlike ReLUs (pennington2017resurrecting). These activations are also compared in terms of generalization performance, revealing distinct behaviors for ReLUs and sigmoids (oostwal2021hidden). Notably, these studies often consider averaging over weight initializations. **C**: Architecture design, particularly the selection of activation functions, has been extensively studied (dubey2022activation), with a focus on ReLU versus differentiable activations such as sigmoid

CBA

BAC

ACB

CAB

Selection 3

**A**: Weisbrich and J.C. Cuevas for useful discussions**B**: W.B. acknowledges support from the DFG via SFB 1432 (ID 425217212) and BE 3803/14-1 (ID 467596333). W.W. acknowledges support from the Swiss National Science Foundation (grant number 200020_207538). F.N. acknowledges support from the European Research Council (grant number 804273) and the Swiss National Science Foundation (grant number 200021_201082). **C**: We thank the Cleanroom Operations Team of the Binnig and Rohrer Nanotechnology Center (BRNC) for their help and support. We are grateful to H

BCA

CBA

ACB

ABC

Selection 1

**A**: JK is funded through the NSERC CGS-D program. JW is supported by the European Union’s Horizon 2020 Framework: ERC grant 682608 and the “Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics”. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.**B**: Acknowledgements.We would like to thank Chris Beem, Pieter Bomans, Ramiro Cayuso, Kevin Costello, Richard Eager, Owen Gwilliam, Ji Hoon Lee, Surya Raghavendran, and Keyou Zeng for useful conversations. This research was supported in part by a grant from the Krembil Foundation**C**: DG is supported by the NSERC Discovery Grant program and by the Perimeter Institute for Theoretical Physics. KB and DG are supported by the Simons Foundation through grant 994308 for the Simons Collaboration on Confinement and QCD Strings

BAC

CBA

BAC

CAB

Selection 4

**A**: The first says that the asymptotic subrank of any concise tensor is at least the cube-root of its smallest dimension**B**: We prove two general lower bounds on the asymptotic subrank of concise tensors that depend only on the dimensions of the tensor**C**: The second says that the asymptotic subrank of any “narrow enough” tensor (meaning that one dimension is much smaller than the others) is maximal.

ABC

BAC

BCA

Selection 2

**A**: (2012)**B**: For the moving frame and partial wave decomposition of the scattering amplitude in the finite volume, we follow the procedure described in Doring et al**C**: The two-meson loop function in the finite volume, G~~𝐺\widetilde{G}over~ start_ARG italic_G end_ARG in Eq. (13) projected in partial waves, is a matrix with non-diagonal elements due to the partial weave mixing. Its elements are,

CBA

ABC

BAC

Selection 4

**A**: We have derived analytical expressions for the auto-correlators and cross-correlators of the current-current fluctuations in a double quantum dot that are valid at both zero and finite voltages, temperatures and frequencies, whatever the values of inter-dot and dot-reservoirs couplings are. We have highlighted specific features such as the reduction of the zero-frequency noise, as well as the possibility of having a negative Δ⁢TΔ𝑇\Delta Troman_Δ italic_T-noise, meaning that the noise can be further reduced by applying a temperature gradient between the two reservoirs**B**: Moreover, it leads at finite frequency to a change of sign in the cross-correlator in the vicinity of honeycomb vertices. By including Coulomb interactions at the Hatree-Fock level, one shows that a change of sign in the cross-correlator can also be obtained due to the presence of interactions, even at zero-frequency**C**: The approach presented in this work can be extended to take spin-orbit coupling into account, leading to effective g-factor[50] and Pauli spin blockade[51, 52], which are all the more important to describe realistic situations in double quantum dot systems and spin qubits, as experimentally studied. We believe that the tools developed in this article will be invaluable in the realization of such project, which remains to be done.

CBA

ABC

BCA

Selection 2

**A**: The observed ForcePho photometry for the disc (blue), core (red) and combined core+disc galaxy (lilac) is overplotted. We find the synthetic photometry matches the photometry of the combined core + disc galaxy, highlighting that the combined medium- and broad-band photometry traces both the stellar continuum and nebular emission line.**B**: The 1D NIRSpec spectrum (black) and synthetically derived photometry from the spectrum (orange points)**C**: Figure 16: The NIRSpec spectrum compared to the ForcePho photometry

CBA

CAB

BCA

ABC

Selection 1

**A**: The convergence with respect to the number of active bands in Hartree-Fock (HF) calculations requires careful consideration. Including more bands allows states to lower their energy by accessing higher bands, which is generally beneficial as it suggests the system is approaching the correct physical Hilbert space**B**: As shown in Fig. S6, states can indeed reduce their energy when more active bands are included. For states discussed in the main text, the energy reduction remains within 0.1%percent0.10.1\%0.1 %, leaving no changes in the phase diagram**C**: Second, adding more bands introduces new degrees of freedom, which can lead to new, potentially competing states. However, whether these new degrees of freedom are physically relevant depends on the system under study.

CAB

ABC

CBA

Selection 3

**A**: In Sect. 3 we study the asymptotic expansion of the Borodin–Forrester hard-to-soft edge transition law (6)**B**: Here we lay the foundational work for the concrete functional form of all the expansion terms in this paper**C**: Whereas the general structure of the expansions, which gives their uniformity and differentiability, is found by expanding operator determinants, the appealing functional form of the expansion terms, as displayed in (31), is established by combining the Tracy–Widom theory with factorizations of the β=2𝛽2\beta=2italic_β = 2 hard- and soft-edge distributions. By going beyond the first order terms, the proof of the functional form is subject to the linear form hypothesis, the evidence of which is detailed in Appendix D.

CBA

CAB

ABC

ACB

Selection 3

**A**: The data refers to a spin chain with the same parameters as in Fig. S2, but N=2,M=2formulae-sequence𝑁2𝑀2N=2,M=2italic_N = 2 , italic_M = 2**B**: The plots represent the exact time evolution (black solid line) and the dynamics predicted by the ML algorithm (red dashed line). In this case, the overall dynamics is well captured.**C**: Figure S3: Full plot of the ML algorithm’s performance. In figure the 15151515 non-trivial components of the coherence vector visubscript𝑣𝑖v_{i}italic_v start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT

ABC

CAB

BCA

CAB

Selection 3

**A**: Determining the exact optimal POVM for our system in order to fully utilize its precision potential for maximizing temperature information is an intriguing question with significant practical implications. If an experimental approach can be devised, possibly involving a combination of field quadrature measurements, it would be immensely valuable. However, due to the analytical complexities involved, we leave this avenue open for future research. **B**: Experimental access to temperature-sensitive field quadratures and their second moments is feasible through techniques such as homodyne, heterodyne, and tomographic state reconstruction methods Cenni et al. (2022); Khan et al. (2022)**C**: We can infer the temperature through straightforward quantum optical quadrature measurements Raymer and Beck (2004) on the cavity photons. The calculations show that the corresponding CFI (∼3similar-toabsent3\sim 3∼ 3) is about 20%percent\%% of the QFI ( ∼15similar-toabsent15\sim 15∼ 15), as determined by comparing Figs. 4 and 6. Therefore, while our exploration of suboptimal measurements holds practical relevance, our investigation into QFI highlights the fundamental potential of the system

ACB

ABC

CAB

ABC

Selection 3

**A**: (1996); Polychronakos (1999); Cattani and Bassalo (2009); Surya (2004), ewkons Hoyuelos and Sisterna (2016) modifications of statistics due to quantum gravity Swain (2008); Balachandran et al. (2001); Baez et al. (2006), non-commutative geometry Arzano and Benedetti (2009) and others Maslov (2009); Trifonov (2009); Bagarello (2011); Niven and Grendar (2009). **B**: Earliest work along these lines dates back to Gentile and his attempt to interpolate between two statistics Gentile j. (1940), and since then, we have seen dozens of generalized and exotic statistics, such as parastatistics Green (1953), quons and intermediate statistics Greenberg (1991, 1999); Lavagno and Narayana Swamy (2010); Fivel (1990), infinite statistics Greenberg (1990); Medvedev (1997), generalizations of fractal and topology-dependent statistics CHEN et al**C**: While these approaches agree at the level of ordinary statistics (bosons and fermions), all of them have been criticized for their ad hoc nature Messiah and Greenberg (1964); Mirman (1973); van Enk (2019). This leaves the door open for various generalizations, many of which resort to somewhat arbitrary assumptions added to the quantum formalism

CAB

ABC

CBA

Selection 4

**A**: The survey is supported by several software and data processing pipelines. The imaging from the public DESI Legacy Imaging Surveys (Zou et al., 2017; Dey et al., 2019; Schlegel et al., 2023) supports the target selection pipeline for spectroscopic follow-up**B**: Specific details are provided for the Bright Galaxy Survey (BGS; Ruiz-Macias et al., 2020), luminous red galaxies (LRGs; Zhou et al., 2020, 2023), emission line galaxies (ELGs; Raichoor et al., 2020, 2023a), and quasars (QSOs; Yèche et al., 2020; Chaussidon et al., 2023). A planning pipeline optimizes the tiling of observations throughout the survey (Schlafly et al., 2023). Fibres are assigned to targets for each pointing in another pipeline (Raichoor et al., 2023b). Resultant spectra are processed with a ‘spectroperfectionist’ (Bolton & Schlegel, 2010) data reduction pipeline (Guy et al., 2023) followed by a template fit yielding redshifts and a final classifications for each source (Bailey et al., 2023).**C**: Target selection employs quality cuts, as well as various colour selections and machine learning classification tools, tailored to provide a highly complete and low contamination sample for each tracer type. Identification and prioritization of all targets are described in Myers et al. (2023)

CBA

BCA

ACB

Selection 4

**A**: Returning to immobility, the Carroll symmetry effects only the CoM and implies, for a two-particle Carroll system with the BGL potential (I.2), the immobility of the latter**B**: fig.1a. **C**: The relative coordinates are not affected by the Carroll action (III.7) and they can indeed move, as illustrated in sec.III, cf

CBA

CAB

ACB

BAC

Selection 3

**A**: In this section, we provide a few numerical tests and compare our algorithm with previous works**B**: First, we briefly introduce the three different algorithms for QPE : ML-QCELS[12], MM-QCELS [16] and QMEGS [17]**C**: The last two can be used for QEEP as well.

ABC

BAC

CBA

BCA

Selection 1

**A**: It is worth noting that solving PDEs using ANNs has sound theoretical foundations, e.g., Hornik et al**B**: [28, 29] have shown that ANNs with multiple layers can approximate any continuous functions, and recently Zhou et al**C**: [30] have extended the earlier work to CNNs. In addition to the direct solution of PDEs using ANNs, neural solvers with convergence guarantees have been proposed for fast iterative solutions [31].

CAB

ABC

BAC

Selection 2

**A**: The anemometer on the left side of the fin, anemometer one, increased in value and when the percent difference threshold was exceeded, the foil began to converge towards that sensor, decreasing the percent difference measurement until it was within an acceptable range [Fig. 2]. The position of the hydrofoil depicts a clear story of what was occurring within the system, moving to positions of approximately 90°, 140°, 105°, 60°, 150°, 105°, 150°, and 130°throughout time**B**: The foil was able to quickly and consistently move to the new location and maintain its position until a new flow direction was encountered [Fig. 3]. We can see that the rise and fall time of the foil heading is approximately forty degrees per second with the servo motor used. The sign of the percent differences indicate what side the flow was originating, i.e. left or right, and we can further assess the hydrofoil’s ability to accurately orientate itself in the direction of flow. **C**: After calibrating the anemometers, we see they exhibit a percent difference, with no flow speed, of approximately 1.72% with anemometer one having a resting voltage of 0.58 volts and anemometer two with 0.59 volts. The first 10 seconds of the data set were devoted to allowing the temperature dependent resistor to stabilize. Afterwards the fan was turned on at the 140°location

BCA

BAC

ACB

CBA

Selection 1

**A**: My goal in introducing spacetime representation theory (and the ISE Method) is to gain some mathematical control over the range of all possible spacetime representations of our theories**B**: This should then help us answer some of the interesting philosophical questions which are raised by the possibility of alternative spacetime framings for our theories. **C**: This paper has introduced spacetime representation theory as a general framework for understanding our capacity to topologically redescribe our spacetime theories

CAB

BCA

CAB

ABC

Selection 2

**A**: We choose occupancies n~l=1subscript~𝑛𝑙1\tilde{n}_{l}{=}1over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT = 1 and n~u=0subscript~𝑛𝑢0\tilde{n}_{u}{=}0over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT = 0**B**: n~lsubscript~𝑛𝑙\tilde{n}_{l}over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT and n~usubscript~𝑛𝑢\tilde{n}_{u}over~ start_ARG italic_n end_ARG start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT of the orbitals |Θl⟩ketsubscriptΘ𝑙|\Theta_{l}\rangle| roman_Θ start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT ⟩ and |Θu⟩ketsubscriptΘ𝑢|\Theta_{u}\rangle| roman_Θ start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT ⟩, respectively**C**: Orbiton frequencies

BAC

CAB

ABC

ACB

Selection 1

**A**: Performing a measurement on spin N𝑁Nitalic_N, we studied whether its influence will be achieved spin 1111 or not**B**: (3)**C**: In this paper, we considered a spin chain, from spin 1111 to spin N𝑁Nitalic_N, which interact through the free Hamiltonian H𝐻Hitalic_H in Eq

BCA

ACB

CBA

BAC

Selection 3

**A**: Experimental proposals over several decades have considered superfluid helium as a target material [7, 8, 9, 10], with increasing theoretical attention over the past few years [11, 12, 13, 14, 15, 16, 17, 18]**B**: There are a number of proposals at various stages of development based on this idea, including HeRALD [19], DeLIGHT [20], ALETHEIA [21], and others [22, 23]. These experiments are projected to be sensitive to dark matter masses above 𝒪⁢(1)𝒪1\mathcal{O}(1)caligraphic_O ( 1 ) MeV.**C**: Recent experimental proposals have focused on nuclear scattering leading to the quantum evaporation of helium atoms, which can then be detected

ABC

CAB

ABC

ACB

Selection 4

**A**: There is also evidence that the intermediate velocity cloud (IVC) gas is organized into filaments that are aligned with their local magnetic fields (Panopoulou et al., 2019; Pelgrims et al., 2021). The difference could be caused by the Hessian algorithm being more sensitive than the RHT to artifacts in low-signal velocity channels. We explore this in Section 4.3. **B**: Using the RHT algorithm for determining the polarization angle, the H i intensity maps as the weighting (see Section 4), and the Spearman rank correlation coefficient and mean angle alignment as the correlation metrics, Clark & Hensley (2019) did not see the decrease in the correlation after a certain velocity that we see in Figure 1**C**: The correlation asymptotes instead

BAC

CBA

CAB

CBA

Selection 3

**A**: It is therefore concluded that a BSM resolution of the fine-structure anomaly in heavy muonic atoms with a single new boson is disfavoured**B**: Finally, new experimental data including additional elements with improved precision could also shed light on the muonic puzzle, or even bring back some of the previously excluded resolutions. **C**: This motivates further a careful re-investigation of the wide range of effects entering the binding energy calculations as was accomplished with NP in Ref. [8] or SE in Ref. [9]

CBA

ACB

ABC

Selection 3

**A**: Nowadays, the most advanced ones are superconducting qubits (used, for example, by IBM, Google, and Rigetti), trapped ions (used by AQT, Quantinuum and IonQ), neutral atoms (used by PasQal, QuEra, and Atom Computing), and photons (used by Quandela and Xanadu)**B**: In principle, a DQC system could integrate heterogeneous QPUs, based on different quantum technologies**C**: Other promising quantum technologies are emerging, such as molecular nanomagnets [24] (which are particularly suitable to act as multilevel logical units, i.e., qudits).

ACB

CBA

BAC

Selection 4

**A**: In the previous section, we discussed the example of rare-earth trihalides, where the giant magnetic response of chiral phonons originates from the coupling of CEF-split electronic levels with chiral optical phonons**B**: We begin with a general analysis of orbital configurations and then perform calculations for the concrete example of CoTiO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT. **C**: In this section, we show that chiral optical phonons in 3⁢d3𝑑3d3 italic_d-electron magnets with octahedral ligand configuration can yield a similarly strong response

ACB

BAC

CBA

ABC

Selection 1

**A**: A detailed analysis of the complexity of Algorithm 1 is provided in Sec. 2.5**B**: In Sec. 2.3, the correctness of Algorithm 1 is established. Example quantum circuits are provided in Sec. 2.4 to illustrate how Algorithm 1 works**C**: Quantum state preparation of a class of nonuniform superposition states using a variation of Algorithm 1 is described in Sec. 3 and some illustrative examples along with relevant quantum circuits are given in Sec. 3.1. Finally, the conclusion of the article is summarized in Sec. 4.

BAC

ABC

CAB

ABC

Selection 1

**A**: In Szegedy’s quantization this requirement is satisfied due to Proposition 2.1. Because dependence of the result on the state of the coin it is important to include this additional degree of freedom into the definition of the correspondence.**B**: It is natural to demand the same one-step transition probabilities**C**: In order to compare quantum walks with discrete random walks one needs to establish a correspondence between them

CBA

BCA

ABC

Selection 1

**A**: This work formulates the problem of quantum soft-covering in its most natural setting, and presents a one-shot characterization of the problem in terms of smoothed one-shot quantum entropic quantities**B**: We also contribute to the study of second-order asymptotics and provide achievability bounds for the same. As a part of future work, we aim to study optimal second order performance limits for the formulated quantum soft-covering problem.**C**: By leveraging the one-shot result, we provide a single-letter characterization of the optimal rate of the quantum soft-covering problem in terms of the minimal coherent information

ACB

ABC

BCA

Selection 1

**A**: Besides the Zeeman effect lifting the degeneracy of the Landau levels, the splitting also spatially separates spin-polarized edge states with opposite spin [58]**B**: This separation occurs in the direction perpendicular to the boundary (y-direction in this case)**C**: Thus, in a QH/SC heterostructure in the LLL, one edge state moves closer to the interface and the other moves further away. To account for this spatial shift, we consider the modified tunneling Hamiltonian,

CAB

BCA

ACB

ABC

Selection 4

**A**: Left: A 3D joint configuration of edges and vertex colors under the Edwards–Sokal coupling, including the full interface, ℐℐ\mathcal{I}caligraphic_I**B**: Figure 5**C**: Right: The same model, with just the full interface displayed. Note that the full interface should not be thought of as a surface — there are many sheets of faces sticking out and creating overhangs.

CAB

BCA

BAC

ACB

Selection 3

**A**: As shown in Fig. 2(a)-(c), there are many extrema for these quantities**B**: The typical local minima marked with the gray dashed lines in Fig. 2(a) manifest that the extended degree suddenly drops at specifical chemical potentials. Interestingly, the local extrema of the DOS and ΔΔ\Deltaroman_Δ shown in Fig. 2(b) and (c) almost coincide with those of the extended degree shown in Fig. 2(a). These results show that the more localized the single particle state around the Fermi energy is, the smaller the DOS is and the weaker the pairing gap amplitude is. **C**: The μ𝜇\muitalic_μ- dependences of the DOS at Fermi level and the pairing gap amplitude ΔΔ\Deltaroman_Δ at zero temperature are shown in Fig. 2(b) and (c), in comparison with the extended degree shown in Fig. 2(a)

BAC

BCA

ABC

Selection 3

**A**: Furthermore, it was suggested that quantum coherence in energy transfer may be responsible for its high efficiency [14, 15, 16]**B**: However, while fully quantum models for exciton transfer are available, classical models can equally well describe it or are compatible with the experimental findings on the process – hence it has been difficult to assess whether it is genuinely quantum [17, 18]. **C**: We focus on energy transfer via excitons because it is key for several biological processes, e.g., photosynthesis, in different biological systems of different scales, e.g., Fenna-Matthews-Olson (FMO) complex or polydiacetylene

CAB

BCA

CBA

CAB

Selection 2

**A**: AUROC metric, higher is better: mAUC denotes the AUROC averaged over all the mediator masses for a given signal**B**: Entries associated to an (*) were averaged over three random seeds: 42424242, 51515151, and 73737373. Top three best results in boldface.**C**: Table 1: Comparison of anomaly detection baselines and models on test-set, best scores only

BCA

ABC

ACB

CBA

Selection 1

**A**: We thank RoaRQ consortium for useful discussions on dataset coverage, Shrihan Agarwal for useful discussions on TSP, Timothy Proctor for manuscript feedback, and Neil Mehta for testing portions of the dataset. We acknowledge support from Sandia National Laboratories’ Laboratory Directed Research and Development Program under the Truman Fellowship. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S**B**: Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.**C**: Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis

BCA

ACB

CBA

ABC

Selection 2

**A**: The KS theorem rules out non-contextual hidden-variable theories via the existence of a finite set of three-dimensional vectors, referred to as a KS vector system [3]**B**: The first KS vector system, discovered in 1967, contains 117 vectors [3]. Another theorem that relies on the existence of KS systems in an essential way is the “Free Will” theorem of John Conway and Simon Kochen [5].**C**: A KS vector system (or simply a KS system) is a combinatorial object that witnesses a contradiction between non-contextuality (i.e., the assumption that observables can be assigned values prior to measurement and independent of measurement context) and the SPIN axiom of QM

ABC

BAC

BCA

ACB

Selection 4

**A**: We can utilize biholomorphic mappings to extend the solution from the unit disk to more general, simply connected domains**B**: The Riemann mapping theorem establishes that any simply connected domain is biholomorphically equivalent to the unit disk with boundary regularity for smooth Jordan domains**C**: Therefore, by leveraging this theorem, the solutions can be readily extended (Theorem 3.4). However, we need the following result before generalizing the equivalence of problems to any such domain.

CBA

BCA

ABC

CBA

Selection 3

**A**: In Fig**B**: 4, we visualize the energy conditions, for positive and negative values of the model parameter ϵ1subscriptitalic-ϵ1\epsilon_{1}italic_ϵ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, in terms of the total stress-energy tensor**C**: The plots verify that all energy conditions are fulfilled by the present model of the pulsar J0740+6620.

BCA

ABC

ACB

BCA

Selection 2

**A**: The top original network is divided into boxes of a fixed diameter, some of which are marked with different colours. In the new network after renormalization (shown below), these boxes are replaced by nodes with the corresponding colours. Again, the macroscopic and microscopic characteristics of the network after renormalization (represented by red triangles in Fig. 2) are similar to those of the original network.**B**: It is divided again into new smaller boxes, some of which are marked with different colours. Both macroscopic and microscopic characteristics of this new network (represented by green squares in Fig. 2) are similar to those of the original network (indicated by navy circles in Fig. 2). Part b) of this figure illustrates renormalization procedure applied to the same network as in part a**C**: Figure 1: Schematic illustration of the idea of geometric self-similarity in complex networks on the example of the fractal model of nested BA networks (for the definition of the model, see “Methods” section). Part a) of the figure shows that the network can be subdivided into parts—boxes of a given diameter—each of which is (at least approximately) a reduced-size copy of the entire network. In the top picture shown, one such box, marked in red, is extracted from the original network and treated as a new network (shown below)

CAB

BCA

ACB

CBA

Selection 4

**A**: The relation among I-Love-Q, Quasi Normal modes (QNMs) frequencies and the combination of mass and radius, moment of inertia and QNMs frequencies, and moment of inertia and compactness of NSs are insensitive to EoS [67]. Pappas and Apostolatos found three hair theorems for NSs in GR, which is an approximate generalization of the BH no-hair theorem [68] . Among all the universal relations, I-Love-Q relations are more insensitive to EoS than others. Therefore, studying these I-Love-Q relations in the different modified theories of gravity is of utmost interest**B**: Pani and Berti [69] calculated the I-Love-Q relations in scalar-tensor theory, Sham et al. [70] in EiBI gravity and Yagi et al. [71] in dCS gravity. Kleihaus et al. [72] studied the I-Q relation for rapidly rotating NSs in EdGB gravity.**C**: In modified theories of gravity, the blackhole solution is the Kerr metric, the blackhole solution in GR, or is deviated from the Kerr solution by a small margin such that these modified theories cannot be distinguished from GR using present and future astrophysics observations. Unlike the blackholes, the coupling of matter with gravity in the NS provides alternative ways to test modified theories of gravity in the strong field regime [66]. The cost of the coupling of matter with gravity is paid off by the fact that the mass-radius relation is sensitive to both the EoS and the underlying theory of gravity. However, various universal relations, independent of EoS, can be found for NSs which opens the windows of possibilities of the comparative studies of NSs in different modified theories of gravity without prior details knowledge of EoS

ABC

BCA

CAB

CBA

Selection 2

**A**: We have so far remained entirely agnostic as to the Yukawa couplings with charged leptons that generate neutrino masses**B**: Scalar masses above 30⁢μ⁢eV30𝜇eV30~{}{\rm\mu eV}30 italic_μ roman_eV are both consistent with constraints from BBN, and predict RHNs in the mass range of a few GeV. It is well known that leptogenesis by oscillations (or ARS leptogenesis for Akhmedov, Rubakov, and Smirnov Akhmedov:1998qx ) is operational in this mass range. It is therefore tempting to ask if the mechanism may operate within the model at hand, thereby supplying an explanation of dark matter, neutrino masses, and the observed baryon asymmetry. **C**: Before moving on to phenomenological signatures, let us comment on the possibility of explaining the baryon asymmetry within the model

BAC

CAB

BCA

Selection 4

**A**: Whereas the V-magnitudes displays a large spread or a dip that spans for months caused by the active pulsation and foreign variable dust (Kiss et al., 2006; Massey et al., 2009). This is likely due to lower bolometric corrections and minor extinction values in the said photometric region (Cardelli et al., 1989). **B**: As previously mentioned in the 1st section, the analysis includes the use of NIR K-band magnitudes with a wavelength of ∼similar-to\sim∼2.20 ±plus-or-minus\pm± 0.10 μ𝜇\muitalic_μm to determine the luminosity Lbol more precisely than the use of conventional V-band magnitudes**C**: It may appear that the K-magnitudes are constant showing almost no variation in time

CBA

CAB

BCA

CBA

Selection 2

**A**: Further, one can observe some bouncing profiles because we are exploring early and late-time expansion of the universe through a single cosmological model. When the model shifts from an inflationary-dominated phase to late-time acceleration through the matter-dominated phase, at that moment we can observe the bouncing behaviour. We can see this type of evolution in pressure (p𝑝pitalic_p) and equation of state parameters (ω𝜔\omegaitalic_ω) as these profiles play an important role in the evolution process, whereas density profiles evolve smoothly as time goes on for both models. **B**: Our observations reveal that both models exhibit accelerated expansion during early and late-time cosmic evolution. Specifically, Model-I demonstrates a ΛΛ\Lambdaroman_ΛCDM-like expansion during early and late epochs, whereas Model-II exhibits quintessence-like behaviour in the early universe and evolves toward a phantom-like expansion in late times**C**: This late-time accelerated expansion can be attributed to a substantial amount of negative pressure within the universe. The comprehensive evolution of the equation of state parameter delineates a trajectory commencing with early-time inflation, transitioning into a decelerated phase, and subsequently entering a second phase of accelerated cosmic expansion

BAC

BCA

CBA

CAB

Selection 4

**A**: However, the encoding maps generated by such tensor networks are generally non-isometric. Hence they are distinct from the conventional quantum codes and cannot always be unitarily encoded.**B**: To scale up beyond small atomic examples, one can also create more complicated tensor network encoding maps that inherit some non-trivial area operators by gluing these atomic “legos” with Bell fusion — each connected edge in the tensor network is prepared by projecting two physical qubits of the respective seed codes into a Bell state**C**: Some of the code properties can be deduced from a more refined version of operator pushing

BCA

CAB

ACB

ABC

Selection 2

**A**: In this section, we discuss under which conditions they could be also exploited to explore the dynamical phase transition studied in the present paper.**B**: Recently, this platform has been extensively used to investigate a variety of non-equilibrium phenomena with light [59, 44, 40, 43, 57, 41, 58, 42, 20, 45]**C**: A representative example of nonlinear dispersive medium for light are vapors of hot atoms optically illuminated in the vicinity of an atomic resonance

ACB

CBA

BAC

ACB

Selection 2